Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8036,2,Mod(1,8036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8036, 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("8036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8036.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: | \(64.1677830643\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 18x^{8} + 32x^{7} + 110x^{6} - 154x^{5} - 282x^{4} + 256x^{3} + 253x^{2} - 126x - 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.58799\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8036.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.58799 | −1.49418 | −0.747089 | − | 0.664724i | \(-0.768549\pi\) | ||||
−0.747089 | + | 0.664724i | \(0.768549\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.78481 | −1.69262 | −0.846308 | − | 0.532694i | \(-0.821180\pi\) | ||||
−0.846308 | + | 0.532694i | \(0.821180\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.69770 | 1.23257 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.59611 | −1.08427 | −0.542134 | − | 0.840292i | \(-0.682383\pi\) | ||||
−0.542134 | + | 0.840292i | \(0.682383\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.80530 | −1.05540 | −0.527700 | − | 0.849431i | \(-0.676946\pi\) | ||||
−0.527700 | + | 0.849431i | \(0.676946\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.79504 | 2.52907 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.90120 | −1.18872 | −0.594358 | − | 0.804201i | \(-0.702594\pi\) | ||||
−0.594358 | + | 0.804201i | \(0.702594\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.726528 | −0.166677 | −0.0833384 | − | 0.996521i | \(-0.526558\pi\) | ||||
−0.0833384 | + | 0.996521i | \(0.526558\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.67934 | 0.558681 | 0.279340 | − | 0.960192i | \(-0.409884\pi\) | ||||
0.279340 | + | 0.960192i | \(0.409884\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.32475 | 1.86495 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.80564 | −0.347496 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.31419 | −0.244038 | −0.122019 | − | 0.992528i | \(-0.538937\pi\) | ||||
−0.122019 | + | 0.992528i | \(0.538937\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.60193 | −0.826531 | −0.413266 | − | 0.910611i | \(-0.635612\pi\) | ||||
−0.413266 | + | 0.910611i | \(0.635612\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.30670 | 1.62009 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.36856 | 1.04698 | 0.523492 | − | 0.852031i | \(-0.324629\pi\) | ||||
0.523492 | + | 0.852031i | \(0.324629\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.84809 | 1.57696 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.79538 | −1.03629 | −0.518143 | − | 0.855294i | \(-0.673376\pi\) | ||||
−0.518143 | + | 0.855294i | \(0.673376\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −13.9951 | −2.08626 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.58539 | 1.39817 | 0.699086 | − | 0.715037i | \(-0.253590\pi\) | ||||
0.699086 | + | 0.715037i | \(0.253590\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.6843 | 1.77615 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.00523 | 0.412800 | 0.206400 | − | 0.978468i | \(-0.433825\pi\) | ||||
0.206400 | + | 0.978468i | \(0.433825\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.6106 | 1.83525 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.88025 | 0.249045 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.98541 | −0.649045 | −0.324522 | − | 0.945878i | \(-0.605204\pi\) | ||||
−0.324522 | + | 0.945878i | \(0.605204\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.28749 | 0.292883 | 0.146442 | − | 0.989219i | \(-0.453218\pi\) | ||||
0.146442 | + | 0.989219i | \(0.453218\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14.4023 | 1.78639 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.58747 | −0.682618 | −0.341309 | − | 0.939951i | \(-0.610870\pi\) | ||||
−0.341309 | + | 0.939951i | \(0.610870\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.93410 | −0.834768 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.69196 | −0.200799 | −0.100400 | − | 0.994947i | \(-0.532012\pi\) | ||||
−0.100400 | + | 0.994947i | \(0.532012\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.259201 | −0.0303371 | −0.0151686 | − | 0.999885i | \(-0.504828\pi\) | ||||
−0.0151686 | + | 0.999885i | \(0.504828\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −24.1324 | −2.78657 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.89788 | 0.326037 | 0.163019 | − | 0.986623i | \(-0.447877\pi\) | ||||
0.163019 | + | 0.986623i | \(0.447877\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.42011 | −0.713346 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.2415 | 1.45344 | 0.726722 | − | 0.686931i | \(-0.241043\pi\) | ||||
0.726722 | + | 0.686931i | \(0.241043\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18.5501 | 2.01204 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.40110 | 0.364636 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.3487 | 1.83895 | 0.919477 | − | 0.393143i | \(-0.128612\pi\) | ||||
0.919477 | + | 0.393143i | \(0.128612\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.9098 | 1.23498 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.74977 | 0.282120 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.39398 | −0.141537 | −0.0707687 | − | 0.997493i | \(-0.522545\pi\) | ||||
−0.0707687 | + | 0.997493i | \(0.522545\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13.2973 | −1.33643 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 20.0334 | 1.99340 | 0.996699 | − | 0.0811850i | \(-0.0258705\pi\) | ||||
0.996699 | + | 0.0811850i | \(0.0258705\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.2645 | −1.10993 | −0.554963 | − | 0.831875i | \(-0.687268\pi\) | ||||
