Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9200,2,Mod(1,9200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9200, 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("9200.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9200.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: | \(73.4623698596\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.791953.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 7x^{3} + 7x^{2} + 9x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 4600) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.08344\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9200.1 |
$q$-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 | ||||||||
\(3\) | −3.08344 | −1.78022 | −0.890112 | − | 0.455742i | \(-0.849374\pi\) | ||||
−0.890112 | + | 0.455742i | \(0.849374\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.555022 | 0.209779 | 0.104889 | − | 0.994484i | \(-0.466551\pi\) | ||||
0.104889 | + | 0.994484i | \(0.466551\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.50759 | 2.16920 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.65190 | −1.40260 | −0.701301 | − | 0.712866i | \(-0.747397\pi\) | ||||
−0.701301 | + | 0.712866i | \(0.747397\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.02256 | 1.39301 | 0.696504 | − | 0.717553i | \(-0.254738\pi\) | ||||
0.696504 | + | 0.717553i | \(0.254738\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.32867 | 0.322251 | 0.161125 | − | 0.986934i | \(-0.448488\pi\) | ||||
0.161125 | + | 0.986934i | \(0.448488\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.196402 | 0.0450577 | 0.0225288 | − | 0.999746i | \(-0.492828\pi\) | ||||
0.0225288 | + | 0.999746i | \(0.492828\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.71138 | −0.373453 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −10.8154 | −2.08143 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.812298 | −0.150840 | −0.0754200 | − | 0.997152i | \(-0.524030\pi\) | ||||
−0.0754200 | + | 0.997152i | \(0.524030\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.11145 | 0.379227 | 0.189613 | − | 0.981859i | \(-0.439277\pi\) | ||||
0.189613 | + | 0.981859i | \(0.439277\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 14.3439 | 2.49694 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.64564 | −0.928138 | −0.464069 | − | 0.885799i | \(-0.653611\pi\) | ||||
−0.464069 | + | 0.885799i | \(0.653611\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −15.4868 | −2.47987 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.89714 | −0.764804 | −0.382402 | − | 0.923996i | \(-0.624903\pi\) | ||||
−0.382402 | + | 0.923996i | \(0.624903\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.66507 | −0.253920 | −0.126960 | − | 0.991908i | \(-0.540522\pi\) | ||||
−0.126960 | + | 0.991908i | \(0.540522\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.89310 | 1.44306 | 0.721528 | − | 0.692385i | \(-0.243440\pi\) | ||||
0.721528 | + | 0.692385i | \(0.243440\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.69195 | −0.955993 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.09688 | −0.573678 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.23261 | 0.306673 | 0.153336 | − | 0.988174i | \(-0.450998\pi\) | ||||
0.153336 | + | 0.988174i | \(0.450998\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.605593 | −0.0802127 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.43488 | −0.316994 | −0.158497 | − | 0.987359i | \(-0.550665\pi\) | ||||
−0.158497 | + | 0.987359i | \(0.550665\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.71138 | −0.731267 | −0.365633 | − | 0.930759i | \(-0.619148\pi\) | ||||
−0.365633 | + | 0.930759i | \(0.619148\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.61185 | 0.455051 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.91830 | −0.845205 | −0.422602 | − | 0.906315i | \(-0.638883\pi\) | ||||
−0.422602 | + | 0.906315i | \(0.638883\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.08344 | 0.371202 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.0120411 | −0.00142902 | −0.000714510 | − | 1.00000i | \(-0.500227\pi\) | ||||
−0.000714510 | 1.00000i | \(0.500227\pi\) | ||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.2989 | 1.79061 | 0.895303 | − | 0.445458i | \(-0.146959\pi\) | ||||
0.895303 | + | 0.445458i | \(0.146959\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.58191 | −0.294236 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.6351 | −1.19654 | −0.598272 | − | 0.801293i | \(-0.704146\pi\) | ||||
−0.598272 | + | 0.801293i | \(0.704146\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 13.8260 | 1.53622 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.64020 | 0.619092 | 0.309546 | − | 0.950884i | \(-0.399823\pi\) | ||||
0.309546 | + | 0.950884i | \(0.399823\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.50467 | 0.268529 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.06693 | 0.961093 | 0.480547 | − | 0.876969i | \(-0.340438\pi\) | ||||
0.480547 | + | 0.876969i | \(0.340438\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.78763 | 0.292223 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.51051 | −0.675108 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.0720 | −1.42880 | −0.714398 | − | 0.699739i | \(-0.753299\pi\) | ||||
−0.714398 | + | 0.699739i | \(0.753299\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −30.2727 | −3.04252 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.53015 | 0.749278 | 0.374639 | − | 0.927171i | \(-0.377767\pi\) | ||||
