Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.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: | \(63.9442019386\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 16x^{8} + 26x^{7} + 93x^{6} - 113x^{5} - 230x^{4} + 197x^{3} + 201x^{2} - 115x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(2.67231\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-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 | ||||||||
\(3\) | 2.67231 | 1.54286 | 0.771430 | − | 0.636314i | \(-0.219542\pi\) | ||||
0.771430 | + | 0.636314i | \(0.219542\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.943895 | 0.422123 | 0.211061 | − | 0.977473i | \(-0.432308\pi\) | ||||
0.211061 | + | 0.977473i | \(0.432308\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.14126 | 1.38042 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.52238 | 0.651276 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.622063 | −0.150873 | −0.0754363 | − | 0.997151i | \(-0.524035\pi\) | ||||
−0.0754363 | + | 0.997151i | \(0.524035\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.30010 | −0.527679 | −0.263840 | − | 0.964567i | \(-0.584989\pi\) | ||||
−0.263840 | + | 0.964567i | \(0.584989\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.67231 | −0.583147 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.63973 | −1.38448 | −0.692240 | − | 0.721668i | \(-0.743376\pi\) | ||||
−0.692240 | + | 0.721668i | \(0.743376\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.10906 | −0.821813 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.04980 | 0.586934 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.44550 | −1.75398 | −0.876992 | − | 0.480504i | \(-0.840454\pi\) | ||||
−0.876992 | + | 0.480504i | \(0.840454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.80361 | −1.22196 | −0.610982 | − | 0.791645i | \(-0.709225\pi\) | ||||
−0.610982 | + | 0.791645i | \(0.709225\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.67231 | −0.465190 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.943895 | −0.159547 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.75243 | 0.616896 | 0.308448 | − | 0.951241i | \(-0.400190\pi\) | ||||
0.308448 | + | 0.951241i | \(0.400190\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.67231 | −0.427913 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.0796215 | 0.0124348 | 0.00621739 | − | 0.999981i | \(-0.498021\pi\) | ||||
0.00621739 | + | 0.999981i | \(0.498021\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.71975 | 1.02475 | 0.512376 | − | 0.858761i | \(-0.328765\pi\) | ||||
0.512376 | + | 0.858761i | \(0.328765\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.90891 | 0.582706 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.55768 | 0.664806 | 0.332403 | − | 0.943137i | \(-0.392141\pi\) | ||||
0.332403 | + | 0.943137i | \(0.392141\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.66235 | −0.232775 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.69712 | −0.782559 | −0.391280 | − | 0.920272i | \(-0.627968\pi\) | ||||
−0.391280 | + | 0.920272i | \(0.627968\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.943895 | −0.127275 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.14659 | −0.814135 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.42152 | −0.705822 | −0.352911 | − | 0.935657i | \(-0.614808\pi\) | ||||
−0.352911 | + | 0.935657i | \(0.614808\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.72339 | −0.732805 | −0.366403 | − | 0.930456i | \(-0.619411\pi\) | ||||
−0.366403 | + | 0.930456i | \(0.619411\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.14126 | −0.521749 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.943895 | −0.117076 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.881277 | 0.107665 | 0.0538326 | − | 0.998550i | \(-0.482856\pi\) | ||||
0.0538326 | + | 0.998550i | \(0.482856\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −17.7434 | −2.13606 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.0794 | −1.67092 | −0.835459 | − | 0.549553i | \(-0.814798\pi\) | ||||
−0.835459 | + | 0.549553i | \(0.814798\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.92776 | 1.16196 | 0.580978 | − | 0.813919i | \(-0.302670\pi\) | ||||
0.580978 | + | 0.813919i | \(0.302670\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −10.9807 | −1.26794 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.9505 | 1.45705 | 0.728524 | − | 0.685020i | \(-0.240207\pi\) | ||||
0.728524 | + | 0.685020i | \(0.240207\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.27376 | −0.474862 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.11394 | 0.561327 | 0.280664 | − | 0.959806i | \(-0.409445\pi\) | ||||
0.280664 | + | 0.959806i | \(0.409445\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.587162 | −0.0636867 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −25.2413 | −2.70615 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.5642 | −1.86180 | −0.930902 | − | 0.365269i | \(-0.880977\pi\) | ||||
−0.930902 | + | 0.365269i | \(0.880977\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −18.1814 | −1.88532 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.17105 | −0.222745 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.32556 | −0.642263 | −0.321131 | − | 0.947035i | \(-0.604063\pi\) | ||||
−0.321131 | + | 0.947035i | \(0.604063\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.14126 | −0.416212 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.252869 | 0.0251614 | 0.0125807 | − | 0.999921i | \(-0.495995\pi\) | ||||
0.0125807 | + | 0.999921i | \(0.495995\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.98359 | −0.293982 | −0.146991 | − | 0.989138i | \(-0.546959\pi\) | ||||
−0.146991 | + | 0.989138i | \(0.546959\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.52238 | −0.246159 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.8680 | −1.34067 | −0.670337 | − | 0.742057i | \(-0.733850\pi\) | ||||
−0.670337 | + | 0.742057i | \(0.733850\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.22019 | −0.404220 | −0.202110 | − | 0.979363i | \(-0.564780\pi\) | ||||
−0.202110 | + | 0.979363i | \(0.564780\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.0277 | 0.951785 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.97460 | 0.467971 | 0.233986 | − | 0.972240i | \(-0.424823\pi\) | ||||
