Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.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: | \(64.2476334663\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 46 x^{14} + 192 x^{13} + 752 x^{12} - 3378 x^{11} - 5277 x^{10} + 27132 x^{9} + \cdots - 4260 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(-1.16198\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8046.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.16198 | 0.519654 | 0.259827 | − | 0.965655i | \(-0.416334\pi\) | ||||
0.259827 | + | 0.965655i | \(0.416334\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.20200 | 0.454312 | 0.227156 | − | 0.973858i | \(-0.427057\pi\) | ||||
0.227156 | + | 0.973858i | \(0.427057\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.16198 | −0.367451 | ||||||||
\(11\) | −6.54441 | −1.97321 | −0.986606 | − | 0.163120i | \(-0.947844\pi\) | ||||
−0.986606 | + | 0.163120i | \(0.947844\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.22516 | −1.72655 | −0.863274 | − | 0.504736i | \(-0.831590\pi\) | ||||
−0.863274 | + | 0.504736i | \(0.831590\pi\) | |||||||
\(14\) | −1.20200 | −0.321247 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.41568 | −1.31350 | −0.656748 | − | 0.754110i | \(-0.728069\pi\) | ||||
−0.656748 | + | 0.754110i | \(0.728069\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.55699 | 1.50428 | 0.752138 | − | 0.659005i | \(-0.229023\pi\) | ||||
0.752138 | + | 0.659005i | \(0.229023\pi\) | |||||||
\(20\) | 1.16198 | 0.259827 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.54441 | 1.39527 | ||||||||
\(23\) | 5.20334 | 1.08497 | 0.542486 | − | 0.840065i | \(-0.317483\pi\) | ||||
0.542486 | + | 0.840065i | \(0.317483\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.64980 | −0.729959 | ||||||||
\(26\) | 6.22516 | 1.22085 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.20200 | 0.227156 | ||||||||
\(29\) | −7.94963 | −1.47621 | −0.738104 | − | 0.674687i | \(-0.764279\pi\) | ||||
−0.738104 | + | 0.674687i | \(0.764279\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.69843 | 1.74189 | 0.870945 | − | 0.491380i | \(-0.163507\pi\) | ||||
0.870945 | + | 0.491380i | \(0.163507\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.41568 | 0.928782 | ||||||||
\(35\) | 1.39670 | 0.236085 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.452266 | −0.0743520 | −0.0371760 | − | 0.999309i | \(-0.511836\pi\) | ||||
−0.0371760 | + | 0.999309i | \(0.511836\pi\) | |||||||
\(38\) | −6.55699 | −1.06368 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.16198 | −0.183726 | ||||||||
\(41\) | 3.44983 | 0.538772 | 0.269386 | − | 0.963032i | \(-0.413179\pi\) | ||||
0.269386 | + | 0.963032i | \(0.413179\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.03734 | −0.615688 | −0.307844 | − | 0.951437i | \(-0.599608\pi\) | ||||
−0.307844 | + | 0.951437i | \(0.599608\pi\) | |||||||
\(44\) | −6.54441 | −0.986606 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.20334 | −0.767191 | ||||||||
\(47\) | −7.01004 | −1.02252 | −0.511259 | − | 0.859426i | \(-0.670821\pi\) | ||||
−0.511259 | + | 0.859426i | \(0.670821\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.55520 | −0.793601 | ||||||||
\(50\) | 3.64980 | 0.516159 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.22516 | −0.863274 | ||||||||
\(53\) | 7.59192 | 1.04283 | 0.521415 | − | 0.853303i | \(-0.325404\pi\) | ||||
0.521415 | + | 0.853303i | \(0.325404\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.60448 | −1.02539 | ||||||||
\(56\) | −1.20200 | −0.160624 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.94963 | 1.04384 | ||||||||
\(59\) | 2.60856 | 0.339606 | 0.169803 | − | 0.985478i | \(-0.445687\pi\) | ||||
0.169803 | + | 0.985478i | \(0.445687\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.4221 | 1.33442 | 0.667210 | − | 0.744870i | \(-0.267489\pi\) | ||||
0.667210 | + | 0.744870i | \(0.267489\pi\) | |||||||
\(62\) | −9.69843 | −1.23170 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −7.23352 | −0.897208 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.1512 | −1.60668 | −0.803338 | − | 0.595524i | \(-0.796945\pi\) | ||||
−0.803338 | + | 0.595524i | \(0.796945\pi\) | |||||||
\(68\) | −5.41568 | −0.656748 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.39670 | −0.166937 | ||||||||
\(71\) | 6.49535 | 0.770856 | 0.385428 | − | 0.922738i | \(-0.374054\pi\) | ||||
0.385428 | + | 0.922738i | \(0.374054\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.0143359 | 0.00167789 | 0.000838945 | − | 1.00000i | \(-0.499733\pi\) | ||||
0.000838945 | 1.00000i | \(0.499733\pi\) | ||||||||
\(74\) | 0.452266 | 0.0525748 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.55699 | 0.752138 | ||||||||
\(77\) | −7.86635 | −0.896454 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.36611 | 0.716244 | 0.358122 | − | 0.933675i | \(-0.383417\pi\) | ||||
0.358122 | + | 0.933675i | \(0.383417\pi\) | |||||||
\(80\) | 1.16198 | 0.129914 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.44983 | −0.380970 | ||||||||
\(83\) | 4.94655 | 0.542954 | 0.271477 | − | 0.962445i | \(-0.412488\pi\) | ||||
0.271477 | + | 0.962445i | \(0.412488\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.29293 | −0.682564 | ||||||||
\(86\) | 4.03734 | 0.435357 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.54441 | 0.697636 | ||||||||
\(89\) | −0.749144 | −0.0794091 | −0.0397046 | − | 0.999211i | \(-0.512642\pi\) | ||||
−0.0397046 | + | 0.999211i | \(0.512642\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.48262 | −0.784391 | ||||||||
\(92\) | 5.20334 | 0.542486 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.01004 | 0.723030 | ||||||||
\(95\) | 7.61910 | 0.781704 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.71701 | −0.478940 | −0.239470 | − | 0.970904i | \(-0.576974\pi\) | ||||
−0.239470 | + | 0.970904i | \(0.576974\pi\) | |||||||
\(98\) | 5.55520 | 0.561160 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.64980 | −0.364980 | ||||||||
\(101\) | −11.1377 | −1.10824 | −0.554121 | − | 0.832436i | \(-0.686946\pi\) | ||||
−0.554121 | + | 0.832436i | \(0.686946\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.56735 | 0.647100 | 0.323550 | − | 0.946211i | \(-0.395124\pi\) | ||||
0.323550 | + | 0.946211i | \(0.395124\pi\) | |||||||
\(104\) | 6.22516 | 0.610427 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.59192 | −0.737393 | ||||||||
\(107\) | −4.86501 | −0.470318 | −0.235159 | − | 0.971957i | \(-0.575561\pi\) | ||||
−0.235159 | + | 0.971957i | \(0.575561\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.8402 | 1.32565 | 0.662826 | − | 0.748774i | \(-0.269357\pi\) | ||||
