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 | 277.8 | ||
Character | \(\chi\) | \(=\) | 690.277 |
Dual form | 690.3.k.b.553.8 |
$q$-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 | ||||||||
\(5\) | −2.55939 | + | 4.29529i | −0.511878 | + | 0.859058i | ||||
\(6\) | 2.44949 | 0.408248 | ||||||||
\(7\) | 5.47277 | + | 5.47277i | 0.781824 | + | 0.781824i | 0.980138 | − | 0.198315i | \(-0.0635468\pi\) |
−0.198315 | + | 0.980138i | \(0.563547\pi\) | |||||||
\(8\) | 2.00000 | − | 2.00000i | 0.250000 | − | 0.250000i | ||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | 6.85468 | − | 1.73590i | 0.685468 | − | 0.173590i | ||||
\(11\) | 18.3249 | 1.66590 | 0.832950 | − | 0.553348i | \(-0.186650\pi\) | ||||
0.832950 | + | 0.553348i | \(0.186650\pi\) | |||||||
\(12\) | −2.44949 | − | 2.44949i | −0.204124 | − | 0.204124i | ||||
\(13\) | 7.21738 | − | 7.21738i | 0.555183 | − | 0.555183i | −0.372749 | − | 0.927932i | \(-0.621585\pi\) |
0.927932 | + | 0.372749i | \(0.121585\pi\) | |||||||
\(14\) | − | 10.9455i | − | 0.781824i | ||||||
\(15\) | −2.12604 | − | 8.39523i | −0.141736 | − | 0.559682i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | 1.48954 | + | 1.48954i | 0.0876198 | + | 0.0876198i | 0.749558 | − | 0.661938i | \(-0.230266\pi\) |
−0.661938 | + | 0.749558i | \(0.730266\pi\) | |||||||
\(18\) | −3.00000 | + | 3.00000i | −0.166667 | + | 0.166667i | ||||
\(19\) | − | 13.9116i | − | 0.732190i | −0.930578 | − | 0.366095i | \(-0.880695\pi\) | ||
0.930578 | − | 0.366095i | \(-0.119305\pi\) | |||||||
\(20\) | −8.59058 | − | 5.11878i | −0.429529 | − | 0.255939i | ||||
\(21\) | −13.4055 | −0.638357 | ||||||||
\(22\) | −18.3249 | − | 18.3249i | −0.832950 | − | 0.832950i | ||||
\(23\) | −3.39116 | + | 3.39116i | −0.147442 | + | 0.147442i | ||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | −11.8991 | − | 21.9866i | −0.475963 | − | 0.879465i | ||||
\(26\) | −14.4348 | −0.555183 | ||||||||
\(27\) | 3.67423 | + | 3.67423i | 0.136083 | + | 0.136083i | ||||
\(28\) | −10.9455 | + | 10.9455i | −0.390912 | + | 0.390912i | ||||
\(29\) | 0.950775i | 0.0327854i | 0.999866 | + | 0.0163927i | \(0.00521818\pi\) | ||||
−0.999866 | + | 0.0163927i | \(0.994782\pi\) | |||||||
\(30\) | −6.26919 | + | 10.5213i | −0.208973 | + | 0.350709i | ||||
\(31\) | 56.4791 | 1.82191 | 0.910954 | − | 0.412508i | \(-0.135347\pi\) | ||||
0.910954 | + | 0.412508i | \(0.135347\pi\) | |||||||
\(32\) | 4.00000 | + | 4.00000i | 0.125000 | + | 0.125000i | ||||
\(33\) | −22.4433 | + | 22.4433i | −0.680101 | + | 0.680101i | ||||
\(34\) | − | 2.97907i | − | 0.0876198i | ||||||
\(35\) | −37.5141 | + | 9.50020i | −1.07183 | + | 0.271434i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 44.4969 | + | 44.4969i | 1.20262 | + | 1.20262i | 0.973367 | + | 0.229254i | \(0.0736285\pi\) |
0.229254 | + | 0.973367i | \(0.426372\pi\) | |||||||
\(38\) | −13.9116 | + | 13.9116i | −0.366095 | + | 0.366095i | ||||
\(39\) | 17.6789i | 0.453305i | ||||||||
\(40\) | 3.47181 | + | 13.7094i | 0.0867952 | + | 0.342734i | ||||
\(41\) | −44.8287 | −1.09338 | −0.546692 | − | 0.837334i | \(-0.684113\pi\) | ||||
−0.546692 | + | 0.837334i | \(0.684113\pi\) | |||||||
\(42\) | 13.4055 | + | 13.4055i | 0.319178 | + | 0.319178i | ||||
\(43\) | 31.1063 | − | 31.1063i | 0.723402 | − | 0.723402i | −0.245895 | − | 0.969296i | \(-0.579082\pi\) |
0.969296 | + | 0.245895i | \(0.0790818\pi\) | |||||||
\(44\) | 36.6498i | 0.832950i | ||||||||
\(45\) | 12.8859 | + | 7.67816i | 0.286353 | + | 0.170626i | ||||
\(46\) | 6.78233 | 0.147442 | ||||||||
\(47\) | 25.7168 | + | 25.7168i | 0.547165 | + | 0.547165i | 0.925620 | − | 0.378455i | \(-0.123544\pi\) |
−0.378455 | + | 0.925620i | \(0.623544\pi\) | |||||||
\(48\) | 4.89898 | − | 4.89898i | 0.102062 | − | 0.102062i | ||||
\(49\) | 10.9024i | 0.222497i | ||||||||
\(50\) | −10.0876 | + | 33.8857i | −0.201751 | + | 0.677714i | ||||
\(51\) | −3.64860 | −0.0715412 | ||||||||
\(52\) | 14.4348 | + | 14.4348i | 0.277591 | + | 0.277591i | ||||
\(53\) | −17.7789 | + | 17.7789i | −0.335450 | + | 0.335450i | −0.854652 | − | 0.519202i | \(-0.826229\pi\) |
0.519202 | + | 0.854652i | \(0.326229\pi\) | |||||||
\(54\) | − | 7.34847i | − | 0.136083i | ||||||
\(55\) | −46.9005 | + | 78.7108i | −0.852737 | + | 1.43111i | ||||
\(56\) | 21.8911 | 0.390912 | ||||||||
\(57\) | 17.0382 | + | 17.0382i | 0.298915 | + | 0.298915i | ||||
\(58\) | 0.950775 | − | 0.950775i | 0.0163927 | − | 0.0163927i | ||||
\(59\) | 0.459649i | 0.00779066i | 0.999992 | + | 0.00389533i | \(0.00123992\pi\) | ||||
−0.999992 | + | 0.00389533i | \(0.998760\pi\) | |||||||
\(60\) | 16.7905 | − | 4.25208i | 0.279841 | − | 0.0708680i | ||||
\(61\) | 24.6543 | 0.404169 | 0.202084 | − | 0.979368i | \(-0.435228\pi\) | ||||
0.202084 | + | 0.979368i | \(0.435228\pi\) | |||||||
\(62\) | −56.4791 | − | 56.4791i | −0.910954 | − | 0.910954i | ||||
\(63\) | 16.4183 | − | 16.4183i | 0.260608 | − | 0.260608i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | 12.5287 | + | 49.4728i | 0.192749 | + | 0.761120i | ||||
\(66\) | 44.8867 | 0.680101 | ||||||||
\(67\) | −32.6237 | − | 32.6237i | −0.486920 | − | 0.486920i | 0.420413 | − | 0.907333i | \(-0.361885\pi\) |
−0.907333 | + | 0.420413i | \(0.861885\pi\) | |||||||
\(68\) | −2.97907 | + | 2.97907i | −0.0438099 | + | 0.0438099i | ||||
\(69\) | − | 8.30662i | − | 0.120386i | ||||||
\(70\) | 47.0143 | + | 28.0139i | 0.671632 | + | 0.400198i | ||||
\(71\) | 46.7310 | 0.658183 | 0.329092 | − | 0.944298i | \(-0.393258\pi\) | ||||
0.329092 | + | 0.944298i | \(0.393258\pi\) | |||||||
\(72\) | −6.00000 | − | 6.00000i | −0.0833333 | − | 0.0833333i | ||||
\(73\) | −0.372008 | + | 0.372008i | −0.00509599 | + | 0.00509599i | −0.709650 | − | 0.704554i | \(-0.751147\pi\) |
0.704554 | + | 0.709650i | \(0.251147\pi\) | |||||||
\(74\) | − | 88.9939i | − | 1.20262i | ||||||
\(75\) | 41.5013 | + | 12.3547i | 0.553351 | + | 0.164729i | ||||
\(76\) | 27.8232 | 0.366095 | ||||||||
\(77\) | 100.288 | + | 100.288i | 1.30244 | + | 1.30244i | ||||
\(78\) | 17.6789 | − | 17.6789i | 0.226652 | − | 0.226652i | ||||
\(79\) | 65.5336i | 0.829539i | 0.909926 | + | 0.414770i | \(0.136138\pi\) | ||||
−0.909926 | + | 0.414770i | \(0.863862\pi\) | |||||||
\(80\) | 10.2376 | − | 17.1812i | 0.127969 | − | 0.214765i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 44.8287 | + | 44.8287i | 0.546692 | + | 0.546692i | ||||
\(83\) | −85.4484 | + | 85.4484i | −1.02950 | + | 1.02950i | −0.0299470 | + | 0.999551i | \(0.509534\pi\) |
−0.999551 | + | 0.0299470i | \(0.990466\pi\) | |||||||
\(84\) | − | 26.8110i | − | 0.319178i | ||||||
\(85\) | −10.2103 | + | 2.58569i | −0.120121 | + | 0.0304199i | ||||
\(86\) | −62.2125 | −0.723402 | ||||||||
\(87\) | −1.16446 | − | 1.16446i | −0.0133846 | − | 0.0133846i | ||||
\(88\) | 36.6498 | − | 36.6498i | 0.416475 | − | 0.416475i | ||||
\(89\) | − | 64.0437i | − | 0.719592i | −0.933031 | − | 0.359796i | \(-0.882846\pi\) | ||
0.933031 | − | 0.359796i | \(-0.117154\pi\) | |||||||
\(90\) | −5.20771 | − | 20.5640i | −0.0578635 | − | 0.228489i | ||||
\(91\) | 78.9980 | 0.868110 | ||||||||
\(92\) | −6.78233 | − | 6.78233i | −0.0737210 | − | 0.0737210i | ||||
\(93\) | −69.1725 | + | 69.1725i | −0.743791 | + | 0.743791i | ||||
\(94\) | − | 51.4335i | − | 0.547165i | ||||||
\(95\) | 59.7544 | + | 35.6052i | 0.628994 | + | 0.374791i | ||||
\(96\) | −9.79796 | −0.102062 | ||||||||
\(97\) | 49.4654 | + | 49.4654i | 0.509953 | + | 0.509953i | 0.914512 | − | 0.404559i | \(-0.132575\pi\) |
−0.404559 | + | 0.914512i | \(0.632575\pi\) | |||||||
\(98\) | 10.9024 | − | 10.9024i | 0.111249 | − | 0.111249i | ||||
\(99\) | − | 54.9747i | − | 0.555300i | ||||||
\(100\) | 43.9733 | − | 23.7981i | 0.439733 | − | 0.237981i | ||||
\(101\) | −122.832 | −1.21616 | −0.608078 | − | 0.793877i | \(-0.708059\pi\) | ||||
−0.608078 | + | 0.793877i | \(0.708059\pi\) | |||||||
\(102\) | 3.64860 | + | 3.64860i | 0.0357706 | + | 0.0357706i | ||||
\(103\) | 40.9149 | − | 40.9149i | 0.397232 | − | 0.397232i | −0.480024 | − | 0.877256i | \(-0.659372\pi\) |
0.877256 | + | 0.480024i | \(0.159372\pi\) | |||||||
\(104\) | − | 28.8695i | − | 0.277591i | ||||||
\(105\) | 34.3098 | − | 57.5805i | 0.326760 | − | 0.548386i | ||||
\(106\) | 35.5577 | 0.335450 | ||||||||
\(107\) | 124.288 | + | 124.288i | 1.16157 | + | 1.16157i | 0.984131 | + | 0.177442i | \(0.0567822\pi\) |
0.177442 | + | 0.984131i | \(0.443218\pi\) | |||||||
\(108\) | −7.34847 | + | 7.34847i | −0.0680414 | + | 0.0680414i | ||||
\(109\) | − | 28.6845i | − | 0.263161i | −0.991306 | − | 0.131580i | \(-0.957995\pi\) | ||
0.991306 | − | 0.131580i | \(-0.0420051\pi\) | |||||||
\(110\) | 125.611 | − | 31.8103i | 1.14192 | − | 0.289184i | ||||
\(111\) | −108.995 | −0.981935 | ||||||||
\(112\) | −21.8911 | − | 21.8911i | −0.195456 | − | 0.195456i | ||||
\(113\) | −124.706 | + | 124.706i | −1.10360 | + | 1.10360i | −0.109624 | + | 0.993973i | \(0.534965\pi\) |
−0.993973 | + | 0.109624i | \(0.965035\pi\) | |||||||
\(114\) | − | 34.0763i | − | 0.298915i | ||||||
\(115\) | −5.88674 | − | 23.2454i | −0.0511890 | − | 0.202133i | ||||
\(116\) | −1.90155 | −0.0163927 | ||||||||
\(117\) | −21.6521 | − | 21.6521i | −0.185061 | − | 0.185061i | ||||
\(118\) | 0.459649 | − | 0.459649i | 0.00389533 | − | 0.00389533i | ||||
