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: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 277.17 | ||
Character | \(\chi\) | \(=\) | 690.277 |
Dual form | 690.3.k.a.553.17 |
$q$-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 | ||||||||
\(5\) | 3.38409 | + | 3.68075i | 0.676817 | + | 0.736151i | ||||
\(6\) | 2.44949 | 0.408248 | ||||||||
\(7\) | −0.957772 | − | 0.957772i | −0.136825 | − | 0.136825i | 0.635377 | − | 0.772202i | \(-0.280845\pi\) |
−0.772202 | + | 0.635377i | \(0.780845\pi\) | |||||||
\(8\) | −2.00000 | + | 2.00000i | −0.250000 | + | 0.250000i | ||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | −0.296667 | + | 7.06484i | −0.0296667 | + | 0.706484i | ||||
\(11\) | −8.07242 | −0.733856 | −0.366928 | − | 0.930249i | \(-0.619590\pi\) | ||||
−0.366928 | + | 0.930249i | \(0.619590\pi\) | |||||||
\(12\) | 2.44949 | + | 2.44949i | 0.204124 | + | 0.204124i | ||||
\(13\) | −16.4529 | + | 16.4529i | −1.26561 | + | 1.26561i | −0.317274 | + | 0.948334i | \(0.602767\pi\) |
−0.948334 | + | 0.317274i | \(0.897233\pi\) | |||||||
\(14\) | − | 1.91554i | − | 0.136825i | ||||||
\(15\) | 8.65263 | + | 0.363341i | 0.576842 | + | 0.0242227i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | 10.2171 | + | 10.2171i | 0.601006 | + | 0.601006i | 0.940579 | − | 0.339574i | \(-0.110283\pi\) |
−0.339574 | + | 0.940579i | \(0.610283\pi\) | |||||||
\(18\) | 3.00000 | − | 3.00000i | 0.166667 | − | 0.166667i | ||||
\(19\) | 22.2917i | 1.17325i | 0.809859 | + | 0.586624i | \(0.199543\pi\) | ||||
−0.809859 | + | 0.586624i | \(0.800457\pi\) | |||||||
\(20\) | −7.36151 | + | 6.76817i | −0.368075 | + | 0.338409i | ||||
\(21\) | −2.34605 | −0.111717 | ||||||||
\(22\) | −8.07242 | − | 8.07242i | −0.366928 | − | 0.366928i | ||||
\(23\) | −3.39116 | + | 3.39116i | −0.147442 | + | 0.147442i | ||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | −2.09590 | + | 24.9120i | −0.0838362 | + | 0.996480i | ||||
\(26\) | −32.9058 | −1.26561 | ||||||||
\(27\) | −3.67423 | − | 3.67423i | −0.136083 | − | 0.136083i | ||||
\(28\) | 1.91554 | − | 1.91554i | 0.0684123 | − | 0.0684123i | ||||
\(29\) | 9.67981i | 0.333787i | 0.985975 | + | 0.166893i | \(0.0533736\pi\) | ||||
−0.985975 | + | 0.166893i | \(0.946626\pi\) | |||||||
\(30\) | 8.28929 | + | 9.01597i | 0.276310 | + | 0.300532i | ||||
\(31\) | 56.2127 | 1.81331 | 0.906656 | − | 0.421871i | \(-0.138627\pi\) | ||||
0.906656 | + | 0.421871i | \(0.138627\pi\) | |||||||
\(32\) | −4.00000 | − | 4.00000i | −0.125000 | − | 0.125000i | ||||
\(33\) | −9.88665 | + | 9.88665i | −0.299595 | + | 0.299595i | ||||
\(34\) | 20.4342i | 0.601006i | ||||||||
\(35\) | 0.284139 | − | 6.76651i | 0.00811826 | − | 0.193329i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | −21.1313 | − | 21.1313i | −0.571116 | − | 0.571116i | 0.361325 | − | 0.932440i | \(-0.382325\pi\) |
−0.932440 | + | 0.361325i | \(0.882325\pi\) | |||||||
\(38\) | −22.2917 | + | 22.2917i | −0.586624 | + | 0.586624i | ||||
\(39\) | 40.3012i | 1.03336i | ||||||||
\(40\) | −14.1297 | − | 0.593334i | −0.353242 | − | 0.0148333i | ||||
\(41\) | 0.341891 | 0.00833881 | 0.00416941 | − | 0.999991i | \(-0.498673\pi\) | ||||
0.00416941 | + | 0.999991i | \(0.498673\pi\) | |||||||
\(42\) | −2.34605 | − | 2.34605i | −0.0558584 | − | 0.0558584i | ||||
\(43\) | 10.7117 | − | 10.7117i | 0.249109 | − | 0.249109i | −0.571496 | − | 0.820605i | \(-0.693637\pi\) |
0.820605 | + | 0.571496i | \(0.193637\pi\) | |||||||
\(44\) | − | 16.1448i | − | 0.366928i | ||||||
\(45\) | 11.0423 | − | 10.1523i | 0.245384 | − | 0.225606i | ||||
\(46\) | −6.78233 | −0.147442 | ||||||||
\(47\) | 11.4105 | + | 11.4105i | 0.242777 | + | 0.242777i | 0.817998 | − | 0.575221i | \(-0.195084\pi\) |
−0.575221 | + | 0.817998i | \(0.695084\pi\) | |||||||
\(48\) | −4.89898 | + | 4.89898i | −0.102062 | + | 0.102062i | ||||
\(49\) | − | 47.1653i | − | 0.962558i | ||||||
\(50\) | −27.0079 | + | 22.8161i | −0.540158 | + | 0.456322i | ||||
\(51\) | 25.0267 | 0.490719 | ||||||||
\(52\) | −32.9058 | − | 32.9058i | −0.632804 | − | 0.632804i | ||||
\(53\) | 1.59872 | − | 1.59872i | 0.0301645 | − | 0.0301645i | −0.691864 | − | 0.722028i | \(-0.743210\pi\) |
0.722028 | + | 0.691864i | \(0.243210\pi\) | |||||||
\(54\) | − | 7.34847i | − | 0.136083i | ||||||
\(55\) | −27.3178 | − | 29.7126i | −0.496687 | − | 0.540229i | ||||
\(56\) | 3.83109 | 0.0684123 | ||||||||
\(57\) | 27.3017 | + | 27.3017i | 0.478977 | + | 0.478977i | ||||
\(58\) | −9.67981 | + | 9.67981i | −0.166893 | + | 0.166893i | ||||
\(59\) | − | 10.4110i | − | 0.176458i | −0.996100 | − | 0.0882289i | \(-0.971879\pi\) | ||
0.996100 | − | 0.0882289i | \(-0.0281207\pi\) | |||||||
\(60\) | −0.726682 | + | 17.3053i | −0.0121114 | + | 0.288421i | ||||
\(61\) | 11.0126 | 0.180534 | 0.0902671 | − | 0.995918i | \(-0.471228\pi\) | ||||
0.0902671 | + | 0.995918i | \(0.471228\pi\) | |||||||
\(62\) | 56.2127 | + | 56.2127i | 0.906656 | + | 0.906656i | ||||
\(63\) | −2.87332 | + | 2.87332i | −0.0456082 | + | 0.0456082i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | −116.237 | − | 4.88103i | −1.78826 | − | 0.0750928i | ||||
\(66\) | −19.7733 | −0.299595 | ||||||||
\(67\) | 86.5905 | + | 86.5905i | 1.29240 | + | 1.29240i | 0.933301 | + | 0.359094i | \(0.116914\pi\) |
0.359094 | + | 0.933301i | \(0.383086\pi\) | |||||||
\(68\) | −20.4342 | + | 20.4342i | −0.300503 | + | 0.300503i | ||||
\(69\) | 8.30662i | 0.120386i | ||||||||
\(70\) | 7.05065 | − | 6.48237i | 0.100724 | − | 0.0926053i | ||||
\(71\) | −127.113 | −1.79032 | −0.895162 | − | 0.445741i | \(-0.852940\pi\) | ||||
−0.895162 | + | 0.445741i | \(0.852940\pi\) | |||||||
\(72\) | 6.00000 | + | 6.00000i | 0.0833333 | + | 0.0833333i | ||||
\(73\) | −28.1347 | + | 28.1347i | −0.385407 | + | 0.385407i | −0.873046 | − | 0.487638i | \(-0.837858\pi\) |
0.487638 | + | 0.873046i | \(0.337858\pi\) | |||||||
\(74\) | − | 42.2626i | − | 0.571116i | ||||||
\(75\) | 27.9439 | + | 33.0778i | 0.372585 | + | 0.441037i | ||||
\(76\) | −44.5834 | −0.586624 | ||||||||
\(77\) | 7.73154 | + | 7.73154i | 0.100410 | + | 0.100410i | ||||
\(78\) | −40.3012 | + | 40.3012i | −0.516682 | + | 0.516682i | ||||
\(79\) | 72.7818i | 0.921289i | 0.887585 | + | 0.460645i | \(0.152382\pi\) | ||||
−0.887585 | + | 0.460645i | \(0.847618\pi\) | |||||||
\(80\) | −13.5363 | − | 14.7230i | −0.169204 | − | 0.184038i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 0.341891 | + | 0.341891i | 0.00416941 | + | 0.00416941i | ||||
\(83\) | 61.3355 | − | 61.3355i | 0.738982 | − | 0.738982i | −0.233399 | − | 0.972381i | \(-0.574985\pi\) |
0.972381 | + | 0.233399i | \(0.0749849\pi\) | |||||||
\(84\) | − | 4.69211i | − | 0.0558584i | ||||||
\(85\) | −3.03107 | + | 72.1822i | −0.0356597 | + | 0.849202i | ||||
\(86\) | 21.4234 | 0.249109 | ||||||||
\(87\) | 11.8553 | + | 11.8553i | 0.136268 | + | 0.136268i | ||||
\(88\) | 16.1448 | − | 16.1448i | 0.183464 | − | 0.183464i | ||||
\(89\) | 58.5171i | 0.657495i | 0.944418 | + | 0.328748i | \(0.106627\pi\) | ||||
−0.944418 | + | 0.328748i | \(0.893373\pi\) | |||||||
\(90\) | 21.1945 | + | 0.890001i | 0.235495 | + | 0.00988890i | ||||
\(91\) | 31.5163 | 0.346333 | ||||||||
\(92\) | −6.78233 | − | 6.78233i | −0.0737210 | − | 0.0737210i | ||||
\(93\) | 68.8462 | − | 68.8462i | 0.740281 | − | 0.740281i | ||||
\(94\) | 22.8211i | 0.242777i | ||||||||
\(95\) | −82.0504 | + | 75.4371i | −0.863688 | + | 0.794075i | ||||
\(96\) | −9.79796 | −0.102062 | ||||||||
\(97\) | −101.479 | − | 101.479i | −1.04618 | − | 1.04618i | −0.998881 | − | 0.0472966i | \(-0.984939\pi\) |
−0.0472966 | − | 0.998881i | \(-0.515061\pi\) | |||||||
\(98\) | 47.1653 | − | 47.1653i | 0.481279 | − | 0.481279i | ||||
\(99\) | 24.2172i | 0.244619i | ||||||||
\(100\) | −49.8240 | − | 4.19181i | −0.498240 | − | 0.0419181i | ||||
\(101\) | 197.512 | 1.95557 | 0.977783 | − | 0.209620i | \(-0.0672227\pi\) | ||||
0.977783 | + | 0.209620i | \(0.0672227\pi\) | |||||||
\(102\) | 25.0267 | + | 25.0267i | 0.245360 | + | 0.245360i | ||||
\(103\) | 80.9301 | − | 80.9301i | 0.785729 | − | 0.785729i | −0.195062 | − | 0.980791i | \(-0.562491\pi\) |
0.980791 | + | 0.195062i | \(0.0624908\pi\) | |||||||
\(104\) | − | 65.8116i | − | 0.632804i | ||||||
\(105\) | −7.93925 | − | 8.63524i | −0.0756119 | − | 0.0822404i | ||||
\(106\) | 3.19744 | 0.0301645 | ||||||||
\(107\) | 70.4148 | + | 70.4148i | 0.658082 | + | 0.658082i | 0.954926 | − | 0.296844i | \(-0.0959340\pi\) |
−0.296844 | + | 0.954926i | \(0.595934\pi\) | |||||||
\(108\) | 7.34847 | − | 7.34847i | 0.0680414 | − | 0.0680414i | ||||
\(109\) | − | 92.6182i | − | 0.849708i | −0.905262 | − | 0.424854i | \(-0.860325\pi\) | ||
0.905262 | − | 0.424854i | \(-0.139675\pi\) | |||||||
\(110\) | 2.39482 | − | 57.0303i | 0.0217711 | − | 0.518458i | ||||
\(111\) | −51.7608 | −0.466314 | ||||||||
\(112\) | 3.83109 | + | 3.83109i | 0.0342061 | + | 0.0342061i | ||||
\(113\) | −61.6480 | + | 61.6480i | −0.545557 | + | 0.545557i | −0.925153 | − | 0.379595i | \(-0.876063\pi\) |
0.379595 | + | 0.925153i | \(0.376063\pi\) | |||||||
\(114\) | 54.6033i | 0.478977i | ||||||||
\(115\) | −23.9580 | − | 1.00605i | −0.208331 | − | 0.00874823i | ||||
\(116\) | −19.3596 | −0.166893 | ||||||||
\(117\) | 49.3587 | + | 49.3587i | 0.421869 | + | 0.421869i | ||||
\(118\) | 10.4110 | − | 10.4110i | 0.0882289 | − | 0.0882289i | ||||
