Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4004,2,Mod(1,4004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4004.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: | \(31.9721009693\) |
Analytic rank: | \(0\) |
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: | \( x^{10} - 2x^{9} - 18x^{8} + 32x^{7} + 93x^{6} - 119x^{5} - 174x^{4} + 107x^{3} + 51x^{2} - 17x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-1.69862\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4004.1 |
$q$-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 | ||||||||
\(3\) | 1.69862 | 0.980701 | 0.490351 | − | 0.871525i | \(-0.336869\pi\) | ||||
0.490351 | + | 0.871525i | \(0.336869\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.84237 | −1.71836 | −0.859180 | − | 0.511674i | \(-0.829026\pi\) | ||||
−0.859180 | + | 0.511674i | \(0.829026\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.114675 | −0.0382250 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.52674 | −1.68520 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.95435 | −0.959070 | −0.479535 | − | 0.877523i | \(-0.659195\pi\) | ||||
−0.479535 | + | 0.877523i | \(0.659195\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.644451 | −0.147847 | −0.0739236 | − | 0.997264i | \(-0.523552\pi\) | ||||
−0.0739236 | + | 0.997264i | \(0.523552\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.69862 | −0.370670 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.08955 | 1.89530 | 0.947651 | − | 0.319309i | \(-0.103451\pi\) | ||||
0.947651 | + | 0.319309i | \(0.103451\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.76379 | 1.95276 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.29066 | −1.01819 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.91006 | 1.09747 | 0.548736 | − | 0.835996i | \(-0.315109\pi\) | ||||
0.548736 | + | 0.835996i | \(0.315109\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.51833 | −0.272699 | −0.136350 | − | 0.990661i | \(-0.543537\pi\) | ||||
−0.136350 | + | 0.990661i | \(0.543537\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.69862 | −0.295693 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.84237 | 0.649479 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.94012 | −0.812150 | −0.406075 | − | 0.913840i | \(-0.633103\pi\) | ||||
−0.406075 | + | 0.913840i | \(0.633103\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.69862 | −0.271998 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.71529 | −0.736405 | −0.368202 | − | 0.929746i | \(-0.620027\pi\) | ||||
−0.368202 | + | 0.929746i | \(0.620027\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.12792 | 0.934499 | 0.467249 | − | 0.884126i | \(-0.345245\pi\) | ||||
0.467249 | + | 0.884126i | \(0.345245\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.440624 | 0.0656843 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.9510 | −1.74324 | −0.871619 | − | 0.490184i | \(-0.836930\pi\) | ||||
−0.871619 | + | 0.490184i | \(0.836930\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.71695 | −0.940561 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.05783 | 0.420025 | 0.210012 | − | 0.977699i | \(-0.432650\pi\) | ||||
0.210012 | + | 0.977699i | \(0.432650\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.84237 | 0.518105 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.09468 | −0.144994 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.39174 | 0.311378 | 0.155689 | − | 0.987806i | \(-0.450240\pi\) | ||||
0.155689 | + | 0.987806i | \(0.450240\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.58904 | −0.971677 | −0.485838 | − | 0.874049i | \(-0.661486\pi\) | ||||
−0.485838 | + | 0.874049i | \(0.661486\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.114675 | 0.0144477 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.84237 | 0.476587 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.4609 | 1.64451 | 0.822255 | − | 0.569119i | \(-0.192716\pi\) | ||||
0.822255 | + | 0.569119i | \(0.192716\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 15.4397 | 1.85872 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.90183 | 1.05645 | 0.528227 | − | 0.849104i | \(-0.322857\pi\) | ||||
0.528227 | + | 0.849104i | \(0.322857\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.4086 | 1.68640 | 0.843202 | − | 0.537597i | \(-0.180668\pi\) | ||||
0.843202 | + | 0.537597i | \(0.180668\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 16.5850 | 1.91507 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.1673 | 1.81896 | 0.909480 | − | 0.415747i | \(-0.136480\pi\) | ||||
0.909480 | + | 0.415747i | \(0.136480\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.64282 | −0.960314 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.07356 | 0.886188 | 0.443094 | − | 0.896475i | \(-0.353881\pi\) | ||||
0.443094 | + | 0.896475i | \(0.353881\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 15.1941 | 1.64803 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.0390 | 1.07629 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.46837 | −0.367647 | −0.183823 | − | 0.982959i | \(-0.558847\pi\) | ||||
−0.183823 | + | 0.982959i | \(0.558847\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.57907 | −0.267437 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.47622 | 0.254055 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.7099 | 1.08742 | 0.543711 | − | 0.839272i | \(-0.317019\pi\) | ||||
0.543711 | + | 0.839272i | \(0.317019\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.114675 | 0.0115253 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.92179 | −0.589240 | −0.294620 | − | 0.955614i | \(-0.595193\pi\) | ||||
−0.294620 | + | 0.955614i | \(0.595193\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.8342 | −1.16606 | −0.583028 | − | 0.812452i | \(-0.698132\pi\) | ||||
−0.583028 | + | 0.812452i | \(0.698132\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.52674 | 0.636945 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.00613 | 0.773982 | 0.386991 | − | 0.922084i | \(-0.373515\pi\) | ||||
0.386991 | + | 0.922084i | \(0.373515\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.05604 | −0.484281 | −0.242140 | − | 0.970241i | \(-0.577849\pi\) | ||||
