Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1176,4,Mod(1,1176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1176, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1176.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1176.a (trivial) |
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: | yes |
Analytic conductor: | \(69.3862461668\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 152x^{2} - 177x + 2922 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3}\cdot 7 \) |
Twist minimal: | no (minimal twist has level 168) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.92665\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1176.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −15.8130 | −1.41435 | −0.707177 | − | 0.707037i | \(-0.750031\pi\) | ||||
−0.707177 | + | 0.707037i | \(0.750031\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −30.2479 | −0.829099 | −0.414550 | − | 0.910027i | \(-0.636061\pi\) | ||||
−0.414550 | + | 0.910027i | \(0.636061\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −61.6298 | −1.31485 | −0.657424 | − | 0.753521i | \(-0.728354\pi\) | ||||
−0.657424 | + | 0.753521i | \(0.728354\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −47.4389 | −0.816577 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 56.1448 | 0.801007 | 0.400503 | − | 0.916295i | \(-0.368835\pi\) | ||||
0.400503 | + | 0.916295i | \(0.368835\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −139.400 | −1.68319 | −0.841596 | − | 0.540107i | \(-0.818384\pi\) | ||||
−0.841596 | + | 0.540107i | \(0.818384\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.14480 | −0.0738395 | −0.0369197 | − | 0.999318i | \(-0.511755\pi\) | ||||
−0.0369197 | + | 0.999318i | \(0.511755\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 125.049 | 1.00040 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.217857 | −0.00139500 | −0.000697500 | − | 1.00000i | \(-0.500222\pi\) | ||||
−0.000697500 | 1.00000i | \(0.500222\pi\) | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 176.581 | 1.02306 | 0.511529 | − | 0.859266i | \(-0.329079\pi\) | ||||
0.511529 | + | 0.859266i | \(0.329079\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −90.7438 | −0.478681 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 211.080 | 0.937874 | 0.468937 | − | 0.883232i | \(-0.344637\pi\) | ||||
0.468937 | + | 0.883232i | \(0.344637\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −184.889 | −0.759128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −293.305 | −1.11723 | −0.558616 | − | 0.829427i | \(-0.688667\pi\) | ||||
−0.558616 | + | 0.829427i | \(0.688667\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 434.591 | 1.54127 | 0.770634 | − | 0.637278i | \(-0.219940\pi\) | ||||
0.770634 | + | 0.637278i | \(0.219940\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −142.317 | −0.471451 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 483.396 | 1.50022 | 0.750112 | − | 0.661311i | \(-0.230000\pi\) | ||||
0.750112 | + | 0.661311i | \(0.230000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 168.434 | 0.462461 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 20.5073 | 0.0531489 | 0.0265745 | − | 0.999647i | \(-0.491540\pi\) | ||||
0.0265745 | + | 0.999647i | \(0.491540\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 478.309 | 1.17264 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −418.201 | −0.971792 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −231.348 | −0.510490 | −0.255245 | − | 0.966876i | \(-0.582156\pi\) | ||||
−0.255245 | + | 0.966876i | \(0.582156\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −838.701 | −1.76041 | −0.880203 | − | 0.474598i | \(-0.842593\pi\) | ||||
−0.880203 | + | 0.474598i | \(0.842593\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 974.549 | 1.85966 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −624.040 | −1.13789 | −0.568945 | − | 0.822375i | \(-0.692648\pi\) | ||||
−0.568945 | + | 0.822375i | \(0.692648\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −24.4344 | −0.0426312 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 227.106 | 0.379613 | 0.189806 | − | 0.981822i | \(-0.439214\pi\) | ||||
0.189806 | + | 0.981822i | \(0.439214\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 43.0494 | 0.0690213 | 0.0345107 | − | 0.999404i | \(-0.489013\pi\) | ||||
0.0345107 | + | 0.999404i | \(0.489013\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 375.148 | 0.577579 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −309.060 | −0.440152 | −0.220076 | − | 0.975483i | \(-0.570630\pi\) | ||||
−0.220076 | + | 0.975483i | \(0.570630\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1233.99 | 1.63190 | 0.815951 | − | 0.578122i | \(-0.196214\pi\) | ||||
0.815951 | + | 0.578122i | \(0.196214\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −887.815 | −1.13291 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.653571 | −0.000805404 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1144.36 | 1.36294 | 0.681470 | − | 0.731846i | \(-0.261341\pi\) | ||||
0.681470 | + | 0.731846i | \(0.261341\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 529.742 | 0.590663 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2204.33 | 2.38063 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1688.12 | 1.76704 | 0.883520 | − | 0.468394i | \(-0.155167\pi\) | ||||
0.883520 | + | 0.468394i | \(0.155167\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −272.231 | −0.276366 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1487.86 | −1.46582 | −0.732909 | − | 0.680327i | \(-0.761838\pi\) | ||||
−0.732909 | + | 0.680327i | \(0.761838\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −778.408 | −0.744648 | −0.372324 | − | 0.928103i | \(-0.621439\pi\) | ||||
−0.372324 | + | 0.928103i | \(0.621439\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1302.08 | 1.17642 | 0.588209 | − | 0.808709i | \(-0.299833\pi\) | ||||
