Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(223,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.223");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.p (of order \(2\), degree \(1\), 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: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 223.5 | ||
Character | \(\chi\) | \(=\) | 1344.223 |
Dual form | 1344.4.p.d.223.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 3.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 12.8225 | 1.14688 | 0.573440 | − | 0.819247i | \(-0.305608\pi\) | ||||
0.573440 | + | 0.819247i | \(0.305608\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.32908 | + | 17.4053i | −0.341738 | + | 0.939795i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 25.0429 | 0.686429 | 0.343214 | − | 0.939257i | \(-0.388484\pi\) | ||||
0.343214 | + | 0.939257i | \(0.388484\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −64.1604 | −1.36884 | −0.684419 | − | 0.729089i | \(-0.739944\pi\) | ||||
−0.684419 | + | 0.729089i | \(0.739944\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 38.4675i | − | 0.662152i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 77.4251i | 1.10461i | 0.833643 | + | 0.552304i | \(0.186251\pi\) | ||||
−0.833643 | + | 0.552304i | \(0.813749\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 49.9995i | − | 0.603720i | −0.953352 | − | 0.301860i | \(-0.902393\pi\) | ||
0.953352 | − | 0.301860i | \(-0.0976075\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 52.2158 | + | 18.9872i | 0.542591 | + | 0.197303i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 80.5687i | 0.730423i | 0.930925 | + | 0.365212i | \(0.119003\pi\) | ||||
−0.930925 | + | 0.365212i | \(0.880997\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 39.4169 | 0.315335 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 159.100i | − | 1.01876i | −0.860541 | − | 0.509381i | \(-0.829874\pi\) | ||
0.860541 | − | 0.509381i | \(-0.170126\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −96.5596 | −0.559440 | −0.279720 | − | 0.960082i | \(-0.590242\pi\) | ||||
−0.279720 | + | 0.960082i | \(0.590242\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 75.1287i | − | 0.396310i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −81.1547 | + | 223.179i | −0.391933 | + | 1.07783i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 274.101i | − | 1.21789i | −0.793212 | − | 0.608946i | \(-0.791593\pi\) | ||
0.793212 | − | 0.608946i | \(-0.208407\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 192.481i | 0.790299i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 299.796i | 1.14196i | 0.820964 | + | 0.570980i | \(0.193436\pi\) | ||||
−0.820964 | + | 0.570980i | \(0.806564\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −385.824 | −1.36832 | −0.684158 | − | 0.729334i | \(-0.739830\pi\) | ||||
−0.684158 | + | 0.729334i | \(0.739830\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −115.403 | −0.382294 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −418.362 | −1.29839 | −0.649196 | − | 0.760622i | \(-0.724894\pi\) | ||||
−0.649196 | + | 0.760622i | \(0.724894\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −262.886 | − | 220.318i | −0.766430 | − | 0.642327i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 232.275 | 0.637746 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 665.385i | − | 1.72448i | −0.506497 | − | 0.862242i | \(-0.669060\pi\) | ||
0.506497 | − | 0.862242i | \(-0.330940\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 321.113 | 0.787252 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −149.999 | −0.348558 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 445.655i | 0.983380i | 0.870770 | + | 0.491690i | \(0.163621\pi\) | ||||
−0.870770 | + | 0.491690i | \(0.836379\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −599.783 | −1.25892 | −0.629461 | − | 0.777032i | \(-0.716724\pi\) | ||||
−0.629461 | + | 0.777032i | \(0.716724\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 56.9617 | − | 156.647i | 0.113913 | − | 0.313265i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −822.697 | −1.56989 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 675.504 | 1.23173 | 0.615866 | − | 0.787851i | \(-0.288806\pi\) | ||||
0.615866 | + | 0.787851i | \(0.288806\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 241.706 | 0.421710 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 877.093i | 1.46608i | 0.680185 | + | 0.733041i | \(0.261900\pi\) | ||||
−0.680185 | + | 0.733041i | \(0.738100\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 696.060i | − | 1.11600i | −0.829842 | − | 0.557998i | \(-0.811570\pi\) | ||
0.829842 | − | 0.557998i | \(-0.188430\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 118.251i | − | 0.182059i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −158.498 | + | 435.878i | −0.234579 | + | 0.645102i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1248.56i | − | 1.77815i | −0.457760 | − | 0.889076i | \(-0.651348\pi\) | ||
0.457760 | − | 0.889076i | \(-0.348652\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 238.303i | − | 0.315146i | −0.987507 | − | 0.157573i | \(-0.949633\pi\) | ||
0.987507 | − | 0.157573i | \(-0.0503670\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 992.784i | 1.26685i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −477.299 | −0.588182 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 743.503i | − | 0.885519i | −0.896640 | − | 0.442759i | \(-0.854000\pi\) | ||
0.896640 | − | 0.442759i | \(-0.146000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 406.076 | − | 1116.73i | 0.467784 | − | 1.28643i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 289.679i | 0.322993i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 641.120i | − | 0.692395i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1552.16i | − | 1.62472i | −0.583153 | − | 0.812362i | \(-0.698181\pi\) | ||
0.583153 | − | 0.812362i | \(-0.301819\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −225.386 | −0.228810 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1202.46 | −1.18464 | −0.592322 | − | 0.805701i | \(-0.701789\pi\) | ||||
−0.592322 | + | 0.805701i | \(0.701789\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −404.562 | −0.387016 | −0.193508 | − | 0.981099i | \(-0.561987\pi\) | ||||
−0.193508 | + | 0.981099i | \(0.561987\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 669.537 | + | 243.464i | 0.622287 | + | 0.226282i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1065.72 | 0.962871 | 0.481436 | − | 0.876481i | \(-0.340116\pi\) | ||||
0.481436 | + | 0.876481i | \(0.340116\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 359.515i | 0.315920i | 0.987445 | + | 0.157960i | \(0.0504918\pi\) | ||||
−0.987445 | + | 0.157960i | \(0.949508\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −822.304 | −0.703150 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 828.461 | 0.689691 | 0.344845 | − | 0.938660i | \(-0.387931\pi\) | ||||
