Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3584,2,Mod(1,3584)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3584, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3584.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3584 = 2^{9} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3584.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: | \(28.6183840844\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 19x^{8} + 44x^{7} + 86x^{6} - 236x^{5} - 58x^{4} + 368x^{3} - 194x^{2} - 12x + 18 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.00182\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3584.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.99347 | −1.72828 | −0.864141 | − | 0.503250i | \(-0.832138\pi\) | ||||
−0.864141 | + | 0.503250i | \(0.832138\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.369776 | −0.165369 | −0.0826844 | − | 0.996576i | \(-0.526349\pi\) | ||||
−0.0826844 | + | 0.996576i | \(0.526349\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.96088 | 1.98696 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.93465 | −1.18634 | −0.593170 | − | 0.805077i | \(-0.702124\pi\) | ||||
−0.593170 | + | 0.805077i | \(0.702124\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.07457 | −1.68478 | −0.842391 | − | 0.538867i | \(-0.818853\pi\) | ||||
−0.842391 | + | 0.538867i | \(0.818853\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.10691 | 0.285804 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.75635 | 1.63866 | 0.819328 | − | 0.573325i | \(-0.194347\pi\) | ||||
0.819328 | + | 0.573325i | \(0.194347\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.117109 | −0.0268666 | −0.0134333 | − | 0.999910i | \(-0.504276\pi\) | ||||
−0.0134333 | + | 0.999910i | \(0.504276\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.99347 | 0.653229 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.67135 | −1.80810 | −0.904050 | − | 0.427426i | \(-0.859420\pi\) | ||||
−0.904050 | + | 0.427426i | \(0.859420\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.86327 | −0.972653 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −8.86331 | −1.70574 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.27619 | 1.16546 | 0.582730 | − | 0.812666i | \(-0.301985\pi\) | ||||
0.582730 | + | 0.812666i | \(0.301985\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.808080 | 0.145136 | 0.0725678 | − | 0.997363i | \(-0.476881\pi\) | ||||
0.0725678 | + | 0.997363i | \(0.476881\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 11.7783 | 2.05033 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.369776 | 0.0625035 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.1743 | −1.67264 | −0.836319 | − | 0.548243i | \(-0.815297\pi\) | ||||
−0.836319 | + | 0.548243i | \(0.815297\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 18.1840 | 2.91178 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.27490 | −1.13615 | −0.568074 | − | 0.822977i | \(-0.692311\pi\) | ||||
−0.568074 | + | 0.822977i | \(0.692311\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.0365776 | 0.00557804 | 0.00278902 | − | 0.999996i | \(-0.499112\pi\) | ||||
0.00278902 | + | 0.999996i | \(0.499112\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.20419 | −0.328581 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.06779 | −0.593349 | −0.296674 | − | 0.954979i | \(-0.595878\pi\) | ||||
−0.296674 | + | 0.954979i | \(0.595878\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −20.2250 | −2.83206 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.53918 | −0.348784 | −0.174392 | − | 0.984676i | \(-0.555796\pi\) | ||||
−0.174392 | + | 0.984676i | \(0.555796\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.45494 | 0.196184 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.350562 | 0.0464331 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.53975 | 0.721213 | 0.360607 | − | 0.932718i | \(-0.382570\pi\) | ||||
0.360607 | + | 0.932718i | \(0.382570\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.02663 | 0.771631 | 0.385815 | − | 0.922576i | \(-0.373920\pi\) | ||||
0.385815 | + | 0.922576i | \(0.373920\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.96088 | −0.751000 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.24623 | 0.278610 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.88072 | −0.596275 | −0.298138 | − | 0.954523i | \(-0.596365\pi\) | ||||
−0.298138 | + | 0.954523i | \(0.596365\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 25.9574 | 3.12491 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.35733 | −0.279763 | −0.139882 | − | 0.990168i | \(-0.544672\pi\) | ||||
−0.139882 | + | 0.990168i | \(0.544672\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.82414 | −0.798706 | −0.399353 | − | 0.916797i | \(-0.630765\pi\) | ||||
−0.399353 | + | 0.916797i | \(0.630765\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 14.5581 | 1.68102 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.93465 | 0.448395 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.35733 | −0.715255 | −0.357627 | − | 0.933864i | \(-0.616414\pi\) | ||||
−0.357627 | + | 0.933864i | \(0.616414\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.64944 | 0.961049 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.65033 | −0.949497 | −0.474748 | − | 0.880122i | \(-0.657461\pi\) | ||||
−0.474748 | + | 0.880122i | \(0.657461\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.49834 | −0.270983 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −18.7876 | −2.01424 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.56443 | −0.377829 | −0.188915 | − | 0.981994i | \(-0.560497\pi\) | ||||
−0.188915 | + | 0.981994i | \(0.560497\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.07457 | 0.636788 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.41897 | −0.250835 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.0433041 | 0.00444290 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.211290 | −0.0214532 | −0.0107266 | − | 0.999942i | \(-0.503414\pi\) | ||||
−0.0107266 | + | 0.999942i | \(0.503414\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −23.4540 | −2.35721 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.84907 | 0.980019 | 0.490010 | − | 0.871717i | \(-0.336993\pi\) | ||||
0.490010 | + | 0.871717i | \(0.336993\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.6587 | 1.14877 | 0.574385 | − | 0.818585i | \(-0.305241\pi\) | ||||
0.574385 | + | 0.818585i | \(0.305241\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.10691 | −0.108024 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.4269 | −1.00801 | −0.504005 | − | 0.863701i | \(-0.668141\pi\) | ||||