−0.554963 | + | 0.831875i | \(0.687268\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.9772 | −1.06121 | −0.530605 | − | 0.847619i | \(-0.678035\pi\) | ||||
−0.530605 | + | 0.847619i | \(0.678035\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.3625 | −1.66302 | −0.831511 | − | 0.555508i | \(-0.812524\pi\) | ||||
−0.831511 | + | 0.555508i | \(0.812524\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −16.4818 | −1.56438 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.3203 | 1.34714 | 0.673569 | − | 0.739124i | \(-0.264760\pi\) | ||||
0.673569 | + | 0.739124i | \(0.264760\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.1408 | −0.945632 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −14.0709 | −1.30085 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.93200 | 0.175636 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.58799 | 0.233351 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −16.3683 | −1.46403 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.8284 | 1.13834 | 0.569169 | − | 0.822221i | \(-0.307265\pi\) | ||||
0.569169 | + | 0.822221i | \(0.307265\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 17.5864 | 1.54839 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.7714 | 1.46532 | 0.732660 | − | 0.680594i | \(-0.238278\pi\) | ||||
0.732660 | + | 0.680594i | \(0.238278\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.83401 | 0.588178 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.3762 | 1.05737 | 0.528684 | − | 0.848818i | \(-0.322686\pi\) | ||||
0.528684 | + | 0.848818i | \(0.322686\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.5902 | 1.32235 | 0.661173 | − | 0.750233i | \(-0.270059\pi\) | ||||
0.661173 | + | 0.750233i | \(0.270059\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −24.8069 | −2.08912 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.6843 | 1.14434 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.97394 | 0.413063 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.5452 | 1.35543 | 0.677717 | − | 0.735323i | \(-0.262970\pi\) | ||||
0.677717 | + | 0.735323i | \(0.262970\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.20029 | 0.341815 | 0.170907 | − | 0.985287i | \(-0.445330\pi\) | ||||
0.170907 | + | 0.985287i | \(0.445330\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −18.1232 | −1.46517 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 17.4174 | 1.39900 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.4113 | −1.46939 | −0.734693 | − | 0.678400i | \(-0.762674\pi\) | ||||
−0.734693 | + | 0.678400i | \(0.762674\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.77750 | −0.616796 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.747023 | 0.0585114 | 0.0292557 | − | 0.999572i | \(-0.490686\pi\) | ||||
0.0292557 | + | 0.999572i | \(0.490686\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −35.2240 | −2.74219 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.55850 | −0.275365 | −0.137683 | − | 0.990476i | \(-0.543965\pi\) | ||||
−0.137683 | + | 0.990476i | \(0.543965\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.48032 | 0.113871 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.68648 | −0.205440 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.3522 | −0.939122 | −0.469561 | − | 0.882900i | \(-0.655588\pi\) | ||||
−0.469561 | + | 0.882900i | \(0.655588\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.9022 | 0.969788 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.1605 | 1.43212 | 0.716062 | − | 0.698037i | \(-0.245943\pi\) | ||||
0.716062 | + | 0.698037i | \(0.245943\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.1901 | −1.35206 | −0.676031 | − | 0.736873i | \(-0.736302\pi\) | ||||
−0.676031 | + | 0.736873i | \(0.736302\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.92001 | −0.437620 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −24.1037 | −1.77214 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.6252 | 1.28889 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.5726 | −0.765003 | −0.382502 | − | 0.923955i | \(-0.624937\pi\) | ||||
−0.382502 | + | 0.923955i | \(0.624937\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.02663 | −0.433806 | −0.216903 | − | 0.976193i | \(-0.569596\pi\) | ||||
−0.216903 | + | 0.976193i | \(0.569596\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −37.2731 | −2.66918 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.15800 | −0.581233 | −0.290617 | − | 0.956840i | \(-0.593860\pi\) | ||||
−0.290617 | + | 0.956840i | \(0.593860\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.2537 | 0.797751 | 0.398875 | − | 0.917005i | \(-0.369401\pi\) | ||||
0.398875 | + | 0.917005i | \(0.369401\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.4603 | 1.01995 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.78481 | 0.264342 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.90739 | 0.688611 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.61267 | 0.180722 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.5779 | 0.797055 | 0.398527 | − | 0.917156i | \(-0.369521\pi\) | ||||
0.398527 | + | 0.917156i | \(0.369521\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.37879 | 0.300030 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 25.7192 | 1.75403 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.670809 | 0.0453291 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.6505 | 1.25457 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.3491 | 1.09482 | 0.547410 | − | 0.836865i | \(-0.315614\pi\) | ||||
0.547410 | + | 0.836865i | \(0.315614\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 34.4801 | 2.29868 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.86697 | −0.256660 | −0.128330 | − | 0.991732i | \(-0.540962\pi\) | ||||
