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: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 2 x^{14} + 58 x^{13} + 178264 x^{12} - 331354 x^{11} + 307862 x^{10} + \cdots + 22\!\cdots\!01 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{17}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 223.11 | ||
Root | \(5.50749 - 5.50749i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.223 |
Dual form | 1344.4.p.a.223.3 |
$q$-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 | ||||||||
\(5\) | −4.35176 | −0.389233 | −0.194617 | − | 0.980879i | \(-0.562346\pi\) | ||||
−0.194617 | + | 0.980879i | \(0.562346\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.09314 | − | 17.1081i | −0.382993 | − | 0.923751i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −43.1344 | −1.18232 | −0.591159 | − | 0.806555i | \(-0.701329\pi\) | ||||
−0.591159 | + | 0.806555i | \(0.701329\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 26.5241 | 0.565882 | 0.282941 | − | 0.959137i | \(-0.408690\pi\) | ||||
0.282941 | + | 0.959137i | \(0.408690\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 13.0553i | − | 0.224724i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 76.6921i | 1.09415i | 0.837083 | + | 0.547075i | \(0.184259\pi\) | ||||
−0.837083 | + | 0.547075i | \(0.815741\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 58.7403i | 0.709261i | 0.935007 | + | 0.354630i | \(0.115393\pi\) | ||||
−0.935007 | + | 0.354630i | \(0.884607\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 51.3243 | − | 21.2794i | 0.533328 | − | 0.221121i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 0.747396i | − | 0.00677578i | −0.999994 | − | 0.00338789i | \(-0.998922\pi\) | ||
0.999994 | − | 0.00338789i | \(-0.00107840\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −106.062 | −0.848498 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 27.0000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 64.9778i | 0.416071i | 0.978121 | + | 0.208036i | \(0.0667070\pi\) | ||||
−0.978121 | + | 0.208036i | \(0.933293\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −165.456 | −0.958605 | −0.479302 | − | 0.877650i | \(-0.659110\pi\) | ||||
−0.479302 | + | 0.877650i | \(0.659110\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 129.403i | − | 0.682612i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 30.8676 | + | 74.4503i | 0.149074 | + | 0.359554i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 389.771i | 1.73184i | 0.500184 | + | 0.865919i | \(0.333266\pi\) | ||||
−0.500184 | + | 0.865919i | \(0.666734\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 79.5723i | 0.326712i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 290.660i | − | 1.10716i | −0.832796 | − | 0.553579i | \(-0.813262\pi\) | ||
0.832796 | − | 0.553579i | \(-0.186738\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 32.4066 | 0.114929 | 0.0574647 | − | 0.998348i | \(-0.481698\pi\) | ||||
0.0574647 | + | 0.998348i | \(0.481698\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 39.1658 | 0.129744 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 368.457 | 1.14351 | 0.571756 | − | 0.820424i | \(-0.306263\pi\) | ||||
0.571756 | + | 0.820424i | \(0.306263\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −242.375 | + | 242.700i | −0.706632 | + | 0.707581i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −230.076 | −0.631708 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 588.016i | − | 1.52397i | −0.647596 | − | 0.761984i | \(-0.724226\pi\) | ||
0.647596 | − | 0.761984i | \(-0.275774\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 187.710 | 0.460197 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −176.221 | −0.409492 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 471.583i | − | 1.04059i | −0.853986 | − | 0.520296i | \(-0.825822\pi\) | ||
0.853986 | − | 0.520296i | \(-0.174178\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 448.047 | 0.940434 | 0.470217 | − | 0.882551i | \(-0.344176\pi\) | ||||
0.470217 | + | 0.882551i | \(0.344176\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 63.8382 | + | 153.973i | 0.127664 | + | 0.307917i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −115.426 | −0.220260 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 707.632 | 1.29031 | 0.645157 | − | 0.764050i | \(-0.276792\pi\) | ||||
0.645157 | + | 0.764050i | \(0.276792\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.24219 | 0.00391200 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 997.655i | − | 1.66760i | −0.552064 | − | 0.833802i | \(-0.686160\pi\) | ||
0.552064 | − | 0.833802i | \(-0.313840\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1225.05i | − | 1.96413i | −0.188553 | − | 0.982063i | \(-0.560380\pi\) | ||
0.188553 | − | 0.982063i | \(-0.439620\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 318.187i | − | 0.489880i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 305.958 | + | 737.947i | 0.452820 | + | 1.09217i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 160.665i | 0.228813i | 0.993434 | + | 0.114407i | \(0.0364966\pi\) | ||||
−0.993434 | + | 0.114407i | \(0.963503\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 1000.97i | − | 1.32375i | −0.749616 | − | 0.661873i | \(-0.769762\pi\) | ||
0.749616 | − | 0.661873i | \(-0.230238\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 333.745i | − | 0.425879i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −194.933 | −0.240219 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1138.80i | 1.35632i | 0.734915 | + | 0.678160i | \(0.237222\pi\) | ||||
−0.734915 | + | 0.678160i | \(0.762778\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −188.139 | − | 453.777i | −0.216729 | − | 0.522734i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 496.368i | − | 0.553451i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 255.624i | − | 0.276068i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 729.761i | 0.763876i | 0.924188 | + | 0.381938i | \(0.124743\pi\) | ||||
−0.924188 | + | 0.381938i | \(0.875257\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 388.209 | 0.394106 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 313.536 | 0.308891 | 0.154446 | − | 0.988001i | \(-0.450641\pi\) | ||||
0.154446 | + | 0.988001i | \(0.450641\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −141.702 | −0.135557 | −0.0677784 | − | 0.997700i | \(-0.521591\pi\) | ||||
−0.0677784 | + | 0.997700i | \(0.521591\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −223.351 | + | 92.6028i | −0.207589 | + | 0.0860677i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 960.650 | 0.867940 | 0.433970 | − | 0.900927i | \(-0.357112\pi\) | ||||
0.433970 | + | 0.900927i | \(0.357112\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1044.39i | 0.917750i | 0.888501 | + | 0.458875i | \(0.151747\pi\) | ||||
