Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.10784448.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 11x^{4} - 4x^{3} + 31x^{2} + 22x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.0816388\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.34292 | −0.775337 | −0.387669 | − | 0.921799i | \(-0.626719\pi\) | ||||
−0.387669 | + | 0.921799i | \(0.626719\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.34292 | 0.548246 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.19656 | −0.398853 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.34292 | −0.387669 | ||||||||
\(13\) | −4.31157 | −1.19582 | −0.597908 | − | 0.801565i | \(-0.704001\pi\) | ||||
−0.597908 | + | 0.801565i | \(0.704001\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −1.34292 | −0.346741 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.63565 | 0.639240 | 0.319620 | − | 0.947546i | \(-0.396445\pi\) | ||||
0.319620 | + | 0.947546i | \(0.396445\pi\) | |||||||
\(18\) | 1.19656 | 0.282031 | ||||||||
\(19\) | −1.56877 | −0.359901 | −0.179951 | − | 0.983676i | \(-0.557594\pi\) | ||||
−0.179951 | + | 0.983676i | \(0.557594\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 1.34292 | 0.293050 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.45794 | 1.13806 | 0.569030 | − | 0.822317i | \(-0.307319\pi\) | ||||
0.569030 | + | 0.822317i | \(0.307319\pi\) | |||||||
\(24\) | 1.34292 | 0.274123 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.31157 | 0.845569 | ||||||||
\(27\) | 5.63565 | 1.08458 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −2.83920 | −0.527226 | −0.263613 | − | 0.964629i | \(-0.584914\pi\) | ||||
−0.263613 | + | 0.964629i | \(0.584914\pi\) | |||||||
\(30\) | 1.34292 | 0.245183 | ||||||||
\(31\) | 1.14637 | 0.205893 | 0.102947 | − | 0.994687i | \(-0.467173\pi\) | ||||
0.102947 | + | 0.994687i | \(0.467173\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.63565 | −0.452011 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | −1.19656 | −0.199426 | ||||||||
\(37\) | −0.839198 | −0.137963 | −0.0689816 | − | 0.997618i | \(-0.521975\pi\) | ||||
−0.0689816 | + | 0.997618i | \(0.521975\pi\) | |||||||
\(38\) | 1.56877 | 0.254489 | ||||||||
\(39\) | 5.79011 | 0.927160 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −3.47854 | −0.543256 | −0.271628 | − | 0.962402i | \(-0.587562\pi\) | ||||
−0.271628 | + | 0.962402i | \(0.587562\pi\) | |||||||
\(42\) | −1.34292 | −0.207218 | ||||||||
\(43\) | 2.01075 | 0.306637 | 0.153318 | − | 0.988177i | \(-0.451004\pi\) | ||||
0.153318 | + | 0.988177i | \(0.451004\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.19656 | −0.178372 | ||||||||
\(46\) | −5.45794 | −0.804729 | ||||||||
\(47\) | −8.39442 | −1.22445 | −0.612226 | − | 0.790683i | \(-0.709726\pi\) | ||||
−0.612226 | + | 0.790683i | \(0.709726\pi\) | |||||||
\(48\) | −1.34292 | −0.193834 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −3.53948 | −0.495626 | ||||||||
\(52\) | −4.31157 | −0.597908 | ||||||||
\(53\) | 1.40604 | 0.193134 | 0.0965672 | − | 0.995326i | \(-0.469214\pi\) | ||||
0.0965672 | + | 0.995326i | \(0.469214\pi\) | |||||||
\(54\) | −5.63565 | −0.766915 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 2.10674 | 0.279045 | ||||||||
\(58\) | 2.83920 | 0.372805 | ||||||||
\(59\) | 2.32408 | 0.302569 | 0.151285 | − | 0.988490i | \(-0.451659\pi\) | ||||
0.151285 | + | 0.988490i | \(0.451659\pi\) | |||||||
\(60\) | −1.34292 | −0.173371 | ||||||||
\(61\) | 5.24387 | 0.671409 | 0.335704 | − | 0.941967i | \(-0.391026\pi\) | ||||
0.335704 | + | 0.941967i | \(0.391026\pi\) | |||||||
\(62\) | −1.14637 | −0.145589 | ||||||||
\(63\) | 1.19656 | 0.150752 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.31157 | −0.534785 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.60636 | −0.196248 | −0.0981241 | − | 0.995174i | \(-0.531284\pi\) | ||||
−0.0981241 | + | 0.995174i | \(0.531284\pi\) | |||||||
\(68\) | 2.63565 | 0.319620 | ||||||||
\(69\) | −7.32959 | −0.882379 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | −13.8057 | −1.63844 | −0.819220 | − | 0.573480i | \(-0.805593\pi\) | ||||
−0.819220 | + | 0.573480i | \(0.805593\pi\) | |||||||
\(72\) | 1.19656 | 0.141016 | ||||||||
\(73\) | 1.14830 | 0.134398 | 0.0671990 | − | 0.997740i | \(-0.478594\pi\) | ||||
0.0671990 | + | 0.997740i | \(0.478594\pi\) | |||||||
\(74\) | 0.839198 | 0.0975548 | ||||||||
\(75\) | −1.34292 | −0.155067 | ||||||||
\(76\) | −1.56877 | −0.179951 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.79011 | −0.655601 | ||||||||
\(79\) | −9.65408 | −1.08617 | −0.543084 | − | 0.839678i | \(-0.682744\pi\) | ||||
−0.543084 | + | 0.839678i | \(0.682744\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −3.97858 | −0.442064 | ||||||||
\(82\) | 3.47854 | 0.384140 | ||||||||
\(83\) | 2.51880 | 0.276475 | 0.138237 | − | 0.990399i | \(-0.455856\pi\) | ||||
0.138237 | + | 0.990399i | \(0.455856\pi\) | |||||||
\(84\) | 1.34292 | 0.146525 | ||||||||
\(85\) | 2.63565 | 0.285877 | ||||||||
\(86\) | −2.01075 | −0.216825 | ||||||||
\(87\) | 3.81282 | 0.408778 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.19326 | 0.232485 | 0.116242 | − | 0.993221i | \(-0.462915\pi\) | ||||
0.116242 | + | 0.993221i | \(0.462915\pi\) | |||||||
\(90\) | 1.19656 | 0.126128 | ||||||||
\(91\) | 4.31157 | 0.451976 | ||||||||
\(92\) | 5.45794 | 0.569030 | ||||||||
\(93\) | −1.53948 | −0.159637 | ||||||||
\(94\) | 8.39442 | 0.865818 | ||||||||
\(95\) | −1.56877 | −0.160953 | ||||||||
\(96\) | 1.34292 | 0.137062 | ||||||||
\(97\) | −7.56372 | −0.767979 | −0.383990 | − | 0.923337i | \(-0.625450\pi\) | ||||
−0.383990 | + | 0.923337i | \(0.625450\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −17.6449 | −1.75574 | −0.877868 | − | 0.478902i | \(-0.841035\pi\) | ||||
−0.877868 | + | 0.478902i | \(0.841035\pi\) | |||||||
\(102\) | 3.53948 | 0.350461 | ||||||||
\(103\) | 10.1528 | 1.00039 | 0.500194 | − | 0.865913i | \(-0.333262\pi\) | ||||
0.500194 | + | 0.865913i | \(0.333262\pi\) | |||||||
\(104\) | 4.31157 | 0.422785 | ||||||||
\(105\) | 1.34292 | 0.131056 | ||||||||
\(106\) | −1.40604 | −0.136567 | ||||||||
\(107\) | −15.4232 | −1.49102 | −0.745508 | − | 0.666497i | \(-0.767793\pi\) | ||||
−0.745508 | + | 0.666497i | \(0.767793\pi\) | |||||||
\(108\) | 5.63565 | 0.542291 | ||||||||
\(109\) | −8.49656 | −0.813823 | −0.406911 | − | 0.913468i | \(-0.633394\pi\) | ||||
−0.406911 | + | 0.913468i | \(0.633394\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.12698 | 0.106968 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 2.72299 | 0.256158 | 0.128079 | − | 0.991764i | \(-0.459119\pi\) | ||||
0.128079 | + | 0.991764i | \(0.459119\pi\) | |||||||
\(114\) | −2.10674 | −0.197314 | ||||||||
\(115\) | 5.45794 | 0.508956 | ||||||||
\(116\) | −2.83920 | −0.263613 | ||||||||
\(117\) | 5.15905 | 0.476954 | ||||||||
\(118\) | −2.32408 | −0.213949 | ||||||||
\(119\) | −2.63565 | −0.241610 | ||||||||