0.344845 | + | 0.938660i | \(0.387931\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1033.09i | 0.837708i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 577.443 | 0.456279 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1347.60 | − | 490.029i | −1.03811 | − | 0.377486i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −703.854 | −0.528816 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 899.389 | 0.659310 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1097.39 | −0.785229 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 876.572i | 0.612466i | 0.951957 | + | 0.306233i | \(0.0990687\pi\) | ||||
−0.951957 | + | 0.306233i | \(0.900931\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1157.47i | 0.789998i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1083.04i | 0.722335i | 0.932501 | + | 0.361167i | \(0.117622\pi\) | ||||
−0.932501 | + | 0.361167i | \(0.882378\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 870.254 | + | 316.451i | 0.567373 | + | 0.206314i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 346.208i | 0.220717i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −751.836 | −0.468859 | −0.234430 | − | 0.972133i | \(-0.575322\pi\) | ||||
−0.234430 | + | 0.972133i | \(0.575322\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 543.555i | 0.331681i | 0.986153 | + | 0.165841i | \(0.0530337\pi\) | ||||
−0.986153 | + | 0.165841i | \(0.946966\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1255.09i | 0.749626i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1606.76 | −0.939609 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 2040.06i | − | 1.16840i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −660.955 | + | 788.657i | −0.370848 | + | 0.442499i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 1056.44i | − | 0.580855i | −0.956897 | − | 0.290427i | \(-0.906203\pi\) | ||
0.956897 | − | 0.290427i | \(-0.0937974\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2092.13i | 1.12752i | 0.825939 | + | 0.563759i | \(0.190645\pi\) | ||||
−0.825939 | + | 0.563759i | \(0.809355\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 696.826i | − | 0.368203i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1238.14 | −0.641610 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1185.70 | −0.602735 | −0.301367 | − | 0.953508i | \(-0.597443\pi\) | ||||
−0.301367 | + | 0.953508i | \(0.597443\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1996.15 | −0.995631 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1402.32 | − | 509.925i | −0.686448 | − | 0.249613i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 903.635 | 0.434222 | 0.217111 | − | 0.976147i | \(-0.430337\pi\) | ||||
0.217111 | + | 0.976147i | \(0.430337\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 963.338i | − | 0.454520i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 474.632 | 0.219929 | 0.109964 | − | 0.993936i | \(-0.464926\pi\) | ||||
0.109964 | + | 0.993936i | \(0.464926\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1919.55 | 0.873715 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 449.996i | 0.201240i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1641.33 | 0.721317 | 0.360658 | − | 0.932698i | \(-0.382552\pi\) | ||||
0.360658 | + | 0.932698i | \(0.382552\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −249.473 | + | 686.061i | −0.107762 | + | 0.296351i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1336.97 | 0.567755 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1802.11 | 0.752491 | 0.376246 | − | 0.926520i | \(-0.377215\pi\) | ||||
0.376246 | + | 0.926520i | \(0.377215\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2068.45 | −0.849429 | −0.424715 | − | 0.905327i | \(-0.639626\pi\) | ||||
−0.424715 | + | 0.905327i | \(0.639626\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1799.35i | 0.726840i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 3514.67i | − | 1.39678i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1938.95i | 0.758234i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −469.942 | − | 170.885i | −0.180864 | − | 0.0657675i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2179.61i | 0.825711i | 0.910797 | + | 0.412855i | \(0.135469\pi\) | ||||
−0.910797 | + | 0.412855i | \(0.864531\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4489.81 | −1.67453 | −0.837263 | − | 0.546801i | \(-0.815845\pi\) | ||||
−0.837263 | + | 0.546801i | \(0.815845\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2468.09i | 0.906378i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4519.08i | 1.63437i | 0.576376 | + | 0.817185i | \(0.304467\pi\) | ||||
−0.576376 | + | 0.817185i | \(0.695533\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −826.598 | −0.294452 | −0.147226 | − | 0.989103i | \(-0.547034\pi\) | ||||
−0.147226 | + | 0.989103i | \(0.547034\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 2026.51i | − | 0.711140i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2769.17 | + | 1006.95i | 0.957428 | + | 0.348150i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3844.14i | 1.30969i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 725.118i | − | 0.243474i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1252.13i | − | 0.414411i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4709.17 | −1.53646 | −0.768229 | − | 0.640175i | \(-0.778862\pi\) | ||||
−0.768229 | + | 0.640175i | \(0.778862\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2631.28 | 0.846443 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4947.23 | −1.56930 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 611.133 | − | 1680.65i | 0.191182 | − | 0.525759i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2088.18 | −0.644321 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 4967.62i | − | 1.51203i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5775.09 | −1.73421 | −0.867104 | − | 0.498127i | \(-0.834021\pi\) | ||||
−0.867104 | + | 0.498127i | \(0.834021\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −354.752 | −0.105112 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2280.11i | 0.666678i | 0.942807 | + | 0.333339i | \(0.108175\pi\) | ||||
−0.942807 | + | 0.333339i | \(0.891825\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3692.99 | −1.06567 | −0.532837 | − | 0.846218i | \(-0.678874\pi\) | ||||
−0.532837 | + | 0.846218i | \(0.678874\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1307.63 | + | 475.495i | 0.372450 | + | 0.135434i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3140.07 | 0.882887 | 0.441443 | − | 0.897289i | \(-0.354467\pi\) | ||||
0.441443 | + | 0.897289i | \(0.354467\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5364.45 | −1.48910 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3745.68 | −1.02662 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 310.784i | − | 0.0841127i | −0.999115 | − | 0.0420563i | \(-0.986609\pi\) | ||