0.662826 | + | 0.748774i | \(0.269357\pi\) | |||||||
\(110\) | 7.60448 | 0.725059 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.20200 | 0.113578 | ||||||||
\(113\) | −7.75371 | −0.729408 | −0.364704 | − | 0.931124i | \(-0.618830\pi\) | ||||
−0.364704 | + | 0.931124i | \(0.618830\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.04619 | 0.563810 | ||||||||
\(116\) | −7.94963 | −0.738104 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.60856 | −0.240137 | ||||||||
\(119\) | −6.50963 | −0.596737 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 31.8292 | 2.89357 | ||||||||
\(122\) | −10.4221 | −0.943577 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.69843 | 0.870945 | ||||||||
\(125\) | −10.0509 | −0.898981 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.28473 | 0.735151 | 0.367575 | − | 0.929994i | \(-0.380188\pi\) | ||||
0.367575 | + | 0.929994i | \(0.380188\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.23352 | 0.634422 | ||||||||
\(131\) | 20.2814 | 1.77200 | 0.885998 | − | 0.463689i | \(-0.153475\pi\) | ||||
0.885998 | + | 0.463689i | \(0.153475\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.88148 | 0.683411 | ||||||||
\(134\) | 13.1512 | 1.13609 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.41568 | 0.464391 | ||||||||
\(137\) | 4.25353 | 0.363403 | 0.181702 | − | 0.983354i | \(-0.441840\pi\) | ||||
0.181702 | + | 0.983354i | \(0.441840\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.9154 | −1.77402 | −0.887012 | − | 0.461747i | \(-0.847223\pi\) | ||||
−0.887012 | + | 0.461747i | \(0.847223\pi\) | |||||||
\(140\) | 1.39670 | 0.118043 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.49535 | −0.545078 | ||||||||
\(143\) | 40.7400 | 3.40685 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.23733 | −0.767118 | ||||||||
\(146\) | −0.0143359 | −0.00118645 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.452266 | −0.0371760 | ||||||||
\(149\) | 1.00000 | 0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 23.0985 | 1.87973 | 0.939865 | − | 0.341545i | \(-0.110950\pi\) | ||||
0.939865 | + | 0.341545i | \(0.110950\pi\) | |||||||
\(152\) | −6.55699 | −0.531842 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.86635 | 0.633889 | ||||||||
\(155\) | 11.2694 | 0.905181 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.88220 | 0.788685 | 0.394343 | − | 0.918963i | \(-0.370972\pi\) | ||||
0.394343 | + | 0.918963i | \(0.370972\pi\) | |||||||
\(158\) | −6.36611 | −0.506461 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.16198 | −0.0918628 | ||||||||
\(161\) | 6.25440 | 0.492916 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 24.9483 | 1.95410 | 0.977052 | − | 0.213003i | \(-0.0683245\pi\) | ||||
0.977052 | + | 0.213003i | \(0.0683245\pi\) | |||||||
\(164\) | 3.44983 | 0.269386 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.94655 | −0.383927 | ||||||||
\(167\) | 0.483805 | 0.0374379 | 0.0187190 | − | 0.999825i | \(-0.494041\pi\) | ||||
0.0187190 | + | 0.999825i | \(0.494041\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.7526 | 1.98097 | ||||||||
\(170\) | 6.29293 | 0.482646 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.03734 | −0.307844 | ||||||||
\(173\) | −13.8608 | −1.05382 | −0.526908 | − | 0.849922i | \(-0.676649\pi\) | ||||
−0.526908 | + | 0.849922i | \(0.676649\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.38704 | −0.331629 | ||||||||
\(176\) | −6.54441 | −0.493303 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.749144 | 0.0561507 | ||||||||
\(179\) | −12.5615 | −0.938888 | −0.469444 | − | 0.882962i | \(-0.655546\pi\) | ||||
−0.469444 | + | 0.882962i | \(0.655546\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.32741 | 0.618972 | 0.309486 | − | 0.950904i | \(-0.399843\pi\) | ||||
0.309486 | + | 0.950904i | \(0.399843\pi\) | |||||||
\(182\) | 7.48262 | 0.554648 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.20334 | −0.383595 | ||||||||
\(185\) | −0.525525 | −0.0386374 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 35.4424 | 2.59181 | ||||||||
\(188\) | −7.01004 | −0.511259 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.61910 | −0.552748 | ||||||||
\(191\) | 23.8583 | 1.72633 | 0.863164 | − | 0.504924i | \(-0.168480\pi\) | ||||
0.863164 | + | 0.504924i | \(0.168480\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.94641 | −0.140105 | −0.0700527 | − | 0.997543i | \(-0.522317\pi\) | ||||
−0.0700527 | + | 0.997543i | \(0.522317\pi\) | |||||||
\(194\) | 4.71701 | 0.338662 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.55520 | −0.396800 | ||||||||
\(197\) | 6.79778 | 0.484322 | 0.242161 | − | 0.970236i | \(-0.422144\pi\) | ||||
0.242161 | + | 0.970236i | \(0.422144\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.86635 | −0.415855 | −0.207927 | − | 0.978144i | \(-0.566672\pi\) | ||||
−0.207927 | + | 0.978144i | \(0.566672\pi\) | |||||||
\(200\) | 3.64980 | 0.258080 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 11.1377 | 0.783646 | ||||||||
\(203\) | −9.55542 | −0.670659 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.00864 | 0.279975 | ||||||||
\(206\) | −6.56735 | −0.457569 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.22516 | −0.431637 | ||||||||
\(209\) | −42.9116 | −2.96826 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.0082 | 1.17090 | 0.585448 | − | 0.810710i | \(-0.300919\pi\) | ||||
0.585448 | + | 0.810710i | \(0.300919\pi\) | |||||||
\(212\) | 7.59192 | 0.521415 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.86501 | 0.332565 | ||||||||
\(215\) | −4.69132 | −0.319945 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.6575 | 0.791362 | ||||||||
\(218\) | −13.8402 | −0.937377 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −7.60448 | −0.512694 | ||||||||
\(221\) | 33.7135 | 2.26781 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.0866 | −0.742410 | −0.371205 | − | 0.928551i | \(-0.621055\pi\) | ||||
−0.371205 | + | 0.928551i | \(0.621055\pi\) | |||||||
\(224\) | −1.20200 | −0.0803118 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.75371 | 0.515769 | ||||||||
\(227\) | 18.9421 | 1.25723 | 0.628616 | − | 0.777716i | \(-0.283622\pi\) | ||||
0.628616 | + | 0.777716i | \(0.283622\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.84801 | −0.188202 | −0.0941008 | − | 0.995563i | \(-0.529998\pi\) | ||||
−0.0941008 | + | 0.995563i | \(0.529998\pi\) | |||||||
\(230\) | −6.04619 | −0.398674 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.94963 | 0.521919 | ||||||||
\(233\) | 9.74322 | 0.638300 | 0.319150 | − | 0.947704i | \(-0.396603\pi\) | ||||
0.319150 | + | 0.947704i | \(0.396603\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.14554 | −0.531356 | ||||||||
