Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} - 20 x^{14} + 38 x^{13} + 155 x^{12} - 275 x^{11} - 593 x^{10} + 957 x^{9} + 1177 x^{8} - 1655 x^{7} - 1150 x^{6} + 1279 x^{5} + 474 x^{4} - 280 x^{3} - 83 x^{2} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 889) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Root | \(2.70451\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.70451 | 1.91238 | 0.956189 | − | 0.292751i | \(-0.0945706\pi\) | ||||
0.956189 | + | 0.292751i | \(0.0945706\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.31438 | 2.65719 | ||||||||
\(5\) | 1.33706 | 0.597950 | 0.298975 | − | 0.954261i | \(-0.403355\pi\) | ||||
0.298975 | + | 0.954261i | \(0.403355\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 8.96376 | 3.16917 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.61609 | 1.14351 | ||||||||
\(11\) | 5.62240 | 1.69522 | 0.847609 | − | 0.530621i | \(-0.178041\pi\) | ||||
0.847609 | + | 0.530621i | \(0.178041\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.64074 | 1.00976 | 0.504879 | − | 0.863190i | \(-0.331537\pi\) | ||||
0.504879 | + | 0.863190i | \(0.331537\pi\) | |||||||
\(14\) | −2.70451 | −0.722811 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 13.6138 | 3.40346 | ||||||||
\(17\) | 6.28684 | 1.52478 | 0.762392 | − | 0.647116i | \(-0.224025\pi\) | ||||
0.762392 | + | 0.647116i | \(0.224025\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.90229 | 0.665830 | 0.332915 | − | 0.942957i | \(-0.391968\pi\) | ||||
0.332915 | + | 0.942957i | \(0.391968\pi\) | |||||||
\(20\) | 7.10563 | 1.58887 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 15.2058 | 3.24190 | ||||||||
\(23\) | −5.83444 | −1.21656 | −0.608282 | − | 0.793721i | \(-0.708141\pi\) | ||||
−0.608282 | + | 0.793721i | \(0.708141\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.21228 | −0.642455 | ||||||||
\(26\) | 9.84641 | 1.93104 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.31438 | −1.00432 | ||||||||
\(29\) | 4.25704 | 0.790513 | 0.395256 | − | 0.918571i | \(-0.370656\pi\) | ||||
0.395256 | + | 0.918571i | \(0.370656\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.19551 | −1.65156 | −0.825781 | − | 0.563991i | \(-0.809265\pi\) | ||||
−0.825781 | + | 0.563991i | \(0.809265\pi\) | |||||||
\(32\) | 18.8912 | 3.33953 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 17.0028 | 2.91596 | ||||||||
\(35\) | −1.33706 | −0.226004 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.71198 | −1.26784 | −0.633921 | − | 0.773398i | \(-0.718555\pi\) | ||||
−0.633921 | + | 0.773398i | \(0.718555\pi\) | |||||||
\(38\) | 7.84927 | 1.27332 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 11.9851 | 1.89501 | ||||||||
\(41\) | −2.94873 | −0.460514 | −0.230257 | − | 0.973130i | \(-0.573957\pi\) | ||||
−0.230257 | + | 0.973130i | \(0.573957\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.41716 | −1.43610 | −0.718051 | − | 0.695990i | \(-0.754966\pi\) | ||||
−0.718051 | + | 0.695990i | \(0.754966\pi\) | |||||||
\(44\) | 29.8796 | 4.50451 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −15.7793 | −2.32653 | ||||||||
\(47\) | −1.87098 | −0.272911 | −0.136456 | − | 0.990646i | \(-0.543571\pi\) | ||||
−0.136456 | + | 0.990646i | \(0.543571\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −8.68764 | −1.22862 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 19.3482 | 2.68312 | ||||||||
\(53\) | −11.9975 | −1.64799 | −0.823993 | − | 0.566601i | \(-0.808258\pi\) | ||||
−0.823993 | + | 0.566601i | \(0.808258\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.51748 | 1.01366 | ||||||||
\(56\) | −8.96376 | −1.19783 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 11.5132 | 1.51176 | ||||||||
\(59\) | −5.75850 | −0.749693 | −0.374847 | − | 0.927087i | \(-0.622305\pi\) | ||||
−0.374847 | + | 0.927087i | \(0.622305\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.977997 | 0.125220 | 0.0626098 | − | 0.998038i | \(-0.480058\pi\) | ||||
0.0626098 | + | 0.998038i | \(0.480058\pi\) | |||||||
\(62\) | −24.8693 | −3.15841 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 23.8639 | 2.98298 | ||||||||
\(65\) | 4.86787 | 0.603785 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.352164 | −0.0430237 | −0.0215119 | − | 0.999769i | \(-0.506848\pi\) | ||||
−0.0215119 | + | 0.999769i | \(0.506848\pi\) | |||||||
\(68\) | 33.4107 | 4.05164 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.61609 | −0.432205 | ||||||||
\(71\) | 13.3286 | 1.58181 | 0.790905 | − | 0.611940i | \(-0.209610\pi\) | ||||
0.790905 | + | 0.611940i | \(0.209610\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.9574 | −1.39951 | −0.699753 | − | 0.714385i | \(-0.746707\pi\) | ||||