0.999115 | − | 0.0420563i | \(-0.0133909\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 457.833i | 0.122372i | 0.998126 | + | 0.0611859i | \(0.0194883\pi\) | ||||
−0.998126 | + | 0.0611859i | \(0.980512\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 243.000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3370.85 | − | 2825.04i | −0.879004 | − | 0.736673i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3207.99i | 0.826394i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −714.909 | −0.181950 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 807.916i | − | 0.203168i | −0.994827 | − | 0.101584i | \(-0.967609\pi\) | ||
0.994827 | − | 0.101584i | \(-0.0323911\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2017.67i | 0.501383i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2978.35 | 0.731418 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1749.36i | 0.424599i | 0.977205 | + | 0.212299i | \(0.0680952\pi\) | ||||
−0.977205 | + | 0.212299i | \(0.931905\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4770.80 | + | 1734.81i | 1.14457 | + | 0.416200i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1431.90i | 0.339587i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 1360.35i | − | 0.318945i | −0.987202 | − | 0.159473i | \(-0.949021\pi\) | ||
0.987202 | − | 0.159473i | \(-0.0509793\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 8531.91i | − | 1.97778i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2230.51 | −0.511255 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2224.06 | −0.504102 | −0.252051 | − | 0.967714i | \(-0.581105\pi\) | ||||
−0.252051 | + | 0.967714i | \(0.581105\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2918.59 | 0.654212 | 0.327106 | − | 0.944988i | \(-0.393927\pi\) | ||||
0.327106 | + | 0.944988i | \(0.393927\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3350.18 | − | 1218.23i | −0.742719 | − | 0.270075i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 987.113 | 0.216455 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 1632.84i | − | 0.354180i | −0.984195 | − | 0.177090i | \(-0.943332\pi\) | ||
0.984195 | − | 0.177090i | \(-0.0566684\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 869.037 | 0.186480 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7615.42 | −1.61672 | −0.808360 | − | 0.588689i | \(-0.799644\pi\) | ||||
−0.808360 | + | 0.588689i | \(0.799644\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2867.07i | 0.602226i | 0.953589 | + | 0.301113i | \(0.0973581\pi\) | ||||
−0.953589 | + | 0.301113i | \(0.902642\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1923.36 | −0.399754 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5218.03 | − | 1897.43i | −1.07321 | − | 0.390251i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1081.64 | −0.220159 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4656.49 | −0.938035 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1133.07 | 0.225920 | 0.112960 | − | 0.993600i | \(-0.463967\pi\) | ||||
0.112960 | + | 0.993600i | \(0.463967\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5714.42i | 1.12782i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 676.158i | 0.132103i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 5169.32i | − | 0.999831i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2441.91 | − | 6715.36i | 0.467606 | − | 1.28594i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3607.37i | 0.683954i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7690.72 | −1.44383 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 206.149i | − | 0.0383242i | −0.999816 | − | 0.0191621i | \(-0.993900\pi\) | ||
0.999816 | − | 0.0191621i | \(-0.00609985\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1213.69i | 0.223444i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6296.00 | −1.14795 | −0.573977 | − | 0.818871i | \(-0.694600\pi\) | ||||
−0.573977 | + | 0.818871i | \(0.694600\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7997.75i | 1.44428i | 0.691747 | + | 0.722140i | \(0.256842\pi\) | ||||
−0.691747 | + | 0.722140i | \(0.743158\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 730.392 | − | 2008.61i | 0.130644 | − | 0.359278i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5830.42i | 1.03303i | 0.856279 | + | 0.516513i | \(0.172770\pi\) | ||||
−0.856279 | + | 0.516513i | \(0.827230\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 3984.32i | − | 0.699307i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 3197.17i | − | 0.555914i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3871.22 | 0.666874 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2529.00 | −0.431643 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1078.55 | 0.182397 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2647.85 | − | 7281.70i | 0.443710 | − | 1.22022i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5022.44 | −0.834013 | −0.417007 | − | 0.908903i | \(-0.636921\pi\) | ||||
−0.417007 | + | 0.908903i | \(0.636921\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2466.91i | 0.405964i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8661.66 | 1.41265 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8480.49 | 1.37081 | 0.685403 | − | 0.728164i | \(-0.259626\pi\) | ||||
0.685403 | + | 0.728164i | \(0.259626\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 2485.38i | − | 0.398193i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2418.13 | −0.384015 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5498.52 | − | 3181.18i | 0.865575 | − | 0.500780i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3099.28 | 0.483651 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9890.27 | 1.53008 | 0.765040 | − | 0.643983i | \(-0.222719\pi\) | ||||
0.765040 | + | 0.643983i | \(0.222719\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6913.69 | 1.06041 | 0.530203 | − | 0.847871i | \(-0.322116\pi\) | ||||
0.530203 | + | 0.847871i | \(0.322116\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 1732.33i | − | 0.263433i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 5062.99i | − | 0.763388i | −0.924289 | − | 0.381694i | \(-0.875341\pi\) | ||
0.924289 | − | 0.381694i | \(-0.124659\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11246.5i | 1.68142i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1470.09 | + | 4042.81i | −0.217942 | + | 0.599350i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 7551.38i | − | 1.11016i | −0.831798 | − | 0.555079i | \(-0.812688\pi\) | ||
0.831798 | − | 0.555079i | \(-0.187312\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4359.05 | 0.635522 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2111.56i | 0.305312i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 8925.25i | − | 1.27991i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12597.1 | −1.79173 | −0.895864 | − | 0.444329i | \(-0.853442\pi\) | ||||
