Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8004,2,Mod(1,8004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8004, 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("8004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8004.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.9122617778\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} - 49 x^{14} + 130 x^{13} + 932 x^{12} - 2028 x^{11} - 8965 x^{10} + 14400 x^{9} + \cdots + 3888 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-0.434018\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8004.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.434018 | −0.194099 | −0.0970495 | − | 0.995280i | \(-0.530941\pi\) | ||||
−0.0970495 | + | 0.995280i | \(0.530941\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.25969 | −0.854084 | −0.427042 | − | 0.904232i | \(-0.640444\pi\) | ||||
−0.427042 | + | 0.904232i | \(0.640444\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.49169 | 1.05278 | 0.526392 | − | 0.850242i | \(-0.323544\pi\) | ||||
0.526392 | + | 0.850242i | \(0.323544\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.02170 | 1.39277 | 0.696384 | − | 0.717669i | \(-0.254791\pi\) | ||||
0.696384 | + | 0.717669i | \(0.254791\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.434018 | −0.112063 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.922556 | −0.223753 | −0.111876 | − | 0.993722i | \(-0.535686\pi\) | ||||
−0.111876 | + | 0.993722i | \(0.535686\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.87027 | 1.34673 | 0.673367 | − | 0.739309i | \(-0.264848\pi\) | ||||
0.673367 | + | 0.739309i | \(0.264848\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.25969 | −0.493106 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.81163 | −0.962326 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.57575 | 1.71986 | 0.859928 | − | 0.510416i | \(-0.170508\pi\) | ||||
0.859928 | + | 0.510416i | \(0.170508\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.49169 | 0.607826 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.980749 | 0.165777 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.89227 | 0.475487 | 0.237743 | − | 0.971328i | \(-0.423592\pi\) | ||||
0.237743 | + | 0.971328i | \(0.423592\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.02170 | 0.804115 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.70503 | −0.890975 | −0.445488 | − | 0.895288i | \(-0.646970\pi\) | ||||
−0.445488 | + | 0.895288i | \(0.646970\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.57680 | 0.697956 | 0.348978 | − | 0.937131i | \(-0.386529\pi\) | ||||
0.348978 | + | 0.937131i | \(0.386529\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.434018 | −0.0646996 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.28633 | −0.187631 | −0.0938155 | − | 0.995590i | \(-0.529906\pi\) | ||||
−0.0938155 | + | 0.995590i | \(0.529906\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.89378 | −0.270541 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.922556 | −0.129184 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.88390 | −1.35766 | −0.678829 | − | 0.734296i | \(-0.737512\pi\) | ||||
−0.678829 | + | 0.734296i | \(0.737512\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.51546 | −0.204344 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.87027 | 0.777537 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.268728 | −0.0349855 | −0.0174927 | − | 0.999847i | \(-0.505568\pi\) | ||||
−0.0174927 | + | 0.999847i | \(0.505568\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.59157 | −0.587890 | −0.293945 | − | 0.955822i | \(-0.594968\pi\) | ||||
−0.293945 | + | 0.955822i | \(0.594968\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.25969 | −0.284695 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.17951 | −0.270335 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.9610 | 1.58344 | 0.791719 | − | 0.610886i | \(-0.209187\pi\) | ||||
0.791719 | + | 0.610886i | \(0.209187\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.25321 | −0.148728 | −0.0743640 | − | 0.997231i | \(-0.523693\pi\) | ||||
−0.0743640 | + | 0.997231i | \(0.523693\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.10581 | −0.246466 | −0.123233 | − | 0.992378i | \(-0.539326\pi\) | ||||
−0.123233 | + | 0.992378i | \(0.539326\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.81163 | −0.555599 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.89016 | −0.899167 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.21562 | −1.03684 | −0.518419 | − | 0.855127i | \(-0.673479\pi\) | ||||
−0.518419 | + | 0.855127i | \(0.673479\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.24748 | 0.356457 | 0.178228 | − | 0.983989i | \(-0.442963\pi\) | ||||
0.178228 | + | 0.983989i | \(0.442963\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.400406 | 0.0434301 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.36608 | 0.886803 | 0.443401 | − | 0.896323i | \(-0.353772\pi\) | ||||
0.443401 | + | 0.896323i | \(0.353772\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.3475 | −1.18954 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.57575 | 0.992959 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.54781 | −0.261399 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.502057 | 0.0509761 | 0.0254881 | − | 0.999675i | \(-0.491886\pi\) | ||||
0.0254881 | + | 0.999675i | \(0.491886\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.49169 | 0.350928 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.47938 | 0.943234 | 0.471617 | − | 0.881803i | \(-0.343670\pi\) | ||||
0.471617 | + | 0.881803i | \(0.343670\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.20742 | 0.710168 | 0.355084 | − | 0.934834i | \(-0.384452\pi\) | ||||
0.355084 | + | 0.934834i | \(0.384452\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.980749 | 0.0957113 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.72557 | 0.843532 | 0.421766 | − | 0.906705i | \(-0.361410\pi\) | ||||
0.421766 | + | 0.906705i | \(0.361410\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.9076 | −1.23633 | −0.618164 | − | 0.786049i | \(-0.712123\pi\) | ||||
−0.618164 | + | 0.786049i | \(0.712123\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.89227 | 0.274522 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.2048 | 1.71256 | 0.856281 | − | 0.516510i | \(-0.172769\pi\) | ||||