−0.128330 | + | 0.991732i | \(0.540962\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.6084 | −1.75833 | −0.879167 | − | 0.476514i | \(-0.841900\pi\) | ||||
−0.879167 | + | 0.476514i | \(0.841900\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.62705 | 0.499665 | 0.249832 | − | 0.968289i | \(-0.419624\pi\) | ||||
0.249832 | + | 0.968289i | \(0.419624\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −36.2788 | −2.36657 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.49969 | −0.487157 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28.2707 | 1.82868 | 0.914340 | − | 0.404948i | \(-0.132710\pi\) | ||||
0.914340 | + | 0.404948i | \(0.132710\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −27.1444 | −1.74852 | −0.874261 | − | 0.485457i | \(-0.838653\pi\) | ||||
−0.874261 | + | 0.485457i | \(0.838653\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.0321 | 1.41336 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.76466 | 0.175911 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −34.2689 | −2.17170 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.8143 | −0.998188 | −0.499094 | − | 0.866548i | \(-0.666334\pi\) | ||||
−0.499094 | + | 0.866548i | \(0.666334\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.63519 | −0.605759 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −48.0075 | −3.00634 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 26.8521 | 1.67499 | 0.837493 | − | 0.546448i | \(-0.184020\pi\) | ||||
0.837493 | + | 0.546448i | \(0.184020\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.85947 | −0.300793 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.32193 | −0.389827 | −0.194913 | − | 0.980820i | \(-0.562443\pi\) | ||||
−0.194913 | + | 0.980820i | \(0.562443\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.3742 | −0.698711 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −44.8982 | −2.74772 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.15268 | −0.253193 | −0.126597 | − | 0.991954i | \(-0.540405\pi\) | ||||
−0.126597 | + | 0.991954i | \(0.540405\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.95643 | 0.240336 | 0.120168 | − | 0.992754i | \(-0.461657\pi\) | ||||
0.120168 | + | 0.992754i | \(0.461657\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −33.5328 | −2.02211 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.26011 | 0.135797 | 0.0678985 | − | 0.997692i | \(-0.478371\pi\) | ||||
0.0678985 | + | 0.997692i | \(0.478371\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −17.0166 | −1.01875 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.7417 | 0.879414 | 0.439707 | − | 0.898141i | \(-0.355082\pi\) | ||||
0.439707 | + | 0.898141i | \(0.355082\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.419276 | 0.0249234 | 0.0124617 | − | 0.999922i | \(-0.496033\pi\) | ||||
0.0124617 | + | 0.999922i | \(0.496033\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.11637 | −0.421537 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.02174 | 0.413044 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.60761 | 0.211482 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.3460 | −0.604419 | −0.302209 | − | 0.953242i | \(-0.597724\pi\) | ||||
−0.302209 | + | 0.953242i | \(0.597724\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.8688 | 1.09858 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.49329 | 0.376779 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.1957 | −0.589632 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −51.8463 | −2.97849 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.65771 | −0.495739 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.0647 | −1.43052 | −0.715259 | − | 0.698860i | \(-0.753691\pi\) | ||||
−0.715259 | + | 0.698860i | \(0.753691\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 29.1525 | 1.65843 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.52589 | 0.0865253 | 0.0432627 | − | 0.999064i | \(-0.486225\pi\) | ||||
0.0432627 | + | 0.999064i | \(0.486225\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.46504 | 0.308902 | 0.154451 | − | 0.988000i | \(-0.450639\pi\) | ||||
0.154451 | + | 0.988000i | \(0.450639\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.45336 | −0.474788 | −0.237394 | − | 0.971413i | \(-0.576293\pi\) | ||||
−0.237394 | + | 0.971413i | \(0.576293\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.72595 | 0.264603 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 28.4090 | 1.58564 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.56086 | 0.198131 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −35.4835 | −1.96827 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 44.9339 | 2.48485 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.7945 | 0.978075 | 0.489037 | − | 0.872263i | \(-0.337348\pi\) | ||||
0.489037 | + | 0.872263i | \(0.337348\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 23.5490 | 1.29048 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 21.1475 | 1.15541 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.12448 | 0.333622 | 0.166811 | − | 0.985989i | \(-0.446653\pi\) | ||||
0.166811 | + | 0.985989i | \(0.446653\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −37.0608 | −2.01286 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.5490 | 0.896181 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 26.2442 | 1.41294 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.2673 | 1.30273 | 0.651367 | − | 0.758762i | \(-0.274196\pi\) | ||||
0.651367 | + | 0.758762i | \(0.274196\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.76708 | −0.362233 | −0.181117 | − | 0.983462i | \(-0.557971\pi\) | ||||
−0.181117 | + | 0.983462i | \(0.557971\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.87102 | 0.366748 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.4903 | −0.558343 | −0.279171 | − | 0.960241i | \(-0.590060\pi\) | ||||