0.588209 | + | 0.808709i | \(0.299833\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 469.082 | 0.412201 | 0.206100 | − | 0.978531i | \(-0.433923\pi\) | ||||
0.206100 | + | 0.978531i | \(0.433923\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 633.240 | 0.541482 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1653.86 | 1.37684 | 0.688418 | − | 0.725314i | \(-0.258306\pi\) | ||||
0.688418 | + | 0.725314i | \(0.258306\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 128.793 | 0.104435 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −554.668 | −0.438283 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −416.063 | −0.312594 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −879.914 | −0.645034 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.781685 | −0.000559328 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 163.760 | 0.114420 | 0.0572100 | − | 0.998362i | \(-0.481780\pi\) | ||||
0.0572100 | + | 0.998362i | \(0.481780\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1303.77 | 0.889851 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −521.894 | −0.348077 | −0.174038 | − | 0.984739i | \(-0.555682\pi\) | ||||
−0.174038 | + | 0.984739i | \(0.555682\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −426.950 | −0.272192 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2676.89 | 1.66936 | 0.834679 | − | 0.550736i | \(-0.185653\pi\) | ||||
0.834679 | + | 0.550736i | \(0.185653\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 853.692 | 0.520930 | 0.260465 | − | 0.965483i | \(-0.416124\pi\) | ||||
0.260465 | + | 0.965483i | \(0.416124\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1450.19 | 0.866154 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1864.17 | 1.09014 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.44496 | 0.00197302 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 557.686 | 0.306627 | 0.153313 | − | 0.988178i | \(-0.451006\pi\) | ||||
0.153313 | + | 0.988178i | \(0.451006\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1769.35 | 0.953560 | 0.476780 | − | 0.879023i | \(-0.341804\pi\) | ||||
0.476780 | + | 0.879023i | \(0.341804\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 505.303 | 0.267002 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2792.26 | −1.44697 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2404.89 | −1.22249 | −0.611247 | − | 0.791440i | \(-0.709332\pi\) | ||||
−0.611247 | + | 0.791440i | \(0.709332\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 61.5219 | 0.0306855 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3378.79 | 1.62360 | 0.811802 | − | 0.583932i | \(-0.198487\pi\) | ||||
0.811802 | + | 0.583932i | \(0.198487\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1434.93 | 0.677024 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −805.900 | −0.373428 | −0.186714 | − | 0.982414i | \(-0.559784\pi\) | ||||
−0.186714 | + | 0.982414i | \(0.559784\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1601.23 | 0.728826 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1254.60 | −0.561064 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −840.504 | −0.369378 | −0.184689 | − | 0.982797i | \(-0.559128\pi\) | ||||
−0.184689 | + | 0.982797i | \(0.559128\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −694.043 | −0.294731 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1604.61 | 0.670024 | 0.335012 | − | 0.942214i | \(-0.391260\pi\) | ||||
0.335012 | + | 0.942214i | \(0.391260\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3779.43 | −1.55206 | −0.776029 | − | 0.630697i | \(-0.782769\pi\) | ||||
−0.776029 | + | 0.630697i | \(0.782769\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2516.10 | −1.01637 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3337.80 | −1.32649 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1698.26 | −0.664114 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1849.60 | −0.700691 | −0.350346 | − | 0.936621i | \(-0.613936\pi\) | ||||
−0.350346 | + | 0.936621i | \(0.613936\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −353.003 | −0.131656 | −0.0658282 | − | 0.997831i | \(-0.520969\pi\) | ||||
−0.0658282 | + | 0.997831i | \(0.520969\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2923.65 | 1.07368 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4448.22 | 1.60874 | 0.804372 | − | 0.594125i | \(-0.202502\pi\) | ||||
0.804372 | + | 0.594125i | \(0.202502\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2240.15 | −0.797991 | −0.398995 | − | 0.916953i | \(-0.630641\pi\) | ||||
−0.398995 | + | 0.916953i | \(0.630641\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1872.12 | −0.656961 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4638.01 | 1.58016 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −73.3032 | −0.0246132 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4216.58 | 1.39553 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1224.34 | 0.399463 | 0.199732 | − | 0.979851i | \(-0.435993\pi\) | ||||
0.199732 | + | 0.979851i | \(0.435993\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 681.318 | 0.219170 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6872.17 | −2.17990 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 129.148 | 0.0398495 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3460.19 | −1.05320 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3457.37 | −1.03822 | −0.519108 | − | 0.854708i | \(-0.673736\pi\) | ||||
−0.519108 | + | 0.854708i | \(0.673736\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1125.44 | 0.333465 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5178.22 | −1.51405 | −0.757027 | − | 0.653383i | \(-0.773349\pi\) | ||||
−0.757027 | + | 0.653383i | \(0.773349\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2311.88 | 0.667134 | 0.333567 | − | 0.942726i | \(-0.391748\pi\) | ||||