−0.242140 | + | 0.970241i | \(0.577849\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.39140 | −0.796476 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.89270 | −0.460267 | −0.230133 | − | 0.973159i | \(-0.573916\pi\) | ||||
−0.230133 | + | 0.973159i | \(0.573916\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −34.9254 | −3.25681 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.114675 | 0.0106017 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.95435 | 0.362494 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.00951 | −0.722193 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −18.3043 | −1.63718 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.58091 | 0.140283 | 0.0701416 | − | 0.997537i | \(-0.477655\pi\) | ||||
0.0701416 | + | 0.997537i | \(0.477655\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.4090 | 0.916464 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.5796 | 1.71068 | 0.855340 | − | 0.518067i | \(-0.173348\pi\) | ||||
0.855340 | + | 0.518067i | \(0.173348\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.644451 | 0.0558810 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 20.3287 | 1.74961 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.95843 | 0.850806 | 0.425403 | − | 0.905004i | \(-0.360132\pi\) | ||||
0.425403 | + | 0.905004i | \(0.360132\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.8376 | 1.93706 | 0.968530 | − | 0.248896i | \(-0.0800678\pi\) | ||||
0.968530 | + | 0.248896i | \(0.0800678\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −20.3003 | −1.70960 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −22.7086 | −1.88585 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.69862 | 0.140100 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.54032 | −0.208111 | −0.104055 | − | 0.994571i | \(-0.533182\pi\) | ||||
−0.104055 | + | 0.994571i | \(0.533182\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.29694 | −0.512438 | −0.256219 | − | 0.966619i | \(-0.582477\pi\) | ||||
−0.256219 | + | 0.966619i | \(0.582477\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.453465 | 0.0366605 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.83397 | 0.468596 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.9627 | 1.67301 | 0.836503 | − | 0.547962i | \(-0.184596\pi\) | ||||
0.836503 | + | 0.547962i | \(0.184596\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.19410 | 0.411919 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.08955 | −0.716357 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.15810 | −0.169035 | −0.0845176 | − | 0.996422i | \(-0.526935\pi\) | ||||
−0.0845176 | + | 0.996422i | \(0.526935\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.52674 | 0.508106 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.1307 | 1.09347 | 0.546734 | − | 0.837307i | \(-0.315871\pi\) | ||||
0.546734 | + | 0.837307i | \(0.315871\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.0739025 | 0.00565147 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.10180 | −0.463911 | −0.231956 | − | 0.972726i | \(-0.574512\pi\) | ||||
−0.231956 | + | 0.972726i | \(0.574512\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.76379 | −0.738074 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.06266 | 0.305369 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 23.4714 | 1.75433 | 0.877167 | − | 0.480185i | \(-0.159431\pi\) | ||||
0.877167 | + | 0.480185i | \(0.159431\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.97598 | −0.592850 | −0.296425 | − | 0.955056i | \(-0.595794\pi\) | ||||
−0.296425 | + | 0.955056i | \(0.595794\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.8909 | −0.952924 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 18.9817 | 1.39557 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.95435 | 0.289170 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.29066 | 0.384839 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.9334 | −1.44233 | −0.721164 | − | 0.692764i | \(-0.756393\pi\) | ||||
−0.721164 | + | 0.692764i | \(0.756393\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.84685 | −0.708791 | −0.354396 | − | 0.935096i | \(-0.615313\pi\) | ||||
−0.354396 | + | 0.935096i | \(0.615313\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.52674 | 0.467390 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.7165 | −1.40474 | −0.702372 | − | 0.711811i | \(-0.747875\pi\) | ||||
−0.702372 | + | 0.711811i | \(0.747875\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.2245 | 1.15013 | 0.575063 | − | 0.818109i | \(-0.304978\pi\) | ||||
0.575063 | + | 0.818109i | \(0.304978\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 22.8650 | 1.61277 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.91006 | −0.414805 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 18.1179 | 1.26541 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.04234 | −0.0724479 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.644451 | 0.0445776 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.97045 | −0.273337 | −0.136669 | − | 0.990617i | \(-0.543640\pi\) | ||||
−0.136669 | + | 0.990617i | \(0.543640\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.1209 | 1.03606 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −23.5457 | −1.60580 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.51833 | 0.103071 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 24.4749 | 1.65386 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.95435 | 0.265998 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.3421 | 1.42917 | 0.714586 | − | 0.699548i | \(-0.246615\pi\) | ||||
0.714586 | + | 0.699548i | \(0.246615\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.11966 | −0.0746443 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.5761 | −1.43205 | −0.716027 | − | 0.698072i | \(-0.754041\pi\) | ||||
−0.716027 | + | 0.698072i | \(0.754041\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.4871 | 1.08950 | 0.544748 | − | 0.838600i | \(-0.316625\pi\) | ||||
0.544748 | + | 0.838600i | \(0.316625\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.69862 | 0.111761 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24.2029 | −1.58558 | −0.792792 | − | 0.609493i | \(-0.791373\pi\) | ||||
−0.792792 | + | 0.609493i | \(0.791373\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 45.9203 | 2.99551 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 27.4621 | 1.78386 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −27.1848 | −1.75844 | −0.879219 | − | 0.476418i | \(-0.841935\pi\) | ||||