\(119\) | − | 19.5713i | − | 0.164465i | ||||||
\(120\) | −18.0319 | + | 16.5786i | −0.150266 | + | 0.138155i | ||||
\(121\) | −55.8361 | −0.461455 | ||||||||
\(122\) | 11.0126 | + | 11.0126i | 0.0902671 | + | 0.0902671i | ||||
\(123\) | 0.418730 | − | 0.418730i | 0.00340431 | − | 0.00340431i | ||||
\(124\) | 112.425i | 0.906656i | ||||||||
\(125\) | −98.7876 | + | 76.5898i | −0.790301 | + | 0.612719i | ||||
\(126\) | −5.74663 | −0.0456082 | ||||||||
\(127\) | 78.6155 | + | 78.6155i | 0.619020 | + | 0.619020i | 0.945280 | − | 0.326260i | \(-0.105789\pi\) |
−0.326260 | + | 0.945280i | \(0.605789\pi\) | |||||||
\(128\) | 8.00000 | − | 8.00000i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | − | 26.2381i | − | 0.203396i | ||||||
\(130\) | −111.356 | − | 121.118i | −0.856586 | − | 0.931678i | ||||
\(131\) | 12.2443 | 0.0934677 | 0.0467338 | − | 0.998907i | \(-0.485119\pi\) | ||||
0.0467338 | + | 0.998907i | \(0.485119\pi\) | |||||||
\(132\) | −19.7733 | − | 19.7733i | −0.149798 | − | 0.149798i | ||||
\(133\) | 21.3504 | − | 21.3504i | 0.160529 | − | 0.160529i | ||||
\(134\) | 173.181i | 1.29240i | ||||||||
\(135\) | 1.09002 | − | 25.9579i | 0.00807425 | − | 0.192281i | ||||
\(136\) | −40.8684 | −0.300503 | ||||||||
\(137\) | 57.0677 | + | 57.0677i | 0.416552 | + | 0.416552i | 0.884014 | − | 0.467461i | \(-0.154831\pi\) |
−0.467461 | + | 0.884014i | \(0.654831\pi\) | |||||||
\(138\) | −8.30662 | + | 8.30662i | −0.0601929 | + | 0.0601929i | ||||
\(139\) | − | 258.802i | − | 1.86189i | −0.365164 | − | 0.930943i | \(-0.618987\pi\) | ||
0.365164 | − | 0.930943i | \(-0.381013\pi\) | |||||||
\(140\) | 13.5330 | + | 0.568278i | 0.0966644 | + | 0.00405913i | ||||
\(141\) | 27.9500 | 0.198227 | ||||||||
\(142\) | −127.113 | − | 127.113i | −0.895162 | − | 0.895162i | ||||
\(143\) | 132.815 | − | 132.815i | 0.928774 | − | 0.928774i | ||||
\(144\) | 12.0000i | 0.0833333i | ||||||||
\(145\) | −35.6290 | + | 32.7573i | −0.245717 | + | 0.225913i | ||||
\(146\) | −56.2695 | −0.385407 | ||||||||
\(147\) | −57.7655 | − | 57.7655i | −0.392963 | − | 0.392963i | ||||
\(148\) | 42.2626 | − | 42.2626i | 0.285558 | − | 0.285558i | ||||
\(149\) | − | 189.848i | − | 1.27415i | −0.770803 | − | 0.637074i | \(-0.780145\pi\) | ||
0.770803 | − | 0.637074i | \(-0.219855\pi\) | |||||||
\(150\) | −5.13390 | + | 61.0217i | −0.0342260 | + | 0.406811i | ||||
\(151\) | 87.3704 | 0.578612 | 0.289306 | − | 0.957237i | \(-0.406576\pi\) | ||||
0.289306 | + | 0.957237i | \(0.406576\pi\) | |||||||
\(152\) | −44.5834 | − | 44.5834i | −0.293312 | − | 0.293312i | ||||
\(153\) | 30.6513 | − | 30.6513i | 0.200335 | − | 0.200335i | ||||
\(154\) | 15.4631i | 0.100410i | ||||||||
\(155\) | 190.229 | + | 206.905i | 1.22728 | + | 1.33487i | ||||
\(156\) | −80.6024 | −0.516682 | ||||||||
\(157\) | −141.182 | − | 141.182i | −0.899247 | − | 0.899247i | 0.0961225 | − | 0.995370i | \(-0.469356\pi\) |
−0.995370 | + | 0.0961225i | \(0.969356\pi\) | |||||||
\(158\) | −72.7818 | + | 72.7818i | −0.460645 | + | 0.460645i | ||||
\(159\) | − | 3.91605i | − | 0.0246292i | ||||||
\(160\) | 1.18667 | − | 28.2594i | 0.00741667 | − | 0.176621i | ||||
\(161\) | 6.49593 | 0.0403474 | ||||||||
\(162\) | −9.00000 | − | 9.00000i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | −4.11911 | + | 4.11911i | −0.0252706 | + | 0.0252706i | −0.719629 | − | 0.694359i | \(-0.755688\pi\) |
0.694359 | + | 0.719629i | \(0.255688\pi\) | |||||||
\(164\) | 0.683783i | 0.00416941i | ||||||||
\(165\) | −69.8476 | − | 2.93304i | −0.423319 | − | 0.0177760i | ||||
\(166\) | 122.671 | 0.738982 | ||||||||
\(167\) | −189.466 | − | 189.466i | −1.13453 | − | 1.13453i | −0.989415 | − | 0.145113i | \(-0.953646\pi\) |
−0.145113 | − | 0.989415i | \(-0.546354\pi\) | |||||||
\(168\) | 4.69211 | − | 4.69211i | 0.0279292 | − | 0.0279292i | ||||
\(169\) | − | 372.396i | − | 2.20353i | ||||||
\(170\) | −75.2132 | + | 69.1511i | −0.442431 | + | 0.406771i | ||||
\(171\) | 66.8752 | 0.391083 | ||||||||
\(172\) | 21.4234 | + | 21.4234i | 0.124554 | + | 0.124554i | ||||
\(173\) | −36.0695 | + | 36.0695i | −0.208494 | + | 0.208494i | −0.803627 | − | 0.595133i | \(-0.797099\pi\) |
0.595133 | + | 0.803627i | \(0.297099\pi\) | |||||||
\(174\) | 23.7106i | 0.136268i | ||||||||
\(175\) | 25.8674 | − | 21.8526i | 0.147814 | − | 0.124872i | ||||
\(176\) | 32.2897 | 0.183464 | ||||||||
\(177\) | −12.7508 | − | 12.7508i | −0.0720386 | − | 0.0720386i | ||||
\(178\) | −58.5171 | + | 58.5171i | −0.328748 | + | 0.328748i | ||||
\(179\) | 253.350i | 1.41536i | 0.706531 | + | 0.707682i | \(0.250259\pi\) | ||||
−0.706531 | + | 0.707682i | \(0.749741\pi\) | |||||||
\(180\) | 20.3045 | + | 22.0845i | 0.112803 | + | 0.122692i | ||||
\(181\) | 67.8558 | 0.374894 | 0.187447 | − | 0.982275i | \(-0.439979\pi\) | ||||
0.187447 | + | 0.982275i | \(0.439979\pi\) | |||||||
\(182\) | 31.5163 | + | 31.5163i | 0.173166 | + | 0.173166i | ||||
\(183\) | 13.4876 | − | 13.4876i | 0.0737028 | − | 0.0737028i | ||||
\(184\) | − | 13.5647i | − | 0.0737210i | ||||||
\(185\) | 6.26895 | − | 149.289i | 0.0338862 | − | 0.806968i | ||||
\(186\) | 137.692 | 0.740281 | ||||||||
\(187\) | −82.4767 | − | 82.4767i | −0.441052 | − | 0.441052i | ||||
\(188\) | −22.8211 | + | 22.8211i | −0.121389 | + | 0.121389i | ||||
\(189\) | 7.03816i | 0.0372389i | ||||||||
\(190\) | −157.487 | − | 6.61322i | −0.828882 | − | 0.0348064i | ||||
\(191\) | −29.7286 | −0.155647 | −0.0778235 | − | 0.996967i | \(-0.524797\pi\) | ||||
−0.0778235 | + | 0.996967i | \(0.524797\pi\) | |||||||
\(192\) | −9.79796 | − | 9.79796i | −0.0510310 | − | 0.0510310i | ||||
\(193\) | 99.2409 | − | 99.2409i | 0.514202 | − | 0.514202i | −0.401610 | − | 0.915811i | \(-0.631549\pi\) |
0.915811 | + | 0.401610i | \(0.131549\pi\) | |||||||
\(194\) | − | 202.958i | − | 1.04618i | ||||||
\(195\) | −148.339 | + | 136.383i | −0.760712 | + | 0.699399i | ||||
\(196\) | 94.3307 | 0.481279 | ||||||||
\(197\) | 80.0266 | + | 80.0266i | 0.406227 | + | 0.406227i | 0.880420 | − | 0.474194i | \(-0.157260\pi\) |
−0.474194 | + | 0.880420i | \(0.657260\pi\) | |||||||
\(198\) | −24.2172 | + | 24.2172i | −0.122309 | + | 0.122309i | ||||
\(199\) | − | 262.310i | − | 1.31814i | −0.752082 | − | 0.659070i | \(-0.770950\pi\) | ||
0.752082 | − | 0.659070i | \(-0.229050\pi\) | |||||||
\(200\) | −45.6322 | − | 54.0158i | −0.228161 | − | 0.270079i | ||||
\(201\) | 212.103 | 1.05524 | ||||||||
\(202\) | 197.512 | + | 197.512i | 0.977783 | + | 0.977783i | ||||
\(203\) | 9.27105 | − | 9.27105i | 0.0456702 | − | 0.0456702i | ||||
\(204\) | 50.0533i | 0.245360i | ||||||||
\(205\) | 1.15699 | + | 1.25842i | 0.00564385 | + | 0.00613862i | ||||
\(206\) | 161.860 | 0.785729 | ||||||||
\(207\) | 10.1735 | + | 10.1735i | 0.0491473 | + | 0.0491473i | ||||
\(208\) | 65.8116 | − | 65.8116i | 0.316402 | − | 0.316402i | ||||
\(209\) | − | 179.948i | − | 0.860996i | ||||||
\(210\) | 0.695996 | − | 16.5745i | 0.00331427 | − | 0.0789262i | ||||
\(211\) | 269.701 | 1.27820 | 0.639102 | − | 0.769122i | \(-0.279306\pi\) | ||||
0.639102 | + | 0.769122i | \(0.279306\pi\) | |||||||
\(212\) | 3.19744 | + | 3.19744i | 0.0150823 | + | 0.0150823i | ||||
\(213\) | −155.681 | + | 155.681i | −0.730897 | + | 0.730897i | ||||
\(214\) | 140.830i | 0.658082i | ||||||||
\(215\) | 75.6763 | + | 3.17780i | 0.351983 | + | 0.0147805i | ||||
\(216\) | 14.6969 | 0.0680414 | ||||||||
\(217\) | −53.8389 | − | 53.8389i | −0.248106 | − | 0.248106i | ||||
\(218\) | 92.6182 | − | 92.6182i | 0.424854 | − | 0.424854i | ||||
\(219\) | 68.9157i | 0.314684i | ||||||||
\(220\) | 59.4252 | − | 54.6355i | 0.270114 | − | 0.248343i | ||||
\(221\) | −336.202 | −1.52128 | ||||||||
\(222\) | −51.7608 | − | 51.7608i | −0.233157 | − | 0.233157i | ||||
\(223\) | 2.67761 | − | 2.67761i | 0.0120072 | − | 0.0120072i | −0.701078 | − | 0.713085i | \(-0.747297\pi\) |
0.713085 | + | 0.701078i | \(0.247297\pi\) | |||||||
\(224\) | 7.66218i | 0.0342061i | ||||||||
\(225\) | 74.7360 | + | 6.28771i | 0.332160 | + | 0.0279454i | ||||
\(226\) | −123.296 | −0.545557 | ||||||||
\(227\) | 145.152 | + | 145.152i | 0.639437 | + | 0.639437i | 0.950417 | − | 0.310979i | \(-0.100657\pi\) |
−0.310979 | + | 0.950417i | \(0.600657\pi\) | |||||||
\(228\) | −54.6033 | + | 54.6033i | −0.239488 | + | 0.239488i | ||||
\(229\) | − | 59.4180i | − | 0.259467i | −0.991549 | − | 0.129734i | \(-0.958588\pi\) | ||
0.991549 | − | 0.129734i | \(-0.0414123\pi\) | |||||||
\(230\) | −22.9520 | − | 24.9641i | −0.0997913 | − | 0.108540i | ||||
\(231\) | 18.9383 | 0.0819841 | ||||||||
\(232\) | −19.3596 | − | 19.3596i | −0.0834467 | − | 0.0834467i | ||||
\(233\) | −236.967 | + | 236.967i | −1.01702 | + | 1.01702i | −0.0171724 | + | 0.999853i | \(0.505466\pi\) |
−0.999853 | + | 0.0171724i | \(0.994534\pi\) | |||||||
\(234\) | 98.7174i | 0.421869i | ||||||||
\(235\) | −3.38513 | + | 80.6137i | −0.0144048 | + | 0.343037i | ||||
\(236\) | 20.8220 | 0.0882289 | ||||||||
\(237\) | 89.1392 | + | 89.1392i | 0.376115 | + | 0.376115i | ||||
\(238\) | 19.5713 | − | 19.5713i | 0.0822324 | − | 0.0822324i | ||||
\(239\) | 258.221i | 1.08042i | 0.841530 | + | 0.540210i | \(0.181655\pi\) | ||||
−0.841530 | + | 0.540210i | \(0.818345\pi\) | |||||||
\(240\) | −34.6105 | − | 1.45336i | −0.144210 | − | 0.00605569i | ||||