−0.699753 | + | 0.714385i | \(0.746707\pi\) | |||||||
\(74\) | −20.8571 | −2.42459 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 15.4238 | 1.76924 | ||||||||
\(77\) | −5.62240 | −0.640732 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.00843871 | 0.000949429 0 | 0.000474714 | − | 1.00000i | \(-0.499849\pi\) | ||||
0.000474714 | 1.00000i | \(0.499849\pi\) | ||||||||
\(80\) | 18.2025 | 2.03510 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.97486 | −0.880676 | ||||||||
\(83\) | −0.0999682 | −0.0109729 | −0.00548647 | − | 0.999985i | \(-0.501746\pi\) | ||||
−0.00548647 | + | 0.999985i | \(0.501746\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.40587 | 0.911745 | ||||||||
\(86\) | −25.4688 | −2.74637 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 50.3979 | 5.37243 | ||||||||
\(89\) | −8.26088 | −0.875651 | −0.437826 | − | 0.899060i | \(-0.644251\pi\) | ||||
−0.437826 | + | 0.899060i | \(0.644251\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.64074 | −0.381653 | ||||||||
\(92\) | −31.0064 | −3.23264 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.06010 | −0.521909 | ||||||||
\(95\) | 3.88053 | 0.398133 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.01769 | 0.306400 | 0.153200 | − | 0.988195i | \(-0.451042\pi\) | ||||
0.153200 | + | 0.988195i | \(0.451042\pi\) | |||||||
\(98\) | 2.70451 | 0.273197 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −17.0712 | −1.70712 | ||||||||
\(101\) | 16.7322 | 1.66491 | 0.832457 | − | 0.554089i | \(-0.186933\pi\) | ||||
0.832457 | + | 0.554089i | \(0.186933\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.76048 | 0.567597 | 0.283799 | − | 0.958884i | \(-0.408405\pi\) | ||||
0.283799 | + | 0.958884i | \(0.408405\pi\) | |||||||
\(104\) | 32.6347 | 3.20009 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −32.4474 | −3.15157 | ||||||||
\(107\) | 4.24934 | 0.410799 | 0.205399 | − | 0.978678i | \(-0.434151\pi\) | ||||
0.205399 | + | 0.978678i | \(0.434151\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.0625 | −1.44273 | −0.721365 | − | 0.692556i | \(-0.756485\pi\) | ||||
−0.721365 | + | 0.692556i | \(0.756485\pi\) | |||||||
\(110\) | 20.3311 | 1.93849 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −13.6138 | −1.28639 | ||||||||
\(113\) | −11.1372 | −1.04770 | −0.523850 | − | 0.851810i | \(-0.675505\pi\) | ||||
−0.523850 | + | 0.851810i | \(0.675505\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.80098 | −0.727445 | ||||||||
\(116\) | 22.6235 | 2.10054 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −15.5739 | −1.43370 | ||||||||
\(119\) | −6.28684 | −0.576314 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.6114 | 1.87376 | ||||||||
\(122\) | 2.64500 | 0.239467 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −48.8684 | −4.38851 | ||||||||
\(125\) | −10.9803 | −0.982107 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | 26.7576 | 2.36506 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 13.1652 | 1.15467 | ||||||||
\(131\) | 10.4598 | 0.913879 | 0.456940 | − | 0.889498i | \(-0.348946\pi\) | ||||
0.456940 | + | 0.889498i | \(0.348946\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.90229 | −0.251660 | ||||||||
\(134\) | −0.952432 | −0.0822776 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 56.3538 | 4.83230 | ||||||||
\(137\) | −8.31758 | −0.710619 | −0.355309 | − | 0.934749i | \(-0.615624\pi\) | ||||
−0.355309 | + | 0.934749i | \(0.615624\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.6143 | 0.900292 | 0.450146 | − | 0.892955i | \(-0.351372\pi\) | ||||
0.450146 | + | 0.892955i | \(0.351372\pi\) | |||||||
\(140\) | −7.10563 | −0.600535 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 36.0472 | 3.02502 | ||||||||
\(143\) | 20.4697 | 1.71176 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.69191 | 0.472687 | ||||||||
\(146\) | −32.3389 | −2.67638 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −40.9844 | −3.36889 | ||||||||
\(149\) | 0.259521 | 0.0212608 | 0.0106304 | − | 0.999943i | \(-0.496616\pi\) | ||||
0.0106304 | + | 0.999943i | \(0.496616\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.6993 | −1.11484 | −0.557419 | − | 0.830232i | \(-0.688208\pi\) | ||||
−0.557419 | + | 0.830232i | \(0.688208\pi\) | |||||||
\(152\) | 26.0154 | 2.11013 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −15.2058 | −1.22532 | ||||||||
\(155\) | −12.2949 | −0.987552 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.4947 | 1.39623 | 0.698113 | − | 0.715988i | \(-0.254023\pi\) | ||||
0.698113 | + | 0.715988i | \(0.254023\pi\) | |||||||