−0.879219 | + | 0.476418i | \(0.841935\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.0746 | 1.03545 | 0.517727 | − | 0.855546i | \(-0.326778\pi\) | ||||
0.517727 | + | 0.855546i | \(0.326778\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.19108 | 0.0764076 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.84237 | −0.245480 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.644451 | 0.0410055 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.7139 | 0.869086 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.7228 | −0.992415 | −0.496208 | − | 0.868204i | \(-0.665275\pi\) | ||||
−0.496208 | + | 0.868204i | \(0.665275\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.08955 | −0.571455 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 25.8090 | 1.61622 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.92503 | −0.619107 | −0.309553 | − | 0.950882i | \(-0.600180\pi\) | ||||
−0.309553 | + | 0.950882i | \(0.600180\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.94012 | 0.306964 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.677737 | −0.0419509 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.6730 | 0.966437 | 0.483218 | − | 0.875500i | \(-0.339468\pi\) | ||||
0.483218 | + | 0.875500i | \(0.339468\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.7493 | −0.721753 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.89147 | −0.360552 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.74980 | 0.472514 | 0.236257 | − | 0.971691i | \(-0.424079\pi\) | ||||
0.236257 | + | 0.971691i | \(0.424079\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.74990 | −0.349282 | −0.174641 | − | 0.984632i | \(-0.555876\pi\) | ||||
−0.174641 | + | 0.984632i | \(0.555876\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.69862 | 0.102805 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.76379 | −0.588779 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.86436 | −0.172102 | −0.0860512 | − | 0.996291i | \(-0.527425\pi\) | ||||
−0.0860512 | + | 0.996291i | \(0.527425\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.174114 | 0.0104239 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.90503 | 0.113645 | 0.0568223 | − | 0.998384i | \(-0.481903\pi\) | ||||
0.0568223 | + | 0.998384i | \(0.481903\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.36551 | 0.497278 | 0.248639 | − | 0.968596i | \(-0.420017\pi\) | ||||
0.248639 | + | 0.968596i | \(0.420017\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.20617 | 0.249152 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.71529 | 0.278335 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.36315 | −0.0801854 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 18.1920 | 1.06644 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.9454 | −0.989961 | −0.494981 | − | 0.868904i | \(-0.664825\pi\) | ||||
−0.494981 | + | 0.868904i | \(0.664825\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.18994 | −0.535059 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.29066 | 0.306995 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.08955 | −0.525662 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.12792 | −0.353207 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.0589 | −0.577869 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 29.1599 | 1.66969 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.2064 | 1.15324 | 0.576619 | − | 0.817013i | \(-0.304372\pi\) | ||||
0.576619 | + | 0.817013i | \(0.304372\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −20.1018 | −1.14355 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.0387 | −0.852767 | −0.426384 | − | 0.904542i | \(-0.640213\pi\) | ||||
−0.426384 | + | 0.904542i | \(0.640213\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.3600 | −1.03777 | −0.518883 | − | 0.854845i | \(-0.673652\pi\) | ||||
−0.518883 | + | 0.854845i | \(0.673652\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.440624 | −0.0248263 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.3785 | −1.08841 | −0.544203 | − | 0.838953i | \(-0.683168\pi\) | ||||
−0.544203 | + | 0.838953i | \(0.683168\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.91006 | −0.330900 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.5994 | 0.759045 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.54838 | 0.141796 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.76379 | −0.541598 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.58831 | −0.474935 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.9510 | 0.658882 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.1575 | 1.82250 | 0.911251 | − | 0.411851i | \(-0.135118\pi\) | ||||
0.911251 | + | 0.411851i | \(0.135118\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.566508 | 0.0310444 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −51.7217 | −2.82586 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.2109 | −0.719643 | −0.359822 | − | 0.933021i | \(-0.617162\pi\) | ||||
−0.359822 | + | 0.933021i | \(0.617162\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.31086 | −0.451384 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.51833 | 0.0822220 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −59.3251 | −3.19396 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 33.2100 | 1.78280 | 0.891402 | − | 0.453213i | \(-0.149722\pi\) | ||||
0.891402 | + | 0.453213i | \(0.149722\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.6881 | −1.58917 | −0.794584 | − | 0.607154i | \(-0.792311\pi\) | ||||
−0.794584 | + | 0.607154i | \(0.792311\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.29066 | 0.282395 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.8351 | −1.05572 | −0.527859 | − | 0.849332i | \(-0.677005\pi\) | ||||
−0.527859 | + | 0.849332i | \(0.677005\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −34.2041 | −1.81537 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.71695 | 0.355499 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.3063 | 1.44117 | 0.720585 | − | 0.693367i | \(-0.243874\pi\) | ||||