\(119\) | 16.3038i | 0.137006i | ||||||||
\(120\) | −21.0425 | − | 12.5384i | −0.175355 | − | 0.104487i | ||||
\(121\) | 214.802 | 1.77522 | ||||||||
\(122\) | −24.6543 | − | 24.6543i | −0.202084 | − | 0.202084i | ||||
\(123\) | 54.9038 | − | 54.9038i | 0.446372 | − | 0.446372i | ||||
\(124\) | 112.958i | 0.910954i | ||||||||
\(125\) | 124.893 | + | 5.16236i | 0.999147 | + | 0.0412989i | ||||
\(126\) | −32.8366 | −0.260608 | ||||||||
\(127\) | −18.1196 | − | 18.1196i | −0.142674 | − | 0.142674i | 0.632162 | − | 0.774836i | \(-0.282168\pi\) |
−0.774836 | + | 0.632162i | \(0.782168\pi\) | |||||||
\(128\) | −8.00000 | + | 8.00000i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 76.1945i | 0.590655i | ||||||||
\(130\) | 36.9441 | − | 62.0015i | 0.284186 | − | 0.476934i | ||||
\(131\) | −88.8228 | −0.678037 | −0.339018 | − | 0.940780i | \(-0.610095\pi\) | ||||
−0.339018 | + | 0.940780i | \(0.610095\pi\) | |||||||
\(132\) | −44.8867 | − | 44.8867i | −0.340050 | − | 0.340050i | ||||
\(133\) | 76.1350 | − | 76.1350i | 0.572443 | − | 0.572443i | ||||
\(134\) | 65.2473i | 0.486920i | ||||||||
\(135\) | −25.1857 | + | 6.37812i | −0.186561 | + | 0.0472453i | ||||
\(136\) | 5.95814 | 0.0438099 | ||||||||
\(137\) | 84.4843 | + | 84.4843i | 0.616674 | + | 0.616674i | 0.944677 | − | 0.328003i | \(-0.106376\pi\) |
−0.328003 | + | 0.944677i | \(0.606376\pi\) | |||||||
\(138\) | −8.30662 | + | 8.30662i | −0.0601929 | + | 0.0601929i | ||||
\(139\) | − | 1.42790i | − | 0.0102727i | −0.999987 | − | 0.00513633i | \(-0.998365\pi\) | ||
0.999987 | − | 0.00513633i | \(-0.00163495\pi\) | |||||||
\(140\) | −19.0004 | − | 75.0281i | −0.135717 | − | 0.535915i | ||||
\(141\) | −62.9930 | −0.446759 | ||||||||
\(142\) | −46.7310 | − | 46.7310i | −0.329092 | − | 0.329092i | ||||
\(143\) | 132.258 | − | 132.258i | 0.924879 | − | 0.924879i | ||||
\(144\) | 12.0000i | 0.0833333i | ||||||||
\(145\) | −4.08386 | − | 2.43340i | −0.0281645 | − | 0.0167821i | ||||
\(146\) | 0.744015 | 0.00509599 | ||||||||
\(147\) | −13.3526 | − | 13.3526i | −0.0908341 | − | 0.0908341i | ||||
\(148\) | −88.9939 | + | 88.9939i | −0.601310 | + | 0.601310i | ||||
\(149\) | − | 267.416i | − | 1.79474i | −0.441280 | − | 0.897369i | \(-0.645475\pi\) | ||
0.441280 | − | 0.897369i | \(-0.354525\pi\) | |||||||
\(150\) | −29.1466 | − | 53.8560i | −0.194311 | − | 0.359040i | ||||
\(151\) | −160.559 | −1.06331 | −0.531653 | − | 0.846962i | \(-0.678429\pi\) | ||||
−0.531653 | + | 0.846962i | \(0.678429\pi\) | |||||||
\(152\) | −27.8232 | − | 27.8232i | −0.183047 | − | 0.183047i | ||||
\(153\) | 4.46861 | − | 4.46861i | 0.0292066 | − | 0.0292066i | ||||
\(154\) | − | 200.576i | − | 1.30244i | ||||||
\(155\) | −144.552 | + | 242.594i | −0.932594 | + | 1.56513i | ||||
\(156\) | −35.3578 | −0.226652 | ||||||||
\(157\) | 93.2547 | + | 93.2547i | 0.593979 | + | 0.593979i | 0.938704 | − | 0.344725i | \(-0.112028\pi\) |
−0.344725 | + | 0.938704i | \(0.612028\pi\) | |||||||
\(158\) | 65.5336 | − | 65.5336i | 0.414770 | − | 0.414770i | ||||
\(159\) | − | 43.5491i | − | 0.273894i | ||||||
\(160\) | −27.4187 | + | 6.94362i | −0.171367 | + | 0.0433976i | ||||
\(161\) | −37.1181 | −0.230547 | ||||||||
\(162\) | 9.00000 | + | 9.00000i | 0.0555556 | + | 0.0555556i | ||||
\(163\) | −213.296 | + | 213.296i | −1.30857 | + | 1.30857i | −0.386115 | + | 0.922451i | \(0.626183\pi\) |
−0.922451 | + | 0.386115i | \(0.873817\pi\) | |||||||
\(164\) | − | 89.6575i | − | 0.546692i | ||||||
\(165\) | −38.9595 | − | 153.842i | −0.236118 | − | 0.932375i | ||||
\(166\) | 170.897 | 1.02950 | ||||||||
\(167\) | −13.9577 | − | 13.9577i | −0.0835792 | − | 0.0835792i | 0.664081 | − | 0.747660i | \(-0.268823\pi\) |
−0.747660 | + | 0.664081i | \(0.768823\pi\) | |||||||
\(168\) | −26.8110 | + | 26.8110i | −0.159589 | + | 0.159589i | ||||
\(169\) | 64.8190i | 0.383544i | ||||||||
\(170\) | 12.7960 | + | 7.62460i | 0.0752705 | + | 0.0448506i | ||||
\(171\) | −41.7348 | −0.244063 | ||||||||
\(172\) | 62.2125 | + | 62.2125i | 0.361701 | + | 0.361701i | ||||
\(173\) | −187.546 | + | 187.546i | −1.08408 | + | 1.08408i | −0.0879593 | + | 0.996124i | \(0.528035\pi\) |
−0.996124 | + | 0.0879593i | \(0.971965\pi\) | |||||||
\(174\) | 2.32891i | 0.0133846i | ||||||||
\(175\) | 55.2069 | − | 185.449i | 0.315468 | − | 1.05971i | ||||
\(176\) | −73.2996 | −0.416475 | ||||||||
\(177\) | −0.562953 | − | 0.562953i | −0.00318052 | − | 0.00318052i | ||||
\(178\) | −64.0437 | + | 64.0437i | −0.359796 | + | 0.359796i | ||||
\(179\) | − | 59.2046i | − | 0.330752i | −0.986231 | − | 0.165376i | \(-0.947116\pi\) | ||
0.986231 | − | 0.165376i | \(-0.0528837\pi\) | |||||||
\(180\) | −15.3563 | + | 25.7718i | −0.0853129 | + | 0.143176i | ||||
\(181\) | 218.953 | 1.20968 | 0.604842 | − | 0.796346i | \(-0.293236\pi\) | ||||
0.604842 | + | 0.796346i | \(0.293236\pi\) | |||||||
\(182\) | −78.9980 | − | 78.9980i | −0.434055 | − | 0.434055i | ||||
\(183\) | −30.1952 | + | 30.1952i | −0.165001 | + | 0.165001i | ||||
\(184\) | 13.5647i | 0.0737210i | ||||||||
\(185\) | −305.012 | + | 77.2424i | −1.64872 | + | 0.417527i | ||||
\(186\) | 138.345 | 0.743791 | ||||||||
\(187\) | 27.2956 | + | 27.2956i | 0.145966 | + | 0.145966i | ||||
\(188\) | −51.4335 | + | 51.4335i | −0.273583 | + | 0.273583i | ||||
\(189\) | 40.2165i | 0.212786i | ||||||||
\(190\) | −24.1492 | − | 95.3596i | −0.127101 | − | 0.501893i | ||||
\(191\) | −24.7100 | −0.129371 | −0.0646857 | − | 0.997906i | \(-0.520604\pi\) | ||||
−0.0646857 | + | 0.997906i | \(0.520604\pi\) | |||||||
\(192\) | 9.79796 | + | 9.79796i | 0.0510310 | + | 0.0510310i | ||||
\(193\) | 116.701 | − | 116.701i | 0.604667 | − | 0.604667i | −0.336880 | − | 0.941548i | \(-0.609372\pi\) |
0.941548 | + | 0.336880i | \(0.109372\pi\) | |||||||
\(194\) | − | 98.9308i | − | 0.509953i | ||||||
\(195\) | −75.9360 | − | 45.2471i | −0.389415 | − | 0.232037i | ||||
\(196\) | −21.8047 | −0.111249 | ||||||||
\(197\) | 124.625 | + | 124.625i | 0.632612 | + | 0.632612i | 0.948722 | − | 0.316111i | \(-0.102377\pi\) |
−0.316111 | + | 0.948722i | \(0.602377\pi\) | |||||||
\(198\) | −54.9747 | + | 54.9747i | −0.277650 | + | 0.277650i | ||||
\(199\) | − | 261.088i | − | 1.31200i | −0.754760 | − | 0.656001i | \(-0.772247\pi\) | ||
0.754760 | − | 0.656001i | \(-0.227753\pi\) | |||||||
\(200\) | −67.7714 | − | 20.1751i | −0.338857 | − | 0.100876i | ||||
\(201\) | 79.9113 | 0.397569 | ||||||||
\(202\) | 122.832 | + | 122.832i | 0.608078 | + | 0.608078i | ||||
\(203\) | −5.20337 | + | 5.20337i | −0.0256324 | + | 0.0256324i | ||||
\(204\) | − | 7.29721i | − | 0.0357706i | ||||||
\(205\) | 114.734 | − | 192.552i | 0.559679 | − | 0.939280i | ||||
\(206\) | −81.8298 | −0.397232 | ||||||||
\(207\) | 10.1735 | + | 10.1735i | 0.0491473 | + | 0.0491473i | ||||
\(208\) | −28.8695 | + | 28.8695i | −0.138796 | + | 0.138796i | ||||
\(209\) | − | 254.929i | − | 1.21975i | ||||||
\(210\) | −91.8903 | + | 23.2706i | −0.437573 | + | 0.110813i | ||||
\(211\) | −164.286 | −0.778605 | −0.389303 | − | 0.921110i | \(-0.627284\pi\) | ||||
−0.389303 | + | 0.921110i | \(0.627284\pi\) | |||||||
\(212\) | −35.5577 | − | 35.5577i | −0.167725 | − | 0.167725i | ||||
\(213\) | −57.2335 | + | 57.2335i | −0.268702 | + | 0.268702i | ||||
\(214\) | − | 248.577i | − | 1.16157i | ||||||
\(215\) | 53.9975 | + | 213.224i | 0.251151 | + | 0.991737i | ||||
\(216\) | 14.6969 | 0.0680414 | ||||||||
\(217\) | 309.097 | + | 309.097i | 1.42441 | + | 1.42441i | ||||
\(218\) | −28.6845 | + | 28.6845i | −0.131580 | + | 0.131580i | ||||
\(219\) | − | 0.911229i | − | 0.00416086i | ||||||
\(220\) | −157.422 | − | 93.8011i | −0.715553 | − | 0.426368i | ||||
\(221\) | 21.5011 | 0.0972900 | ||||||||
\(222\) | 108.995 | + | 108.995i | 0.490968 | + | 0.490968i | ||||
\(223\) | −187.046 | + | 187.046i | −0.838771 | + | 0.838771i | −0.988697 | − | 0.149926i | \(-0.952097\pi\) |
0.149926 | + | 0.988697i | \(0.452097\pi\) | |||||||
\(224\) | 43.7821i | 0.195456i | ||||||||
\(225\) | −65.9599 | + | 35.6972i | −0.293155 | + | 0.158654i | ||||
\(226\) | 249.413 | 1.10360 | ||||||||
\(227\) | −218.115 | − | 218.115i | −0.960860 | − | 0.960860i | 0.0384021 | − | 0.999262i | \(-0.487773\pi\) |
−0.999262 | + | 0.0384021i | \(0.987773\pi\) | |||||||
\(228\) | −34.0763 | + | 34.0763i | −0.149458 | + | 0.149458i | ||||
\(229\) | − | 358.055i | − | 1.56356i | −0.623556 | − | 0.781779i | \(-0.714313\pi\) | ||
0.623556 | − | 0.781779i | \(-0.285687\pi\) | |||||||
\(230\) | −17.3586 | + | 29.1321i | −0.0754722 | + | 0.126661i | ||||
\(231\) | −245.654 | −1.06344 | ||||||||
\(232\) | 1.90155 | + | 1.90155i | 0.00819634 | + | 0.00819634i | ||||
\(233\) | 40.1742 | − | 40.1742i | 0.172422 | − | 0.172422i | −0.615621 | − | 0.788042i | \(-0.711095\pi\) |
0.788042 | + | 0.615621i | \(0.211095\pi\) | |||||||
\(234\) | 43.3043i | 0.185061i | ||||||||
\(235\) | −176.280 | + | 44.6419i | −0.750129 | + | 0.189965i | ||||
\(236\) | −0.919298 | −0.00389533 | ||||||||
\(237\) | −80.2619 | − | 80.2619i | −0.338658 | − | 0.338658i | ||||
\(238\) | 16.3038 | − | 16.3038i | 0.0685032 | − | 0.0685032i | ||||
\(239\) | − | 42.3559i | − | 0.177221i | −0.996066 | − | 0.0886106i | \(-0.971757\pi\) | ||
0.996066 | − | 0.0886106i | \(-0.0282427\pi\) | |||||||
\(240\) | 8.50416 | + | 33.5809i | 0.0354340 | + | 0.139921i | ||||