\(120\) | 1.34292 | 0.122592 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −5.24387 | −0.474758 | ||||||||
\(123\) | 4.67141 | 0.421207 | ||||||||
\(124\) | 1.14637 | 0.102947 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.19656 | −0.106598 | ||||||||
\(127\) | 9.21928 | 0.818079 | 0.409040 | − | 0.912517i | \(-0.365864\pi\) | ||||
0.409040 | + | 0.912517i | \(0.365864\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −2.70028 | −0.237747 | ||||||||
\(130\) | 4.31157 | 0.378150 | ||||||||
\(131\) | −17.5357 | −1.53210 | −0.766052 | − | 0.642779i | \(-0.777781\pi\) | ||||
−0.766052 | + | 0.642779i | \(0.777781\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.56877 | 0.136030 | ||||||||
\(134\) | 1.60636 | 0.138768 | ||||||||
\(135\) | 5.63565 | 0.485040 | ||||||||
\(136\) | −2.63565 | −0.226005 | ||||||||
\(137\) | 9.12927 | 0.779966 | 0.389983 | − | 0.920822i | \(-0.372481\pi\) | ||||
0.389983 | + | 0.920822i | \(0.372481\pi\) | |||||||
\(138\) | 7.32959 | 0.623936 | ||||||||
\(139\) | −0.657844 | −0.0557976 | −0.0278988 | − | 0.999611i | \(-0.508882\pi\) | ||||
−0.0278988 | + | 0.999611i | \(0.508882\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | 11.2731 | 0.949363 | ||||||||
\(142\) | 13.8057 | 1.15855 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.19656 | −0.0997131 | ||||||||
\(145\) | −2.83920 | −0.235783 | ||||||||
\(146\) | −1.14830 | −0.0950337 | ||||||||
\(147\) | −1.34292 | −0.110762 | ||||||||
\(148\) | −0.839198 | −0.0689816 | ||||||||
\(149\) | 20.5982 | 1.68747 | 0.843737 | − | 0.536757i | \(-0.180351\pi\) | ||||
0.843737 | + | 0.536757i | \(0.180351\pi\) | |||||||
\(150\) | 1.34292 | 0.109649 | ||||||||
\(151\) | 4.29219 | 0.349293 | 0.174647 | − | 0.984631i | \(-0.444122\pi\) | ||||
0.174647 | + | 0.984631i | \(0.444122\pi\) | |||||||
\(152\) | 1.56877 | 0.127244 | ||||||||
\(153\) | −3.15371 | −0.254962 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.14637 | 0.0920783 | ||||||||
\(156\) | 5.79011 | 0.463580 | ||||||||
\(157\) | 10.9039 | 0.870226 | 0.435113 | − | 0.900376i | \(-0.356708\pi\) | ||||
0.435113 | + | 0.900376i | \(0.356708\pi\) | |||||||
\(158\) | 9.65408 | 0.768037 | ||||||||
\(159\) | −1.88820 | −0.149744 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −5.45794 | −0.430146 | ||||||||
\(162\) | 3.97858 | 0.312587 | ||||||||
\(163\) | 12.3525 | 0.967526 | 0.483763 | − | 0.875199i | \(-0.339270\pi\) | ||||
0.483763 | + | 0.875199i | \(0.339270\pi\) | |||||||
\(164\) | −3.47854 | −0.271628 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.51880 | −0.195497 | ||||||||
\(167\) | 6.93334 | 0.536518 | 0.268259 | − | 0.963347i | \(-0.413552\pi\) | ||||
0.268259 | + | 0.963347i | \(0.413552\pi\) | |||||||
\(168\) | −1.34292 | −0.103609 | ||||||||
\(169\) | 5.58967 | 0.429975 | ||||||||
\(170\) | −2.63565 | −0.202145 | ||||||||
\(171\) | 1.87713 | 0.143548 | ||||||||
\(172\) | 2.01075 | 0.153318 | ||||||||
\(173\) | 11.5843 | 0.880741 | 0.440370 | − | 0.897816i | \(-0.354847\pi\) | ||||
0.440370 | + | 0.897816i | \(0.354847\pi\) | |||||||
\(174\) | −3.81282 | −0.289049 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.12106 | −0.234593 | ||||||||
\(178\) | −2.19326 | −0.164392 | ||||||||
\(179\) | 20.4825 | 1.53093 | 0.765466 | − | 0.643476i | \(-0.222508\pi\) | ||||
0.765466 | + | 0.643476i | \(0.222508\pi\) | |||||||
\(180\) | −1.19656 | −0.0891861 | ||||||||
\(181\) | −8.01175 | −0.595509 | −0.297754 | − | 0.954642i | \(-0.596238\pi\) | ||||
−0.297754 | + | 0.954642i | \(0.596238\pi\) | |||||||
\(182\) | −4.31157 | −0.319595 | ||||||||
\(183\) | −7.04211 | −0.520568 | ||||||||
\(184\) | −5.45794 | −0.402365 | ||||||||
\(185\) | −0.839198 | −0.0616990 | ||||||||
\(186\) | 1.53948 | 0.112880 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −8.39442 | −0.612226 | ||||||||
\(189\) | −5.63565 | −0.409934 | ||||||||
\(190\) | 1.56877 | 0.113811 | ||||||||
\(191\) | 7.72371 | 0.558868 | 0.279434 | − | 0.960165i | \(-0.409853\pi\) | ||||
0.279434 | + | 0.960165i | \(0.409853\pi\) | |||||||
\(192\) | −1.34292 | −0.0969171 | ||||||||
\(193\) | 16.3855 | 1.17945 | 0.589727 | − | 0.807603i | \(-0.299235\pi\) | ||||
0.589727 | + | 0.807603i | \(0.299235\pi\) | |||||||
\(194\) | 7.56372 | 0.543043 | ||||||||
\(195\) | 5.79011 | 0.414639 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −5.51971 | −0.393263 | −0.196631 | − | 0.980477i | \(-0.563000\pi\) | ||||
−0.196631 | + | 0.980477i | \(0.563000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.27443 | 0.303006 | 0.151503 | − | 0.988457i | \(-0.451589\pi\) | ||||
0.151503 | + | 0.988457i | \(0.451589\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 2.15722 | 0.152159 | ||||||||
\(202\) | 17.6449 | 1.24149 | ||||||||
\(203\) | 2.83920 | 0.199273 | ||||||||
\(204\) | −3.53948 | −0.247813 | ||||||||
\(205\) | −3.47854 | −0.242952 | ||||||||
\(206\) | −10.1528 | −0.707381 | ||||||||
\(207\) | −6.53074 | −0.453918 | ||||||||
\(208\) | −4.31157 | −0.298954 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.34292 | −0.0926705 | ||||||||
\(211\) | 19.6106 | 1.35005 | 0.675026 | − | 0.737794i | \(-0.264132\pi\) | ||||
0.675026 | + | 0.737794i | \(0.264132\pi\) | |||||||
\(212\) | 1.40604 | 0.0965672 | ||||||||
\(213\) | 18.5400 | 1.27034 | ||||||||
\(214\) | 15.4232 | 1.05431 | ||||||||
\(215\) | 2.01075 | 0.137132 | ||||||||
\(216\) | −5.63565 | −0.383458 | ||||||||
\(217\) | −1.14637 | −0.0778204 | ||||||||
\(218\) | 8.49656 | 0.575459 | ||||||||
\(219\) | −1.54207 | −0.104204 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.3638 | −0.764413 | ||||||||
\(222\) | −1.12698 | −0.0756378 | ||||||||
\(223\) | 4.01943 | 0.269161 | 0.134580 | − | 0.990903i | \(-0.457031\pi\) | ||||
0.134580 | + | 0.990903i | \(0.457031\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −1.19656 | −0.0797705 | ||||||||
\(226\) | −2.72299 | −0.181131 | ||||||||
\(227\) | −20.4787 | −1.35922 | −0.679610 | − | 0.733574i | \(-0.737851\pi\) | ||||
−0.679610 | + | 0.733574i | \(0.737851\pi\) | |||||||
\(228\) | 2.10674 | 0.139522 | ||||||||
\(229\) | 8.74872 | 0.578132 | 0.289066 | − | 0.957309i | \(-0.406655\pi\) | ||||
0.289066 | + | 0.957309i | \(0.406655\pi\) | |||||||
\(230\) | −5.45794 | −0.359886 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.83920 | 0.186402 | ||||||||
\(233\) | −14.1462 | −0.926748 | −0.463374 | − | 0.886163i | \(-0.653361\pi\) | ||||
−0.463374 | + | 0.886163i | \(0.653361\pi\) | |||||||
\(234\) | −5.15905 | −0.337257 | ||||||||
\(235\) | −8.39442 | −0.547591 | ||||||||
\(236\) | 2.32408 | 0.151285 | ||||||||
\(237\) | 12.9647 | 0.842147 | ||||||||
\(238\) | 2.63565 | 0.170844 | ||||||||
\(239\) | −2.12134 | −0.137218 | −0.0686091 | − | 0.997644i | \(-0.521856\pi\) | ||||
−0.0686091 | + | 0.997644i | \(0.521856\pi\) | |||||||
\(240\) | −1.34292 | −0.0866853 | ||||||||
\(241\) | −17.4357 | −1.12313 | −0.561566 | − | 0.827432i | \(-0.689801\pi\) | ||||