\(158\) | 0.0228226 | 0.00181567 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 25.2587 | 1.99687 | ||||||||
\(161\) | 5.83444 | 0.459818 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.6923 | 1.07246 | 0.536232 | − | 0.844070i | \(-0.319847\pi\) | ||||
0.536232 | + | 0.844070i | \(0.319847\pi\) | |||||||
\(164\) | −15.6706 | −1.22367 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.270365 | −0.0209844 | ||||||||
\(167\) | −2.64032 | −0.204314 | −0.102157 | − | 0.994768i | \(-0.532574\pi\) | ||||
−0.102157 | + | 0.994768i | \(0.532574\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.254955 | 0.0196119 | ||||||||
\(170\) | 22.7338 | 1.74360 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −50.0463 | −3.81600 | ||||||||
\(173\) | 7.97546 | 0.606363 | 0.303181 | − | 0.952933i | \(-0.401951\pi\) | ||||
0.303181 | + | 0.952933i | \(0.401951\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.21228 | 0.242825 | ||||||||
\(176\) | 76.5425 | 5.76961 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −22.3416 | −1.67458 | ||||||||
\(179\) | 1.58809 | 0.118700 | 0.0593499 | − | 0.998237i | \(-0.481097\pi\) | ||||
0.0593499 | + | 0.998237i | \(0.481097\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.41012 | 0.104814 | 0.0524068 | − | 0.998626i | \(-0.483311\pi\) | ||||
0.0524068 | + | 0.998626i | \(0.483311\pi\) | |||||||
\(182\) | −9.84641 | −0.729864 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −52.2985 | −3.85550 | ||||||||
\(185\) | −10.3114 | −0.758106 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 35.3472 | 2.58484 | ||||||||
\(188\) | −9.94312 | −0.725176 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.4949 | 0.761382 | ||||||||
\(191\) | 11.2562 | 0.814473 | 0.407236 | − | 0.913323i | \(-0.366492\pi\) | ||||
0.407236 | + | 0.913323i | \(0.366492\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.69721 | −0.338112 | −0.169056 | − | 0.985606i | \(-0.554072\pi\) | ||||
−0.169056 | + | 0.985606i | \(0.554072\pi\) | |||||||
\(194\) | 8.16138 | 0.585953 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.31438 | 0.379598 | ||||||||
\(197\) | 8.77065 | 0.624883 | 0.312441 | − | 0.949937i | \(-0.398853\pi\) | ||||
0.312441 | + | 0.949937i | \(0.398853\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.91493 | 0.206634 | 0.103317 | − | 0.994648i | \(-0.467054\pi\) | ||||
0.103317 | + | 0.994648i | \(0.467054\pi\) | |||||||
\(200\) | −28.7941 | −2.03605 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 45.2524 | 3.18395 | ||||||||
\(203\) | −4.25704 | −0.298786 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.94262 | −0.275364 | ||||||||
\(206\) | 15.5793 | 1.08546 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 49.5644 | 3.43667 | ||||||||
\(209\) | 16.3178 | 1.12873 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.30272 | 0.0896832 | 0.0448416 | − | 0.998994i | \(-0.485722\pi\) | ||||
0.0448416 | + | 0.998994i | \(0.485722\pi\) | |||||||
\(212\) | −63.7593 | −4.37901 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 11.4924 | 0.785602 | ||||||||
\(215\) | −12.5913 | −0.858718 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.19551 | 0.624232 | ||||||||
\(218\) | −40.7368 | −2.75904 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 39.9507 | 2.69347 | ||||||||
\(221\) | 22.8887 | 1.53966 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.75374 | 0.184404 | 0.0922019 | − | 0.995740i | \(-0.470609\pi\) | ||||
0.0922019 | + | 0.995740i | \(0.470609\pi\) | |||||||
\(224\) | −18.8912 | −1.26222 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −30.1207 | −2.00360 | ||||||||
\(227\) | 11.1830 | 0.742239 | 0.371119 | − | 0.928585i | \(-0.378974\pi\) | ||||
0.371119 | + | 0.928585i | \(0.378974\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.8890 | −1.24822 | −0.624110 | − | 0.781336i | \(-0.714538\pi\) | ||||
−0.624110 | + | 0.781336i | \(0.714538\pi\) | |||||||
\(230\) | −21.0978 | −1.39115 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 38.1591 | 2.50527 | ||||||||
\(233\) | −21.0749 | −1.38066 | −0.690332 | − | 0.723493i | \(-0.742536\pi\) | ||||
−0.690332 | + | 0.723493i | \(0.742536\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.50161 | −0.163187 | ||||||||
\(236\) | −30.6028 | −1.99208 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −17.0028 | −1.10213 | ||||||||
\(239\) | 23.5137 | 1.52097 | 0.760486 | − | 0.649354i | \(-0.224961\pi\) | ||||
0.760486 | + | 0.649354i | \(0.224961\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.30607 | 0.406210 | 0.203105 | − | 0.979157i | \(-0.434897\pi\) | ||||