−0.888501 | + | 0.458875i | \(0.848253\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1169.31 | −0.999877 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 45.9468 | 0.0382506 | 0.0191253 | − | 0.999817i | \(-0.493912\pi\) | ||||
0.0191253 | + | 0.999817i | \(0.493912\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.25249i | 0.00263736i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −238.717 | −0.188627 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1312.06 | − | 543.987i | 1.01072 | − | 0.419052i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 529.573 | 0.397876 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 871.981 | 0.639219 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1005.53 | 0.719496 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 340.925i | − | 0.238206i | −0.992882 | − | 0.119103i | \(-0.961998\pi\) | ||
0.992882 | − | 0.119103i | \(-0.0380019\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 97.2199i | 0.0663545i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 732.678i | − | 0.488659i | −0.969692 | − | 0.244330i | \(-0.921432\pi\) | ||
0.969692 | − | 0.244330i | \(-0.0785679\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1004.94 | − | 416.653i | 0.655180 | − | 0.271642i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 117.497i | 0.0749079i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 292.821 | 0.182609 | 0.0913044 | − | 0.995823i | \(-0.470896\pi\) | ||||
0.0913044 | + | 0.995823i | \(0.470896\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1618.66i | − | 0.987717i | −0.869542 | − | 0.493858i | \(-0.835586\pi\) | ||
0.869542 | − | 0.493858i | \(-0.164414\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1105.37i | 0.660206i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1144.10 | −0.669052 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 282.767i | − | 0.161949i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −728.101 | − | 727.124i | −0.408522 | − | 0.407974i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1405.12i | 0.772561i | 0.922381 | + | 0.386280i | \(0.126240\pi\) | ||||
−0.922381 | + | 0.386280i | \(0.873760\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 463.962i | 0.250044i | 0.992154 | + | 0.125022i | \(0.0399002\pi\) | ||||
−0.992154 | + | 0.125022i | \(0.960100\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 690.229i | − | 0.364717i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 720.024 | 0.373121 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3761.11 | 1.91191 | 0.955953 | − | 0.293521i | \(-0.0948272\pi\) | ||||
0.955953 | + | 0.293521i | \(0.0948272\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1764.05 | 0.879863 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.7865 | + | 5.30139i | −0.00625913 | + | 0.00259508i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1828.77 | −0.878775 | −0.439388 | − | 0.898298i | \(-0.644805\pi\) | ||||
−0.439388 | + | 0.898298i | \(0.644805\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 563.131i | 0.265695i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 376.850 | 0.174620 | 0.0873100 | − | 0.996181i | \(-0.472173\pi\) | ||||
0.0873100 | + | 0.996181i | \(0.472173\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1493.47 | −0.679778 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 528.663i | − | 0.236420i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3388.91 | 1.48933 | 0.744665 | − | 0.667438i | \(-0.232609\pi\) | ||||
0.744665 | + | 0.667438i | \(0.232609\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 752.314 | + | 1814.52i | 0.324969 | + | 0.783801i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1414.75 | 0.600786 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −326.185 | −0.136202 | −0.0681011 | − | 0.997678i | \(-0.521694\pi\) | ||||
−0.0681011 | + | 0.997678i | \(0.521694\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1651.06 | 0.678024 | 0.339012 | − | 0.940782i | \(-0.389907\pi\) | ||||
0.339012 | + | 0.940782i | \(0.389907\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1344.14i | 0.542960i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 1696.19i | − | 0.674089i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3308.06i | − | 1.29363i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −461.919 | + | 191.515i | −0.177776 | + | 0.0737071i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1762.41i | 0.667664i | 0.942633 | + | 0.333832i | \(0.108342\pi\) | ||||
−0.942633 | + | 0.333832i | \(0.891658\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4353.22 | 1.62358 | 0.811792 | − | 0.583946i | \(-0.198492\pi\) | ||||
0.811792 | + | 0.583946i | \(0.198492\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 346.279i | − | 0.127167i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1469.72i | 0.531541i | 0.964036 | + | 0.265770i | \(0.0856263\pi\) | ||||
−0.964036 | + | 0.265770i | \(0.914374\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2812.82 | −1.00199 | −0.500994 | − | 0.865450i | \(-0.667032\pi\) | ||||
−0.500994 | + | 0.865450i | \(0.667032\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2122.90i | 0.744963i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1111.65 | − | 460.896i | 0.384346 | − | 0.159353i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1264.88i | 0.430943i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.72657i | 0.00225859i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 2533.73i | − | 0.838572i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2434.21 | 0.794208 | 0.397104 | − | 0.917774i | \(-0.370015\pi\) | ||||
0.397104 | + | 0.917774i | \(0.370015\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2992.96 | 0.962791 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −141.026 | −0.0447343 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1173.60 | + | 2830.64i | 0.367139 | + | 0.885512i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3675.15 | 1.13399 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2034.19i | 0.619160i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 849.910 | 0.255221 | 0.127610 | − | 0.991824i | \(-0.459269\pi\) | ||||
0.127610 | + | 0.991824i | \(0.459269\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 954.560 | 0.282833 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 2287.25i | − | 0.668768i | −0.942437 | − | 0.334384i | \(-0.891472\pi\) | ||
0.942437 | − | 0.334384i | \(-0.108528\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2263.21 | 0.653088 | 0.326544 | − | 0.945182i | \(-0.394116\pi\) | ||||
0.326544 | + | 0.945182i | \(0.394116\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2213.84 | + | 917.874i | −0.630563 | + | 0.261436i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6311.21 | −1.77451 | −0.887255 | − | 0.461279i | \(-0.847391\pi\) | ||||