\(241\) | 138.250 | 0.573652 | 0.286826 | − | 0.957983i | \(-0.407400\pi\) | ||||
0.286826 | + | 0.957983i | \(0.407400\pi\) | |||||||
\(242\) | −214.802 | − | 214.802i | −0.887612 | − | 0.887612i | ||||
\(243\) | 11.0227 | − | 11.0227i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 49.3086i | 0.202084i | ||||||||
\(245\) | −46.8288 | − | 27.9034i | −0.191138 | − | 0.113891i | ||||
\(246\) | −109.808 | −0.446372 | ||||||||
\(247\) | −100.405 | − | 100.405i | −0.406499 | − | 0.406499i | ||||
\(248\) | 112.958 | − | 112.958i | 0.455477 | − | 0.455477i | ||||
\(249\) | − | 209.305i | − | 0.840582i | ||||||
\(250\) | −119.731 | − | 130.056i | −0.478924 | − | 0.520223i | ||||
\(251\) | −167.580 | −0.667649 | −0.333824 | − | 0.942635i | \(-0.608339\pi\) | ||||
−0.333824 | + | 0.942635i | \(0.608339\pi\) | |||||||
\(252\) | 32.8366 | + | 32.8366i | 0.130304 | + | 0.130304i | ||||
\(253\) | −62.1428 | + | 62.1428i | −0.245624 | + | 0.245624i | ||||
\(254\) | 36.2391i | 0.142674i | ||||||||
\(255\) | 9.33819 | − | 15.6718i | 0.0366204 | − | 0.0614581i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −137.640 | − | 137.640i | −0.535565 | − | 0.535565i | 0.386658 | − | 0.922223i | \(-0.373629\pi\) |
−0.922223 | + | 0.386658i | \(0.873629\pi\) | |||||||
\(258\) | 76.1945 | − | 76.1945i | 0.295327 | − | 0.295327i | ||||
\(259\) | 487.043i | 1.88047i | ||||||||
\(260\) | −98.9456 | + | 25.0573i | −0.380560 | + | 0.0963744i | ||||
\(261\) | 2.85233 | 0.0109285 | ||||||||
\(262\) | 88.8228 | + | 88.8228i | 0.339018 | + | 0.339018i | ||||
\(263\) | −147.620 | + | 147.620i | −0.561293 | + | 0.561293i | −0.929675 | − | 0.368381i | \(-0.879912\pi\) |
0.368381 | + | 0.929675i | \(0.379912\pi\) | |||||||
\(264\) | 89.7733i | 0.340050i | ||||||||
\(265\) | −30.8624 | − | 121.868i | −0.116462 | − | 0.459881i | ||||
\(266\) | −152.270 | −0.572443 | ||||||||
\(267\) | 78.4372 | + | 78.4372i | 0.293772 | + | 0.293772i | ||||
\(268\) | 65.2473 | − | 65.2473i | 0.243460 | − | 0.243460i | ||||
\(269\) | 43.0679i | 0.160104i | 0.996791 | + | 0.0800518i | \(0.0255086\pi\) | ||||
−0.996791 | + | 0.0800518i | \(0.974491\pi\) | |||||||
\(270\) | 31.5638 | + | 18.8076i | 0.116903 | + | 0.0696577i | ||||
\(271\) | −455.005 | −1.67898 | −0.839492 | − | 0.543372i | \(-0.817147\pi\) | ||||
−0.839492 | + | 0.543372i | \(0.817147\pi\) | |||||||
\(272\) | −5.95814 | − | 5.95814i | −0.0219049 | − | 0.0219049i | ||||
\(273\) | −96.7524 | + | 96.7524i | −0.354405 | + | 0.354405i | ||||
\(274\) | − | 168.969i | − | 0.616674i | ||||||
\(275\) | −218.049 | − | 402.903i | −0.792906 | − | 1.46510i | ||||
\(276\) | 16.6132 | 0.0601929 | ||||||||
\(277\) | 75.2499 | + | 75.2499i | 0.271660 | + | 0.271660i | 0.829768 | − | 0.558108i | \(-0.188472\pi\) |
−0.558108 | + | 0.829768i | \(0.688472\pi\) | |||||||
\(278\) | −1.42790 | + | 1.42790i | −0.00513633 | + | 0.00513633i | ||||
\(279\) | − | 169.437i | − | 0.607303i | ||||||
\(280\) | −56.0277 | + | 94.0285i | −0.200099 | + | 0.335816i | ||||
\(281\) | 34.5423 | 0.122926 | 0.0614632 | − | 0.998109i | \(-0.480423\pi\) | ||||
0.0614632 | + | 0.998109i | \(0.480423\pi\) | |||||||
\(282\) | 62.9930 | + | 62.9930i | 0.223379 | + | 0.223379i | ||||
\(283\) | 84.0695 | − | 84.0695i | 0.297065 | − | 0.297065i | −0.542798 | − | 0.839863i | \(-0.682635\pi\) |
0.839863 | + | 0.542798i | \(0.182635\pi\) | |||||||
\(284\) | 93.4620i | 0.329092i | ||||||||
\(285\) | −116.791 | + | 29.5766i | −0.409794 | + | 0.103778i | ||||
\(286\) | −264.515 | −0.924879 | ||||||||
\(287\) | −245.337 | − | 245.337i | −0.854833 | − | 0.854833i | ||||
\(288\) | 12.0000 | − | 12.0000i | 0.0416667 | − | 0.0416667i | ||||
\(289\) | − | 284.563i | − | 0.984646i | ||||||
\(290\) | 1.65045 | + | 6.51726i | 0.00569122 | + | 0.0224733i | ||||
\(291\) | −121.165 | −0.416375 | ||||||||
\(292\) | −0.744015 | − | 0.744015i | −0.00254800 | − | 0.00254800i | ||||
\(293\) | 358.395 | − | 358.395i | 1.22319 | − | 1.22319i | 0.256700 | − | 0.966491i | \(-0.417365\pi\) |
0.966491 | − | 0.256700i | \(-0.0826354\pi\) | |||||||
\(294\) | 26.7052i | 0.0908341i | ||||||||
\(295\) | −1.97433 | − | 1.17642i | −0.00669263 | − | 0.00398786i | ||||
\(296\) | 177.988 | 0.601310 | ||||||||
\(297\) | 67.3300 | + | 67.3300i | 0.226700 | + | 0.226700i | ||||
\(298\) | −267.416 | + | 267.416i | −0.897369 | + | 0.897369i | ||||
\(299\) | 48.9506i | 0.163714i | ||||||||
\(300\) | −24.7094 | + | 83.0027i | −0.0823647 | + | 0.276676i | ||||
\(301\) | 340.475 | 1.13115 | ||||||||
\(302\) | 160.559 | + | 160.559i | 0.531653 | + | 0.531653i | ||||
\(303\) | 150.438 | − | 150.438i | 0.496494 | − | 0.496494i | ||||
\(304\) | 55.6464i | 0.183047i | ||||||||
\(305\) | −63.0999 | + | 105.897i | −0.206885 | + | 0.347205i | ||||
\(306\) | −8.93722 | −0.0292066 | ||||||||
\(307\) | −43.1449 | − | 43.1449i | −0.140537 | − | 0.140537i | 0.633338 | − | 0.773875i | \(-0.281684\pi\) |
−0.773875 | + | 0.633338i | \(0.781684\pi\) | |||||||
\(308\) | −200.576 | + | 200.576i | −0.651220 | + | 0.651220i | ||||
\(309\) | 100.221i | 0.324338i | ||||||||
\(310\) | 387.146 | − | 98.0424i | 1.24886 | − | 0.316266i | ||||
\(311\) | 188.459 | 0.605976 | 0.302988 | − | 0.952994i | \(-0.402016\pi\) | ||||
0.302988 | + | 0.952994i | \(0.402016\pi\) | |||||||
\(312\) | 35.3578 | + | 35.3578i | 0.113326 | + | 0.113326i | ||||
\(313\) | −140.266 | + | 140.266i | −0.448134 | + | 0.448134i | −0.894734 | − | 0.446600i | \(-0.852635\pi\) |
0.446600 | + | 0.894734i | \(0.352635\pi\) | |||||||
\(314\) | − | 186.509i | − | 0.593979i | ||||||
\(315\) | 28.5006 | + | 112.542i | 0.0904781 | + | 0.357277i | ||||
\(316\) | −131.067 | −0.414770 | ||||||||
\(317\) | −127.294 | − | 127.294i | −0.401557 | − | 0.401557i | 0.477224 | − | 0.878782i | \(-0.341643\pi\) |
−0.878782 | + | 0.477224i | \(0.841643\pi\) | |||||||
\(318\) | −43.5491 | + | 43.5491i | −0.136947 | + | 0.136947i | ||||
\(319\) | 17.4229i | 0.0546171i | ||||||||
\(320\) | 34.3623 | + | 20.4751i | 0.107382 | + | 0.0639847i | ||||
\(321\) | −304.443 | −0.948421 | ||||||||
\(322\) | 37.1181 | + | 37.1181i | 0.115274 | + | 0.115274i | ||||
\(323\) | 20.7218 | − | 20.7218i | 0.0641543 | − | 0.0641543i | ||||
\(324\) | − | 18.0000i | − | 0.0555556i | ||||||
\(325\) | −244.566 | − | 72.8058i | −0.752510 | − | 0.224018i | ||||
\(326\) | 426.592 | 1.30857 | ||||||||
\(327\) | 35.1312 | + | 35.1312i | 0.107435 | + | 0.107435i | ||||
\(328\) | −89.6575 | + | 89.6575i | −0.273346 | + | 0.273346i | ||||
\(329\) | 281.484i | 0.855574i | ||||||||
\(330\) | −114.882 | + | 192.801i | −0.348128 | + | 0.584246i | ||||
\(331\) | 432.406 | 1.30636 | 0.653182 | − | 0.757201i | \(-0.273434\pi\) | ||||
0.653182 | + | 0.757201i | \(0.273434\pi\) | |||||||
\(332\) | −170.897 | − | 170.897i | −0.514749 | − | 0.514749i | ||||
\(333\) | 133.491 | − | 133.491i | 0.400873 | − | 0.400873i | ||||
\(334\) | 27.9154i | 0.0835792i | ||||||||
\(335\) | 223.625 | − | 56.6316i | 0.667537 | − | 0.169049i | ||||
\(336\) | 53.6219 | 0.159589 | ||||||||
\(337\) | 251.277 | + | 251.277i | 0.745630 | + | 0.745630i | 0.973655 | − | 0.228025i | \(-0.0732269\pi\) |
−0.228025 | + | 0.973655i | \(0.573227\pi\) | |||||||
\(338\) | 64.8190 | − | 64.8190i | 0.191772 | − | 0.191772i | ||||
\(339\) | − | 305.467i | − | 0.901083i | ||||||
\(340\) | −5.17138 | − | 20.4206i | −0.0152100 | − | 0.0600605i | ||||
\(341\) | 1034.97 | 3.03512 | ||||||||
\(342\) | 41.7348 | + | 41.7348i | 0.122032 | + | 0.122032i | ||||
\(343\) | 208.500 | − | 208.500i | 0.607870 | − | 0.607870i | ||||
\(344\) | − | 124.425i | − | 0.361701i | ||||||
\(345\) | 35.6794 | + | 21.2599i | 0.103418 | + | 0.0616228i | ||||
\(346\) | 375.093 | 1.08408 | ||||||||
\(347\) | 151.537 | + | 151.537i | 0.436707 | + | 0.436707i | 0.890902 | − | 0.454195i | \(-0.150073\pi\) |
−0.454195 | + | 0.890902i | \(0.650073\pi\) | |||||||
\(348\) | 2.32891 | − | 2.32891i | 0.00669228 | − | 0.00669228i | ||||
\(349\) | 642.693i | 1.84153i | 0.390120 | + | 0.920764i | \(0.372434\pi\) | ||||
−0.390120 | + | 0.920764i | \(0.627566\pi\) | |||||||
\(350\) | −240.655 | + | 130.242i | −0.687587 | + | 0.372119i | ||||
\(351\) | 53.0367 | 0.151102 | ||||||||
\(352\) | 73.2996 | + | 73.2996i | 0.208238 | + | 0.208238i | ||||
\(353\) | 412.979 | − | 412.979i | 1.16991 | − | 1.16991i | 0.187681 | − | 0.982230i | \(-0.439903\pi\) |
0.982230 | − | 0.187681i | \(-0.0600973\pi\) | |||||||
\(354\) | 1.12591i | 0.00318052i | ||||||||
\(355\) | −119.603 | + | 200.723i | −0.336909 | + | 0.565418i | ||||
\(356\) | 128.087 | 0.359796 | ||||||||
\(357\) | −19.9680 | − | 19.9680i | −0.0559326 | − | 0.0559326i | ||||
\(358\) | −59.2046 | + | 59.2046i | −0.165376 | + | 0.165376i | ||||
\(359\) | − | 149.819i | − | 0.417324i | −0.977988 | − | 0.208662i | \(-0.933089\pi\) | ||
0.977988 | − | 0.208662i | \(-0.0669109\pi\) | |||||||
\(360\) | 41.1281 | − | 10.4154i | 0.114245 | − | 0.0289317i | ||||
\(361\) | 167.467 | 0.463898 | ||||||||
\(362\) | −218.953 | − | 218.953i | −0.604842 | − | 0.604842i | ||||
\(363\) | −263.078 | + | 263.078i | −0.724732 | + | 0.724732i | ||||
\(364\) | 157.996i | 0.434055i | ||||||||
\(365\) | −0.645770 | − | 2.54999i | −0.00176923 | − | 0.00698628i | ||||
\(366\) | 60.3905 | 0.165001 | ||||||||
\(367\) | −257.690 | − | 257.690i | −0.702152 | − | 0.702152i | 0.262720 | − | 0.964872i | \(-0.415380\pi\) |