0.203105 | + | 0.979157i | \(0.434897\pi\) | |||||||
\(242\) | 55.7438 | 3.58334 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.19744 | 0.332732 | ||||||||
\(245\) | 1.33706 | 0.0854215 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.5665 | 0.672328 | ||||||||
\(248\) | −82.4264 | −5.23408 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −29.6963 | −1.87816 | ||||||||
\(251\) | −23.2776 | −1.46927 | −0.734635 | − | 0.678463i | \(-0.762647\pi\) | ||||
−0.734635 | + | 0.678463i | \(0.762647\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −32.8036 | −2.06234 | ||||||||
\(254\) | −2.70451 | −0.169696 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 24.6385 | 1.53991 | ||||||||
\(257\) | 11.5727 | 0.721888 | 0.360944 | − | 0.932588i | \(-0.382455\pi\) | ||||
0.360944 | + | 0.932588i | \(0.382455\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.71198 | 0.479199 | ||||||||
\(260\) | 25.8697 | 1.60437 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 28.2887 | 1.74768 | ||||||||
\(263\) | −21.4848 | −1.32481 | −0.662404 | − | 0.749147i | \(-0.730464\pi\) | ||||
−0.662404 | + | 0.749147i | \(0.730464\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.0414 | −0.985413 | ||||||||
\(266\) | −7.84927 | −0.481269 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.87153 | −0.114322 | ||||||||
\(269\) | 12.8595 | 0.784058 | 0.392029 | − | 0.919953i | \(-0.371773\pi\) | ||||
0.392029 | + | 0.919953i | \(0.371773\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.0688 | 1.58357 | 0.791784 | − | 0.610802i | \(-0.209153\pi\) | ||||
0.791784 | + | 0.610802i | \(0.209153\pi\) | |||||||
\(272\) | 85.5881 | 5.18954 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −22.4950 | −1.35897 | ||||||||
\(275\) | −18.0607 | −1.08910 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.50628 | −0.571177 | −0.285589 | − | 0.958352i | \(-0.592189\pi\) | ||||
−0.285589 | + | 0.958352i | \(0.592189\pi\) | |||||||
\(278\) | 28.7064 | 1.72170 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −11.9851 | −0.716245 | ||||||||
\(281\) | −20.6327 | −1.23085 | −0.615423 | − | 0.788197i | \(-0.711015\pi\) | ||||
−0.615423 | + | 0.788197i | \(0.711015\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 31.5610 | 1.87611 | 0.938053 | − | 0.346491i | \(-0.112627\pi\) | ||||
0.938053 | + | 0.346491i | \(0.112627\pi\) | |||||||
\(284\) | 70.8330 | 4.20316 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 55.3605 | 3.27353 | ||||||||
\(287\) | 2.94873 | 0.174058 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 22.5244 | 1.32496 | ||||||||
\(290\) | 15.3938 | 0.903957 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −63.5460 | −3.71875 | ||||||||
\(293\) | 15.4752 | 0.904068 | 0.452034 | − | 0.892001i | \(-0.350699\pi\) | ||||
0.452034 | + | 0.892001i | \(0.350699\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.69945 | −0.448279 | ||||||||
\(296\) | −69.1284 | −4.01800 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.701878 | 0.0406587 | ||||||||
\(299\) | −21.2417 | −1.22844 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.41716 | 0.542796 | ||||||||
\(302\) | −37.0500 | −2.13199 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 39.5113 | 2.26613 | ||||||||
\(305\) | 1.30764 | 0.0748751 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.92375 | 0.395159 | 0.197580 | − | 0.980287i | \(-0.436692\pi\) | ||||
0.197580 | + | 0.980287i | \(0.436692\pi\) | |||||||
\(308\) | −29.8796 | −1.70255 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −33.2517 | −1.88857 | ||||||||
\(311\) | 30.2612 | 1.71596 | 0.857979 | − | 0.513685i | \(-0.171720\pi\) | ||||
0.857979 | + | 0.513685i | \(0.171720\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.08717 | 0.513637 | 0.256819 | − | 0.966460i | \(-0.417326\pi\) | ||||
0.256819 | + | 0.966460i | \(0.417326\pi\) | |||||||
\(314\) | 47.3145 | 2.67011 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.0448465 | 0.00252281 | ||||||||
\(317\) | −10.5839 | −0.594449 | −0.297224 | − | 0.954808i | \(-0.596061\pi\) | ||||
−0.297224 | + | 0.954808i | \(0.596061\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23.9348 | 1.34009 | ||||||||
\(320\) | 31.9074 | 1.78368 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 15.7793 | 0.879346 | ||||||||
\(323\) | 18.2462 | 1.01525 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.6951 | −0.648725 | ||||||||
\(326\) | 37.0310 | 2.05096 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −26.4317 | −1.45945 | ||||||||
\(329\) | 1.87098 | 0.103151 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.1975 | −0.835329 | −0.417665 | − | 0.908601i | \(-0.637151\pi\) | ||||