−0.561566 | + | 0.827432i | \(0.689801\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.5640 | −0.741833 | ||||||||
\(244\) | 5.24387 | 0.335704 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −4.67141 | −0.297838 | ||||||||
\(247\) | 6.76388 | 0.430376 | ||||||||
\(248\) | −1.14637 | −0.0727943 | ||||||||
\(249\) | −3.38256 | −0.214361 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 0.936840 | 0.0591328 | 0.0295664 | − | 0.999563i | \(-0.490587\pi\) | ||||
0.0295664 | + | 0.999563i | \(0.490587\pi\) | |||||||
\(252\) | 1.19656 | 0.0753760 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −9.21928 | −0.578469 | ||||||||
\(255\) | −3.53948 | −0.221651 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.7242 | 0.856095 | 0.428047 | − | 0.903756i | \(-0.359202\pi\) | ||||
0.428047 | + | 0.903756i | \(0.359202\pi\) | |||||||
\(258\) | 2.70028 | 0.168112 | ||||||||
\(259\) | 0.839198 | 0.0521452 | ||||||||
\(260\) | −4.31157 | −0.267392 | ||||||||
\(261\) | 3.39726 | 0.210285 | ||||||||
\(262\) | 17.5357 | 1.08336 | ||||||||
\(263\) | 18.9341 | 1.16753 | 0.583763 | − | 0.811924i | \(-0.301580\pi\) | ||||
0.583763 | + | 0.811924i | \(0.301580\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.40604 | 0.0863723 | ||||||||
\(266\) | −1.56877 | −0.0961877 | ||||||||
\(267\) | −2.94538 | −0.180254 | ||||||||
\(268\) | −1.60636 | −0.0981241 | ||||||||
\(269\) | 12.9639 | 0.790422 | 0.395211 | − | 0.918590i | \(-0.370672\pi\) | ||||
0.395211 | + | 0.918590i | \(0.370672\pi\) | |||||||
\(270\) | −5.63565 | −0.342975 | ||||||||
\(271\) | −23.5085 | −1.42804 | −0.714020 | − | 0.700125i | \(-0.753127\pi\) | ||||
−0.714020 | + | 0.700125i | \(0.753127\pi\) | |||||||
\(272\) | 2.63565 | 0.159810 | ||||||||
\(273\) | −5.79011 | −0.350434 | ||||||||
\(274\) | −9.12927 | −0.551519 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −7.32959 | −0.441190 | ||||||||
\(277\) | −2.44560 | −0.146942 | −0.0734710 | − | 0.997297i | \(-0.523408\pi\) | ||||
−0.0734710 | + | 0.997297i | \(0.523408\pi\) | |||||||
\(278\) | 0.657844 | 0.0394549 | ||||||||
\(279\) | −1.37169 | −0.0821211 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | 18.0116 | 1.07448 | 0.537242 | − | 0.843428i | \(-0.319466\pi\) | ||||
0.537242 | + | 0.843428i | \(0.319466\pi\) | |||||||
\(282\) | −11.2731 | −0.671301 | ||||||||
\(283\) | 9.78930 | 0.581914 | 0.290957 | − | 0.956736i | \(-0.406026\pi\) | ||||
0.290957 | + | 0.956736i | \(0.406026\pi\) | |||||||
\(284\) | −13.8057 | −0.819220 | ||||||||
\(285\) | 2.10674 | 0.124793 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.47854 | 0.205332 | ||||||||
\(288\) | 1.19656 | 0.0705078 | ||||||||
\(289\) | −10.0533 | −0.591372 | ||||||||
\(290\) | 2.83920 | 0.166723 | ||||||||
\(291\) | 10.1575 | 0.595443 | ||||||||
\(292\) | 1.14830 | 0.0671990 | ||||||||
\(293\) | 8.44836 | 0.493558 | 0.246779 | − | 0.969072i | \(-0.420628\pi\) | ||||
0.246779 | + | 0.969072i | \(0.420628\pi\) | |||||||
\(294\) | 1.34292 | 0.0783209 | ||||||||
\(295\) | 2.32408 | 0.135313 | ||||||||
\(296\) | 0.839198 | 0.0487774 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −20.5982 | −1.19322 | ||||||||
\(299\) | −23.5323 | −1.36091 | ||||||||
\(300\) | −1.34292 | −0.0775337 | ||||||||
\(301\) | −2.01075 | −0.115898 | ||||||||
\(302\) | −4.29219 | −0.246988 | ||||||||
\(303\) | 23.6958 | 1.36129 | ||||||||
\(304\) | −1.56877 | −0.0899753 | ||||||||
\(305\) | 5.24387 | 0.300263 | ||||||||
\(306\) | 3.15371 | 0.180286 | ||||||||
\(307\) | 9.34689 | 0.533455 | 0.266728 | − | 0.963772i | \(-0.414058\pi\) | ||||
0.266728 | + | 0.963772i | \(0.414058\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.6345 | −0.775638 | ||||||||
\(310\) | −1.14637 | −0.0651092 | ||||||||
\(311\) | −27.6729 | −1.56919 | −0.784593 | − | 0.620011i | \(-0.787128\pi\) | ||||
−0.784593 | + | 0.620011i | \(0.787128\pi\) | |||||||
\(312\) | −5.79011 | −0.327801 | ||||||||
\(313\) | 5.34524 | 0.302131 | 0.151065 | − | 0.988524i | \(-0.451730\pi\) | ||||
0.151065 | + | 0.988524i | \(0.451730\pi\) | |||||||
\(314\) | −10.9039 | −0.615343 | ||||||||
\(315\) | 1.19656 | 0.0674184 | ||||||||
\(316\) | −9.65408 | −0.543084 | ||||||||
\(317\) | 7.13917 | 0.400976 | 0.200488 | − | 0.979696i | \(-0.435747\pi\) | ||||
0.200488 | + | 0.979696i | \(0.435747\pi\) | |||||||
\(318\) | 1.88820 | 0.105885 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 20.7122 | 1.15604 | ||||||||
\(322\) | 5.45794 | 0.304159 | ||||||||
\(323\) | −4.13474 | −0.230063 | ||||||||
\(324\) | −3.97858 | −0.221032 | ||||||||
\(325\) | −4.31157 | −0.239163 | ||||||||
\(326\) | −12.3525 | −0.684144 | ||||||||
\(327\) | 11.4102 | 0.630987 | ||||||||
\(328\) | 3.47854 | 0.192070 | ||||||||
\(329\) | 8.39442 | 0.462799 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.83207 | 0.320559 | 0.160280 | − | 0.987072i | \(-0.448760\pi\) | ||||
0.160280 | + | 0.987072i | \(0.448760\pi\) | |||||||
\(332\) | 2.51880 | 0.138237 | ||||||||
\(333\) | 1.00415 | 0.0550270 | ||||||||
\(334\) | −6.93334 | −0.379375 | ||||||||
\(335\) | −1.60636 | −0.0877649 | ||||||||
\(336\) | 1.34292 | 0.0732625 | ||||||||
\(337\) | −22.2848 | −1.21393 | −0.606964 | − | 0.794729i | \(-0.707613\pi\) | ||||
−0.606964 | + | 0.794729i | \(0.707613\pi\) | |||||||
\(338\) | −5.58967 | −0.304038 | ||||||||
\(339\) | −3.65677 | −0.198609 | ||||||||
\(340\) | 2.63565 | 0.142938 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −1.87713 | −0.101503 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −2.01075 | −0.108412 | ||||||||
\(345\) | −7.32959 | −0.394612 | ||||||||
\(346\) | −11.5843 | −0.622778 | ||||||||
\(347\) | −16.6253 | −0.892495 | −0.446248 | − | 0.894910i | \(-0.647240\pi\) | ||||
−0.446248 | + | 0.894910i | \(0.647240\pi\) | |||||||
\(348\) | 3.81282 | 0.204389 | ||||||||
\(349\) | −3.23934 | −0.173398 | −0.0866989 | − | 0.996235i | \(-0.527632\pi\) | ||||
−0.0866989 | + | 0.996235i | \(0.527632\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | −24.2985 | −1.29696 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.6580 | −1.31241 | −0.656205 | − | 0.754582i | \(-0.727839\pi\) | ||||
−0.656205 | + | 0.754582i | \(0.727839\pi\) | |||||||
\(354\) | 3.12106 | 0.165882 | ||||||||
\(355\) | −13.8057 | −0.732732 | ||||||||
\(356\) | 2.19326 | 0.116242 | ||||||||
\(357\) | 3.53948 | 0.187329 | ||||||||
\(358\) | −20.4825 | −1.08253 | ||||||||
\(359\) | −20.7493 | −1.09511 | −0.547554 | − | 0.836771i | \(-0.684441\pi\) | ||||
−0.547554 | + | 0.836771i | \(0.684441\pi\) | |||||||
\(360\) | 1.19656 | 0.0630641 | ||||||||
\(361\) | −16.5390 | −0.870471 | ||||||||
\(362\) | 8.01175 | 0.421088 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.31157 | 0.225988 | ||||||||
\(365\) | 1.14830 | 0.0601046 | ||||||||
\(366\) | 7.04211 | 0.368097 | ||||||||
\(367\) | 2.12160 | 0.110746 | 0.0553732 | − | 0.998466i | \(-0.482365\pi\) | ||||
0.0553732 | + | 0.998466i | \(0.482365\pi\) | |||||||