−0.279171 | + | 0.960241i | \(0.590060\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.40375 | 0.339876 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −36.6271 | −1.93310 | −0.966552 | − | 0.256469i | \(-0.917441\pi\) | ||||
−0.966552 | + | 0.256469i | \(0.917441\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.4722 | −0.972219 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.99999 | −0.262431 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.981024 | 0.0513491 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.14736 | 0.477488 | 0.238744 | − | 0.971083i | \(-0.423264\pi\) | ||||
0.238744 | + | 0.971083i | \(0.423264\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.69770 | −0.192495 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.8244 | −0.612242 | −0.306121 | − | 0.951993i | \(-0.599031\pi\) | ||||
−0.306121 | + | 0.951993i | \(0.599031\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 42.3611 | 2.18752 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.00087 | 0.257558 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.2821 | −0.887720 | −0.443860 | − | 0.896096i | \(-0.646391\pi\) | ||||
−0.443860 | + | 0.896096i | \(0.646391\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −33.1998 | −1.70088 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.3230 | 1.44724 | 0.723619 | − | 0.690200i | \(-0.242477\pi\) | ||||
0.723619 | + | 0.690200i | \(0.242477\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −25.1273 | −1.27729 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −32.3079 | −1.63807 | −0.819037 | − | 0.573741i | \(-0.805492\pi\) | ||||
−0.819037 | + | 0.573741i | \(0.805492\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.1320 | −0.664112 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −43.4041 | −2.18945 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.9679 | −0.551856 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.4571 | −1.12709 | −0.563545 | − | 0.826085i | \(-0.690563\pi\) | ||||
−0.563545 | + | 0.826085i | \(0.690563\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.0371 | −0.950669 | −0.475335 | − | 0.879805i | \(-0.657673\pi\) | ||||
−0.475335 | + | 0.879805i | \(0.657673\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.5117 | 0.872322 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 24.2989 | 1.20742 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −22.9020 | −1.13521 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.7091 | 0.875660 | 0.437830 | − | 0.899058i | \(-0.355747\pi\) | ||||
0.437830 | + | 0.899058i | \(0.355747\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −32.0295 | −1.57990 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −50.1165 | −2.46012 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −40.3474 | −1.97582 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.55936 | 0.271593 | 0.135796 | − | 0.990737i | \(-0.456641\pi\) | ||||
0.135796 | + | 0.990737i | \(0.456641\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.8300 | 1.21014 | 0.605071 | − | 0.796172i | \(-0.293145\pi\) | ||||
0.605071 | + | 0.796172i | \(0.293145\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 35.4439 | 1.72334 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −45.7025 | −2.21689 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −35.4148 | −1.70984 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.6624 | −0.802598 | −0.401299 | − | 0.915947i | \(-0.631441\pi\) | ||||
−0.401299 | + | 0.915947i | \(0.631441\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.0719 | 1.30099 | 0.650496 | − | 0.759510i | \(-0.274561\pi\) | ||||
0.650496 | + | 0.759510i | \(0.274561\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.8725 | −0.617190 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.94661 | −0.0931191 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.77885 | 0.466719 | 0.233360 | − | 0.972391i | \(-0.425028\pi\) | ||||
0.233360 | + | 0.972391i | \(0.425028\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −33.3426 | −1.58416 | −0.792078 | − | 0.610420i | \(-0.791001\pi\) | ||||
−0.792078 | + | 0.610420i | \(0.791001\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −65.6613 | −3.11264 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −42.8188 | −2.02526 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.5152 | −0.920981 | −0.460490 | − | 0.887665i | \(-0.652326\pi\) | ||||
−0.460490 | + | 0.887665i | \(0.652326\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.59611 | 0.169334 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.8703 | −0.510732 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.0689 | −0.471001 | −0.235500 | − | 0.971874i | \(-0.575673\pi\) | ||||
−0.235500 | + | 0.971874i | \(0.575673\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.84981 | 0.413074 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.8841 | 0.506923 | 0.253462 | − | 0.967345i | \(-0.418431\pi\) | ||||
0.253462 | + | 0.967345i | \(0.418431\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.76854 | −0.361035 | −0.180517 | − | 0.983572i | \(-0.557777\pi\) | ||||
−0.180517 | + | 0.983572i | \(0.557777\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −45.0761 | −2.09035 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.61280 | 0.167180 | 0.0835902 | − | 0.996500i | \(-0.473361\pi\) | ||||
0.0835902 | + | 0.996500i | \(0.473361\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 47.6484 | 2.19552 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 24.4369 | 1.12361 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.77469 | −0.310844 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.1124 | 0.508803 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −26.6680 | −1.21849 | −0.609247 | − | 0.792981i | \(-0.708528\pi\) | ||||