−0.417665 | + | 0.908601i | \(0.637151\pi\) | |||||||
\(332\) | −0.531269 | −0.0291572 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.14078 | −0.390726 | ||||||||
\(335\) | −0.470864 | −0.0257260 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.39847 | 0.130653 | 0.0653264 | − | 0.997864i | \(-0.479191\pi\) | ||||
0.0653264 | + | 0.997864i | \(0.479191\pi\) | |||||||
\(338\) | 0.689528 | 0.0375054 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 44.6720 | 2.42268 | ||||||||
\(341\) | −51.7008 | −2.79976 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −84.4132 | −4.55125 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 21.5697 | 1.15959 | ||||||||
\(347\) | −20.2731 | −1.08832 | −0.544158 | − | 0.838982i | \(-0.683151\pi\) | ||||
−0.544158 | + | 0.838982i | \(0.683151\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.06968 | −0.217845 | −0.108922 | − | 0.994050i | \(-0.534740\pi\) | ||||
−0.108922 | + | 0.994050i | \(0.534740\pi\) | |||||||
\(350\) | 8.68764 | 0.464374 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 106.214 | 5.66123 | ||||||||
\(353\) | −23.2003 | −1.23483 | −0.617415 | − | 0.786638i | \(-0.711820\pi\) | ||||
−0.617415 | + | 0.786638i | \(0.711820\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.8211 | 0.945843 | ||||||||
\(356\) | −43.9014 | −2.32677 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.29502 | 0.226999 | ||||||||
\(359\) | 6.23773 | 0.329215 | 0.164607 | − | 0.986359i | \(-0.447364\pi\) | ||||
0.164607 | + | 0.986359i | \(0.447364\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.5767 | −0.556670 | ||||||||
\(362\) | 3.81369 | 0.200443 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −19.3482 | −1.01412 | ||||||||
\(365\) | −15.9877 | −0.836835 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.3363 | −0.591749 | −0.295874 | − | 0.955227i | \(-0.595611\pi\) | ||||
−0.295874 | + | 0.955227i | \(0.595611\pi\) | |||||||
\(368\) | −79.4291 | −4.14053 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −27.8872 | −1.44979 | ||||||||
\(371\) | 11.9975 | 0.622880 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.735946 | −0.0381059 | −0.0190529 | − | 0.999818i | \(-0.506065\pi\) | ||||
−0.0190529 | + | 0.999818i | \(0.506065\pi\) | |||||||
\(374\) | 95.5968 | 4.94319 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −16.7711 | −0.864902 | ||||||||
\(377\) | 15.4988 | 0.798227 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.5206 | −0.540408 | −0.270204 | − | 0.962803i | \(-0.587091\pi\) | ||||
−0.270204 | + | 0.962803i | \(0.587091\pi\) | |||||||
\(380\) | 20.6226 | 1.05792 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 30.4426 | 1.55758 | ||||||||
\(383\) | −27.6080 | −1.41070 | −0.705350 | − | 0.708859i | \(-0.749210\pi\) | ||||
−0.705350 | + | 0.708859i | \(0.749210\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.51748 | −0.383126 | ||||||||
\(386\) | −12.7036 | −0.646599 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 16.0372 | 0.814163 | ||||||||
\(389\) | −22.1840 | −1.12477 | −0.562386 | − | 0.826875i | \(-0.690117\pi\) | ||||
−0.562386 | + | 0.826875i | \(0.690117\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −36.6802 | −1.85500 | ||||||||
\(392\) | 8.96376 | 0.452738 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 23.7203 | 1.19501 | ||||||||
\(395\) | 0.0112830 | 0.000567711 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.54547 | −0.0775650 | −0.0387825 | − | 0.999248i | \(-0.512348\pi\) | ||||
−0.0387825 | + | 0.999248i | \(0.512348\pi\) | |||||||
\(398\) | 7.88347 | 0.395163 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −43.7314 | −2.18657 | ||||||||
\(401\) | 15.0038 | 0.749256 | 0.374628 | − | 0.927175i | \(-0.377771\pi\) | ||||
0.374628 | + | 0.927175i | \(0.377771\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −33.4784 | −1.66768 | ||||||||
\(404\) | 88.9211 | 4.42399 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −11.5132 | −0.571391 | ||||||||
\(407\) | −43.3598 | −2.14927 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.77463 | 0.137197 | 0.0685984 | − | 0.997644i | \(-0.478147\pi\) | ||||
0.0685984 | + | 0.997644i | \(0.478147\pi\) | |||||||
\(410\) | −10.6628 | −0.526600 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 30.6134 | 1.50821 | ||||||||
\(413\) | 5.75850 | 0.283357 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.133663 | −0.00656127 | ||||||||
\(416\) | 68.7780 | 3.37212 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 44.1317 | 2.15855 | ||||||||
\(419\) | 0.450977 | 0.0220317 | 0.0110158 | − | 0.999939i | \(-0.496493\pi\) | ||||