−0.504005 | + | 0.863701i | \(0.668141\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.2092 | −1.26521 | −0.632607 | − | 0.774473i | \(-0.718015\pi\) | ||||
−0.632607 | + | 0.774473i | \(0.718015\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 30.4564 | 2.89079 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19.3760 | 1.82274 | 0.911369 | − | 0.411590i | \(-0.135027\pi\) | ||||
0.911369 | + | 0.411590i | \(0.135027\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.20645 | 0.299003 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −36.2098 | −3.34759 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.75635 | −0.619354 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.48145 | 0.407405 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 21.7772 | 1.96359 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.64720 | 0.326215 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.5931 | −1.64987 | −0.824936 | − | 0.565227i | \(-0.808789\pi\) | ||||
−0.824936 | + | 0.565227i | \(0.808789\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.109494 | −0.00964043 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.06663 | −0.267933 | −0.133966 | − | 0.990986i | \(-0.542771\pi\) | ||||
−0.133966 | + | 0.990986i | \(0.542771\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.117109 | 0.0101546 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.27744 | 0.282077 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.90239 | 0.589711 | 0.294855 | − | 0.955542i | \(-0.404729\pi\) | ||||
0.294855 | + | 0.955542i | \(0.404729\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.9927 | 1.61094 | 0.805472 | − | 0.592634i | \(-0.201912\pi\) | ||||
0.805472 | + | 0.592634i | \(0.201912\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.1768 | 1.02547 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 23.9013 | 1.99873 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.32078 | −0.192731 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.99347 | −0.246897 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.6726 | −1.03818 | −0.519090 | − | 0.854720i | \(-0.673729\pi\) | ||||
−0.519090 | + | 0.854720i | \(0.673729\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.87845 | 0.803897 | 0.401949 | − | 0.915662i | \(-0.368333\pi\) | ||||
0.401949 | + | 0.915662i | \(0.368333\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 40.2738 | 3.25594 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.298809 | −0.0240009 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.0877 | −0.884898 | −0.442449 | − | 0.896794i | \(-0.645890\pi\) | ||||
−0.442449 | + | 0.896794i | \(0.645890\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.60097 | 0.602796 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.67135 | 0.683398 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.6611 | 0.835045 | 0.417523 | − | 0.908667i | \(-0.362898\pi\) | ||||
0.417523 | + | 0.908667i | \(0.362898\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.35532 | −0.339061 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.6840 | 1.05890 | 0.529448 | − | 0.848342i | \(-0.322399\pi\) | ||||
0.529448 | + | 0.848342i | \(0.322399\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.9004 | 1.83849 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.698072 | −0.0533829 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.242470 | −0.0184346 | −0.00921731 | − | 0.999958i | \(-0.502934\pi\) | ||||
−0.00921731 | + | 0.999958i | \(0.502934\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.86327 | 0.367628 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −16.5831 | −1.24646 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.776129 | −0.0580106 | −0.0290053 | − | 0.999579i | \(-0.509234\pi\) | ||||
−0.0290053 | + | 0.999579i | \(0.509234\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.0614 | 1.11951 | 0.559754 | − | 0.828659i | \(-0.310896\pi\) | ||||
0.559754 | + | 0.828659i | \(0.310896\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −18.0406 | −1.33360 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.76220 | 0.276602 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −26.5839 | −1.94400 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.86331 | 0.644711 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.4209 | −1.11582 | −0.557910 | − | 0.829902i | \(-0.688397\pi\) | ||||
−0.557910 | + | 0.829902i | \(0.688397\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.75377 | 0.702092 | 0.351046 | − | 0.936358i | \(-0.385826\pi\) | ||||
0.351046 | + | 0.936358i | \(0.385826\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.72402 | −0.481517 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.3127 | 1.51847 | 0.759234 | − | 0.650817i | \(-0.225574\pi\) | ||||
0.759234 | + | 0.650817i | \(0.225574\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.2290 | −0.866892 | −0.433446 | − | 0.901180i | \(-0.642702\pi\) | ||||
−0.433446 | + | 0.901180i | \(0.642702\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.6103 | 1.03053 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.27619 | −0.440502 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.69008 | 0.187884 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −51.6888 | −3.59262 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.460782 | 0.0318730 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.6543 | 1.62843 | 0.814213 | − | 0.580566i | \(-0.197169\pi\) | ||||
0.814213 | + | 0.580566i | \(0.197169\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.05659 | 0.483509 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.0135255 | −0.000922434 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.808080 | −0.0548561 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 20.4279 | 1.38039 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −41.0419 | −2.76078 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.2530 | 0.686591 | 0.343296 | − | 0.939227i | \(-0.388457\pi\) | ||||
0.343296 | + | 0.939227i | \(0.388457\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −28.9893 | −1.93262 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.9299 | 0.791818 | 0.395909 | − | 0.918290i | \(-0.370430\pi\) | ||||
0.395909 | + | 0.918290i | \(0.370430\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.89932 | −0.389838 | −0.194919 | − | 0.980819i | \(-0.562444\pi\) | ||||