0.233986 | + | 0.972240i | \(0.424823\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.26721 | −0.584420 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.14126 | −0.382859 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.622063 | 0.0570245 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.212774 | 0.0191851 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.59800 | −0.769028 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.4344 | 1.90200 | 0.950999 | − | 0.309193i | \(-0.100059\pi\) | ||||
0.950999 | + | 0.309193i | \(0.100059\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 17.9573 | 1.58105 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.9358 | 1.74180 | 0.870899 | − | 0.491462i | \(-0.163537\pi\) | ||||
0.870899 | + | 0.491462i | \(0.163537\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.30010 | 0.199444 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.87869 | 0.247758 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.30422 | 0.624042 | 0.312021 | − | 0.950075i | \(-0.398994\pi\) | ||||
0.312021 | + | 0.950075i | \(0.398994\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.24746 | −0.360265 | −0.180133 | − | 0.983642i | \(-0.557653\pi\) | ||||
−0.180133 | + | 0.983642i | \(0.557653\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.1795 | 1.02570 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.91556 | −0.740397 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.67231 | 0.220409 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.38025 | 0.113075 | 0.0565374 | − | 0.998400i | \(-0.481994\pi\) | ||||
0.0565374 | + | 0.998400i | \(0.481994\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.9083 | −1.70149 | −0.850746 | − | 0.525577i | \(-0.823849\pi\) | ||||
−0.850746 | + | 0.525577i | \(0.823849\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.57612 | −0.208267 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.42189 | −0.515818 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.86501 | −0.547888 | −0.273944 | − | 0.961746i | \(-0.588328\pi\) | ||||
−0.273944 | + | 0.961746i | \(0.588328\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −15.2245 | −1.20738 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.63973 | 0.523284 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.6584 | 1.61809 | 0.809046 | − | 0.587745i | \(-0.199984\pi\) | ||||
0.809046 | + | 0.587745i | \(0.199984\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.52238 | −0.196367 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.9293 | 1.23265 | 0.616323 | − | 0.787494i | \(-0.288622\pi\) | ||||
0.616323 | + | 0.787494i | \(0.288622\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.52530 | −0.728418 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.27650 | 0.477193 | 0.238597 | − | 0.971119i | \(-0.423313\pi\) | ||||
0.238597 | + | 0.971119i | \(0.423313\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.10906 | 0.310616 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14.4880 | −1.08899 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.1482 | 0.982741 | 0.491371 | − | 0.870951i | \(-0.336496\pi\) | ||||
0.491371 | + | 0.870951i | \(0.336496\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.59416 | 0.415811 | 0.207905 | − | 0.978149i | \(-0.433335\pi\) | ||||
0.207905 | + | 0.978149i | \(0.433335\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −15.2947 | −1.13062 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.54190 | 0.260406 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.622063 | 0.0454898 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.04980 | −0.221840 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.3362 | 0.747902 | 0.373951 | − | 0.927448i | \(-0.378003\pi\) | ||||
0.373951 | + | 0.927448i | \(0.378003\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.56178 | −0.112419 | −0.0562096 | − | 0.998419i | \(-0.517901\pi\) | ||||
−0.0562096 | + | 0.998419i | \(0.517901\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.52238 | −0.180632 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.63858 | 0.330485 | 0.165243 | − | 0.986253i | \(-0.447159\pi\) | ||||
0.165243 | + | 0.986253i | \(0.447159\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.04937 | −0.145276 | −0.0726380 | − | 0.997358i | \(-0.523142\pi\) | ||||
−0.0726380 | + | 0.997358i | \(0.523142\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.35505 | 0.166112 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.44550 | 0.662944 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.0751543 | 0.00524900 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −27.4968 | −1.91116 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.30010 | 0.159101 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.4861 | −1.68569 | −0.842847 | − | 0.538153i | \(-0.819122\pi\) | ||||
−0.842847 | + | 0.538153i | \(0.819122\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −37.6246 | −2.57799 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.34273 | 0.432571 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.80361 | 0.461859 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 26.5301 | 1.79274 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.622063 | 0.0418445 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.54602 | −0.237459 | −0.118729 | − | 0.992927i | \(-0.537882\pi\) | ||||
−0.118729 | + | 0.992927i | \(0.537882\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −17.0167 | −1.13445 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.4468 | 1.15798 | 0.578992 | − | 0.815334i | \(-0.303446\pi\) | ||||
0.578992 | + | 0.815334i | \(0.303446\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.4112 | −0.952318 | −0.476159 | − | 0.879359i | \(-0.657971\pi\) | ||||
−0.476159 | + | 0.879359i | \(0.657971\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.67231 | 0.175825 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.9702 | 1.37380 | 0.686902 | − | 0.726750i | \(-0.258970\pi\) | ||||
0.686902 | + | 0.726750i | \(0.258970\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.30197 | 0.280630 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 34.6079 | 2.24802 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.5110 | −1.19738 | −0.598688 | − | 0.800983i | \(-0.704311\pi\) | ||||