\(236\) | 2.60856 | 0.169803 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.50963 | 0.421957 | ||||||||
\(239\) | 6.42430 | 0.415554 | 0.207777 | − | 0.978176i | \(-0.433377\pi\) | ||||
0.207777 | + | 0.978176i | \(0.433377\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.0728 | −0.970927 | −0.485463 | − | 0.874257i | \(-0.661349\pi\) | ||||
−0.485463 | + | 0.874257i | \(0.661349\pi\) | |||||||
\(242\) | −31.8292 | −2.04606 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.4221 | 0.667210 | ||||||||
\(245\) | −6.45505 | −0.412398 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −40.8183 | −2.59721 | ||||||||
\(248\) | −9.69843 | −0.615851 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 10.0509 | 0.635675 | ||||||||
\(251\) | −13.7711 | −0.869222 | −0.434611 | − | 0.900618i | \(-0.643114\pi\) | ||||
−0.434611 | + | 0.900618i | \(0.643114\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −34.0528 | −2.14088 | ||||||||
\(254\) | −8.28473 | −0.519830 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −20.6170 | −1.28605 | −0.643026 | − | 0.765844i | \(-0.722321\pi\) | ||||
−0.643026 | + | 0.765844i | \(0.722321\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.543622 | −0.0337790 | ||||||||
\(260\) | −7.23352 | −0.448604 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −20.2814 | −1.25299 | ||||||||
\(263\) | 8.91070 | 0.549457 | 0.274729 | − | 0.961522i | \(-0.411412\pi\) | ||||
0.274729 | + | 0.961522i | \(0.411412\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.82168 | 0.541911 | ||||||||
\(266\) | −7.88148 | −0.483244 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −13.1512 | −0.803338 | ||||||||
\(269\) | 13.6612 | 0.832936 | 0.416468 | − | 0.909150i | \(-0.363268\pi\) | ||||
0.416468 | + | 0.909150i | \(0.363268\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.6514 | 1.55821 | 0.779104 | − | 0.626894i | \(-0.215674\pi\) | ||||
0.779104 | + | 0.626894i | \(0.215674\pi\) | |||||||
\(272\) | −5.41568 | −0.328374 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.25353 | −0.256965 | ||||||||
\(275\) | 23.8858 | 1.44036 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.54881 | 0.453564 | 0.226782 | − | 0.973946i | \(-0.427179\pi\) | ||||
0.226782 | + | 0.973946i | \(0.427179\pi\) | |||||||
\(278\) | 20.9154 | 1.25442 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.39670 | −0.0834687 | ||||||||
\(281\) | −7.26882 | −0.433621 | −0.216811 | − | 0.976214i | \(-0.569565\pi\) | ||||
−0.216811 | + | 0.976214i | \(0.569565\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.41231 | 0.262285 | 0.131142 | − | 0.991364i | \(-0.458135\pi\) | ||||
0.131142 | + | 0.991364i | \(0.458135\pi\) | |||||||
\(284\) | 6.49535 | 0.385428 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −40.7400 | −2.40900 | ||||||||
\(287\) | 4.14668 | 0.244771 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.3296 | 0.725272 | ||||||||
\(290\) | 9.23733 | 0.542434 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.0143359 | 0.000838945 0 | ||||||||
\(293\) | 29.8166 | 1.74190 | 0.870952 | − | 0.491368i | \(-0.163503\pi\) | ||||
0.870952 | + | 0.491368i | \(0.163503\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.03110 | 0.176478 | ||||||||
\(296\) | 0.452266 | 0.0262874 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.00000 | −0.0579284 | ||||||||
\(299\) | −32.3916 | −1.87326 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.85287 | −0.279715 | ||||||||
\(302\) | −23.0985 | −1.32917 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.55699 | 0.376069 | ||||||||
\(305\) | 12.1103 | 0.693437 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.43966 | −0.139239 | −0.0696194 | − | 0.997574i | \(-0.522178\pi\) | ||||
−0.0696194 | + | 0.997574i | \(0.522178\pi\) | |||||||
\(308\) | −7.86635 | −0.448227 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −11.2694 | −0.640059 | ||||||||
\(311\) | −4.86640 | −0.275948 | −0.137974 | − | 0.990436i | \(-0.544059\pi\) | ||||
−0.137974 | + | 0.990436i | \(0.544059\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.9292 | −1.57865 | −0.789325 | − | 0.613976i | \(-0.789569\pi\) | ||||
−0.789325 | + | 0.613976i | \(0.789569\pi\) | |||||||
\(314\) | −9.88220 | −0.557685 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.36611 | 0.358122 | ||||||||
\(317\) | −34.3555 | −1.92960 | −0.964799 | − | 0.262989i | \(-0.915292\pi\) | ||||
−0.964799 | + | 0.262989i | \(0.915292\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 52.0256 | 2.91287 | ||||||||
\(320\) | 1.16198 | 0.0649568 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.25440 | −0.348544 | ||||||||
\(323\) | −35.5106 | −1.97586 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.7206 | 1.26031 | ||||||||
\(326\) | −24.9483 | −1.38176 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.44983 | −0.190485 | ||||||||
\(329\) | −8.42604 | −0.464543 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −35.3008 | −1.94031 | −0.970155 | − | 0.242487i | \(-0.922037\pi\) | ||||
−0.970155 | + | 0.242487i | \(0.922037\pi\) | |||||||
\(332\) | 4.94655 | 0.271477 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.483805 | −0.0264726 | ||||||||
\(335\) | −15.2815 | −0.834916 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.2600 | 0.940211 | 0.470105 | − | 0.882610i | \(-0.344216\pi\) | ||||
0.470105 | + | 0.882610i | \(0.344216\pi\) | |||||||
\(338\) | −25.7526 | −1.40076 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.29293 | −0.341282 | ||||||||
\(341\) | −63.4705 | −3.43712 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.0913 | −0.814854 | ||||||||
\(344\) | 4.03734 | 0.217679 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13.8608 | 0.745160 | ||||||||
\(347\) | −16.3930 | −0.880021 | −0.440011 | − | 0.897993i | \(-0.645025\pi\) | ||||
−0.440011 | + | 0.897993i | \(0.645025\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.1877 | 0.598865 | 0.299433 | − | 0.954117i | \(-0.403203\pi\) | ||||
0.299433 | + | 0.954117i | \(0.403203\pi\) | |||||||
\(350\) | 4.38704 | 0.234497 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.54441 | 0.348818 | ||||||||
\(353\) | −2.97652 | −0.158424 | −0.0792121 | − | 0.996858i | \(-0.525240\pi\) | ||||
−0.0792121 | + | 0.996858i | \(0.525240\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.54748 | 0.400579 | ||||||||
\(356\) | −0.749144 | −0.0397046 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.5615 | 0.663894 | ||||||||
\(359\) | −12.4611 | −0.657670 | −0.328835 | − | 0.944387i | \(-0.606656\pi\) | ||||
−0.328835 | + | 0.944387i | \(0.606656\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 23.9941 | 1.26285 | ||||||||