−0.194919 | + | 0.980819i | \(0.562444\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.7783 | −0.774953 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.61032 | 0.564081 | 0.282040 | − | 0.959403i | \(-0.408989\pi\) | ||||
0.282040 | + | 0.959403i | \(0.408989\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.50417 | 0.0981213 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 19.0305 | 1.23616 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.0485 | 1.16746 | 0.583729 | − | 0.811949i | \(-0.301593\pi\) | ||||
0.583729 | + | 0.811949i | \(0.301593\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.9635 | 1.02830 | 0.514148 | − | 0.857701i | \(-0.328108\pi\) | ||||
0.514148 | + | 0.857701i | \(0.328108\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.698072 | 0.0447813 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.369776 | −0.0236241 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.711386 | 0.0452644 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 25.8945 | 1.64100 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.6242 | 1.30179 | 0.650895 | − | 0.759168i | \(-0.274394\pi\) | ||||
0.650895 | + | 0.759168i | \(0.274394\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 34.1187 | 2.14502 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.47870 | 0.468334 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.66877 | −0.353608 | −0.176804 | − | 0.984246i | \(-0.556576\pi\) | ||||
−0.176804 | + | 0.984246i | \(0.556576\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.1743 | 0.632198 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 37.4116 | 2.31572 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.2910 | 0.696231 | 0.348115 | − | 0.937452i | \(-0.386822\pi\) | ||||
0.348115 | + | 0.937452i | \(0.386822\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.938928 | 0.0576779 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.6700 | 0.652995 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.242470 | 0.0147836 | 0.00739182 | − | 0.999973i | \(-0.497647\pi\) | ||||
0.00739182 | + | 0.999973i | \(0.497647\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.25299 | −0.136859 | −0.0684297 | − | 0.997656i | \(-0.521799\pi\) | ||||
−0.0684297 | + | 0.997656i | \(0.521799\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −18.1840 | −1.10055 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 19.1352 | 1.15390 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.5105 | −1.05211 | −0.526053 | − | 0.850452i | \(-0.676329\pi\) | ||||
−0.526053 | + | 0.850452i | \(0.676329\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.81687 | 0.288378 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −32.7772 | −1.95532 | −0.977661 | − | 0.210190i | \(-0.932592\pi\) | ||||
−0.977661 | + | 0.210190i | \(0.932592\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.7190 | 1.46939 | 0.734696 | − | 0.678396i | \(-0.237325\pi\) | ||||
0.734696 | + | 0.678396i | \(0.237325\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.129629 | −0.00767859 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.27490 | 0.429424 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 28.6483 | 1.68519 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.632490 | 0.0370772 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.7531 | −0.920303 | −0.460152 | − | 0.887840i | \(-0.652205\pi\) | ||||
−0.460152 | + | 0.887840i | \(0.652205\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.04846 | −0.119266 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 34.8740 | 2.02359 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 52.6747 | 3.04625 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.0365776 | −0.00210830 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −29.4829 | −1.69375 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.22850 | −0.127604 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.7863 | 0.900971 | 0.450485 | − | 0.892784i | \(-0.351251\pi\) | ||||
0.450485 | + | 0.892784i | \(0.351251\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −34.9001 | −1.98540 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.2186 | 0.806261 | 0.403130 | − | 0.915143i | \(-0.367922\pi\) | ||||
0.403130 | + | 0.915143i | \(0.367922\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.8794 | 1.51931 | 0.759656 | − | 0.650325i | \(-0.225367\pi\) | ||||
0.759656 | + | 0.650325i | \(0.225367\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.20419 | 0.124192 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.832075 | −0.0467340 | −0.0233670 | − | 0.999727i | \(-0.507439\pi\) | ||||
−0.0233670 | + | 0.999727i | \(0.507439\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −24.6946 | −1.38263 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 31.2127 | 1.74212 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.791229 | −0.0440252 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 29.5422 | 1.63871 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 39.5414 | 2.18665 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.06779 | 0.224265 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.4164 | 0.737433 | 0.368716 | − | 0.929542i | \(-0.379797\pi\) | ||||
0.368716 | + | 0.929542i | \(0.379797\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −60.6475 | −3.32346 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.80477 | 0.0986054 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.6613 | 0.798653 | 0.399326 | − | 0.916809i | \(-0.369244\pi\) | ||||
0.399326 | + | 0.916809i | \(0.369244\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −58.0014 | −3.15021 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.17951 | −0.172180 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.59843 | −0.516762 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.02974 | 0.323693 | 0.161847 | − | 0.986816i | \(-0.448255\pi\) | ||||
0.161847 | + | 0.986816i | \(0.448255\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.9754 | 1.33690 | 0.668452 | − | 0.743756i | \(-0.266957\pi\) | ||||
0.668452 | + | 0.743756i | \(0.266957\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 53.8408 | 2.87381 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.2968 | −1.18674 | −0.593370 | − | 0.804930i | \(-0.702203\pi\) | ||||
−0.593370 | + | 0.804930i | \(0.702203\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.871682 | 0.0462641 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 20.2250 | 1.07042 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −26.4896 | −1.39807 | −0.699035 | − | 0.715087i | \(-0.746387\pi\) | ||||