0.374639 | + | 0.927171i | \(0.377767\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.4476 | 1.42357 | 0.711784 | − | 0.702399i | \(-0.247888\pi\) | ||||
0.711784 | + | 0.702399i | \(0.247888\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.35862 | −0.228016 | −0.114008 | − | 0.993480i | \(-0.536369\pi\) | ||||
−0.114008 | + | 0.993480i | \(0.536369\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.3578 | −0.992101 | −0.496050 | − | 0.868294i | \(-0.665217\pi\) | ||||
−0.496050 | + | 0.868294i | \(0.665217\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 17.4080 | 1.65229 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −19.2723 | −1.81298 | −0.906491 | − | 0.422226i | \(-0.861249\pi\) | ||||
−0.906491 | + | 0.422226i | \(0.861249\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 32.6848 | 3.02171 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.737442 | 0.0676012 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.6402 | 0.967291 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 15.1000 | 1.36152 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.4934 | 1.64102 | 0.820510 | − | 0.571632i | \(-0.193689\pi\) | ||||
0.820510 | + | 0.571632i | \(0.193689\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.13413 | 0.452035 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.7727 | 1.29070 | 0.645351 | − | 0.763887i | \(-0.276711\pi\) | ||||
0.645351 | + | 0.763887i | \(0.276711\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.109007 | 0.00945213 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.6173 | 0.992533 | 0.496266 | − | 0.868170i | \(-0.334704\pi\) | ||||
0.496266 | + | 0.868170i | \(0.334704\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.1389 | −0.944787 | −0.472393 | − | 0.881388i | \(-0.656610\pi\) | ||||
−0.472393 | + | 0.881388i | \(0.656610\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −30.5047 | −2.56896 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −23.3645 | −1.95384 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 20.6342 | 1.70188 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.4796 | −1.02237 | −0.511184 | − | 0.859472i | \(-0.670793\pi\) | ||||
−0.511184 | + | 0.859472i | \(0.670793\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.32673 | −0.107968 | −0.0539840 | − | 0.998542i | \(-0.517192\pi\) | ||||
−0.0539840 | + | 0.998542i | \(0.517192\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.64646 | 0.699025 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 23.1754 | 1.84960 | 0.924798 | − | 0.380458i | \(-0.124234\pi\) | ||||
0.924798 | + | 0.380458i | \(0.124234\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.88412 | −0.545946 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.555022 | −0.0437418 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −25.0682 | −1.96349 | −0.981746 | − | 0.190196i | \(-0.939088\pi\) | ||||
−0.981746 | + | 0.190196i | \(0.939088\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.39603 | 0.340175 | 0.170087 | − | 0.985429i | \(-0.445595\pi\) | ||||
0.170087 | + | 0.985429i | \(0.445595\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.2261 | 0.940473 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.27810 | 0.0977389 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.4211 | 1.47656 | 0.738281 | − | 0.674493i | \(-0.235638\pi\) | ||||
0.738281 | + | 0.674493i | \(0.235638\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.50779 | 0.564320 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.4169 | −0.778592 | −0.389296 | − | 0.921113i | \(-0.627282\pi\) | ||||
−0.389296 | + | 0.921113i | \(0.627282\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.13693 | −0.679143 | −0.339571 | − | 0.940580i | \(-0.610282\pi\) | ||||
−0.339571 | + | 0.940580i | \(0.610282\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 17.6107 | 1.30182 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.18086 | −0.451989 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.00280 | −0.436640 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.49819 | 0.108405 | 0.0542026 | − | 0.998530i | \(-0.482738\pi\) | ||||
0.0542026 | + | 0.998530i | \(0.482738\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.4113 | 1.03735 | 0.518675 | − | 0.854972i | \(-0.326425\pi\) | ||||
0.518675 | + | 0.854972i | \(0.326425\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.4686 | 1.74331 | 0.871657 | − | 0.490116i | \(-0.163046\pi\) | ||||
0.871657 | + | 0.490116i | \(0.163046\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.61185 | 0.114261 | 0.0571307 | − | 0.998367i | \(-0.481805\pi\) | ||||
0.0571307 | + | 0.998367i | \(0.481805\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 21.3321 | 1.50465 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.450843 | −0.0316430 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.50759 | −0.452309 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.913642 | −0.0631979 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.25081 | −0.430324 | −0.215162 | − | 0.976578i | \(-0.569028\pi\) | ||||
−0.215162 | + | 0.976578i | \(0.569028\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.0371281 | 0.00254398 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.17190 | 0.0795536 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −47.1733 | −3.18768 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.67334 | 0.448898 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.2953 | −1.42604 | −0.713019 | − | 0.701144i | \(-0.752673\pi\) | ||||
−0.713019 | + | 0.701144i | \(0.752673\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.5174 | −0.698061 | −0.349031 | − | 0.937111i | \(-0.613489\pi\) | ||||