−0.598688 | + | 0.800983i | \(0.704311\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.19427 | 0.205761 | 0.102881 | − | 0.994694i | \(-0.467194\pi\) | ||||
0.102881 | + | 0.994694i | \(0.467194\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −20.5702 | −1.31958 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.943895 | 0.0603032 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.30010 | 0.146352 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.6660 | 0.866050 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.4037 | −1.16163 | −0.580816 | − | 0.814035i | \(-0.697266\pi\) | ||||
−0.580816 | + | 0.814035i | \(0.697266\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.63973 | 0.417436 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.56908 | −0.0982597 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.4668 | 0.964794 | 0.482397 | − | 0.875953i | \(-0.339766\pi\) | ||||
0.482397 | + | 0.875953i | \(0.339766\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.75243 | −0.233165 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −39.1162 | −2.42123 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.6139 | 0.654479 | 0.327240 | − | 0.944941i | \(-0.393882\pi\) | ||||
0.327240 | + | 0.944941i | \(0.393882\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.37748 | −0.330336 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −46.9371 | −2.87250 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.9925 | −0.914110 | −0.457055 | − | 0.889438i | \(-0.651096\pi\) | ||||
−0.457055 | + | 0.889438i | \(0.651096\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.58603 | 0.278581 | 0.139291 | − | 0.990252i | \(-0.455518\pi\) | ||||
0.139291 | + | 0.990252i | \(0.455518\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.67231 | 0.161736 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.10906 | 0.247786 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.5269 | 0.872836 | 0.436418 | − | 0.899744i | \(-0.356247\pi\) | ||||
0.436418 | + | 0.899744i | \(0.356247\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −28.1755 | −1.68682 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.1373 | −1.08198 | −0.540989 | − | 0.841030i | \(-0.681950\pi\) | ||||
−0.540989 | + | 0.841030i | \(0.681950\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.331455 | 0.0197030 | 0.00985149 | − | 0.999951i | \(-0.496864\pi\) | ||||
0.00985149 | + | 0.999951i | \(0.496864\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.80173 | −0.343665 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.0796215 | −0.00469991 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.6130 | −0.977237 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.9039 | −0.990922 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.1755 | 1.00340 | 0.501702 | − | 0.865040i | \(-0.332707\pi\) | ||||
0.501702 | + | 0.865040i | \(0.332707\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.11735 | −0.297944 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.04980 | −0.176967 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.63973 | 0.383985 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.71975 | −0.387320 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.675745 | 0.0388205 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.40228 | −0.309334 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.7290 | 0.897701 | 0.448850 | − | 0.893607i | \(-0.351834\pi\) | ||||
0.448850 | + | 0.893607i | \(0.351834\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.97309 | −0.453573 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.20898 | 0.522193 | 0.261097 | − | 0.965313i | \(-0.415916\pi\) | ||||
0.261097 | + | 0.965313i | \(0.415916\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.6431 | −1.33639 | −0.668194 | − | 0.743987i | \(-0.732933\pi\) | ||||
−0.668194 | + | 0.743987i | \(0.732933\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.90891 | −0.220242 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −21.7679 | −1.22261 | −0.611305 | − | 0.791395i | \(-0.709355\pi\) | ||||
−0.611305 | + | 0.791395i | \(0.709355\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.44550 | 0.528846 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −37.0597 | −2.06847 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.43081 | 0.0796123 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.10906 | 0.227930 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.2777 | −0.623656 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.55768 | −0.251273 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.00474 | 0.165155 | 0.0825776 | − | 0.996585i | \(-0.473685\pi\) | ||||
0.0825776 | + | 0.996585i | \(0.473685\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 15.5398 | 0.851575 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.831833 | 0.0454479 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.2933 | 1.48676 | 0.743381 | − | 0.668868i | \(-0.233221\pi\) | ||||
0.743381 | + | 0.668868i | \(0.233221\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.2937 | 0.722014 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.80361 | 0.368436 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −16.7479 | −0.901679 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.4221 | −1.25736 | −0.628682 | − | 0.777662i | \(-0.716405\pi\) | ||||
−0.628682 | + | 0.777662i | \(0.716405\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.119337 | −0.00638799 | −0.00319399 | − | 0.999995i | \(-0.501017\pi\) | ||||
−0.00319399 | + | 0.999995i | \(0.501017\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.04980 | −0.162786 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.8199 | −0.575884 | −0.287942 | − | 0.957648i | \(-0.592971\pi\) | ||||
−0.287942 | + | 0.957648i | \(0.592971\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.2895 | −0.705332 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.66235 | 0.0879808 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −34.2412 | −1.80718 | −0.903591 | − | 0.428395i | \(-0.859079\pi\) | ||||
−0.903591 | + | 0.428395i | \(0.859079\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.7095 | −0.721555 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.67231 | 0.140260 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.37076 | 0.490488 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.382253 | −0.0199535 | −0.00997673 | − | 0.999950i | \(-0.503176\pi\) | ||||