−0.699035 | + | 0.715087i | \(0.746387\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9863 | −0.999278 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −13.4151 | −0.704110 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.52340 | 0.132081 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.2138 | 0.533157 | 0.266579 | − | 0.963813i | \(-0.414107\pi\) | ||||
0.266579 | + | 0.963813i | \(0.414107\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −43.3648 | −2.25748 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.53918 | 0.131828 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.9320 | −0.876708 | −0.438354 | − | 0.898802i | \(-0.644438\pi\) | ||||
−0.438354 | + | 0.898802i | \(0.644438\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.9178 | −0.563792 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −38.1251 | −1.96354 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.34665 | −0.0691729 | −0.0345865 | − | 0.999402i | \(-0.511011\pi\) | ||||
−0.0345865 | + | 0.999402i | \(0.511011\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 55.6579 | 2.85144 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.0473 | −0.717784 | −0.358892 | − | 0.933379i | \(-0.616845\pi\) | ||||
−0.358892 | + | 0.933379i | \(0.616845\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.45494 | −0.0741505 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.218035 | 0.0110833 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.17440 | 0.211651 | 0.105825 | − | 0.994385i | \(-0.466252\pi\) | ||||
0.105825 | + | 0.994385i | \(0.466252\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −58.5867 | −2.96285 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.17987 | 0.463063 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.35079 | 0.118281 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.4578 | −1.07694 | −0.538469 | − | 0.842645i | \(-0.680997\pi\) | ||||
−0.538469 | + | 0.842645i | \(0.680997\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.350562 | −0.0175501 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.747050 | −0.0373059 | −0.0186530 | − | 0.999826i | \(-0.505938\pi\) | ||||
−0.0186530 | + | 0.999826i | \(0.505938\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.90874 | −0.244522 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.19835 | −0.158927 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 40.0321 | 1.98432 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.69274 | 0.380382 | 0.190191 | − | 0.981747i | \(-0.439089\pi\) | ||||
0.190191 | + | 0.981747i | \(0.439089\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −20.6621 | −1.01919 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.53975 | −0.272593 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.19868 | 0.157017 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −56.8542 | −2.78416 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.5196 | −0.807036 | −0.403518 | − | 0.914972i | \(-0.632213\pi\) | ||||
−0.403518 | + | 0.914972i | \(0.632213\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.5105 | −0.853411 | −0.426705 | − | 0.904391i | \(-0.640326\pi\) | ||||
−0.426705 | + | 0.904391i | \(0.640326\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −24.2476 | −1.17896 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −32.8579 | −1.59384 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.02663 | −0.291649 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −71.5478 | −3.45436 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.3912 | −1.31939 | −0.659693 | − | 0.751535i | \(-0.729314\pi\) | ||||
−0.659693 | + | 0.751535i | \(0.729314\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.9749 | −1.39245 | −0.696223 | − | 0.717826i | \(-0.745137\pi\) | ||||
−0.696223 | + | 0.717826i | \(0.745137\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.94720 | 0.333093 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.01549 | 0.0485776 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 34.1407 | 1.62945 | 0.814724 | − | 0.579848i | \(-0.196888\pi\) | ||||
0.814724 | + | 0.579848i | \(0.196888\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.96088 | 0.283851 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.9122 | 0.898546 | 0.449273 | − | 0.893394i | \(-0.351683\pi\) | ||||
0.449273 | + | 0.893394i | \(0.351683\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.31804 | 0.0624811 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 37.9351 | 1.79427 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.8293 | −1.36054 | −0.680270 | − | 0.732962i | \(-0.738137\pi\) | ||||
−0.680270 | + | 0.732962i | \(0.738137\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.6242 | 1.34786 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −29.5709 | −1.38936 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.24623 | −0.105305 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.0906 | −1.12691 | −0.563456 | − | 0.826146i | \(-0.690528\pi\) | ||||
−0.563456 | + | 0.826146i | \(0.690528\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −59.8836 | −2.79513 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.2107 | 0.987882 | 0.493941 | − | 0.869496i | \(-0.335556\pi\) | ||||
0.493941 | + | 0.869496i | \(0.335556\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.5565 | 0.722973 | 0.361486 | − | 0.932377i | \(-0.382269\pi\) | ||||
0.361486 | + | 0.932377i | \(0.382269\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.894475 | 0.0414803 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.50838 | −0.116074 | −0.0580371 | − | 0.998314i | \(-0.518484\pi\) | ||||
−0.0580371 | + | 0.998314i | \(0.518484\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.88072 | 0.225371 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 33.1909 | 1.52935 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.143920 | −0.00661746 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.569532 | 0.0261319 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −15.1358 | −0.693019 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.1184 | −1.14769 | −0.573845 | − | 0.818964i | \(-0.694549\pi\) | ||||
−0.573845 | + | 0.818964i | \(0.694549\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 61.8042 | 2.81803 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −25.9574 | −1.18110 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.0781298 | 0.00354769 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.0804 | −0.773987 | −0.386993 | − | 0.922082i | \(-0.626486\pi\) | ||||