0.333567 | + | 0.942726i | \(0.391748\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4742.97 | 1.33357 | 0.666787 | − | 0.745249i | \(-0.267669\pi\) | ||||
0.666787 | + | 0.745249i | \(0.267669\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7643.91 | −2.12185 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −927.181 | −0.254122 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1412.59 | −0.382313 | −0.191157 | − | 0.981560i | \(-0.561224\pi\) | ||||
−0.191157 | + | 0.981560i | \(0.561224\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1881.15 | −0.502804 | −0.251402 | − | 0.967883i | \(-0.580892\pi\) | ||||
−0.251402 | + | 0.967883i | \(0.580892\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8591.22 | 2.21314 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3701.96 | 0.942179 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4519.64 | 1.13656 | 0.568281 | − | 0.822834i | \(-0.307609\pi\) | ||||
0.568281 | + | 0.822834i | \(0.307609\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 246.363 | 0.0612202 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2663.44 | −0.654084 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7912.65 | 1.92054 | 0.960268 | − | 0.279079i | \(-0.0900291\pi\) | ||||
0.960268 | + | 0.279079i | \(0.0900291\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.96071 | −0.000465000 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3431.16 | −0.804466 | −0.402233 | − | 0.915537i | \(-0.631766\pi\) | ||||
−0.402233 | + | 0.915537i | \(0.631766\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −324.281 | −0.0751714 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3433.07 | 0.786894 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8299.19 | 1.88108 | 0.940540 | − | 0.339682i | \(-0.110319\pi\) | ||||
0.940540 | + | 0.339682i | \(0.110319\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5924.49 | −1.32800 | −0.663998 | − | 0.747734i | \(-0.731142\pi\) | ||||
−0.663998 | + | 0.747734i | \(0.731142\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3782.49 | −0.829427 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1520.60 | 0.329834 | 0.164917 | − | 0.986307i | \(-0.447264\pi\) | ||||
0.164917 | + | 0.986307i | \(0.447264\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1589.22 | 0.341019 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −352.333 | −0.0747986 | −0.0373993 | − | 0.999300i | \(-0.511907\pi\) | ||||
−0.0373993 | + | 0.999300i | \(0.511907\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4288.49 | 0.900792 | 0.450396 | − | 0.892829i | \(-0.351283\pi\) | ||||
0.450396 | + | 0.892829i | \(0.351283\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6613.00 | 1.37446 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1760.76 | −0.358388 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5064.37 | 1.02020 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2661.99 | 0.530767 | 0.265384 | − | 0.964143i | \(-0.414501\pi\) | ||||
0.265384 | + | 0.964143i | \(0.414501\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3658.29 | 0.722013 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −816.694 | −0.159560 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 501.962 | 0.0970877 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4463.58 | −0.846290 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13262.3 | 2.48983 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 145.970 | 0.0271366 | 0.0135683 | − | 0.999908i | \(-0.495681\pi\) | ||||
0.0135683 | + | 0.999908i | \(0.495681\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2335.22 | −0.429923 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3416.51 | 0.622935 | 0.311467 | − | 0.950257i | \(-0.399180\pi\) | ||||
0.311467 | + | 0.950257i | \(0.399180\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3682.35 | 0.664980 | 0.332490 | − | 0.943107i | \(-0.392111\pi\) | ||||
0.332490 | + | 0.943107i | \(0.392111\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1376.78 | −0.243936 | −0.121968 | − | 0.992534i | \(-0.538920\pi\) | ||||
−0.121968 | + | 0.992534i | \(0.538920\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.58972 | 0.00115659 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3906.24 | 0.679205 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7826.61 | −1.34825 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7706.77 | −1.31537 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1407.24 | 0.237984 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2174.93 | 0.361163 | 0.180581 | − | 0.983560i | \(-0.442202\pi\) | ||||
0.180581 | + | 0.983560i | \(0.442202\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1899.72 | 0.312625 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9867.92 | 1.60938 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6321.14 | −1.02176 | −0.510882 | − | 0.859651i | \(-0.670681\pi\) | ||||
−0.510882 | + | 0.859651i | \(0.670681\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4961.59 | 0.794916 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5341.20 | −0.848217 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 386.380 | 0.0602956 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11624.4 | −1.79836 | −0.899181 | − | 0.437577i | \(-0.855837\pi\) | ||||
−0.899181 | + | 0.437577i | \(0.855837\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9841.79 | −1.50951 | −0.754755 | − | 0.656007i | \(-0.772244\pi\) | ||||
−0.754755 | + | 0.656007i | \(0.772244\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1664.00 | −0.253043 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4531.88 | 0.683308 | 0.341654 | − | 0.939826i | \(-0.389013\pi\) | ||||
0.341654 | + | 0.939826i | \(0.389013\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3591.22 | −0.536907 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2280.10 | −0.335207 | −0.167603 | − | 0.985855i | \(-0.553603\pi\) | ||||