−0.895864 | + | 0.444329i | \(0.853442\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 2698.17i | − | 0.380653i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11581.2 | + | 4211.27i | 1.62066 | + | 0.589322i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9549.28i | 1.32558i | 0.748803 | + | 0.662792i | \(0.230629\pi\) | ||||
−0.748803 | + | 0.662792i | \(0.769371\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3292.17i | 0.453352i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10207.9i | 1.39452i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1603.13 | 0.217276 | 0.108638 | − | 0.994081i | \(-0.465351\pi\) | ||||
0.108638 | + | 0.994081i | \(0.465351\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2629.72 | 0.353608 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −402.889 | −0.0537511 | −0.0268756 | − | 0.999639i | \(-0.508556\pi\) | ||||
−0.0268756 | + | 0.999639i | \(0.508556\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2032.35 | + | 5589.05i | −0.269034 | + | 0.739855i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3472.42 | 0.456105 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 8540.21i | − | 1.11313i | −0.830806 | − | 0.556563i | \(-0.812120\pi\) | ||
0.830806 | − | 0.556563i | \(-0.187880\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6238.04 | −0.806831 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3249.13 | 0.417040 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 16009.7i | − | 2.03933i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11977.7 | 1.51421 | 0.757106 | − | 0.653292i | \(-0.226613\pi\) | ||||
0.757106 | + | 0.653292i | \(0.226613\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 949.352 | − | 2610.76i | 0.119115 | − | 0.327573i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 58.8089 | 0.00732364 | 0.00366182 | − | 0.999993i | \(-0.498834\pi\) | ||||
0.00366182 | + | 0.999993i | \(0.498834\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6195.30 | 0.765782 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1038.62 | 0.127431 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 6864.29i | − | 0.835996i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 805.417i | − | 0.0973723i | −0.998814 | − | 0.0486862i | \(-0.984497\pi\) | ||
0.998814 | − | 0.0486862i | \(-0.0155034\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2255.51i | 0.270696i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7756.75 | − | 2820.59i | −0.924176 | − | 0.336058i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 3055.64i | − | 0.361435i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1630.66 | 0.191496 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 7784.37i | − | 0.907616i | −0.891099 | − | 0.453808i | \(-0.850065\pi\) | ||
0.891099 | − | 0.453808i | \(-0.149935\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4998.41i | 0.578640i | 0.957232 | + | 0.289320i | \(0.0934292\pi\) | ||||
−0.957232 | + | 0.289320i | \(0.906571\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3765.26 | 0.432797 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3051.86i | 0.348322i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3796.07 | − | 10439.4i | 0.430222 | − | 1.18313i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4820.28i | 0.542484i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5983.17i | 0.668675i | 0.942453 | + | 0.334338i | \(0.108513\pi\) | ||||
−0.942453 | + | 0.334338i | \(0.891487\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3739.75i | 0.415060i | 0.978229 | + | 0.207530i | \(0.0665425\pi\) | ||||
−0.978229 | + | 0.207530i | \(0.933458\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6120.18 | −0.674575 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4028.40 | 0.440971 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8032.79 | −0.873313 | −0.436656 | − | 0.899628i | \(-0.643837\pi\) | ||||
−0.436656 | + | 0.899628i | \(0.643837\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2365.97 | + | 1982.86i | 0.255477 | + | 0.214109i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10025.1 | 1.07519 | 0.537595 | − | 0.843203i | \(-0.319333\pi\) | ||||
0.537595 | + | 0.843203i | \(0.319333\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 9533.58i | − | 1.01558i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3169.33 | −0.335357 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4911.85 | 0.516268 | 0.258134 | − | 0.966109i | \(-0.416892\pi\) | ||||
0.258134 | + | 0.966109i | \(0.416892\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7507.77i | 0.783873i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6276.40 | 0.650973 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5206.91 | − | 14319.3i | 0.536492 | − | 1.47538i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10828.7 | 1.10842 | 0.554208 | − | 0.832378i | \(-0.313021\pi\) | ||||
0.554208 | + | 0.832378i | \(0.313021\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2090.48 | −0.212582 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7105.06 | −0.717821 | −0.358911 | − | 0.933372i | \(-0.616852\pi\) | ||||
−0.358911 | + | 0.933372i | \(0.616852\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14241.0i | 1.42945i | 0.699403 | + | 0.714727i | \(0.253449\pi\) | ||||
−0.699403 | + | 0.714727i | \(0.746551\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3714.41i | 0.370434i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5568.41i | 0.551767i | 0.961191 | + | 0.275884i | \(0.0889705\pi\) | ||||
−0.961191 | + | 0.275884i | \(0.911030\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4275.32 | + | 11757.3i | −0.420929 | + | 1.15757i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3557.11i | 0.347989i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9662.15 | −0.939252 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 1970.83i | − | 0.190374i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5988.46i | 0.574828i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14755.8 | 1.40754 | 0.703768 | − | 0.710430i | \(-0.251499\pi\) | ||||
0.703768 | + | 0.710430i | \(0.251499\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17586.4i | 1.66710i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1529.78 | + | 4206.96i | −0.144114 | + | 0.396321i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 19902.6i | − | 1.86336i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2870.19i | 0.267065i | 0.991044 | + | 0.133533i | \(0.0426321\pi\) | ||||
−0.991044 | + | 0.133533i | \(0.957368\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 2710.91i | − | 0.250698i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13050.2 | −1.19949 | −0.599745 | − | 0.800191i | \(-0.704731\pi\) | ||||