−0.386993 | + | 0.922082i | \(0.626486\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −31.9138 | −1.44319 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.8459 | 0.579727 | 0.289864 | − | 0.957068i | \(-0.406390\pi\) | ||||
0.289864 | + | 0.957068i | \(0.406390\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 42.4041 | 1.90979 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.67271 | 0.389809 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.35733 | 0.105740 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.94086 | 0.176417 | 0.0882086 | − | 0.996102i | \(-0.471886\pi\) | ||||
0.0882086 | + | 0.996102i | \(0.471886\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −40.9625 | −1.83007 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −38.0573 | −1.69689 | −0.848447 | − | 0.529281i | \(-0.822462\pi\) | ||||
−0.848447 | + | 0.529281i | \(0.822462\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.64195 | −0.162065 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −71.5451 | −3.17743 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.0223 | 0.710176 | 0.355088 | − | 0.934833i | \(-0.384451\pi\) | ||||
0.355088 | + | 0.934833i | \(0.384451\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.82414 | 0.301882 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.03797 | 0.0458276 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.31112 | −0.189971 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.0053 | 0.703914 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.725826 | 0.0318602 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.2497 | −0.755722 | −0.377861 | − | 0.925862i | \(-0.623340\pi\) | ||||
−0.377861 | + | 0.925862i | \(0.623340\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −36.6235 | −1.60143 | −0.800717 | − | 0.599043i | \(-0.795548\pi\) | ||||
−0.800717 | + | 0.599043i | \(0.795548\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −14.5581 | −0.635366 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.45967 | 0.237827 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 52.1922 | 2.26923 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 33.0217 | 1.43302 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 44.1919 | 1.91416 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.85563 | 0.166693 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.32332 | 0.100259 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.93465 | −0.169477 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.2577 | −1.12891 | −0.564454 | − | 0.825465i | \(-0.690913\pi\) | ||||
−0.564454 | + | 0.825465i | \(0.690913\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −45.0860 | −1.93483 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.88445 | 0.209227 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.75319 | −0.160475 | −0.0802374 | − | 0.996776i | \(-0.525568\pi\) | ||||
−0.0802374 | + | 0.996776i | \(0.525568\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 35.9240 | 1.53320 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.734998 | −0.0313120 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.35733 | 0.270341 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11.2620 | −0.478047 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.15042 | −0.175859 | −0.0879294 | − | 0.996127i | \(-0.528025\pi\) | ||||
−0.0879294 | + | 0.996127i | \(0.528025\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.222193 | −0.00939778 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 79.5781 | 3.35979 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.13556 | −0.132148 | −0.0660740 | − | 0.997815i | \(-0.521047\pi\) | ||||
−0.0660740 | + | 0.997815i | \(0.521047\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.16477 | −0.301424 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.64944 | −0.363242 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.9020 | 0.666647 | 0.333323 | − | 0.942813i | \(-0.391830\pi\) | ||||
0.333323 | + | 0.942813i | \(0.391830\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.50038 | −0.355730 | −0.177865 | − | 0.984055i | \(-0.556919\pi\) | ||||
−0.177865 | + | 0.984055i | \(0.556919\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 46.1621 | 1.92845 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 42.1711 | 1.75865 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −32.4207 | −1.34969 | −0.674846 | − | 0.737959i | \(-0.735790\pi\) | ||||
−0.674846 | + | 0.737959i | \(0.735790\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −29.1976 | −1.21341 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.65033 | 0.358876 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.99079 | 0.413776 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 13.3895 | 0.553587 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.3326 | −0.756666 | −0.378333 | − | 0.925670i | \(-0.623503\pi\) | ||||
−0.378333 | + | 0.925670i | \(0.623503\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.0946334 | −0.00389930 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −63.7991 | −2.62434 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.3751 | −1.00096 | −0.500482 | − | 0.865747i | \(-0.666844\pi\) | ||||
−0.500482 | + | 0.865747i | \(0.666844\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.49834 | 0.102422 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 36.6072 | 1.49823 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 41.8673 | 1.71065 | 0.855325 | − | 0.518091i | \(-0.173357\pi\) | ||||
0.855325 | + | 0.518091i | \(0.173357\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.9937 | 1.18268 | 0.591340 | − | 0.806423i | \(-0.298599\pi\) | ||||
0.591340 | + | 0.806423i | \(0.298599\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −29.0934 | −1.18478 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.65713 | −0.0673720 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.7589 | 1.32964 | 0.664821 | − | 0.747003i | \(-0.268508\pi\) | ||||
0.664821 | + | 0.747003i | \(0.268508\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 18.7876 | 0.761312 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.7101 | 0.999663 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.94718 | 0.0786459 | 0.0393230 | − | 0.999227i | \(-0.487480\pi\) | ||||
0.0393230 | + | 0.999227i | \(0.487480\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.05269 | −0.324716 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.14258 | −0.0459985 | −0.0229992 | − | 0.999735i | \(-0.507322\pi\) | ||||