0.856281 | + | 0.516510i | \(0.172769\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.434018 | −0.0404724 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.02170 | 0.464256 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.08469 | 0.191104 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.19192 | 0.108356 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.70503 | −0.514405 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.25843 | 0.380885 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.38726 | −0.566777 | −0.283389 | − | 0.959005i | \(-0.591459\pi\) | ||||
−0.283389 | + | 0.959005i | \(0.591459\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.57680 | 0.402965 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.83334 | −0.334920 | −0.167460 | − | 0.985879i | \(-0.553557\pi\) | ||||
−0.167460 | + | 0.985879i | \(0.553557\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.2650 | −1.15022 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.434018 | −0.0373544 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.7808 | 0.921069 | 0.460535 | − | 0.887642i | \(-0.347658\pi\) | ||||
0.460535 | + | 0.887642i | \(0.347658\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.97508 | 0.676438 | 0.338219 | − | 0.941067i | \(-0.390176\pi\) | ||||
0.338219 | + | 0.941067i | \(0.390176\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.28633 | −0.108329 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17.5342 | 1.46629 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.434018 | 0.0360433 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.89378 | −0.156197 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.6244 | −1.11616 | −0.558078 | − | 0.829788i | \(-0.688461\pi\) | ||||
−0.558078 | + | 0.829788i | \(0.688461\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.216471 | −0.0176161 | −0.00880807 | − | 0.999961i | \(-0.502804\pi\) | ||||
−0.00880807 | + | 0.999961i | \(0.502804\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.922556 | −0.0745842 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.15605 | −0.333822 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.63225 | 0.210076 | 0.105038 | − | 0.994468i | \(-0.466504\pi\) | ||||
0.105038 | + | 0.994468i | \(0.466504\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.88390 | −0.783844 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.25969 | −0.178089 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.0811 | −1.25957 | −0.629786 | − | 0.776769i | \(-0.716857\pi\) | ||||
−0.629786 | + | 0.776769i | \(0.716857\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.51546 | −0.117978 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.56463 | −0.198457 | −0.0992285 | − | 0.995065i | \(-0.531637\pi\) | ||||
−0.0992285 | + | 0.995065i | \(0.531637\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.2174 | 0.939804 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.87027 | 0.448911 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.88517 | −0.523470 | −0.261735 | − | 0.965140i | \(-0.584295\pi\) | ||||
−0.261735 | + | 0.965140i | \(0.584295\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.8728 | 0.821907 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.268728 | −0.0201989 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.43773 | −0.406435 | −0.203217 | − | 0.979134i | \(-0.565140\pi\) | ||||
−0.203217 | + | 0.979134i | \(0.565140\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.5095 | 1.59878 | 0.799392 | − | 0.600809i | \(-0.205155\pi\) | ||||
0.799392 | + | 0.600809i | \(0.205155\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.59157 | −0.339418 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.25530 | −0.0922915 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.22128 | −0.235563 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.25969 | −0.164369 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.6965 | −1.64226 | −0.821132 | − | 0.570738i | \(-0.806657\pi\) | ||||
−0.821132 | + | 0.570738i | \(0.806657\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.6343 | 1.62925 | 0.814627 | − | 0.579985i | \(-0.196942\pi\) | ||||
0.814627 | + | 0.579985i | \(0.196942\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.17951 | −0.156078 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.3349 | 0.736332 | 0.368166 | − | 0.929760i | \(-0.379986\pi\) | ||||
0.368166 | + | 0.929760i | \(0.379986\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.80944 | 0.128268 | 0.0641339 | − | 0.997941i | \(-0.479572\pi\) | ||||
0.0641339 | + | 0.997941i | \(0.479572\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.9610 | 0.914198 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.25969 | 0.158599 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.47609 | 0.172937 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 20.4972 | 1.41782 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.37416 | −0.645343 | −0.322672 | − | 0.946511i | \(-0.604581\pi\) | ||||
−0.322672 | + | 0.946511i | \(0.604581\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.25321 | −0.0858682 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.98642 | −0.135472 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −21.6383 | −1.46890 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.10581 | −0.142297 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.63280 | −0.311636 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.80672 | 0.522776 | 0.261388 | − | 0.965234i | \(-0.415820\pi\) | ||||
0.261388 | + | 0.965234i | \(0.415820\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.81163 | −0.320775 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.27849 | 0.0848562 | 0.0424281 | − | 0.999100i | \(-0.486491\pi\) | ||||
0.0424281 | + | 0.999100i | \(0.486491\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.8626 | 1.57689 | 0.788443 | − | 0.615108i | \(-0.210888\pi\) | ||||
0.788443 | + | 0.615108i | \(0.210888\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.89016 | −0.519134 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.8170 | 0.708648 | 0.354324 | − | 0.935123i | \(-0.384711\pi\) | ||||