−0.599745 | + | 0.800191i | \(0.704731\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12318.3 | 1.12533 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2890.02 | −0.262417 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15266.0 | − | 5551.19i | −1.37782 | − | 0.501016i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10021.7 | −0.899063 | −0.449531 | − | 0.893265i | \(-0.648409\pi\) | ||||
−0.449531 | + | 0.893265i | \(0.648409\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 1423.90i | − | 0.126976i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13625.2 | 1.20779 | 0.603894 | − | 0.797065i | \(-0.293615\pi\) | ||||
0.603894 | + | 0.797065i | \(0.293615\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15418.5 | −1.35865 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 5758.66i | − | 0.504440i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6931.67 | −0.603617 | −0.301808 | − | 0.953369i | \(-0.597590\pi\) | ||||
−0.301808 | + | 0.953369i | \(0.597590\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12115.1 | + | 4405.42i | 1.04881 | + | 0.381378i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1349.99 | 0.116186 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5187.50 | −0.443861 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10477.0 | −0.891253 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 4923.98i | − | 0.416452i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20497.7i | 1.72365i | 0.507207 | + | 0.861824i | \(0.330678\pi\) | ||||
−0.507207 | + | 0.861824i | \(0.669322\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 17220.5i | − | 1.43977i | −0.694094 | − | 0.719885i | \(-0.744195\pi\) | ||
0.694094 | − | 0.719885i | \(-0.255805\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2058.18 | + | 748.418i | 0.171098 | + | 0.0622165i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 7476.14i | − | 0.617961i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5675.68 | 0.466482 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 4010.90i | − | 0.327793i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 19235.0i | − | 1.56316i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13665.2 | 1.10430 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 5406.33i | − | 0.434451i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6583.41 | − | 5517.41i | −0.526100 | − | 0.440912i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6118.24i | 0.486218i | 0.969999 | + | 0.243109i | \(0.0781672\pi\) | ||||
−0.969999 | + | 0.243109i | \(0.921833\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6205.35i | 0.490418i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4609.89i | 0.362323i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −391.181 | −0.0305772 | −0.0152886 | − | 0.999883i | \(-0.504867\pi\) | ||||
−0.0152886 | + | 0.999883i | \(0.504867\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5398.04 | 0.419641 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7954.91 | −0.615047 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 21731.5 | + | 7902.23i | 1.67110 | + | 0.607662i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10544.0 | −0.806429 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 14903.1i | − | 1.13369i | −0.823824 | − | 0.566846i | \(-0.808163\pi\) | ||
0.823824 | − | 0.566846i | \(-0.191837\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24754.6 | 1.87300 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5816.84 | 0.437767 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18651.1i | 1.39618i | 0.716010 | + | 0.698090i | \(0.245966\pi\) | ||||
−0.716010 | + | 0.698090i | \(0.754034\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10623.0 | 0.790993 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −512.655 | + | 1409.83i | −0.0379709 | + | 0.104422i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14380.9 | −1.05954 | −0.529770 | − | 0.848141i | \(-0.677722\pi\) | ||||
−0.529770 | + | 0.848141i | \(0.677722\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26145.9 | −1.91623 | −0.958117 | − | 0.286376i | \(-0.907549\pi\) | ||||
−0.958117 | + | 0.286376i | \(0.907549\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6538.82 | 0.476724 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3175.77i | 0.230328i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 18408.8i | − | 1.32820i | −0.747645 | − | 0.664099i | \(-0.768815\pi\) | ||
0.747645 | − | 0.664099i | \(-0.231185\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13469.4i | 0.966788i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4147.72 | + | 1508.24i | 0.296173 | + | 0.107697i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 16663.2i | − | 1.18374i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7404.28 | 0.523298 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 25942.5i | − | 1.82412i | −0.410053 | − | 0.912062i | \(-0.634490\pi\) | ||
0.410053 | − | 0.912062i | \(-0.365510\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4827.94i | 0.337745i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13557.2 | 0.943604 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19221.9i | 1.33111i | 0.746347 | + | 0.665557i | \(0.231806\pi\) | ||||
−0.746347 | + | 0.665557i | \(0.768194\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17279.7 | − | 6283.41i | −1.19058 | − | 0.432932i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2479.79i | 0.170002i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 14280.0i | − | 0.974068i | −0.873383 | − | 0.487034i | \(-0.838079\pi\) | ||
0.873383 | − | 0.487034i | \(-0.161921\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 5677.17i | − | 0.385319i | −0.981266 | − | 0.192659i | \(-0.938289\pi\) | ||
0.981266 | − | 0.192659i | \(-0.0617113\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6079.54 | −0.410577 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9025.18 | −0.606489 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16394.3 | 1.09625 | 0.548124 | − | 0.836397i | \(-0.315342\pi\) | ||||
0.548124 | + | 0.836397i | \(0.315342\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3020.86 | − | 8307.52i | 0.201004 | − | 0.552771i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 26842.3 | 1.77729 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 2171.28i | − | 0.143063i | −0.997438 | − | 0.0715313i | \(-0.977211\pi\) | ||
0.997438 | − | 0.0715313i | \(-0.0227886\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11532.4 | 0.756150 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6024.75 | −0.393108 | −0.196554 | − | 0.980493i | \(-0.562975\pi\) | ||||
−0.196554 | + | 0.980493i | \(0.562975\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 13135.5i | − | 0.852926i | −0.904505 | − | 0.426463i | \(-0.859760\pi\) | ||