\(368\) | 5.45794 | 0.284515 | ||||||||
\(369\) | 4.16227 | 0.216679 | ||||||||
\(370\) | 0.839198 | 0.0436278 | ||||||||
\(371\) | −1.40604 | −0.0729979 | ||||||||
\(372\) | −1.53948 | −0.0798184 | ||||||||
\(373\) | 7.19996 | 0.372800 | 0.186400 | − | 0.982474i | \(-0.440318\pi\) | ||||
0.186400 | + | 0.982474i | \(0.440318\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.34292 | −0.0693482 | ||||||||
\(376\) | 8.39442 | 0.432909 | ||||||||
\(377\) | 12.2414 | 0.630465 | ||||||||
\(378\) | 5.63565 | 0.289867 | ||||||||
\(379\) | −23.1300 | −1.18811 | −0.594055 | − | 0.804424i | \(-0.702474\pi\) | ||||
−0.594055 | + | 0.804424i | \(0.702474\pi\) | |||||||
\(380\) | −1.56877 | −0.0804764 | ||||||||
\(381\) | −12.3808 | −0.634287 | ||||||||
\(382\) | −7.72371 | −0.395180 | ||||||||
\(383\) | 31.4479 | 1.60691 | 0.803455 | − | 0.595365i | \(-0.202993\pi\) | ||||
0.803455 | + | 0.595365i | \(0.202993\pi\) | |||||||
\(384\) | 1.34292 | 0.0685308 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16.3855 | −0.834000 | ||||||||
\(387\) | −2.40598 | −0.122303 | ||||||||
\(388\) | −7.56372 | −0.383990 | ||||||||
\(389\) | 17.5618 | 0.890420 | 0.445210 | − | 0.895426i | \(-0.353129\pi\) | ||||
0.445210 | + | 0.895426i | \(0.353129\pi\) | |||||||
\(390\) | −5.79011 | −0.293194 | ||||||||
\(391\) | 14.3852 | 0.727493 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 23.5491 | 1.18790 | ||||||||
\(394\) | 5.51971 | 0.278079 | ||||||||
\(395\) | −9.65408 | −0.485749 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.7839 | 1.64538 | 0.822689 | − | 0.568492i | \(-0.192473\pi\) | ||||
0.822689 | + | 0.568492i | \(0.192473\pi\) | |||||||
\(398\) | −4.27443 | −0.214258 | ||||||||
\(399\) | −2.10674 | −0.105469 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 9.25146 | 0.461996 | 0.230998 | − | 0.972954i | \(-0.425801\pi\) | ||||
0.230998 | + | 0.972954i | \(0.425801\pi\) | |||||||
\(402\) | −2.15722 | −0.107592 | ||||||||
\(403\) | −4.94264 | −0.246210 | ||||||||
\(404\) | −17.6449 | −0.877868 | ||||||||
\(405\) | −3.97858 | −0.197697 | ||||||||
\(406\) | −2.83920 | −0.140907 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 3.53948 | 0.175230 | ||||||||
\(409\) | 0.0174947 | 0.000865057 0 | 0.000432529 | − | 1.00000i | \(-0.499862\pi\) | ||||
0.000432529 | 1.00000i | \(0.499862\pi\) | ||||||||
\(410\) | 3.47854 | 0.171793 | ||||||||
\(411\) | −12.2599 | −0.604737 | ||||||||
\(412\) | 10.1528 | 0.500194 | ||||||||
\(413\) | −2.32408 | −0.114360 | ||||||||
\(414\) | 6.53074 | 0.320968 | ||||||||
\(415\) | 2.51880 | 0.123643 | ||||||||
\(416\) | 4.31157 | 0.211392 | ||||||||
\(417\) | 0.883434 | 0.0432620 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.4579 | 1.58567 | 0.792837 | − | 0.609433i | \(-0.208603\pi\) | ||||
0.792837 | + | 0.609433i | \(0.208603\pi\) | |||||||
\(420\) | 1.34292 | 0.0655279 | ||||||||
\(421\) | 9.15329 | 0.446104 | 0.223052 | − | 0.974807i | \(-0.428398\pi\) | ||||
0.223052 | + | 0.974807i | \(0.428398\pi\) | |||||||
\(422\) | −19.6106 | −0.954631 | ||||||||
\(423\) | 10.0444 | 0.488376 | ||||||||
\(424\) | −1.40604 | −0.0682833 | ||||||||
\(425\) | 2.63565 | 0.127848 | ||||||||
\(426\) | −18.5400 | −0.898268 | ||||||||
\(427\) | −5.24387 | −0.253769 | ||||||||
\(428\) | −15.4232 | −0.745508 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.01075 | −0.0969670 | ||||||||
\(431\) | 26.0024 | 1.25249 | 0.626247 | − | 0.779625i | \(-0.284590\pi\) | ||||
0.626247 | + | 0.779625i | \(0.284590\pi\) | |||||||
\(432\) | 5.63565 | 0.271146 | ||||||||
\(433\) | 23.6006 | 1.13417 | 0.567085 | − | 0.823659i | \(-0.308071\pi\) | ||||
0.567085 | + | 0.823659i | \(0.308071\pi\) | |||||||
\(434\) | 1.14637 | 0.0550273 | ||||||||
\(435\) | 3.81282 | 0.182811 | ||||||||
\(436\) | −8.49656 | −0.406911 | ||||||||
\(437\) | −8.56227 | −0.409589 | ||||||||
\(438\) | 1.54207 | 0.0736832 | ||||||||
\(439\) | −31.7894 | −1.51722 | −0.758612 | − | 0.651543i | \(-0.774122\pi\) | ||||
−0.758612 | + | 0.651543i | \(0.774122\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.19656 | −0.0569789 | ||||||||
\(442\) | 11.3638 | 0.540522 | ||||||||
\(443\) | 36.1071 | 1.71550 | 0.857750 | − | 0.514067i | \(-0.171862\pi\) | ||||
0.857750 | + | 0.514067i | \(0.171862\pi\) | |||||||
\(444\) | 1.12698 | 0.0534840 | ||||||||
\(445\) | 2.19326 | 0.103970 | ||||||||
\(446\) | −4.01943 | −0.190326 | ||||||||
\(447\) | −27.6619 | −1.30836 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −4.52269 | −0.213439 | −0.106719 | − | 0.994289i | \(-0.534035\pi\) | ||||
−0.106719 | + | 0.994289i | \(0.534035\pi\) | |||||||
\(450\) | 1.19656 | 0.0564063 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 2.72299 | 0.128079 | ||||||||
\(453\) | −5.76408 | −0.270820 | ||||||||
\(454\) | 20.4787 | 0.961114 | ||||||||
\(455\) | 4.31157 | 0.202130 | ||||||||
\(456\) | −2.10674 | −0.0986572 | ||||||||
\(457\) | 15.1593 | 0.709120 | 0.354560 | − | 0.935033i | \(-0.384631\pi\) | ||||
0.354560 | + | 0.935033i | \(0.384631\pi\) | |||||||
\(458\) | −8.74872 | −0.408801 | ||||||||
\(459\) | 14.8536 | 0.693308 | ||||||||
\(460\) | 5.45794 | 0.254478 | ||||||||
\(461\) | 27.6126 | 1.28605 | 0.643024 | − | 0.765846i | \(-0.277680\pi\) | ||||
0.643024 | + | 0.765846i | \(0.277680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.3557 | 0.620692 | 0.310346 | − | 0.950624i | \(-0.399555\pi\) | ||||
0.310346 | + | 0.950624i | \(0.399555\pi\) | |||||||
\(464\) | −2.83920 | −0.131806 | ||||||||
\(465\) | −1.53948 | −0.0713917 | ||||||||
\(466\) | 14.1462 | 0.655310 | ||||||||
\(467\) | 26.3287 | 1.21835 | 0.609173 | − | 0.793038i | \(-0.291502\pi\) | ||||
0.609173 | + | 0.793038i | \(0.291502\pi\) | |||||||
\(468\) | 5.15905 | 0.238477 | ||||||||
\(469\) | 1.60636 | 0.0741749 | ||||||||
\(470\) | 8.39442 | 0.387206 | ||||||||
\(471\) | −14.6431 | −0.674719 | ||||||||
\(472\) | −2.32408 | −0.106974 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −12.9647 | −0.595488 | ||||||||
\(475\) | −1.56877 | −0.0719803 | ||||||||
\(476\) | −2.63565 | −0.120805 | ||||||||
\(477\) | −1.68241 | −0.0770322 | ||||||||
\(478\) | 2.12134 | 0.0970279 | ||||||||
\(479\) | −8.18258 | −0.373872 | −0.186936 | − | 0.982372i | \(-0.559856\pi\) | ||||
−0.186936 | + | 0.982372i | \(0.559856\pi\) | |||||||
\(480\) | 1.34292 | 0.0612958 | ||||||||
\(481\) | 3.61826 | 0.164979 | ||||||||
\(482\) | 17.4357 | 0.794174 | ||||||||
\(483\) | 7.32959 | 0.333508 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.56372 | −0.343451 | ||||||||
\(486\) | 11.5640 | 0.524555 | ||||||||
\(487\) | −9.09993 | −0.412357 | −0.206179 | − | 0.978514i | \(-0.566103\pi\) | ||||
−0.206179 | + | 0.978514i | \(0.566103\pi\) | |||||||
\(488\) | −5.24387 | −0.237379 | ||||||||
\(489\) | −16.5885 | −0.750159 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | 3.80239 | 0.171600 | 0.0857998 | − | 0.996312i | \(-0.472655\pi\) | ||||