0.354324 | + | 0.935123i | \(0.384711\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.558292 | 0.0364190 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.21562 | −0.598619 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.8482 | 1.67198 | 0.835992 | − | 0.548742i | \(-0.184893\pi\) | ||||
0.835992 | + | 0.548742i | \(0.184893\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.80834 | −0.245317 | −0.122658 | − | 0.992449i | \(-0.539142\pi\) | ||||
−0.122658 | + | 0.992449i | \(0.539142\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.821937 | 0.0525116 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 29.4787 | 1.87569 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.24748 | 0.205800 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.6031 | −1.74229 | −0.871147 | − | 0.491023i | \(-0.836623\pi\) | ||||
−0.871147 | + | 0.491023i | \(0.836623\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.49169 | 0.219521 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.400406 | 0.0250744 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.90359 | 0.617769 | 0.308885 | − | 0.951100i | \(-0.400044\pi\) | ||||
0.308885 | + | 0.951100i | \(0.400044\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.53565 | −0.406106 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −22.5105 | −1.38805 | −0.694027 | − | 0.719949i | \(-0.744165\pi\) | ||||
−0.694027 | + | 0.719949i | \(0.744165\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.28980 | 0.263520 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.36608 | 0.511996 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.7434 | 1.26475 | 0.632373 | − | 0.774664i | \(-0.282081\pi\) | ||||
0.632373 | + | 0.774664i | \(0.282081\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.7623 | 1.26122 | 0.630611 | − | 0.776099i | \(-0.282805\pi\) | ||||
0.630611 | + | 0.776099i | \(0.282805\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −11.3475 | −0.686782 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −16.8007 | −1.01312 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.1310 | 1.32973 | 0.664863 | − | 0.746966i | \(-0.268490\pi\) | ||||
0.664863 | + | 0.746966i | \(0.268490\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.57575 | 0.573285 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.5397 | 1.16564 | 0.582821 | − | 0.812600i | \(-0.301949\pi\) | ||||
0.582821 | + | 0.812600i | \(0.301949\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.4356 | −0.858109 | −0.429054 | − | 0.903279i | \(-0.641153\pi\) | ||||
−0.429054 | + | 0.903279i | \(0.641153\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.54781 | −0.150919 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.8916 | 0.760968 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.1489 | −0.949935 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.502057 | 0.0294311 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.35213 | −0.371095 | −0.185548 | − | 0.982635i | \(-0.559406\pi\) | ||||
−0.185548 | + | 0.982635i | \(0.559406\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.116633 | 0.00679064 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.49169 | 0.202609 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.02170 | 0.290412 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.3422 | −0.596113 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.47938 | 0.544576 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.99282 | 0.114109 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.6533 | 0.779232 | 0.389616 | − | 0.920977i | \(-0.372608\pi\) | ||||
0.389616 | + | 0.920977i | \(0.372608\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.20742 | 0.410016 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.0516 | 1.70407 | 0.852034 | − | 0.523486i | \(-0.175369\pi\) | ||||
0.852034 | + | 0.523486i | \(0.175369\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.8442 | 1.06513 | 0.532567 | − | 0.846388i | \(-0.321227\pi\) | ||||
0.532567 | + | 0.846388i | \(0.321227\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.980749 | 0.0552589 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.1249 | 0.737166 | 0.368583 | − | 0.929595i | \(-0.379843\pi\) | ||||
0.368583 | + | 0.929595i | \(0.379843\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.49169 | −0.195497 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.72557 | 0.487014 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.41565 | −0.301335 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −24.1625 | −1.34030 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.9076 | −0.713794 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.90672 | 0.160253 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.6848 | 1.68659 | 0.843293 | − | 0.537454i | \(-0.180614\pi\) | ||||
0.843293 | + | 0.537454i | \(0.180614\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.89227 | 0.158496 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.62531 | −0.307343 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.9484 | −0.868767 | −0.434384 | − | 0.900728i | \(-0.643034\pi\) | ||||
−0.434384 | + | 0.900728i | \(0.643034\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.2048 | 0.988748 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 33.4356 | 1.81064 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0972 | 1.08515 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.434018 | −0.0233668 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.32704 | −0.124922 | −0.0624610 | − | 0.998047i | \(-0.519895\pi\) | ||||
−0.0624610 | + | 0.998047i | \(0.519895\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.6041 | 1.63820 | 0.819101 | − | 0.573649i | \(-0.194473\pi\) | ||||
0.819101 | + | 0.573649i | \(0.194473\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.02170 | 0.268038 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.1607 | 0.594025 | 0.297013 | − | 0.954874i | \(-0.404010\pi\) | ||||
0.297013 | + | 0.954874i | \(0.404010\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.543914 | 0.0288680 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.08469 | 0.110334 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.9648 | 1.05370 | 0.526851 | − | 0.849957i | \(-0.323372\pi\) | ||||