−0.349031 | + | 0.937111i | \(0.613489\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.0063 | −1.58638 | −0.793190 | − | 0.608975i | \(-0.791581\pi\) | ||||
−0.793190 | + | 0.608975i | \(0.791581\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.96115 | 0.523805 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.3112 | −0.741021 | −0.370510 | − | 0.928828i | \(-0.620817\pi\) | ||||
−0.370510 | + | 0.928828i | \(0.620817\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 32.7927 | 2.13012 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.5592 | 1.65329 | 0.826644 | − | 0.562726i | \(-0.190247\pi\) | ||||
0.826644 | + | 0.562726i | \(0.190247\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.1617 | −1.04106 | −0.520532 | − | 0.853842i | \(-0.674266\pi\) | ||||
−0.520532 | + | 0.853842i | \(0.674266\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.1852 | −0.653380 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.986440 | 0.0627657 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −17.3912 | −1.10212 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.3497 | 0.842627 | 0.421313 | − | 0.906915i | \(-0.361569\pi\) | ||||
0.421313 | + | 0.906915i | \(0.361569\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.65190 | 0.292463 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.1834 | 0.635222 | 0.317611 | − | 0.948221i | \(-0.397119\pi\) | ||||
0.317611 | + | 0.948221i | \(0.397119\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.13345 | −0.194703 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.28610 | −0.327201 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.3073 | 1.43719 | 0.718594 | − | 0.695430i | \(-0.244786\pi\) | ||||
0.718594 | + | 0.695430i | \(0.244786\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −27.9573 | −1.71096 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.80817 | 0.598015 | 0.299007 | − | 0.954251i | \(-0.403344\pi\) | ||||
0.299007 | + | 0.954251i | \(0.403344\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.08332 | 0.369535 | 0.184768 | − | 0.982782i | \(-0.440847\pi\) | ||||
0.184768 | + | 0.982782i | \(0.440847\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.59549 | −0.520223 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.0445722 | 0.00267809 | 0.00133904 | − | 0.999999i | \(-0.499574\pi\) | ||||
0.00133904 | + | 0.999999i | \(0.499574\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.7404 | 0.822617 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.9996 | 1.67032 | 0.835158 | − | 0.550010i | \(-0.185376\pi\) | ||||
0.835158 | + | 0.550010i | \(0.185376\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.1798 | 0.724013 | 0.362006 | − | 0.932176i | \(-0.382092\pi\) | ||||
0.362006 | + | 0.932176i | \(0.382092\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.71802 | −0.160440 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.2346 | −0.896155 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 43.3902 | 2.54358 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.71056 | 0.158352 | 0.0791762 | − | 0.996861i | \(-0.474771\pi\) | ||||
0.0791762 | + | 0.996861i | \(0.474771\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 50.3124 | 2.91942 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.02256 | −0.290462 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.924148 | −0.0532670 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −23.2188 | −1.33388 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −32.1631 | −1.83564 | −0.917821 | − | 0.396994i | \(-0.870053\pi\) | ||||
−0.917821 | + | 0.396994i | \(0.870053\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −44.5484 | −2.53427 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.07951 | 0.231328 | 0.115664 | − | 0.993288i | \(-0.463100\pi\) | ||||
0.115664 | + | 0.993288i | \(0.463100\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.7806 | −0.778925 | −0.389462 | − | 0.921042i | \(-0.627339\pi\) | ||||
−0.389462 | + | 0.921042i | \(0.627339\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.4630 | −0.587658 | −0.293829 | − | 0.955858i | \(-0.594930\pi\) | ||||
−0.293829 | + | 0.955858i | \(0.594930\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.77873 | 0.211568 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.27266 | 0.405920 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.260954 | 0.0145199 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 31.9377 | 1.76616 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.49088 | 0.302722 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.6451 | 0.695038 | 0.347519 | − | 0.937673i | \(-0.387024\pi\) | ||||
0.347519 | + | 0.937673i | \(0.387024\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −36.7395 | −2.01331 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.5733 | −1.33859 | −0.669295 | − | 0.742997i | \(-0.733404\pi\) | ||||
−0.669295 | + | 0.742997i | \(0.733404\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 59.4248 | 3.22751 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.82224 | −0.531904 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.59933 | −0.410325 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.50569 | −0.188195 | −0.0940977 | − | 0.995563i | \(-0.529997\pi\) | ||||
−0.0940977 | + | 0.995563i | \(0.529997\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.1085 | −0.969327 | −0.484664 | − | 0.874701i | \(-0.661058\pi\) | ||||
−0.484664 | + | 0.874701i | \(0.661058\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −54.3212 | −2.89945 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.1915 | 1.07469 | 0.537343 | − | 0.843364i | \(-0.319428\pi\) | ||||