0.904505 | − | 0.426463i | \(-0.140240\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2175.36 | −0.140570 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12940.9 | + | 4705.69i | 0.832206 | + | 0.302615i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18998.4 | −1.21590 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3756.40 | −0.239260 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21222.3 | 1.34529 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 13957.4i | − | 0.880562i | −0.897860 | − | 0.440281i | \(-0.854879\pi\) | ||
0.897860 | − | 0.440281i | \(-0.145121\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14127.5i | 0.887074i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11239.9i | 0.702426i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16866.8 | + | 14135.7i | 1.04912 | + | 0.879242i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 7893.84i | − | 0.488694i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24561.9 | 1.51348 | 0.756738 | − | 0.653718i | \(-0.226792\pi\) | ||||
0.756738 | + | 0.653718i | \(0.226792\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15778.3i | 0.967708i | 0.875149 | + | 0.483854i | \(0.160763\pi\) | ||||
−0.875149 | + | 0.483854i | \(0.839237\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14841.7i | 0.906033i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11167.7 | −0.678588 | −0.339294 | − | 0.940680i | \(-0.610188\pi\) | ||||
−0.339294 | + | 0.940680i | \(0.610188\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11160.5i | 0.675020i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5041.94 | − | 1833.40i | −0.303547 | − | 0.110379i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 15738.6i | − | 0.943185i | −0.881817 | − | 0.471592i | \(-0.843679\pi\) | ||
0.881817 | − | 0.471592i | \(-0.156321\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13887.3i | 0.828432i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6264.54i | 0.371999i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21821.3 | 1.28989 | 0.644944 | − | 0.764230i | \(-0.276881\pi\) | ||||
0.644944 | + | 0.764230i | \(0.276881\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5703.63 | −0.335621 | −0.167810 | − | 0.985819i | \(-0.553670\pi\) | ||||
−0.167810 | + | 0.985819i | \(0.553670\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −14902.9 | −0.872970 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11158.8 | + | 4057.69i | 0.650709 | + | 0.236618i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12818.5 | 0.744127 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17325.3i | 1.00125i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15020.3 | −0.864161 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30185.3 | 1.72891 | 0.864456 | − | 0.502708i | \(-0.167663\pi\) | ||||
0.864456 | + | 0.502708i | \(0.167663\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1064.26i | 0.0606863i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12990.9 | 0.737488 | 0.368744 | − | 0.929531i | \(-0.379788\pi\) | ||||
0.368744 | + | 0.929531i | \(0.379788\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27015.8 | + | 9823.76i | 1.52691 | + | 0.555230i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6840.32 | 0.384907 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3636.79 | −0.203745 | −0.101872 | − | 0.994797i | \(-0.532483\pi\) | ||||
−0.101872 | + | 0.994797i | \(0.532483\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9640.43 | −0.537725 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11079.0i | 0.615267i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 42691.3i | 2.36054i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 869.636i | 0.0478763i | 0.999713 | + | 0.0239381i | \(0.00762048\pi\) | ||||
−0.999713 | + | 0.0239381i | \(0.992380\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1426.49 | − | 3922.90i | 0.0781929 | − | 0.215034i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6969.74i | 0.380399i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −23211.7 | −1.26142 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 9420.20i | − | 0.509735i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 8128.07i | − | 0.437936i | −0.975732 | − | 0.218968i | \(-0.929731\pi\) | ||
0.975732 | − | 0.218968i | \(-0.0702690\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13704.9 | −0.735265 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16093.4i | 0.859732i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7610.45 | − | 20929.1i | 0.404838 | − | 1.11332i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6488.87i | 0.343716i | 0.985122 | + | 0.171858i | \(0.0549770\pi\) | ||||
−0.985122 | + | 0.171858i | \(0.945023\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11237.0i | 0.592717i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 7779.69i | − | 0.408628i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −20602.7 | −1.07762 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −932.351 | −0.0485625 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19419.9 | −1.00729 | −0.503645 | − | 0.863911i | \(-0.668008\pi\) | ||||
−0.503645 | + | 0.863911i | \(0.668008\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2560.50 | − | 7041.50i | 0.132258 | − | 0.363716i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1373.50 | 0.0706514 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 6271.22i | − | 0.321252i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29343.3 | 1.49695 | 0.748475 | − | 0.663163i | \(-0.230786\pi\) | ||||
0.748475 | + | 0.663163i | \(0.230786\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 29872.4i | − | 1.51145i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27788.9 | 1.40028 | 0.700140 | − | 0.714006i | \(-0.253121\pi\) | ||||
0.700140 | + | 0.714006i | \(0.253121\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8475.11 | + | 10112.6i | −0.425318 | + | 0.507493i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16916.6 | 0.845495 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12588.2 | −0.626607 | −0.313304 | − | 0.949653i | \(-0.601436\pi\) | ||||
−0.313304 | + | 0.949653i | \(0.601436\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9623.96 | 0.477119 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 8137.53i | − | 0.401799i | −0.979612 | − | 0.200900i | \(-0.935613\pi\) | ||
0.979612 | − | 0.200900i | \(-0.0643865\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 13546.3i | − | 0.666171i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2144.73i | 0.105049i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6745.03 | + | 18549.2i | −0.329050 | + | 0.904902i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2723.45i | 0.132331i | 0.997809 | + | 0.0661653i | \(0.0210765\pi\) | ||||