0.526851 | + | 0.849957i | \(0.323372\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.4601 | 0.813690 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.19192 | 0.0625595 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.913959 | 0.0478388 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.2584 | −1.63168 | −0.815839 | − | 0.578280i | \(-0.803724\pi\) | ||||
−0.815839 | + | 0.578280i | \(0.803724\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.70503 | −0.296992 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 22.3346 | 1.15955 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.08153 | −0.159556 | −0.0797778 | − | 0.996813i | \(-0.525421\pi\) | ||||
−0.0797778 | + | 0.996813i | \(0.525421\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.25843 | 0.219904 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.02170 | −0.258631 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.6639 | 0.804600 | 0.402300 | − | 0.915508i | \(-0.368211\pi\) | ||||
0.402300 | + | 0.915508i | \(0.368211\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.38726 | −0.327229 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −31.6604 | −1.61777 | −0.808886 | − | 0.587965i | \(-0.799929\pi\) | ||||
−0.808886 | + | 0.587965i | \(0.799929\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.42447 | 0.174527 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.57680 | 0.232652 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.6235 | −0.741439 | −0.370719 | − | 0.928745i | \(-0.620889\pi\) | ||||
−0.370719 | + | 0.928745i | \(0.620889\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.922556 | −0.0466556 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.83334 | −0.193366 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.99975 | 0.201249 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.6325 | −0.533628 | −0.266814 | − | 0.963748i | \(-0.585971\pi\) | ||||
−0.266814 | + | 0.963748i | \(0.585971\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −13.2650 | −0.664082 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.3394 | −0.516326 | −0.258163 | − | 0.966101i | \(-0.583117\pi\) | ||||
−0.258163 | + | 0.966101i | \(0.583117\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 48.0865 | 2.39536 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.434018 | −0.0215665 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.0989 | 0.500585 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.1147 | 1.53852 | 0.769262 | − | 0.638933i | \(-0.220624\pi\) | ||||
0.769262 | + | 0.638933i | \(0.220624\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.7808 | 0.531780 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.607244 | 0.0298805 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.40946 | −0.0691879 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.97508 | 0.390541 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.74209 | −0.0851067 | −0.0425534 | − | 0.999094i | \(-0.513549\pi\) | ||||
−0.0425534 | + | 0.999094i | \(0.513549\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.80160 | −0.477701 | −0.238850 | − | 0.971056i | \(-0.576771\pi\) | ||||
−0.238850 | + | 0.971056i | \(0.576771\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.28633 | −0.0625437 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.43899 | 0.215323 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.3755 | 0.502107 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 17.5342 | 0.846560 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.75416 | 0.132663 | 0.0663316 | − | 0.997798i | \(-0.478870\pi\) | ||||
0.0663316 | + | 0.997798i | \(0.478870\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.90262 | −0.379776 | −0.189888 | − | 0.981806i | \(-0.560812\pi\) | ||||
−0.189888 | + | 0.981806i | \(0.560812\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.434018 | 0.0208096 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.87027 | 0.280813 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.8389 | 0.803679 | 0.401839 | − | 0.915710i | \(-0.368371\pi\) | ||||
0.401839 | + | 0.915710i | \(0.368371\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.89378 | −0.0901802 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.6857 | −1.26788 | −0.633938 | − | 0.773384i | \(-0.718562\pi\) | ||||
−0.633938 | + | 0.773384i | \(0.718562\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.63103 | −0.172127 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.6244 | −0.644413 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.79784 | −0.415196 | −0.207598 | − | 0.978214i | \(-0.566565\pi\) | ||||
−0.207598 | + | 0.978214i | \(0.566565\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.9202 | −0.938005 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.216471 | −0.0101707 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.92502 | 0.230889 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.9992 | 1.68397 | 0.841986 | − | 0.539500i | \(-0.181387\pi\) | ||||
0.841986 | + | 0.539500i | \(0.181387\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.922556 | −0.0430612 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −41.4402 | −1.93006 | −0.965031 | − | 0.262134i | \(-0.915574\pi\) | ||||
−0.965031 | + | 0.262134i | \(0.915574\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.188109 | −0.00874218 | −0.00437109 | − | 0.999990i | \(-0.501391\pi\) | ||||
−0.00437109 | + | 0.999990i | \(0.501391\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.15605 | −0.192732 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −31.3961 | −1.45284 | −0.726420 | − | 0.687251i | \(-0.758817\pi\) | ||||
−0.726420 | + | 0.687251i | \(0.758817\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −29.2879 | −1.35239 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.63225 | 0.121288 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.9808 | 0.734797 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −28.2456 | −1.29600 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.88390 | −0.452553 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −36.6453 | −1.67437 | −0.837183 | − | 0.546922i | \(-0.815799\pi\) | ||||
−0.837183 | + | 0.546922i | \(0.815799\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.5241 | 0.662243 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.25969 | −0.102820 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.217902 | −0.00989441 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.4622 | −1.01786 | −0.508929 | − | 0.860808i | \(-0.669958\pi\) | ||||