\(241\) | 380.361 | 1.57826 | 0.789130 | − | 0.614226i | \(-0.210532\pi\) | ||||
0.789130 | + | 0.614226i | \(0.210532\pi\) | |||||||
\(242\) | −55.8361 | − | 55.8361i | −0.230728 | − | 0.230728i | ||||
\(243\) | −11.0227 | + | 11.0227i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | 22.0252i | 0.0902671i | ||||||||
\(245\) | 173.604 | − | 159.612i | 0.708588 | − | 0.651476i | ||||
\(246\) | 0.837459 | 0.00340431 | ||||||||
\(247\) | −366.764 | − | 366.764i | −1.48487 | − | 1.48487i | ||||
\(248\) | −112.425 | + | 112.425i | −0.453328 | + | 0.453328i | ||||
\(249\) | − | 150.241i | − | 0.603376i | ||||||
\(250\) | −175.377 | − | 22.1978i | −0.701510 | − | 0.0887912i | ||||
\(251\) | 115.175 | 0.458864 | 0.229432 | − | 0.973325i | \(-0.426313\pi\) | ||||
0.229432 | + | 0.973325i | \(0.426313\pi\) | |||||||
\(252\) | −5.74663 | − | 5.74663i | −0.0228041 | − | 0.0228041i | ||||
\(253\) | 27.3749 | − | 27.3749i | 0.108201 | − | 0.108201i | ||||
\(254\) | 157.231i | 0.619020i | ||||||||
\(255\) | 84.6925 | + | 92.1170i | 0.332127 | + | 0.361243i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 265.052 | + | 265.052i | 1.03133 | + | 1.03133i | 0.999493 | + | 0.0318362i | \(0.0101355\pi\) |
0.0318362 | + | 0.999493i | \(0.489865\pi\) | |||||||
\(258\) | 26.2381 | − | 26.2381i | 0.101698 | − | 0.101698i | ||||
\(259\) | 40.4779i | 0.156285i | ||||||||
\(260\) | 9.76206 | − | 232.474i | 0.0375464 | − | 0.894132i | ||||
\(261\) | 29.0394 | 0.111262 | ||||||||
\(262\) | 12.2443 | + | 12.2443i | 0.0467338 | + | 0.0467338i | ||||
\(263\) | 11.8740 | − | 11.8740i | 0.0451481 | − | 0.0451481i | −0.684172 | − | 0.729320i | \(-0.739836\pi\) |
0.729320 | + | 0.684172i | \(0.239836\pi\) | |||||||
\(264\) | − | 39.5466i | − | 0.149798i | ||||||
\(265\) | 11.2947 | + | 0.474287i | 0.0426215 | + | 0.00178976i | ||||
\(266\) | 42.7008 | 0.160529 | ||||||||
\(267\) | 71.6685 | + | 71.6685i | 0.268421 | + | 0.268421i | ||||
\(268\) | −173.181 | + | 173.181i | −0.646198 | + | 0.646198i | ||||
\(269\) | 170.641i | 0.634353i | 0.948367 | + | 0.317177i | \(0.102735\pi\) | ||||
−0.948367 | + | 0.317177i | \(0.897265\pi\) | |||||||
\(270\) | 27.0479 | − | 24.8679i | 0.100177 | − | 0.0921032i | ||||
\(271\) | 95.8232 | 0.353591 | 0.176796 | − | 0.984248i | \(-0.443427\pi\) | ||||
0.176796 | + | 0.984248i | \(0.443427\pi\) | |||||||
\(272\) | −40.8684 | − | 40.8684i | −0.150251 | − | 0.150251i | ||||
\(273\) | 38.5994 | − | 38.5994i | 0.141390 | − | 0.141390i | ||||
\(274\) | 114.135i | 0.416552i | ||||||||
\(275\) | 16.9190 | − | 201.100i | 0.0615237 | − | 0.731273i | ||||
\(276\) | −16.6132 | −0.0601929 | ||||||||
\(277\) | 98.3010 | + | 98.3010i | 0.354877 | + | 0.354877i | 0.861921 | − | 0.507043i | \(-0.169262\pi\) |
−0.507043 | + | 0.861921i | \(0.669262\pi\) | |||||||
\(278\) | 258.802 | − | 258.802i | 0.930943 | − | 0.930943i | ||||
\(279\) | − | 168.638i | − | 0.604437i | ||||||
\(280\) | 12.9647 | + | 14.1013i | 0.0463026 | + | 0.0503618i | ||||
\(281\) | 155.796 | 0.554433 | 0.277216 | − | 0.960808i | \(-0.410588\pi\) | ||||
0.277216 | + | 0.960808i | \(0.410588\pi\) | |||||||
\(282\) | 27.9500 | + | 27.9500i | 0.0991135 | + | 0.0991135i | ||||
\(283\) | 141.426 | − | 141.426i | 0.499737 | − | 0.499737i | −0.411619 | − | 0.911356i | \(-0.635036\pi\) |
0.911356 | + | 0.411619i | \(0.135036\pi\) | |||||||
\(284\) | − | 254.226i | − | 0.895162i | ||||||
\(285\) | −8.09950 | + | 192.882i | −0.0284193 | + | 0.676779i | ||||
\(286\) | 265.629 | 0.928774 | ||||||||
\(287\) | −0.327454 | − | 0.327454i | −0.00114095 | − | 0.00114095i | ||||
\(288\) | −12.0000 | + | 12.0000i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | − | 80.2219i | − | 0.277584i | ||||||
\(290\) | −68.3863 | − | 2.87168i | −0.235815 | − | 0.00990234i | ||||
\(291\) | −248.572 | −0.854200 | ||||||||
\(292\) | −56.2695 | − | 56.2695i | −0.192704 | − | 0.192704i | ||||
\(293\) | 182.330 | − | 182.330i | 0.622287 | − | 0.622287i | −0.323829 | − | 0.946116i | \(-0.604970\pi\) |
0.946116 | + | 0.323829i | \(0.104970\pi\) | |||||||
\(294\) | − | 115.531i | − | 0.392963i | ||||||
\(295\) | 38.3204 | − | 35.2318i | 0.129900 | − | 0.119430i | ||||
\(296\) | 84.5251 | 0.285558 | ||||||||
\(297\) | 29.6600 | + | 29.6600i | 0.0998652 | + | 0.0998652i | ||||
\(298\) | 189.848 | − | 189.848i | 0.637074 | − | 0.637074i | ||||
\(299\) | − | 111.589i | − | 0.373207i | ||||||
\(300\) | −66.1556 | + | 55.8878i | −0.220519 | + | 0.186293i | ||||
\(301\) | −20.5187 | −0.0681684 | ||||||||
\(302\) | 87.3704 | + | 87.3704i | 0.289306 | + | 0.289306i | ||||
\(303\) | 241.902 | − | 241.902i | 0.798356 | − | 0.798356i | ||||
\(304\) | − | 89.1669i | − | 0.293312i | ||||||
\(305\) | 37.2675 | + | 40.5346i | 0.122189 | + | 0.132900i | ||||
\(306\) | 61.3026 | 0.200335 | ||||||||
\(307\) | 360.897 | + | 360.897i | 1.17556 | + | 1.17556i | 0.980864 | + | 0.194696i | \(0.0623719\pi\) |
0.194696 | + | 0.980864i | \(0.437628\pi\) | |||||||
\(308\) | −15.4631 | + | 15.4631i | −0.0502048 | + | 0.0502048i | ||||
\(309\) | − | 198.237i | − | 0.641545i | ||||||
\(310\) | −16.6764 | + | 397.134i | −0.0537949 | + | 1.28108i | ||||
\(311\) | 171.586 | 0.551723 | 0.275862 | − | 0.961197i | \(-0.411037\pi\) | ||||
0.275862 | + | 0.961197i | \(0.411037\pi\) | |||||||
\(312\) | −80.6024 | − | 80.6024i | −0.258341 | − | 0.258341i | ||||
\(313\) | −416.142 | + | 416.142i | −1.32953 | + | 1.32953i | −0.423746 | + | 0.905781i | \(0.639285\pi\) |
−0.905781 | + | 0.423746i | \(0.860715\pi\) | |||||||
\(314\) | − | 282.364i | − | 0.899247i | ||||||
\(315\) | −20.2995 | − | 0.852418i | −0.0644429 | − | 0.00270609i | ||||
\(316\) | −145.564 | −0.460645 | ||||||||
\(317\) | 224.319 | + | 224.319i | 0.707630 | + | 0.707630i | 0.966036 | − | 0.258407i | \(-0.0831975\pi\) |
−0.258407 | + | 0.966036i | \(0.583197\pi\) | |||||||
\(318\) | 3.91605 | − | 3.91605i | 0.0123146 | − | 0.0123146i | ||||
\(319\) | − | 78.1395i | − | 0.244951i | ||||||
\(320\) | 29.4460 | − | 27.0727i | 0.0920189 | − | 0.0846022i | ||||
\(321\) | 172.480 | 0.537322 | ||||||||
\(322\) | 6.49593 | + | 6.49593i | 0.0201737 | + | 0.0201737i | ||||
\(323\) | −227.757 | + | 227.757i | −0.705129 | + | 0.705129i | ||||
\(324\) | − | 18.0000i | − | 0.0555556i | ||||||
\(325\) | −375.391 | − | 444.358i | −1.15505 | − | 1.36726i | ||||
\(326\) | −8.23822 | −0.0252706 | ||||||||
\(327\) | −113.434 | − | 113.434i | −0.346892 | − | 0.346892i | ||||
\(328\) | −0.683783 | + | 0.683783i | −0.00208470 | + | 0.00208470i | ||||
\(329\) | − | 21.8574i | − | 0.0664358i | ||||||
\(330\) | −66.9146 | − | 72.7807i | −0.202771 | − | 0.220547i | ||||
\(331\) | 269.054 | 0.812853 | 0.406426 | − | 0.913684i | \(-0.366775\pi\) | ||||
0.406426 | + | 0.913684i | \(0.366775\pi\) | |||||||
\(332\) | 122.671 | + | 122.671i | 0.369491 | + | 0.369491i | ||||
\(333\) | −63.3938 | + | 63.3938i | −0.190372 | + | 0.190372i | ||||
\(334\) | − | 378.932i | − | 1.13453i | ||||||
\(335\) | −25.6885 | + | 611.748i | −0.0766822 | + | 1.82611i | ||||
\(336\) | 9.38421 | 0.0279292 | ||||||||
\(337\) | −94.3863 | − | 94.3863i | −0.280078 | − | 0.280078i | 0.553062 | − | 0.833140i | \(-0.313459\pi\) |
−0.833140 | + | 0.553062i | \(0.813459\pi\) | |||||||
\(338\) | 372.396 | − | 372.396i | 1.10176 | − | 1.10176i | ||||
\(339\) | 151.006i | 0.445445i | ||||||||
\(340\) | −144.364 | − | 6.06215i | −0.424601 | − | 0.0178298i | ||||
\(341\) | −453.772 | −1.33071 | ||||||||
\(342\) | 66.8752 | + | 66.8752i | 0.195541 | + | 0.195541i | ||||
\(343\) | −92.1045 | + | 92.1045i | −0.268526 | + | 0.268526i | ||||
\(344\) | 42.8467i | 0.124554i | ||||||||
\(345\) | −30.5746 | + | 28.1103i | −0.0886221 | + | 0.0814793i | ||||
\(346\) | −72.1389 | −0.208494 | ||||||||
\(347\) | 150.970 | + | 150.970i | 0.435072 | + | 0.435072i | 0.890349 | − | 0.455278i | \(-0.150460\pi\) |
−0.455278 | + | 0.890349i | \(0.650460\pi\) | |||||||
\(348\) | −23.7106 | + | 23.7106i | −0.0681339 | + | 0.0681339i | ||||
\(349\) | − | 417.741i | − | 1.19697i | −0.801135 | − | 0.598483i | \(-0.795770\pi\) | ||
0.801135 | − | 0.598483i | \(-0.204230\pi\) | |||||||
\(350\) | 47.7200 | + | 4.01480i | 0.136343 | + | 0.0114709i | ||||
\(351\) | 120.904 | 0.344455 | ||||||||
\(352\) | 32.2897 | + | 32.2897i | 0.0917320 | + | 0.0917320i | ||||
\(353\) | −367.544 | + | 367.544i | −1.04120 | + | 1.04120i | −0.0420875 | + | 0.999114i | \(0.513401\pi\) |
−0.999114 | + | 0.0420875i | \(0.986599\pi\) | |||||||
\(354\) | − | 25.5017i | − | 0.0720386i | ||||||
\(355\) | −430.162 | − | 467.872i | −1.21172 | − | 1.31795i | ||||
\(356\) | −117.034 | −0.328748 | ||||||||
\(357\) | −23.9698 | − | 23.9698i | −0.0671424 | − | 0.0671424i | ||||
\(358\) | −253.350 | + | 253.350i | −0.707682 | + | 0.707682i | ||||
\(359\) | − | 392.377i | − | 1.09297i | −0.837468 | − | 0.546486i | \(-0.815965\pi\) | ||
0.837468 | − | 0.546486i | \(-0.184035\pi\) | |||||||
\(360\) | −1.78000 | + | 42.3891i | −0.00494445 | + | 0.117747i | ||||
\(361\) | −135.921 | −0.376512 | ||||||||
\(362\) | 67.8558 | + | 67.8558i | 0.187447 | + | 0.187447i | ||||
\(363\) | −68.3850 | + | 68.3850i | −0.188388 | + | 0.188388i | ||||
\(364\) | 63.0325i | 0.173166i | ||||||||
\(365\) | −198.767 | − | 8.34664i | −0.544568 | − | 0.0228675i | ||||
\(366\) | 26.9752 | 0.0737028 | ||||||||