0.0110158 | + | 0.999939i | \(0.496493\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.4479 | 1.48394 | 0.741970 | − | 0.670433i | \(-0.233892\pi\) | ||||
0.741970 | + | 0.670433i | \(0.233892\pi\) | |||||||
\(422\) | 3.52323 | 0.171508 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −107.543 | −5.22274 | ||||||||
\(425\) | −20.1951 | −0.979605 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.977997 | −0.0473286 | ||||||||
\(428\) | 22.5826 | 1.09157 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −34.0533 | −1.64219 | ||||||||
\(431\) | 25.9282 | 1.24892 | 0.624459 | − | 0.781058i | \(-0.285320\pi\) | ||||
0.624459 | + | 0.781058i | \(0.285320\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −32.5540 | −1.56444 | −0.782222 | − | 0.623000i | \(-0.785914\pi\) | ||||
−0.782222 | + | 0.623000i | \(0.785914\pi\) | |||||||
\(434\) | 24.8693 | 1.19377 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −80.0480 | −3.83360 | ||||||||
\(437\) | −16.9332 | −0.810026 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.2502 | −0.632399 | −0.316199 | − | 0.948693i | \(-0.602407\pi\) | ||||
−0.316199 | + | 0.948693i | \(0.602407\pi\) | |||||||
\(440\) | 67.3849 | 3.21245 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 61.9028 | 2.94442 | ||||||||
\(443\) | 2.91409 | 0.138453 | 0.0692264 | − | 0.997601i | \(-0.477947\pi\) | ||||
0.0692264 | + | 0.997601i | \(0.477947\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.0453 | −0.523596 | ||||||||
\(446\) | 7.44751 | 0.352650 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −23.8639 | −1.12746 | ||||||||
\(449\) | −31.6089 | −1.49172 | −0.745859 | − | 0.666104i | \(-0.767961\pi\) | ||||
−0.745859 | + | 0.666104i | \(0.767961\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.5789 | −0.780671 | ||||||||
\(452\) | −59.1873 | −2.78394 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 30.2444 | 1.41944 | ||||||||
\(455\) | −4.86787 | −0.228209 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.01306 | −0.0941671 | −0.0470835 | − | 0.998891i | \(-0.514993\pi\) | ||||
−0.0470835 | + | 0.998891i | \(0.514993\pi\) | |||||||
\(458\) | −51.0855 | −2.38707 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −41.4574 | −1.93296 | ||||||||
\(461\) | −18.0592 | −0.841100 | −0.420550 | − | 0.907269i | \(-0.638163\pi\) | ||||
−0.420550 | + | 0.907269i | \(0.638163\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.4181 | 0.902438 | 0.451219 | − | 0.892413i | \(-0.350989\pi\) | ||||
0.451219 | + | 0.892413i | \(0.350989\pi\) | |||||||
\(464\) | 57.9547 | 2.69048 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −56.9973 | −2.64035 | ||||||||
\(467\) | 25.5878 | 1.18406 | 0.592032 | − | 0.805914i | \(-0.298326\pi\) | ||||
0.592032 | + | 0.805914i | \(0.298326\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.352164 | 0.0162614 | ||||||||
\(470\) | −6.76564 | −0.312076 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −51.6178 | −2.37590 | ||||||||
\(473\) | −52.9470 | −2.43451 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.32295 | −0.427766 | ||||||||
\(476\) | −33.4107 | −1.53137 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 63.5929 | 2.90867 | ||||||||
\(479\) | 25.6165 | 1.17045 | 0.585223 | − | 0.810872i | \(-0.301007\pi\) | ||||
0.585223 | + | 0.810872i | \(0.301007\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −28.0773 | −1.28021 | ||||||||
\(482\) | 17.0548 | 0.776826 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 109.537 | 4.97894 | ||||||||
\(485\) | 4.03483 | 0.183212 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.7048 | −0.938225 | −0.469112 | − | 0.883139i | \(-0.655426\pi\) | ||||
−0.469112 | + | 0.883139i | \(0.655426\pi\) | |||||||
\(488\) | 8.76653 | 0.396842 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.61609 | 0.163358 | ||||||||
\(491\) | 24.8187 | 1.12005 | 0.560026 | − | 0.828475i | \(-0.310791\pi\) | ||||
0.560026 | + | 0.828475i | \(0.310791\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.7634 | 1.20536 | ||||||||
\(494\) | 28.5771 | 1.28574 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −125.186 | −5.62102 | ||||||||
\(497\) | −13.3286 | −0.597868 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37.6772 | 1.68666 | 0.843332 | − | 0.537393i | \(-0.180591\pi\) | ||||
0.843332 | + | 0.537393i | \(0.180591\pi\) | |||||||
\(500\) | −58.3534 | −2.60964 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −62.9545 | −2.80980 | ||||||||
\(503\) | −20.7543 | −0.925390 | −0.462695 | − | 0.886517i | \(-0.653118\pi\) | ||||
−0.462695 | + | 0.886517i | \(0.653118\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.3719 | 0.995536 | ||||||||