−0.0229992 | + | 0.999735i | \(0.507322\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.4805 | −1.38589 | −0.692943 | − | 0.720992i | \(-0.743686\pi\) | ||||
−0.692943 | + | 0.720992i | \(0.743686\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 76.8568 | 3.08416 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.56443 | 0.142806 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.9677 | 0.918707 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.37934 | −0.0550855 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −68.7409 | −2.74088 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.20195 | −0.286705 | −0.143352 | − | 0.989672i | \(-0.545788\pi\) | ||||
−0.143352 | + | 0.989672i | \(0.545788\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −70.8084 | −2.81438 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.87528 | 0.272837 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.07457 | −0.240683 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.0517 | −0.555878 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.6807 | 0.698345 | 0.349173 | − | 0.937058i | \(-0.386463\pi\) | ||||
0.349173 | + | 0.937058i | \(0.386463\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.9615 | 1.45762 | 0.728810 | − | 0.684716i | \(-0.240074\pi\) | ||||
0.728810 | + | 0.684716i | \(0.240074\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.0404883 | 0.00159423 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.6129 | −0.731747 | −0.365873 | − | 0.930665i | \(-0.619230\pi\) | ||||
−0.365873 | + | 0.930665i | \(0.619230\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −21.7969 | −0.855605 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.41897 | 0.0948068 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28.0079 | 1.09604 | 0.548018 | − | 0.836467i | \(-0.315383\pi\) | ||||
0.548018 | + | 0.836467i | \(0.315383\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.13397 | 0.0443077 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −40.6779 | −1.58700 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −40.9629 | −1.59569 | −0.797843 | − | 0.602865i | \(-0.794026\pi\) | ||||
−0.797843 | + | 0.602865i | \(0.794026\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.8098 | 0.653825 | 0.326912 | − | 0.945055i | \(-0.393992\pi\) | ||||
0.326912 | + | 0.945055i | \(0.393992\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 122.858 | 4.77140 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.0433041 | −0.00167926 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −54.4230 | −2.10727 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −30.6920 | −1.18662 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −23.7127 | −0.915417 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.69460 | −0.335152 | −0.167576 | − | 0.985859i | \(-0.553594\pi\) | ||||
−0.167576 | + | 0.985859i | \(0.553594\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 43.1046 | 1.65910 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −39.2305 | −1.50775 | −0.753876 | − | 0.657017i | \(-0.771818\pi\) | ||||
−0.753876 | + | 0.657017i | \(0.771818\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.211290 | 0.00810855 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −35.7119 | −1.36848 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 41.6065 | 1.59203 | 0.796015 | − | 0.605277i | \(-0.206938\pi\) | ||||
0.796015 | + | 0.605277i | \(0.206938\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.55234 | −0.0975198 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.6595 | 0.673751 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.4244 | 0.587624 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.0503 | 0.572541 | 0.286271 | − | 0.958149i | \(-0.407584\pi\) | ||||
0.286271 | + | 0.958149i | \(0.407584\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 23.4540 | 0.890942 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.02306 | −0.266400 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −49.1518 | −1.86176 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −25.7747 | −0.974890 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32.4666 | −1.22625 | −0.613123 | − | 0.789987i | \(-0.710087\pi\) | ||||
−0.613123 | + | 0.789987i | \(0.710087\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.19150 | 0.0449381 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.50270 | −0.169581 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.84907 | −0.370412 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.9483 | 1.53785 | 0.768923 | − | 0.639342i | \(-0.220793\pi\) | ||||
0.768923 | + | 0.639342i | \(0.220793\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −37.8952 | −1.42118 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.00714 | −0.262420 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.83812 | −0.330527 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −54.0276 | −2.01770 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 42.4750 | 1.58405 | 0.792025 | − | 0.610489i | \(-0.209027\pi\) | ||||
0.792025 | + | 0.610489i | \(0.209027\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.6587 | −0.434194 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −47.7862 | −1.77719 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −30.5228 | −1.13359 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.84716 | 0.105595 | 0.0527977 | − | 0.998605i | \(-0.483186\pi\) | ||||
0.0527977 | + | 0.998605i | \(0.483186\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −28.0380 | −1.03844 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.247131 | 0.00914049 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.3001 | −0.602058 | −0.301029 | − | 0.953615i | \(-0.597330\pi\) | ||||
−0.301029 | + | 0.953615i | \(0.597330\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.10691 | 0.0408291 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.2039 | 0.707386 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.70803 | 0.0628308 | 0.0314154 | − | 0.999506i | \(-0.489999\pi\) | ||||
0.0314154 | + | 0.999506i | \(0.489999\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.12951 | −0.0782297 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.6504 | −0.757591 | −0.378796 | − | 0.925480i | \(-0.623662\pi\) | ||||
−0.378796 | + | 0.925480i | \(0.623662\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.68602 | 0.171683 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −51.5635 | −1.88661 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.4269 | 0.380992 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.5679 | 1.18842 | 0.594210 | − | 0.804310i | \(-0.297465\pi\) | ||||