−0.167603 | + | 0.985855i | \(0.553603\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12573.5 | 1.83314 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1248.19 | −0.180476 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −680.739 | −0.0976205 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6337.51 | 0.901404 | 0.450702 | − | 0.892674i | \(-0.351174\pi\) | ||||
0.450702 | + | 0.892674i | \(0.351174\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2639.74 | −0.372410 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3624.96 | −0.503199 | −0.251600 | − | 0.967831i | \(-0.580957\pi\) | ||||
−0.251600 | + | 0.967831i | \(0.580957\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.34506 | −0.000322928 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.4265 | 0.00183421 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 268.622 | 0.0364068 | 0.0182034 | − | 0.999834i | \(-0.494205\pi\) | ||||
0.0182034 | + | 0.999834i | \(0.494205\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 491.280 | 0.0660604 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2137.39 | −0.285158 | −0.142579 | − | 0.989783i | \(-0.545540\pi\) | ||||
−0.142579 | + | 0.989783i | \(0.545540\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3911.32 | 0.513756 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1463.23 | 0.190717 | 0.0953583 | − | 0.995443i | \(-0.469600\pi\) | ||||
0.0953583 | + | 0.995443i | \(0.469600\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −457.288 | −0.0591459 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1565.68 | −0.200962 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4887.15 | 0.622530 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1237.44 | −0.156436 | −0.0782180 | − | 0.996936i | \(-0.524923\pi\) | ||||
−0.0782180 | + | 0.996936i | \(0.524923\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6179.89 | −0.769598 | −0.384799 | − | 0.923000i | \(-0.625729\pi\) | ||||
−0.384799 | + | 0.923000i | \(0.625729\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10882.6 | −1.34517 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1280.85 | −0.157150 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6384.73 | −0.777591 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2254.98 | −0.272620 | −0.136310 | − | 0.990666i | \(-0.543524\pi\) | ||||
−0.136310 | + | 0.990666i | \(0.543524\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8030.67 | 0.963805 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −19513.0 | −2.30808 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2561.08 | 0.300759 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1404.53 | −0.163761 | −0.0818806 | − | 0.996642i | \(-0.526093\pi\) | ||||
−0.0818806 | + | 0.996642i | \(0.526093\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13068.1 | 1.51283 | 0.756414 | − | 0.654094i | \(-0.226950\pi\) | ||||
0.756414 | + | 0.654094i | \(0.226950\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4350.56 | 0.500074 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7020.88 | 0.801323 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5592.52 | 0.629392 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5362.79 | −0.599342 | −0.299671 | − | 0.954043i | \(-0.596877\pi\) | ||||
−0.299671 | + | 0.954043i | \(0.596877\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2495.82 | −0.277001 | −0.138501 | − | 0.990362i | \(-0.544228\pi\) | ||||
−0.138501 | + | 0.990362i | \(0.544228\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.3349 | 0.00113913 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1135.39 | 0.124286 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3762.12 | 0.409012 | 0.204506 | − | 0.978865i | \(-0.434441\pi\) | ||||
0.204506 | + | 0.978865i | \(0.434441\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11445.3 | 1.22750 | 0.613748 | − | 0.789502i | \(-0.289661\pi\) | ||||
0.613748 | + | 0.789502i | \(0.289661\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18095.7 | −1.92768 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1673.06 | 0.177031 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9420.02 | −0.990107 | −0.495054 | − | 0.868862i | \(-0.664852\pi\) | ||||
−0.495054 | + | 0.868862i | \(0.664852\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8871.85 | 0.926296 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5308.05 | 0.550538 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11464.0 | 1.17344 | 0.586719 | − | 0.809790i | \(-0.300419\pi\) | ||||
0.586719 | + | 0.809790i | \(0.300419\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1515.91 | 0.154154 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9751.10 | −0.985149 | −0.492575 | − | 0.870270i | \(-0.663944\pi\) | ||||
−0.492575 | + | 0.870270i | \(0.663944\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2182.03 | 0.219023 | 0.109512 | − | 0.993986i | \(-0.465071\pi\) | ||||
0.109512 | + | 0.993986i | \(0.465071\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8376.78 | −0.835406 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3196.34 | 0.316722 | 0.158361 | − | 0.987381i | \(-0.449379\pi\) | ||||
0.158361 | + | 0.987381i | \(0.449379\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7214.68 | −0.705807 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13145.5 | −1.27786 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17432.0 | −1.68386 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 184.566 | 0.0177163 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12143.6 | −1.15836 | −0.579180 | − | 0.815200i | \(-0.696627\pi\) | ||||
−0.579180 | + | 0.815200i | \(0.696627\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13008.8 | −1.23316 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −26694.2 | −2.49922 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20302.5 | −1.88910 | −0.944551 | − | 0.328364i | \(-0.893503\pi\) | ||||