0.720585 | + | 0.693367i | \(0.243874\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5847 | −0.978141 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.69862 | 0.0891547 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −55.3633 | −2.89785 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.2744 | −1.58031 | −0.790155 | − | 0.612907i | \(-0.790000\pi\) | ||||
−0.790155 | + | 0.612907i | \(0.790000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.540726 | 0.0281491 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.05783 | −0.158754 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.9451 | 0.722050 | 0.361025 | − | 0.932556i | \(-0.382427\pi\) | ||||
0.361025 | + | 0.932556i | \(0.382427\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −31.0921 | −1.60559 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.91006 | −0.304384 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.1449 | −0.572474 | −0.286237 | − | 0.958159i | \(-0.592404\pi\) | ||||
−0.286237 | + | 0.958159i | \(0.592404\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.68537 | 0.137576 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.8868 | 1.01617 | 0.508083 | − | 0.861308i | \(-0.330354\pi\) | ||||
0.508083 | + | 0.861308i | \(0.330354\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.84237 | −0.195825 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.702719 | −0.0357212 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.6695 | 0.946582 | 0.473291 | − | 0.880906i | \(-0.343066\pi\) | ||||
0.473291 | + | 0.880906i | \(0.343066\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −35.9432 | −1.81773 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 33.2584 | 1.67767 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −62.1206 | −3.12563 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.3387 | 1.32190 | 0.660950 | − | 0.750430i | \(-0.270153\pi\) | ||||
0.660950 | + | 0.750430i | \(0.270153\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.09468 | 0.0548026 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.38231 | −0.118967 | −0.0594835 | − | 0.998229i | \(-0.518945\pi\) | ||||
−0.0594835 | + | 0.998229i | \(0.518945\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.51833 | 0.0756332 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 33.2089 | 1.65016 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.94012 | 0.244872 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.6750 | 0.972864 | 0.486432 | − | 0.873718i | \(-0.338298\pi\) | ||||
0.486432 | + | 0.873718i | \(0.338298\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.9156 | 0.834386 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.39174 | −0.117690 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −31.0216 | −1.52279 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 38.7925 | 1.89968 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −37.5432 | −1.83411 | −0.917053 | − | 0.398766i | \(-0.869439\pi\) | ||||
−0.917053 | + | 0.398766i | \(0.869439\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.3135 | 0.746334 | 0.373167 | − | 0.927764i | \(-0.378272\pi\) | ||||
0.373167 | + | 0.927764i | \(0.378272\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.37049 | 0.0666353 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −38.6094 | −1.87283 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.58904 | 0.367259 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.69862 | 0.0820104 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 36.3218 | 1.74956 | 0.874779 | − | 0.484522i | \(-0.161006\pi\) | ||||
0.874779 | + | 0.484522i | \(0.161006\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.6305 | 1.42395 | 0.711977 | − | 0.702203i | \(-0.247800\pi\) | ||||
0.711977 | + | 0.702203i | \(0.247800\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −38.5735 | −1.84946 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.85777 | −0.280215 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.44318 | −0.116607 | −0.0583034 | − | 0.998299i | \(-0.518569\pi\) | ||||
−0.0583034 | + | 0.998299i | \(0.518569\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.114675 | −0.00546072 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.65000 | 0.0783939 | 0.0391969 | − | 0.999232i | \(-0.487520\pi\) | ||||
0.0391969 | + | 0.999232i | \(0.487520\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.3268 | 0.631750 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.31504 | −0.204095 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.8922 | −0.844387 | −0.422194 | − | 0.906506i | \(-0.638740\pi\) | ||||
−0.422194 | + | 0.906506i | \(0.638740\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.71529 | 0.222034 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.6961 | −0.502548 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.84237 | −0.180133 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.1950 | 1.08502 | 0.542508 | − | 0.840051i | \(-0.317475\pi\) | ||||
0.542508 | + | 0.840051i | \(0.317475\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 20.9211 | 0.976514 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.97389 | −0.278232 | −0.139116 | − | 0.990276i | \(-0.544426\pi\) | ||||
−0.139116 | + | 0.990276i | \(0.544426\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.8461 | −0.922326 | −0.461163 | − | 0.887316i | \(-0.652568\pi\) | ||||
−0.461163 | + | 0.887316i | \(0.652568\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.90972 | 0.459552 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.16050 | −0.192525 | −0.0962624 | − | 0.995356i | \(-0.530689\pi\) | ||||
−0.0962624 | + | 0.995356i | \(0.530689\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.4609 | −0.621567 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 35.6078 | 1.64072 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.12792 | −0.281762 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.29229 | −0.288710 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.350656 | −0.0160555 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.39739 | −0.292304 | −0.146152 | − | 0.989262i | \(-0.546689\pi\) | ||||
−0.146152 | + | 0.989262i | \(0.546689\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.94012 | 0.225250 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −15.4397 | −0.702532 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −41.1512 | −1.86858 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.7555 | −0.940520 | −0.470260 | − | 0.882528i | \(-0.655840\pi\) | ||||