−0.609247 | + | 0.792981i | \(0.708528\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.2343 | −1.10499 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.27595 | 0.239568 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.5887 | 0.615763 | 0.307882 | − | 0.951425i | \(-0.400380\pi\) | ||||
0.307882 | + | 0.951425i | \(0.400380\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.93329 | −0.0874264 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.9300 | −1.17021 | −0.585103 | − | 0.810959i | \(-0.698946\pi\) | ||||
−0.585103 | + | 0.810959i | \(0.698946\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.44108 | 0.290092 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 50.3278 | 2.26207 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.5967 | 0.474371 | 0.237186 | − | 0.971464i | \(-0.423775\pi\) | ||||
0.237186 | + | 0.971464i | \(0.423775\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.20938 | 0.411445 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.10153 | 0.0491148 | 0.0245574 | − | 0.999698i | \(-0.492182\pi\) | ||||
0.0245574 | + | 0.999698i | \(0.492182\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −75.8225 | −3.37406 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.83107 | −0.170144 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.6687 | −0.517208 | −0.258604 | − | 0.965983i | \(-0.583262\pi\) | ||||
−0.258604 | + | 0.965983i | \(0.583262\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.31185 | 0.0579196 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 42.6340 | 1.87868 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −34.4701 | −1.51599 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 31.9674 | 1.40322 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.47208 | −0.152115 | −0.0760573 | − | 0.997103i | \(-0.524233\pi\) | ||||
−0.0760573 | + | 0.997103i | \(0.524233\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.1404 | 0.793223 | 0.396611 | − | 0.917987i | \(-0.370186\pi\) | ||||
0.396611 | + | 0.917987i | \(0.370186\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.5550 | 0.982510 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.8211 | −0.687876 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −18.4345 | −0.799991 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.80530 | 0.164826 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 41.5467 | 1.79622 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −49.5872 | −2.13985 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.7015 | −1.36295 | −0.681477 | − | 0.731840i | \(-0.738662\pi\) | ||||
−0.681477 | + | 0.731840i | \(0.738662\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 47.0759 | 2.02022 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 65.7135 | 2.81486 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.3885 | 0.615207 | 0.307603 | − | 0.951515i | \(-0.400473\pi\) | ||||
0.307603 | + | 0.951515i | \(0.400473\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.45846 | 0.360998 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.954792 | 0.0406755 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 62.3803 | 2.64790 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.52585 | 0.107024 | 0.0535118 | − | 0.998567i | \(-0.482959\pi\) | ||||
0.0535118 | + | 0.998567i | \(0.482959\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 25.8585 | 1.09370 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −45.6140 | −1.92582 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.6852 | 0.450325 | 0.225163 | − | 0.974321i | \(-0.427709\pi\) | ||||
0.225163 | + | 0.974321i | \(0.427709\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −54.1995 | −2.28019 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.0959 | −0.800541 | −0.400271 | − | 0.916397i | \(-0.631084\pi\) | ||||
−0.400271 | + | 0.916397i | \(0.631084\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.3286 | −1.60400 | −0.802001 | − | 0.597323i | \(-0.796231\pi\) | ||||
−0.802001 | + | 0.597323i | \(0.796231\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 27.3617 | 1.14305 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.9842 | 1.04191 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.9868 | 1.12347 | 0.561737 | − | 0.827316i | \(-0.310133\pi\) | ||||
0.561737 | + | 0.827316i | \(0.310133\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.5969 | 0.648184 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.8071 | −0.447585 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 53.2555 | 2.20184 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −29.5370 | −1.21912 | −0.609560 | − | 0.792740i | \(-0.708654\pi\) | ||||
−0.609560 | + | 0.792740i | \(0.708654\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.34343 | 0.137764 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21.1128 | 0.868466 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 28.4935 | 1.17009 | 0.585044 | − | 0.811002i | \(-0.301077\pi\) | ||||
0.585044 | + | 0.811002i | \(0.301077\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −29.1244 | −1.19198 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 34.9502 | 1.42803 | 0.714014 | − | 0.700132i | \(-0.246875\pi\) | ||||
0.714014 | + | 0.700132i | \(0.246875\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.2328 | −0.621360 | −0.310680 | − | 0.950515i | \(-0.600557\pi\) | ||||
−0.310680 | + | 0.950515i | \(0.600557\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −20.6608 | −0.841372 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.31223 | −0.297284 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.9275 | −0.646476 | −0.323238 | − | 0.946318i | \(-0.604772\pi\) | ||||
−0.323238 | + | 0.946318i | \(0.604772\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −36.4753 | −1.47563 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.2603 | 0.495189 | 0.247594 | − | 0.968864i | \(-0.420360\pi\) | ||||