\(362\) | −8.32741 | −0.437679 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.48262 | −0.392196 | ||||||||
\(365\) | 0.0166581 | 0.000871923 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.7698 | 0.927576 | 0.463788 | − | 0.885946i | \(-0.346490\pi\) | ||||
0.463788 | + | 0.885946i | \(0.346490\pi\) | |||||||
\(368\) | 5.20334 | 0.271243 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.525525 | 0.0273207 | ||||||||
\(371\) | 9.12546 | 0.473770 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.84727 | 0.458094 | 0.229047 | − | 0.973415i | \(-0.426439\pi\) | ||||
0.229047 | + | 0.973415i | \(0.426439\pi\) | |||||||
\(374\) | −35.4424 | −1.83268 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.01004 | 0.361515 | ||||||||
\(377\) | 49.4877 | 2.54875 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.97758 | 0.101582 | 0.0507908 | − | 0.998709i | \(-0.483826\pi\) | ||||
0.0507908 | + | 0.998709i | \(0.483826\pi\) | |||||||
\(380\) | 7.61910 | 0.390852 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −23.8583 | −1.22070 | ||||||||
\(383\) | 26.7331 | 1.36600 | 0.683000 | − | 0.730418i | \(-0.260675\pi\) | ||||
0.683000 | + | 0.730418i | \(0.260675\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.14056 | −0.465846 | ||||||||
\(386\) | 1.94641 | 0.0990695 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.71701 | −0.239470 | ||||||||
\(389\) | −16.3202 | −0.827465 | −0.413732 | − | 0.910399i | \(-0.635775\pi\) | ||||
−0.413732 | + | 0.910399i | \(0.635775\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −28.1796 | −1.42511 | ||||||||
\(392\) | 5.55520 | 0.280580 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.79778 | −0.342467 | ||||||||
\(395\) | 7.39731 | 0.372199 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.2921 | 0.918054 | 0.459027 | − | 0.888422i | \(-0.348198\pi\) | ||||
0.459027 | + | 0.888422i | \(0.348198\pi\) | |||||||
\(398\) | 5.86635 | 0.294054 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.64980 | −0.182490 | ||||||||
\(401\) | 5.80074 | 0.289675 | 0.144837 | − | 0.989455i | \(-0.453734\pi\) | ||||
0.144837 | + | 0.989455i | \(0.453734\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −60.3743 | −3.00746 | ||||||||
\(404\) | −11.1377 | −0.554121 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.55542 | 0.474228 | ||||||||
\(407\) | 2.95981 | 0.146712 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.2740 | 1.05193 | 0.525967 | − | 0.850505i | \(-0.323704\pi\) | ||||
0.525967 | + | 0.850505i | \(0.323704\pi\) | |||||||
\(410\) | −4.00864 | −0.197973 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.56735 | 0.323550 | ||||||||
\(413\) | 3.13548 | 0.154287 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.74780 | 0.282148 | ||||||||
\(416\) | 6.22516 | 0.305213 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 42.9116 | 2.09887 | ||||||||
\(419\) | 26.7929 | 1.30892 | 0.654460 | − | 0.756097i | \(-0.272896\pi\) | ||||
0.654460 | + | 0.756097i | \(0.272896\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.6344 | −1.05440 | −0.527198 | − | 0.849742i | \(-0.676757\pi\) | ||||
−0.527198 | + | 0.849742i | \(0.676757\pi\) | |||||||
\(422\) | −17.0082 | −0.827948 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7.59192 | −0.368696 | ||||||||
\(425\) | 19.7661 | 0.958799 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.5274 | 0.606243 | ||||||||
\(428\) | −4.86501 | −0.235159 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.69132 | 0.226235 | ||||||||
\(431\) | −13.1356 | −0.632722 | −0.316361 | − | 0.948639i | \(-0.602461\pi\) | ||||
−0.316361 | + | 0.948639i | \(0.602461\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.1794 | −0.873645 | −0.436823 | − | 0.899548i | \(-0.643896\pi\) | ||||
−0.436823 | + | 0.899548i | \(0.643896\pi\) | |||||||
\(434\) | −11.6575 | −0.559577 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13.8402 | 0.662826 | ||||||||
\(437\) | 34.1182 | 1.63210 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.8456 | 0.994905 | 0.497452 | − | 0.867491i | \(-0.334269\pi\) | ||||
0.497452 | + | 0.867491i | \(0.334269\pi\) | |||||||
\(440\) | 7.60448 | 0.362530 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −33.7135 | −1.60359 | ||||||||
\(443\) | 5.09801 | 0.242214 | 0.121107 | − | 0.992639i | \(-0.461356\pi\) | ||||
0.121107 | + | 0.992639i | \(0.461356\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.870492 | −0.0412653 | ||||||||
\(446\) | 11.0866 | 0.524963 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.20200 | 0.0567890 | ||||||||
\(449\) | −8.13634 | −0.383978 | −0.191989 | − | 0.981397i | \(-0.561494\pi\) | ||||
−0.191989 | + | 0.981397i | \(0.561494\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.5771 | −1.06311 | ||||||||
\(452\) | −7.75371 | −0.364704 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −18.9421 | −0.888997 | ||||||||
\(455\) | −8.69467 | −0.407612 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.54401 | 0.446450 | 0.223225 | − | 0.974767i | \(-0.428342\pi\) | ||||
0.223225 | + | 0.974767i | \(0.428342\pi\) | |||||||
\(458\) | 2.84801 | 0.133079 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.04619 | 0.281905 | ||||||||
\(461\) | 39.9662 | 1.86141 | 0.930706 | − | 0.365767i | \(-0.119193\pi\) | ||||
0.930706 | + | 0.365767i | \(0.119193\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.8056 | −0.781021 | −0.390510 | − | 0.920598i | \(-0.627701\pi\) | ||||
−0.390510 | + | 0.920598i | \(0.627701\pi\) | |||||||
\(464\) | −7.94963 | −0.369052 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.74322 | −0.451346 | ||||||||
\(467\) | −39.1289 | −1.81067 | −0.905334 | − | 0.424700i | \(-0.860380\pi\) | ||||
−0.905334 | + | 0.424700i | \(0.860380\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.8077 | −0.729932 | ||||||||
\(470\) | 8.14554 | 0.375726 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.60856 | −0.120069 | ||||||||
\(473\) | 26.4220 | 1.21488 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −23.9317 | −1.09806 | ||||||||
\(476\) | −6.50963 | −0.298368 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.42430 | −0.293841 | ||||||||
\(479\) | 32.3479 | 1.47801 | 0.739006 | − | 0.673698i | \(-0.235295\pi\) | ||||
0.739006 | + | 0.673698i | \(0.235295\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.81543 | 0.128372 | ||||||||
\(482\) | 15.0728 | 0.686549 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 31.8292 | 1.44678 | ||||||||
\(485\) | −5.48108 | −0.248883 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.4954 | 0.566222 | 0.283111 | − | 0.959087i | \(-0.408634\pi\) | ||||