−0.887255 | + | 0.461279i | \(0.847391\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1603.44 | −0.445092 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −481.995 | −0.132105 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 2083.06i | − | 0.563774i | −0.959448 | − | 0.281887i | \(-0.909040\pi\) | ||
0.959448 | − | 0.281887i | \(-0.0909603\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2487.56i | 0.664887i | 0.943123 | + | 0.332443i | \(0.107873\pi\) | ||||
−0.943123 | + | 0.332443i | \(0.892127\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1054.76 | − | 1056.17i | 0.275045 | − | 0.275414i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1558.03i | 0.401358i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3002.91 | 0.764265 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 7731.44i | − | 1.94424i | −0.234483 | − | 0.972120i | \(-0.575340\pi\) | ||
0.234483 | − | 0.972120i | \(-0.424660\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 32.2385i | 0.00801113i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1001.24 | 0.245882 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 515.804i | − | 0.125194i | −0.998039 | − | 0.0625972i | \(-0.980062\pi\) | ||
0.998039 | − | 0.0625972i | \(-0.0199383\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6668.25 | − | 2764.70i | 1.59979 | − | 0.663283i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 584.800i | − | 0.138690i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 2690.82i | − | 0.630886i | −0.948945 | − | 0.315443i | \(-0.897847\pi\) | ||
0.948945 | − | 0.315443i | \(-0.102153\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2558.90i | 0.593178i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3416.40 | −0.783071 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −292.293 | −0.0662507 | −0.0331254 | − | 0.999451i | \(-0.510546\pi\) | ||||
−0.0331254 | + | 0.999451i | \(0.510546\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2946.93 | −0.660565 | −0.330282 | − | 0.943882i | \(-0.607144\pi\) | ||||
−0.330282 | + | 0.943882i | \(0.607144\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1361.33 | − | 564.417i | 0.301800 | − | 0.125128i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4574.93 | 1.00319 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2058.88i | 0.446593i | 0.974751 | + | 0.223296i | \(0.0716818\pi\) | ||||
−0.974751 | + | 0.223296i | \(0.928318\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1489.10 | 0.319535 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5425.14 | −1.15173 | −0.575866 | − | 0.817544i | \(-0.695335\pi\) | ||||
−0.575866 | + | 0.817544i | \(0.695335\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 3570.12i | − | 0.749901i | −0.927045 | − | 0.374950i | \(-0.877660\pi\) | ||
0.927045 | − | 0.374950i | \(-0.122340\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 766.871 | 0.159388 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4972.65 | + | 2061.69i | −1.02274 | + | 0.424035i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −968.671 | −0.197165 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2189.28 | −0.441024 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1942.50 | 0.387311 | 0.193655 | − | 0.981070i | \(-0.437966\pi\) | ||||
0.193655 | + | 0.981070i | \(0.437966\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2052.22i | 0.405033i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1164.63i | 0.227537i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 19.8240i | − | 0.00383429i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −229.865 | − | 554.416i | −0.0440172 | − | 0.106166i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 940.609i | 0.178338i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1949.79 | −0.366048 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 766.366i | 0.142472i | 0.997460 | + | 0.0712358i | \(0.0226943\pi\) | ||||
−0.997460 | + | 0.0712358i | \(0.977306\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 425.107i | − | 0.0782638i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6733.22 | 1.22767 | 0.613836 | − | 0.789434i | \(-0.289626\pi\) | ||||
0.613836 | + | 0.789434i | \(0.289626\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 7627.66i | − | 1.37745i | −0.725024 | − | 0.688723i | \(-0.758171\pi\) | ||
0.725024 | − | 0.688723i | \(-0.241829\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −277.809 | − | 670.053i | −0.0496912 | − | 0.119851i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 8243.80i | − | 1.46062i | −0.683114 | − | 0.730312i | \(-0.739375\pi\) | ||
0.683114 | − | 0.730312i | \(-0.260625\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 2802.77i | − | 0.491929i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2881.95i | 0.501105i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4504.92 | −0.776038 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2813.20 | −0.480149 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3133.18 | −0.529863 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2613.52 | − | 6303.61i | −0.437957 | − | 1.05632i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1133.57 | −0.188237 | −0.0941187 | − | 0.995561i | \(-0.530003\pi\) | ||||
−0.0941187 | + | 0.995561i | \(0.530003\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 3507.94i | − | 0.577279i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3079.44 | −0.502233 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7101.55 | 1.14791 | 0.573956 | − | 0.818886i | \(-0.305408\pi\) | ||||
0.573956 | + | 0.818886i | \(0.305408\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 137.841i | 0.0220840i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7136.83 | 1.13338 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5871.34 | + | 2425.07i | 0.924264 | + | 0.381753i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.75746 | −0.00152268 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6829.95 | 1.05663 | 0.528315 | − | 0.849048i | \(-0.322824\pi\) | ||||
0.528315 | + | 0.849048i | \(0.322824\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5310.28 | −0.814478 | −0.407239 | − | 0.913322i | \(-0.633508\pi\) | ||||
−0.407239 | + | 0.913322i | \(0.633508\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 716.151i | − | 0.108904i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 147.157i | 0.0221880i | 0.999938 | + | 0.0110940i | \(0.00353140\pi\) | ||||
−0.999938 | + | 0.0110940i | \(0.996469\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4341.55i | 0.649086i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1631.96 | + | 3936.17i | 0.241940 | + | 0.583541i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 9618.54i | − | 1.41406i | −0.707184 | − | 0.707030i | \(-0.750035\pi\) | ||
0.707184 | − | 0.707030i | \(-0.249965\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3408.58 | 0.496949 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1588.72i | 0.229714i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5331.12i | 0.764503i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7096.51 | 1.00936 | 0.504680 | − | 0.863307i | \(-0.331611\pi\) | ||||