0.247594 | + | 0.968864i | \(0.420360\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.79504 | −0.394974 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.8405 | −1.44288 | −0.721441 | − | 0.692475i | \(-0.756520\pi\) | ||||
−0.721441 | + | 0.692475i | \(0.756520\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.41570 | −0.0970953 | −0.0485476 | − | 0.998821i | \(-0.515459\pi\) | ||||
−0.0485476 | + | 0.998821i | \(0.515459\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.83793 | −0.194139 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.3272 | 0.613090 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.76157 | −0.270031 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −31.2136 | −1.24457 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.1822 | −1.20154 | −0.600768 | − | 0.799423i | \(-0.705138\pi\) | ||||
−0.600768 | + | 0.799423i | \(0.705138\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −29.9635 | −1.19094 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −48.5531 | −1.92677 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.25638 | −0.247498 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.9868 | −0.670938 | −0.335469 | − | 0.942051i | \(-0.608895\pi\) | ||||
−0.335469 | + | 0.942051i | \(0.608895\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.216985 | 0.00855705 | 0.00427853 | − | 0.999991i | \(-0.498638\pi\) | ||||
0.00427853 | + | 0.999991i | \(0.498638\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −66.5610 | −2.62084 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.3789 | −0.761863 | −0.380931 | − | 0.924603i | \(-0.624397\pi\) | ||||
−0.380931 | + | 0.924603i | \(0.624397\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.9281 | 0.703738 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 42.7962 | 1.67475 | 0.837373 | − | 0.546632i | \(-0.184090\pi\) | ||||
0.837373 | + | 0.546632i | \(0.184090\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −63.4763 | −2.48023 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.958446 | −0.0373925 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.67207 | 0.376770 | 0.188385 | − | 0.982095i | \(-0.439675\pi\) | ||||
0.188385 | + | 0.982095i | \(0.439675\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.74266 | −0.223363 | −0.111682 | − | 0.993744i | \(-0.535624\pi\) | ||||
−0.111682 | + | 0.993744i | \(0.535624\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −48.2674 | −1.87455 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.52115 | −0.136339 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −42.3115 | −1.63586 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.22607 | −0.317564 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.67554 | −0.372965 | −0.186482 | − | 0.982458i | \(-0.559709\pi\) | ||||
−0.186482 | + | 0.982458i | \(0.559709\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −16.8372 | −0.648063 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.8582 | 0.801646 | 0.400823 | − | 0.916155i | \(-0.368724\pi\) | ||||
0.400823 | + | 0.916155i | \(0.368724\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.0077 | 0.383495 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.5389 | 1.16854 | 0.584270 | − | 0.811560i | \(-0.301381\pi\) | ||||
0.584270 | + | 0.811560i | \(0.301381\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −46.8414 | −1.78972 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 68.8624 | 2.62726 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.4358 | −0.435669 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 46.9732 | 1.78694 | 0.893472 | − | 0.449119i | \(-0.148262\pi\) | ||||
0.893472 | + | 0.449119i | \(0.148262\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −59.0060 | −2.23823 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.90120 | 0.185646 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19.7388 | −0.746588 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.8159 | 1.23944 | 0.619719 | − | 0.784824i | \(-0.287247\pi\) | ||||
0.619719 | + | 0.784824i | \(0.287247\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.62693 | −0.174508 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 93.8893 | 3.53608 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.6674 | −0.625957 | −0.312979 | − | 0.949760i | \(-0.601327\pi\) | ||||
−0.312979 | + | 0.949760i | \(0.601327\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.7155 | 0.401862 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12.3301 | −0.461767 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −51.7923 | −1.93692 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −73.1643 | −2.73237 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.33891 | 0.199108 | 0.0995538 | − | 0.995032i | \(-0.468258\pi\) | ||||
0.0995538 | + | 0.995032i | \(0.468258\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 70.2493 | 2.61260 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.2545 | −0.455119 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.2839 | 0.603938 | 0.301969 | − | 0.953318i | \(-0.402356\pi\) | ||||
0.301969 | + | 0.953318i | \(0.402356\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −37.7586 | −1.39847 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 33.3055 | 1.23185 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.7554 | 1.32066 | 0.660328 | − | 0.750978i | \(-0.270417\pi\) | ||||
0.660328 | + | 0.750978i | \(0.270417\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 20.0931 | 0.740140 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.2364 | 0.486910 | 0.243455 | − | 0.969912i | \(-0.421719\pi\) | ||||