−0.944551 | + | 0.328364i | \(0.893503\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10136.4 | 0.937389 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2562.41 | 0.235519 | 0.117760 | − | 0.993042i | \(-0.462429\pi\) | ||||
0.117760 | + | 0.993042i | \(0.462429\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.2315 | −0.00111740 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4304.78 | 0.390880 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11656.1 | −1.04569 | −0.522844 | − | 0.852428i | \(-0.675129\pi\) | ||||
−0.522844 | + | 0.852428i | \(0.675129\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2417.70 | −0.215598 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18532.8 | −1.64281 | −0.821407 | − | 0.570342i | \(-0.806811\pi\) | ||||
−0.821407 | + | 0.570342i | \(0.806811\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23527.5 | 2.07318 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4803.69 | 0.420788 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18732.1 | 1.63121 | 0.815605 | − | 0.578609i | \(-0.196404\pi\) | ||||
0.815605 | + | 0.578609i | \(0.196404\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3763.81 | −0.323931 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12308.9 | 1.05320 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14621.7 | −1.24383 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2521.51 | −0.213260 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3323.25 | −0.279452 | −0.139726 | − | 0.990190i | \(-0.544622\pi\) | ||||
−0.139726 | + | 0.990190i | \(0.544622\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23297.4 | −1.94785 | −0.973925 | − | 0.226869i | \(-0.927151\pi\) | ||||
−0.973925 | + | 0.226869i | \(0.927151\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9914.08 | 0.819476 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12100.7 | −0.994548 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2082.13 | −0.170163 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18076.3 | 1.46899 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −20589.7 | −1.66387 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4813.83 | 0.386838 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9050.01 | 0.719206 | 0.359603 | − | 0.933105i | \(-0.382912\pi\) | ||||
0.359603 | + | 0.933105i | \(0.382912\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11338.3 | −0.896081 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7417.56 | −0.582997 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12316.7 | −0.962749 | −0.481374 | − | 0.876515i | \(-0.659862\pi\) | ||||
−0.481374 | + | 0.876515i | \(0.659862\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7548.31 | −0.586802 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 30.3694 | 0.00234805 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10013.4 | −0.765847 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24904.1 | 1.89447 | 0.947236 | − | 0.320538i | \(-0.103864\pi\) | ||||
0.947236 | + | 0.320538i | \(0.103864\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −26783.8 | −2.02653 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5094.79 | −0.383426 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4146.59 | −0.310405 | −0.155203 | − | 0.987883i | \(-0.549603\pi\) | ||||
−0.155203 | + | 0.987883i | \(0.549603\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −26152.5 | −1.94733 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7297.48 | 0.537656 | 0.268828 | − | 0.963188i | \(-0.413364\pi\) | ||||
0.268828 | + | 0.963188i | \(0.413364\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11564.9 | −0.847593 | −0.423797 | − | 0.905757i | \(-0.639303\pi\) | ||||
−0.423797 | + | 0.905757i | \(0.639303\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5548.79 | −0.404544 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1018.50 | −0.0738687 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9473.45 | 0.683509 | 0.341755 | − | 0.939789i | \(-0.388979\pi\) | ||||
0.341755 | + | 0.939789i | \(0.388979\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1059.01 | −0.0760119 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −620.303 | −0.0440657 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8770.94 | 0.619887 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7336.02 | 0.515826 | 0.257913 | − | 0.966168i | \(-0.416965\pi\) | ||||
0.257913 | + | 0.966168i | \(0.416965\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24615.4 | −1.72200 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13344.7 | 0.928809 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18081.5 | 1.25214 | 0.626068 | − | 0.779768i | \(-0.284663\pi\) | ||||
0.626068 | + | 0.779768i | \(0.284663\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6720.45 | −0.460720 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −192.433 | −0.0131262 | −0.00656310 | − | 0.999978i | \(-0.502089\pi\) | ||||
−0.00656310 | + | 0.999978i | \(0.502089\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5055.76 | −0.343143 | −0.171571 | − | 0.985172i | \(-0.554884\pi\) | ||||
−0.171571 | + | 0.985172i | \(0.554884\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5616.36 | −0.379297 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6579.19 | 0.442119 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20235.7 | 1.35312 | 0.676560 | − | 0.736388i | \(-0.263470\pi\) | ||||
0.676560 | + | 0.736388i | \(0.263470\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −29791.6 | −1.97257 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3840.51 | −0.253045 | −0.126523 | − | 0.991964i | \(-0.540382\pi\) | ||||
−0.126523 | + | 0.991964i | \(0.540382\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13914.0 | 0.912306 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5720.89 | −0.373281 | −0.186641 | − | 0.982428i | \(-0.559760\pi\) | ||||
−0.186641 | + | 0.982428i | \(0.559760\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22940.3 | 1.48957 | 0.744787 | − | 0.667302i | \(-0.232551\pi\) | ||||