0.537343 | + | 0.843364i | \(0.319428\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.27386 | −0.120345 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.43409 | 0.497912 | 0.248956 | − | 0.968515i | \(-0.419912\pi\) | ||||
0.248956 | + | 0.968515i | \(0.419912\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9614 | −0.997970 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −32.8084 | −1.72199 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.3412 | −1.58380 | −0.791899 | − | 0.610652i | \(-0.790908\pi\) | ||||
−0.791899 | + | 0.610652i | \(0.790908\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −31.8686 | −1.65901 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.23915 | 0.0643333 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.7893 | −0.765758 | −0.382879 | − | 0.923798i | \(-0.625067\pi\) | ||||
−0.382879 | + | 0.923798i | \(0.625067\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.07982 | −0.210121 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.2405 | 0.577385 | 0.288693 | − | 0.957422i | \(-0.406779\pi\) | ||||
0.288693 | + | 0.957422i | \(0.406779\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −57.0231 | −2.92138 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.4602 | −1.55644 | −0.778221 | − | 0.627991i | \(-0.783878\pi\) | ||||
−0.778221 | + | 0.627991i | \(0.783878\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.8356 | −0.550803 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.94011 | 0.0983673 | 0.0491836 | − | 0.998790i | \(-0.484338\pi\) | ||||
0.0491836 | + | 0.998790i | \(0.484338\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.32867 | −0.0671939 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −45.5509 | −2.29774 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.3206 | −0.919487 | −0.459743 | − | 0.888052i | \(-0.652059\pi\) | ||||
−0.459743 | + | 0.888052i | \(0.652059\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.336117 | −0.0168269 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.32199 | −0.0660170 | −0.0330085 | − | 0.999455i | \(-0.510509\pi\) | ||||
−0.0330085 | + | 0.999455i | \(0.510509\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.6049 | 0.528266 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 26.2630 | 1.30181 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.9963 | 1.08765 | 0.543823 | − | 0.839200i | \(-0.316976\pi\) | ||||
0.543823 | + | 0.839200i | \(0.316976\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −35.8212 | −1.76693 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.35141 | −0.0664985 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 34.3460 | 1.68193 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.3194 | −1.38349 | −0.691746 | − | 0.722141i | \(-0.743158\pi\) | ||||
−0.691746 | + | 0.722141i | \(0.743158\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.7650 | 0.719602 | 0.359801 | − | 0.933029i | \(-0.382845\pi\) | ||||
0.359801 | + | 0.933029i | \(0.382845\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 64.3802 | 3.13027 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.16994 | −0.153404 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 72.0429 | 3.47826 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.0514 | 1.30302 | 0.651510 | − | 0.758640i | \(-0.274136\pi\) | ||||
0.651510 | + | 0.758640i | \(0.274136\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −38.2700 | −1.83914 | −0.919570 | − | 0.392926i | \(-0.871463\pi\) | ||||
−0.919570 | + | 0.392926i | \(0.871463\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.196402 | −0.00939517 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.39959 | 0.114526 | 0.0572630 | − | 0.998359i | \(-0.481763\pi\) | ||||
0.0572630 | + | 0.998359i | \(0.481763\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −43.5485 | −2.07374 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.6542 | −0.506198 | −0.253099 | − | 0.967440i | \(-0.581450\pi\) | ||||
−0.253099 | + | 0.967440i | \(0.581450\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 38.4800 | 1.82004 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.9533 | −1.36639 | −0.683195 | − | 0.730236i | \(-0.739410\pi\) | ||||
−0.683195 | + | 0.730236i | \(0.739410\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.7810 | 1.07272 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.09090 | 0.192207 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −38.5855 | −1.80496 | −0.902478 | − | 0.430736i | \(-0.858254\pi\) | ||||
−0.902478 | + | 0.430736i | \(0.858254\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −14.3702 | −0.670743 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.07659 | −0.376164 | −0.188082 | − | 0.982153i | \(-0.560227\pi\) | ||||
−0.188082 | + | 0.982153i | \(0.560227\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.07771 | −0.282455 | −0.141228 | − | 0.989977i | \(-0.545105\pi\) | ||||
−0.141228 | + | 0.989977i | \(0.545105\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.2961 | 0.476446 | 0.238223 | − | 0.971210i | \(-0.423435\pi\) | ||||
0.238223 | + | 0.971210i | \(0.423435\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.83981 | −0.177306 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −71.4598 | −3.29270 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.74572 | 0.356149 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.5289 | 0.665233 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 33.9760 | 1.55240 | 0.776201 | − | 0.630486i | \(-0.217144\pi\) | ||||