0.0857998 | + | 0.996312i | \(0.472655\pi\) | |||||||
\(492\) | 4.67141 | 0.210603 | ||||||||
\(493\) | −7.48314 | −0.337024 | ||||||||
\(494\) | −6.76388 | −0.304321 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.14637 | 0.0514733 | ||||||||
\(497\) | 13.8057 | 0.619272 | ||||||||
\(498\) | 3.38256 | 0.151576 | ||||||||
\(499\) | −22.9856 | −1.02898 | −0.514488 | − | 0.857497i | \(-0.672018\pi\) | ||||
−0.514488 | + | 0.857497i | \(0.672018\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −9.31094 | −0.415982 | ||||||||
\(502\) | −0.936840 | −0.0418132 | ||||||||
\(503\) | −13.4287 | −0.598756 | −0.299378 | − | 0.954135i | \(-0.596779\pi\) | ||||
−0.299378 | + | 0.954135i | \(0.596779\pi\) | |||||||
\(504\) | −1.19656 | −0.0532989 | ||||||||
\(505\) | −17.6449 | −0.785189 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.50650 | −0.333375 | ||||||||
\(508\) | 9.21928 | 0.409040 | ||||||||
\(509\) | 36.9453 | 1.63757 | 0.818785 | − | 0.574100i | \(-0.194648\pi\) | ||||
0.818785 | + | 0.574100i | \(0.194648\pi\) | |||||||
\(510\) | 3.53948 | 0.156731 | ||||||||
\(511\) | −1.14830 | −0.0507977 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −8.84106 | −0.390342 | ||||||||
\(514\) | −13.7242 | −0.605350 | ||||||||
\(515\) | 10.1528 | 0.447387 | ||||||||
\(516\) | −2.70028 | −0.118873 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −0.839198 | −0.0368722 | ||||||||
\(519\) | −15.5569 | −0.682871 | ||||||||
\(520\) | 4.31157 | 0.189075 | ||||||||
\(521\) | 12.8367 | 0.562388 | 0.281194 | − | 0.959651i | \(-0.409270\pi\) | ||||
0.281194 | + | 0.959651i | \(0.409270\pi\) | |||||||
\(522\) | −3.39726 | −0.148694 | ||||||||
\(523\) | 8.66972 | 0.379100 | 0.189550 | − | 0.981871i | \(-0.439297\pi\) | ||||
0.189550 | + | 0.981871i | \(0.439297\pi\) | |||||||
\(524\) | −17.5357 | −0.766052 | ||||||||
\(525\) | 1.34292 | 0.0586100 | ||||||||
\(526\) | −18.9341 | −0.825565 | ||||||||
\(527\) | 3.02142 | 0.131615 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.78911 | 0.295179 | ||||||||
\(530\) | −1.40604 | −0.0610745 | ||||||||
\(531\) | −2.78090 | −0.120681 | ||||||||
\(532\) | 1.56877 | 0.0680149 | ||||||||
\(533\) | 14.9980 | 0.649634 | ||||||||
\(534\) | 2.94538 | 0.127459 | ||||||||
\(535\) | −15.4232 | −0.666803 | ||||||||
\(536\) | 1.60636 | 0.0693842 | ||||||||
\(537\) | −27.5064 | −1.18699 | ||||||||
\(538\) | −12.9639 | −0.558913 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5.63565 | 0.242520 | ||||||||
\(541\) | 38.6634 | 1.66227 | 0.831136 | − | 0.556070i | \(-0.187691\pi\) | ||||
0.831136 | + | 0.556070i | \(0.187691\pi\) | |||||||
\(542\) | 23.5085 | 1.00978 | ||||||||
\(543\) | 10.7592 | 0.461720 | ||||||||
\(544\) | −2.63565 | −0.113003 | ||||||||
\(545\) | −8.49656 | −0.363953 | ||||||||
\(546\) | 5.79011 | 0.247794 | ||||||||
\(547\) | 6.20768 | 0.265421 | 0.132711 | − | 0.991155i | \(-0.457632\pi\) | ||||
0.132711 | + | 0.991155i | \(0.457632\pi\) | |||||||
\(548\) | 9.12927 | 0.389983 | ||||||||
\(549\) | −6.27459 | −0.267793 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.45406 | 0.189749 | ||||||||
\(552\) | 7.32959 | 0.311968 | ||||||||
\(553\) | 9.65408 | 0.410533 | ||||||||
\(554\) | 2.44560 | 0.103904 | ||||||||
\(555\) | 1.12698 | 0.0478376 | ||||||||
\(556\) | −0.657844 | −0.0278988 | ||||||||
\(557\) | 36.9739 | 1.56663 | 0.783317 | − | 0.621623i | \(-0.213526\pi\) | ||||
0.783317 | + | 0.621623i | \(0.213526\pi\) | |||||||
\(558\) | 1.37169 | 0.0580684 | ||||||||
\(559\) | −8.66950 | −0.366681 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −18.0116 | −0.759776 | ||||||||
\(563\) | −26.0483 | −1.09780 | −0.548901 | − | 0.835887i | \(-0.684954\pi\) | ||||
−0.548901 | + | 0.835887i | \(0.684954\pi\) | |||||||
\(564\) | 11.2731 | 0.474681 | ||||||||
\(565\) | 2.72299 | 0.114557 | ||||||||
\(566\) | −9.78930 | −0.411475 | ||||||||
\(567\) | 3.97858 | 0.167085 | ||||||||
\(568\) | 13.8057 | 0.579276 | ||||||||
\(569\) | 18.6278 | 0.780920 | 0.390460 | − | 0.920620i | \(-0.372316\pi\) | ||||
0.390460 | + | 0.920620i | \(0.372316\pi\) | |||||||
\(570\) | −2.10674 | −0.0882417 | ||||||||
\(571\) | −34.4156 | −1.44025 | −0.720123 | − | 0.693846i | \(-0.755915\pi\) | ||||
−0.720123 | + | 0.693846i | \(0.755915\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.3724 | −0.433311 | ||||||||
\(574\) | −3.47854 | −0.145191 | ||||||||
\(575\) | 5.45794 | 0.227612 | ||||||||
\(576\) | −1.19656 | −0.0498566 | ||||||||
\(577\) | 24.5630 | 1.02257 | 0.511285 | − | 0.859411i | \(-0.329170\pi\) | ||||
0.511285 | + | 0.859411i | \(0.329170\pi\) | |||||||
\(578\) | 10.0533 | 0.418163 | ||||||||
\(579\) | −22.0045 | −0.914474 | ||||||||
\(580\) | −2.83920 | −0.117891 | ||||||||
\(581\) | −2.51880 | −0.104498 | ||||||||
\(582\) | −10.1575 | −0.421042 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −1.14830 | −0.0475169 | ||||||||
\(585\) | 5.15905 | 0.213300 | ||||||||
\(586\) | −8.44836 | −0.348999 | ||||||||
\(587\) | 18.3415 | 0.757037 | 0.378518 | − | 0.925594i | \(-0.376434\pi\) | ||||
0.378518 | + | 0.925594i | \(0.376434\pi\) | |||||||
\(588\) | −1.34292 | −0.0553812 | ||||||||
\(589\) | −1.79839 | −0.0741013 | ||||||||
\(590\) | −2.32408 | −0.0956809 | ||||||||
\(591\) | 7.41254 | 0.304911 | ||||||||
\(592\) | −0.839198 | −0.0344908 | ||||||||
\(593\) | 10.9987 | 0.451664 | 0.225832 | − | 0.974166i | \(-0.427490\pi\) | ||||
0.225832 | + | 0.974166i | \(0.427490\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.63565 | −0.108051 | ||||||||
\(596\) | 20.5982 | 0.843737 | ||||||||
\(597\) | −5.74023 | −0.234932 | ||||||||
\(598\) | 23.5323 | 0.962308 | ||||||||
\(599\) | 4.76034 | 0.194502 | 0.0972511 | − | 0.995260i | \(-0.468995\pi\) | ||||
0.0972511 | + | 0.995260i | \(0.468995\pi\) | |||||||
\(600\) | 1.34292 | 0.0548246 | ||||||||
\(601\) | 16.5137 | 0.673608 | 0.336804 | − | 0.941575i | \(-0.390654\pi\) | ||||
0.336804 | + | 0.941575i | \(0.390654\pi\) | |||||||
\(602\) | 2.01075 | 0.0819521 | ||||||||
\(603\) | 1.92210 | 0.0782741 | ||||||||
\(604\) | 4.29219 | 0.174647 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −23.6958 | −0.962576 | ||||||||
\(607\) | −3.14655 | −0.127714 | −0.0638572 | − | 0.997959i | \(-0.520340\pi\) | ||||
−0.0638572 | + | 0.997959i | \(0.520340\pi\) | |||||||
\(608\) | 1.56877 | 0.0636222 | ||||||||
\(609\) | −3.81282 | −0.154503 | ||||||||
\(610\) | −5.24387 | −0.212318 | ||||||||
\(611\) | 36.1932 | 1.46422 | ||||||||
\(612\) | −3.15371 | −0.127481 | ||||||||
\(613\) | 45.9924 | 1.85761 | 0.928807 | − | 0.370564i | \(-0.120836\pi\) | ||||
0.928807 | + | 0.370564i | \(0.120836\pi\) | |||||||
\(614\) | −9.34689 | −0.377210 | ||||||||
\(615\) | 4.67141 | 0.188369 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 45.5056 | 1.83198 | 0.915992 | − | 0.401196i | \(-0.131405\pi\) | ||||
0.915992 | + | 0.401196i | \(0.131405\pi\) | |||||||
\(618\) | 13.6345 | 0.548459 | ||||||||