−0.997809 | + | 0.0661653i | \(0.978924\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2423.75 | −0.117299 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 26826.4i | 1.29313i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 8168.46i | − | 0.392190i | −0.980585 | − | 0.196095i | \(-0.937174\pi\) | ||
0.980585 | − | 0.196095i | \(-0.0628261\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6053.02 | 0.289474 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24255.5i | 1.15540i | 0.816248 | + | 0.577702i | \(0.196050\pi\) | ||||
−0.816248 | + | 0.577702i | \(0.803950\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6257.46 | − | 2275.40i | −0.296901 | − | 0.107962i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 8935.06i | − | 0.422285i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 28593.4i | − | 1.34609i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 13226.7i | − | 0.620241i | −0.950697 | − | 0.310121i | \(-0.899631\pi\) | ||
0.950697 | − | 0.310121i | \(-0.100369\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5248.07 | 0.245142 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24347.2 | 1.13287 | 0.566434 | − | 0.824107i | \(-0.308323\pi\) | ||||
0.566434 | + | 0.824107i | \(0.308323\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3806.08 | −0.176411 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5204.42 | − | 14312.4i | 0.240293 | − | 0.660817i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14989.7 | 0.689423 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21964.9i | 1.00636i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4295.69 | 0.196061 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15203.7 | −0.691265 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31493.4i | 1.42645i | 0.700933 | + | 0.713227i | \(0.252767\pi\) | ||||
−0.700933 | + | 0.713227i | \(0.747233\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4081.04 | −0.184143 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5243.39 | + | 14419.6i | −0.235694 | + | 0.648168i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 38482.3 | 1.72326 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −25595.7 | −1.14187 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −27985.5 | −1.24378 | −0.621892 | − | 0.783103i | \(-0.713636\pi\) | ||||
−0.621892 | + | 0.783103i | \(0.713636\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 32391.7i | − | 1.43421i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6691.53i | 0.295173i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 17431.4i | − | 0.766052i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17981.3 | − | 6538.53i | −0.787274 | − | 0.286277i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6672.18i | 0.291043i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −31789.5 | −1.38153 | −0.690766 | − | 0.723079i | \(-0.742726\pi\) | ||||
−0.690766 | + | 0.723079i | \(0.742726\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 24872.1i | − | 1.07692i | −0.842652 | − | 0.538458i | \(-0.819007\pi\) | ||
0.842652 | − | 0.538458i | \(-0.180993\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 8755.76i | − | 0.377709i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11586.9 | 0.498001 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19291.0i | 0.826080i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3654.68 | + | 10050.5i | −0.155928 | + | 0.428809i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7964.00i | 0.338545i | 0.985569 | + | 0.169272i | \(0.0541418\pi\) | ||||
−0.985569 | + | 0.169272i | \(0.945858\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2998.32i | 0.126993i | 0.997982 | + | 0.0634963i | \(0.0202251\pi\) | ||||
−0.997982 | + | 0.0634963i | \(0.979775\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 2961.34i | − | 0.124970i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 43518.7 | 1.82986 | 0.914930 | − | 0.403612i | \(-0.132245\pi\) | ||||
0.914930 | + | 0.403612i | \(0.132245\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35520.8 | −1.48816 | −0.744082 | − | 0.668089i | \(-0.767113\pi\) | ||||
−0.744082 | + | 0.668089i | \(0.767113\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4898.52 | −0.204486 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17058.2 | − | 20353.9i | 0.709520 | − | 0.846605i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6085.98 | 0.252232 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 2607.11i | − | 0.107664i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30875.0 | 1.27047 | 0.635234 | − | 0.772319i | \(-0.280903\pi\) | ||||
0.635234 | + | 0.772319i | \(0.280903\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −923.747 | −0.0378756 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 22846.3i | 0.933413i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 24613.5 | 1.00205 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4454.74 | − | 12250.8i | 0.180716 | − | 0.496979i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8601.22 | 0.347695 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 22084.0 | 0.889576 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8198.79 | −0.329099 | −0.164549 | − | 0.986369i | \(-0.552617\pi\) | ||||
−0.164549 | + | 0.986369i | \(0.552617\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5770.08i | 0.230798i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13833.3i | 0.551384i | 0.961246 | + | 0.275692i | \(0.0889070\pi\) | ||||
−0.961246 | + | 0.275692i | \(0.911093\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 38843.1i | − | 1.54285i | −0.636319 | − | 0.771426i | \(-0.719544\pi\) | ||
0.636319 | − | 0.771426i | \(-0.280456\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5692.30 | + | 15654.1i | −0.225311 | + | 0.619617i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 45262.8i | − | 1.78536i | −0.450693 | − | 0.892679i | \(-0.648823\pi\) | ||
0.450693 | − | 0.892679i | \(-0.351177\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21045.9 | 0.827264 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3244.92i | 0.127109i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 31267.5i | − | 1.22057i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −43340.6 | −1.68604 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13969.5i | 0.541575i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6945.47 | − | 19100.4i | 0.268342 | − | 0.737954i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 15537.9i | − | 0.598262i | −0.954212 | − | 0.299131i | \(-0.903303\pi\) | ||
0.954212 | − | 0.299131i | \(-0.0966968\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 3399.21i | − | 0.130435i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 39484.6i | − | 1.50995i | −0.655751 | − | 0.754977i | \(-0.727648\pi\) | ||
0.655751 | − | 0.754977i | \(-0.272352\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30198.1 | 1.15090 | 0.575452 | − | 0.817835i | \(-0.304826\pi\) | ||||