0.243455 | + | 0.969912i | \(0.421719\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.15491 | −0.262842 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 39.0119 | 1.43121 | 0.715604 | − | 0.698506i | \(-0.246151\pi\) | ||||
0.715604 | + | 0.698506i | \(0.246151\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −62.6203 | −2.29423 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 48.9631 | 1.79147 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.0871 | 0.660008 | 0.330004 | − | 0.943980i | \(-0.392950\pi\) | ||||
0.330004 | + | 0.943980i | \(0.392950\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 40.9272 | 1.49147 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.8973 | −0.578561 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.57240 | −0.129841 | −0.0649205 | − | 0.997890i | \(-0.520679\pi\) | ||||
−0.0649205 | + | 0.997890i | \(0.520679\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 24.9358 | 0.905112 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.71186 | −0.315804 | −0.157902 | − | 0.987455i | \(-0.550473\pi\) | ||||
−0.157902 | + | 0.987455i | \(0.550473\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 68.5926 | 2.47997 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.9710 | 0.685002 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.38267 | −0.158043 | −0.0790216 | − | 0.996873i | \(-0.525180\pi\) | ||||
−0.0790216 | + | 0.996873i | \(0.525180\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −69.4930 | −2.50273 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −32.7723 | −1.17874 | −0.589370 | − | 0.807863i | \(-0.700624\pi\) | ||||
−0.589370 | + | 0.807863i | \(0.700624\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −42.9119 | −1.54144 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.726528 | 0.0260306 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.08449 | 0.217720 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.37295 | 0.0848023 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 69.6834 | 2.48711 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.7887 | 1.27573 | 0.637865 | − | 0.770148i | \(-0.279818\pi\) | ||||
0.637865 | + | 0.770148i | \(0.279818\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.3611 | 0.582470 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.70460 | −0.309109 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 29.4363 | 1.04400 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −46.6956 | −1.65404 | −0.827022 | − | 0.562170i | \(-0.809967\pi\) | ||||
−0.827022 | + | 0.562170i | \(0.809967\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −46.9799 | −1.66203 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 64.1501 | 2.26663 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.932113 | 0.0328936 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.7471 | 0.378315 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −52.6645 | −1.85159 | −0.925793 | − | 0.378030i | \(-0.876602\pi\) | ||||
−0.925793 | + | 0.378030i | \(0.876602\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −51.2790 | −1.80065 | −0.900324 | − | 0.435220i | \(-0.856671\pi\) | ||||
−0.900324 | + | 0.435220i | \(0.856671\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.2392 | −0.359105 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.82734 | −0.0990373 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.93703 | 0.172725 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.6346 | −0.545651 | −0.272825 | − | 0.962064i | \(-0.587958\pi\) | ||||
−0.272825 | + | 0.962064i | \(0.587958\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.5894 | 1.44972 | 0.724858 | − | 0.688898i | \(-0.241905\pi\) | ||||
0.724858 | + | 0.688898i | \(0.241905\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 86.7827 | 3.02138 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.1201 | 0.699645 | 0.349823 | − | 0.936816i | \(-0.386242\pi\) | ||||
0.349823 | + | 0.936816i | \(0.386242\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 54.9561 | 1.90870 | 0.954352 | − | 0.298684i | \(-0.0965477\pi\) | ||||
0.954352 | + | 0.298684i | \(0.0965477\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.84916 | −0.202905 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.4682 | 0.466088 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.30944 | 0.287216 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 32.4924 | 1.12176 | 0.560881 | − | 0.827896i | \(-0.310463\pi\) | ||||
0.560881 | + | 0.827896i | \(0.310463\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.2729 | −0.940445 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −38.1513 | −1.31400 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.60274 | −0.192740 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.08508 | −0.0372400 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.0635 | 0.584930 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.7697 | 0.711140 | 0.355570 | − | 0.934650i | \(-0.384287\pi\) | ||||
0.355570 | + | 0.934650i | \(0.384287\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.1678 | 0.347732 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 40.2776 | 1.37586 | 0.687928 | − | 0.725779i | \(-0.258521\pi\) | ||||
0.687928 | + | 0.725779i | \(0.258521\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 48.9883 | 1.67146 | 0.835730 | − | 0.549141i | \(-0.185045\pi\) | ||||
0.835730 | + | 0.549141i | \(0.185045\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.1659 | −0.924739 | −0.462370 | − | 0.886687i | \(-0.653001\pi\) | ||||
−0.462370 | + | 0.886687i | \(0.653001\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 46.7508 | 1.58957 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −18.1722 | −0.617160 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.4211 | −0.353511 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.2620 | 0.720436 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.15453 | −0.174454 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −40.8059 | −1.37792 | −0.688959 | − | 0.724800i | \(-0.741932\pi\) | ||||