−0.964872 | + | 0.262720i | \(0.915380\pi\) | |||||||
\(368\) | 13.5647 | − | 13.5647i | 0.0368605 | − | 0.0368605i | ||||
\(369\) | 134.486i | 0.364461i | ||||||||
\(370\) | 382.255 | + | 227.770i | 1.03312 | + | 0.615594i | ||||
\(371\) | −194.599 | −0.524526 | ||||||||
\(372\) | −138.345 | − | 138.345i | −0.371895 | − | 0.371895i | ||||
\(373\) | −274.503 | + | 274.503i | −0.735934 | + | 0.735934i | −0.971788 | − | 0.235854i | \(-0.924211\pi\) |
0.235854 | + | 0.971788i | \(0.424211\pi\) | |||||||
\(374\) | − | 54.5912i | − | 0.145966i | ||||||
\(375\) | −159.285 | + | 146.640i | −0.424760 | + | 0.391040i | ||||
\(376\) | 102.867 | 0.273583 | ||||||||
\(377\) | 6.86210 | + | 6.86210i | 0.0182019 | + | 0.0182019i | ||||
\(378\) | 40.2165 | − | 40.2165i | 0.106393 | − | 0.106393i | ||||
\(379\) | − | 543.361i | − | 1.43367i | −0.697243 | − | 0.716834i | \(-0.745590\pi\) | ||
0.697243 | − | 0.716834i | \(-0.254410\pi\) | |||||||
\(380\) | −71.2104 | + | 119.509i | −0.187396 | + | 0.314497i | ||||
\(381\) | 44.3837 | 0.116493 | ||||||||
\(382\) | 24.7100 | + | 24.7100i | 0.0646857 | + | 0.0646857i | ||||
\(383\) | 322.889 | − | 322.889i | 0.843053 | − | 0.843053i | −0.146202 | − | 0.989255i | \(-0.546705\pi\) |
0.989255 | + | 0.146202i | \(0.0467049\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | −687.442 | + | 174.090i | −1.78556 | + | 0.452182i | ||||
\(386\) | −233.402 | −0.604667 | ||||||||
\(387\) | −93.3188 | − | 93.3188i | −0.241134 | − | 0.241134i | ||||
\(388\) | −98.9308 | + | 98.9308i | −0.254976 | + | 0.254976i | ||||
\(389\) | 720.417i | 1.85197i | 0.377557 | + | 0.925986i | \(0.376764\pi\) | ||||
−0.377557 | + | 0.925986i | \(0.623236\pi\) | |||||||
\(390\) | 30.6889 | + | 121.183i | 0.0786894 | + | 0.310726i | ||||
\(391\) | −10.1025 | −0.0258377 | ||||||||
\(392\) | 21.8047 | + | 21.8047i | 0.0556243 | + | 0.0556243i | ||||
\(393\) | 108.785 | − | 108.785i | 0.276807 | − | 0.276807i | ||||
\(394\) | − | 249.249i | − | 0.632612i | ||||||
\(395\) | −281.486 | − | 167.726i | −0.712623 | − | 0.424622i | ||||
\(396\) | 109.949 | 0.277650 | ||||||||
\(397\) | 139.692 | + | 139.692i | 0.351869 | + | 0.351869i | 0.860804 | − | 0.508936i | \(-0.169961\pi\) |
−0.508936 | + | 0.860804i | \(0.669961\pi\) | |||||||
\(398\) | −261.088 | + | 261.088i | −0.656001 | + | 0.656001i | ||||
\(399\) | 186.492i | 0.467398i | ||||||||
\(400\) | 47.5963 | + | 87.9465i | 0.118991 | + | 0.219866i | ||||
\(401\) | 410.867 | 1.02461 | 0.512303 | − | 0.858805i | \(-0.328793\pi\) | ||||
0.512303 | + | 0.858805i | \(0.328793\pi\) | |||||||
\(402\) | −79.9113 | − | 79.9113i | −0.198784 | − | 0.198784i | ||||
\(403\) | 407.631 | − | 407.631i | 1.01149 | − | 1.01149i | ||||
\(404\) | − | 245.664i | − | 0.608078i | ||||||
\(405\) | 23.0345 | − | 38.6576i | 0.0568753 | − | 0.0954509i | ||||
\(406\) | 10.4067 | 0.0256324 | ||||||||
\(407\) | 815.402 | + | 815.402i | 2.00345 | + | 2.00345i | ||||
\(408\) | −7.29721 | + | 7.29721i | −0.0178853 | + | 0.0178853i | ||||
\(409\) | 185.429i | 0.453372i | 0.973968 | + | 0.226686i | \(0.0727891\pi\) | ||||
−0.973968 | + | 0.226686i | \(0.927211\pi\) | |||||||
\(410\) | −307.287 | + | 77.8184i | −0.749480 | + | 0.189801i | ||||
\(411\) | −206.943 | −0.503512 | ||||||||
\(412\) | 81.8298 | + | 81.8298i | 0.198616 | + | 0.198616i | ||||
\(413\) | −2.51555 | + | 2.51555i | −0.00609092 | + | 0.00609092i | ||||
\(414\) | − | 20.3470i | − | 0.0491473i | ||||||
\(415\) | −148.330 | − | 585.721i | −0.357422 | − | 1.41138i | ||||
\(416\) | 57.7390 | 0.138796 | ||||||||
\(417\) | 1.74881 | + | 1.74881i | 0.00419379 | + | 0.00419379i | ||||
\(418\) | −254.929 | + | 254.929i | −0.609877 | + | 0.609877i | ||||
\(419\) | 203.166i | 0.484884i | 0.970166 | + | 0.242442i | \(0.0779484\pi\) | ||||
−0.970166 | + | 0.242442i | \(0.922052\pi\) | |||||||
\(420\) | 115.161 | + | 68.6197i | 0.274193 | + | 0.163380i | ||||
\(421\) | −622.636 | −1.47895 | −0.739473 | − | 0.673187i | \(-0.764925\pi\) | ||||
−0.739473 | + | 0.673187i | \(0.764925\pi\) | |||||||
\(422\) | 164.286 | + | 164.286i | 0.389303 | + | 0.389303i | ||||
\(423\) | 77.1503 | − | 77.1503i | 0.182388 | − | 0.182388i | ||||
\(424\) | 71.1154i | 0.167725i | ||||||||
\(425\) | 15.0258 | − | 50.4740i | 0.0353548 | − | 0.118762i | ||||
\(426\) | 114.467 | 0.268702 | ||||||||
\(427\) | 134.927 | + | 134.927i | 0.315989 | + | 0.315989i | ||||
\(428\) | −248.577 | + | 248.577i | −0.580787 | + | 0.580787i | ||||
\(429\) | 323.964i | 0.755161i | ||||||||
\(430\) | 159.226 | − | 267.221i | 0.370293 | − | 0.621444i | ||||
\(431\) | 645.267 | 1.49714 | 0.748570 | − | 0.663056i | \(-0.230741\pi\) | ||||
0.748570 | + | 0.663056i | \(0.230741\pi\) | |||||||
\(432\) | −14.6969 | − | 14.6969i | −0.0340207 | − | 0.0340207i | ||||
\(433\) | 332.543 | − | 332.543i | 0.767998 | − | 0.767998i | −0.209756 | − | 0.977754i | \(-0.567267\pi\) |
0.977754 | + | 0.209756i | \(0.0672669\pi\) | |||||||
\(434\) | − | 618.194i | − | 1.42441i | ||||||
\(435\) | 7.98198 | − | 2.02139i | 0.0183494 | − | 0.00464686i | ||||
\(436\) | 57.3690 | 0.131580 | ||||||||
\(437\) | 47.1765 | + | 47.1765i | 0.107955 | + | 0.107955i | ||||
\(438\) | −0.911229 | + | 0.911229i | −0.00208043 | + | 0.00208043i | ||||
\(439\) | − | 42.1637i | − | 0.0960448i | −0.998846 | − | 0.0480224i | \(-0.984708\pi\) | ||
0.998846 | − | 0.0480224i | \(-0.0152919\pi\) | |||||||
\(440\) | 63.6205 | + | 251.223i | 0.144592 | + | 0.570961i | ||||
\(441\) | 32.7071 | 0.0741657 | ||||||||
\(442\) | −21.5011 | − | 21.5011i | −0.0486450 | − | 0.0486450i | ||||
\(443\) | −18.6195 | + | 18.6195i | −0.0420305 | + | 0.0420305i | −0.727810 | − | 0.685779i | \(-0.759462\pi\) |
0.685779 | + | 0.727810i | \(0.259462\pi\) | |||||||
\(444\) | − | 217.990i | − | 0.490968i | ||||||
\(445\) | 275.086 | + | 163.913i | 0.618172 | + | 0.368343i | ||||
\(446\) | 374.092 | 0.838771 | ||||||||
\(447\) | 327.517 | + | 327.517i | 0.732699 | + | 0.732699i | ||||
\(448\) | 43.7821 | − | 43.7821i | 0.0977280 | − | 0.0977280i | ||||
\(449\) | − | 256.938i | − | 0.572245i | −0.958193 | − | 0.286123i | \(-0.907633\pi\) | ||
0.958193 | − | 0.286123i | \(-0.0923665\pi\) | |||||||
\(450\) | 101.657 | + | 30.2627i | 0.225905 | + | 0.0672505i | ||||
\(451\) | −821.482 | −1.82147 | ||||||||
\(452\) | −249.413 | − | 249.413i | −0.551798 | − | 0.551798i | ||||
\(453\) | 196.644 | − | 196.644i | 0.434093 | − | 0.434093i | ||||
\(454\) | 436.231i | 0.960860i | ||||||||
\(455\) | −202.187 | + | 339.320i | −0.444366 | + | 0.745757i | ||||
\(456\) | 68.1527 | 0.149458 | ||||||||
\(457\) | −343.079 | − | 343.079i | −0.750719 | − | 0.750719i | 0.223894 | − | 0.974613i | \(-0.428123\pi\) |
−0.974613 | + | 0.223894i | \(0.928123\pi\) | |||||||
\(458\) | −358.055 | + | 358.055i | −0.781779 | + | 0.781779i | ||||
\(459\) | 10.9458i | 0.0238471i | ||||||||
\(460\) | 46.4907 | − | 11.7735i | 0.101067 | − | 0.0255945i | ||||
\(461\) | −518.066 | −1.12379 | −0.561893 | − | 0.827210i | \(-0.689927\pi\) | ||||
−0.561893 | + | 0.827210i | \(0.689927\pi\) | |||||||
\(462\) | 245.654 | + | 245.654i | 0.531719 | + | 0.531719i | ||||
\(463\) | 581.305 | − | 581.305i | 1.25552 | − | 1.25552i | 0.302307 | − | 0.953211i | \(-0.402243\pi\) |
0.953211 | − | 0.302307i | \(-0.0977567\pi\) | |||||||
\(464\) | − | 3.80310i | − | 0.00819634i | ||||||
\(465\) | −120.077 | − | 474.156i | −0.258230 | − | 1.01969i | ||||
\(466\) | −80.3485 | −0.172422 | ||||||||
\(467\) | −175.982 | − | 175.982i | −0.376835 | − | 0.376835i | 0.493124 | − | 0.869959i | \(-0.335855\pi\) |
−0.869959 | + | 0.493124i | \(0.835855\pi\) | |||||||
\(468\) | 43.3043 | − | 43.3043i | 0.0925305 | − | 0.0925305i | ||||
\(469\) | − | 357.084i | − | 0.761372i | ||||||
\(470\) | 220.922 | + | 131.638i | 0.470047 | + | 0.280082i | ||||
\(471\) | −228.426 | −0.484982 | ||||||||
\(472\) | 0.919298 | + | 0.919298i | 0.00194766 | + | 0.00194766i | ||||
\(473\) | 570.019 | − | 570.019i | 1.20511 | − | 1.20511i | ||||
\(474\) | 160.524i | 0.338658i | ||||||||
\(475\) | −305.869 | + | 165.535i | −0.643936 | + | 0.348495i | ||||
\(476\) | −32.6075 | −0.0685032 | ||||||||
\(477\) | 53.3366 | + | 53.3366i | 0.111817 | + | 0.111817i | ||||
\(478\) | −42.3559 | + | 42.3559i | −0.0886106 | + | 0.0886106i | ||||
\(479\) | 92.7211i | 0.193572i | 0.995305 | + | 0.0967861i | \(0.0308563\pi\) | ||||
−0.995305 | + | 0.0967861i | \(0.969144\pi\) | |||||||
\(480\) | 25.0768 | − | 42.0851i | 0.0522433 | − | 0.0876773i | ||||
\(481\) | 642.302 | 1.33535 | ||||||||
\(482\) | −138.250 | − | 138.250i | −0.286826 | − | 0.286826i | ||||
\(483\) | 45.4602 | − | 45.4602i | 0.0941205 | − | 0.0941205i | ||||
\(484\) | 429.604i | 0.887612i | ||||||||
\(485\) | −339.069 | + | 85.8672i | −0.699112 | + | 0.177046i | ||||
\(486\) | −22.0454 | −0.0453609 | ||||||||
\(487\) | −359.308 | − | 359.308i | −0.737800 | − | 0.737800i | 0.234352 | − | 0.972152i | \(-0.424703\pi\) |
−0.972152 | + | 0.234352i | \(0.924703\pi\) | |||||||
\(488\) | 49.3086 | − | 49.3086i | 0.101042 | − | 0.101042i | ||||
\(489\) | − | 522.467i | − | 1.06844i | ||||||
\(490\) | 18.9255 | + | 74.7322i | 0.0386234 | + | 0.152515i | ||||
\(491\) | 215.844 | 0.439601 | 0.219801 | − | 0.975545i | \(-0.429459\pi\) | ||||