−0.508929 | + | 0.860808i | \(0.669958\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.0811 | −0.727214 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.7683 | −0.982388 | −0.491194 | − | 0.871050i | \(-0.663439\pi\) | ||||
−0.491194 | + | 0.871050i | \(0.663439\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.922556 | 0.0415498 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.51546 | −0.0681148 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.83186 | 0.127026 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.1913 | 0.814356 | 0.407178 | − | 0.913349i | \(-0.366513\pi\) | ||||
0.407178 | + | 0.913349i | \(0.366513\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.56463 | −0.114579 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.5579 | 0.872044 | 0.436022 | − | 0.899936i | \(-0.356387\pi\) | ||||
0.436022 | + | 0.899936i | \(0.356387\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.11423 | −0.183081 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.2174 | 0.542596 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 25.2850 | 1.12074 | 0.560369 | − | 0.828243i | \(-0.310659\pi\) | ||||
0.560369 | + | 0.828243i | \(0.310659\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.75848 | 0.210503 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.87027 | 0.259179 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.12815 | −0.137843 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.49148 | −0.197535 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.88517 | −0.302225 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.75838 | −0.164658 | −0.0823289 | − | 0.996605i | \(-0.526236\pi\) | ||||
−0.0823289 | + | 0.996605i | \(0.526236\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −37.4445 | −1.63734 | −0.818668 | − | 0.574268i | \(-0.805287\pi\) | ||||
−0.818668 | + | 0.574268i | \(0.805287\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 10.8728 | 0.474528 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.83416 | −0.384822 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.268728 | −0.0116618 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −28.6489 | −1.24092 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.78706 | −0.163729 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.43773 | −0.234655 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.61251 | −0.284821 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −36.7346 | −1.57934 | −0.789671 | − | 0.613530i | \(-0.789749\pi\) | ||||
−0.789671 | + | 0.613530i | \(0.789749\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 21.5095 | 0.923059 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.60215 | 0.239970 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.53085 | −0.279239 | −0.139620 | − | 0.990205i | \(-0.544588\pi\) | ||||
−0.139620 | + | 0.990205i | \(0.544588\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.59157 | −0.195963 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.87027 | −0.250082 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 20.8245 | 0.885547 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.25530 | −0.0532845 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.6425 | −1.17125 | −0.585625 | − | 0.810582i | \(-0.699151\pi\) | ||||
−0.585625 | + | 0.810582i | \(0.699151\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.9833 | 0.972090 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.22128 | −0.136003 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.6355 | −0.490376 | −0.245188 | − | 0.969476i | \(-0.578850\pi\) | ||||
−0.245188 | + | 0.969476i | \(0.578850\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.90121 | −0.332407 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.25969 | −0.0948982 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.2384 | 1.09997 | 0.549986 | − | 0.835174i | \(-0.314633\pi\) | ||||
0.549986 | + | 0.835174i | \(0.314633\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.60075 | −0.359930 | −0.179965 | − | 0.983673i | \(-0.557598\pi\) | ||||
−0.179965 | + | 0.983673i | \(0.557598\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −22.6965 | −0.948162 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.81163 | −0.200659 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.96052 | 0.331401 | 0.165700 | − | 0.986176i | \(-0.447012\pi\) | ||||
0.165700 | + | 0.986176i | \(0.447012\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 22.6343 | 0.940650 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.33830 | −0.304444 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −34.5116 | −1.42932 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.17951 | −0.0901116 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.4480 | 0.926527 | 0.463264 | − | 0.886221i | \(-0.346678\pi\) | ||||
0.463264 | + | 0.886221i | \(0.346678\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 56.2123 | 2.31619 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.3349 | 0.425122 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.2147 | 0.871185 | 0.435593 | − | 0.900144i | \(-0.356539\pi\) | ||||
0.435593 | + | 0.900144i | \(0.356539\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.904795 | −0.0370930 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.80944 | 0.0740554 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.2582 | −0.419139 | −0.209570 | − | 0.977794i | \(-0.567206\pi\) | ||||
−0.209570 | + | 0.977794i | \(0.567206\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.8975 | −1.09717 | −0.548586 | − | 0.836094i | \(-0.684833\pi\) | ||||
−0.548586 | + | 0.836094i | \(0.684833\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.9610 | 0.527812 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.517315 | −0.0210318 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.4719 | 0.790339 | 0.395170 | − | 0.918608i | \(-0.370686\pi\) | ||||
0.395170 | + | 0.918608i | \(0.370686\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.25969 | 0.0915674 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.45958 | −0.261327 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −35.4825 | −1.43313 | −0.716563 | − | 0.697523i | \(-0.754286\pi\) | ||||