0.575452 | + | 0.817835i | \(0.304826\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 17143.3 | 0.651147 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24805.1 | −0.938976 | −0.469488 | − | 0.882939i | \(-0.655562\pi\) | ||||
−0.469488 | + | 0.882939i | \(0.655562\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15257.0 | − | 5547.89i | −0.575593 | − | 0.209303i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2028.47 | 0.0762698 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 20917.9i | 0.783864i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23107.6 | 0.863018 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −15508.0 | −0.577253 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15362.6i | 0.569936i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 51517.5 | 1.90488 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −20146.1 | − | 7325.73i | −0.742436 | − | 0.269972i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −26522.7 | −0.974194 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1393.42 | −0.0510119 | −0.0255059 | − | 0.999675i | \(-0.508120\pi\) | ||||
−0.0255059 | + | 0.999675i | \(0.508120\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10822.1 | 0.394881 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 31078.8i | − | 1.13028i | −0.824995 | − | 0.565141i | \(-0.808822\pi\) | ||
0.824995 | − | 0.565141i | \(-0.191178\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 5967.79i | − | 0.216326i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 23072.2i | 0.833598i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −18850.6 | − | 6854.66i | −0.678847 | − | 0.246849i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46707.6i | 1.67654i | 0.545253 | + | 0.838272i | \(0.316434\pi\) | ||||
−0.545253 | + | 0.838272i | \(0.683566\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −618.446 | −0.0221265 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 56274.6i | − | 2.00683i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 10804.2i | − | 0.384044i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3641.06 | 0.129005 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 35085.6i | − | 1.23910i | −0.784958 | − | 0.619549i | \(-0.787316\pi\) | ||
0.784958 | − | 0.619549i | \(-0.212684\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11015.8 | + | 13144.2i | −0.387786 | + | 0.462709i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18888.0i | 0.662771i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 24862.2i | 0.869604i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 8314.62i | − | 0.289890i | −0.989440 | − | 0.144945i | \(-0.953699\pi\) | ||
0.989440 | − | 0.144945i | \(-0.0463005\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 23993.3 | 0.833856 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40367.5 | 1.39845 | 0.699225 | − | 0.714902i | \(-0.253529\pi\) | ||||
0.699225 | + | 0.714902i | \(0.253529\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24154.2 | −0.834114 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6025.84 | − | 2191.18i | −0.207429 | − | 0.0754275i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9649.94 | −0.331131 | −0.165565 | − | 0.986199i | \(-0.552945\pi\) | ||||
−0.165565 | + | 0.986199i | \(0.552945\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 44659.5i | 1.52762i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17491.3 | 0.596418 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −58010.8 | −1.97183 | −0.985915 | − | 0.167250i | \(-0.946511\pi\) | ||||
−0.985915 | + | 0.167250i | \(0.946511\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 27948.0i | 0.946992i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11953.0 | −0.403745 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4758.43 | − | 13085.9i | 0.160227 | − | 0.440631i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20467.2 | −0.687027 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9591.50 | −0.320957 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −57570.6 | −1.92048 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1452.77i | 0.0483124i | 0.999708 | + | 0.0241562i | \(0.00768990\pi\) | ||||
−0.999708 | + | 0.0241562i | \(0.992310\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 11613.6i | − | 0.385020i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 57626.6i | 1.90456i | 0.305227 | + | 0.952280i | \(0.401268\pi\) | ||||
−0.305227 | + | 0.952280i | \(0.598732\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9460.71 | − | 3440.20i | −0.311713 | − | 0.113348i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7587.01i | 0.249209i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 45343.0 | 1.48480 | 0.742401 | − | 0.669956i | \(-0.233687\pi\) | ||||
0.742401 | + | 0.669956i | \(0.233687\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 18619.5i | − | 0.607846i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 3235.64i | − | 0.105307i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 46702.1 | 1.51533 | 0.757663 | − | 0.652646i | \(-0.226341\pi\) | ||||
0.757663 | + | 0.652646i | \(0.226341\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 57945.9i | 1.87443i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −21845.1 | − | 7943.54i | −0.704495 | − | 0.256176i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 31085.3i | − | 0.999450i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6796.04i | 0.217844i | 0.994050 | + | 0.108922i | \(0.0347399\pi\) | ||||
−0.994050 | + | 0.108922i | \(0.965260\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15067.3i | 0.481518i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10599.1 | −0.337702 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24424.9 | −0.775872 | −0.387936 | − | 0.921686i | \(-0.626812\pi\) | ||||
−0.387936 | + | 0.921686i | \(0.626812\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7400.74 | 0.234383 |
(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 | 1344.4.p.d.223.5 | yes | 32 | |
4.3 | odd | 2 | inner | 1344.4.p.d.223.16 | yes | 32 | |
7.6 | odd | 2 | 1344.4.p.c.223.4 | yes | 32 | ||
8.3 | odd | 2 | 1344.4.p.c.223.3 | ✓ | 32 | ||
8.5 | even | 2 | 1344.4.p.c.223.12 | yes | 32 | ||
28.27 | even | 2 | 1344.4.p.c.223.11 | yes | 32 | ||
56.13 | odd | 2 | inner | 1344.4.p.d.223.15 | yes | 32 | |
56.27 | even | 2 | inner | 1344.4.p.d.223.6 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.4.p.c.223.3 | ✓ | 32 | 8.3 | odd | 2 | ||
1344.4.p.c.223.4 | yes | 32 | 7.6 | odd | 2 | ||
1344.4.p.c.223.11 | yes | 32 | 28.27 | even | 2 | ||
1344.4.p.c.223.12 | yes | 32 | 8.5 | even | 2 | ||
1344.4.p.d.223.5 | yes | 32 | 1.1 | even | 1 | trivial | |
1344.4.p.d.223.6 | yes | 32 | 56.27 | even | 2 | inner | |
1344.4.p.d.223.15 | yes | 32 | 56.13 | odd | 2 | inner | |
1344.4.p.d.223.16 | yes | 32 | 4.3 | odd | 2 | inner |