−0.00997673 | + | 0.999950i | \(0.503176\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.329733 | 0.0171652 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.69712 | 0.295780 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.3857 | 1.41798 | 0.708989 | − | 0.705219i | \(-0.249151\pi\) | ||||
0.708989 | + | 0.705219i | \(0.249151\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −22.9765 | −1.18650 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.44550 | 0.486468 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.4156 | 1.51098 | 0.755489 | − | 0.655161i | \(-0.227399\pi\) | ||||
0.755489 | + | 0.655161i | \(0.227399\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 57.2795 | 2.93452 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.7429 | −0.855520 | −0.427760 | − | 0.903892i | \(-0.640697\pi\) | ||||
−0.427760 | + | 0.903892i | \(0.640697\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.943895 | 0.0481053 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 27.8282 | 1.41459 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 35.7424 | 1.81221 | 0.906105 | − | 0.423052i | \(-0.139041\pi\) | ||||
0.906105 | + | 0.423052i | \(0.139041\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.13033 | 0.208880 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 53.2747 | 2.68735 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.2239 | 0.615053 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.2038 | −1.46570 | −0.732849 | − | 0.680391i | \(-0.761810\pi\) | ||||
−0.732849 | + | 0.680391i | \(0.761810\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.14659 | 0.307714 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.4926 | 1.37292 | 0.686458 | − | 0.727170i | \(-0.259165\pi\) | ||||
0.686458 | + | 0.727170i | \(0.259165\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.80361 | 0.338912 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.03398 | −0.200450 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.75243 | −0.186001 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.97056 | 0.196331 | 0.0981657 | − | 0.995170i | \(-0.468702\pi\) | ||||
0.0981657 | + | 0.995170i | \(0.468702\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.5192 | 0.962809 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.42152 | 0.266776 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.82702 | 0.236949 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.3506 | −0.555839 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.1363 | 1.42340 | 0.711701 | − | 0.702483i | \(-0.247925\pi\) | ||||
0.711701 | + | 0.702483i | \(0.247925\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.2393 | −0.986401 | −0.493200 | − | 0.869916i | \(-0.664173\pi\) | ||||
−0.493200 | + | 0.869916i | \(0.664173\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 18.8745 | 0.917711 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.55610 | 0.123989 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.72339 | 0.276974 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.67231 | 0.129020 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.8811 | −1.29482 | −0.647409 | − | 0.762143i | \(-0.724147\pi\) | ||||
−0.647409 | + | 0.762143i | \(0.724147\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.4491 | 1.31912 | 0.659561 | − | 0.751651i | \(-0.270742\pi\) | ||||
0.659561 | + | 0.751651i | \(0.270742\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −23.8252 | −1.14233 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.2720 | 0.730561 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.8693 | 0.518764 | 0.259382 | − | 0.965775i | \(-0.416481\pi\) | ||||
0.259382 | + | 0.965775i | \(0.416481\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.14126 | 0.197203 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.56409 | −0.359381 | −0.179690 | − | 0.983723i | \(-0.557510\pi\) | ||||
−0.179690 | + | 0.983723i | \(0.557510\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.5788 | −0.785910 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.68847 | 0.174459 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.9356 | −1.12959 | −0.564796 | − | 0.825230i | \(-0.691045\pi\) | ||||
−0.564796 | + | 0.825230i | \(0.691045\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.0796215 | −0.00374923 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −55.8735 | −2.62517 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.943895 | 0.0442505 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.1799 | 0.569752 | 0.284876 | − | 0.958564i | \(-0.408048\pi\) | ||||
0.284876 | + | 0.958564i | \(0.408048\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.89717 | −0.0885522 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.5468 | −1.32956 | −0.664779 | − | 0.747040i | \(-0.731474\pi\) | ||||
−0.664779 | + | 0.747040i | \(0.731474\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.0101 | −0.929947 | −0.464973 | − | 0.885325i | \(-0.653936\pi\) | ||||
−0.464973 | + | 0.885325i | \(0.653936\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −17.1613 | −0.795836 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.84287 | 0.131552 | 0.0657762 | − | 0.997834i | \(-0.479048\pi\) | ||||
0.0657762 | + | 0.997834i | \(0.479048\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.881277 | −0.0406936 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.3455 | −0.845314 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.71975 | −0.308974 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.45125 | 0.433653 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −23.5932 | −1.08026 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −33.2946 | −1.52127 | −0.760635 | − | 0.649180i | \(-0.775112\pi\) | ||||
−0.760635 | + | 0.649180i | \(0.775112\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.75243 | −0.171096 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 17.7434 | 0.807354 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.97066 | −0.271114 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.12895 | 0.277729 | 0.138865 | − | 0.990311i | \(-0.455655\pi\) | ||||