0.504680 | + | 0.863307i | \(0.331611\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2615.94i | 0.369053i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10059.8 | + | 4170.88i | −1.40777 | + | 0.583669i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12908.5i | 1.79190i | 0.444160 | + | 0.895948i | \(0.353502\pi\) | ||||
−0.444160 | + | 0.895948i | \(0.646498\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3016.58i | 0.415401i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1723.48i | 0.235447i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9161.34 | 1.24165 | 0.620826 | − | 0.783948i | \(-0.286797\pi\) | ||||
0.620826 | + | 0.783948i | \(0.286797\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1022.78 | 0.137529 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9816.05 | 1.30960 | 0.654800 | − | 0.755802i | \(-0.272753\pi\) | ||||
0.654800 | + | 0.755802i | \(0.272753\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1331.45 | − | 3211.37i | −0.176253 | − | 0.425108i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −291.660 | −0.0383098 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4106.75i | 0.535271i | 0.963520 | + | 0.267636i | \(0.0862423\pi\) | ||||
−0.963520 | + | 0.267636i | \(0.913758\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 57.3194 | 0.00741372 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2198.03 | 0.282127 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 699.175i | − | 0.0890616i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6582.72 | 0.832184 | 0.416092 | − | 0.909323i | \(-0.363399\pi\) | ||||
0.416092 | + | 0.909323i | \(0.363399\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1249.96 | + | 3014.81i | 0.156833 | + | 0.378269i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9585.89 | −1.19376 | −0.596878 | − | 0.802332i | \(-0.703592\pi\) | ||||
−0.596878 | + | 0.802332i | \(0.703592\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4388.57 | −0.542457 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −352.492 | −0.0432481 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 16812.5i | − | 2.04758i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7390.53i | 0.893492i | 0.894661 | + | 0.446746i | \(0.147417\pi\) | ||||
−0.894661 | + | 0.446746i | \(0.852583\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 878.463i | 0.105429i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8067.89 | + | 3345.00i | −0.961247 | + | 0.398540i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4355.99i | 0.515246i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4855.97 | 0.570259 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5141.45i | 0.599466i | 0.954023 | + | 0.299733i | \(0.0968976\pi\) | ||||
−0.954023 | + | 0.299733i | \(0.903102\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 10171.4i | − | 1.17749i | −0.808319 | − | 0.588744i | \(-0.799623\pi\) | ||
0.808319 | − | 0.588744i | \(-0.200377\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3316.12 | −0.381170 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 8134.13i | − | 0.928384i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3178.06 | − | 7665.23i | −0.360180 | − | 0.868727i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 3432.30i | − | 0.386277i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 16075.1i | − | 1.79655i | −0.439438 | − | 0.898273i | \(-0.644822\pi\) | ||
0.439438 | − | 0.898273i | \(-0.355178\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 120.502i | 0.0133740i | 0.999978 | + | 0.00668702i | \(0.00212856\pi\) | ||||
−0.999978 | + | 0.00668702i | \(0.997871\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 848.302 | 0.0935011 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 43.9023 | 0.00480579 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15873.0 | −1.72569 | −0.862844 | − | 0.505470i | \(-0.831319\pi\) | ||||
−0.862844 | + | 0.505470i | \(0.831319\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2181.37 | − | 2184.30i | 0.235544 | − | 0.235860i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9195.34 | −0.986194 | −0.493097 | − | 0.869974i | \(-0.664135\pi\) | ||||
−0.493097 | + | 0.869974i | \(0.664135\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 4955.77i | − | 0.527924i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4215.35 | −0.446038 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5130.99 | −0.539302 | −0.269651 | − | 0.962958i | \(-0.586908\pi\) | ||||
−0.269651 | + | 0.962958i | \(0.586908\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12537.4i | 1.30901i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1391.89 | −0.144363 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 818.736 | + | 1974.73i | 0.0843581 | + | 0.203465i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4512.80 | −0.461925 | −0.230963 | − | 0.972963i | \(-0.574188\pi\) | ||||
−0.230963 | + | 0.972963i | \(0.574188\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2070.69 | 0.210569 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1593.06 | 0.160946 | 0.0804732 | − | 0.996757i | \(-0.474357\pi\) | ||||
0.0804732 | + | 0.996757i | \(0.474357\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 2589.59i | − | 0.259931i | −0.991518 | − | 0.129966i | \(-0.958513\pi\) | ||
0.991518 | − | 0.129966i | \(-0.0414867\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2160.07i | 0.215421i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18926.4i | 1.87539i | 0.347459 | + | 0.937695i | \(0.387044\pi\) | ||||
−0.347459 | + | 0.937695i | \(0.612956\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5019.33 | − | 12106.2i | −0.494182 | − | 1.19193i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11283.3i | 1.10384i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1397.84 | −0.135883 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 6230.13i | − | 0.601806i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5292.15i | 0.507989i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6302.34 | 0.601172 | 0.300586 | − | 0.953755i | \(-0.402818\pi\) | ||||
0.300586 | + | 0.953755i | \(0.402818\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10338.3i | 0.980015i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −15.9042 | − | 38.3596i | −0.00149827 | − | 0.00361371i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 3175.74i | − | 0.297326i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4607.23i | 0.428693i | 0.976758 | + | 0.214347i | \(0.0687622\pi\) | ||||
−0.976758 | + | 0.214347i | \(0.931238\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 5486.31i | − | 0.507361i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3378.29 | 0.310510 | 0.155255 | − | 0.987874i | \(-0.450380\pi\) | ||||