0.283111 | + | 0.959087i | \(0.408634\pi\) | |||||||
\(488\) | −10.4221 | −0.471788 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.45505 | 0.291609 | ||||||||
\(491\) | −28.5946 | −1.29045 | −0.645227 | − | 0.763990i | \(-0.723237\pi\) | ||||
−0.645227 | + | 0.763990i | \(0.723237\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 43.0527 | 1.93899 | ||||||||
\(494\) | 40.8183 | 1.83650 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.69843 | 0.435473 | ||||||||
\(497\) | 7.80739 | 0.350209 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.1731 | 0.992602 | 0.496301 | − | 0.868150i | \(-0.334691\pi\) | ||||
0.496301 | + | 0.868150i | \(0.334691\pi\) | |||||||
\(500\) | −10.0509 | −0.449490 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.7711 | 0.614633 | ||||||||
\(503\) | −2.91304 | −0.129886 | −0.0649430 | − | 0.997889i | \(-0.520687\pi\) | ||||
−0.0649430 | + | 0.997889i | \(0.520687\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.9418 | −0.575903 | ||||||||
\(506\) | 34.0528 | 1.51383 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.28473 | 0.367575 | ||||||||
\(509\) | 6.45412 | 0.286074 | 0.143037 | − | 0.989717i | \(-0.454313\pi\) | ||||
0.143037 | + | 0.989717i | \(0.454313\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.0172317 | 0.000762286 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 20.6170 | 0.909377 | ||||||||
\(515\) | 7.63115 | 0.336269 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 45.8765 | 2.01765 | ||||||||
\(518\) | 0.543622 | 0.0238854 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.23352 | 0.317211 | ||||||||
\(521\) | −19.7036 | −0.863232 | −0.431616 | − | 0.902058i | \(-0.642056\pi\) | ||||
−0.431616 | + | 0.902058i | \(0.642056\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.5604 | 0.461775 | 0.230888 | − | 0.972980i | \(-0.425837\pi\) | ||||
0.230888 | + | 0.972980i | \(0.425837\pi\) | |||||||
\(524\) | 20.2814 | 0.885998 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.91070 | −0.388525 | ||||||||
\(527\) | −52.5237 | −2.28797 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.07476 | 0.177163 | ||||||||
\(530\) | −8.82168 | −0.383189 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.88148 | 0.341705 | ||||||||
\(533\) | −21.4757 | −0.930216 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.65305 | −0.244403 | ||||||||
\(536\) | 13.1512 | 0.568046 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −13.6612 | −0.588975 | ||||||||
\(539\) | 36.3555 | 1.56594 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.89515 | −0.210459 | −0.105230 | − | 0.994448i | \(-0.533558\pi\) | ||||
−0.105230 | + | 0.994448i | \(0.533558\pi\) | |||||||
\(542\) | −25.6514 | −1.10182 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.41568 | 0.232196 | ||||||||
\(545\) | 16.0821 | 0.688880 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.6608 | −1.09718 | −0.548589 | − | 0.836092i | \(-0.684835\pi\) | ||||
−0.548589 | + | 0.836092i | \(0.684835\pi\) | |||||||
\(548\) | 4.25353 | 0.181702 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −23.8858 | −1.01849 | ||||||||
\(551\) | −52.1256 | −2.22063 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.65205 | 0.325398 | ||||||||
\(554\) | −7.54881 | −0.320718 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −20.9154 | −0.887012 | ||||||||
\(557\) | 9.48044 | 0.401699 | 0.200850 | − | 0.979622i | \(-0.435630\pi\) | ||||
0.200850 | + | 0.979622i | \(0.435630\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 25.1331 | 1.06302 | ||||||||
\(560\) | 1.39670 | 0.0590213 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.26882 | 0.306616 | ||||||||
\(563\) | 29.0665 | 1.22501 | 0.612504 | − | 0.790468i | \(-0.290162\pi\) | ||||
0.612504 | + | 0.790468i | \(0.290162\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.00967 | −0.379040 | ||||||||
\(566\) | −4.41231 | −0.185463 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.49535 | −0.272539 | ||||||||
\(569\) | 10.0108 | 0.419673 | 0.209837 | − | 0.977736i | \(-0.432707\pi\) | ||||
0.209837 | + | 0.977736i | \(0.432707\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.37514 | −0.266791 | −0.133396 | − | 0.991063i | \(-0.542588\pi\) | ||||
−0.133396 | + | 0.991063i | \(0.542588\pi\) | |||||||
\(572\) | 40.7400 | 1.70342 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.14668 | −0.173079 | ||||||||
\(575\) | −18.9911 | −0.791985 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.07946 | −0.128200 | −0.0640998 | − | 0.997943i | \(-0.520418\pi\) | ||||
−0.0640998 | + | 0.997943i | \(0.520418\pi\) | |||||||
\(578\) | −12.3296 | −0.512845 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −9.23733 | −0.383559 | ||||||||
\(581\) | 5.94573 | 0.246671 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −49.6846 | −2.05773 | ||||||||
\(584\) | −0.0143359 | −0.000593224 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −29.8166 | −1.23171 | ||||||||
\(587\) | 4.37886 | 0.180735 | 0.0903675 | − | 0.995908i | \(-0.471196\pi\) | ||||
0.0903675 | + | 0.995908i | \(0.471196\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 63.5925 | 2.62028 | ||||||||
\(590\) | −3.03110 | −0.124788 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.452266 | −0.0185880 | ||||||||
\(593\) | 43.8585 | 1.80105 | 0.900526 | − | 0.434803i | \(-0.143182\pi\) | ||||
0.900526 | + | 0.434803i | \(0.143182\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.56408 | −0.310097 | ||||||||
\(596\) | 1.00000 | 0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 32.3916 | 1.32459 | ||||||||
\(599\) | −18.3984 | −0.751738 | −0.375869 | − | 0.926673i | \(-0.622656\pi\) | ||||
−0.375869 | + | 0.926673i | \(0.622656\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.4263 | −0.506878 | −0.253439 | − | 0.967351i | \(-0.581562\pi\) | ||||
−0.253439 | + | 0.967351i | \(0.581562\pi\) | |||||||
\(602\) | 4.85287 | 0.197788 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 23.0985 | 0.939865 | ||||||||
\(605\) | 36.9850 | 1.50365 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.6727 | 0.879667 | 0.439833 | − | 0.898079i | \(-0.355038\pi\) | ||||
0.439833 | + | 0.898079i | \(0.355038\pi\) | |||||||
\(608\) | −6.55699 | −0.265921 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.1103 | −0.490334 | ||||||||
\(611\) | 43.6386 | 1.76543 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.21402 | 0.210592 | 0.105296 | − | 0.994441i | \(-0.466421\pi\) | ||||
0.105296 | + | 0.994441i | \(0.466421\pi\) | |||||||
\(614\) | 2.43966 | 0.0984567 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.86635 | 0.316944 | ||||||||