−0.716563 | + | 0.697523i | \(0.754286\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.47609 | 0.0998454 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.6980 | −0.793012 | −0.396506 | − | 0.918032i | \(-0.629777\pi\) | ||||
−0.396506 | + | 0.918032i | \(0.629777\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.3551 | 1.30046 | 0.650230 | − | 0.759737i | \(-0.274672\pi\) | ||||
0.650230 | + | 0.759737i | \(0.274672\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.9048 | −0.757404 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.2099 | 0.888396 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 20.4972 | 0.818579 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.66828 | −0.106391 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.7436 | 1.78121 | 0.890607 | − | 0.454773i | \(-0.150280\pi\) | ||||
0.890607 | + | 0.454773i | \(0.150280\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.37416 | −0.372589 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.77219 | 0.110011 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.51001 | −0.376800 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.25321 | −0.0495760 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.62045 | 0.182497 | 0.0912483 | − | 0.995828i | \(-0.470914\pi\) | ||||
0.0912483 | + | 0.995828i | \(0.470914\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.8433 | 0.664234 | 0.332117 | − | 0.943238i | \(-0.392237\pi\) | ||||
0.332117 | + | 0.943238i | \(0.392237\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.98642 | −0.0782150 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −26.5057 | −1.04205 | −0.521023 | − | 0.853542i | \(-0.674450\pi\) | ||||
−0.521023 | + | 0.853542i | \(0.674450\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.938317 | −0.0368322 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −21.6383 | −0.848070 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.9743 | 0.703388 | 0.351694 | − | 0.936115i | \(-0.385606\pi\) | ||||
0.351694 | + | 0.936115i | \(0.385606\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.66374 | 0.0650077 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.10581 | −0.0821554 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.15635 | −0.200863 | −0.100431 | − | 0.994944i | \(-0.532022\pi\) | ||||
−0.100431 | + | 0.994944i | \(0.532022\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.14690 | −0.0446092 | −0.0223046 | − | 0.999751i | \(-0.507100\pi\) | ||||
−0.0223046 | + | 0.999751i | \(0.507100\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.63280 | −0.179923 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.75726 | 0.223257 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.80672 | 0.301825 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.0323 | −0.618922 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −42.0563 | −1.62115 | −0.810576 | − | 0.585634i | \(-0.800846\pi\) | ||||
−0.810576 | + | 0.585634i | \(0.800846\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.81163 | −0.185200 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.5900 | −0.714472 | −0.357236 | − | 0.934014i | \(-0.616281\pi\) | ||||
−0.357236 | + | 0.934014i | \(0.616281\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.13449 | −0.0435379 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.27849 | 0.0489918 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.1459 | −1.00044 | −0.500222 | − | 0.865897i | \(-0.666748\pi\) | ||||
−0.500222 | + | 0.865897i | \(0.666748\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.67908 | −0.178779 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23.8626 | 0.910415 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −49.6340 | −1.89090 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.14832 | 0.348018 | 0.174009 | − | 0.984744i | \(-0.444328\pi\) | ||||
0.174009 | + | 0.984744i | \(0.444328\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.89016 | −0.299722 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.46133 | −0.131296 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.26320 | 0.199358 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.8170 | 0.409138 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −45.3203 | −1.71172 | −0.855862 | − | 0.517204i | \(-0.826973\pi\) | ||||
−0.855862 | + | 0.517204i | \(0.826973\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.9784 | 0.640354 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.558292 | 0.0210265 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −21.4205 | −0.805601 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.9814 | 0.825530 | 0.412765 | − | 0.910837i | \(-0.364563\pi\) | ||||
0.412765 | + | 0.910837i | \(0.364563\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.21562 | −0.345613 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.57575 | 0.358615 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.61018 | −0.284604 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 25.8482 | 0.965320 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.1433 | 0.564748 | 0.282374 | − | 0.959304i | \(-0.408878\pi\) | ||||
0.282374 | + | 0.959304i | \(0.408878\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.2866 | −0.606543 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.80834 | −0.141634 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.81163 | 0.178699 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.3237 | 0.568324 | 0.284162 | − | 0.958776i | \(-0.408285\pi\) | ||||
0.284162 | + | 0.958776i | \(0.408285\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.22235 | −0.156169 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.1025 | −0.557825 | −0.278912 | − | 0.960317i | \(-0.589974\pi\) | ||||
−0.278912 | + | 0.960317i | \(0.589974\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.821937 | 0.0303176 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 45.2558 | 1.66702 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.2234 | 1.59000 | 0.794998 | − | 0.606612i | \(-0.207472\pi\) | ||||
0.794998 | + | 0.606612i | \(0.207472\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 29.4787 | 1.08293 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.71900 | −0.136437 | −0.0682185 | − | 0.997670i | \(-0.521732\pi\) | ||||