0.219801 | + | 0.975545i | \(0.429459\pi\) | |||||||
\(492\) | 109.808 | + | 109.808i | 0.223186 | + | 0.223186i | ||||
\(493\) | −1.41621 | + | 1.41621i | −0.00287264 | + | 0.00287264i | ||||
\(494\) | 200.811i | 0.406499i | ||||||||
\(495\) | 236.132 | + | 140.702i | 0.477035 | + | 0.284246i | ||||
\(496\) | −225.917 | −0.455477 | ||||||||
\(497\) | 255.748 | + | 255.748i | 0.514583 | + | 0.514583i | ||||
\(498\) | −209.305 | + | 209.305i | −0.420291 | + | 0.420291i | ||||
\(499\) | − | 236.340i | − | 0.473626i | −0.971555 | − | 0.236813i | \(-0.923897\pi\) | ||
0.971555 | − | 0.236813i | \(-0.0761029\pi\) | |||||||
\(500\) | −10.3247 | + | 249.787i | −0.0206494 | + | 0.499573i | ||||
\(501\) | 34.1893 | 0.0682421 | ||||||||
\(502\) | 167.580 | + | 167.580i | 0.333824 | + | 0.333824i | ||||
\(503\) | 158.114 | − | 158.114i | 0.314342 | − | 0.314342i | −0.532247 | − | 0.846589i | \(-0.678652\pi\) |
0.846589 | + | 0.532247i | \(0.178652\pi\) | |||||||
\(504\) | − | 65.6732i | − | 0.130304i | ||||||
\(505\) | 314.374 | − | 527.599i | 0.622523 | − | 1.04475i | ||||
\(506\) | 124.286 | 0.245624 | ||||||||
\(507\) | −79.3867 | − | 79.3867i | −0.156581 | − | 0.156581i | ||||
\(508\) | 36.2391 | − | 36.2391i | 0.0713368 | − | 0.0713368i | ||||
\(509\) | 895.884i | 1.76009i | 0.474894 | + | 0.880043i | \(0.342486\pi\) | ||||
−0.474894 | + | 0.880043i | \(0.657514\pi\) | |||||||
\(510\) | −25.0100 | + | 6.33363i | −0.0490392 | + | 0.0124189i | ||||
\(511\) | −4.07182 | −0.00796834 | ||||||||
\(512\) | −16.0000 | − | 16.0000i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 51.1145 | − | 51.1145i | 0.0996384 | − | 0.0996384i | ||||
\(514\) | 275.281i | 0.535565i | ||||||||
\(515\) | 71.0243 | + | 280.458i | 0.137911 | + | 0.544579i | ||||
\(516\) | −152.389 | −0.295327 | ||||||||
\(517\) | 471.257 | + | 471.257i | 0.911523 | + | 0.911523i | ||||
\(518\) | 487.043 | − | 487.043i | 0.940237 | − | 0.940237i | ||||
\(519\) | − | 459.393i | − | 0.885150i | ||||||
\(520\) | 124.003 | + | 73.8883i | 0.238467 | + | 0.142093i | ||||
\(521\) | 624.757 | 1.19915 | 0.599575 | − | 0.800319i | \(-0.295336\pi\) | ||||
0.599575 | + | 0.800319i | \(0.295336\pi\) | |||||||
\(522\) | −2.85233 | − | 2.85233i | −0.00546423 | − | 0.00546423i | ||||
\(523\) | −604.436 | + | 604.436i | −1.15571 | + | 1.15571i | −0.170321 | + | 0.985389i | \(0.554480\pi\) |
−0.985389 | + | 0.170321i | \(0.945520\pi\) | |||||||
\(524\) | − | 177.646i | − | 0.339018i | ||||||
\(525\) | 159.513 | + | 294.742i | 0.303834 | + | 0.561413i | ||||
\(526\) | 295.240 | 0.561293 | ||||||||
\(527\) | 84.1277 | + | 84.1277i | 0.159635 | + | 0.159635i | ||||
\(528\) | 89.7733 | − | 89.7733i | 0.170025 | − | 0.170025i | ||||
\(529\) | − | 23.0000i | − | 0.0434783i | ||||||
\(530\) | −91.0060 | + | 152.731i | −0.171709 | + | 0.288171i | ||||
\(531\) | 1.37895 | 0.00259689 | ||||||||
\(532\) | 152.270 | + | 152.270i | 0.286222 | + | 0.286222i | ||||
\(533\) | −323.546 | + | 323.546i | −0.607028 | + | 0.607028i | ||||
\(534\) | − | 156.874i | − | 0.293772i | ||||||
\(535\) | −851.957 | + | 215.753i | −1.59244 | + | 0.403276i | ||||
\(536\) | −130.495 | −0.243460 | ||||||||
\(537\) | 72.5105 | + | 72.5105i | 0.135029 | + | 0.135029i | ||||
\(538\) | 43.0679 | − | 43.0679i | 0.0800518 | − | 0.0800518i | ||||
\(539\) | 199.785i | 0.370658i | ||||||||
\(540\) | −12.7562 | − | 50.3714i | −0.0236227 | − | 0.0932804i | ||||
\(541\) | 1001.87 | 1.85188 | 0.925938 | − | 0.377675i | \(-0.123276\pi\) | ||||
0.925938 | + | 0.377675i | \(0.123276\pi\) | |||||||
\(542\) | 455.005 | + | 455.005i | 0.839492 | + | 0.839492i | ||||
\(543\) | −268.161 | + | 268.161i | −0.493851 | + | 0.493851i | ||||
\(544\) | 11.9163i | 0.0219049i | ||||||||
\(545\) | 123.208 | + | 73.4148i | 0.226070 | + | 0.134706i | ||||
\(546\) | 193.505 | 0.354405 | ||||||||
\(547\) | 408.706 | + | 408.706i | 0.747177 | + | 0.747177i | 0.973948 | − | 0.226771i | \(-0.0728170\pi\) |
−0.226771 | + | 0.973948i | \(0.572817\pi\) | |||||||
\(548\) | −168.969 | + | 168.969i | −0.308337 | + | 0.308337i | ||||
\(549\) | − | 73.9629i | − | 0.134723i | ||||||
\(550\) | −184.854 | + | 620.952i | −0.336098 | + | 1.12900i | ||||
\(551\) | 13.2268 | 0.0240051 | ||||||||
\(552\) | −16.6132 | − | 16.6132i | −0.0300965 | − | 0.0300965i | ||||
\(553\) | −358.650 | + | 358.650i | −0.648554 | + | 0.648554i | ||||
\(554\) | − | 150.500i | − | 0.271660i | ||||||
\(555\) | 278.960 | − | 468.165i | 0.502631 | − | 0.843540i | ||||
\(556\) | 2.85580 | 0.00513633 | ||||||||
\(557\) | 749.003 | + | 749.003i | 1.34471 | + | 1.34471i | 0.891306 | + | 0.453402i | \(0.149790\pi\) |
0.453402 | + | 0.891306i | \(0.350210\pi\) | |||||||
\(558\) | −169.437 | + | 169.437i | −0.303651 | + | 0.303651i | ||||
\(559\) | − | 449.011i | − | 0.803240i | ||||||
\(560\) | 150.056 | − | 38.0008i | 0.267958 | − | 0.0678586i | ||||
\(561\) | −66.8603 | −0.119181 | ||||||||
\(562\) | −34.5423 | − | 34.5423i | −0.0614632 | − | 0.0614632i | ||||
\(563\) | −428.420 | + | 428.420i | −0.760959 | + | 0.760959i | −0.976496 | − | 0.215537i | \(-0.930850\pi\) |
0.215537 | + | 0.976496i | \(0.430850\pi\) | |||||||
\(564\) | − | 125.986i | − | 0.223379i | ||||||
\(565\) | −216.478 | − | 854.823i | −0.383148 | − | 1.51296i | ||||
\(566\) | −168.139 | −0.297065 | ||||||||
\(567\) | −49.2549 | − | 49.2549i | −0.0868693 | − | 0.0868693i | ||||
\(568\) | 93.4620 | − | 93.4620i | 0.164546 | − | 0.164546i | ||||
\(569\) | − | 800.840i | − | 1.40745i | −0.710472 | − | 0.703725i | \(-0.751519\pi\) | ||
0.710472 | − | 0.703725i | \(-0.248481\pi\) | |||||||
\(570\) | 146.368 | + | 87.2145i | 0.256786 | + | 0.153008i | ||||
\(571\) | 675.867 | 1.18366 | 0.591828 | − | 0.806064i | \(-0.298407\pi\) | ||||
0.591828 | + | 0.806064i | \(0.298407\pi\) | |||||||
\(572\) | 264.515 | + | 264.515i | 0.462440 | + | 0.462440i | ||||
\(573\) | 30.2634 | − | 30.2634i | 0.0528157 | − | 0.0528157i | ||||
\(574\) | 490.674i | 0.854833i | ||||||||
\(575\) | 114.912 | + | 34.2086i | 0.199847 | + | 0.0594932i | ||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | −639.279 | − | 639.279i | −1.10794 | − | 1.10794i | −0.993422 | − | 0.114515i | \(-0.963469\pi\) |
−0.114515 | − | 0.993422i | \(-0.536531\pi\) | |||||||
\(578\) | −284.563 | + | 284.563i | −0.492323 | + | 0.492323i | ||||
\(579\) | 285.857i | 0.493709i | ||||||||
\(580\) | 4.86681 | − | 8.16771i | 0.00839104 | − | 0.0140823i | ||||
\(581\) | −935.278 | −1.60977 | ||||||||
\(582\) | 121.165 | + | 121.165i | 0.208187 | + | 0.208187i | ||||
\(583\) | −325.796 | + | 325.796i | −0.558826 | + | 0.558826i | ||||
\(584\) | 1.48803i | 0.00254800i | ||||||||
\(585\) | 148.418 | − | 37.5860i | 0.253707 | − | 0.0642496i | ||||
\(586\) | −716.790 | −1.22319 | ||||||||
\(587\) | −578.249 | − | 578.249i | −0.985092 | − | 0.985092i | 0.0147984 | − | 0.999890i | \(-0.495289\pi\) |
−0.999890 | + | 0.0147984i | \(0.995289\pi\) | |||||||
\(588\) | 26.7052 | − | 26.7052i | 0.0454170 | − | 0.0454170i | ||||
\(589\) | − | 785.715i | − | 1.33398i | ||||||
\(590\) | 0.797906 | + | 3.15075i | 0.00135238 | + | 0.00534025i | ||||
\(591\) | −305.267 | −0.516525 | ||||||||
\(592\) | −177.988 | − | 177.988i | −0.300655 | − | 0.300655i | ||||
\(593\) | 118.071 | − | 118.071i | 0.199109 | − | 0.199109i | −0.600509 | − | 0.799618i | \(-0.705035\pi\) |
0.799618 | + | 0.600509i | \(0.205035\pi\) | |||||||
\(594\) | − | 134.660i | − | 0.226700i | ||||||
\(595\) | −70.0294 | − | 41.7277i | −0.117697 | − | 0.0701305i | ||||
\(596\) | 534.832 | 0.897369 | ||||||||
\(597\) | 319.767 | + | 319.767i | 0.535623 | + | 0.535623i | ||||
\(598\) | 48.9506 | − | 48.9506i | 0.0818572 | − | 0.0818572i | ||||
\(599\) | − | 262.366i | − | 0.438006i | −0.975724 | − | 0.219003i | \(-0.929720\pi\) | ||
0.975724 | − | 0.219003i | \(-0.0702805\pi\) | |||||||
\(600\) | 107.712 | − | 58.2933i | 0.179520 | − | 0.0971555i | ||||
\(601\) | −409.994 | −0.682186 | −0.341093 | − | 0.940030i | \(-0.610797\pi\) | ||||
−0.341093 | + | 0.940030i | \(0.610797\pi\) | |||||||
\(602\) | −340.475 | − | 340.475i | −0.565573 | − | 0.565573i | ||||
\(603\) | −97.8710 | + | 97.8710i | −0.162307 | + | 0.162307i | ||||
\(604\) | − | 321.118i | − | 0.531653i | ||||||
\(605\) | −549.762 | + | 922.637i | −0.908697 | + | 1.52502i | ||||
\(606\) | −300.875 | −0.496494 | ||||||||
\(607\) | 590.141 | + | 590.141i | 0.972226 | + | 0.972226i | 0.999625 | − | 0.0273990i | \(-0.00872246\pi\) |
−0.0273990 | + | 0.999625i | \(0.508722\pi\) | |||||||
\(608\) | 55.6464 | − | 55.6464i | 0.0915237 | − | 0.0915237i | ||||
\(609\) | − | 12.7456i | − | 0.0209287i | ||||||
\(610\) | 168.997 | − | 42.7975i | 0.277045 | − | 0.0701598i | ||||
\(611\) | 371.215 | 0.607554 | ||||||||
\(612\) | 8.93722 | + | 8.93722i | 0.0146033 | + | 0.0146033i | ||||
\(613\) | −29.4751 | + | 29.4751i | −0.0480834 | + | 0.0480834i | −0.730740 | − | 0.682656i | \(-0.760825\pi\) |
0.682656 | + | 0.730740i | \(0.260825\pi\) | |||||||
\(614\) | 86.2897i | 0.140537i | ||||||||
\(615\) | 95.3077 | + | 376.348i | 0.154972 | + | 0.611947i | ||||
\(616\) | 401.152 | 0.651220 | ||||||||
\(617\) | −97.0052 | − | 97.0052i | −0.157221 | − | 0.157221i | 0.624113 | − | 0.781334i | \(-0.285460\pi\) |
−0.781334 | + | 0.624113i | \(0.785460\pi\) | |||||||