\(617\) | −2.69475 | −0.108487 | −0.0542433 | − | 0.998528i | \(-0.517275\pi\) | ||||
−0.0542433 | + | 0.998528i | \(0.517275\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.7411 | 0.914042 | 0.457021 | − | 0.889456i | \(-0.348916\pi\) | ||||
0.457021 | + | 0.889456i | \(0.348916\pi\) | |||||||
\(620\) | 11.2694 | 0.452590 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.86640 | 0.195125 | ||||||||
\(623\) | −0.900469 | −0.0360765 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.57000 | 0.262800 | ||||||||
\(626\) | 27.9292 | 1.11627 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.88220 | 0.394343 | ||||||||
\(629\) | 2.44933 | 0.0976611 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.09179 | 0.282320 | 0.141160 | − | 0.989987i | \(-0.454917\pi\) | ||||
0.141160 | + | 0.989987i | \(0.454917\pi\) | |||||||
\(632\) | −6.36611 | −0.253230 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 34.3555 | 1.36443 | ||||||||
\(635\) | 9.62671 | 0.382024 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 34.5820 | 1.37019 | ||||||||
\(638\) | −52.0256 | −2.05971 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.16198 | −0.0459314 | ||||||||
\(641\) | 36.9150 | 1.45805 | 0.729027 | − | 0.684485i | \(-0.239973\pi\) | ||||
0.729027 | + | 0.684485i | \(0.239973\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.1802 | −0.795830 | −0.397915 | − | 0.917422i | \(-0.630266\pi\) | ||||
−0.397915 | + | 0.917422i | \(0.630266\pi\) | |||||||
\(644\) | 6.25440 | 0.246458 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 35.5106 | 1.39714 | ||||||||
\(647\) | 46.3337 | 1.82157 | 0.910783 | − | 0.412885i | \(-0.135479\pi\) | ||||
0.910783 | + | 0.412885i | \(0.135479\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.0715 | −0.670114 | ||||||||
\(650\) | −22.7206 | −0.891174 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 24.9483 | 0.977052 | ||||||||
\(653\) | −20.0494 | −0.784593 | −0.392296 | − | 0.919839i | \(-0.628319\pi\) | ||||
−0.392296 | + | 0.919839i | \(0.628319\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.5666 | 0.920825 | ||||||||
\(656\) | 3.44983 | 0.134693 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8.42604 | 0.328481 | ||||||||
\(659\) | 1.65080 | 0.0643060 | 0.0321530 | − | 0.999483i | \(-0.489764\pi\) | ||||
0.0321530 | + | 0.999483i | \(0.489764\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.6939 | 0.843796 | 0.421898 | − | 0.906643i | \(-0.361364\pi\) | ||||
0.421898 | + | 0.906643i | \(0.361364\pi\) | |||||||
\(662\) | 35.3008 | 1.37201 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.94655 | −0.191963 | ||||||||
\(665\) | 9.15814 | 0.355137 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −41.3646 | −1.60164 | ||||||||
\(668\) | 0.483805 | 0.0187190 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 15.2815 | 0.590375 | ||||||||
\(671\) | −68.2067 | −2.63309 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.9200 | 0.844954 | 0.422477 | − | 0.906374i | \(-0.361161\pi\) | ||||
0.422477 | + | 0.906374i | \(0.361161\pi\) | |||||||
\(674\) | −17.2600 | −0.664829 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 25.7526 | 0.990484 | ||||||||
\(677\) | 16.8178 | 0.646360 | 0.323180 | − | 0.946338i | \(-0.395248\pi\) | ||||
0.323180 | + | 0.946338i | \(0.395248\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.66983 | −0.217588 | ||||||||
\(680\) | 6.29293 | 0.241323 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 63.4705 | 2.43041 | ||||||||
\(683\) | −5.16341 | −0.197572 | −0.0987862 | − | 0.995109i | \(-0.531496\pi\) | ||||
−0.0987862 | + | 0.995109i | \(0.531496\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.94252 | 0.188844 | ||||||||
\(686\) | 15.0913 | 0.576189 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.03734 | −0.153922 | ||||||||
\(689\) | −47.2609 | −1.80050 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.13851 | −0.195478 | −0.0977391 | − | 0.995212i | \(-0.531161\pi\) | ||||
−0.0977391 | + | 0.995212i | \(0.531161\pi\) | |||||||
\(692\) | −13.8608 | −0.526908 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.3930 | 0.622269 | ||||||||
\(695\) | −24.3034 | −0.921879 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.6832 | −0.707676 | ||||||||
\(698\) | −11.1877 | −0.423462 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.38704 | −0.165815 | ||||||||
\(701\) | −0.572198 | −0.0216116 | −0.0108058 | − | 0.999942i | \(-0.503440\pi\) | ||||
−0.0108058 | + | 0.999942i | \(0.503440\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.96550 | −0.111846 | ||||||||
\(704\) | −6.54441 | −0.246652 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.97652 | 0.112023 | ||||||||
\(707\) | −13.3875 | −0.503488 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.5520 | 0.809401 | 0.404700 | − | 0.914449i | \(-0.367376\pi\) | ||||
0.404700 | + | 0.914449i | \(0.367376\pi\) | |||||||
\(710\) | −7.54748 | −0.283252 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.749144 | 0.0280754 | ||||||||
\(713\) | 50.4643 | 1.88990 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 47.3391 | 1.77038 | ||||||||
\(716\) | −12.5615 | −0.469444 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 12.4611 | 0.465043 | ||||||||
\(719\) | −20.4402 | −0.762290 | −0.381145 | − | 0.924515i | \(-0.624470\pi\) | ||||
−0.381145 | + | 0.924515i | \(0.624470\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.89393 | 0.293985 | ||||||||
\(722\) | −23.9941 | −0.892968 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.32741 | 0.309486 | ||||||||
\(725\) | 29.0145 | 1.07757 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.2348 | 1.01008 | 0.505041 | − | 0.863095i | \(-0.331477\pi\) | ||||
0.505041 | + | 0.863095i | \(0.331477\pi\) | |||||||
\(728\) | 7.48262 | 0.277324 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.0166581 | −0.000616543 0 | ||||||||
\(731\) | 21.8649 | 0.808704 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 51.5419 | 1.90374 | 0.951872 | − | 0.306496i | \(-0.0991567\pi\) | ||||
0.951872 | + | 0.306496i | \(0.0991567\pi\) | |||||||
\(734\) | −17.7698 | −0.655896 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.20334 | −0.191798 | ||||||||
\(737\) | 86.0668 | 3.17031 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.6187 | −1.16311 | −0.581556 | − | 0.813506i | \(-0.697556\pi\) | ||||
−0.581556 | + | 0.813506i | \(0.697556\pi\) | |||||||
\(740\) | −0.525525 | −0.0193187 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.12546 | −0.335006 | ||||||||
\(743\) | 14.9299 | 0.547726 | 0.273863 | − | 0.961769i | \(-0.411699\pi\) | ||||