−0.470260 | + | 0.882528i | \(0.655840\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.66580 | −0.165773 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.1498 | −0.593444 | −0.296722 | − | 0.954964i | \(-0.595894\pi\) | ||||
−0.296722 | + | 0.954964i | \(0.595894\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −23.3704 | −1.05255 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.440624 | −0.0198046 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.90183 | −0.399302 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.3975 | −1.13695 | −0.568474 | − | 0.822701i | \(-0.692466\pi\) | ||||
−0.568474 | + | 0.822701i | \(0.692466\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.0028 | 1.07236 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 35.6641 | 1.59018 | 0.795092 | − | 0.606489i | \(-0.207423\pi\) | ||||
0.795092 | + | 0.606489i | \(0.207423\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.7537 | 1.01253 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.69862 | 0.0754386 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.3928 | −0.948219 | −0.474110 | − | 0.880466i | \(-0.657230\pi\) | ||||
−0.474110 | + | 0.880466i | \(0.657230\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.4086 | −0.637401 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.40958 | 0.150536 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 45.4712 | 2.00370 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.9510 | 0.525606 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.3647 | −0.454958 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.5101 | 1.51191 | 0.755957 | − | 0.654621i | \(-0.227172\pi\) | ||||
0.755957 | + | 0.654621i | \(0.227172\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.9307 | 1.35250 | 0.676252 | − | 0.736670i | \(-0.263603\pi\) | ||||
0.676252 | + | 0.736670i | \(0.263603\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −16.5850 | −0.723830 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.00399 | 0.261538 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 59.6199 | 2.59217 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.274273 | −0.0119024 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.71529 | 0.204242 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −30.7625 | −1.32998 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 39.8691 | 1.72048 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.24004 | 0.354267 | 0.177133 | − | 0.984187i | \(-0.443318\pi\) | ||||
0.177133 | + | 0.984187i | \(0.443318\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.5482 | −0.581408 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.4272 | 0.832168 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.780352 | −0.0333654 | −0.0166827 | − | 0.999861i | \(-0.505311\pi\) | ||||
−0.0166827 | + | 0.999861i | \(0.505311\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.870273 | 0.0371424 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.80875 | −0.162258 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.1673 | −0.687503 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 32.2429 | 1.36863 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.4952 | −0.698923 | −0.349461 | − | 0.936951i | \(-0.613635\pi\) | ||||
−0.349461 | + | 0.936951i | \(0.613635\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.12792 | −0.259183 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.71695 | 0.283590 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.33174 | 0.0561260 | 0.0280630 | − | 0.999606i | \(-0.491066\pi\) | ||||
0.0280630 | + | 0.999606i | \(0.491066\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.7996 | 0.790903 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.64282 | 0.362965 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.4028 | −1.02302 | −0.511509 | − | 0.859278i | \(-0.670913\pi\) | ||||
−0.511509 | + | 0.859278i | \(0.670913\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.2551 | 0.763952 | 0.381976 | − | 0.924172i | \(-0.375244\pi\) | ||||
0.381976 | + | 0.924172i | \(0.375244\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −33.8593 | −1.41449 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 88.7485 | 3.70107 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.4256 | 1.01685 | 0.508426 | − | 0.861106i | \(-0.330227\pi\) | ||||
0.508426 | + | 0.861106i | \(0.330227\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.7261 | −0.695113 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.07356 | −0.334948 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.05783 | −0.126642 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.440624 | −0.0182176 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.0589 | −0.415175 | −0.207588 | − | 0.978216i | \(-0.566561\pi\) | ||||
−0.207588 | + | 0.978216i | \(0.566561\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.978487 | 0.0403179 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −33.4909 | −1.37763 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.35178 | −0.219771 | −0.109886 | − | 0.993944i | \(-0.535048\pi\) | ||||
−0.109886 | + | 0.993944i | \(0.535048\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15.1941 | −0.622895 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 27.5594 | 1.12793 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −38.9731 | −1.59240 | −0.796199 | − | 0.605035i | \(-0.793159\pi\) | ||||
−0.796199 | + | 0.605035i | \(0.793159\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.3094 | 0.461320 | 0.230660 | − | 0.973034i | \(-0.425912\pi\) | ||||
0.230660 | + | 0.973034i | \(0.425912\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.54363 | −0.0628615 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.84237 | −0.156214 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.0931 | −0.612611 | −0.306306 | − | 0.951933i | \(-0.599093\pi\) | ||||
−0.306306 | + | 0.951933i | \(0.599093\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.0390 | −0.406800 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.9510 | 0.483487 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −35.7707 | −1.44477 | −0.722383 | − | 0.691493i | \(-0.756953\pi\) | ||||