\(618\) | 100.221 | − | 100.221i | 0.162169 | − | 0.162169i | ||||
\(619\) | 464.849i | 0.750968i | 0.926829 | + | 0.375484i | \(0.122524\pi\) | ||||
−0.926829 | + | 0.375484i | \(0.877476\pi\) | |||||||
\(620\) | −485.189 | − | 289.104i | −0.782563 | − | 0.466297i | ||||
\(621\) | −24.9199 | −0.0401286 | ||||||||
\(622\) | −188.459 | − | 188.459i | −0.302988 | − | 0.302988i | ||||
\(623\) | 350.496 | − | 350.496i | 0.562594 | − | 0.562594i | ||||
\(624\) | − | 70.7156i | − | 0.113326i | ||||||
\(625\) | −341.824 | + | 523.241i | −0.546919 | + | 0.837186i | ||||
\(626\) | 280.532 | 0.448134 | ||||||||
\(627\) | 312.223 | + | 312.223i | 0.497963 | + | 0.497963i | ||||
\(628\) | −186.509 | + | 186.509i | −0.296989 | + | 0.296989i | ||||
\(629\) | 132.560i | 0.210747i | ||||||||
\(630\) | 84.0416 | − | 141.043i | 0.133399 | − | 0.223877i | ||||
\(631\) | −1003.19 | −1.58984 | −0.794920 | − | 0.606714i | \(-0.792487\pi\) | ||||
−0.794920 | + | 0.606714i | \(0.792487\pi\) | |||||||
\(632\) | 131.067 | + | 131.067i | 0.207385 | + | 0.207385i | ||||
\(633\) | 201.208 | − | 201.208i | 0.317864 | − | 0.317864i | ||||
\(634\) | 254.587i | 0.401557i | ||||||||
\(635\) | 124.204 | − | 31.4538i | 0.195596 | − | 0.0495336i | ||||
\(636\) | 87.0982 | 0.136947 | ||||||||
\(637\) | 78.6864 | + | 78.6864i | 0.123527 | + | 0.123527i | ||||
\(638\) | 17.4229 | − | 17.4229i | 0.0273086 | − | 0.0273086i | ||||
\(639\) | − | 140.193i | − | 0.219394i | ||||||
\(640\) | −13.8872 | − | 54.8374i | −0.0216988 | − | 0.0856835i | ||||
\(641\) | −118.638 | −0.185082 | −0.0925410 | − | 0.995709i | \(-0.529499\pi\) | ||||
−0.0925410 | + | 0.995709i | \(0.529499\pi\) | |||||||
\(642\) | 304.443 | + | 304.443i | 0.474210 | + | 0.474210i | ||||
\(643\) | −790.836 | + | 790.836i | −1.22992 | + | 1.22992i | −0.265920 | + | 0.963995i | \(0.585676\pi\) |
−0.963995 | + | 0.265920i | \(0.914324\pi\) | |||||||
\(644\) | − | 74.2362i | − | 0.115274i | ||||||
\(645\) | −327.278 | − | 195.011i | −0.507407 | − | 0.302343i | ||||
\(646\) | −41.4437 | −0.0641543 | ||||||||
\(647\) | −672.665 | − | 672.665i | −1.03967 | − | 1.03967i | −0.999180 | − | 0.0404870i | \(-0.987109\pi\) |
−0.0404870 | − | 0.999180i | \(-0.512891\pi\) | |||||||
\(648\) | −18.0000 | + | 18.0000i | −0.0277778 | + | 0.0277778i | ||||
\(649\) | 8.42302i | 0.0129785i | ||||||||
\(650\) | 171.760 | + | 317.372i | 0.264246 | + | 0.488264i | ||||
\(651\) | −757.130 | −1.16303 | ||||||||
\(652\) | −426.592 | − | 426.592i | −0.654283 | − | 0.654283i | ||||
\(653\) | 702.904 | − | 702.904i | 1.07642 | − | 1.07642i | 0.0795956 | − | 0.996827i | \(-0.474637\pi\) |
0.996827 | − | 0.0795956i | \(-0.0253629\pi\) | |||||||
\(654\) | − | 70.2624i | − | 0.107435i | ||||||
\(655\) | 227.332 | − | 381.520i | 0.347072 | − | 0.582473i | ||||
\(656\) | 179.315 | 0.273346 | ||||||||
\(657\) | 1.11602 | + | 1.11602i | 0.00169866 | + | 0.00169866i | ||||
\(658\) | 281.484 | − | 281.484i | 0.427787 | − | 0.427787i | ||||
\(659\) | 1097.53i | 1.66545i | 0.553683 | + | 0.832727i | \(0.313222\pi\) | ||||
−0.553683 | + | 0.832727i | \(0.686778\pi\) | |||||||
\(660\) | 307.684 | − | 77.9189i | 0.466187 | − | 0.118059i | ||||
\(661\) | −620.423 | −0.938613 | −0.469306 | − | 0.883035i | \(-0.655496\pi\) | ||||
−0.469306 | + | 0.883035i | \(0.655496\pi\) | |||||||
\(662\) | −432.406 | − | 432.406i | −0.653182 | − | 0.653182i | ||||
\(663\) | −26.3333 | + | 26.3333i | −0.0397185 | + | 0.0397185i | ||||
\(664\) | 341.793i | 0.514749i | ||||||||
\(665\) | 132.163 | + | 521.881i | 0.198741 | + | 0.784783i | ||||
\(666\) | −266.982 | −0.400873 | ||||||||
\(667\) | −3.22424 | − | 3.22424i | −0.00483394 | − | 0.00483394i | ||||
\(668\) | 27.9154 | − | 27.9154i | 0.0417896 | − | 0.0417896i | ||||
\(669\) | − | 458.167i | − | 0.684854i | ||||||
\(670\) | −280.256 | − | 166.993i | −0.418293 | − | 0.249244i | ||||
\(671\) | 451.788 | 0.673305 | ||||||||
\(672\) | −53.6219 | − | 53.6219i | −0.0797946 | − | 0.0797946i | ||||
\(673\) | −512.487 | + | 512.487i | −0.761496 | + | 0.761496i | −0.976593 | − | 0.215097i | \(-0.930993\pi\) |
0.215097 | + | 0.976593i | \(0.430993\pi\) | |||||||
\(674\) | − | 502.555i | − | 0.745630i | ||||||
\(675\) | 37.0641 | − | 124.504i | 0.0549098 | − | 0.184450i | ||||
\(676\) | −129.638 | −0.191772 | ||||||||
\(677\) | −141.059 | − | 141.059i | −0.208359 | − | 0.208359i | 0.595211 | − | 0.803570i | \(-0.297069\pi\) |
−0.803570 | + | 0.595211i | \(0.797069\pi\) | |||||||
\(678\) | −305.467 | + | 305.467i | −0.450542 | + | 0.450542i | ||||
\(679\) | 541.425i | 0.797386i | ||||||||
\(680\) | −15.2492 | + | 25.5920i | −0.0224253 | + | 0.0376352i | ||||
\(681\) | 534.271 | 0.784539 | ||||||||
\(682\) | −1034.97 | − | 1034.97i | −1.51756 | − | 1.51756i | ||||
\(683\) | −606.606 | + | 606.606i | −0.888150 | + | 0.888150i | −0.994345 | − | 0.106196i | \(-0.966133\pi\) |
0.106196 | + | 0.994345i | \(0.466133\pi\) | |||||||
\(684\) | − | 83.4696i | − | 0.122032i | ||||||
\(685\) | −579.113 | + | 146.657i | −0.845420 | + | 0.214097i | ||||
\(686\) | −416.999 | −0.607870 | ||||||||
\(687\) | 438.526 | + | 438.526i | 0.638320 | + | 0.638320i | ||||
\(688\) | −124.425 | + | 124.425i | −0.180850 | + | 0.180850i | ||||
\(689\) | 256.633i | 0.372472i | ||||||||
\(690\) | −14.4195 | − | 56.9392i | −0.0208978 | − | 0.0825206i | ||||
\(691\) | 646.171 | 0.935125 | 0.467563 | − | 0.883960i | \(-0.345132\pi\) | ||||
0.467563 | + | 0.883960i | \(0.345132\pi\) | |||||||
\(692\) | −375.093 | − | 375.093i | −0.542042 | − | 0.542042i | ||||
\(693\) | 300.864 | − | 300.864i | 0.434147 | − | 0.434147i | ||||
\(694\) | − | 303.075i | − | 0.436707i | ||||||
\(695\) | 6.13324 | + | 3.65455i | 0.00882481 | + | 0.00525834i | ||||
\(696\) | −4.65783 | −0.00669228 | ||||||||
\(697\) | −66.7740 | − | 66.7740i | −0.0958020 | − | 0.0958020i | ||||
\(698\) | 642.693 | − | 642.693i | 0.920764 | − | 0.920764i | ||||
\(699\) | 98.4064i | 0.140782i | ||||||||
\(700\) | 370.897 | + | 110.414i | 0.529853 | + | 0.157734i | ||||
\(701\) | −439.029 | −0.626290 | −0.313145 | − | 0.949705i | \(-0.601383\pi\) | ||||
−0.313145 | + | 0.949705i | \(0.601383\pi\) | |||||||
\(702\) | −53.0367 | − | 53.0367i | −0.0755508 | − | 0.0755508i | ||||
\(703\) | 619.024 | − | 619.024i | 0.880546 | − | 0.880546i | ||||
\(704\) | − | 146.599i | − | 0.208238i | ||||||
\(705\) | 161.223 | − | 270.573i | 0.228686 | − | 0.383792i | ||||
\(706\) | −825.957 | −1.16991 | ||||||||
\(707\) | −672.230 | − | 672.230i | −0.950820 | − | 0.950820i | ||||
\(708\) | 1.12591 | − | 1.12591i | 0.00159026 | − | 0.00159026i | ||||
\(709\) | 101.093i | 0.142585i | 0.997455 | + | 0.0712927i | \(0.0227124\pi\) | ||||
−0.997455 | + | 0.0712927i | \(0.977288\pi\) | |||||||
\(710\) | 320.326 | − | 81.1205i | 0.451163 | − | 0.114254i | ||||
\(711\) | 196.601 | 0.276513 | ||||||||
\(712\) | −128.087 | − | 128.087i | −0.179898 | − | 0.179898i | ||||
\(713\) | −191.530 | + | 191.530i | −0.268626 | + | 0.268626i | ||||
\(714\) | 39.9359i | 0.0559326i | ||||||||
\(715\) | 229.587 | + | 906.584i | 0.321100 | + | 1.26795i | ||||
\(716\) | 118.409 | 0.165376 | ||||||||
\(717\) | 51.8751 | + | 51.8751i | 0.0723502 | + | 0.0723502i | ||||
\(718\) | −149.819 | + | 149.819i | −0.208662 | + | 0.208662i | ||||
\(719\) | − | 1336.70i | − | 1.85911i | −0.368680 | − | 0.929556i | \(-0.620190\pi\) | ||
0.368680 | − | 0.929556i | \(-0.379810\pi\) | |||||||
\(720\) | −51.5435 | − | 30.7127i | −0.0715882 | − | 0.0426565i | ||||
\(721\) | 447.835 | 0.621131 | ||||||||
\(722\) | −167.467 | − | 167.467i | −0.231949 | − | 0.231949i | ||||
\(723\) | −169.321 | + | 169.321i | −0.234192 | + | 0.234192i | ||||
\(724\) | 437.906i | 0.604842i | ||||||||
\(725\) | 20.9043 | − | 11.3133i | 0.0288336 | − | 0.0156046i | ||||
\(726\) | 526.155 | 0.724732 | ||||||||
\(727\) | −512.751 | − | 512.751i | −0.705297 | − | 0.705297i | 0.260246 | − | 0.965542i | \(-0.416196\pi\) |
−0.965542 | + | 0.260246i | \(0.916196\pi\) | |||||||
\(728\) | 157.996 | − | 157.996i | 0.217028 | − | 0.217028i | ||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | −1.90422 | + | 3.19576i | −0.00260852 | + | 0.00437776i | ||||
\(731\) | 92.6678 | 0.126769 | ||||||||
\(732\) | −60.3905 | − | 60.3905i | −0.0825006 | − | 0.0825006i | ||||
\(733\) | 163.456 | − | 163.456i | 0.222995 | − | 0.222995i | −0.586763 | − | 0.809759i | \(-0.699598\pi\) |
0.809759 | + | 0.586763i | \(0.199598\pi\) | |||||||
\(734\) | 515.380i | 0.702152i | ||||||||
\(735\) | 91.5279 | − | 23.1789i | 0.124528 | − | 0.0315359i | ||||
\(736\) | −27.1293 | −0.0368605 | ||||||||
\(737\) | −597.826 | − | 597.826i | −0.811161 | − | 0.811161i | ||||
\(738\) | 134.486 | − | 134.486i | 0.182231 | − | 0.182231i | ||||
\(739\) | 622.996i | 0.843026i | 0.906822 | + | 0.421513i | \(0.138501\pi\) | ||||
−0.906822 | + | 0.421513i | \(0.861499\pi\) | |||||||
\(740\) | −154.485 | − | 610.025i | −0.208763 | − | 0.824358i | ||||
\(741\) | 245.942 | 0.331905 | ||||||||
\(742\) | 194.599 | + | 194.599i | 0.262263 | + | 0.262263i | ||||
\(743\) | 499.375 | − | 499.375i | 0.672106 | − | 0.672106i | −0.286095 | − | 0.958201i | \(-0.592357\pi\) |
0.958201 | + | 0.286095i | \(0.0923572\pi\) | |||||||
\(744\) | 276.690i | 0.371895i | ||||||||
\(745\) | 1148.63 | + | 684.422i | 1.54179 | + | 0.918687i | ||||