−0.688959 | + | 0.724800i | \(0.741932\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 26.7753 | 0.903109 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −47.3129 | −1.59401 | −0.797005 | − | 0.603972i | \(-0.793584\pi\) | ||||
−0.797005 | + | 0.603972i | \(0.793584\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.7892 | 1.30536 | 0.652680 | − | 0.757633i | \(-0.273644\pi\) | ||||
0.652680 | + | 0.757633i | \(0.273644\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −48.8323 | −1.64148 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.43098 | 0.0816243 | 0.0408122 | − | 0.999167i | \(-0.487005\pi\) | ||||
0.0408122 | + | 0.999167i | \(0.487005\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23.0874 | 0.773458 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.96405 | −0.233043 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −72.5188 | −2.42404 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 26.3864 | 0.881015 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.04779 | 0.201705 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.7292 | −0.490701 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 68.8462 | 2.28852 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 45.0206 | 1.49488 | 0.747442 | − | 0.664327i | \(-0.231282\pi\) | ||||
0.747442 | + | 0.664327i | \(0.231282\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 74.0775 | 2.45700 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.0034 | 1.49103 | 0.745515 | − | 0.666489i | \(-0.232204\pi\) | ||||
0.745515 | + | 0.666489i | \(0.232204\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −47.6179 | −1.57592 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 22.4061 | 0.740722 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −44.8526 | −1.47955 | −0.739775 | − | 0.672854i | \(-0.765068\pi\) | ||||
−0.739775 | + | 0.672854i | \(0.765068\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 64.8672 | 2.13745 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.43843 | 0.211924 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 59.3852 | 1.95257 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −41.6528 | −1.36806 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31.8648 | −1.04545 | −0.522724 | − | 0.852502i | \(-0.675084\pi\) | ||||
−0.522724 | + | 0.852502i | \(0.675084\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.94899 | −0.129284 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −66.7081 | −2.18159 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.1454 | −0.854134 | −0.427067 | − | 0.904220i | \(-0.640453\pi\) | ||||
−0.427067 | + | 0.904220i | \(0.640453\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.1435 | −0.461555 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 49.8800 | 1.62604 | 0.813021 | − | 0.582234i | \(-0.197821\pi\) | ||||
0.813021 | + | 0.582234i | \(0.197821\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.67934 | −0.0872512 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.0360 | −0.651081 | −0.325541 | − | 0.945528i | \(-0.605546\pi\) | ||||
−0.325541 | + | 0.945528i | \(0.605546\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.986336 | 0.0320178 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.8772 | 0.709418 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 48.9363 | 1.58520 | 0.792601 | − | 0.609741i | \(-0.208726\pi\) | ||||
0.792601 | + | 0.609741i | \(0.208726\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 40.0151 | 1.29486 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.2307 | −0.395363 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.82223 | −0.316846 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −40.5906 | −1.30801 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.8096 | 0.734268 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.69266 | −0.0544324 | −0.0272162 | − | 0.999630i | \(-0.508664\pi\) | ||||
−0.0272162 | + | 0.999630i | \(0.508664\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.21547 | −0.296043 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.8308 | −0.861042 | −0.430521 | − | 0.902580i | \(-0.641670\pi\) | ||||
−0.430521 | + | 0.902580i | \(0.641670\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 91.8310 | 2.94095 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 54.1829 | 1.73347 | 0.866733 | − | 0.498772i | \(-0.166216\pi\) | ||||
0.866733 | + | 0.498772i | \(0.166216\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −62.3877 | −1.99392 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −64.2012 | −2.04979 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 48.8385 | 1.55771 | 0.778853 | − | 0.627207i | \(-0.215802\pi\) | ||||
0.778853 | + | 0.627207i | \(0.215802\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 30.8764 | 0.983805 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18.2071 | −0.578953 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.6007 | 1.00383 | 0.501914 | − | 0.864917i | \(-0.332629\pi\) | ||||
0.501914 | + | 0.864917i | \(0.332629\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −46.0520 | −1.46142 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −42.5929 | −1.35029 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.2713 | 0.673668 | 0.336834 | − | 0.941564i | \(-0.390644\pi\) | ||||
0.336834 | + | 0.941564i | \(0.390644\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11.4993 | −0.363823 |
(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 | 8036.2.a.o.1.3 | ✓ | 10 | |
7.6 | odd | 2 | 8036.2.a.p.1.8 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8036.2.a.o.1.3 | ✓ | 10 | 1.1 | even | 1 | trivial | |
8036.2.a.p.1.8 | yes | 10 | 7.6 | odd | 2 |