−0.722383 | + | 0.691493i | \(0.756953\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 30.7755 | 1.24099 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −33.9746 | −1.36777 | −0.683883 | − | 0.729592i | \(-0.739710\pi\) | ||||
−0.683883 | + | 0.729592i | \(0.739710\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.3408 | 1.21950 | 0.609749 | − | 0.792594i | \(-0.291270\pi\) | ||||
0.609749 | + | 0.792594i | \(0.291270\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −48.0897 | −1.92977 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.46837 | 0.138958 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.5127 | 0.860509 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.09468 | 0.0437173 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19.5349 | 0.778908 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.2634 | −0.607627 | −0.303814 | − | 0.952731i | \(-0.598260\pi\) | ||||
−0.303814 | + | 0.952731i | \(0.598260\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.74431 | −0.268062 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.07444 | −0.241057 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.02082 | −0.0403829 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.0881 | 1.06992 | 0.534958 | − | 0.844879i | \(-0.320327\pi\) | ||||
0.534958 | + | 0.844879i | \(0.320327\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.7248 | 0.462380 | 0.231190 | − | 0.972909i | \(-0.425738\pi\) | ||||
0.231190 | + | 0.972909i | \(0.425738\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −39.9953 | −1.57481 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.9856 | −0.589143 | −0.294571 | − | 0.955629i | \(-0.595177\pi\) | ||||
−0.294571 | + | 0.955629i | \(0.595177\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.39174 | −0.0938839 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.57907 | 0.101082 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.88481 | 0.308556 | 0.154278 | − | 0.988027i | \(-0.450695\pi\) | ||||
0.154278 | + | 0.988027i | \(0.450695\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −75.2322 | −2.93956 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.65231 | −0.0644628 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 46.0052 | 1.79211 | 0.896054 | − | 0.443946i | \(-0.146422\pi\) | ||||
0.896054 | + | 0.443946i | \(0.146422\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 44.3021 | 1.72315 | 0.861576 | − | 0.507629i | \(-0.169478\pi\) | ||||
0.861576 | + | 0.507629i | \(0.169478\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.71695 | 0.260865 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.47622 | −0.0960237 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 53.7198 | 2.08004 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 36.2522 | 1.40159 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.58904 | 0.292971 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 41.2852 | 1.59143 | 0.795714 | − | 0.605672i | \(-0.207096\pi\) | ||||
0.795714 | + | 0.605672i | \(0.207096\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −51.6569 | −1.98828 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.5689 | 0.483061 | 0.241531 | − | 0.970393i | \(-0.422351\pi\) | ||||
0.241531 | + | 0.970393i | \(0.422351\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.7099 | −0.411007 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −36.6497 | −1.40442 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.20600 | −0.237466 | −0.118733 | − | 0.992926i | \(-0.537883\pi\) | ||||
−0.118733 | + | 0.992926i | \(0.537883\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −38.2639 | −1.46199 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 28.0053 | 1.06847 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.05783 | −0.116494 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.7028 | −0.749529 | −0.374765 | − | 0.927120i | \(-0.622276\pi\) | ||||
−0.374765 | + | 0.927120i | \(0.622276\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.114675 | −0.00435615 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −87.7505 | −3.32857 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.6459 | 0.706263 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −41.1116 | −1.55498 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.4217 | 0.544700 | 0.272350 | − | 0.962198i | \(-0.412199\pi\) | ||||
0.272350 | + | 0.962198i | \(0.412199\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.18366 | 0.120074 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 78.0013 | 2.93770 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.92179 | 0.222712 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 43.3911 | 1.62959 | 0.814794 | − | 0.579750i | \(-0.196850\pi\) | ||||
0.814794 | + | 0.579750i | \(0.196850\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.85398 | −0.0695298 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.8009 | −0.516848 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.84237 | −0.143696 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −46.1767 | −1.72450 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −35.9937 | −1.34234 | −0.671169 | − | 0.741305i | \(-0.734207\pi\) | ||||
−0.671169 | + | 0.741305i | \(0.734207\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.8342 | 0.440727 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 27.3046 | 1.01547 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 57.7047 | 2.14310 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.9224 | −0.887234 | −0.443617 | − | 0.896216i | \(-0.646305\pi\) | ||||
−0.443617 | + | 0.896216i | \(0.646305\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.9517 | 1.03525 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24.2319 | −0.896249 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.47363 | 0.165237 | 0.0826187 | − | 0.996581i | \(-0.473672\pi\) | ||||
0.0826187 | + | 0.996581i | \(0.473672\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.52674 | −0.240742 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.4609 | −0.495839 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −47.9236 | −1.76290 | −0.881449 | − | 0.472279i | \(-0.843431\pi\) | ||||
−0.881449 | + | 0.472279i | \(0.843431\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.09468 | 0.0402141 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.4625 | 1.04419 | 0.522093 | − | 0.852888i | \(-0.325151\pi\) | ||||