\(367\) | −400.857 | − | 400.857i | −1.09225 | − | 1.09225i | −0.995288 | − | 0.0969643i | \(-0.969087\pi\) |
−0.0969643 | − | 0.995288i | \(-0.530913\pi\) | |||||||
\(368\) | 13.5647 | − | 13.5647i | 0.0368605 | − | 0.0368605i | ||||
\(369\) | − | 1.02567i | − | 0.00277960i | ||||||
\(370\) | 155.558 | − | 143.020i | 0.420427 | − | 0.386541i | ||||
\(371\) | −3.06242 | −0.00825450 | ||||||||
\(372\) | 137.692 | + | 137.692i | 0.370141 | + | 0.370141i | ||||
\(373\) | −239.306 | + | 239.306i | −0.641572 | + | 0.641572i | −0.950942 | − | 0.309370i | \(-0.899882\pi\) |
0.309370 | + | 0.950942i | \(0.399882\pi\) | |||||||
\(374\) | − | 164.953i | − | 0.441052i | ||||||
\(375\) | −27.1866 | + | 214.793i | −0.0724977 | + | 0.572780i | ||||
\(376\) | −45.6422 | −0.121389 | ||||||||
\(377\) | −159.261 | − | 159.261i | −0.422443 | − | 0.422443i | ||||
\(378\) | −7.03816 | + | 7.03816i | −0.0186195 | + | 0.0186195i | ||||
\(379\) | − | 164.467i | − | 0.433951i | −0.976177 | − | 0.216975i | \(-0.930381\pi\) | ||
0.976177 | − | 0.216975i | \(-0.0696191\pi\) | |||||||
\(380\) | −150.874 | − | 164.101i | −0.397038 | − | 0.431844i | ||||
\(381\) | 192.568 | 0.505428 | ||||||||
\(382\) | −29.7286 | − | 29.7286i | −0.0778235 | − | 0.0778235i | ||||
\(383\) | −97.6018 | + | 97.6018i | −0.254835 | + | 0.254835i | −0.822949 | − | 0.568115i | \(-0.807673\pi\) |
0.568115 | + | 0.822949i | \(0.307673\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | −2.29369 | + | 54.6221i | −0.00595764 | + | 0.141876i | ||||
\(386\) | 198.482 | 0.514202 | ||||||||
\(387\) | −32.1350 | − | 32.1350i | −0.0830362 | − | 0.0830362i | ||||
\(388\) | 202.958 | − | 202.958i | 0.523089 | − | 0.523089i | ||||
\(389\) | − | 591.161i | − | 1.51969i | −0.650102 | − | 0.759847i | \(-0.725274\pi\) | ||
0.650102 | − | 0.759847i | \(-0.274726\pi\) | |||||||
\(390\) | −284.722 | − | 11.9560i | −0.730056 | − | 0.0306565i | ||||
\(391\) | −69.2957 | −0.177227 | ||||||||
\(392\) | 94.3307 | + | 94.3307i | 0.240640 | + | 0.240640i | ||||
\(393\) | 14.9961 | − | 14.9961i | 0.0381580 | − | 0.0381580i | ||||
\(394\) | 160.053i | 0.406227i | ||||||||
\(395\) | −267.892 | + | 246.300i | −0.678208 | + | 0.623545i | ||||
\(396\) | −48.4345 | −0.122309 | ||||||||
\(397\) | −2.74699 | − | 2.74699i | −0.00691938 | − | 0.00691938i | 0.703639 | − | 0.710558i | \(-0.251557\pi\) |
−0.710558 | + | 0.703639i | \(0.751557\pi\) | |||||||
\(398\) | 262.310 | − | 262.310i | 0.659070 | − | 0.659070i | ||||
\(399\) | − | 52.2976i | − | 0.131072i | ||||||
\(400\) | 8.38362 | − | 99.6480i | 0.0209590 | − | 0.249120i | ||||
\(401\) | 259.213 | 0.646416 | 0.323208 | − | 0.946328i | \(-0.395239\pi\) | ||||
0.323208 | + | 0.946328i | \(0.395239\pi\) | |||||||
\(402\) | 212.103 | + | 212.103i | 0.527618 | + | 0.527618i | ||||
\(403\) | −924.861 | + | 924.861i | −2.29494 | + | 2.29494i | ||||
\(404\) | 395.024i | 0.977783i | ||||||||
\(405\) | −30.4568 | − | 33.1268i | −0.0752019 | − | 0.0817945i | ||||
\(406\) | 18.5421 | 0.0456702 | ||||||||
\(407\) | 170.580 | + | 170.580i | 0.419117 | + | 0.419117i | ||||
\(408\) | −50.0533 | + | 50.0533i | −0.122680 | + | 0.122680i | ||||
\(409\) | 67.6142i | 0.165316i | 0.996578 | + | 0.0826579i | \(0.0263409\pi\) | ||||
−0.996578 | + | 0.0826579i | \(0.973659\pi\) | |||||||
\(410\) | −0.101428 | + | 2.41541i | −0.000247385 | + | 0.00589124i | ||||
\(411\) | 139.787 | 0.340114 | ||||||||
\(412\) | 161.860 | + | 161.860i | 0.392864 | + | 0.392864i | ||||
\(413\) | −9.97137 | + | 9.97137i | −0.0241438 | + | 0.0241438i | ||||
\(414\) | 20.3470i | 0.0491473i | ||||||||
\(415\) | 433.326 | + | 18.1962i | 1.04416 | + | 0.0438463i | ||||
\(416\) | 131.623 | 0.316402 | ||||||||
\(417\) | −316.967 | − | 316.967i | −0.760112 | − | 0.760112i | ||||
\(418\) | 179.948 | − | 179.948i | 0.430498 | − | 0.430498i | ||||
\(419\) | 659.542i | 1.57408i | 0.616899 | + | 0.787042i | \(0.288389\pi\) | ||||
−0.616899 | + | 0.787042i | \(0.711611\pi\) | |||||||
\(420\) | 17.2705 | − | 15.8785i | 0.0411202 | − | 0.0378059i | ||||
\(421\) | 162.043 | 0.384900 | 0.192450 | − | 0.981307i | \(-0.438357\pi\) | ||||
0.192450 | + | 0.981307i | \(0.438357\pi\) | |||||||
\(422\) | 269.701 | + | 269.701i | 0.639102 | + | 0.639102i | ||||
\(423\) | 34.2316 | − | 34.2316i | 0.0809258 | − | 0.0809258i | ||||
\(424\) | 6.39488i | 0.0150823i | ||||||||
\(425\) | −275.942 | + | 233.114i | −0.649276 | + | 0.548504i | ||||
\(426\) | −311.362 | −0.730897 | ||||||||
\(427\) | −10.5475 | − | 10.5475i | −0.0247015 | − | 0.0247015i | ||||
\(428\) | −140.830 | + | 140.830i | −0.329041 | + | 0.329041i | ||||
\(429\) | − | 325.328i | − | 0.758341i | ||||||
\(430\) | 72.4985 | + | 78.8541i | 0.168601 | + | 0.183382i | ||||
\(431\) | −536.271 | −1.24425 | −0.622124 | − | 0.782918i | \(-0.713730\pi\) | ||||
−0.622124 | + | 0.782918i | \(0.713730\pi\) | |||||||
\(432\) | 14.6969 | + | 14.6969i | 0.0340207 | + | 0.0340207i | ||||
\(433\) | 185.531 | − | 185.531i | 0.428479 | − | 0.428479i | −0.459631 | − | 0.888110i | \(-0.652018\pi\) |
0.888110 | + | 0.459631i | \(0.152018\pi\) | |||||||
\(434\) | − | 107.678i | − | 0.248106i | ||||||
\(435\) | −3.51708 | + | 83.7558i | −0.00808523 | + | 0.192542i | ||||
\(436\) | 185.236 | 0.424854 | ||||||||
\(437\) | −75.5949 | − | 75.5949i | −0.172986 | − | 0.172986i | ||||
\(438\) | −68.9157 | + | 68.9157i | −0.157342 | + | 0.157342i | ||||
\(439\) | 568.595i | 1.29521i | 0.761978 | + | 0.647603i | \(0.224228\pi\) | ||||
−0.761978 | + | 0.647603i | \(0.775772\pi\) | |||||||
\(440\) | 114.061 | + | 4.78964i | 0.259229 | + | 0.0108855i | ||||
\(441\) | −141.496 | −0.320853 | ||||||||
\(442\) | −336.202 | − | 336.202i | −0.760638 | − | 0.760638i | ||||
\(443\) | −543.783 | + | 543.783i | −1.22750 | + | 1.22750i | −0.262594 | + | 0.964907i | \(0.584578\pi\) |
−0.964907 | + | 0.262594i | \(0.915422\pi\) | |||||||
\(444\) | − | 103.522i | − | 0.233157i | ||||||
\(445\) | −215.387 | + | 198.027i | −0.484016 | + | 0.445004i | ||||
\(446\) | 5.35522 | 0.0120072 | ||||||||
\(447\) | −232.515 | − | 232.515i | −0.520168 | − | 0.520168i | ||||
\(448\) | −7.66218 | + | 7.66218i | −0.0171031 | + | 0.0171031i | ||||
\(449\) | − | 357.234i | − | 0.795622i | −0.917467 | − | 0.397811i | \(-0.869770\pi\) | ||
0.917467 | − | 0.397811i | \(-0.130230\pi\) | |||||||
\(450\) | 68.4483 | + | 81.0237i | 0.152107 | + | 0.180053i | ||||
\(451\) | −2.75989 | −0.00611949 | ||||||||
\(452\) | −123.296 | − | 123.296i | −0.272779 | − | 0.272779i | ||||
\(453\) | 107.006 | − | 107.006i | 0.236217 | − | 0.236217i | ||||
\(454\) | 290.304i | 0.639437i | ||||||||
\(455\) | 106.654 | + | 116.004i | 0.234404 | + | 0.254953i | ||||
\(456\) | −109.207 | −0.239488 | ||||||||
\(457\) | −10.4610 | − | 10.4610i | −0.0228906 | − | 0.0228906i | 0.695569 | − | 0.718459i | \(-0.255152\pi\) |
−0.718459 | + | 0.695569i | \(0.755152\pi\) | |||||||
\(458\) | 59.4180 | − | 59.4180i | 0.129734 | − | 0.129734i | ||||
\(459\) | − | 75.0800i | − | 0.163573i | ||||||
\(460\) | 2.01209 | − | 47.9161i | 0.00437411 | − | 0.104165i | ||||
\(461\) | 12.5540 | 0.0272321 | 0.0136160 | − | 0.999907i | \(-0.495666\pi\) | ||||
0.0136160 | + | 0.999907i | \(0.495666\pi\) | |||||||
\(462\) | 18.9383 | + | 18.9383i | 0.0409920 | + | 0.0409920i | ||||
\(463\) | −245.657 | + | 245.657i | −0.530577 | + | 0.530577i | −0.920744 | − | 0.390167i | \(-0.872417\pi\) |
0.390167 | + | 0.920744i | \(0.372417\pi\) | |||||||
\(464\) | − | 38.7193i | − | 0.0834467i | ||||||
\(465\) | 486.387 | + | 20.4244i | 1.04599 | + | 0.0439234i | ||||
\(466\) | −473.934 | −1.01702 | ||||||||
\(467\) | −125.860 | − | 125.860i | −0.269507 | − | 0.269507i | 0.559395 | − | 0.828901i | \(-0.311034\pi\) |
−0.828901 | + | 0.559395i | \(0.811034\pi\) | |||||||
\(468\) | −98.7174 | + | 98.7174i | −0.210935 | + | 0.210935i | ||||
\(469\) | − | 165.868i | − | 0.353663i | ||||||
\(470\) | −83.9988 | + | 77.2285i | −0.178721 | + | 0.164316i | ||||
\(471\) | −345.823 | −0.734232 | ||||||||
\(472\) | 20.8220 | + | 20.8220i | 0.0441144 | + | 0.0441144i | ||||
\(473\) | −86.4691 | + | 86.4691i | −0.182810 | + | 0.182810i | ||||
\(474\) | 178.278i | 0.376115i | ||||||||
\(475\) | −555.331 | − | 46.7213i | −1.16912 | − | 0.0983607i | ||||
\(476\) | 39.1426 | 0.0822324 | ||||||||
\(477\) | −4.79616 | − | 4.79616i | −0.0100548 | − | 0.0100548i | ||||
\(478\) | −258.221 | + | 258.221i | −0.540210 | + | 0.540210i | ||||
\(479\) | 268.187i | 0.559890i | 0.960016 | + | 0.279945i | \(0.0903162\pi\) | ||||
−0.960016 | + | 0.279945i | \(0.909684\pi\) | |||||||
\(480\) | −33.1571 | − | 36.0639i | −0.0690774 | − | 0.0751331i | ||||
\(481\) | 695.342 | 1.44562 | ||||||||
\(482\) | 380.361 | + | 380.361i | 0.789130 | + | 0.789130i | ||||
\(483\) | 7.95585 | − | 7.95585i | 0.0164717 | − | 0.0164717i | ||||
\(484\) | − | 111.672i | − | 0.230728i | ||||||
\(485\) | 30.1055 | − | 716.935i | 0.0620732 | − | 1.47822i | ||||
\(486\) | −22.0454 | −0.0453609 | ||||||||
\(487\) | 489.385 | + | 489.385i | 1.00490 | + | 1.00490i | 0.999988 | + | 0.00490986i | \(0.00156286\pi\) |
0.00490986 | + | 0.999988i | \(0.498437\pi\) | |||||||
\(488\) | −22.0252 | + | 22.0252i | −0.0451335 | + | 0.0451335i | ||||
\(489\) | 10.0897i | 0.0206334i | ||||||||
\(490\) | 333.216 | + | 13.9924i | 0.680032 | + | 0.0285559i | ||||