0.776201 | + | 0.630486i | \(0.217144\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −28.3556 | −1.29290 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.71138 | 0.0778703 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.4951 | −0.747464 | −0.373732 | − | 0.927537i | \(-0.621922\pi\) | ||||
−0.373732 | + | 0.927537i | \(0.621922\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 77.2962 | 3.49546 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.4876 | −1.24050 | −0.620249 | − | 0.784405i | \(-0.712968\pi\) | ||||
−0.620249 | + | 0.784405i | \(0.712968\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.07928 | −0.0486082 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.00668310 | −0.000299778 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.2961 | −0.819045 | −0.409523 | − | 0.912300i | \(-0.634305\pi\) | ||||
−0.409523 | + | 0.912300i | \(0.634305\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.5549 | −0.605587 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.97389 | 0.0880115 | 0.0440058 | − | 0.999031i | \(-0.485988\pi\) | ||||
0.0440058 | + | 0.999031i | \(0.485988\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −37.6986 | −1.67425 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −38.3441 | −1.69957 | −0.849787 | − | 0.527126i | \(-0.823269\pi\) | ||||
−0.849787 | + | 0.527126i | \(0.823269\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.49125 | 0.375631 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.12417 | −0.0937844 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −46.0217 | −2.02403 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −59.8839 | −2.62861 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.1814 | −1.01560 | −0.507799 | − | 0.861476i | \(-0.669541\pi\) | ||||
−0.507799 | + | 0.861476i | \(0.669541\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 43.5123 | 1.90266 | 0.951331 | − | 0.308172i | \(-0.0997173\pi\) | ||||
0.951331 | + | 0.308172i | \(0.0997173\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.80542 | 0.122206 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −15.8452 | −0.687622 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −24.5962 | −1.06538 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 32.1197 | 1.38607 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 31.1303 | 1.34088 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.6112 | 0.800158 | 0.400079 | − | 0.916481i | \(-0.368983\pi\) | ||||
0.400079 | + | 0.916481i | \(0.368983\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 28.1732 | 1.20903 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.78956 | −0.290300 | −0.145150 | − | 0.989410i | \(-0.546367\pi\) | ||||
−0.145150 | + | 0.989410i | \(0.546367\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −37.1673 | −1.58626 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.159537 | −0.00679649 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.90272 | −0.251009 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24.9869 | −1.05873 | −0.529364 | − | 0.848395i | \(-0.677570\pi\) | ||||
−0.529364 | + | 0.848395i | \(0.677570\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.36290 | −0.353713 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 19.0583 | 0.804642 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −44.7551 | −1.88620 | −0.943100 | − | 0.332508i | \(-0.892105\pi\) | ||||
−0.943100 | + | 0.332508i | \(0.892105\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.67371 | 0.322265 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −27.4895 | −1.15242 | −0.576211 | − | 0.817301i | \(-0.695469\pi\) | ||||
−0.576211 | + | 0.817301i | \(0.695469\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.40495 | 0.0587952 | 0.0293976 | − | 0.999568i | \(-0.490641\pi\) | ||||
0.0293976 | + | 0.999568i | \(0.490641\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.61957 | −0.192985 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.1987 | 0.799253 | 0.399627 | − | 0.916678i | \(-0.369140\pi\) | ||||
0.399627 | + | 0.916678i | \(0.369140\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −44.4364 | −1.84671 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.13043 | 0.129872 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.3859 | −0.430139 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22.8565 | −0.943390 | −0.471695 | − | 0.881762i | \(-0.656358\pi\) | ||||
−0.471695 | + | 0.881762i | \(0.656358\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.414692 | 0.0170871 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −75.4473 | −3.10349 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.5387 | 1.08981 | 0.544906 | − | 0.838497i | \(-0.316565\pi\) | ||||
0.544906 | + | 0.838497i | \(0.316565\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.97005 | −0.203411 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.82768 | 0.360689 | 0.180345 | − | 0.983603i | \(-0.442279\pi\) | ||||
0.180345 | + | 0.983603i | \(0.442279\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.3072 | −1.23626 | −0.618129 | − | 0.786077i | \(-0.712109\pi\) | ||||
−0.618129 | + | 0.786077i | \(0.712109\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −45.0215 | −1.83342 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 38.0102 | 1.54278 | 0.771392 | − | 0.636360i | \(-0.219561\pi\) | ||||
0.771392 | + | 0.636360i | \(0.219561\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.39015 | 0.0563316 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 49.6887 | 2.01019 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 31.7417 | 1.28204 | 0.641018 | − | 0.767526i | \(-0.278512\pi\) | ||||