0.273863 | + | 0.961769i | \(0.411699\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.16198 | 0.0425717 | ||||||||
\(746\) | −8.84727 | −0.323921 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 35.4424 | 1.29590 | ||||||||
\(749\) | −5.84772 | −0.213671 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −48.9190 | −1.78508 | −0.892540 | − | 0.450969i | \(-0.851078\pi\) | ||||
−0.892540 | + | 0.450969i | \(0.851078\pi\) | |||||||
\(752\) | −7.01004 | −0.255630 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −49.4877 | −1.80223 | ||||||||
\(755\) | 26.8401 | 0.976810 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.9746 | −0.507916 | −0.253958 | − | 0.967215i | \(-0.581732\pi\) | ||||
−0.253958 | + | 0.967215i | \(0.581732\pi\) | |||||||
\(758\) | −1.97758 | −0.0718290 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.61910 | −0.276374 | ||||||||
\(761\) | −17.7366 | −0.642950 | −0.321475 | − | 0.946918i | \(-0.604179\pi\) | ||||
−0.321475 | + | 0.946918i | \(0.604179\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.6359 | 0.602259 | ||||||||
\(764\) | 23.8583 | 0.863164 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −26.7331 | −0.965908 | ||||||||
\(767\) | −16.2387 | −0.586345 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.4891 | 1.31583 | 0.657916 | − | 0.753091i | \(-0.271438\pi\) | ||||
0.657916 | + | 0.753091i | \(0.271438\pi\) | |||||||
\(770\) | 9.14056 | 0.329403 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.94641 | −0.0700527 | ||||||||
\(773\) | −0.753106 | −0.0270873 | −0.0135437 | − | 0.999908i | \(-0.504311\pi\) | ||||
−0.0135437 | + | 0.999908i | \(0.504311\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −35.3973 | −1.27151 | ||||||||
\(776\) | 4.71701 | 0.169331 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 16.3202 | 0.585106 | ||||||||
\(779\) | 22.6205 | 0.810463 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −42.5082 | −1.52106 | ||||||||
\(782\) | 28.1796 | 1.00770 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.55520 | −0.198400 | ||||||||
\(785\) | 11.4829 | 0.409844 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.0619 | −0.608191 | −0.304095 | − | 0.952642i | \(-0.598354\pi\) | ||||
−0.304095 | + | 0.952642i | \(0.598354\pi\) | |||||||
\(788\) | 6.79778 | 0.242161 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −7.39731 | −0.263185 | ||||||||
\(791\) | −9.31993 | −0.331379 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −64.8795 | −2.30394 | ||||||||
\(794\) | −18.2921 | −0.649162 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.86635 | −0.207927 | ||||||||
\(797\) | 5.43382 | 0.192476 | 0.0962379 | − | 0.995358i | \(-0.469319\pi\) | ||||
0.0962379 | + | 0.995358i | \(0.469319\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 37.9641 | 1.34307 | ||||||||
\(800\) | 3.64980 | 0.129040 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5.80074 | −0.204831 | ||||||||
\(803\) | −0.0938199 | −0.00331083 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.26750 | 0.256146 | ||||||||
\(806\) | 60.3743 | 2.12659 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 11.1377 | 0.391823 | ||||||||
\(809\) | 50.4104 | 1.77234 | 0.886168 | − | 0.463364i | \(-0.153358\pi\) | ||||
0.886168 | + | 0.463364i | \(0.153358\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.9799 | −1.43900 | −0.719500 | − | 0.694492i | \(-0.755629\pi\) | ||||
−0.719500 | + | 0.694492i | \(0.755629\pi\) | |||||||
\(812\) | −9.55542 | −0.335330 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.95981 | −0.103741 | ||||||||
\(815\) | 28.9895 | 1.01546 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26.4728 | −0.926165 | ||||||||
\(818\) | −21.2740 | −0.743829 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.00864 | 0.139988 | ||||||||
\(821\) | −13.7785 | −0.480872 | −0.240436 | − | 0.970665i | \(-0.577290\pi\) | ||||
−0.240436 | + | 0.970665i | \(0.577290\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32.3601 | −1.12800 | −0.564001 | − | 0.825774i | \(-0.690739\pi\) | ||||
−0.564001 | + | 0.825774i | \(0.690739\pi\) | |||||||
\(824\) | −6.56735 | −0.228785 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.13548 | −0.109097 | ||||||||
\(827\) | −32.3551 | −1.12510 | −0.562549 | − | 0.826764i | \(-0.690179\pi\) | ||||
−0.562549 | + | 0.826764i | \(0.690179\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.5876 | −0.576112 | −0.288056 | − | 0.957614i | \(-0.593009\pi\) | ||||
−0.288056 | + | 0.957614i | \(0.593009\pi\) | |||||||
\(830\) | −5.74780 | −0.199509 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −6.22516 | −0.215819 | ||||||||
\(833\) | 30.0852 | 1.04239 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.562173 | 0.0194548 | ||||||||
\(836\) | −42.9116 | −1.48413 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −26.7929 | −0.925546 | ||||||||
\(839\) | −39.6490 | −1.36884 | −0.684418 | − | 0.729090i | \(-0.739944\pi\) | ||||
−0.684418 | + | 0.729090i | \(0.739944\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 34.1966 | 1.17919 | ||||||||
\(842\) | 21.6344 | 0.745571 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 17.0082 | 0.585448 | ||||||||
\(845\) | 29.9240 | 1.02942 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 38.2586 | 1.31458 | ||||||||
\(848\) | 7.59192 | 0.260708 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −19.7661 | −0.677973 | ||||||||
\(851\) | −2.35329 | −0.0806698 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −46.4302 | −1.58974 | −0.794870 | − | 0.606779i | \(-0.792461\pi\) | ||||
−0.794870 | + | 0.606779i | \(0.792461\pi\) | |||||||
\(854\) | −12.5274 | −0.428678 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.86501 | 0.166282 | ||||||||
\(857\) | 32.6257 | 1.11447 | 0.557236 | − | 0.830354i | \(-0.311862\pi\) | ||||
0.557236 | + | 0.830354i | \(0.311862\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.8344 | −1.39325 | −0.696626 | − | 0.717435i | \(-0.745316\pi\) | ||||
−0.696626 | + | 0.717435i | \(0.745316\pi\) | |||||||
\(860\) | −4.69132 | −0.159973 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13.1356 | 0.447402 | ||||||||
\(863\) | −23.5119 | −0.800356 | −0.400178 | − | 0.916437i | \(-0.631052\pi\) | ||||
−0.400178 | + | 0.916437i | \(0.631052\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.1060 | −0.547620 | ||||||||
\(866\) | 18.1794 | 0.617761 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 11.6575 | 0.395681 | ||||||||
\(869\) | −41.6624 | −1.41330 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 81.8683 | 2.77400 | ||||||||
\(872\) | −13.8402 | −0.468688 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −34.1182 | −1.15407 | ||||||||