\(746\) | 549.007 | 0.735934 | ||||||||
\(747\) | 256.345 | + | 256.345i | 0.343166 | + | 0.343166i | ||||
\(748\) | −54.5912 | + | 54.5912i | −0.0729829 | + | 0.0729829i | ||||
\(749\) | 1360.40i | 1.81629i | ||||||||
\(750\) | 305.925 | + | 12.6451i | 0.407900 | + | 0.0168602i | ||||
\(751\) | −1496.23 | −1.99231 | −0.996157 | − | 0.0875833i | \(-0.972086\pi\) | ||||
−0.996157 | + | 0.0875833i | \(0.972086\pi\) | |||||||
\(752\) | −102.867 | − | 102.867i | −0.136791 | − | 0.136791i | ||||
\(753\) | 205.243 | − | 205.243i | 0.272566 | − | 0.272566i | ||||
\(754\) | − | 13.7242i | − | 0.0182019i | ||||||
\(755\) | 410.933 | − | 689.648i | 0.544282 | − | 0.913442i | ||||
\(756\) | −80.4329 | −0.106393 | ||||||||
\(757\) | −810.088 | − | 810.088i | −1.07013 | − | 1.07013i | −0.997348 | − | 0.0727809i | \(-0.976813\pi\) |
−0.0727809 | − | 0.997348i | \(-0.523187\pi\) | |||||||
\(758\) | −543.361 | + | 543.361i | −0.716834 | + | 0.716834i | ||||
\(759\) | − | 152.218i | − | 0.200551i | ||||||
\(760\) | 190.719 | − | 48.2984i | 0.250946 | − | 0.0635506i | ||||
\(761\) | 374.404 | 0.491989 | 0.245995 | − | 0.969271i | \(-0.420885\pi\) | ||||
0.245995 | + | 0.969271i | \(0.420885\pi\) | |||||||
\(762\) | −44.3837 | − | 44.3837i | −0.0582463 | − | 0.0582463i | ||||
\(763\) | 156.984 | − | 156.984i | 0.205745 | − | 0.205745i | ||||
\(764\) | − | 49.4199i | − | 0.0646857i | ||||||
\(765\) | 7.75708 | + | 30.6309i | 0.0101400 | + | 0.0400404i | ||||
\(766\) | −645.779 | −0.843053 | ||||||||
\(767\) | 3.31746 | + | 3.31746i | 0.00432524 | + | 0.00432524i | ||||
\(768\) | −19.5959 | + | 19.5959i | −0.0255155 | + | 0.0255155i | ||||
\(769\) | − | 1015.53i | − | 1.32058i | −0.751009 | − | 0.660291i | \(-0.770433\pi\) | ||
0.751009 | − | 0.660291i | \(-0.229567\pi\) | |||||||
\(770\) | 861.532 | + | 513.351i | 1.11887 | + | 0.666690i | ||||
\(771\) | 337.149 | 0.437287 | ||||||||
\(772\) | 233.402 | + | 233.402i | 0.302334 | + | 0.302334i | ||||
\(773\) | 477.540 | − | 477.540i | 0.617774 | − | 0.617774i | −0.327186 | − | 0.944960i | \(-0.606100\pi\) |
0.944960 | + | 0.327186i | \(0.106100\pi\) | |||||||
\(774\) | 186.638i | 0.241134i | ||||||||
\(775\) | −672.049 | − | 1241.79i | −0.867160 | − | 1.60230i | ||||
\(776\) | 197.862 | 0.254976 | ||||||||
\(777\) | −596.503 | − | 596.503i | −0.767700 | − | 0.767700i | ||||
\(778\) | 720.417 | − | 720.417i | 0.925986 | − | 0.925986i | ||||
\(779\) | 623.640i | 0.800564i | ||||||||
\(780\) | 90.4943 | − | 151.872i | 0.116018 | − | 0.194708i | ||||
\(781\) | 856.341 | 1.09647 | ||||||||
\(782\) | 10.1025 | + | 10.1025i | 0.0129188 | + | 0.0129188i | ||||
\(783\) | −3.49337 | + | 3.49337i | −0.00446152 | + | 0.00446152i | ||||
\(784\) | − | 43.6094i | − | 0.0556243i | ||||||
\(785\) | −639.231 | + | 161.881i | −0.814307 | + | 0.206218i | ||||
\(786\) | −217.571 | −0.276807 | ||||||||
\(787\) | 65.3834 | + | 65.3834i | 0.0830793 | + | 0.0830793i | 0.747425 | − | 0.664346i | \(-0.231290\pi\) |
−0.664346 | + | 0.747425i | \(0.731290\pi\) | |||||||
\(788\) | −249.249 | + | 249.249i | −0.316306 | + | 0.316306i | ||||
\(789\) | − | 361.594i | − | 0.458294i | ||||||
\(790\) | 113.760 | + | 449.212i | 0.144000 | + | 0.568623i | ||||
\(791\) | −1364.98 | −1.72564 | ||||||||
\(792\) | −109.949 | − | 109.949i | −0.138825 | − | 0.138825i | ||||
\(793\) | 177.939 | − | 177.939i | 0.224388 | − | 0.224388i | ||||
\(794\) | − | 279.384i | − | 0.351869i | ||||||
\(795\) | 187.056 | + | 111.459i | 0.235291 | + | 0.140200i | ||||
\(796\) | 522.177 | 0.656001 | ||||||||
\(797\) | −879.060 | − | 879.060i | −1.10296 | − | 1.10296i | −0.994052 | − | 0.108910i | \(-0.965264\pi\) |
−0.108910 | − | 0.994052i | \(-0.534736\pi\) | |||||||
\(798\) | 186.492 | − | 186.492i | 0.233699 | − | 0.233699i | ||||
\(799\) | 76.6121i | 0.0958850i | ||||||||
\(800\) | 40.3503 | − | 135.543i | 0.0504378 | − | 0.169429i | ||||
\(801\) | −192.131 | −0.239864 | ||||||||
\(802\) | −410.867 | − | 410.867i | −0.512303 | − | 0.512303i | ||||
\(803\) | −6.81700 | + | 6.81700i | −0.00848942 | + | 0.00848942i | ||||
\(804\) | 159.823i | 0.198784i | ||||||||
\(805\) | 94.9996 | − | 159.433i | 0.118012 | − | 0.198054i | ||||
\(806\) | −815.262 | −1.01149 | ||||||||
\(807\) | −52.7472 | − | 52.7472i | −0.0653620 | − | 0.0653620i | ||||
\(808\) | −245.664 | + | 245.664i | −0.304039 | + | 0.304039i | ||||
\(809\) | 1215.51i | 1.50249i | 0.660024 | + | 0.751244i | \(0.270546\pi\) | ||||
−0.660024 | + | 0.751244i | \(0.729454\pi\) | |||||||
\(810\) | −61.6921 | + | 15.6231i | −0.0761631 | + | 0.0192878i | ||||
\(811\) | −1299.32 | −1.60212 | −0.801062 | − | 0.598581i | \(-0.795731\pi\) | ||||
−0.801062 | + | 0.598581i | \(0.795731\pi\) | |||||||
\(812\) | −10.4067 | − | 10.4067i | −0.0128162 | − | 0.0128162i | ||||
\(813\) | 557.265 | − | 557.265i | 0.685442 | − | 0.685442i | ||||
\(814\) | − | 1630.80i | − | 2.00345i | ||||||
\(815\) | −370.262 | − | 1462.08i | −0.454309 | − | 1.79396i | ||||
\(816\) | 14.5944 | 0.0178853 | ||||||||
\(817\) | −432.738 | − | 432.738i | −0.529667 | − | 0.529667i | ||||
\(818\) | 185.429 | − | 185.429i | 0.226686 | − | 0.226686i | ||||
\(819\) | − | 236.994i | − | 0.289370i | ||||||
\(820\) | 385.105 | + | 229.468i | 0.469640 | + | 0.279839i | ||||
\(821\) | 396.264 | 0.482660 | 0.241330 | − | 0.970443i | \(-0.422416\pi\) | ||||
0.241330 | + | 0.970443i | \(0.422416\pi\) | |||||||
\(822\) | 206.943 | + | 206.943i | 0.251756 | + | 0.251756i | ||||
\(823\) | 24.9125 | − | 24.9125i | 0.0302703 | − | 0.0302703i | −0.691810 | − | 0.722080i | \(-0.743186\pi\) |
0.722080 | + | 0.691810i | \(0.243186\pi\) | |||||||
\(824\) | − | 163.660i | − | 0.198616i | ||||||
\(825\) | 760.508 | + | 226.399i | 0.921828 | + | 0.274423i | ||||
\(826\) | 5.03110 | 0.00609092 | ||||||||
\(827\) | −525.121 | − | 525.121i | −0.634971 | − | 0.634971i | 0.314340 | − | 0.949311i | \(-0.398217\pi\) |
−0.949311 | + | 0.314340i | \(0.898217\pi\) | |||||||
\(828\) | −20.3470 | + | 20.3470i | −0.0245737 | + | 0.0245737i | ||||
\(829\) | − | 259.009i | − | 0.312435i | −0.987723 | − | 0.156218i | \(-0.950070\pi\) | ||
0.987723 | − | 0.156218i | \(-0.0499301\pi\) | |||||||
\(830\) | −437.391 | + | 734.051i | −0.526977 | + | 0.884399i | ||||
\(831\) | −184.324 | −0.221810 | ||||||||
\(832\) | −57.7390 | − | 57.7390i | −0.0693978 | − | 0.0693978i | ||||
\(833\) | −16.2395 | + | 16.2395i | −0.0194951 | + | 0.0194951i | ||||
\(834\) | − | 3.49762i | − | 0.00419379i | ||||||
\(835\) | 95.6757 | − | 24.2293i | 0.114582 | − | 0.0290171i | ||||
\(836\) | 509.858 | 0.609877 | ||||||||
\(837\) | 207.518 | + | 207.518i | 0.247930 | + | 0.247930i | ||||
\(838\) | 203.166 | − | 203.166i | 0.242442 | − | 0.242442i | ||||
\(839\) | − | 537.629i | − | 0.640798i | −0.947283 | − | 0.320399i | \(-0.896183\pi\) | ||
0.947283 | − | 0.320399i | \(-0.103817\pi\) | |||||||
\(840\) | −46.5413 | − | 183.781i | −0.0554063 | − | 0.218786i | ||||
\(841\) | 840.096 | 0.998925 | ||||||||
\(842\) | 622.636 | + | 622.636i | 0.739473 | + | 0.739473i | ||||
\(843\) | −42.3056 | + | 42.3056i | −0.0501845 | + | 0.0501845i | ||||
\(844\) | − | 328.571i | − | 0.389303i | ||||||
\(845\) | −278.416 | − | 165.897i | −0.329487 | − | 0.196328i | ||||
\(846\) | −154.301 | −0.182388 | ||||||||
\(847\) | 1175.56 | + | 1175.56i | 1.38791 | + | 1.38791i | ||||
\(848\) | 71.1154 | − | 71.1154i | 0.0838625 | − | 0.0838625i | ||||
\(849\) | 205.927i | 0.242553i | ||||||||
\(850\) | −65.4998 | + | 35.4482i | −0.0770586 | + | 0.0417037i | ||||
\(851\) | −301.793 | −0.354633 | ||||||||
\(852\) | −114.467 | − | 114.467i | −0.134351 | − | 0.134351i | ||||
\(853\) | −195.388 | + | 195.388i | −0.229060 | + | 0.229060i | −0.812300 | − | 0.583240i | \(-0.801785\pi\) |
0.583240 | + | 0.812300i | \(0.301785\pi\) | |||||||
\(854\) | − | 269.854i | − | 0.315989i | ||||||
\(855\) | 106.816 | − | 179.263i | 0.124930 | − | 0.209665i | ||||
\(856\) | 497.153 | 0.580787 | ||||||||
\(857\) | −379.526 | − | 379.526i | −0.442855 | − | 0.442855i | 0.450116 | − | 0.892970i | \(-0.351383\pi\) |
−0.892970 | + | 0.450116i | \(0.851383\pi\) | |||||||
\(858\) | 323.964 | − | 323.964i | 0.377580 | − | 0.377580i | ||||
\(859\) | 258.507i | 0.300939i | 0.988615 | + | 0.150470i | \(0.0480786\pi\) | ||||
−0.988615 | + | 0.150470i | \(0.951921\pi\) | |||||||
\(860\) | −426.447 | + | 107.995i | −0.495869 | + | 0.125576i | ||||
\(861\) | 600.951 | 0.697969 | ||||||||
\(862\) | −645.267 | − | 645.267i | −0.748570 | − | 0.748570i | ||||
\(863\) | 856.478 | − | 856.478i | 0.992443 | − | 0.992443i | −0.00752867 | − | 0.999972i | \(-0.502396\pi\) |
0.999972 | + | 0.00752867i | \(0.00239647\pi\) | |||||||
\(864\) | 29.3939i | 0.0340207i | ||||||||
\(865\) | −325.563 | − | 1285.57i | −0.376373 | − | 1.48621i | ||||
\(866\) | −665.086 | −0.767998 | ||||||||
\(867\) | 348.517 | + | 348.517i | 0.401980 | + | 0.401980i | ||||
\(868\) | −618.194 | + | 618.194i | −0.712205 | + | 0.712205i | ||||
\(869\) | 1200.90i | 1.38193i | ||||||||
\(870\) | −10.0034 | − | 5.96059i | −0.0114981 | − | 0.00685126i | ||||
\(871\) | −470.915 | −0.540660 | ||||||||
\(872\) | −57.3690 | − | 57.3690i | −0.0657902 | − | 0.0657902i | ||||
\(873\) | 148.396 | − | 148.396i | 0.169984 | − | 0.169984i | ||||
\(874\) | − | 94.3531i | − | 0.107955i | ||||||