0.594210 | + | 0.804310i | \(0.297465\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −61.7380 | −2.24986 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.65281 | −0.132940 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.4453 | 0.634062 | 0.317031 | − | 0.948415i | \(-0.397314\pi\) | ||||
0.317031 | + | 0.948415i | \(0.397314\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −102.133 | −3.70721 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.14810 | −0.114119 | −0.0570593 | − | 0.998371i | \(-0.518172\pi\) | ||||
−0.0570593 | + | 0.998371i | \(0.518172\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.2092 | 0.478206 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −14.8923 | −0.538431 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −33.6516 | −1.21509 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 46.3568 | 1.67167 | 0.835834 | − | 0.548982i | \(-0.184985\pi\) | ||||
0.835834 | + | 0.548982i | \(0.184985\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.9693 | 0.611134 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.39055 | 0.121950 | 0.0609748 | − | 0.998139i | \(-0.480579\pi\) | ||||
0.0609748 | + | 0.998139i | \(0.480579\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.92991 | −0.141167 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −30.4564 | −1.09262 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.851956 | 0.0305245 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.27524 | 0.331894 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −55.6278 | −1.98798 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.09998 | 0.146335 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.966714 | 0.0344596 | 0.0172298 | − | 0.999852i | \(-0.494515\pi\) | ||||
0.0172298 | + | 0.999852i | \(0.494515\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −33.7992 | −1.20328 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.3760 | −0.688930 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −36.6092 | −1.30003 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.81066 | −0.0996837 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.8418 | −0.490301 | −0.245150 | − | 0.969485i | \(-0.578837\pi\) | ||||
−0.245150 | + | 0.969485i | \(0.578837\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27.4834 | −0.972294 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −21.2471 | −0.750731 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 26.8506 | 0.947537 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.20645 | −0.113013 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.725826 | −0.0255503 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.856545 | 0.0301145 | 0.0150573 | − | 0.999887i | \(-0.495207\pi\) | ||||
0.0150573 | + | 0.999887i | \(0.495207\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.6209 | −0.899671 | −0.449836 | − | 0.893111i | \(-0.648517\pi\) | ||||
−0.449836 | + | 0.893111i | \(0.648517\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.74427 | 0.236532 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.94223 | −0.138090 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.00428357 | −0.000149863 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 36.2098 | 1.26527 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33.7705 | 1.17860 | 0.589299 | − | 0.807915i | \(-0.299404\pi\) | ||||
0.589299 | + | 0.807915i | \(0.299404\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.12997 | −0.283393 | −0.141696 | − | 0.989910i | \(-0.545256\pi\) | ||||
−0.141696 | + | 0.989910i | \(0.545256\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −57.2808 | −1.99426 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.2110 | 0.668033 | 0.334016 | − | 0.942567i | \(-0.391596\pi\) | ||||
0.334016 | + | 0.942567i | \(0.391596\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.0789 | −1.14888 | −0.574439 | − | 0.818547i | \(-0.694780\pi\) | ||||
−0.574439 | + | 0.818547i | \(0.694780\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 52.4173 | 1.81834 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.75635 | 0.234094 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.06000 | −0.175108 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.16227 | −0.247564 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.13889 | 0.246462 | 0.123231 | − | 0.992378i | \(-0.460674\pi\) | ||||
0.123231 | + | 0.992378i | \(0.460674\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.3906 | 0.358295 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 98.1175 | 3.37935 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.83778 | −0.304029 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.48145 | −0.153985 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −73.9957 | −2.53953 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 88.2245 | 3.02430 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.34699 | 0.114599 | 0.0572993 | − | 0.998357i | \(-0.481751\pi\) | ||||
0.0572993 | + | 0.998357i | \(0.481751\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.258130 | 0.00882787 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.9947 | 0.478050 | 0.239025 | − | 0.971013i | \(-0.423172\pi\) | ||||
0.239025 | + | 0.971013i | \(0.423172\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.0781 | 1.19685 | 0.598424 | − | 0.801179i | \(-0.295794\pi\) | ||||
0.598424 | + | 0.801179i | \(0.295794\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −21.7772 | −0.742165 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.18861 | −0.142582 | −0.0712910 | − | 0.997456i | \(-0.522712\pi\) | ||||
−0.0712910 | + | 0.997456i | \(0.522712\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.0896594 | 0.00304851 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −85.7579 | −2.91249 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25.0138 | 0.848536 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29.6483 | 1.00459 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.25947 | −0.0426267 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.64720 | −0.123298 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.663532 | 0.0224059 | 0.0112029 | − | 0.999937i | \(-0.496434\pi\) | ||||
0.0112029 | + | 0.999937i | \(0.496434\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 47.1563 | 1.59054 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.5838 | −0.895631 | −0.447816 | − | 0.894126i | \(-0.647798\pi\) | ||||