0.155255 | + | 0.987874i | \(0.450380\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4983.28 | −0.455245 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1689.39 | −0.153399 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −17068.0 | + | 7076.50i | −1.54045 | + | 0.638681i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15145.2 | −1.35870 | −0.679350 | − | 0.733815i | \(-0.737738\pi\) | ||||
−0.679350 | + | 0.733815i | \(0.737738\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1130.55i | 0.100817i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19755.1 | 1.75117 | 0.875583 | − | 0.483068i | \(-0.160477\pi\) | ||||
0.875583 | + | 0.483068i | \(0.160477\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1364.43 | −0.120231 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 4480.42i | − | 0.392470i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13777.1 | −1.19973 | −0.599863 | − | 0.800103i | \(-0.704778\pi\) | ||||
−0.599863 | + | 0.800103i | \(0.704778\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20958.3 | + | 8689.44i | −1.81436 | + | 0.752247i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1585.99 | 0.136497 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 616.655 | 0.0527632 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15893.2 | −1.35199 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10166.7i | 0.859866i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3629.45i | 0.305200i | 0.988288 | + | 0.152600i | \(0.0487646\pi\) | ||||
−0.988288 | + | 0.152600i | \(0.951235\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10629.9i | 0.888740i | 0.895843 | + | 0.444370i | \(0.146573\pi\) | ||||
−0.895843 | + | 0.444370i | \(0.853427\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5443.57 | + | 2256.94i | −0.452527 | + | 0.187621i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 12689.1i | − | 1.04886i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12166.4 | 0.999954 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4244.25i | 0.346864i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 7709.50i | − | 0.626521i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4180.52 | −0.337831 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 978.554i | − | 0.0786363i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10454.7 | − | 10468.7i | 0.835464 | − | 0.836586i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2515.95i | 0.199943i | 0.994990 | + | 0.0999714i | \(0.0318751\pi\) | ||||
−0.994990 | + | 0.0999714i | \(0.968125\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4953.18i | 0.391457i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 4544.95i | − | 0.357219i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11030.6 | −0.862222 | −0.431111 | − | 0.902299i | \(-0.641878\pi\) | ||||
−0.431111 | + | 0.902299i | \(0.641878\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4032.42 | −0.313478 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3816.81 | −0.295103 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2748.68 | − | 1139.62i | 0.211366 | − | 0.0876339i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5088.57 | 0.389185 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 18189.0i | − | 1.38365i | −0.722066 | − | 0.691824i | \(-0.756807\pi\) | ||
0.722066 | − | 0.691824i | \(-0.243193\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 859.557 | 0.0650364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9924.19 | 0.746880 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23074.7i | 1.72732i | 0.504074 | + | 0.863660i | \(0.331834\pi\) | ||||
−0.504074 | + | 0.863660i | \(0.668166\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −199.950 | −0.0148884 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −574.544 | − | 1385.76i | −0.0425548 | − | 0.102639i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5699.50 | 0.419922 | 0.209961 | − | 0.977710i | \(-0.432666\pi\) | ||||
0.209961 | + | 0.977710i | \(0.432666\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7695.91 | 0.564035 | 0.282018 | − | 0.959409i | \(-0.408996\pi\) | ||||
0.282018 | + | 0.959409i | \(0.408996\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5287.24 | −0.385476 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 79.2705i | 0.00574923i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 12406.6i | − | 0.895136i | −0.894250 | − | 0.447568i | \(-0.852290\pi\) | ||
0.894250 | − | 0.447568i | \(-0.147710\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13059.7i | 0.937377i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17124.7 | + | 7100.03i | −1.22281 | + | 0.506986i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25363.7i | 1.80181i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1038.84 | 0.0734199 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 4773.97i | − | 0.335678i | −0.985814 | − | 0.167839i | \(-0.946321\pi\) | ||
0.985814 | − | 0.167839i | \(-0.0536788\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 9718.93i | − | 0.679901i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4409.17 | −0.306885 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 14978.5i | − | 1.03726i | −0.854999 | − | 0.518630i | \(-0.826442\pi\) | ||
0.854999 | − | 0.518630i | \(-0.173558\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5709.75 | + | 2367.30i | −0.393407 | + | 0.163109i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 8438.47i | − | 0.578499i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 13952.5i | − | 0.951724i | −0.879520 | − | 0.475862i | \(-0.842136\pi\) | ||
0.879520 | − | 0.475862i | \(-0.157864\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 3345.06i | − | 0.227035i | −0.993536 | − | 0.113517i | \(-0.963788\pi\) | ||
0.993536 | − | 0.113517i | \(-0.0362117\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6368.69 | −0.430105 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2304.57 | −0.154866 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25460.4 | 1.70248 | 0.851239 | − | 0.524778i | \(-0.175852\pi\) | ||||
0.851239 | + | 0.524778i | \(0.175852\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1382.69 | + | 3334.94i | 0.0920022 | + | 0.221902i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9773.00 | 0.647092 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 8938.60i | − | 0.588950i | −0.955659 | − | 0.294475i | \(-0.904855\pi\) | ||
0.955659 | − | 0.294475i | \(-0.0951448\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3794.65 | −0.248805 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5770.64 | −0.376527 | −0.188264 | − | 0.982119i | \(-0.560286\pi\) | ||||
−0.188264 | + | 0.982119i | \(0.560286\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6297.57i | 0.408918i | 0.978875 | + | 0.204459i | \(0.0655436\pi\) | ||||