\(491\) | 467.500 | 0.952138 | 0.476069 | − | 0.879408i | \(-0.342061\pi\) | ||||
0.476069 | + | 0.879408i | \(0.342061\pi\) | |||||||
\(492\) | 0.837459 | + | 0.837459i | 0.00170215 | + | 0.00170215i | ||||
\(493\) | −98.8996 | + | 98.8996i | −0.200608 | + | 0.200608i | ||||
\(494\) | − | 733.527i | − | 1.48487i | ||||||
\(495\) | −89.1377 | + | 81.9533i | −0.180076 | + | 0.165562i | ||||
\(496\) | −224.851 | −0.453328 | ||||||||
\(497\) | 121.745 | + | 121.745i | 0.244960 | + | 0.244960i | ||||
\(498\) | 150.241 | − | 150.241i | 0.301688 | − | 0.301688i | ||||
\(499\) | − | 344.871i | − | 0.691124i | −0.938396 | − | 0.345562i | \(-0.887688\pi\) | ||
0.938396 | − | 0.345562i | \(-0.112312\pi\) | |||||||
\(500\) | −153.180 | − | 197.575i | −0.306359 | − | 0.395151i | ||||
\(501\) | −464.095 | −0.926338 | ||||||||
\(502\) | 115.175 | + | 115.175i | 0.229432 | + | 0.229432i | ||||
\(503\) | −334.082 | + | 334.082i | −0.664178 | + | 0.664178i | −0.956362 | − | 0.292184i | \(-0.905618\pi\) |
0.292184 | + | 0.956362i | \(0.405618\pi\) | |||||||
\(504\) | − | 11.4933i | − | 0.0228041i | ||||||
\(505\) | 668.398 | + | 726.994i | 1.32356 | + | 1.43959i | ||||
\(506\) | 54.7498 | 0.108201 | ||||||||
\(507\) | −456.090 | − | 456.090i | −0.899586 | − | 0.899586i | ||||
\(508\) | −157.231 | + | 157.231i | −0.309510 | + | 0.309510i | ||||
\(509\) | − | 526.240i | − | 1.03387i | −0.856025 | − | 0.516935i | \(-0.827073\pi\) | ||
0.856025 | − | 0.516935i | \(-0.172927\pi\) | |||||||
\(510\) | −7.42459 | + | 176.809i | −0.0145580 | + | 0.346685i | ||||
\(511\) | 53.8933 | 0.105466 | ||||||||
\(512\) | 16.0000 | + | 16.0000i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 81.9050 | − | 81.9050i | 0.159659 | − | 0.159659i | ||||
\(514\) | 530.103i | 1.03133i | ||||||||
\(515\) | 571.758 | + | 24.0093i | 1.11021 | + | 0.0466200i | ||||
\(516\) | 52.4763 | 0.101698 | ||||||||
\(517\) | −92.1106 | − | 92.1106i | −0.178164 | − | 0.178164i | ||||
\(518\) | −40.4779 | + | 40.4779i | −0.0781426 | + | 0.0781426i | ||||
\(519\) | 88.3518i | 0.170235i | ||||||||
\(520\) | 242.236 | − | 222.712i | 0.465839 | − | 0.428293i | ||||
\(521\) | −924.134 | −1.77377 | −0.886885 | − | 0.461991i | \(-0.847135\pi\) | ||||
−0.886885 | + | 0.461991i | \(0.847135\pi\) | |||||||
\(522\) | 29.0394 | + | 29.0394i | 0.0556311 | + | 0.0556311i | ||||
\(523\) | −234.911 | + | 234.911i | −0.449161 | + | 0.449161i | −0.895076 | − | 0.445914i | \(-0.852879\pi\) |
0.445914 | + | 0.895076i | \(0.352879\pi\) | |||||||
\(524\) | 24.4885i | 0.0467338i | ||||||||
\(525\) | 4.91710 | − | 58.4448i | 0.00936591 | − | 0.111324i | ||||
\(526\) | 23.7479 | 0.0451481 | ||||||||
\(527\) | 574.330 | + | 574.330i | 1.08981 | + | 1.08981i | ||||
\(528\) | 39.5466 | − | 39.5466i | 0.0748989 | − | 0.0748989i | ||||
\(529\) | − | 23.0000i | − | 0.0434783i | ||||||
\(530\) | 10.8204 | + | 11.7690i | 0.0204159 | + | 0.0222057i | ||||
\(531\) | −31.2330 | −0.0588193 | ||||||||
\(532\) | 42.7008 | + | 42.7008i | 0.0802646 | + | 0.0802646i | ||||
\(533\) | −5.62511 | + | 5.62511i | −0.0105537 | + | 0.0105537i | ||||
\(534\) | 143.337i | 0.268421i | ||||||||
\(535\) | −20.8897 | + | 497.470i | −0.0390463 | + | 0.929850i | ||||
\(536\) | −346.362 | −0.646198 | ||||||||
\(537\) | 310.289 | + | 310.289i | 0.577820 | + | 0.577820i | ||||
\(538\) | −170.641 | + | 170.641i | −0.317177 | + | 0.317177i | ||||
\(539\) | 380.738i | 0.706379i | ||||||||
\(540\) | 51.9158 | + | 2.18005i | 0.0961403 | + | 0.00403712i | ||||
\(541\) | −264.669 | −0.489222 | −0.244611 | − | 0.969621i | \(-0.578660\pi\) | ||||
−0.244611 | + | 0.969621i | \(0.578660\pi\) | |||||||
\(542\) | 95.8232 | + | 95.8232i | 0.176796 | + | 0.176796i | ||||
\(543\) | 83.1061 | − | 83.1061i | 0.153050 | − | 0.153050i | ||||
\(544\) | − | 81.7368i | − | 0.150251i | ||||||
\(545\) | 340.905 | − | 313.428i | 0.625513 | − | 0.575097i | ||||
\(546\) | 77.1988 | 0.141390 | ||||||||
\(547\) | 200.828 | + | 200.828i | 0.367145 | + | 0.367145i | 0.866435 | − | 0.499290i | \(-0.166406\pi\) |
−0.499290 | + | 0.866435i | \(0.666406\pi\) | |||||||
\(548\) | −114.135 | + | 114.135i | −0.208276 | + | 0.208276i | ||||
\(549\) | − | 33.0377i | − | 0.0601780i | ||||||
\(550\) | 218.019 | − | 184.181i | 0.396398 | − | 0.334874i | ||||
\(551\) | −215.780 | −0.391615 | ||||||||
\(552\) | −16.6132 | − | 16.6132i | −0.0300965 | − | 0.0300965i | ||||
\(553\) | 69.7084 | − | 69.7084i | 0.126055 | − | 0.126055i | ||||
\(554\) | 196.602i | 0.354877i | ||||||||
\(555\) | −175.163 | − | 190.519i | −0.315609 | − | 0.343277i | ||||
\(556\) | 517.604 | 0.930943 | ||||||||
\(557\) | 361.253 | + | 361.253i | 0.648570 | + | 0.648570i | 0.952647 | − | 0.304077i | \(-0.0983481\pi\) |
−0.304077 | + | 0.952647i | \(0.598348\pi\) | |||||||
\(558\) | 168.638 | − | 168.638i | 0.302219 | − | 0.302219i | ||||
\(559\) | 352.476i | 0.630548i | ||||||||
\(560\) | −1.13656 | + | 27.0660i | −0.00202957 | + | 0.0483322i | ||||
\(561\) | −202.026 | −0.360117 | ||||||||
\(562\) | 155.796 | + | 155.796i | 0.277216 | + | 0.277216i | ||||
\(563\) | −210.985 | + | 210.985i | −0.374752 | + | 0.374752i | −0.869205 | − | 0.494453i | \(-0.835369\pi\) |
0.494453 | + | 0.869205i | \(0.335369\pi\) | |||||||
\(564\) | 55.9000i | 0.0991135i | ||||||||
\(565\) | −435.533 | − | 18.2889i | −0.770855 | − | 0.0323697i | ||||
\(566\) | 282.851 | 0.499737 | ||||||||
\(567\) | 8.61995 | + | 8.61995i | 0.0152027 | + | 0.0152027i | ||||
\(568\) | 254.226 | − | 254.226i | 0.447581 | − | 0.447581i | ||||
\(569\) | − | 1065.34i | − | 1.87230i | −0.351600 | − | 0.936150i | \(-0.614362\pi\) | ||
0.351600 | − | 0.936150i | \(-0.385638\pi\) | |||||||
\(570\) | −200.981 | + | 184.782i | −0.352599 | + | 0.324180i | ||||
\(571\) | −192.279 | −0.336740 | −0.168370 | − | 0.985724i | \(-0.553850\pi\) | ||||
−0.168370 | + | 0.985724i | \(0.553850\pi\) | |||||||
\(572\) | 265.629 | + | 265.629i | 0.464387 | + | 0.464387i | ||||
\(573\) | −36.4099 | + | 36.4099i | −0.0635427 | + | 0.0635427i | ||||
\(574\) | − | 0.654908i | − | 0.00114095i | ||||||
\(575\) | −77.3731 | − | 91.5882i | −0.134562 | − | 0.159284i | ||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | −474.911 | − | 474.911i | −0.823069 | − | 0.823069i | 0.163478 | − | 0.986547i | \(-0.447729\pi\) |
−0.986547 | + | 0.163478i | \(0.947729\pi\) | |||||||
\(578\) | 80.2219 | − | 80.2219i | 0.138792 | − | 0.138792i | ||||
\(579\) | − | 243.090i | − | 0.419844i | ||||||
\(580\) | −65.5147 | − | 71.2580i | −0.112956 | − | 0.122859i | ||||
\(581\) | −117.491 | −0.202222 | ||||||||
\(582\) | −248.572 | − | 248.572i | −0.427100 | − | 0.427100i | ||||
\(583\) | −12.9055 | + | 12.9055i | −0.0221364 | + | 0.0221364i | ||||
\(584\) | − | 112.539i | − | 0.192704i | ||||||
\(585\) | −14.6431 | + | 348.711i | −0.0250309 | + | 0.596088i | ||||
\(586\) | 364.660 | 0.622287 | ||||||||
\(587\) | 344.230 | + | 344.230i | 0.586423 | + | 0.586423i | 0.936661 | − | 0.350238i | \(-0.113899\pi\) |
−0.350238 | + | 0.936661i | \(0.613899\pi\) | |||||||
\(588\) | 115.531 | − | 115.531i | 0.196481 | − | 0.196481i | ||||
\(589\) | 1253.08i | 2.12746i | ||||||||
\(590\) | 73.5521 | + | 3.08860i | 0.124665 | + | 0.00523492i | ||||
\(591\) | 196.024 | 0.331683 | ||||||||
\(592\) | 84.5251 | + | 84.5251i | 0.142779 | + | 0.142779i | ||||
\(593\) | −430.072 | + | 430.072i | −0.725248 | + | 0.725248i | −0.969669 | − | 0.244421i | \(-0.921402\pi\) |
0.244421 | + | 0.969669i | \(0.421402\pi\) | |||||||
\(594\) | 59.3199i | 0.0998652i | ||||||||
\(595\) | 72.0371 | − | 66.2310i | 0.121071 | − | 0.111313i | ||||
\(596\) | 379.696 | 0.637074 | ||||||||
\(597\) | −321.262 | − | 321.262i | −0.538128 | − | 0.538128i | ||||
\(598\) | 111.589 | − | 111.589i | 0.186604 | − | 0.186604i | ||||
\(599\) | − | 1172.10i | − | 1.95677i | −0.206803 | − | 0.978383i | \(-0.566306\pi\) | ||
0.206803 | − | 0.978383i | \(-0.433694\pi\) | |||||||
\(600\) | −122.043 | − | 10.2678i | −0.203406 | − | 0.0171130i | ||||
\(601\) | 812.766 | 1.35236 | 0.676178 | − | 0.736738i | \(-0.263635\pi\) | ||||
0.676178 | + | 0.736738i | \(0.263635\pi\) | |||||||
\(602\) | −20.5187 | − | 20.5187i | −0.0340842 | − | 0.0340842i | ||||
\(603\) | 259.772 | − | 259.772i | 0.430799 | − | 0.430799i | ||||
\(604\) | 174.741i | 0.289306i | ||||||||
\(605\) | −188.954 | − | 205.519i | −0.312321 | − | 0.339701i | ||||
\(606\) | 483.804 | 0.798356 | ||||||||
\(607\) | 194.117 | + | 194.117i | 0.319798 | + | 0.319798i | 0.848689 | − | 0.528892i | \(-0.177392\pi\) |
−0.528892 | + | 0.848689i | \(0.677392\pi\) | |||||||
\(608\) | 89.1669 | − | 89.1669i | 0.146656 | − | 0.146656i | ||||
\(609\) | − | 22.7094i | − | 0.0372896i | ||||||
\(610\) | −3.26707 | + | 77.8022i | −0.00535585 | + | 0.127545i | ||||
\(611\) | −375.473 | −0.614522 | ||||||||
\(612\) | 61.3026 | + | 61.3026i | 0.100168 | + | 0.100168i | ||||
\(613\) | 750.016 | − | 750.016i | 1.22352 | − | 1.22352i | 0.257143 | − | 0.966373i | \(-0.417219\pi\) |
0.966373 | − | 0.257143i | \(-0.0827812\pi\) | |||||||
\(614\) | 721.793i | 1.17556i | ||||||||
\(615\) | 2.95826 | + | 0.124223i | 0.00481018 | + | 0.000201989i | ||||
\(616\) | −30.9261 | −0.0502048 | ||||||||
\(617\) | −399.144 | − | 399.144i | −0.646911 | − | 0.646911i | 0.305334 | − | 0.952245i | \(-0.401232\pi\) |
−0.952245 | + | 0.305334i | \(0.901232\pi\) | |||||||