0.744787 | + | 0.667302i | \(0.232551\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −219.910 | −0.0142104 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15618.8 | −0.999604 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12649.7 | 0.805712 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11851.0 | 0.751244 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7634.81 | 0.481675 | 0.240837 | − | 0.970565i | \(-0.422578\pi\) | ||||
0.240837 | + | 0.970565i | \(0.422578\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3673.01 | 0.230630 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2589.53 | −0.161830 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2043.95 | 0.126538 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2779.60 | −0.171275 | −0.0856376 | − | 0.996326i | \(-0.527293\pi\) | ||||
−0.0856376 | + | 0.996326i | \(0.527293\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18304.5 | 1.12264 | 0.561322 | − | 0.827598i | \(-0.310293\pi\) | ||||
0.561322 | + | 0.827598i | \(0.310293\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −20616.5 | −1.25856 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6552.53 | 0.398156 | 0.199078 | − | 0.979984i | \(-0.436205\pi\) | ||||
0.199078 | + | 0.979984i | \(0.436205\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6997.78 | 0.423247 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31986.1 | −1.91686 | −0.958432 | − | 0.285322i | \(-0.907900\pi\) | ||||
−0.958432 | + | 0.285322i | \(0.907900\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8252.68 | 0.492304 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 387.445 | 0.0230071 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 517.327 | 0.0305799 | 0.0152900 | − | 0.999883i | \(-0.495133\pi\) | ||||
0.0152900 | + | 0.999883i | \(0.495133\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19656.8 | 1.15667 | 0.578336 | − | 0.815798i | \(-0.303702\pi\) | ||||
0.578336 | + | 0.815798i | \(0.303702\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10380.6 | −0.608067 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.77440 | 0.000103006 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10372.1 | −0.599415 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25369.0 | 1.45955 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25836.1 | 1.47981 | 0.739904 | − | 0.672713i | \(-0.234871\pi\) | ||||
0.739904 | + | 0.672713i | \(0.234871\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3376.33 | 0.192526 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26526.2 | 1.50589 | 0.752944 | − | 0.658085i | \(-0.228633\pi\) | ||||
0.752944 | + | 0.658085i | \(0.228633\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15534.7 | −0.874140 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 33878.8 | 1.89800 | 0.949002 | − | 0.315269i | \(-0.102095\pi\) | ||||
0.949002 | + | 0.315269i | \(0.102095\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −42329.5 | −2.36106 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6935.65 | 0.385170 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1263.86 | −0.0698828 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1001.26 | −0.0551227 | −0.0275614 | − | 0.999620i | \(-0.508774\pi\) | ||||
−0.0275614 | + | 0.999620i | \(0.508774\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13499.4 | −0.736779 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16467.5 | −0.894910 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14228.9 | 0.769939 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7713.38 | 0.415592 | 0.207796 | − | 0.978172i | \(-0.433371\pi\) | ||||
0.207796 | + | 0.978172i | \(0.433371\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −29424.7 | −1.57862 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −22931.7 | −1.22505 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10035.1 | 0.531561 | 0.265781 | − | 0.964034i | \(-0.414370\pi\) | ||||
0.265781 | + | 0.964034i | \(0.414370\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2781.54 | −0.146717 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1438.21 | −0.0755421 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −29478.1 | −1.54184 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4237.77 | −0.220729 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20119.4 | −1.04357 | −0.521785 | − | 0.853077i | \(-0.674734\pi\) | ||||
−0.521785 | + | 0.853077i | \(0.674734\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5643.46 | −0.290294 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −27.2429 | −0.00139555 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7567.09 | −0.386035 | −0.193018 | − | 0.981195i | \(-0.561827\pi\) | ||||
−0.193018 | + | 0.981195i | \(0.561827\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24400.0 | 1.23457 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30800.0 | 1.55201 | 0.776006 | − | 0.630726i | \(-0.217243\pi\) | ||||
0.776006 | + | 0.630726i | \(0.217243\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18875.9 | 0.943424 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13319.3 | −0.663003 | −0.331501 | − | 0.943455i | \(-0.607555\pi\) | ||||
−0.331501 | + | 0.943455i | \(0.607555\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 25773.7 | 1.27776 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10747.7 | −0.530682 | −0.265341 | − | 0.964155i | \(-0.585484\pi\) | ||||
−0.265341 | + | 0.964155i | \(0.585484\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8818.66 | −0.433679 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11105.9 | 0.543967 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12213.4 | 0.593439 | 0.296720 | − | 0.954965i | \(-0.404107\pi\) | ||||