0.641018 | + | 0.767526i | \(0.278512\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −46.6699 | −1.87886 | −0.939430 | − | 0.342741i | \(-0.888645\pi\) | ||||
−0.939430 | + | 0.342741i | \(0.888645\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.2223 | −0.933383 | −0.466692 | − | 0.884420i | \(-0.654554\pi\) | ||||
−0.466692 | + | 0.884420i | \(0.654554\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.8154 | 0.434009 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.03235 | 0.201617 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.81716 | 0.112506 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.50121 | −0.299093 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.0906 | 0.521129 | 0.260565 | − | 0.965456i | \(-0.416091\pi\) | ||||
0.260565 | + | 0.965456i | \(0.416091\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19.2740 | 0.766072 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −33.6107 | −1.33171 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.0783588 | −0.00309983 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.8746 | 0.903494 | 0.451747 | − | 0.892146i | \(-0.350801\pi\) | ||||
0.451747 | + | 0.892146i | \(0.350801\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.6333 | −1.20806 | −0.604030 | − | 0.796962i | \(-0.706439\pi\) | ||||
−0.604030 | + | 0.796962i | \(0.706439\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.74454 | −0.343783 | −0.171892 | − | 0.985116i | \(-0.554988\pi\) | ||||
−0.171892 | + | 0.985116i | \(0.554988\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.3268 | 0.444616 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.61348 | −0.141623 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.7443 | 0.968320 | 0.484160 | − | 0.874979i | \(-0.339125\pi\) | ||||
0.484160 | + | 0.874979i | \(0.339125\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 99.5593 | 3.88418 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.30726 | −0.323605 | −0.161803 | − | 0.986823i | \(-0.551731\pi\) | ||||
−0.161803 | + | 0.986823i | \(0.551731\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.1755 | −0.551364 | −0.275682 | − | 0.961249i | \(-0.588904\pi\) | ||||
−0.275682 | + | 0.961249i | \(0.588904\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −20.5768 | −0.799138 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.812298 | 0.0314523 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 65.6627 | 2.53867 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 26.5688 | 1.02568 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.30229 | −0.281482 | −0.140741 | − | 0.990046i | \(-0.544949\pi\) | ||||
−0.140741 | + | 0.990046i | \(0.544949\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −39.7090 | −1.52614 | −0.763071 | − | 0.646315i | \(-0.776309\pi\) | ||||
−0.763071 | + | 0.646315i | \(0.776309\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.81027 | −0.299731 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 32.4296 | 1.24271 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −38.5993 | −1.47696 | −0.738481 | − | 0.674274i | \(-0.764457\pi\) | ||||
−0.738481 | + | 0.674274i | \(0.764457\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 74.0219 | 2.82411 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.2134 | 0.427198 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.4163 | 0.814713 | 0.407357 | − | 0.913269i | \(-0.366451\pi\) | ||||
0.407357 | + | 0.913269i | \(0.366451\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −16.8020 | −0.638255 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.50669 | −0.246459 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 34.8773 | 1.31918 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.40147 | −0.204011 | −0.102005 | − | 0.994784i | \(-0.532526\pi\) | ||||
−0.102005 | + | 0.994784i | \(0.532526\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.10881 | −0.0418197 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.17940 | 0.157182 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.3161 | −0.575208 | −0.287604 | − | 0.957749i | \(-0.592859\pi\) | ||||
−0.287604 | + | 0.957749i | \(0.592859\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −69.2090 | −2.59554 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.11145 | −0.0790742 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −78.8102 | −2.94322 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11.6505 | −0.434491 | −0.217245 | − | 0.976117i | \(-0.569707\pi\) | ||||
−0.217245 | + | 0.976117i | \(0.569707\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.01875 | 0.298634 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 49.8334 | 1.85333 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.8188 | −1.06883 | −0.534415 | − | 0.845223i | \(-0.679468\pi\) | ||||
−0.534415 | + | 0.845223i | \(0.679468\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −10.0725 | −0.373056 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.21233 | −0.0818259 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.2304 | −0.931906 | −0.465953 | − | 0.884810i | \(-0.654288\pi\) | ||||
−0.465953 | + | 0.884810i | \(0.654288\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 32.1833 | 1.18549 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.22800 | 0.0451728 | 0.0225864 | − | 0.999745i | \(-0.492810\pi\) | ||||
0.0225864 | + | 0.999745i | \(0.492810\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.04163 | −0.111737 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −35.1117 | −1.28812 | −0.644061 | − | 0.764974i | \(-0.722752\pi\) | ||||