\(618\) | 198.237 | − | 198.237i | 0.320773 | − | 0.320773i | ||||
\(619\) | 611.969i | 0.988642i | 0.869280 | + | 0.494321i | \(0.164583\pi\) | ||||
−0.869280 | + | 0.494321i | \(0.835417\pi\) | |||||||
\(620\) | −413.810 | + | 380.457i | −0.667435 | + | 0.613640i | ||||
\(621\) | 24.9199 | 0.0401286 | ||||||||
\(622\) | 171.586 | + | 171.586i | 0.275862 | + | 0.275862i | ||||
\(623\) | 56.0460 | − | 56.0460i | 0.0899615 | − | 0.0899615i | ||||
\(624\) | − | 161.205i | − | 0.258341i | ||||||
\(625\) | −616.214 | − | 104.426i | −0.985943 | − | 0.167082i | ||||
\(626\) | −832.284 | −1.32953 | ||||||||
\(627\) | −220.390 | − | 220.390i | −0.351500 | − | 0.351500i | ||||
\(628\) | 282.364 | − | 282.364i | 0.449624 | − | 0.449624i | ||||
\(629\) | − | 431.801i | − | 0.686487i | ||||||
\(630\) | −19.4471 | − | 21.1519i | −0.0308684 | − | 0.0335745i | ||||
\(631\) | −163.115 | −0.258503 | −0.129251 | − | 0.991612i | \(-0.541257\pi\) | ||||
−0.129251 | + | 0.991612i | \(0.541257\pi\) | |||||||
\(632\) | −145.564 | − | 145.564i | −0.230322 | − | 0.230322i | ||||
\(633\) | 330.315 | − | 330.315i | 0.521824 | − | 0.521824i | ||||
\(634\) | 448.637i | 0.707630i | ||||||||
\(635\) | −23.3226 | + | 555.406i | −0.0367285 | + | 0.874655i | ||||
\(636\) | 7.83210 | 0.0123146 | ||||||||
\(637\) | 776.007 | + | 776.007i | 1.21822 | + | 1.21822i | ||||
\(638\) | 78.1395 | − | 78.1395i | 0.122476 | − | 0.122476i | ||||
\(639\) | 381.339i | 0.596775i | ||||||||
\(640\) | 56.5187 | + | 2.37333i | 0.0883105 | + | 0.00370834i | ||||
\(641\) | −292.715 | −0.456653 | −0.228327 | − | 0.973585i | \(-0.573325\pi\) | ||||
−0.228327 | + | 0.973585i | \(0.573325\pi\) | |||||||
\(642\) | 172.480 | + | 172.480i | 0.268661 | + | 0.268661i | ||||
\(643\) | 177.031 | − | 177.031i | 0.275320 | − | 0.275320i | −0.555917 | − | 0.831238i | \(-0.687633\pi\) |
0.831238 | + | 0.555917i | \(0.187633\pi\) | |||||||
\(644\) | 12.9919i | 0.0201737i | ||||||||
\(645\) | 96.5761 | − | 88.7922i | 0.149730 | − | 0.137662i | ||||
\(646\) | −455.513 | −0.705129 | ||||||||
\(647\) | 514.177 | + | 514.177i | 0.794710 | + | 0.794710i | 0.982256 | − | 0.187546i | \(-0.0600533\pi\) |
−0.187546 | + | 0.982256i | \(0.560053\pi\) | |||||||
\(648\) | 18.0000 | − | 18.0000i | 0.0277778 | − | 0.0277778i | ||||
\(649\) | 84.0420i | 0.129495i | ||||||||
\(650\) | 68.9674 | − | 819.749i | 0.106104 | − | 1.26115i | ||||
\(651\) | −131.878 | −0.202577 | ||||||||
\(652\) | −8.23822 | − | 8.23822i | −0.0126353 | − | 0.0126353i | ||||
\(653\) | −490.962 | + | 490.962i | −0.751855 | + | 0.751855i | −0.974825 | − | 0.222970i | \(-0.928425\pi\) |
0.222970 | + | 0.974825i | \(0.428425\pi\) | |||||||
\(654\) | − | 226.867i | − | 0.346892i | ||||||
\(655\) | 41.4357 | + | 45.0681i | 0.0632605 | + | 0.0688063i | ||||
\(656\) | −1.36757 | −0.00208470 | ||||||||
\(657\) | 84.4042 | + | 84.4042i | 0.128469 | + | 0.128469i | ||||
\(658\) | 21.8574 | − | 21.8574i | 0.0332179 | − | 0.0332179i | ||||
\(659\) | − | 629.616i | − | 0.955411i | −0.878520 | − | 0.477705i | \(-0.841469\pi\) | ||
0.878520 | − | 0.477705i | \(-0.158531\pi\) | |||||||
\(660\) | 5.86608 | − | 139.695i | 0.00888801 | − | 0.211659i | ||||
\(661\) | −1084.09 | −1.64008 | −0.820041 | − | 0.572304i | \(-0.806050\pi\) | ||||
−0.820041 | + | 0.572304i | \(0.806050\pi\) | |||||||
\(662\) | 269.054 | + | 269.054i | 0.406426 | + | 0.406426i | ||||
\(663\) | −411.761 | + | 411.761i | −0.621058 | + | 0.621058i | ||||
\(664\) | 245.342i | 0.369491i | ||||||||
\(665\) | 150.837 | + | 6.33395i | 0.226823 | + | 0.00952474i | ||||
\(666\) | −126.788 | −0.190372 | ||||||||
\(667\) | −32.8258 | − | 32.8258i | −0.0492142 | − | 0.0492142i | ||||
\(668\) | 378.932 | − | 378.932i | 0.567264 | − | 0.567264i | ||||
\(669\) | − | 6.55878i | − | 0.00980386i | ||||||
\(670\) | −637.437 | + | 586.060i | −0.951398 | + | 0.874716i | ||||
\(671\) | −88.8982 | −0.132486 | ||||||||
\(672\) | 9.38421 | + | 9.38421i | 0.0139646 | + | 0.0139646i | ||||
\(673\) | 646.098 | − | 646.098i | 0.960026 | − | 0.960026i | −0.0392051 | − | 0.999231i | \(-0.512483\pi\) |
0.999231 | + | 0.0392051i | \(0.0124826\pi\) | |||||||
\(674\) | − | 188.773i | − | 0.280078i | ||||||
\(675\) | 99.2333 | − | 83.8316i | 0.147012 | − | 0.124195i | ||||
\(676\) | 744.792 | 1.10176 | ||||||||
\(677\) | −77.7169 | − | 77.7169i | −0.114796 | − | 0.114796i | 0.647375 | − | 0.762171i | \(-0.275867\pi\) |
−0.762171 | + | 0.647375i | \(0.775867\pi\) | |||||||
\(678\) | −151.006 | + | 151.006i | −0.222723 | + | 0.222723i | ||||
\(679\) | 194.388i | 0.286286i | ||||||||
\(680\) | −138.302 | − | 150.426i | −0.203386 | − | 0.221215i | ||||
\(681\) | 355.549 | 0.522098 | ||||||||
\(682\) | −453.772 | − | 453.772i | −0.665355 | − | 0.665355i | ||||
\(683\) | −458.185 | + | 458.185i | −0.670841 | + | 0.670841i | −0.957910 | − | 0.287069i | \(-0.907319\pi\) |
0.287069 | + | 0.957910i | \(0.407319\pi\) | |||||||
\(684\) | 133.750i | 0.195541i | ||||||||
\(685\) | −16.9301 | + | 403.174i | −0.0247155 | + | 0.588575i | ||||
\(686\) | −184.209 | −0.268526 | ||||||||
\(687\) | −72.7719 | − | 72.7719i | −0.105927 | − | 0.105927i | ||||
\(688\) | −42.8467 | + | 42.8467i | −0.0622772 | + | 0.0622772i | ||||
\(689\) | 52.6072i | 0.0763530i | ||||||||
\(690\) | −58.6850 | − | 2.46430i | −0.0850507 | − | 0.00357145i | ||||
\(691\) | 564.193 | 0.816487 | 0.408244 | − | 0.912873i | \(-0.366141\pi\) | ||||
0.408244 | + | 0.912873i | \(0.366141\pi\) | |||||||
\(692\) | −72.1389 | − | 72.1389i | −0.104247 | − | 0.104247i | ||||
\(693\) | 23.1946 | − | 23.1946i | 0.0334698 | − | 0.0334698i | ||||
\(694\) | 301.940i | 0.435072i | ||||||||
\(695\) | 952.587 | − | 875.809i | 1.37063 | − | 1.26016i | ||||
\(696\) | −47.4212 | −0.0681339 | ||||||||
\(697\) | 3.49314 | + | 3.49314i | 0.00501167 | + | 0.00501167i | ||||
\(698\) | 417.741 | − | 417.741i | 0.598483 | − | 0.598483i | ||||
\(699\) | 580.448i | 0.830397i | ||||||||
\(700\) | 43.7052 | + | 51.7348i | 0.0624360 | + | 0.0739069i | ||||
\(701\) | −607.326 | −0.866371 | −0.433185 | − | 0.901305i | \(-0.642610\pi\) | ||||
−0.433185 | + | 0.901305i | \(0.642610\pi\) | |||||||
\(702\) | 120.904 | + | 120.904i | 0.172227 | + | 0.172227i | ||||
\(703\) | 471.053 | − | 471.053i | 0.670061 | − | 0.670061i | ||||
\(704\) | 64.5793i | 0.0917320i | ||||||||
\(705\) | 94.5852 | + | 102.877i | 0.134163 | + | 0.145925i | ||||
\(706\) | −735.088 | −1.04120 | ||||||||
\(707\) | −189.172 | − | 189.172i | −0.267569 | − | 0.267569i | ||||
\(708\) | 25.5017 | − | 25.5017i | 0.0360193 | − | 0.0360193i | ||||
\(709\) | 1335.32i | 1.88338i | 0.336482 | + | 0.941690i | \(0.390763\pi\) | ||||
−0.336482 | + | 0.941690i | \(0.609237\pi\) | |||||||
\(710\) | 37.7102 | − | 898.033i | 0.0531130 | − | 1.26484i | ||||
\(711\) | 218.346 | 0.307096 | ||||||||
\(712\) | −117.034 | − | 117.034i | −0.164374 | − | 0.164374i | ||||
\(713\) | −190.626 | + | 190.626i | −0.267358 | + | 0.267358i | ||||
\(714\) | − | 47.9397i | − | 0.0671424i | ||||||
\(715\) | 938.315 | + | 39.4017i | 1.31233 | + | 0.0551073i | ||||
\(716\) | −506.701 | −0.707682 | ||||||||
\(717\) | 316.254 | + | 316.254i | 0.441080 | + | 0.441080i | ||||
\(718\) | 392.377 | − | 392.377i | 0.546486 | − | 0.546486i | ||||
\(719\) | 669.180i | 0.930709i | 0.885124 | + | 0.465354i | \(0.154073\pi\) | ||||
−0.885124 | + | 0.465354i | \(0.845927\pi\) | |||||||
\(720\) | −44.1691 | + | 40.6090i | −0.0613459 | + | 0.0564015i | ||||
\(721\) | −155.025 | −0.215014 | ||||||||
\(722\) | −135.921 | − | 135.921i | −0.188256 | − | 0.188256i | ||||
\(723\) | 465.845 | − | 465.845i | 0.644322 | − | 0.644322i | ||||
\(724\) | 135.712i | 0.187447i | ||||||||
\(725\) | −241.143 | − | 20.2880i | −0.332612 | − | 0.0279834i | ||||
\(726\) | −136.770 | −0.188388 | ||||||||
\(727\) | −129.796 | − | 129.796i | −0.178536 | − | 0.178536i | 0.612181 | − | 0.790717i | \(-0.290292\pi\) |
−0.790717 | + | 0.612181i | \(0.790292\pi\) | |||||||
\(728\) | −63.0325 | + | 63.0325i | −0.0865831 | + | 0.0865831i | ||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | −190.421 | − | 207.114i | −0.260850 | − | 0.283718i | ||||
\(731\) | 218.884 | 0.299432 | ||||||||
\(732\) | 26.9752 | + | 26.9752i | 0.0368514 | + | 0.0368514i | ||||
\(733\) | −381.755 | + | 381.755i | −0.520811 | + | 0.520811i | −0.917816 | − | 0.397005i | \(-0.870050\pi\) |
0.397005 | + | 0.917816i | \(0.370050\pi\) | |||||||
\(734\) | − | 801.713i | − | 1.09225i | ||||||
\(735\) | 17.1371 | − | 408.104i | 0.0233158 | − | 0.555244i | ||||
\(736\) | 27.1293 | 0.0368605 | ||||||||
\(737\) | −698.995 | − | 698.995i | −0.948432 | − | 0.948432i | ||||
\(738\) | 1.02567 | − | 1.02567i | 0.00138980 | − | 0.00138980i | ||||
\(739\) | − | 1025.05i | − | 1.38707i | −0.720422 | − | 0.693536i | \(-0.756052\pi\) | ||
0.720422 | − | 0.693536i | \(-0.243948\pi\) | |||||||
\(740\) | 298.578 | + | 12.5379i | 0.403484 | + | 0.0169431i | ||||
\(741\) | −898.384 | −1.21239 | ||||||||
\(742\) | −3.06242 | − | 3.06242i | −0.00412725 | − | 0.00412725i | ||||
\(743\) | −260.972 | + | 260.972i | −0.351241 | + | 0.351241i | −0.860571 | − | 0.509330i | \(-0.829893\pi\) |
0.509330 | + | 0.860571i | \(0.329893\pi\) | |||||||
\(744\) | 275.385i | 0.370141i | ||||||||
\(745\) | 698.784 | − | 642.462i | 0.937965 | − | 0.862365i | ||||