0.296720 | + | 0.954965i | \(0.404107\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13558.9 | 0.656195 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −27978.6 | −1.34867 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30173.2 | −1.44870 | −0.724349 | − | 0.689434i | \(-0.757860\pi\) | ||||
−0.724349 | + | 0.689434i | \(0.757860\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 739.090 | 0.0353455 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15207.3 | 0.724396 | 0.362198 | − | 0.932101i | \(-0.382026\pi\) | ||||
0.362198 | + | 0.932101i | \(0.382026\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7990.33 | −0.377636 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14257.9 | 0.671216 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9368.65 | −0.439327 | −0.219663 | − | 0.975576i | \(-0.570496\pi\) | ||||
−0.219663 | + | 0.975576i | \(0.570496\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23738.0 | 1.10882 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 32516.3 | 1.51298 | 0.756488 | − | 0.654008i | \(-0.226914\pi\) | ||||
0.756488 | + | 0.654008i | \(0.226914\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22081.3 | 1.02346 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 40886.8 | 1.88052 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6869.48 | −0.314737 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.88214 | −0.000268468 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 38028.5 | 1.72904 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −40250.3 | −1.82308 | −0.911542 | − | 0.411207i | \(-0.865107\pi\) | ||||
−0.911542 | + | 0.411207i | \(0.865107\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10293.5 | −0.464458 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 51689.0 | 2.31467 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −972.842 | −0.0434002 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21387.5 | 0.950544 | 0.475272 | − | 0.879839i | \(-0.342350\pi\) | ||||
0.475272 | + | 0.879839i | \(0.342350\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27140.1 | 1.20169 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10299.2 | 0.454313 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1302.16 | −0.0572255 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24897.6 | 1.08604 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19634.1 | −0.853274 | −0.426637 | − | 0.904423i | \(-0.640302\pi\) | ||||
−0.426637 | + | 0.904423i | \(0.640302\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35238.1 | 1.52574 | 0.762872 | − | 0.646549i | \(-0.223789\pi\) | ||||
0.762872 | + | 0.646549i | \(0.223789\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17773.5 | −0.766719 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −53428.7 | −2.29635 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −60582.2 | −2.59425 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7054.80 | −0.299895 | −0.149948 | − | 0.988694i | \(-0.547911\pi\) | ||||
−0.149948 | + | 0.988694i | \(0.547911\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6188.32 | 0.262104 | 0.131052 | − | 0.991376i | \(-0.458165\pi\) | ||||
0.131052 | + | 0.991376i | \(0.458165\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11347.5 | −0.478870 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24000.0 | −1.00915 | −0.504573 | − | 0.863369i | \(-0.668350\pi\) | ||||
−0.504573 | + | 0.863369i | \(0.668350\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8708.86 | −0.364863 | −0.182431 | − | 0.983219i | \(-0.558397\pi\) | ||||
−0.182431 | + | 0.983219i | \(0.558397\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4561.80 | 0.190430 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12743.7 | 0.528158 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4767.67 | 0.196888 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7820.46 | 0.321802 | 0.160901 | − | 0.986971i | \(-0.448560\pi\) | ||||
0.160901 | + | 0.986971i | \(0.448560\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24389.0 | −0.999998 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1057.00 | −0.0431850 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −25320.2 | −1.03082 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12865.5 | 0.520073 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1719.20 | −0.0692521 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31176.8 | 1.25143 | 0.625717 | − | 0.780050i | \(-0.284807\pi\) | ||||
0.625717 | + | 0.780050i | \(0.284807\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 19839.0 | 0.793543 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 895.728 | 0.0357030 | 0.0178515 | − | 0.999841i | \(-0.494317\pi\) | ||||
0.0178515 | + | 0.999841i | \(0.494317\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9115.02 | 0.362049 | 0.181025 | − | 0.983479i | \(-0.442059\pi\) | ||||
0.181025 | + | 0.983479i | \(0.442059\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21126.6 | −0.833325 | −0.416662 | − | 0.909061i | \(-0.636800\pi\) | ||||
−0.416662 | + | 0.909061i | \(0.636800\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13290.8 | 0.522430 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5282.29 | −0.206916 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9348.43 | 0.364930 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38459.5 | 1.49615 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15193.1 | 0.589013 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18749.4 | −0.721920 | −0.360960 | − | 0.932581i | \(-0.617551\pi\) | ||||
−0.360960 | + | 0.932581i | \(0.617551\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7985.96 | 0.306439 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37000.3 | 1.41495 | 0.707475 | − | 0.706739i | \(-0.249834\pi\) | ||||
0.707475 | + | 0.706739i | \(0.249834\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21618.3 | 0.823913 | 0.411956 | − | 0.911204i | \(-0.364846\pi\) | ||||