−0.644061 | + | 0.764974i | \(0.722752\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 36.7041 | 1.34293 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.30909 | −0.0478329 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.7367 | −1.15809 | −0.579044 | − | 0.815296i | \(-0.696574\pi\) | ||||
−0.579044 | + | 0.815296i | \(0.696574\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −41.1630 | −1.50006 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.22287 | −0.117137 | −0.0585685 | − | 0.998283i | \(-0.518654\pi\) | ||||
−0.0585685 | + | 0.998283i | \(0.518654\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −14.3439 | −0.520649 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.60077 | −0.348027 | −0.174014 | − | 0.984743i | \(-0.555674\pi\) | ||||
−0.174014 | + | 0.984743i | \(0.555674\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.74882 | −0.208121 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.2293 | −0.441575 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.9778 | 0.540113 | 0.270056 | − | 0.962844i | \(-0.412958\pi\) | ||||
0.270056 | + | 0.962844i | \(0.412958\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −31.3998 | −1.13084 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28.7430 | 1.03381 | 0.516906 | − | 0.856042i | \(-0.327084\pi\) | ||||
0.516906 | + | 0.856042i | \(0.327084\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.66181 | 0.346616 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.961806 | −0.0344603 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.0560142 | 0.00200435 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.78536 | 0.313963 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.1965 | 1.21897 | 0.609486 | − | 0.792797i | \(-0.291376\pi\) | ||||
0.609486 | + | 0.792797i | \(0.291376\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −71.8666 | −2.55852 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.6965 | −0.380324 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −28.6857 | −1.01866 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.303391 | −0.0107467 | −0.00537334 | − | 0.999986i | \(-0.501710\pi\) | ||||
−0.00537334 | + | 0.999986i | \(0.501710\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.1447 | 0.465026 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 59.0039 | 2.08480 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −71.1692 | −2.51151 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −30.2429 | −1.06460 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.1865 | −0.463611 | −0.231806 | − | 0.972762i | \(-0.574463\pi\) | ||||
−0.231806 | + | 0.972762i | \(0.574463\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.7284 | −0.517185 | −0.258593 | − | 0.965986i | \(-0.583259\pi\) | ||||
−0.258593 | + | 0.965986i | \(0.583259\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.7575 | −0.657856 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.327022 | −0.0114410 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 18.1408 | 0.633890 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.6177 | 1.27797 | 0.638984 | − | 0.769220i | \(-0.279355\pi\) | ||||
0.638984 | + | 0.769220i | \(0.279355\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.420867 | −0.0146705 | −0.00733525 | − | 0.999973i | \(-0.502335\pi\) | ||||
−0.00733525 | + | 0.999973i | \(0.502335\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −35.1118 | −1.22096 | −0.610479 | − | 0.792032i | \(-0.709023\pi\) | ||||
−0.610479 | + | 0.792032i | \(0.709023\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.6234 | −1.23725 | −0.618626 | − | 0.785685i | \(-0.712311\pi\) | ||||
−0.618626 | + | 0.785685i | \(0.712311\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.137436 | −0.00476759 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.89141 | −0.308069 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −22.8362 | −0.789335 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.9998 | 0.690469 | 0.345235 | − | 0.938516i | \(-0.387799\pi\) | ||||
0.345235 | + | 0.938516i | \(0.387799\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3402 | −0.977247 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −86.3350 | −2.97354 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.90554 | 0.202917 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −37.5556 | −1.28890 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.64564 | 0.193530 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42.4994 | 1.45515 | 0.727577 | − | 0.686026i | \(-0.240647\pi\) | ||||
0.727577 | + | 0.686026i | \(0.240647\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.0100 | −0.615208 | −0.307604 | − | 0.951514i | \(-0.599527\pi\) | ||||
−0.307604 | + | 0.951514i | \(0.599527\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.3869 | −0.763832 | −0.381916 | − | 0.924197i | \(-0.624736\pi\) | ||||
−0.381916 | + | 0.924197i | \(0.624736\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.38084 | 0.285618 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.7613 | −0.638642 | −0.319321 | − | 0.947647i | \(-0.603455\pi\) | ||||
−0.319321 | + | 0.947647i | \(0.603455\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 46.9750 | 1.59536 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 49.4735 | 1.67827 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34.7476 | −1.17738 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −91.5749 | −3.09934 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.6345 | −1.06822 | −0.534111 | − | 0.845415i | \(-0.679353\pi\) | ||||