\(746\) | −478.612 | −0.641572 | ||||||||
\(747\) | −184.006 | − | 184.006i | −0.246327 | − | 0.246327i | ||||
\(748\) | 164.953 | − | 164.953i | 0.220526 | − | 0.220526i | ||||
\(749\) | − | 134.883i | − | 0.180084i | ||||||
\(750\) | −241.979 | + | 187.606i | −0.322639 | + | 0.250141i | ||||
\(751\) | 972.680 | 1.29518 | 0.647590 | − | 0.761989i | \(-0.275777\pi\) | ||||
0.647590 | + | 0.761989i | \(0.275777\pi\) | |||||||
\(752\) | −45.6422 | − | 45.6422i | −0.0606944 | − | 0.0606944i | ||||
\(753\) | 141.060 | − | 141.060i | 0.187331 | − | 0.187331i | ||||
\(754\) | − | 318.522i | − | 0.422443i | ||||||
\(755\) | 295.669 | + | 321.589i | 0.391615 | + | 0.425946i | ||||
\(756\) | −14.0763 | −0.0186195 | ||||||||
\(757\) | −697.433 | − | 697.433i | −0.921312 | − | 0.921312i | 0.0758101 | − | 0.997122i | \(-0.475846\pi\) |
−0.997122 | + | 0.0758101i | \(0.975846\pi\) | |||||||
\(758\) | 164.467 | − | 164.467i | 0.216975 | − | 0.216975i | ||||
\(759\) | − | 67.0545i | − | 0.0883459i | ||||||
\(760\) | 13.2264 | − | 314.975i | 0.0174032 | − | 0.414441i | ||||
\(761\) | −545.853 | −0.717284 | −0.358642 | − | 0.933475i | \(-0.616760\pi\) | ||||
−0.358642 | + | 0.933475i | \(0.616760\pi\) | |||||||
\(762\) | 192.568 | + | 192.568i | 0.252714 | + | 0.252714i | ||||
\(763\) | −88.7071 | + | 88.7071i | −0.116261 | + | 0.116261i | ||||
\(764\) | − | 59.4572i | − | 0.0778235i | ||||||
\(765\) | 216.547 | + | 9.09322i | 0.283067 | + | 0.0118866i | ||||
\(766\) | −195.204 | −0.254835 | ||||||||
\(767\) | 171.291 | + | 171.291i | 0.223326 | + | 0.223326i | ||||
\(768\) | 19.5959 | − | 19.5959i | 0.0255155 | − | 0.0255155i | ||||
\(769\) | − | 113.856i | − | 0.148057i | −0.997256 | − | 0.0740286i | \(-0.976414\pi\) | ||
0.997256 | − | 0.0740286i | \(-0.0235856\pi\) | |||||||
\(770\) | −56.9158 | + | 52.3284i | −0.0739166 | + | 0.0679589i | ||||
\(771\) | 649.241 | 0.842077 | ||||||||
\(772\) | 198.482 | + | 198.482i | 0.257101 | + | 0.257101i | ||||
\(773\) | 155.336 | − | 155.336i | 0.200952 | − | 0.200952i | −0.599456 | − | 0.800408i | \(-0.704616\pi\) |
0.800408 | + | 0.599456i | \(0.204616\pi\) | |||||||
\(774\) | − | 64.2701i | − | 0.0830362i | ||||||
\(775\) | −117.816 | + | 1400.37i | −0.152021 | + | 1.80693i | ||||
\(776\) | 405.917 | 0.523089 | ||||||||
\(777\) | 49.5751 | + | 49.5751i | 0.0638032 | + | 0.0638032i | ||||
\(778\) | 591.161 | − | 591.161i | 0.759847 | − | 0.759847i | ||||
\(779\) | 7.62135i | 0.00978350i | ||||||||
\(780\) | −272.766 | − | 296.678i | −0.349700 | − | 0.380356i | ||||
\(781\) | 1026.11 | 1.31384 | ||||||||
\(782\) | −69.2957 | − | 69.2957i | −0.0886135 | − | 0.0886135i | ||||
\(783\) | 35.5659 | − | 35.5659i | 0.0454226 | − | 0.0454226i | ||||
\(784\) | 188.661i | 0.240640i | ||||||||
\(785\) | 41.8840 | − | 997.427i | 0.0533554 | − | 1.27061i | ||||
\(786\) | 29.9922 | 0.0381580 | ||||||||
\(787\) | 560.463 | + | 560.463i | 0.712151 | + | 0.712151i | 0.966985 | − | 0.254834i | \(-0.0820208\pi\) |
−0.254834 | + | 0.966985i | \(0.582021\pi\) | |||||||
\(788\) | −160.053 | + | 160.053i | −0.203113 | + | 0.203113i | ||||
\(789\) | − | 29.0851i | − | 0.0368633i | ||||||
\(790\) | −514.192 | − | 21.5920i | −0.650876 | − | 0.0273316i | ||||
\(791\) | 118.089 | 0.149291 | ||||||||
\(792\) | −48.4345 | − | 48.4345i | −0.0611547 | − | 0.0611547i | ||||
\(793\) | −181.189 | + | 181.189i | −0.228485 | + | 0.228485i | ||||
\(794\) | − | 5.49399i | − | 0.00691938i | ||||||
\(795\) | 14.4140 | − | 13.2523i | 0.0181308 | − | 0.0166695i | ||||
\(796\) | 524.619 | 0.659070 | ||||||||
\(797\) | −651.216 | − | 651.216i | −0.817083 | − | 0.817083i | 0.168601 | − | 0.985684i | \(-0.446075\pi\) |
−0.985684 | + | 0.168601i | \(0.946075\pi\) | |||||||
\(798\) | 52.2976 | − | 52.2976i | 0.0655358 | − | 0.0655358i | ||||
\(799\) | 233.165i | 0.291821i | ||||||||
\(800\) | 108.032 | − | 91.2643i | 0.135039 | − | 0.114080i | ||||
\(801\) | 175.551 | 0.219165 | ||||||||
\(802\) | 259.213 | + | 259.213i | 0.323208 | + | 0.323208i | ||||
\(803\) | 227.115 | − | 227.115i | 0.282833 | − | 0.282833i | ||||
\(804\) | 424.205i | 0.527618i | ||||||||
\(805\) | 21.9828 | + | 23.9099i | 0.0273078 | + | 0.0297017i | ||||
\(806\) | −1849.72 | −2.29494 | ||||||||
\(807\) | 208.992 | + | 208.992i | 0.258974 | + | 0.258974i | ||||
\(808\) | −395.024 | + | 395.024i | −0.488891 | + | 0.488891i | ||||
\(809\) | 181.401i | 0.224229i | 0.993695 | + | 0.112115i | \(0.0357624\pi\) | ||||
−0.993695 | + | 0.112115i | \(0.964238\pi\) | |||||||
\(810\) | 2.67000 | − | 63.5836i | 0.00329630 | − | 0.0784982i | ||||
\(811\) | 1562.39 | 1.92650 | 0.963250 | − | 0.268605i | \(-0.0865628\pi\) | ||||
0.963250 | + | 0.268605i | \(0.0865628\pi\) | |||||||
\(812\) | 18.5421 | + | 18.5421i | 0.0228351 | + | 0.0228351i | ||||
\(813\) | 117.359 | − | 117.359i | 0.144353 | − | 0.144353i | ||||
\(814\) | 341.161i | 0.419117i | ||||||||
\(815\) | −29.1008 | − | 1.22200i | −0.0357066 | − | 0.00149939i | ||||
\(816\) | −100.107 | −0.122680 | ||||||||
\(817\) | 238.782 | + | 238.782i | 0.292266 | + | 0.292266i | ||||
\(818\) | −67.6142 | + | 67.6142i | −0.0826579 | + | 0.0826579i | ||||
\(819\) | − | 94.5488i | − | 0.115444i | ||||||
\(820\) | −2.51684 | + | 2.31398i | −0.00306931 | + | 0.00282193i | ||||
\(821\) | 328.382 | 0.399978 | 0.199989 | − | 0.979798i | \(-0.435909\pi\) | ||||
0.199989 | + | 0.979798i | \(0.435909\pi\) | |||||||
\(822\) | 139.787 | + | 139.787i | 0.170057 | + | 0.170057i | ||||
\(823\) | −198.052 | + | 198.052i | −0.240647 | + | 0.240647i | −0.817118 | − | 0.576471i | \(-0.804429\pi\) |
0.576471 | + | 0.817118i | \(0.304429\pi\) | |||||||
\(824\) | 323.720i | 0.392864i | ||||||||
\(825\) | −225.575 | − | 267.018i | −0.273424 | − | 0.323658i | ||||
\(826\) | −19.9427 | −0.0241438 | ||||||||
\(827\) | −1101.91 | − | 1101.91i | −1.33242 | − | 1.33242i | −0.903200 | − | 0.429221i | \(-0.858788\pi\) |
−0.429221 | − | 0.903200i | \(-0.641212\pi\) | |||||||
\(828\) | −20.3470 | + | 20.3470i | −0.0245737 | + | 0.0245737i | ||||
\(829\) | − | 1093.54i | − | 1.31911i | −0.751658 | − | 0.659554i | \(-0.770745\pi\) | ||
0.751658 | − | 0.659554i | \(-0.229255\pi\) | |||||||
\(830\) | 415.129 | + | 451.522i | 0.500156 | + | 0.544002i | ||||
\(831\) | 240.787 | 0.289756 | ||||||||
\(832\) | 131.623 | + | 131.623i | 0.158201 | + | 0.158201i | ||||
\(833\) | 481.893 | − | 481.893i | 0.578503 | − | 0.578503i | ||||
\(834\) | − | 633.933i | − | 0.760112i | ||||||
\(835\) | 56.2083 | − | 1338.55i | 0.0673154 | − | 1.60305i | ||||
\(836\) | 359.896 | 0.430498 | ||||||||
\(837\) | −206.538 | − | 206.538i | −0.246760 | − | 0.246760i | ||||
\(838\) | −659.542 | + | 659.542i | −0.787042 | + | 0.787042i | ||||
\(839\) | − | 1236.77i | − | 1.47409i | −0.675841 | − | 0.737047i | \(-0.736220\pi\) | ||
0.675841 | − | 0.737047i | \(-0.263780\pi\) | |||||||
\(840\) | 33.1490 | + | 1.39199i | 0.0394631 | + | 0.00165713i | ||||
\(841\) | 747.301 | 0.888586 | ||||||||
\(842\) | 162.043 | + | 162.043i | 0.192450 | + | 0.192450i | ||||
\(843\) | 190.810 | − | 190.810i | 0.226346 | − | 0.226346i | ||||
\(844\) | 539.402i | 0.639102i | ||||||||
\(845\) | 1370.70 | − | 1260.22i | 1.62213 | − | 1.49139i | ||||
\(846\) | 68.4632 | 0.0809258 | ||||||||
\(847\) | 53.4783 | + | 53.4783i | 0.0631384 | + | 0.0631384i | ||||
\(848\) | −6.39488 | + | 6.39488i | −0.00754114 | + | 0.00754114i | ||||
\(849\) | − | 346.421i | − | 0.408034i | ||||||
\(850\) | −509.056 | − | 42.8281i | −0.598890 | − | 0.0503860i | ||||
\(851\) | 143.319 | 0.168413 | ||||||||
\(852\) | −311.362 | − | 311.362i | −0.365448 | − | 0.365448i | ||||
\(853\) | −235.999 | + | 235.999i | −0.276670 | + | 0.276670i | −0.831778 | − | 0.555108i | \(-0.812677\pi\) |
0.555108 | + | 0.831778i | \(0.312677\pi\) | |||||||
\(854\) | − | 21.0951i | − | 0.0247015i | ||||||
\(855\) | 226.311 | + | 246.151i | 0.264692 | + | 0.287896i | ||||
\(856\) | −281.659 | −0.329041 | ||||||||
\(857\) | 529.971 | + | 529.971i | 0.618402 | + | 0.618402i | 0.945121 | − | 0.326719i | \(-0.105943\pi\) |
−0.326719 | + | 0.945121i | \(0.605943\pi\) | |||||||
\(858\) | 325.328 | − | 325.328i | 0.379170 | − | 0.379170i | ||||
\(859\) | 654.648i | 0.762105i | 0.924553 | + | 0.381053i | \(0.124438\pi\) | ||||
−0.924553 | + | 0.381053i | \(0.875562\pi\) | |||||||
\(860\) | −6.35560 | + | 151.353i | −0.00739023 | + | 0.175991i | ||||
\(861\) | −0.802095 | −0.000931586 | ||||||||
\(862\) | −536.271 | − | 536.271i | −0.622124 | − | 0.622124i | ||||
\(863\) | −375.301 | + | 375.301i | −0.434879 | + | 0.434879i | −0.890284 | − | 0.455405i | \(-0.849494\pi\) |
0.455405 | + | 0.890284i | \(0.349494\pi\) | |||||||
\(864\) | 29.3939i | 0.0340207i | ||||||||
\(865\) | −254.825 | − | 10.7006i | −0.294595 | − | 0.0123707i | ||||
\(866\) | 371.063 | 0.428479 | ||||||||
\(867\) | −98.2513 | − | 98.2513i | −0.113323 | − | 0.113323i | ||||
\(868\) | 107.678 | − | 107.678i | 0.124053 | − | 0.124053i | ||||
\(869\) | − | 587.525i | − | 0.676094i | ||||||
\(870\) | −87.2729 | + | 80.2388i | −0.100314 | + | 0.0922285i | ||||
\(871\) | −2849.33 | −3.27133 | ||||||||
\(872\) | 185.236 | + | 185.236i | 0.212427 | + | 0.212427i | ||||
\(873\) | −304.438 | + | 304.438i | −0.348726 | + | 0.348726i | ||||
\(874\) | − | 151.190i | − | 0.172986i | ||||||