\(506\) | −88.7176 | −3.94398 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.31438 | −0.235787 | ||||||||
\(509\) | −12.3887 | −0.549119 | −0.274559 | − | 0.961570i | \(-0.588532\pi\) | ||||
−0.274559 | + | 0.961570i | \(0.588532\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.9574 | 0.528964 | ||||||||
\(512\) | 13.1199 | 0.579821 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 31.2986 | 1.38052 | ||||||||
\(515\) | 7.70210 | 0.339395 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.5194 | −0.462644 | ||||||||
\(518\) | 20.8571 | 0.916409 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 43.6345 | 1.91350 | ||||||||
\(521\) | 4.91067 | 0.215141 | 0.107570 | − | 0.994197i | \(-0.465693\pi\) | ||||
0.107570 | + | 0.994197i | \(0.465693\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.1334 | 1.18646 | 0.593231 | − | 0.805033i | \(-0.297852\pi\) | ||||
0.593231 | + | 0.805033i | \(0.297852\pi\) | |||||||
\(524\) | 55.5875 | 2.42835 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −58.1058 | −2.53353 | ||||||||
\(527\) | −57.8107 | −2.51827 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0407 | 0.480030 | ||||||||
\(530\) | −43.3840 | −1.88448 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −15.4238 | −0.668709 | ||||||||
\(533\) | −10.7355 | −0.465007 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.68161 | 0.245637 | ||||||||
\(536\) | −3.15672 | −0.136349 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 34.7787 | 1.49942 | ||||||||
\(539\) | 5.62240 | 0.242174 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.8380 | 0.809907 | 0.404954 | − | 0.914337i | \(-0.367288\pi\) | ||||
0.404954 | + | 0.914337i | \(0.367288\pi\) | |||||||
\(542\) | 70.5034 | 3.02838 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 118.766 | 5.09206 | ||||||||
\(545\) | −20.1395 | −0.862680 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −35.8740 | −1.53386 | −0.766930 | − | 0.641731i | \(-0.778217\pi\) | ||||
−0.766930 | + | 0.641731i | \(0.778217\pi\) | |||||||
\(548\) | −44.2027 | −1.88825 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −48.8454 | −2.08277 | ||||||||
\(551\) | 12.3552 | 0.526347 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.00843871 | −0.000358850 0 | ||||||||
\(554\) | −25.7098 | −1.09231 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 56.4083 | 2.39224 | ||||||||
\(557\) | 27.0609 | 1.14661 | 0.573304 | − | 0.819343i | \(-0.305661\pi\) | ||||
0.573304 | + | 0.819343i | \(0.305661\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −34.2854 | −1.45012 | ||||||||
\(560\) | −18.2025 | −0.769195 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −55.8014 | −2.35384 | ||||||||
\(563\) | −14.9787 | −0.631278 | −0.315639 | − | 0.948879i | \(-0.602219\pi\) | ||||
−0.315639 | + | 0.948879i | \(0.602219\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.8911 | −0.626473 | ||||||||
\(566\) | 85.3570 | 3.58782 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 119.474 | 5.01302 | ||||||||
\(569\) | −2.07662 | −0.0870566 | −0.0435283 | − | 0.999052i | \(-0.513860\pi\) | ||||
−0.0435283 | + | 0.999052i | \(0.513860\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.6703 | −0.697632 | −0.348816 | − | 0.937191i | \(-0.613416\pi\) | ||||
−0.348816 | + | 0.937191i | \(0.613416\pi\) | |||||||
\(572\) | 108.784 | 4.54847 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.97486 | 0.332864 | ||||||||
\(575\) | 18.7418 | 0.781589 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.3733 | −0.556737 | −0.278368 | − | 0.960474i | \(-0.589794\pi\) | ||||
−0.278368 | + | 0.960474i | \(0.589794\pi\) | |||||||
\(578\) | 60.9175 | 2.53383 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 30.2490 | 1.25602 | ||||||||
\(581\) | 0.0999682 | 0.00414738 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −67.4548 | −2.79369 | ||||||||
\(584\) | −107.183 | −4.43527 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 41.8527 | 1.72892 | ||||||||
\(587\) | 0.270658 | 0.0111713 | 0.00558563 | − | 0.999984i | \(-0.498222\pi\) | ||||
0.00558563 | + | 0.999984i | \(0.498222\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.6880 | −1.09966 | ||||||||
\(590\) | −20.8232 | −0.857279 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −104.990 | −4.31505 | ||||||||
\(593\) | −4.07885 | −0.167498 | −0.0837492 | − | 0.996487i | \(-0.526689\pi\) | ||||
−0.0837492 | + | 0.996487i | \(0.526689\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.40587 | −0.344607 | ||||||||