\(875\) | −12.0812 | −0.408418 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.3090 | 0.516947 | 0.258474 | − | 0.966018i | \(-0.416781\pi\) | ||||
0.258474 | + | 0.966018i | \(0.416781\pi\) | |||||||
\(878\) | −20.8456 | −0.703504 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −7.60448 | −0.256347 | ||||||||
\(881\) | −46.0410 | −1.55116 | −0.775580 | − | 0.631250i | \(-0.782542\pi\) | ||||
−0.775580 | + | 0.631250i | \(0.782542\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −50.1193 | −1.68665 | −0.843325 | − | 0.537404i | \(-0.819405\pi\) | ||||
−0.843325 | + | 0.537404i | \(0.819405\pi\) | |||||||
\(884\) | 33.7135 | 1.13391 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.09801 | −0.171271 | ||||||||
\(887\) | 30.3218 | 1.01811 | 0.509053 | − | 0.860735i | \(-0.329996\pi\) | ||||
0.509053 | + | 0.860735i | \(0.329996\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.95821 | 0.333988 | ||||||||
\(890\) | 0.870492 | 0.0291790 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11.0866 | −0.371205 | ||||||||
\(893\) | −45.9647 | −1.53815 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.5962 | −0.487897 | ||||||||
\(896\) | −1.20200 | −0.0401559 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.13634 | 0.271513 | ||||||||
\(899\) | −77.0989 | −2.57139 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −41.1154 | −1.36975 | ||||||||
\(902\) | 22.5771 | 0.751734 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.75371 | 0.257885 | ||||||||
\(905\) | 9.67630 | 0.321651 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −50.3208 | −1.67087 | −0.835437 | − | 0.549587i | \(-0.814785\pi\) | ||||
−0.835437 | + | 0.549587i | \(0.814785\pi\) | |||||||
\(908\) | 18.9421 | 0.628616 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 8.69467 | 0.288225 | ||||||||
\(911\) | −19.5452 | −0.647561 | −0.323781 | − | 0.946132i | \(-0.604954\pi\) | ||||
−0.323781 | + | 0.946132i | \(0.604954\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −32.3722 | −1.07136 | ||||||||
\(914\) | −9.54401 | −0.315688 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.84801 | −0.0941008 | ||||||||
\(917\) | 24.3782 | 0.805039 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.83794 | −0.0936149 | −0.0468074 | − | 0.998904i | \(-0.514905\pi\) | ||||
−0.0468074 | + | 0.998904i | \(0.514905\pi\) | |||||||
\(920\) | −6.04619 | −0.199337 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −39.9662 | −1.31622 | ||||||||
\(923\) | −40.4346 | −1.33092 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.65068 | 0.0542740 | ||||||||
\(926\) | 16.8056 | 0.552265 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.94963 | 0.260959 | ||||||||
\(929\) | 32.7811 | 1.07551 | 0.537757 | − | 0.843100i | \(-0.319272\pi\) | ||||
0.537757 | + | 0.843100i | \(0.319272\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −36.4254 | −1.19379 | ||||||||
\(932\) | 9.74322 | 0.319150 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 39.1289 | 1.28034 | ||||||||
\(935\) | 41.1835 | 1.34684 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.5231 | −0.343775 | −0.171887 | − | 0.985117i | \(-0.554986\pi\) | ||||
−0.171887 | + | 0.985117i | \(0.554986\pi\) | |||||||
\(938\) | 15.8077 | 0.516140 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.14554 | −0.265678 | ||||||||
\(941\) | 34.4915 | 1.12439 | 0.562196 | − | 0.827004i | \(-0.309957\pi\) | ||||
0.562196 | + | 0.827004i | \(0.309957\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.9506 | 0.584553 | ||||||||
\(944\) | 2.60856 | 0.0849014 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −26.4220 | −0.859053 | ||||||||
\(947\) | 13.1454 | 0.427167 | 0.213583 | − | 0.976925i | \(-0.431487\pi\) | ||||
0.213583 | + | 0.976925i | \(0.431487\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.0892432 | −0.00289696 | ||||||||
\(950\) | 23.9317 | 0.776446 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.50963 | 0.210978 | ||||||||
\(953\) | 3.04290 | 0.0985693 | 0.0492847 | − | 0.998785i | \(-0.484306\pi\) | ||||
0.0492847 | + | 0.998785i | \(0.484306\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 27.7229 | 0.897093 | ||||||||
\(956\) | 6.42430 | 0.207777 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −32.3479 | −1.04511 | ||||||||
\(959\) | 5.11272 | 0.165098 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 63.0596 | 2.03418 | ||||||||
\(962\) | −2.81543 | −0.0907730 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −15.0728 | −0.485463 | ||||||||
\(965\) | −2.26169 | −0.0728064 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.2359 | 0.393479 | 0.196740 | − | 0.980456i | \(-0.436965\pi\) | ||||
0.196740 | + | 0.980456i | \(0.436965\pi\) | |||||||
\(968\) | −31.8292 | −1.02303 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.48108 | 0.175987 | ||||||||
\(971\) | 58.0780 | 1.86381 | 0.931906 | − | 0.362701i | \(-0.118145\pi\) | ||||
0.931906 | + | 0.362701i | \(0.118145\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −25.1403 | −0.805960 | ||||||||
\(974\) | −12.4954 | −0.400379 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.4221 | 0.333605 | ||||||||
\(977\) | 11.1619 | 0.357101 | 0.178551 | − | 0.983931i | \(-0.442859\pi\) | ||||
0.178551 | + | 0.983931i | \(0.442859\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.90270 | 0.156691 | ||||||||
\(980\) | −6.45505 | −0.206199 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 28.5946 | 0.912489 | ||||||||
\(983\) | 52.6756 | 1.68009 | 0.840046 | − | 0.542516i | \(-0.182528\pi\) | ||||
0.840046 | + | 0.542516i | \(0.182528\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.89890 | 0.251680 | ||||||||
\(986\) | −43.0527 | −1.37108 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −40.8183 | −1.29860 | ||||||||
\(989\) | −21.0076 | −0.668004 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.155139 | −0.00492816 | −0.00246408 | − | 0.999997i | \(-0.500784\pi\) | ||||
−0.00246408 | + | 0.999997i | \(0.500784\pi\) | |||||||
\(992\) | −9.69843 | −0.307926 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7.80739 | −0.247635 | ||||||||
\(995\) | −6.81660 | −0.216101 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.4510 | −0.457666 | −0.228833 | − | 0.973466i | \(-0.573491\pi\) | ||||
−0.228833 | + | 0.973466i | \(0.573491\pi\) | |||||||
\(998\) | −22.1731 | −0.701876 | ||||||||
\(999\) | 0 | 0 |
(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 | 8046.2.a.s.1.11 | ✓ | 16 | |
3.2 | odd | 2 | 8046.2.a.t.1.6 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.s.1.11 | ✓ | 16 | 1.1 | even | 1 | trivial | |
8046.2.a.t.1.6 | yes | 16 | 3.2 | odd | 2 |