\(875\) | 655.260 | + | 711.765i | 0.748868 | + | 0.813445i | ||||
\(876\) | 1.82246 | 0.00208043 | ||||||||
\(877\) | −766.900 | − | 766.900i | −0.874458 | − | 0.874458i | 0.118497 | − | 0.992954i | \(-0.462193\pi\) |
−0.992954 | + | 0.118497i | \(0.962193\pi\) | |||||||
\(878\) | −42.1637 | + | 42.1637i | −0.0480224 | + | 0.0480224i | ||||
\(879\) | 877.885i | 0.998732i | ||||||||
\(880\) | 187.602 | − | 314.843i | 0.213184 | − | 0.357776i | ||||
\(881\) | 243.225 | 0.276079 | 0.138039 | − | 0.990427i | \(-0.455920\pi\) | ||||
0.138039 | + | 0.990427i | \(0.455920\pi\) | |||||||
\(882\) | −32.7071 | − | 32.7071i | −0.0370829 | − | 0.0370829i | ||||
\(883\) | −526.787 | + | 526.787i | −0.596588 | + | 0.596588i | −0.939403 | − | 0.342815i | \(-0.888620\pi\) |
0.342815 | + | 0.939403i | \(0.388620\pi\) | |||||||
\(884\) | 43.0022i | 0.0486450i | ||||||||
\(885\) | 3.85886 | − | 0.977232i | 0.00436029 | − | 0.00110422i | ||||
\(886\) | 37.2390 | 0.0420305 | ||||||||
\(887\) | 531.370 | + | 531.370i | 0.599064 | + | 0.599064i | 0.940064 | − | 0.340999i | \(-0.110765\pi\) |
−0.340999 | + | 0.940064i | \(0.610765\pi\) | |||||||
\(888\) | −217.990 | + | 217.990i | −0.245484 | + | 0.245484i | ||||
\(889\) | − | 198.328i | − | 0.223091i | ||||||
\(890\) | −111.174 | − | 438.999i | −0.124914 | − | 0.493258i | ||||
\(891\) | −164.924 | −0.185100 | ||||||||
\(892\) | −374.092 | − | 374.092i | −0.419386 | − | 0.419386i | ||||
\(893\) | 357.762 | − | 357.762i | 0.400629 | − | 0.400629i | ||||
\(894\) | − | 655.033i | − | 0.732699i | ||||||
\(895\) | 254.301 | + | 151.527i | 0.284135 | + | 0.169304i | ||||
\(896\) | −87.5643 | −0.0977280 | ||||||||
\(897\) | −59.9520 | − | 59.9520i | −0.0668361 | − | 0.0668361i | ||||
\(898\) | −256.938 | + | 256.938i | −0.286123 | + | 0.286123i | ||||
\(899\) | 53.6990i | 0.0597319i | ||||||||
\(900\) | −71.3944 | − | 131.920i | −0.0793271 | − | 0.146578i | ||||
\(901\) | −52.9645 | −0.0587841 | ||||||||
\(902\) | 821.482 | + | 821.482i | 0.910734 | + | 0.910734i | ||||
\(903\) | −416.995 | + | 416.995i | −0.461788 | + | 0.461788i | ||||
\(904\) | 498.826i | 0.551798i | ||||||||
\(905\) | −560.385 | + | 940.466i | −0.619210 | + | 1.03919i | ||||
\(906\) | −393.288 | −0.434093 | ||||||||
\(907\) | 433.552 | + | 433.552i | 0.478007 | + | 0.478007i | 0.904494 | − | 0.426487i | \(-0.140249\pi\) |
−0.426487 | + | 0.904494i | \(0.640249\pi\) | |||||||
\(908\) | 436.231 | − | 436.231i | 0.480430 | − | 0.480430i | ||||
\(909\) | 368.495i | 0.405386i | ||||||||
\(910\) | 541.506 | − | 137.133i | 0.595062 | − | 0.150696i | ||||
\(911\) | 1084.05 | 1.18996 | 0.594980 | − | 0.803740i | \(-0.297160\pi\) | ||||
0.594980 | + | 0.803740i | \(0.297160\pi\) | |||||||
\(912\) | −68.1527 | − | 68.1527i | −0.0747288 | − | 0.0747288i | ||||
\(913\) | −1565.83 | + | 1565.83i | −1.71504 | + | 1.71504i | ||||
\(914\) | 686.158i | 0.750719i | ||||||||
\(915\) | −52.4160 | − | 206.979i | −0.0572853 | − | 0.226206i | ||||
\(916\) | 716.110 | 0.781779 | ||||||||
\(917\) | −486.107 | − | 486.107i | −0.530105 | − | 0.530105i | ||||
\(918\) | 10.9458 | − | 10.9458i | 0.0119235 | − | 0.0119235i | ||||
\(919\) | 1372.71i | 1.49370i | 0.664993 | + | 0.746849i | \(0.268434\pi\) | ||||
−0.664993 | + | 0.746849i | \(0.731566\pi\) | |||||||
\(920\) | −58.2642 | − | 34.7172i | −0.0633306 | − | 0.0377361i | ||||
\(921\) | 105.683 | 0.114748 | ||||||||
\(922\) | 518.066 | + | 518.066i | 0.561893 | + | 0.561893i | ||||
\(923\) | 337.275 | − | 337.275i | 0.365412 | − | 0.365412i | ||||
\(924\) | − | 491.308i | − | 0.531719i | ||||||
\(925\) | 448.866 | − | 1507.81i | 0.485261 | − | 1.63007i | ||||
\(926\) | −1162.61 | −1.25552 | ||||||||
\(927\) | −122.745 | − | 122.745i | −0.132411 | − | 0.132411i | ||||
\(928\) | −3.80310 | + | 3.80310i | −0.00409817 | + | 0.00409817i | ||||
\(929\) | − | 668.265i | − | 0.719338i | −0.933080 | − | 0.359669i | \(-0.882890\pi\) | ||
0.933080 | − | 0.359669i | \(-0.117110\pi\) | |||||||
\(930\) | −354.079 | + | 594.232i | −0.380730 | + | 0.638960i | ||||
\(931\) | 151.669 | 0.162910 | ||||||||
\(932\) | 80.3485 | + | 80.3485i | 0.0862108 | + | 0.0862108i | ||||
\(933\) | −230.814 | + | 230.814i | −0.247389 | + | 0.247389i | ||||
\(934\) | 351.964i | 0.376835i | ||||||||
\(935\) | −187.103 | + | 47.3825i | −0.200110 | + | 0.0506765i | ||||
\(936\) | −86.6085 | −0.0925305 | ||||||||
\(937\) | −97.7256 | − | 97.7256i | −0.104296 | − | 0.104296i | 0.653033 | − | 0.757329i | \(-0.273496\pi\) |
−0.757329 | + | 0.653033i | \(0.773496\pi\) | |||||||
\(938\) | −357.084 | + | 357.084i | −0.380686 | + | 0.380686i | ||||
\(939\) | − | 343.580i | − | 0.365900i | ||||||
\(940\) | −89.2837 | − | 352.560i | −0.0949827 | − | 0.375064i | ||||
\(941\) | −1812.51 | −1.92615 | −0.963076 | − | 0.269229i | \(-0.913231\pi\) | ||||
−0.963076 | + | 0.269229i | \(0.913231\pi\) | |||||||
\(942\) | 228.426 | + | 228.426i | 0.242491 | + | 0.242491i | ||||
\(943\) | 152.022 | − | 152.022i | 0.161211 | − | 0.161211i | ||||
\(944\) | − | 1.83860i | − | 0.00194766i | ||||||
\(945\) | −172.741 | − | 102.930i | −0.182795 | − | 0.108920i | ||||
\(946\) | −1140.04 | −1.20511 | ||||||||
\(947\) | −200.460 | − | 200.460i | −0.211679 | − | 0.211679i | 0.593302 | − | 0.804980i | \(-0.297824\pi\) |
−0.804980 | + | 0.593302i | \(0.797824\pi\) | |||||||
\(948\) | 160.524 | − | 160.524i | 0.169329 | − | 0.169329i | ||||
\(949\) | 5.36984i | 0.00565842i | ||||||||
\(950\) | 471.405 | + | 140.334i | 0.496215 | + | 0.147720i | ||||
\(951\) | 311.804 | 0.327870 | ||||||||
\(952\) | 32.6075 | + | 32.6075i | 0.0342516 | + | 0.0342516i | ||||
\(953\) | 639.096 | − | 639.096i | 0.670615 | − | 0.670615i | −0.287243 | − | 0.957858i | \(-0.592739\pi\) |
0.957858 | + | 0.287243i | \(0.0927388\pi\) | |||||||
\(954\) | − | 106.673i | − | 0.111817i | ||||||
\(955\) | 63.2423 | − | 106.136i | 0.0662224 | − | 0.111138i | ||||
\(956\) | 84.7117 | 0.0886106 | ||||||||
\(957\) | −21.3386 | − | 21.3386i | −0.0222973 | − | 0.0222973i | ||||
\(958\) | 92.7211 | − | 92.7211i | 0.0967861 | − | 0.0967861i | ||||
\(959\) | 924.726i | 0.964260i | ||||||||
\(960\) | −67.1619 | + | 17.0083i | −0.0699603 | + | 0.0177170i | ||||
\(961\) | 2228.89 | 2.31935 | ||||||||
\(962\) | −642.302 | − | 642.302i | −0.667674 | − | 0.667674i | ||||
\(963\) | 372.865 | − | 372.865i | 0.387191 | − | 0.387191i | ||||
\(964\) | 276.500i | 0.286826i | ||||||||
\(965\) | 202.581 | + | 799.947i | 0.209929 | + | 0.828960i | ||||
\(966\) | −90.9204 | −0.0941205 | ||||||||
\(967\) | 610.583 | + | 610.583i | 0.631420 | + | 0.631420i | 0.948424 | − | 0.317004i | \(-0.102677\pi\) |
−0.317004 | + | 0.948424i | \(0.602677\pi\) | |||||||
\(968\) | 429.604 | − | 429.604i | 0.443806 | − | 0.443806i | ||||
\(969\) | 50.7579i | 0.0523818i | ||||||||
\(970\) | 424.937 | + | 253.202i | 0.438079 | + | 0.261033i | ||||
\(971\) | 504.845 | 0.519923 | 0.259962 | − | 0.965619i | \(-0.416290\pi\) | ||||
0.259962 | + | 0.965619i | \(0.416290\pi\) | |||||||
\(972\) | 22.0454 | + | 22.0454i | 0.0226805 | + | 0.0226805i | ||||
\(973\) | 7.81456 | − | 7.81456i | 0.00803141 | − | 0.00803141i | ||||
\(974\) | 718.617i | 0.737800i | ||||||||
\(975\) | 388.699 | − | 210.362i | 0.398666 | − | 0.215756i | ||||
\(976\) | −98.6172 | −0.101042 | ||||||||
\(977\) | 489.671 | + | 489.671i | 0.501198 | + | 0.501198i | 0.911810 | − | 0.410612i | \(-0.134685\pi\) |
−0.410612 | + | 0.911810i | \(0.634685\pi\) | |||||||
\(978\) | −522.467 | + | 522.467i | −0.534220 | + | 0.534220i | ||||
\(979\) | − | 1173.59i | − | 1.19877i | ||||||
\(980\) | 55.8067 | − | 93.6577i | 0.0569457 | − | 0.0955690i | ||||
\(981\) | −86.0536 | −0.0877203 | ||||||||
\(982\) | −215.844 | − | 215.844i | −0.219801 | − | 0.219801i | ||||
\(983\) | −737.262 | + | 737.262i | −0.750012 | + | 0.750012i | −0.974481 | − | 0.224469i | \(-0.927935\pi\) |
0.224469 | + | 0.974481i | \(0.427935\pi\) | |||||||
\(984\) | − | 219.615i | − | 0.223186i | ||||||
\(985\) | −854.261 | + | 216.336i | −0.867270 | + | 0.219631i | ||||
\(986\) | 2.83243 | 0.00287264 | ||||||||
\(987\) | −344.746 | − | 344.746i | −0.349287 | − | 0.349287i | ||||
\(988\) | 200.811 | − | 200.811i | 0.203250 | − | 0.203250i | ||||
\(989\) | 210.973i | 0.213319i | ||||||||
\(990\) | −95.4308 | − | 376.834i | −0.0963948 | − | 0.380640i | ||||
\(991\) | −325.586 | −0.328543 | −0.164271 | − | 0.986415i | \(-0.552527\pi\) | ||||
−0.164271 | + | 0.986415i | \(0.552527\pi\) | |||||||
\(992\) | 225.917 | + | 225.917i | 0.227738 | + | 0.227738i | ||||
\(993\) | −529.587 | + | 529.587i | −0.533320 | + | 0.533320i | ||||
\(994\) | − | 511.496i | − | 0.514583i | ||||||
\(995\) | 1121.45 | + | 668.227i | 1.12709 | + | 0.671584i | ||||
\(996\) | 418.610 | 0.420291 | ||||||||
\(997\) | 217.426 | + | 217.426i | 0.218081 | + | 0.218081i | 0.807689 | − | 0.589609i | \(-0.200718\pi\) |
−0.589609 | + | 0.807689i | \(0.700718\pi\) | |||||||
\(998\) | −236.340 | + | 236.340i | −0.236813 | + | 0.236813i | ||||
\(999\) | 326.984i | 0.327312i |
(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.277.8 | ✓ | 48 | |
5.3 | odd | 4 | inner | 690.3.k.b.553.8 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.k.b.277.8 | ✓ | 48 | 1.1 | even | 1 | trivial | |
690.3.k.b.553.8 | yes | 48 | 5.3 | odd | 4 | inner |