−0.447816 | + | 0.894126i | \(0.647798\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.1327 | 1.28327 | 0.641634 | − | 0.767011i | \(-0.278257\pi\) | ||||
0.641634 | + | 0.767011i | \(0.278257\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.13202 | 0.206126 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −50.6497 | −1.70065 | −0.850326 | − | 0.526257i | \(-0.823595\pi\) | ||||
−0.850326 | + | 0.526257i | \(0.823595\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.5931 | 0.623593 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −34.0325 | −1.14013 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.476375 | 0.0159413 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.286994 | 0.00959315 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −157.680 | −5.26479 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.07167 | 0.169150 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.1556 | −0.571536 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.109494 | 0.00364374 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.56936 | −0.185132 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.3370 | −1.20655 | −0.603276 | − | 0.797533i | \(-0.706138\pi\) | ||||
−0.603276 | + | 0.797533i | \(0.706138\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 58.7091 | 1.94726 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.1125 | −0.832015 | −0.416008 | − | 0.909361i | \(-0.636571\pi\) | ||||
−0.416008 | + | 0.909361i | \(0.636571\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 34.0360 | 1.12643 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.67096 | 0.220535 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.06663 | 0.101269 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.4558 | 0.443866 | 0.221933 | − | 0.975062i | \(-0.428763\pi\) | ||||
0.221933 | + | 0.975062i | \(0.428763\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −47.2558 | −1.55713 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.3197 | 0.471340 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 49.4801 | 1.62690 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 69.4963 | 2.28256 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12.3637 | −0.405641 | −0.202820 | − | 0.979216i | \(-0.565011\pi\) | ||||
−0.202820 | + | 0.979216i | \(0.565011\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.117109 | −0.00383809 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −42.5629 | −1.39345 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.83007 | 0.321478 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.9442 | 1.37026 | 0.685129 | − | 0.728422i | \(-0.259746\pi\) | ||||
0.685129 | + | 0.728422i | \(0.259746\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −80.4627 | −2.62580 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.5943 | −0.508360 | −0.254180 | − | 0.967157i | \(-0.581806\pi\) | ||||
−0.254180 | + | 0.967157i | \(0.581806\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 63.0832 | 2.05427 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.27744 | −0.106615 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.8044 | −0.448583 | −0.224291 | − | 0.974522i | \(-0.572007\pi\) | ||||
−0.224291 | + | 0.974522i | \(0.572007\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 41.4537 | 1.34564 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.49080 | 0.0807696 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.06472 | −0.131669 | −0.0658346 | − | 0.997831i | \(-0.520971\pi\) | ||||
−0.0658346 | + | 0.997831i | \(0.520971\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.70229 | 0.184522 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 73.9226 | 2.38958 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.90239 | −0.222890 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.3470 | −0.978936 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −62.1536 | −2.00287 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.60671 | −0.116104 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.3821 | 1.74881 | 0.874406 | − | 0.485195i | \(-0.161251\pi\) | ||||
0.874406 | + | 0.485195i | \(0.161251\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.36852 | 0.0760879 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.5975 | −0.596821 | −0.298410 | − | 0.954438i | \(-0.596456\pi\) | ||||
−0.298410 | + | 0.954438i | \(0.596456\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.9927 | −0.608879 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −88.4339 | −2.83215 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.81062 | −0.0899197 | −0.0449598 | − | 0.998989i | \(-0.514316\pi\) | ||||
−0.0449598 | + | 0.998989i | \(0.514316\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.0248 | 0.448234 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −78.7385 | −2.51393 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 44.4447 | 1.41757 | 0.708783 | − | 0.705427i | \(-0.249245\pi\) | ||||
0.708783 | + | 0.705427i | \(0.249245\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.88093 | −0.251107 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.1768 | −0.387593 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.317177 | −0.0100857 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43.6101 | −1.38532 | −0.692660 | − | 0.721264i | \(-0.743561\pi\) | ||||
−0.692660 | + | 0.721264i | \(0.743561\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −40.1617 | −1.27449 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.52200 | 0.143357 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.23286 | −0.260737 | −0.130369 | − | 0.991466i | \(-0.541616\pi\) | ||||
−0.130369 | + | 0.991466i | \(0.541616\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 90.1776 | 2.85309 |
(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 | 3584.2.a.o.1.2 | ✓ | 10 | |
4.3 | odd | 2 | 3584.2.a.p.1.9 | yes | 10 | ||
8.3 | odd | 2 | 3584.2.a.p.1.2 | yes | 10 | ||
8.5 | even | 2 | inner | 3584.2.a.o.1.9 | yes | 10 | |
16.3 | odd | 4 | 3584.2.b.g.1793.9 | 10 | |||
16.5 | even | 4 | 3584.2.b.h.1793.9 | 10 | |||
16.11 | odd | 4 | 3584.2.b.g.1793.2 | 10 | |||
16.13 | even | 4 | 3584.2.b.h.1793.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3584.2.a.o.1.2 | ✓ | 10 | 1.1 | even | 1 | trivial | |
3584.2.a.o.1.9 | yes | 10 | 8.5 | even | 2 | inner | |
3584.2.a.p.1.2 | yes | 10 | 8.3 | odd | 2 | ||
3584.2.a.p.1.9 | yes | 10 | 4.3 | odd | 2 | ||
3584.2.b.g.1793.2 | 10 | 16.11 | odd | 4 | |||
3584.2.b.g.1793.9 | 10 | 16.3 | odd | 4 | |||
3584.2.b.h.1793.2 | 10 | 16.13 | even | 4 | |||
3584.2.b.h.1793.9 | 10 | 16.5 | even | 4 |