−0.534111 | + | 0.845415i | \(0.679353\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.35783 | −0.281903 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.6850 | 1.33702 | 0.668512 | − | 0.743702i | \(-0.266932\pi\) | ||||
0.668512 | + | 0.743702i | \(0.266932\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.3778 | 0.349242 | 0.174621 | − | 0.984636i | \(-0.444130\pi\) | ||||
0.174621 | + | 0.984636i | \(0.444130\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24.0199 | −0.806508 | −0.403254 | − | 0.915088i | \(-0.632121\pi\) | ||||
−0.403254 | + | 0.915088i | \(0.632121\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.2642 | 0.344251 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −64.3170 | −2.15470 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.94302 | 0.0650207 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.4868 | 0.517088 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.71512 | −0.0572025 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.96641 | 0.0988254 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.84955 | 0.0948271 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.5181 | 0.614885 | 0.307442 | − | 0.951567i | \(-0.400527\pi\) | ||||
0.307442 | + | 0.951567i | \(0.400527\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 49.0032 | 1.62533 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.34956 | 0.110976 | 0.0554879 | − | 0.998459i | \(-0.482329\pi\) | ||||
0.0554879 | + | 0.998459i | \(0.482329\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26.2376 | −0.868339 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.19920 | 0.270761 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.9754 | 1.08776 | 0.543878 | − | 0.839164i | \(-0.316955\pi\) | ||||
0.543878 | + | 0.839164i | \(0.316955\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 99.1728 | 3.26785 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.0604774 | −0.00199064 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 94.0193 | 3.08800 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −36.5008 | −1.19755 | −0.598777 | − | 0.800916i | \(-0.704346\pi\) | ||||
−0.598777 | + | 0.800916i | \(0.704346\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.31431 | −0.0430748 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.5789 | −0.411816 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.4598 | −0.407043 | −0.203521 | − | 0.979071i | \(-0.565239\pi\) | ||||
−0.203521 | + | 0.979071i | \(0.565239\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 42.4916 | 1.38666 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −45.2938 | −1.47653 | −0.738267 | − | 0.674508i | \(-0.764356\pi\) | ||||
−0.738267 | + | 0.674508i | \(0.764356\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.89714 | 0.159473 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.4016 | 1.34537 | 0.672685 | − | 0.739929i | \(-0.265141\pi\) | ||||
0.672685 | + | 0.739929i | \(0.265141\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 76.8399 | 2.49433 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32.2619 | 1.04616 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.3738 | 0.498006 | 0.249003 | − | 0.968503i | \(-0.419897\pi\) | ||||
0.249003 | + | 0.968503i | \(0.419897\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.6515 | −0.376639 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.44785 | 0.208212 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.5418 | −0.856187 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.3489 | −0.494612 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 53.4925 | 1.72020 | 0.860101 | − | 0.510124i | \(-0.170400\pi\) | ||||
0.860101 | + | 0.510124i | \(0.170400\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.804635 | −0.0258486 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.8881 | −0.638241 | −0.319120 | − | 0.947714i | \(-0.603387\pi\) | ||||
−0.319120 | + | 0.947714i | \(0.603387\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.18231 | −0.198196 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.8758 | 0.475919 | 0.237960 | − | 0.971275i | \(-0.423521\pi\) | ||||
0.237960 | + | 0.971275i | \(0.423521\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −42.1785 | −1.34803 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −67.4045 | −2.15206 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.16403 | −0.0371269 | −0.0185634 | − | 0.999828i | \(-0.505909\pi\) | ||||
−0.0185634 | + | 0.999828i | \(0.505909\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.9308 | −0.538913 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.66507 | 0.0529460 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.8693 | 1.52062 | 0.760310 | − | 0.649561i | \(-0.225047\pi\) | ||||
0.760310 | + | 0.649561i | \(0.225047\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −38.9904 | −1.23732 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.4353 | 0.362159 | 0.181079 | − | 0.983468i | \(-0.442041\pi\) | ||||
0.181079 | + | 0.983468i | \(0.442041\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 61.0601 | 1.93186 |
(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 | 9200.2.a.cs.1.1 | 5 | ||
4.3 | odd | 2 | 4600.2.a.bg.1.5 | yes | 5 | ||
5.4 | even | 2 | 9200.2.a.cw.1.5 | 5 | |||
20.3 | even | 4 | 4600.2.e.v.4049.10 | 10 | |||
20.7 | even | 4 | 4600.2.e.v.4049.1 | 10 | |||
20.19 | odd | 2 | 4600.2.a.bc.1.1 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4600.2.a.bc.1.1 | ✓ | 5 | 20.19 | odd | 2 | ||
4600.2.a.bg.1.5 | yes | 5 | 4.3 | odd | 2 | ||
4600.2.e.v.4049.1 | 10 | 20.7 | even | 4 | |||
4600.2.e.v.4049.10 | 10 | 20.3 | even | 4 | |||
9200.2.a.cs.1.1 | 5 | 1.1 | even | 1 | trivial | ||
9200.2.a.cw.1.5 | 5 | 5.4 | even | 2 |