−0.978875 | + | 0.204459i | \(0.934456\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −20.1797 | −0.00130400 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 19482.7 | − | 8077.65i | 1.25290 | − | 0.519461i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8881.97 | 0.568446 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7601.18 | 0.484150 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −29892.4 | −1.89489 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9060.26i | 0.571606i | 0.958288 | + | 0.285803i | \(0.0922603\pi\) | ||||
−0.958288 | + | 0.285803i | \(0.907740\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7302.63i | 0.458536i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1483.62i | 0.0927178i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6428.77 | + | 6437.41i | −0.399870 | + | 0.400407i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8978.89i | 0.555868i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9635.66 | −0.593737 | −0.296869 | − | 0.954918i | \(-0.595942\pi\) | ||||
−0.296869 | + | 0.954918i | \(0.595942\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22309.6i | 1.36828i | 0.729351 | + | 0.684140i | \(0.239822\pi\) | ||||
−0.729351 | + | 0.684140i | \(0.760178\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 423.077i | − | 0.0258274i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8248.87 | −0.501231 | −0.250616 | − | 0.968087i | \(-0.580633\pi\) | ||||
−0.250616 | + | 0.968087i | \(0.580633\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20341.4i | 1.23031i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8491.91 | + | 3520.80i | −0.511251 | + | 0.211968i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13530.5i | 0.810859i | 0.914126 | + | 0.405429i | \(0.132878\pi\) | ||||
−0.914126 | + | 0.405429i | \(0.867122\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3188.44i | 0.190202i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11025.4i | 0.654709i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15900.8 | −0.939917 | −0.469959 | − | 0.882689i | \(-0.655731\pi\) | ||||
−0.469959 | + | 0.882689i | \(0.655731\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15518.3 | −0.913152 | −0.456576 | − | 0.889684i | \(-0.650924\pi\) | ||||
−0.456576 | + | 0.889684i | \(0.650924\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6102.56 | −0.357472 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4373.24 | + | 1813.17i | −0.255018 | + | 0.105732i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 48.5641 | 0.00281921 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2549.73i | 0.147352i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19326.2 | −1.11189 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8192.08 | 0.469215 | 0.234607 | − | 0.972090i | \(-0.424620\pi\) | ||||
0.234607 | + | 0.972090i | \(0.424620\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2863.68i | 0.163293i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17289.6 | 0.981524 | 0.490762 | − | 0.871294i | \(-0.336718\pi\) | ||||
0.490762 | + | 0.871294i | \(0.336718\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12484.8 | − | 5176.29i | 0.705631 | − | 0.292560i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6861.76 | 0.386113 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31297.3 | −1.75338 | −0.876689 | − | 0.481058i | \(-0.840253\pi\) | ||||
−0.876689 | + | 0.481058i | \(0.840253\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1274.29 | −0.0710774 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6789.63i | 0.377060i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 15596.6i | − | 0.862385i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32710.9i | 1.80084i | 0.435021 | + | 0.900420i | \(0.356741\pi\) | ||||
−0.435021 | + | 0.900420i | \(0.643259\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2753.62 | − | 6641.53i | −0.150940 | − | 0.364056i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7044.00i | 0.384452i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22291.3 | 1.21140 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 18933.6i | − | 1.02451i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 4111.40i | − | 0.221520i | −0.993847 | − | 0.110760i | \(-0.964672\pi\) | ||
0.993847 | − | 0.110760i | \(-0.0353285\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22895.3 | −1.22832 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 4810.31i | − | 0.256974i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2223.96 | − | 5364.01i | −0.118303 | − | 0.285339i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 23791.2i | − | 1.26022i | −0.776506 | − | 0.630110i | \(-0.783010\pi\) | ||
0.776506 | − | 0.630110i | \(-0.216990\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 1445.99i | − | 0.0762710i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 123.661i | 0.00649529i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4978.85 | 0.260417 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6249.18 | 0.325495 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 706.487 | 0.0366447 | 0.0183223 | − | 0.999832i | \(-0.494167\pi\) | ||||
0.0183223 | + | 0.999832i | \(0.494167\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1005.11 | + | 2424.26i | 0.0519174 | + | 0.125221i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7462.68 | −0.383873 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 6891.68i | − | 0.353035i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24189.9 | −1.23405 | −0.617024 | − | 0.786944i | \(-0.711662\pi\) | ||||
−0.617024 | + | 0.786944i | \(0.711662\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2485.33i | 0.125750i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23762.4 | 1.19739 | 0.598693 | − | 0.800979i | \(-0.295687\pi\) | ||||
0.598693 | + | 0.800979i | \(0.295687\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3168.52 | + | 3164.27i | 0.159010 | + | 0.158797i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −30523.3 | −1.52556 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22183.4 | −1.10424 | −0.552119 | − | 0.833766i | \(-0.686180\pi\) | ||||
−0.552119 | + | 0.833766i | \(0.686180\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4674.10 | −0.231724 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 22419.7i | − | 1.10700i | −0.832851 | − | 0.553498i | \(-0.813293\pi\) | ||
0.832851 | − | 0.553498i | \(-0.186707\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 6114.72i | − | 0.300706i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9008.74i | 0.441249i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6814.02 | − | 16434.9i | −0.332415 | − | 0.801760i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4193.10i | 0.203739i | 0.994798 | + | 0.101870i | \(0.0324825\pi\) | ||||