0.522093 | + | 0.852888i | \(0.325151\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.76083 | 0.357609 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.925836 | −0.0338746 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.00613 | −0.292538 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.7806 | −0.794785 | −0.397392 | − | 0.917649i | \(-0.630085\pi\) | ||||
−0.397392 | + | 0.917649i | \(0.630085\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −26.7072 | −0.973263 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.1952 | 0.880552 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.44815 | 0.161671 | 0.0808353 | − | 0.996727i | \(-0.474241\pi\) | ||||
0.0808353 | + | 0.996727i | \(0.474241\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −15.4397 | −0.560427 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.3140 | 0.482632 | 0.241316 | − | 0.970447i | \(-0.422421\pi\) | ||||
0.241316 | + | 0.970447i | \(0.422421\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.05604 | 0.183041 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.74238 | −0.0629958 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.39174 | −0.0863606 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 45.2259 | 1.63089 | 0.815444 | − | 0.578836i | \(-0.196493\pi\) | ||||
0.815444 | + | 0.578836i | \(0.196493\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.8589 | −0.607159 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 42.0325 | 1.51180 | 0.755902 | − | 0.654684i | \(-0.227198\pi\) | ||||
0.755902 | + | 0.654684i | \(0.227198\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14.8246 | −0.532516 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.39140 | 0.301040 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.03878 | 0.108875 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.90183 | −0.318533 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −31.2682 | −1.11743 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −80.5464 | −2.87483 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.2808 | 0.794223 | 0.397112 | − | 0.917770i | \(-0.370013\pi\) | ||||
0.397112 | + | 0.917770i | \(0.370013\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 26.6225 | 0.947786 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.89270 | 0.173964 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.58904 | 0.269495 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −19.9576 | −0.707824 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.3429 | −0.508051 | −0.254026 | − | 0.967197i | \(-0.581755\pi\) | ||||
−0.254026 | + | 0.967197i | \(0.581755\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 47.2585 | 1.67189 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.397736 | 0.0140533 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.4086 | −0.508470 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 34.9254 | 1.23096 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.1640 | 0.463395 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 34.0331 | 1.19654 | 0.598270 | − | 0.801295i | \(-0.295855\pi\) | ||||
0.598270 | + | 0.801295i | \(0.295855\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.3269 | 1.66187 | 0.830935 | − | 0.556369i | \(-0.187806\pi\) | ||||
0.830935 | + | 0.556369i | \(0.187806\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.76692 | −0.342541 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.29220 | 0.290463 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.94915 | −0.138163 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.114675 | −0.00400707 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33.5230 | 1.16996 | 0.584981 | − | 0.811047i | \(-0.301102\pi\) | ||||
0.584981 | + | 0.811047i | \(0.301102\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 56.1962 | 1.95888 | 0.979439 | − | 0.201743i | \(-0.0646604\pi\) | ||||
0.979439 | + | 0.201743i | \(0.0646604\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −16.5850 | −0.577416 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.98192 | 0.103691 | 0.0518457 | − | 0.998655i | \(-0.483490\pi\) | ||||
0.0518457 | + | 0.998655i | \(0.483490\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.3752 | 0.846585 | 0.423293 | − | 0.905993i | \(-0.360874\pi\) | ||||
0.423293 | + | 0.905993i | \(0.360874\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.86546 | −0.168781 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.95435 | −0.137010 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −54.2954 | −1.87897 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.03295 | 0.277659 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.2830 | −0.734770 | −0.367385 | − | 0.930069i | \(-0.619747\pi\) | ||||
−0.367385 | + | 0.930069i | \(0.619747\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.92885 | 0.204443 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.23593 | 0.111451 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.84237 | −0.132181 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14.2099 | 0.487681 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −44.9034 | −1.53927 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.2026 | 0.383570 | 0.191785 | − | 0.981437i | \(-0.438572\pi\) | ||||
0.191785 | + | 0.981437i | \(0.438572\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.283961 | −0.00971125 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.01908 | −0.137289 | −0.0686445 | − | 0.997641i | \(-0.521867\pi\) | ||||
−0.0686445 | + | 0.997641i | \(0.521867\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27.9123 | −0.952355 | −0.476178 | − | 0.879349i | \(-0.657978\pi\) | ||||
−0.476178 | + | 0.879349i | \(0.657978\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.00951 | 0.272963 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.05187 | 0.0358059 | 0.0179030 | − | 0.999840i | \(-0.494301\pi\) | ||||
0.0179030 | + | 0.999840i | \(0.494301\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.4454 | 0.797166 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.31548 | −0.0786379 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.1673 | −0.548437 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.4609 | −0.456105 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.22815 | −0.0415667 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 18.3043 | 0.618797 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.06181 | 0.0696224 | 0.0348112 | − | 0.999394i | \(-0.488917\pi\) | ||||