\(619\) | −22.5870 | −0.907849 | −0.453925 | − | 0.891040i | \(-0.649976\pi\) | ||||
−0.453925 | + | 0.891040i | \(0.649976\pi\) | |||||||
\(620\) | 1.14637 | 0.0460391 | ||||||||
\(621\) | 30.7591 | 1.23432 | ||||||||
\(622\) | 27.6729 | 1.10958 | ||||||||
\(623\) | −2.19326 | −0.0878710 | ||||||||
\(624\) | 5.79011 | 0.231790 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −5.34524 | −0.213639 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.9039 | 0.435113 | ||||||||
\(629\) | −2.21184 | −0.0881916 | ||||||||
\(630\) | −1.19656 | −0.0476720 | ||||||||
\(631\) | 14.8009 | 0.589213 | 0.294606 | − | 0.955619i | \(-0.404811\pi\) | ||||
0.294606 | + | 0.955619i | \(0.404811\pi\) | |||||||
\(632\) | 9.65408 | 0.384019 | ||||||||
\(633\) | −26.3356 | −1.04675 | ||||||||
\(634\) | −7.13917 | −0.283533 | ||||||||
\(635\) | 9.21928 | 0.365856 | ||||||||
\(636\) | −1.88820 | −0.0748721 | ||||||||
\(637\) | −4.31157 | −0.170831 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 16.5194 | 0.653496 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −34.5333 | −1.36398 | −0.681992 | − | 0.731360i | \(-0.738886\pi\) | ||||
−0.681992 | + | 0.731360i | \(0.738886\pi\) | |||||||
\(642\) | −20.7122 | −0.817444 | ||||||||
\(643\) | −16.2144 | −0.639434 | −0.319717 | − | 0.947513i | \(-0.603588\pi\) | ||||
−0.319717 | + | 0.947513i | \(0.603588\pi\) | |||||||
\(644\) | −5.45794 | −0.215073 | ||||||||
\(645\) | −2.70028 | −0.106324 | ||||||||
\(646\) | 4.13474 | 0.162679 | ||||||||
\(647\) | −43.3962 | −1.70608 | −0.853041 | − | 0.521844i | \(-0.825244\pi\) | ||||
−0.853041 | + | 0.521844i | \(0.825244\pi\) | |||||||
\(648\) | 3.97858 | 0.156293 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 4.31157 | 0.169114 | ||||||||
\(651\) | 1.53948 | 0.0603370 | ||||||||
\(652\) | 12.3525 | 0.483763 | ||||||||
\(653\) | 7.75135 | 0.303334 | 0.151667 | − | 0.988432i | \(-0.451536\pi\) | ||||
0.151667 | + | 0.988432i | \(0.451536\pi\) | |||||||
\(654\) | −11.4102 | −0.446175 | ||||||||
\(655\) | −17.5357 | −0.685178 | ||||||||
\(656\) | −3.47854 | −0.135814 | ||||||||
\(657\) | −1.37400 | −0.0536050 | ||||||||
\(658\) | −8.39442 | −0.327248 | ||||||||
\(659\) | −6.80255 | −0.264990 | −0.132495 | − | 0.991184i | \(-0.542299\pi\) | ||||
−0.132495 | + | 0.991184i | \(0.542299\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.3537 | −0.674980 | −0.337490 | − | 0.941329i | \(-0.609578\pi\) | ||||
−0.337490 | + | 0.941329i | \(0.609578\pi\) | |||||||
\(662\) | −5.83207 | −0.226670 | ||||||||
\(663\) | 15.2607 | 0.592678 | ||||||||
\(664\) | −2.51880 | −0.0977486 | ||||||||
\(665\) | 1.56877 | 0.0608344 | ||||||||
\(666\) | −1.00415 | −0.0389100 | ||||||||
\(667\) | −15.4962 | −0.600014 | ||||||||
\(668\) | 6.93334 | 0.268259 | ||||||||
\(669\) | −5.39779 | −0.208690 | ||||||||
\(670\) | 1.60636 | 0.0620592 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −1.34292 | −0.0518044 | ||||||||
\(673\) | 47.8170 | 1.84321 | 0.921605 | − | 0.388130i | \(-0.126879\pi\) | ||||
0.921605 | + | 0.388130i | \(0.126879\pi\) | |||||||
\(674\) | 22.2848 | 0.858377 | ||||||||
\(675\) | 5.63565 | 0.216916 | ||||||||
\(676\) | 5.58967 | 0.214987 | ||||||||
\(677\) | 7.12176 | 0.273711 | 0.136856 | − | 0.990591i | \(-0.456300\pi\) | ||||
0.136856 | + | 0.990591i | \(0.456300\pi\) | |||||||
\(678\) | 3.65677 | 0.140437 | ||||||||
\(679\) | 7.56372 | 0.290269 | ||||||||
\(680\) | −2.63565 | −0.101073 | ||||||||
\(681\) | 27.5013 | 1.05385 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.8302 | 0.682252 | 0.341126 | − | 0.940018i | \(-0.389192\pi\) | ||||
0.341126 | + | 0.940018i | \(0.389192\pi\) | |||||||
\(684\) | 1.87713 | 0.0717738 | ||||||||
\(685\) | 9.12927 | 0.348812 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −11.7489 | −0.448247 | ||||||||
\(688\) | 2.01075 | 0.0766591 | ||||||||
\(689\) | −6.06225 | −0.230953 | ||||||||
\(690\) | 7.32959 | 0.279033 | ||||||||
\(691\) | −15.7399 | −0.598772 | −0.299386 | − | 0.954132i | \(-0.596782\pi\) | ||||
−0.299386 | + | 0.954132i | \(0.596782\pi\) | |||||||
\(692\) | 11.5843 | 0.440370 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.6253 | 0.631089 | ||||||||
\(695\) | −0.657844 | −0.0249535 | ||||||||
\(696\) | −3.81282 | −0.144525 | ||||||||
\(697\) | −9.16822 | −0.347271 | ||||||||
\(698\) | 3.23934 | 0.122611 | ||||||||
\(699\) | 18.9973 | 0.718542 | ||||||||
\(700\) | −1.00000 | −0.0377964 | ||||||||
\(701\) | 19.1512 | 0.723329 | 0.361665 | − | 0.932308i | \(-0.382209\pi\) | ||||
0.361665 | + | 0.932308i | \(0.382209\pi\) | |||||||
\(702\) | 24.2985 | 0.917089 | ||||||||
\(703\) | 1.31651 | 0.0496532 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.2731 | 0.424568 | ||||||||
\(706\) | 24.6580 | 0.928014 | ||||||||
\(707\) | 17.6449 | 0.663606 | ||||||||
\(708\) | −3.12106 | −0.117297 | ||||||||
\(709\) | 6.08007 | 0.228342 | 0.114171 | − | 0.993461i | \(-0.463579\pi\) | ||||
0.114171 | + | 0.993461i | \(0.463579\pi\) | |||||||
\(710\) | 13.8057 | 0.518120 | ||||||||
\(711\) | 11.5517 | 0.433221 | ||||||||
\(712\) | −2.19326 | −0.0821958 | ||||||||
\(713\) | 6.25679 | 0.234319 | ||||||||
\(714\) | −3.53948 | −0.132462 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 20.4825 | 0.765466 | ||||||||
\(717\) | 2.84880 | 0.106390 | ||||||||
\(718\) | 20.7493 | 0.774358 | ||||||||
\(719\) | 27.3905 | 1.02149 | 0.510746 | − | 0.859732i | \(-0.329369\pi\) | ||||
0.510746 | + | 0.859732i | \(0.329369\pi\) | |||||||
\(720\) | −1.19656 | −0.0445931 | ||||||||
\(721\) | −10.1528 | −0.378111 | ||||||||
\(722\) | 16.5390 | 0.615516 | ||||||||
\(723\) | 23.4148 | 0.870805 | ||||||||
\(724\) | −8.01175 | −0.297754 | ||||||||
\(725\) | −2.83920 | −0.105445 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.3641 | 1.05197 | 0.525984 | − | 0.850495i | \(-0.323697\pi\) | ||||
0.525984 | + | 0.850495i | \(0.323697\pi\) | |||||||
\(728\) | −4.31157 | −0.159798 | ||||||||
\(729\) | 27.4653 | 1.01724 | ||||||||
\(730\) | −1.14830 | −0.0425004 | ||||||||
\(731\) | 5.29964 | 0.196014 | ||||||||
\(732\) | −7.04211 | −0.260284 | ||||||||
\(733\) | 48.3933 | 1.78745 | 0.893724 | − | 0.448618i | \(-0.148084\pi\) | ||||
0.893724 | + | 0.448618i | \(0.148084\pi\) | |||||||
\(734\) | −2.12160 | −0.0783096 | ||||||||
\(735\) | −1.34292 | −0.0495345 | ||||||||
\(736\) | −5.45794 | −0.201182 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −4.16227 | −0.153215 | ||||||||
\(739\) | −6.07467 | −0.223460 | −0.111730 | − | 0.993739i | \(-0.535639\pi\) | ||||
−0.111730 | + | 0.993739i | \(0.535639\pi\) | |||||||
\(740\) | −0.839198 | −0.0308495 | ||||||||
\(741\) | −9.08337 | −0.333686 | ||||||||
\(742\) | 1.40604 | 0.0516173 | ||||||||
\(743\) | −32.1862 | −1.18080 | −0.590398 | − | 0.807112i | \(-0.701029\pi\) | ||||
−0.590398 | + | 0.807112i | \(0.701029\pi\) | |||||||
\(744\) | 1.53948 | 0.0564401 | ||||||||
\(745\) | 20.5982 | 0.754661 | ||||||||
\(746\) | −7.19996 | −0.263609 | ||||||||