−0.994798 | + | 0.101870i | \(0.967518\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 23194.3 | 1.12251 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 2019.05i | − | 0.0973256i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37722.4i | 1.81115i | 0.424181 | + | 0.905577i | \(0.360562\pi\) | ||||
−0.424181 | + | 0.905577i | \(0.639438\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −96.7154 | −0.00462523 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26381.1i | 1.25666i | 0.777948 | + | 0.628328i | \(0.216261\pi\) | ||||
−0.777948 | + | 0.628328i | \(0.783739\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17867.6 | − | 7408.03i | 0.847773 | − | 0.351492i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3003.71i | 0.141960i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 12508.3i | − | 0.588851i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11955.6i | 0.560637i | 0.959907 | + | 0.280318i | \(0.0904400\pi\) | ||||
−0.959907 | + | 0.280318i | \(0.909560\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1547.41 | 0.0722810 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11231.8 | 0.522614 | 0.261307 | − | 0.965256i | \(-0.415847\pi\) | ||||
0.261307 | + | 0.965256i | \(0.415847\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17548.6 | 0.813374 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8294.10 | + | 20004.8i | 0.382946 | + | 0.923638i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17073.5 | 0.785264 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 43033.2i | 1.97164i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1754.40 | 0.0800730 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16367.4 | −0.744177 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28526.7i | 1.29208i | 0.763303 | + | 0.646041i | \(0.223576\pi\) | ||||
−0.763303 | + | 0.646041i | \(0.776424\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8072.45 | 0.364242 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −325.907 | − | 786.064i | −0.0146497 | − | 0.0353340i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11884.0 | 0.532174 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7676.71 | −0.342472 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20195.5 | −0.897568 | −0.448784 | − | 0.893640i | \(-0.648143\pi\) | ||||
−0.448784 | + | 0.893640i | \(0.648143\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28257.7i | 1.25117i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 10249.2i | − | 0.452106i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 52841.7i | 2.32222i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 55.6439 | − | 23.0703i | 0.00243626 | − | 0.00101009i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 876.880i | − | 0.0382499i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20974.4 | −0.911521 | −0.455760 | − | 0.890102i | \(-0.650633\pi\) | ||||
−0.455760 | + | 0.890102i | \(0.650633\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 33677.8i | − | 1.45818i | −0.684416 | − | 0.729092i | \(-0.739943\pi\) | ||
0.684416 | − | 0.729092i | \(-0.260057\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 8840.78i | − | 0.381377i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7958.37 | 0.342048 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1903.58i | 0.0815149i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1693.25 | + | 4083.99i | 0.0722430 | + | 0.174245i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 12454.1i | − | 0.529418i | −0.964328 | − | 0.264709i | \(-0.914724\pi\) | ||
0.964328 | − | 0.264709i | \(-0.0852760\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 27909.6i | − | 1.18210i | −0.806635 | − | 0.591050i | \(-0.798714\pi\) | ||
0.806635 | − | 0.591050i | \(-0.201286\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13724.8i | 0.579194i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7350.79 | 0.309083 | 0.154542 | − | 0.987986i | \(-0.450610\pi\) | ||||
0.154542 | + | 0.987986i | \(0.450610\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13101.8 | −0.548905 | −0.274453 | − | 0.961601i | \(-0.588497\pi\) | ||||
−0.274453 | + | 0.961601i | \(0.588497\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6176.64 | −0.257840 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18613.2 | − | 18588.2i | −0.774200 | − | 0.773162i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1639.96 | −0.0679679 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4467.31i | 0.184484i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21819.6 | 0.897850 | 0.448925 | − | 0.893569i | \(-0.351807\pi\) | ||||
0.448925 | + | 0.893569i | \(0.351807\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20166.9 | 0.826885 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 16275.4i | − | 0.664953i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6499.23 | 0.264592 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3756.33 | − | 9059.99i | −0.152384 | − | 0.367538i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10710.4 | 0.432955 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 291.314 | 0.0117346 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34494.6 | −1.38461 | −0.692306 | − | 0.721604i | \(-0.743405\pi\) | ||||
−0.692306 | + | 0.721604i | \(0.743405\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2300.61i | 0.0920226i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 41632.1i | − | 1.65942i | −0.558191 | − | 0.829712i | \(-0.688505\pi\) | ||
0.558191 | − | 0.829712i | \(-0.311495\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5117.73i | 0.203277i | 0.994821 | + | 0.101638i | \(0.0324084\pi\) | ||||
−0.994821 | + | 0.101638i | \(0.967592\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6185.08 | − | 14917.9i | −0.244816 | − | 0.590479i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 16578.1i | − | 0.653913i | −0.945039 | − | 0.326956i | \(-0.893977\pi\) | ||
0.945039 | − | 0.326956i | \(-0.106023\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14747.7 | −0.579697 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 2906.01i | − | 0.113833i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 6930.18i | − | 0.270530i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18769.3 | 0.730165 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 6567.85i | − | 0.254625i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7132.34 | − | 17202.7i | −0.275562 | − | 0.664636i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 11830.6i | − | 0.455521i | −0.973717 | − | 0.227760i | \(-0.926860\pi\) | ||
0.973717 | − | 0.227760i | \(-0.0731403\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5827.50i | 0.223614i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 37236.4i | − | 1.42398i | −0.702190 | − | 0.711989i | \(-0.747794\pi\) | ||
0.702190 | − | 0.711989i | \(-0.252206\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7687.64 | 0.292989 | 0.146495 | − | 0.989211i | \(-0.453201\pi\) | ||||