0.0348112 | + | 0.999394i | \(0.488917\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −28.7839 | −0.970856 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.6430 | −0.459644 | −0.229822 | − | 0.973233i | \(-0.573814\pi\) | ||||
−0.229822 | + | 0.973233i | \(0.573814\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.3678 | 0.483517 | 0.241758 | − | 0.970336i | \(-0.422276\pi\) | ||||
0.241758 | + | 0.970336i | \(0.422276\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −15.6103 | −0.524733 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.8604 | 0.532539 | 0.266270 | − | 0.963899i | \(-0.414209\pi\) | ||||
0.266270 | + | 0.963899i | \(0.414209\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.58091 | −0.0530221 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.64282 | 0.289546 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.70186 | 0.257733 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −90.1857 | −3.01458 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −15.4397 | −0.515517 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.97340 | −0.299280 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.0917 | −0.402833 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.4090 | −0.346391 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 30.6466 | 1.01873 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.65489 | −0.187768 | −0.0938838 | − | 0.995583i | \(-0.529928\pi\) | ||||
−0.0938838 | + | 0.995583i | \(0.529928\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.679082 | 0.0225237 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.5578 | −0.449189 | −0.224594 | − | 0.974452i | \(-0.572106\pi\) | ||||
−0.224594 | + | 0.974452i | \(0.572106\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.07356 | −0.267196 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 49.5317 | 1.63747 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −19.5796 | −0.646576 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −55.8746 | −1.84313 | −0.921566 | − | 0.388222i | \(-0.873089\pi\) | ||||
−0.921566 | + | 0.388222i | \(0.873089\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 34.3230 | 1.13098 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.90183 | −0.293007 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −48.2343 | −1.58593 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.35708 | 0.0445725 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32.4785 | 1.06558 | 0.532792 | − | 0.846246i | \(-0.321143\pi\) | ||||
0.532792 | + | 0.846246i | \(0.321143\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.644451 | −0.0211210 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −25.5451 | −0.836310 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −15.1941 | −0.496899 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.7046 | 1.13375 | 0.566875 | − | 0.823804i | \(-0.308152\pi\) | ||||
0.566875 | + | 0.823804i | \(0.308152\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −31.1867 | −1.01774 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.3037 | 0.368489 | 0.184245 | − | 0.982880i | \(-0.441016\pi\) | ||||
0.184245 | + | 0.982880i | \(0.441016\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −42.8599 | −1.39571 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −20.3287 | −0.661292 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.92651 | 0.322568 | 0.161284 | − | 0.986908i | \(-0.448436\pi\) | ||||
0.161284 | + | 0.986908i | \(0.448436\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.4086 | −0.467724 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −32.9168 | −1.06740 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.9685 | 0.387699 | 0.193850 | − | 0.981031i | \(-0.437903\pi\) | ||||
0.193850 | + | 0.981031i | \(0.437903\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 76.5914 | 2.47844 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.0390 | −0.324514 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.95843 | −0.321574 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.6947 | −0.925635 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.918103 | −0.0295855 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 37.8352 | 1.21796 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.4649 | −0.561633 | −0.280816 | − | 0.959762i | \(-0.590605\pi\) | ||||
−0.280816 | + | 0.959762i | \(0.590605\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.32875 | 0.139059 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48.2923 | 1.54977 | 0.774887 | − | 0.632100i | \(-0.217807\pi\) | ||||
0.774887 | + | 0.632100i | \(0.217807\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.8376 | −0.732140 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −16.5850 | −0.531146 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.92048 | −0.189413 | −0.0947064 | − | 0.995505i | \(-0.530191\pi\) | ||||
−0.0947064 | + | 0.995505i | \(0.530191\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.46837 | 0.110850 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.579802 | 0.0185116 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.4494 | −0.365180 | −0.182590 | − | 0.983189i | \(-0.558448\pi\) | ||||
−0.182590 | + | 0.983189i | \(0.558448\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 75.7581 | 2.41385 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 20.3003 | 0.646166 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 55.7000 | 1.77116 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.5659 | 0.367402 | 0.183701 | − | 0.982982i | \(-0.441192\pi\) | ||||
0.183701 | + | 0.982982i | \(0.441192\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 56.3222 | 1.78733 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −62.3406 | −1.97633 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.5600 | −0.809494 | −0.404747 | − | 0.914429i | \(-0.632640\pi\) | ||||
−0.404747 | + | 0.914429i | \(0.632640\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 26.1365 | 0.826922 |
(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 | 4004.2.a.j.1.9 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4004.2.a.j.1.9 | ✓ | 10 | 1.1 | even | 1 | trivial |