0.411956 | + | 0.911204i | \(0.364846\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10974.9 | 0.416854 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8303.70 | 0.314330 | 0.157165 | − | 0.987572i | \(-0.449765\pi\) | ||||
0.157165 | + | 0.987572i | \(0.449765\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2450.08 | −0.0921221 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −67385.6 | −2.52516 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25373.6 | −0.947650 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1505.89 | 0.0560536 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −38.4693 | −0.00142717 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1151.38 | 0.0425726 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 59763.9 | 2.19516 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34544.5 | −1.26464 | −0.632321 | − | 0.774706i | \(-0.717898\pi\) | ||||
−0.632321 | + | 0.774706i | \(0.717898\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13390.7 | −0.488606 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10505.3 | −0.382059 | −0.191030 | − | 0.981584i | \(-0.561183\pi\) | ||||
−0.191030 | + | 0.981584i | \(0.561183\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −37325.6 | −1.35301 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 39787.0 | 1.43751 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32201.6 | 1.15586 | 0.577929 | − | 0.816087i | \(-0.303861\pi\) | ||||
0.577929 | + | 0.816087i | \(0.303861\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 437.909 | 0.0156673 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13996.5 | −0.499133 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 26395.4 | 0.938245 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7005.67 | −0.248216 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −37034.8 | −1.30794 | −0.653968 | − | 0.756522i | \(-0.726897\pi\) | ||||
−0.653968 | + | 0.756522i | \(0.726897\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10249.5 | 0.359651 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 26854.6 | 0.939292 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7207.18 | −0.251279 | −0.125639 | − | 0.992076i | \(-0.540098\pi\) | ||||
−0.125639 | + | 0.992076i | \(0.540098\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11047.1 | 0.383927 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21718.9 | −0.752407 | −0.376203 | − | 0.926537i | \(-0.622771\pi\) | ||||
−0.376203 | + | 0.926537i | \(0.622771\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2388.91 | 0.0824958 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −131.343 | −0.00450693 | −0.00225347 | − | 0.999997i | \(-0.500717\pi\) | ||||
−0.00225347 | + | 0.999997i | \(0.500717\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2653.13 | −0.0907525 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4130.33 | −0.140836 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −39810.0 | −1.35317 | −0.676586 | − | 0.736363i | \(-0.736541\pi\) | ||||
−0.676586 | + | 0.736363i | \(0.736541\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 29247.6 | 0.991025 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 19.7692 | 0.000667760 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1389.69 | 0.0466480 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11718.7 | 0.392139 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5582.01 | 0.186209 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18858.5 | 0.627145 | 0.313573 | − | 0.949564i | \(-0.398474\pi\) | ||||
0.313573 | + | 0.949564i | \(0.398474\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −23479.8 | −0.778412 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −48355.1 | −1.59813 | −0.799067 | − | 0.601242i | \(-0.794673\pi\) | ||||
−0.799067 | + | 0.601242i | \(0.794673\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −23120.3 | −0.759428 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5085.72 | −0.166537 | −0.0832685 | − | 0.996527i | \(-0.526536\pi\) | ||||
−0.0832685 | + | 0.996527i | \(0.526536\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −34614.4 | −1.13001 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4221.73 | 0.137400 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 48617.7 | 1.57748 | 0.788741 | − | 0.614726i | \(-0.210733\pi\) | ||||
0.788741 | + | 0.614726i | \(0.210733\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −70339.5 | −2.27533 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3539.66 | −0.113806 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35000.1 | 1.12191 | 0.560955 | − | 0.827846i | \(-0.310434\pi\) | ||||
0.560955 | + | 0.827846i | \(0.310434\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6524.79 | 0.208517 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 35423.4 | 1.12864 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32807.9 | 1.04216 | 0.521081 | − | 0.853507i | \(-0.325529\pi\) | ||||
0.521081 | + | 0.853507i | \(0.325529\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5699.16 | 0.180494 |
(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 | 1176.4.a.bd.1.1 | 4 | ||
4.3 | odd | 2 | 2352.4.a.cm.1.1 | 4 | |||
7.2 | even | 3 | 168.4.q.f.25.4 | ✓ | 8 | ||
7.4 | even | 3 | 168.4.q.f.121.4 | yes | 8 | ||
7.6 | odd | 2 | 1176.4.a.ba.1.4 | 4 | |||
21.2 | odd | 6 | 504.4.s.j.361.1 | 8 | |||
21.11 | odd | 6 | 504.4.s.j.289.1 | 8 | |||
28.11 | odd | 6 | 336.4.q.m.289.4 | 8 | |||
28.23 | odd | 6 | 336.4.q.m.193.4 | 8 | |||
28.27 | even | 2 | 2352.4.a.cp.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.4.q.f.25.4 | ✓ | 8 | 7.2 | even | 3 | ||
168.4.q.f.121.4 | yes | 8 | 7.4 | even | 3 | ||
336.4.q.m.193.4 | 8 | 28.23 | odd | 6 | |||
336.4.q.m.289.4 | 8 | 28.11 | odd | 6 | |||
504.4.s.j.289.1 | 8 | 21.11 | odd | 6 | |||
504.4.s.j.361.1 | 8 | 21.2 | odd | 6 | |||
1176.4.a.ba.1.4 | 4 | 7.6 | odd | 2 | |||
1176.4.a.bd.1.1 | 4 | 1.1 | even | 1 | trivial | ||
2352.4.a.cm.1.1 | 4 | 4.3 | odd | 2 | |||
2352.4.a.cp.1.4 | 4 | 28.27 | even | 2 |