0.138865 | + | 0.990311i | \(0.455655\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 55.2058 | 2.49649 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −31.3676 | −1.41560 | −0.707799 | − | 0.706413i | \(-0.750312\pi\) | ||||
−0.707799 | + | 0.706413i | \(0.750312\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.87570 | 0.264628 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.90891 | −0.175693 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.0794 | 0.631547 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.9022 | 0.711882 | 0.355941 | − | 0.934508i | \(-0.384160\pi\) | ||||
0.355941 | + | 0.934508i | \(0.384160\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 42.5680 | 1.90180 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 39.8665 | 1.77756 | 0.888779 | − | 0.458336i | \(-0.151554\pi\) | ||||
0.888779 | + | 0.458336i | \(0.151554\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.238682 | 0.0106212 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.67231 | 0.118682 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −34.8910 | −1.54652 | −0.773259 | − | 0.634090i | \(-0.781375\pi\) | ||||
−0.773259 | + | 0.634090i | \(0.781375\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.92776 | −0.439178 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.01484 | −0.309713 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.81619 | −0.124096 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.55768 | −0.200446 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.7728 | 0.736243 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.5113 | −0.679564 | −0.339782 | − | 0.940504i | \(-0.610353\pi\) | ||||
−0.339782 | + | 0.940504i | \(0.610353\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −39.1321 | −1.71113 | −0.855565 | − | 0.517696i | \(-0.826790\pi\) | ||||
−0.855565 | + | 0.517696i | \(0.826790\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 10.9807 | 0.479237 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.23227 | 0.184361 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.0860 | 0.916783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −22.4519 | −0.974330 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.0796215 | −0.00344879 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.0900 | −0.565929 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 35.1361 | 1.51623 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.0457 | −0.818839 | −0.409419 | − | 0.912346i | \(-0.634269\pi\) | ||||
−0.409419 | + | 0.912346i | \(0.634269\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14.9493 | 0.641538 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.98341 | −0.170631 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.4349 | −1.13028 | −0.565138 | − | 0.824996i | \(-0.691177\pi\) | ||||
−0.565138 | + | 0.824996i | \(0.691177\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −23.7020 | −1.01158 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.7256 | 0.925541 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.9505 | −0.550712 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.46507 | 0.401770 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.44948 | −0.230902 | −0.115451 | − | 0.993313i | \(-0.536831\pi\) | ||||
−0.115451 | + | 0.993313i | \(0.536831\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.71975 | −0.284215 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.66235 | 0.0701844 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 35.5127 | 1.49668 | 0.748341 | − | 0.663314i | \(-0.230851\pi\) | ||||
0.748341 | + | 0.663314i | \(0.230851\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.69550 | 0.197541 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.27376 | 0.179481 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.65028 | 0.362639 | 0.181319 | − | 0.983424i | \(-0.441963\pi\) | ||||
0.181319 | + | 0.983424i | \(0.441963\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.05741 | 0.127949 | 0.0639744 | − | 0.997952i | \(-0.479622\pi\) | ||||
0.0639744 | + | 0.997952i | \(0.479622\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 27.6216 | 1.15391 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 27.2831 | 1.13778 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.44179 | 0.101653 | 0.0508266 | − | 0.998707i | \(-0.483814\pi\) | ||||
0.0508266 | + | 0.998707i | \(0.483814\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.17356 | −0.173447 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.11394 | −0.212162 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.69712 | 0.235951 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.90891 | −0.161614 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.0088 | −1.11477 | −0.557386 | − | 0.830253i | \(-0.688196\pi\) | ||||
−0.557386 | + | 0.830253i | \(0.688196\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.6490 | 0.644805 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.3957 | 0.509893 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −30.0961 | −1.23590 | −0.617950 | − | 0.786217i | \(-0.712037\pi\) | ||||
−0.617950 | + | 0.786217i | \(0.712037\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.587162 | 0.0240713 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.47656 | −0.224141 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.7143 | 0.519494 | 0.259747 | − | 0.965677i | \(-0.416361\pi\) | ||||
0.259747 | + | 0.965677i | \(0.416361\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.4621 | −1.16099 | −0.580497 | − | 0.814262i | \(-0.697142\pi\) | ||||
−0.580497 | + | 0.814262i | \(0.697142\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.64960 | 0.148623 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.943895 | 0.0383748 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.7279 | −0.678963 | −0.339482 | − | 0.940613i | \(-0.610252\pi\) | ||||
−0.339482 | + | 0.940613i | \(0.610252\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 25.2413 | 1.02283 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.55768 | −0.184384 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.26254 | 0.0509937 | 0.0254968 | − | 0.999675i | \(-0.491883\pi\) | ||||
0.0254968 | + | 0.999675i | \(0.491883\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.200836 | 0.00809848 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −36.7618 | −1.47997 | −0.739987 | − | 0.672622i | \(-0.765168\pi\) | ||||