\(875\) | 167.972 | + | 21.2604i | 0.191968 | + | 0.0242976i | ||||
\(876\) | −137.831 | −0.157342 | ||||||||
\(877\) | −728.781 | − | 728.781i | −0.830993 | − | 0.830993i | 0.156660 | − | 0.987653i | \(-0.449927\pi\) |
−0.987653 | + | 0.156660i | \(0.949927\pi\) | |||||||
\(878\) | −568.595 | + | 568.595i | −0.647603 | + | 0.647603i | ||||
\(879\) | − | 446.616i | − | 0.508095i | ||||||
\(880\) | 109.271 | + | 118.850i | 0.124172 | + | 0.135057i | ||||
\(881\) | −269.607 | −0.306024 | −0.153012 | − | 0.988224i | \(-0.548897\pi\) | ||||
−0.153012 | + | 0.988224i | \(0.548897\pi\) | |||||||
\(882\) | −141.496 | − | 141.496i | −0.160426 | − | 0.160426i | ||||
\(883\) | −133.635 | + | 133.635i | −0.151343 | + | 0.151343i | −0.778717 | − | 0.627375i | \(-0.784129\pi\) |
0.627375 | + | 0.778717i | \(0.284129\pi\) | |||||||
\(884\) | − | 672.404i | − | 0.760638i | ||||||
\(885\) | 3.78275 | − | 90.0826i | 0.00427429 | − | 0.101788i | ||||
\(886\) | −1087.57 | −1.22750 | ||||||||
\(887\) | −991.486 | − | 991.486i | −1.11780 | − | 1.11780i | −0.992064 | − | 0.125733i | \(-0.959872\pi\) |
−0.125733 | − | 0.992064i | \(-0.540128\pi\) | |||||||
\(888\) | 103.522 | − | 103.522i | 0.116578 | − | 0.116578i | ||||
\(889\) | − | 150.591i | − | 0.169394i | ||||||
\(890\) | −413.414 | − | 17.3601i | −0.464510 | − | 0.0195057i | ||||
\(891\) | 72.6517 | 0.0815396 | ||||||||
\(892\) | 5.35522 | + | 5.35522i | 0.00600361 | + | 0.00600361i | ||||
\(893\) | −254.361 | + | 254.361i | −0.284838 | + | 0.284838i | ||||
\(894\) | − | 465.031i | − | 0.520168i | ||||||
\(895\) | −932.520 | + | 857.360i | −1.04192 | + | 0.957944i | ||||
\(896\) | −15.3244 | −0.0171031 | ||||||||
\(897\) | −136.668 | − | 136.668i | −0.152361 | − | 0.152361i | ||||
\(898\) | 357.234 | − | 357.234i | 0.397811 | − | 0.397811i | ||||
\(899\) | 544.128i | 0.605259i | ||||||||
\(900\) | −12.5754 | + | 149.472i | −0.0139727 | + | 0.166080i | ||||
\(901\) | 32.6686 | 0.0362581 | ||||||||
\(902\) | −2.75989 | − | 2.75989i | −0.00305974 | − | 0.00305974i | ||||
\(903\) | −25.1302 | + | 25.1302i | −0.0278296 | + | 0.0278296i | ||||
\(904\) | − | 246.592i | − | 0.272779i | ||||||
\(905\) | 229.630 | + | 249.761i | 0.253735 | + | 0.275979i | ||||
\(906\) | 214.013 | 0.236217 | ||||||||
\(907\) | 354.932 | + | 354.932i | 0.391325 | + | 0.391325i | 0.875159 | − | 0.483835i | \(-0.160756\pi\) |
−0.483835 | + | 0.875159i | \(0.660756\pi\) | |||||||
\(908\) | −290.304 | + | 290.304i | −0.319719 | + | 0.319719i | ||||
\(909\) | − | 592.536i | − | 0.651855i | ||||||
\(910\) | −9.34983 | + | 222.657i | −0.0102745 | + | 0.244678i | ||||
\(911\) | 723.733 | 0.794438 | 0.397219 | − | 0.917724i | \(-0.369975\pi\) | ||||
0.397219 | + | 0.917724i | \(0.369975\pi\) | |||||||
\(912\) | −109.207 | − | 109.207i | −0.119744 | − | 0.119744i | ||||
\(913\) | −495.126 | + | 495.126i | −0.542306 | + | 0.542306i | ||||
\(914\) | − | 20.9220i | − | 0.0228906i | ||||||
\(915\) | 95.2878 | + | 4.00133i | 0.104140 | + | 0.00437303i | ||||
\(916\) | 118.836 | 0.129734 | ||||||||
\(917\) | −11.7272 | − | 11.7272i | −0.0127887 | − | 0.0127887i | ||||
\(918\) | 75.0800 | − | 75.0800i | 0.0817865 | − | 0.0817865i | ||||
\(919\) | − | 890.603i | − | 0.969100i | −0.874764 | − | 0.484550i | \(-0.838983\pi\) | ||
0.874764 | − | 0.484550i | \(-0.161017\pi\) | |||||||
\(920\) | 49.9282 | − | 45.9040i | 0.0542698 | − | 0.0498956i | ||||
\(921\) | 884.013 | 0.959840 | ||||||||
\(922\) | 12.5540 | + | 12.5540i | 0.0136160 | + | 0.0136160i | ||||
\(923\) | 2091.38 | − | 2091.38i | 2.26585 | − | 2.26585i | ||||
\(924\) | 37.8766i | 0.0409920i | ||||||||
\(925\) | 570.711 | − | 482.133i | 0.616985 | − | 0.521225i | ||||
\(926\) | −491.314 | −0.530577 | ||||||||
\(927\) | −242.790 | − | 242.790i | −0.261910 | − | 0.261910i | ||||
\(928\) | 38.7193 | − | 38.7193i | 0.0417233 | − | 0.0417233i | ||||
\(929\) | 1160.33i | 1.24901i | 0.781023 | + | 0.624503i | \(0.214698\pi\) | ||||
−0.781023 | + | 0.624503i | \(0.785302\pi\) | |||||||
\(930\) | 465.963 | + | 506.812i | 0.501035 | + | 0.544959i | ||||
\(931\) | 1051.40 | 1.12932 | ||||||||
\(932\) | −473.934 | − | 473.934i | −0.508512 | − | 0.508512i | ||||
\(933\) | 210.149 | − | 210.149i | 0.225240 | − | 0.225240i | ||||
\(934\) | − | 251.719i | − | 0.269507i | ||||||
\(935\) | 24.4681 | − | 582.685i | 0.0261691 | − | 0.623192i | ||||
\(936\) | −197.435 | −0.210935 | ||||||||
\(937\) | −822.908 | − | 822.908i | −0.878237 | − | 0.878237i | 0.115115 | − | 0.993352i | \(-0.463276\pi\) |
−0.993352 | + | 0.115115i | \(0.963276\pi\) | |||||||
\(938\) | 165.868 | − | 165.868i | 0.176831 | − | 0.176831i | ||||
\(939\) | 1019.34i | 1.08555i | ||||||||
\(940\) | −161.227 | − | 6.77026i | −0.171518 | − | 0.00720240i | ||||
\(941\) | −149.470 | −0.158842 | −0.0794209 | − | 0.996841i | \(-0.525307\pi\) | ||||
−0.0794209 | + | 0.996841i | \(0.525307\pi\) | |||||||
\(942\) | −345.823 | − | 345.823i | −0.367116 | − | 0.367116i | ||||
\(943\) | −1.15941 | + | 1.15941i | −0.00122949 | + | 0.00122949i | ||||
\(944\) | 41.6440i | 0.0441144i | ||||||||
\(945\) | −25.9057 | + | 23.8177i | −0.0274135 | + | 0.0252040i | ||||
\(946\) | −172.938 | −0.182810 | ||||||||
\(947\) | 658.096 | + | 658.096i | 0.694927 | + | 0.694927i | 0.963312 | − | 0.268385i | \(-0.0864899\pi\) |
−0.268385 | + | 0.963312i | \(0.586490\pi\) | |||||||
\(948\) | −178.278 | + | 178.278i | −0.188057 | + | 0.188057i | ||||
\(949\) | − | 925.796i | − | 0.975549i | ||||||
\(950\) | −508.610 | − | 602.052i | −0.535379 | − | 0.633739i | ||||
\(951\) | 549.466 | 0.577777 | ||||||||
\(952\) | 39.1426 | + | 39.1426i | 0.0411162 | + | 0.0411162i | ||||
\(953\) | 446.146 | − | 446.146i | 0.468149 | − | 0.468149i | −0.433166 | − | 0.901314i | \(-0.642603\pi\) |
0.901314 | + | 0.433166i | \(0.142603\pi\) | |||||||
\(954\) | − | 9.59232i | − | 0.0100548i | ||||||
\(955\) | −100.604 | − | 109.424i | −0.105345 | − | 0.114580i | ||||
\(956\) | −516.441 | −0.540210 | ||||||||
\(957\) | −95.7009 | − | 95.7009i | −0.100001 | − | 0.100001i | ||||
\(958\) | −268.187 | + | 268.187i | −0.279945 | + | 0.279945i | ||||
\(959\) | − | 109.316i | − | 0.113989i | ||||||
\(960\) | 2.90673 | − | 69.2210i | 0.00302784 | − | 0.0721052i | ||||
\(961\) | 2198.86 | 2.28810 | ||||||||
\(962\) | 695.342 | + | 695.342i | 0.722808 | + | 0.722808i | ||||
\(963\) | 211.244 | − | 211.244i | 0.219361 | − | 0.219361i | ||||
\(964\) | 760.722i | 0.789130i | ||||||||
\(965\) | 701.121 | + | 29.4415i | 0.726550 | + | 0.0305093i | ||||
\(966\) | 15.9117 | 0.0164717 | ||||||||
\(967\) | 525.716 | + | 525.716i | 0.543657 | + | 0.543657i | 0.924599 | − | 0.380942i | \(-0.124400\pi\) |
−0.380942 | + | 0.924599i | \(0.624400\pi\) | |||||||
\(968\) | 111.672 | − | 111.672i | 0.115364 | − | 0.115364i | ||||
\(969\) | 557.888i | 0.575735i | ||||||||
\(970\) | 747.040 | − | 686.829i | 0.770144 | − | 0.708071i | ||||
\(971\) | 5.25830 | 0.00541535 | 0.00270767 | − | 0.999996i | \(-0.499138\pi\) | ||||
0.00270767 | + | 0.999996i | \(0.499138\pi\) | |||||||
\(972\) | −22.0454 | − | 22.0454i | −0.0226805 | − | 0.0226805i | ||||
\(973\) | −247.874 | + | 247.874i | −0.254752 | + | 0.254752i | ||||
\(974\) | 978.770i | 1.00490i | ||||||||
\(975\) | −1003.98 | − | 84.4675i | −1.02973 | − | 0.0866333i | ||||
\(976\) | −44.0503 | −0.0451335 | ||||||||
\(977\) | 787.336 | + | 787.336i | 0.805871 | + | 0.805871i | 0.984006 | − | 0.178135i | \(-0.0570063\pi\) |
−0.178135 | + | 0.984006i | \(0.557006\pi\) | |||||||
\(978\) | −10.0897 | + | 10.0897i | −0.0103167 | + | 0.0103167i | ||||
\(979\) | − | 472.374i | − | 0.482507i | ||||||
\(980\) | 319.223 | + | 347.208i | 0.325738 | + | 0.354294i | ||||
\(981\) | −277.855 | −0.283236 | ||||||||
\(982\) | 467.500 | + | 467.500i | 0.476069 | + | 0.476069i | ||||
\(983\) | 488.883 | − | 488.883i | 0.497337 | − | 0.497337i | −0.413271 | − | 0.910608i | \(-0.635614\pi\) |
0.910608 | + | 0.413271i | \(0.135614\pi\) | |||||||
\(984\) | 1.67492i | 0.00170215i | ||||||||
\(985\) | −23.7413 | + | 565.376i | −0.0241028 | + | 0.573985i | ||||
\(986\) | −197.799 | −0.200608 | ||||||||
\(987\) | −26.7697 | − | 26.7697i | −0.0271223 | − | 0.0271223i | ||||
\(988\) | 733.527 | − | 733.527i | 0.742436 | − | 0.742436i | ||||
\(989\) | 72.6501i | 0.0734582i | ||||||||
\(990\) | −171.091 | − | 7.18446i | −0.172819 | − | 0.00725703i | ||||
\(991\) | −800.982 | −0.808257 | −0.404128 | − | 0.914702i | \(-0.632425\pi\) | ||||
−0.404128 | + | 0.914702i | \(0.632425\pi\) | |||||||
\(992\) | −224.851 | − | 224.851i | −0.226664 | − | 0.226664i | ||||
\(993\) | 329.523 | − | 329.523i | 0.331846 | − | 0.331846i | ||||
\(994\) | 243.491i | 0.244960i | ||||||||
\(995\) | 965.498 | − | 887.679i | 0.970349 | − | 0.892140i | ||||
\(996\) | 300.481 | 0.301688 | ||||||||
\(997\) | 857.497 | + | 857.497i | 0.860077 | + | 0.860077i | 0.991347 | − | 0.131270i | \(-0.0419054\pi\) |
−0.131270 | + | 0.991347i | \(0.541905\pi\) | |||||||
\(998\) | 344.871 | − | 344.871i | 0.345562 | − | 0.345562i | ||||
\(999\) | 155.283i | 0.155438i |
(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.a.277.17 | ✓ | 40 | |
5.3 | odd | 4 | inner | 690.3.k.a.553.17 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.k.a.277.17 | ✓ | 40 | 1.1 | even | 1 | trivial | |
690.3.k.a.553.17 | yes | 40 | 5.3 | odd | 4 | inner |