\(747\) | −3.01389 | −0.110273 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.4232 | 0.563551 | ||||||||
\(750\) | 1.34292 | 0.0490366 | ||||||||
\(751\) | −24.5881 | −0.897234 | −0.448617 | − | 0.893724i | \(-0.648083\pi\) | ||||
−0.448617 | + | 0.893724i | \(0.648083\pi\) | |||||||
\(752\) | −8.39442 | −0.306113 | ||||||||
\(753\) | −1.25810 | −0.0458479 | ||||||||
\(754\) | −12.2414 | −0.445806 | ||||||||
\(755\) | 4.29219 | 0.156209 | ||||||||
\(756\) | −5.63565 | −0.204967 | ||||||||
\(757\) | −25.5181 | −0.927470 | −0.463735 | − | 0.885974i | \(-0.653491\pi\) | ||||
−0.463735 | + | 0.885974i | \(0.653491\pi\) | |||||||
\(758\) | 23.1300 | 0.840121 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.56877 | 0.0569054 | ||||||||
\(761\) | 13.0436 | 0.472830 | 0.236415 | − | 0.971652i | \(-0.424028\pi\) | ||||
0.236415 | + | 0.971652i | \(0.424028\pi\) | |||||||
\(762\) | 12.3808 | 0.448509 | ||||||||
\(763\) | 8.49656 | 0.307596 | ||||||||
\(764\) | 7.72371 | 0.279434 | ||||||||
\(765\) | −3.15371 | −0.114023 | ||||||||
\(766\) | −31.4479 | −1.13626 | ||||||||
\(767\) | −10.0204 | −0.361817 | ||||||||
\(768\) | −1.34292 | −0.0484586 | ||||||||
\(769\) | 48.0699 | 1.73344 | 0.866722 | − | 0.498792i | \(-0.166223\pi\) | ||||
0.866722 | + | 0.498792i | \(0.166223\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.4306 | −0.663762 | ||||||||
\(772\) | 16.3855 | 0.589727 | ||||||||
\(773\) | −40.5127 | −1.45714 | −0.728570 | − | 0.684972i | \(-0.759815\pi\) | ||||
−0.728570 | + | 0.684972i | \(0.759815\pi\) | |||||||
\(774\) | 2.40598 | 0.0864811 | ||||||||
\(775\) | 1.14637 | 0.0411787 | ||||||||
\(776\) | 7.56372 | 0.271522 | ||||||||
\(777\) | −1.12698 | −0.0404301 | ||||||||
\(778\) | −17.5618 | −0.629622 | ||||||||
\(779\) | 5.45704 | 0.195519 | ||||||||
\(780\) | 5.79011 | 0.207319 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −14.3852 | −0.514415 | ||||||||
\(783\) | −16.0007 | −0.571820 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 10.9039 | 0.389177 | ||||||||
\(786\) | −23.5491 | −0.839970 | ||||||||
\(787\) | −36.3703 | −1.29646 | −0.648231 | − | 0.761444i | \(-0.724491\pi\) | ||||
−0.648231 | + | 0.761444i | \(0.724491\pi\) | |||||||
\(788\) | −5.51971 | −0.196631 | ||||||||
\(789\) | −25.4270 | −0.905226 | ||||||||
\(790\) | 9.65408 | 0.343477 | ||||||||
\(791\) | −2.72299 | −0.0968185 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22.6093 | −0.802881 | ||||||||
\(794\) | −32.7839 | −1.16346 | ||||||||
\(795\) | −1.88820 | −0.0669677 | ||||||||
\(796\) | 4.27443 | 0.151503 | ||||||||
\(797\) | 30.7299 | 1.08851 | 0.544254 | − | 0.838920i | \(-0.316813\pi\) | ||||
0.544254 | + | 0.838920i | \(0.316813\pi\) | |||||||
\(798\) | 2.10674 | 0.0745779 | ||||||||
\(799\) | −22.1248 | −0.782719 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −2.62436 | −0.0927272 | ||||||||
\(802\) | −9.25146 | −0.326680 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 2.15722 | 0.0760793 | ||||||||
\(805\) | −5.45794 | −0.192367 | ||||||||
\(806\) | 4.94264 | 0.174097 | ||||||||
\(807\) | −17.4095 | −0.612843 | ||||||||
\(808\) | 17.6449 | 0.620747 | ||||||||
\(809\) | 45.6988 | 1.60668 | 0.803342 | − | 0.595517i | \(-0.203053\pi\) | ||||
0.803342 | + | 0.595517i | \(0.203053\pi\) | |||||||
\(810\) | 3.97858 | 0.139793 | ||||||||
\(811\) | 9.43169 | 0.331191 | 0.165596 | − | 0.986194i | \(-0.447045\pi\) | ||||
0.165596 | + | 0.986194i | \(0.447045\pi\) | |||||||
\(812\) | 2.83920 | 0.0996363 | ||||||||
\(813\) | 31.5701 | 1.10721 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.3525 | 0.432691 | ||||||||
\(816\) | −3.53948 | −0.123907 | ||||||||
\(817\) | −3.15441 | −0.110359 | ||||||||
\(818\) | −0.0174947 | −0.000611688 0 | ||||||||
\(819\) | −5.15905 | −0.180272 | ||||||||
\(820\) | −3.47854 | −0.121476 | ||||||||
\(821\) | 12.2170 | 0.426376 | 0.213188 | − | 0.977011i | \(-0.431615\pi\) | ||||
0.213188 | + | 0.977011i | \(0.431615\pi\) | |||||||
\(822\) | 12.2599 | 0.427613 | ||||||||
\(823\) | 8.03161 | 0.279964 | 0.139982 | − | 0.990154i | \(-0.455295\pi\) | ||||
0.139982 | + | 0.990154i | \(0.455295\pi\) | |||||||
\(824\) | −10.1528 | −0.353691 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.32408 | 0.0808651 | ||||||||
\(827\) | −9.90168 | −0.344315 | −0.172158 | − | 0.985069i | \(-0.555074\pi\) | ||||
−0.172158 | + | 0.985069i | \(0.555074\pi\) | |||||||
\(828\) | −6.53074 | −0.226959 | ||||||||
\(829\) | −20.2243 | −0.702420 | −0.351210 | − | 0.936297i | \(-0.614230\pi\) | ||||
−0.351210 | + | 0.936297i | \(0.614230\pi\) | |||||||
\(830\) | −2.51880 | −0.0874290 | ||||||||
\(831\) | 3.28426 | 0.113930 | ||||||||
\(832\) | −4.31157 | −0.149477 | ||||||||
\(833\) | 2.63565 | 0.0913200 | ||||||||
\(834\) | −0.883434 | −0.0305908 | ||||||||
\(835\) | 6.93334 | 0.239938 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.46052 | 0.223308 | ||||||||
\(838\) | −32.4579 | −1.12124 | ||||||||
\(839\) | 35.7528 | 1.23432 | 0.617162 | − | 0.786836i | \(-0.288282\pi\) | ||||
0.617162 | + | 0.786836i | \(0.288282\pi\) | |||||||
\(840\) | −1.34292 | −0.0463352 | ||||||||
\(841\) | −20.9390 | −0.722033 | ||||||||
\(842\) | −9.15329 | −0.315443 | ||||||||
\(843\) | −24.1883 | −0.833088 | ||||||||
\(844\) | 19.6106 | 0.675026 | ||||||||
\(845\) | 5.58967 | 0.192291 | ||||||||
\(846\) | −10.0444 | −0.345334 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.40604 | 0.0482836 | ||||||||
\(849\) | −13.1463 | −0.451179 | ||||||||
\(850\) | −2.63565 | −0.0904022 | ||||||||
\(851\) | −4.58029 | −0.157010 | ||||||||
\(852\) | 18.5400 | 0.635171 | ||||||||
\(853\) | −23.0500 | −0.789218 | −0.394609 | − | 0.918849i | \(-0.629120\pi\) | ||||
−0.394609 | + | 0.918849i | \(0.629120\pi\) | |||||||
\(854\) | 5.24387 | 0.179442 | ||||||||
\(855\) | 1.87713 | 0.0641964 | ||||||||
\(856\) | 15.4232 | 0.527154 | ||||||||
\(857\) | −27.3702 | −0.934948 | −0.467474 | − | 0.884007i | \(-0.654836\pi\) | ||||
−0.467474 | + | 0.884007i | \(0.654836\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.4968 | 1.48409 | 0.742045 | − | 0.670350i | \(-0.233856\pi\) | ||||
0.742045 | + | 0.670350i | \(0.233856\pi\) | |||||||
\(860\) | 2.01075 | 0.0685660 | ||||||||
\(861\) | −4.67141 | −0.159201 | ||||||||
\(862\) | −26.0024 | −0.885647 | ||||||||
\(863\) | −17.9594 | −0.611345 | −0.305672 | − | 0.952137i | \(-0.598881\pi\) | ||||
−0.305672 | + | 0.952137i | \(0.598881\pi\) | |||||||
\(864\) | −5.63565 | −0.191729 | ||||||||
\(865\) | 11.5843 | 0.393879 | ||||||||
\(866\) | −23.6006 | −0.801980 | ||||||||
\(867\) | 13.5008 | 0.458513 | ||||||||
\(868\) | −1.14637 | −0.0389102 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −3.81282 | −0.129267 | ||||||||
\(871\) | 6.92595 | 0.234677 | ||||||||
\(872\) | 8.49656 | 0.287730 | ||||||||
\(873\) | 9.05042 | 0.306310 | ||||||||
\(874\) | 8.56227 | 0.289623 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | −1.54207 | −0.0521019 | ||||||||