−0.739987 | + | 0.672622i | \(0.765168\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.8761 | 0.999856 | 0.499928 | − | 0.866067i | \(-0.333360\pi\) | ||||
0.499928 | + | 0.866067i | \(0.333360\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −20.2498 | −0.812597 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.5642 | 0.703696 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.4297 | 0.497188 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.14659 | 0.245471 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.33425 | −0.0930727 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.3940 | 0.612826 | 0.306413 | − | 0.951899i | \(-0.400871\pi\) | ||||
0.306413 | + | 0.951899i | \(0.400871\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −65.4346 | −2.60079 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20.2319 | 0.802877 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −58.3064 | −2.30657 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.890745 | 0.0351823 | 0.0175912 | − | 0.999845i | \(-0.494400\pi\) | ||||
0.0175912 | + | 0.999845i | \(0.494400\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.2157 | −0.797230 | −0.398615 | − | 0.917118i | \(-0.630509\pi\) | ||||
−0.398615 | + | 0.917118i | \(0.630509\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 16.9498 | 0.667397 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.7779 | 0.934805 | 0.467402 | − | 0.884045i | \(-0.345190\pi\) | ||||
0.467402 | + | 0.884045i | \(0.345190\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.42152 | 0.212813 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 18.1814 | 0.712584 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.6339 | 0.611800 | 0.305900 | − | 0.952064i | \(-0.401043\pi\) | ||||
0.305900 | + | 0.952064i | \(0.401043\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.8173 | 0.735252 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 41.1134 | 1.60399 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.22340 | 0.164520 | 0.0822602 | − | 0.996611i | \(-0.473786\pi\) | ||||
0.0822602 | + | 0.996611i | \(0.473786\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.21814 | 0.202962 | 0.101481 | − | 0.994837i | \(-0.467642\pi\) | ||||
0.101481 | + | 0.994837i | \(0.467642\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.66235 | 0.0645602 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.17105 | 0.0841898 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 62.7155 | 2.42836 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.47607 | −0.366366 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.72339 | 0.220949 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.0488 | −0.502993 | −0.251497 | − | 0.967858i | \(-0.580923\pi\) | ||||
−0.251497 | + | 0.967858i | \(0.580923\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −12.5318 | −0.482349 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −47.4039 | −1.82188 | −0.910940 | − | 0.412540i | \(-0.864642\pi\) | ||||
−0.910940 | + | 0.412540i | \(0.864642\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.32556 | 0.242753 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 46.6232 | 1.78661 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.29654 | 0.317458 | 0.158729 | − | 0.987322i | \(-0.449260\pi\) | ||||
0.158729 | + | 0.987322i | \(0.449260\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.89441 | 0.263422 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −38.5112 | −1.46929 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.69712 | 0.217043 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.1261 | −0.423258 | −0.211629 | − | 0.977350i | \(-0.567877\pi\) | ||||
−0.211629 | + | 0.977350i | \(0.567877\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.14126 | 0.157313 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.00916 | −0.152076 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.0495296 | −0.00187607 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 56.0390 | 2.11959 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.96866 | 0.225433 | 0.112717 | − | 0.993627i | \(-0.464045\pi\) | ||||
0.112717 | + | 0.993627i | \(0.464045\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.63097 | −0.325523 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.4962 | 0.432972 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.252869 | −0.00951011 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.04032 | 0.0390702 | 0.0195351 | − | 0.999809i | \(-0.493781\pi\) | ||||
0.0195351 | + | 0.999809i | \(0.493781\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 53.6314 | 2.01134 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 45.1741 | 1.69178 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.943895 | 0.0352997 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −49.4671 | −1.84738 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.67643 | 0.0625202 | 0.0312601 | − | 0.999511i | \(-0.490048\pi\) | ||||
0.0312601 | + | 0.999511i | \(0.490048\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.98359 | 0.111115 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.53609 | 0.317461 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 38.8121 | 1.44145 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.49034 | −0.240713 | −0.120357 | − | 0.992731i | \(-0.538404\pi\) | ||||
−0.120357 | + | 0.992731i | \(0.538404\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −42.1488 | −1.56107 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.18011 | −0.154607 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.8230 | −0.842986 | −0.421493 | − | 0.906832i | \(-0.638494\pi\) | ||||
−0.421493 | + | 0.906832i | \(0.638494\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.52238 | 0.0930395 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.881277 | −0.0324623 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.6535 | −0.722967 | −0.361483 | − | 0.932379i | \(-0.617730\pi\) | ||||
−0.361483 | + | 0.932379i | \(0.617730\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.14659 | 0.225800 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −52.4646 | −1.92474 | −0.962371 | − | 0.271741i | \(-0.912401\pi\) | ||||