0.146495 | + | 0.989211i | \(0.453201\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6156.65 | −0.233846 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −830.437 | −0.0314356 | −0.0157178 | − | 0.999876i | \(-0.505003\pi\) | ||||
−0.0157178 | + | 0.999876i | \(0.505003\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5832.58 | + | 2418.23i | −0.220043 | + | 0.0912315i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3493.88 | −0.131369 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 21643.3i | 0.811047i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1419.48 | 0.0530144 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 59.4720 | 0.00221373 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 10750.9i | − | 0.398848i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 45096.2 | 1.66745 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1663.25 | − | 689.594i | 0.0612951 | − | 0.0254133i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7185.01 | −0.263909 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30689.8 | 1.12353 | 0.561763 | − | 0.827298i | \(-0.310123\pi\) | ||||
0.561763 | + | 0.827298i | \(0.310123\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2821.83 | −0.102964 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 8924.46i | − | 0.324567i | −0.986744 | − | 0.162284i | \(-0.948114\pi\) | ||
0.986744 | − | 0.162284i | \(-0.0518859\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 43176.3i | 1.56509i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 5849.37i | − | 0.211338i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12534.7 | + | 5196.98i | −0.451399 | + | 0.187153i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 18566.2i | − | 0.666422i | −0.942852 | − | 0.333211i | \(-0.891868\pi\) | ||
0.942852 | − | 0.333211i | \(-0.108132\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2299.10 | −0.0822560 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 26461.9i | − | 0.943666i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 41340.0i | − | 1.46946i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1275.32 | 0.0451856 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 4047.86i | − | 0.142956i | −0.997442 | − | 0.0714779i | \(-0.977228\pi\) | ||
0.997442 | − | 0.0714779i | \(-0.0227716\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14256.3 | − | 14237.2i | −0.501859 | − | 0.501186i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 20199.7i | 0.708797i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14395.9i | 0.503525i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 28211.1i | − | 0.983581i | −0.870713 | − | 0.491791i | \(-0.836343\pi\) | ||
0.870713 | − | 0.491791i | \(-0.163657\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 22883.0 | 0.795269 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 43313.0 | 1.50049 | 0.750247 | − | 0.661158i | \(-0.229935\pi\) | ||||
0.750247 | + | 0.661158i | \(0.229935\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −217.238 | −0.00750186 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2010.16 | − | 833.426i | 0.0691963 | − | 0.0286892i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36121.7 | −1.23949 | −0.619745 | − | 0.784804i | \(-0.712764\pi\) | ||||
−0.619745 | + | 0.784804i | \(0.712764\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 32493.3i | − | 1.11146i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24731.4 | 0.843292 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36180.3 | 1.22979 | 0.614897 | − | 0.788607i | \(-0.289198\pi\) | ||||
0.614897 | + | 0.788607i | \(0.289198\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 7669.60i | − | 0.259877i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8408.32 | 0.284015 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2077.02 | − | 5009.62i | −0.0699379 | − | 0.168685i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2415.37 | −0.0810770 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8645.85 | −0.289313 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −18944.2 | −0.631953 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3564.98i | 0.118554i | 0.998242 | + | 0.0592772i | \(0.0188796\pi\) | ||||
−0.998242 | + | 0.0592772i | \(0.981120\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 13514.7i | − | 0.448046i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 11726.3i | − | 0.387555i | −0.981046 | − | 0.193777i | \(-0.937926\pi\) | ||
0.981046 | − | 0.193777i | \(-0.0620739\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −27692.2 | + | 11481.4i | −0.912405 | + | 0.378289i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 8439.61i | − | 0.277214i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43817.1 | −1.43483 | −0.717416 | − | 0.696645i | \(-0.754676\pi\) | ||||
−0.717416 | + | 0.696645i | \(0.754676\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 49121.3i | − | 1.60360i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 9399.54i | − | 0.305917i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −36423.2 | −1.18181 | −0.590906 | − | 0.806741i | \(-0.701230\pi\) | ||||
−0.590906 | + | 0.806741i | \(0.701230\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 6395.89i | − | 0.206893i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 18910.8 | − | 7840.55i | 0.609866 | − | 0.252855i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 24.2206i | − | 0.000778736i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17147.5i | 0.549656i | 0.961493 | + | 0.274828i | \(0.0886209\pi\) | ||||
−0.961493 | + | 0.274828i | \(0.911379\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 3400.71i | − | 0.108679i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12240.7 | 0.390007 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37323.2 | 1.18560 | 0.592798 | − | 0.805351i | \(-0.298023\pi\) | ||||
0.592798 | + | 0.805351i | \(0.298023\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10523.8 | 0.333292 |
(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.a.223.11 | yes | 16 | |
4.3 | odd | 2 | inner | 1344.4.p.a.223.4 | yes | 16 | |
7.6 | odd | 2 | 1344.4.p.b.223.6 | yes | 16 | ||
8.3 | odd | 2 | 1344.4.p.b.223.14 | yes | 16 | ||
8.5 | even | 2 | 1344.4.p.b.223.5 | yes | 16 | ||
28.27 | even | 2 | 1344.4.p.b.223.13 | yes | 16 | ||
56.13 | odd | 2 | inner | 1344.4.p.a.223.12 | yes | 16 | |
56.27 | even | 2 | inner | 1344.4.p.a.223.3 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.4.p.a.223.3 | ✓ | 16 | 56.27 | even | 2 | inner | |
1344.4.p.a.223.4 | yes | 16 | 4.3 | odd | 2 | inner | |
1344.4.p.a.223.11 | yes | 16 | 1.1 | even | 1 | trivial | |
1344.4.p.a.223.12 | yes | 16 | 56.13 | odd | 2 | inner | |
1344.4.p.b.223.5 | yes | 16 | 8.5 | even | 2 | ||
1344.4.p.b.223.6 | yes | 16 | 7.6 | odd | 2 | ||
1344.4.p.b.223.13 | yes | 16 | 28.27 | even | 2 | ||
1344.4.p.b.223.14 | yes | 16 | 8.3 | odd | 2 |