\(877\) | −32.8608 | −1.10963 | −0.554816 | − | 0.831973i | \(-0.687211\pi\) | ||||
−0.554816 | + | 0.831973i | \(0.687211\pi\) | |||||||
\(878\) | 31.7894 | 1.07284 | ||||||||
\(879\) | −11.3455 | −0.382674 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.9270 | −0.839812 | −0.419906 | − | 0.907568i | \(-0.637937\pi\) | ||||
−0.419906 | + | 0.907568i | \(0.637937\pi\) | |||||||
\(882\) | 1.19656 | 0.0402902 | ||||||||
\(883\) | −18.1957 | −0.612334 | −0.306167 | − | 0.951978i | \(-0.599047\pi\) | ||||
−0.306167 | + | 0.951978i | \(0.599047\pi\) | |||||||
\(884\) | −11.3638 | −0.382207 | ||||||||
\(885\) | −3.12106 | −0.104913 | ||||||||
\(886\) | −36.1071 | −1.21304 | ||||||||
\(887\) | 38.9219 | 1.30687 | 0.653434 | − | 0.756983i | \(-0.273328\pi\) | ||||
0.653434 | + | 0.756983i | \(0.273328\pi\) | |||||||
\(888\) | −1.12698 | −0.0378189 | ||||||||
\(889\) | −9.21928 | −0.309205 | ||||||||
\(890\) | −2.19326 | −0.0735182 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.01943 | 0.134580 | ||||||||
\(893\) | 13.1689 | 0.440682 | ||||||||
\(894\) | 27.6619 | 0.925151 | ||||||||
\(895\) | 20.4825 | 0.684654 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 31.6021 | 1.05516 | ||||||||
\(898\) | 4.52269 | 0.150924 | ||||||||
\(899\) | −3.25476 | −0.108552 | ||||||||
\(900\) | −1.19656 | −0.0398853 | ||||||||
\(901\) | 3.70583 | 0.123459 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.70028 | 0.0898598 | ||||||||
\(904\) | −2.72299 | −0.0905655 | ||||||||
\(905\) | −8.01175 | −0.266320 | ||||||||
\(906\) | 5.76408 | 0.191499 | ||||||||
\(907\) | −47.4377 | −1.57514 | −0.787572 | − | 0.616223i | \(-0.788662\pi\) | ||||
−0.787572 | + | 0.616223i | \(0.788662\pi\) | |||||||
\(908\) | −20.4787 | −0.679610 | ||||||||
\(909\) | 21.1132 | 0.700280 | ||||||||
\(910\) | −4.31157 | −0.142927 | ||||||||
\(911\) | −10.2118 | −0.338333 | −0.169167 | − | 0.985587i | \(-0.554108\pi\) | ||||
−0.169167 | + | 0.985587i | \(0.554108\pi\) | |||||||
\(912\) | 2.10674 | 0.0697612 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −15.1593 | −0.501423 | ||||||||
\(915\) | −7.04211 | −0.232805 | ||||||||
\(916\) | 8.74872 | 0.289066 | ||||||||
\(917\) | 17.5357 | 0.579081 | ||||||||
\(918\) | −14.8536 | −0.490243 | ||||||||
\(919\) | 33.7533 | 1.11342 | 0.556710 | − | 0.830707i | \(-0.312064\pi\) | ||||
0.556710 | + | 0.830707i | \(0.312064\pi\) | |||||||
\(920\) | −5.45794 | −0.179943 | ||||||||
\(921\) | −12.5522 | −0.413608 | ||||||||
\(922\) | −27.6126 | −0.909373 | ||||||||
\(923\) | 59.5244 | 1.95927 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.839198 | −0.0275927 | ||||||||
\(926\) | −13.3557 | −0.438895 | ||||||||
\(927\) | −12.1484 | −0.399007 | ||||||||
\(928\) | 2.83920 | 0.0932012 | ||||||||
\(929\) | 41.2273 | 1.35262 | 0.676312 | − | 0.736615i | \(-0.263577\pi\) | ||||
0.676312 | + | 0.736615i | \(0.263577\pi\) | |||||||
\(930\) | 1.53948 | 0.0504816 | ||||||||
\(931\) | −1.56877 | −0.0514145 | ||||||||
\(932\) | −14.1462 | −0.463374 | ||||||||
\(933\) | 37.1626 | 1.21665 | ||||||||
\(934\) | −26.3287 | −0.861500 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.15905 | −0.168629 | ||||||||
\(937\) | 32.2808 | 1.05457 | 0.527283 | − | 0.849690i | \(-0.323211\pi\) | ||||
0.527283 | + | 0.849690i | \(0.323211\pi\) | |||||||
\(938\) | −1.60636 | −0.0524496 | ||||||||
\(939\) | −7.17825 | −0.234253 | ||||||||
\(940\) | −8.39442 | −0.273796 | ||||||||
\(941\) | 47.3632 | 1.54400 | 0.771998 | − | 0.635625i | \(-0.219257\pi\) | ||||
0.771998 | + | 0.635625i | \(0.219257\pi\) | |||||||
\(942\) | 14.6431 | 0.477098 | ||||||||
\(943\) | −18.9857 | −0.618258 | ||||||||
\(944\) | 2.32408 | 0.0756424 | ||||||||
\(945\) | −5.63565 | −0.183328 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.4907 | 0.828335 | 0.414167 | − | 0.910201i | \(-0.364073\pi\) | ||||
0.414167 | + | 0.910201i | \(0.364073\pi\) | |||||||
\(948\) | 12.9647 | 0.421073 | ||||||||
\(949\) | −4.95097 | −0.160715 | ||||||||
\(950\) | 1.56877 | 0.0508977 | ||||||||
\(951\) | −9.58736 | −0.310891 | ||||||||
\(952\) | 2.63565 | 0.0854220 | ||||||||
\(953\) | 39.8135 | 1.28969 | 0.644843 | − | 0.764315i | \(-0.276923\pi\) | ||||
0.644843 | + | 0.764315i | \(0.276923\pi\) | |||||||
\(954\) | 1.68241 | 0.0544700 | ||||||||
\(955\) | 7.72371 | 0.249934 | ||||||||
\(956\) | −2.12134 | −0.0686091 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.18258 | 0.264367 | ||||||||
\(959\) | −9.12927 | −0.294800 | ||||||||
\(960\) | −1.34292 | −0.0433427 | ||||||||
\(961\) | −29.6858 | −0.957608 | ||||||||
\(962\) | −3.61826 | −0.116657 | ||||||||
\(963\) | 18.4547 | 0.594695 | ||||||||
\(964\) | −17.4357 | −0.561566 | ||||||||
\(965\) | 16.3855 | 0.527468 | ||||||||
\(966\) | −7.32959 | −0.235826 | ||||||||
\(967\) | −29.9522 | −0.963198 | −0.481599 | − | 0.876392i | \(-0.659944\pi\) | ||||
−0.481599 | + | 0.876392i | \(0.659944\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.55264 | 0.178377 | ||||||||
\(970\) | 7.56372 | 0.242856 | ||||||||
\(971\) | 8.45499 | 0.271333 | 0.135667 | − | 0.990755i | \(-0.456682\pi\) | ||||
0.135667 | + | 0.990755i | \(0.456682\pi\) | |||||||
\(972\) | −11.5640 | −0.370917 | ||||||||
\(973\) | 0.657844 | 0.0210895 | ||||||||
\(974\) | 9.09993 | 0.291581 | ||||||||
\(975\) | 5.79011 | 0.185432 | ||||||||
\(976\) | 5.24387 | 0.167852 | ||||||||
\(977\) | −4.10946 | −0.131473 | −0.0657366 | − | 0.997837i | \(-0.520940\pi\) | ||||
−0.0657366 | + | 0.997837i | \(0.520940\pi\) | |||||||
\(978\) | 16.5885 | 0.530442 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | 10.1666 | 0.324595 | ||||||||
\(982\) | −3.80239 | −0.121339 | ||||||||
\(983\) | 20.8447 | 0.664842 | 0.332421 | − | 0.943131i | \(-0.392135\pi\) | ||||
0.332421 | + | 0.943131i | \(0.392135\pi\) | |||||||
\(984\) | −4.67141 | −0.148919 | ||||||||
\(985\) | −5.51971 | −0.175873 | ||||||||
\(986\) | 7.48314 | 0.238312 | ||||||||
\(987\) | −11.2731 | −0.358825 | ||||||||
\(988\) | 6.76388 | 0.215188 | ||||||||
\(989\) | 10.9746 | 0.348971 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.5690 | 0.939290 | 0.469645 | − | 0.882855i | \(-0.344382\pi\) | ||||
0.469645 | + | 0.882855i | \(0.344382\pi\) | |||||||
\(992\) | −1.14637 | −0.0363971 | ||||||||
\(993\) | −7.83202 | −0.248542 | ||||||||
\(994\) | −13.8057 | −0.437891 | ||||||||
\(995\) | 4.27443 | 0.135508 | ||||||||
\(996\) | −3.38256 | −0.107181 | ||||||||
\(997\) | −57.0730 | −1.80752 | −0.903760 | − | 0.428040i | \(-0.859204\pi\) | ||||
−0.903760 | + | 0.428040i | \(0.859204\pi\) | |||||||
\(998\) | 22.9856 | 0.727596 | ||||||||
\(999\) | −4.72943 | −0.149632 |
(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 | 8470.2.a.cz.1.1 | ✓ | 6 | |
11.10 | odd | 2 | 8470.2.a.df.1.2 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8470.2.a.cz.1.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
8470.2.a.df.1.2 | yes | 6 | 11.10 | odd | 2 |