−0.962371 | + | 0.271741i | \(0.912401\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.30281 | 0.0477314 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 21.1781 | 0.774867 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.8680 | 0.506727 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.7094 | 0.828677 | 0.414338 | − | 0.910123i | \(-0.364013\pi\) | ||||
0.414338 | + | 0.910123i | \(0.364013\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −49.1805 | −1.79224 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.7352 | −0.718238 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.6724 | −0.569623 | −0.284812 | − | 0.958584i | \(-0.591931\pi\) | ||||
−0.284812 | + | 0.958584i | \(0.591931\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 17.7434 | 0.644046 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.3546 | 0.701602 | 0.350801 | − | 0.936450i | \(-0.385909\pi\) | ||||
0.350801 | + | 0.936450i | \(0.385909\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.22019 | 0.152781 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.43159 | −0.0879143 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.42152 | 0.195760 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.32834 | 0.192145 | 0.0960725 | − | 0.995374i | \(-0.469372\pi\) | ||||
0.0960725 | + | 0.995374i | \(0.469372\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 41.3322 | 1.48854 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.32303 | −0.263391 | −0.131696 | − | 0.991290i | \(-0.542042\pi\) | ||||
−0.131696 | + | 0.991290i | \(0.542042\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 27.9564 | 1.00422 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.0277 | −0.359741 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.183137 | −0.00656158 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.0794 | 0.503801 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −28.8068 | −1.02947 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.47985 | −0.231276 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.0448 | 1.28486 | 0.642430 | − | 0.766345i | \(-0.277927\pi\) | ||||
0.642430 | + | 0.766345i | \(0.277927\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 28.3636 | 1.00977 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.97460 | −0.176876 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.72339 | 0.203244 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14.3703 | −0.509662 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −50.6311 | −1.79345 | −0.896723 | − | 0.442593i | \(-0.854059\pi\) | ||||
−0.896723 | + | 0.442593i | \(0.854059\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.83517 | −0.100301 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −72.7380 | −2.57007 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.92776 | −0.350343 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.26721 | 0.220890 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −40.0647 | −1.41034 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.182728 | −0.00642436 | −0.00321218 | − | 0.999995i | \(-0.501022\pi\) | ||||
−0.00321218 | + | 0.999995i | \(0.501022\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.2195 | −0.674886 | −0.337443 | − | 0.941346i | \(-0.609562\pi\) | ||||
−0.337443 | + | 0.941346i | \(0.609562\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.2553 | 0.429812 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.4994 | 0.683033 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.4561 | −0.540740 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.14126 | 0.144707 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.75003 | 0.200678 | 0.100339 | − | 0.994953i | \(-0.468007\pi\) | ||||
0.100339 | + | 0.994953i | \(0.468007\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.184311 | −0.00642468 | −0.00321234 | − | 0.999995i | \(-0.501023\pi\) | ||||
−0.00321234 | + | 0.999995i | \(0.501023\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.9807 | 0.382299 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.2284 | 1.08592 | 0.542959 | − | 0.839759i | \(-0.317304\pi\) | ||||
0.542959 | + | 0.839759i | \(0.317304\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.0865 | −1.14914 | −0.574570 | − | 0.818455i | \(-0.694831\pi\) | ||||
−0.574570 | + | 0.818455i | \(0.694831\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 38.8204 | 1.34666 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.622063 | −0.0215532 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.0356 | 0.520327 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −20.7496 | −0.717212 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.7184 | −0.508134 | −0.254067 | − | 0.967187i | \(-0.581768\pi\) | ||||
−0.254067 | + | 0.967187i | \(0.581768\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 60.2174 | 2.07646 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −48.4684 | −1.66934 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.943895 | 0.0324710 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.885753 | 0.0303990 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24.9151 | −0.854080 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −44.3126 | −1.51723 | −0.758617 | − | 0.651537i | \(-0.774125\pi\) | ||||
−0.758617 | + | 0.651537i | \(0.774125\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.99089 | −0.307482 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 57.0681 | 1.94941 | 0.974704 | − | 0.223499i | \(-0.0717481\pi\) | ||||
0.974704 | + | 0.223499i | \(0.0717481\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.9776 | 0.579268 | 0.289634 | − | 0.957137i | \(-0.406466\pi\) | ||||
0.289634 | + | 0.957137i | \(0.406466\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.212774 | −0.00725130 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31.6259 | 1.07656 | 0.538280 | − | 0.842766i | \(-0.319074\pi\) | ||||
0.538280 | + | 0.842766i | \(0.319074\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.92435 | 0.201434 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −44.3952 | −1.50774 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.9505 | −0.439316 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.881277 | −0.0298609 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −26.1958 | −0.886592 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.59800 | 0.290665 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.8296 | 0.534528 | 0.267264 | − | 0.963623i | \(-0.413880\pi\) | ||||