−0.0682185 | + | 0.997670i | \(0.521732\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.91325 | 0.216645 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.24748 | 0.118819 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −19.7171 | −0.720448 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.61239 | −0.277780 | −0.138890 | − | 0.990308i | \(-0.544353\pi\) | ||||
−0.138890 | + | 0.990308i | \(0.544353\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −27.6031 | −1.00591 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.0939523 | 0.00341927 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.1191 | 0.985660 | 0.492830 | − | 0.870126i | \(-0.335962\pi\) | ||||
0.492830 | + | 0.870126i | \(0.335962\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.49169 | 0.126740 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.1490 | 0.585400 | 0.292700 | − | 0.956204i | \(-0.405446\pi\) | ||||
0.292700 | + | 0.956204i | \(0.405446\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 29.1673 | 1.05593 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.400406 | 0.0144767 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.34947 | −0.0487266 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −54.4394 | −1.96314 | −0.981568 | − | 0.191111i | \(-0.938791\pi\) | ||||
−0.981568 | + | 0.191111i | \(0.938791\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.90359 | 0.356669 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −35.7818 | −1.28698 | −0.643492 | − | 0.765453i | \(-0.722515\pi\) | ||||
−0.643492 | + | 0.765453i | \(0.722515\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −46.0750 | −1.65506 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.53565 | −0.234465 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −33.4901 | −1.19991 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.37581 | −0.156579 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.14244 | −0.0407756 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.1538 | 1.60956 | 0.804780 | − | 0.593573i | \(-0.202283\pi\) | ||||
0.804780 | + | 0.593573i | \(0.202283\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −22.5105 | −0.801393 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −41.1372 | −1.46267 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23.0575 | −0.818794 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.28980 | 0.152143 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33.1561 | 1.17445 | 0.587225 | − | 0.809424i | \(-0.300220\pi\) | ||||
0.587225 | + | 0.809424i | \(0.300220\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.18671 | 0.0419829 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.36608 | 0.295601 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.35283 | −0.259476 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.980749 | 0.0345668 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.7434 | 0.730201 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 52.4675 | 1.84466 | 0.922329 | − | 0.386405i | \(-0.126283\pi\) | ||||
0.922329 | + | 0.386405i | \(0.126283\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.74967 | −0.272128 | −0.136064 | − | 0.990700i | \(-0.543445\pi\) | ||||
−0.136064 | + | 0.990700i | \(0.543445\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.7623 | 0.728166 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.97951 | 0.244482 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.8671 | 0.939960 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −11.3475 | −0.396514 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.4881 | −0.749940 | −0.374970 | − | 0.927037i | \(-0.622347\pi\) | ||||
−0.374970 | + | 0.927037i | \(0.622347\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36.5549 | −1.27422 | −0.637112 | − | 0.770772i | \(-0.719871\pi\) | ||||
−0.637112 | + | 0.770772i | \(0.719871\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −16.8007 | −0.584926 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.0011 | −1.14756 | −0.573781 | − | 0.819009i | \(-0.694524\pi\) | ||||
−0.573781 | + | 0.819009i | \(0.694524\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.66918 | −0.162167 | −0.0810837 | − | 0.996707i | \(-0.525838\pi\) | ||||
−0.0810837 | + | 0.996707i | \(0.525838\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.1310 | 0.767717 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.74712 | 0.0605342 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.11310 | 0.0385203 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.57575 | 0.330986 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 36.5811 | 1.26292 | 0.631459 | − | 0.775409i | \(-0.282456\pi\) | ||||
0.631459 | + | 0.775409i | \(0.282456\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.5397 | 0.672984 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.30260 | −0.182415 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.69337 | −0.0925453 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.4356 | −0.495429 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.89227 | 0.0991458 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −54.0770 | −1.85156 | −0.925780 | − | 0.378062i | \(-0.876591\pi\) | ||||
−0.925780 | + | 0.378062i | \(0.876591\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.54781 | −0.0871331 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.5237 | 0.871874 | 0.435937 | − | 0.899977i | \(-0.356417\pi\) | ||||
0.435937 | + | 0.899977i | \(0.356417\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.6725 | 1.14889 | 0.574446 | − | 0.818542i | \(-0.305218\pi\) | ||||
0.574446 | + | 0.818542i | \(0.305218\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.8916 | 0.439345 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −50.3410 | −1.71363 | −0.856814 | − | 0.515626i | \(-0.827559\pi\) | ||||
−0.856814 | + | 0.515626i | \(0.827559\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.98829 | 0.101605 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.1489 | −0.548445 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −32.1781 | −1.09157 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 65.0862 | 2.20536 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.502057 | 0.0169920 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.62274 | −0.325308 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.2179 | 0.513873 | 0.256936 | − | 0.966428i | \(-0.417287\pi\) | ||||