0.267264 | + | 0.963623i | \(0.413880\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 45.8984 | 1.54811 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.28259 | −0.0432114 | −0.0216057 | − | 0.999767i | \(-0.506878\pi\) | ||||
−0.0216057 | + | 0.999767i | \(0.506878\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.17237 | −0.275022 | −0.137511 | − | 0.990500i | \(-0.543910\pi\) | ||||
−0.137511 | + | 0.990500i | \(0.543910\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.6752 | −0.459685 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 31.6676 | 1.06330 | 0.531648 | − | 0.846966i | \(-0.321573\pi\) | ||||
0.531648 | + | 0.846966i | \(0.321573\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21.4344 | −0.718888 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.27376 | 0.143176 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.4831 | −0.350804 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.4105 | 0.414837 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17.7434 | 0.592436 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 64.2634 | 2.14331 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.54397 | 0.118067 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −17.9573 | −0.597580 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.28030 | 0.175523 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.37750 | 0.244966 | 0.122483 | − | 0.992471i | \(-0.460914\pi\) | ||||
0.122483 | + | 0.992471i | \(0.460914\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.04719 | 0.0347333 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.1627 | 1.13186 | 0.565931 | − | 0.824453i | \(-0.308517\pi\) | ||||
0.565931 | + | 0.824453i | \(0.308517\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.11394 | −0.169247 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −14.4366 | −0.477259 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −19.9358 | −0.658338 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22.3652 | −0.737759 | −0.368880 | − | 0.929477i | \(-0.620259\pi\) | ||||
−0.368880 | + | 0.929477i | \(0.620259\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 42.0328 | 1.38503 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.0794 | 0.463429 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.4190 | −0.506973 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.3558 | −0.405818 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −32.8077 | −1.07638 | −0.538192 | − | 0.842822i | \(-0.680893\pi\) | ||||
−0.538192 | + | 0.842822i | \(0.680893\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.30010 | −0.0753827 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 24.6093 | 0.805671 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.587162 | 0.0192023 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.7488 | 0.971850 | 0.485925 | − | 0.874001i | \(-0.338483\pi\) | ||||
0.485925 | + | 0.874001i | \(0.338483\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −63.1818 | −2.06186 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.9579 | −0.715806 | −0.357903 | − | 0.933759i | \(-0.616508\pi\) | ||||
−0.357903 | + | 0.933759i | \(0.616508\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.528665 | −0.0172157 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.87869 | −0.0936437 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.7444 | 0.381642 | 0.190821 | − | 0.981625i | \(-0.438885\pi\) | ||||
0.190821 | + | 0.981625i | \(0.438885\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.92776 | −0.322269 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −58.1708 | −1.88632 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.524312 | 0.0169841 | 0.00849206 | − | 0.999964i | \(-0.497297\pi\) | ||||
0.00849206 | + | 0.999964i | \(0.497297\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.75629 | 0.315706 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 25.2413 | 0.815936 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.30422 | −0.235866 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.2890 | 0.493195 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −57.4311 | −1.85069 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.47415 | −0.0474547 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.6593 | 1.56478 | 0.782389 | − | 0.622790i | \(-0.214001\pi\) | ||||
0.782389 | + | 0.622790i | \(0.214001\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.82357 | 0.122831 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 59.2641 | 1.90187 | 0.950937 | − | 0.309385i | \(-0.100123\pi\) | ||||
0.950937 | + | 0.309385i | \(0.100123\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.24746 | 0.136167 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10.9807 | 0.351664 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29.3365 | 0.938557 | 0.469279 | − | 0.883050i | \(-0.344514\pi\) | ||||
0.469279 | + | 0.883050i | \(0.344514\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.5642 | 0.561355 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.4769 | −0.557994 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.19772 | 0.165782 | 0.0828908 | − | 0.996559i | \(-0.473585\pi\) | ||||
0.0828908 | + | 0.996559i | \(0.473585\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.37833 | 0.139505 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.1795 | −0.387679 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −44.6173 | −1.41875 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43.5533 | 1.38352 | 0.691759 | − | 0.722129i | \(-0.256836\pi\) | ||||
0.691759 | + | 0.722129i | \(0.256836\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.02959 | 0.254811 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.93439 | −0.0613243 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.0598 | −1.23704 | −0.618518 | − | 0.785770i | \(-0.712267\pi\) | ||||
−0.618518 | + | 0.785770i | \(0.712267\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11.4442 | 0.362077 |
(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 | 8008.2.a.u.1.9 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.u.1.9 | ✓ | 10 | 1.1 | even | 1 | trivial |