0.256936 | + | 0.966428i | \(0.417287\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.35213 | −0.214252 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.4235 | 1.32821 | 0.664105 | − | 0.747639i | \(-0.268813\pi\) | ||||
0.664105 | + | 0.747639i | \(0.268813\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30.1861 | −1.01584 | −0.507921 | − | 0.861404i | \(-0.669586\pi\) | ||||
−0.507921 | + | 0.861404i | \(0.669586\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.116633 | 0.00392058 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.3380 | −0.649305 | −0.324653 | − | 0.945833i | \(-0.605247\pi\) | ||||
−0.324653 | + | 0.945833i | \(0.605247\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.4332 | 0.484075 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.49169 | 0.116976 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.55113 | −0.252689 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.36007 | 0.0788885 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.02170 | 0.167670 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.57575 | −0.319369 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.11845 | 0.303780 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.3422 | −0.344166 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.33550 | −0.310322 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.4290 | −1.20960 | −0.604802 | − | 0.796376i | \(-0.706748\pi\) | ||||
−0.604802 | + | 0.796376i | \(0.706748\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.47938 | 0.314411 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −45.6790 | −1.51341 | −0.756707 | − | 0.653754i | \(-0.773193\pi\) | ||||
−0.756707 | + | 0.653754i | \(0.773193\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.3392 | 0.375272 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.99282 | 0.0658807 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.66217 | 0.286050 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.1818 | 0.962617 | 0.481309 | − | 0.876551i | \(-0.340162\pi\) | ||||
0.481309 | + | 0.876551i | \(0.340162\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.6533 | 0.449890 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.29322 | −0.207144 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.9165 | −0.457573 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.20742 | 0.236723 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32.7941 | 1.07594 | 0.537971 | − | 0.842964i | \(-0.319191\pi\) | ||||
0.537971 | + | 0.842964i | \(0.319191\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.1170 | −0.364346 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 30.0516 | 0.983844 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.39810 | 0.0457226 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.6579 | 0.511521 | 0.255760 | − | 0.966740i | \(-0.417674\pi\) | ||||
0.255760 | + | 0.966740i | \(0.417674\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18.8442 | 0.614956 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −54.5724 | −1.77901 | −0.889504 | − | 0.456927i | \(-0.848950\pi\) | ||||
−0.889504 | + | 0.456927i | \(0.848950\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.70503 | −0.185781 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.980749 | 0.0319038 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.79570 | −0.318318 | −0.159159 | − | 0.987253i | \(-0.550878\pi\) | ||||
−0.159159 | + | 0.987253i | \(0.550878\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.5747 | −0.343270 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.1249 | 0.425603 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.2918 | 0.624924 | 0.312462 | − | 0.949930i | \(-0.398846\pi\) | ||||
0.312462 | + | 0.949930i | \(0.398846\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.85072 | 0.318762 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.49169 | −0.112870 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −24.3614 | −0.786670 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 60.6950 | 1.95790 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.72557 | 0.281177 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.82371 | −0.316236 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.0831 | 0.388565 | 0.194282 | − | 0.980946i | \(-0.437762\pi\) | ||||
0.194282 | + | 0.980946i | \(0.437762\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.41565 | −0.173976 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.7988 | 0.442825 | 0.221412 | − | 0.975180i | \(-0.428933\pi\) | ||||
0.221412 | + | 0.975180i | \(0.428933\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.0212 | −0.577734 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −24.1625 | −0.773821 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −36.4835 | −1.16721 | −0.583605 | − | 0.812038i | \(-0.698358\pi\) | ||||
−0.583605 | + | 0.812038i | \(0.698358\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 29.2118 | 0.933613 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.9076 | −0.412109 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.07110 | 0.0341627 | 0.0170814 | − | 0.999854i | \(-0.494563\pi\) | ||||
0.0170814 | + | 0.999854i | \(0.494563\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.48554 | −0.142921 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.90672 | 0.0925219 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.57680 | 0.145534 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.9592 | 0.475196 | 0.237598 | − | 0.971364i | \(-0.423640\pi\) | ||||
0.237598 | + | 0.971364i | \(0.423640\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 30.6848 | 0.973751 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.785330 | −0.0248966 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.3969 | 1.08936 | 0.544680 | − | 0.838644i | \(-0.316651\pi\) | ||||
0.544680 | + | 0.838644i | \(0.316651\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.89227 | 0.0915075 |
(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 | 8004.2.a.j.1.8 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.j.1.8 | ✓ | 16 | 1.1 | even | 1 | trivial |