\(596\) | 1.37919 | 0.0564939 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −57.4483 | −2.34923 | ||||||||
\(599\) | 6.85182 | 0.279958 | 0.139979 | − | 0.990154i | \(-0.455297\pi\) | ||||
0.139979 | + | 0.990154i | \(0.455297\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.956812 | 0.0390292 | 0.0195146 | − | 0.999810i | \(-0.493788\pi\) | ||||
0.0195146 | + | 0.999810i | \(0.493788\pi\) | |||||||
\(602\) | 25.4688 | 1.03803 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −72.8035 | −2.96233 | ||||||||
\(605\) | 27.5586 | 1.12042 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.9541 | 0.728734 | 0.364367 | − | 0.931255i | \(-0.381285\pi\) | ||||
0.364367 | + | 0.931255i | \(0.381285\pi\) | |||||||
\(608\) | 54.8278 | 2.22356 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.53652 | 0.143190 | ||||||||
\(611\) | −6.81176 | −0.275574 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 45.8740 | 1.85283 | 0.926417 | − | 0.376500i | \(-0.122873\pi\) | ||||
0.926417 | + | 0.376500i | \(0.122873\pi\) | |||||||
\(614\) | 18.7253 | 0.755693 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −50.3979 | −2.03059 | ||||||||
\(617\) | −42.3860 | −1.70640 | −0.853198 | − | 0.521588i | \(-0.825340\pi\) | ||||
−0.853198 | + | 0.521588i | \(0.825340\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.43782 | 0.0577910 | 0.0288955 | − | 0.999582i | \(-0.490801\pi\) | ||||
0.0288955 | + | 0.999582i | \(0.490801\pi\) | |||||||
\(620\) | −65.3398 | −2.62411 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 81.8418 | 3.28156 | ||||||||
\(623\) | 8.26088 | 0.330965 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.38011 | 0.0552043 | ||||||||
\(626\) | 24.5763 | 0.982268 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 92.9732 | 3.71003 | ||||||||
\(629\) | −48.4840 | −1.93318 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.4516 | 0.774356 | 0.387178 | − | 0.922005i | \(-0.373450\pi\) | ||||
0.387178 | + | 0.922005i | \(0.373450\pi\) | |||||||
\(632\) | 0.0756426 | 0.00300890 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −28.6242 | −1.13681 | ||||||||
\(635\) | −1.33706 | −0.0530595 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.64074 | 0.144251 | ||||||||
\(638\) | 64.7319 | 2.56276 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 35.7765 | 1.41419 | ||||||||
\(641\) | 28.1948 | 1.11363 | 0.556813 | − | 0.830638i | \(-0.312024\pi\) | ||||
0.556813 | + | 0.830638i | \(0.312024\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.11642 | −0.122900 | −0.0614499 | − | 0.998110i | \(-0.519572\pi\) | ||||
−0.0614499 | + | 0.998110i | \(0.519572\pi\) | |||||||
\(644\) | 31.0064 | 1.22182 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 49.3471 | 1.94154 | ||||||||
\(647\) | 48.4587 | 1.90511 | 0.952553 | − | 0.304372i | \(-0.0984465\pi\) | ||||
0.952553 | + | 0.304372i | \(0.0984465\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −32.3766 | −1.27089 | ||||||||
\(650\) | −31.6294 | −1.24061 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 72.7661 | 2.84974 | ||||||||
\(653\) | 32.8131 | 1.28408 | 0.642038 | − | 0.766673i | \(-0.278089\pi\) | ||||
0.642038 | + | 0.766673i | \(0.278089\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.9854 | 0.546455 | ||||||||
\(656\) | −40.1435 | −1.56734 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.06010 | 0.197263 | ||||||||
\(659\) | 41.8057 | 1.62852 | 0.814259 | − | 0.580502i | \(-0.197144\pi\) | ||||
0.814259 | + | 0.580502i | \(0.197144\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.9351 | 1.51440 | 0.757201 | − | 0.653182i | \(-0.226566\pi\) | ||||
0.757201 | + | 0.653182i | \(0.226566\pi\) | |||||||
\(662\) | −41.1018 | −1.59747 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.896091 | −0.0347751 | ||||||||
\(665\) | −3.88053 | −0.150480 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.8375 | −0.961710 | ||||||||
\(668\) | −14.0317 | −0.542902 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.27346 | −0.0491979 | ||||||||
\(671\) | 5.49869 | 0.212275 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.7975 | 0.416213 | 0.208106 | − | 0.978106i | \(-0.433270\pi\) | ||||
0.208106 | + | 0.978106i | \(0.433270\pi\) | |||||||
\(674\) | 6.48668 | 0.249858 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.35493 | 0.0521125 | ||||||||
\(677\) | −5.24314 | −0.201510 | −0.100755 | − | 0.994911i | \(-0.532126\pi\) | ||||
−0.100755 | + | 0.994911i | \(0.532126\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.01769 | −0.115808 | ||||||||
\(680\) | 75.3483 | 2.88947 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −139.825 | −5.35419 | ||||||||
\(683\) | −11.9241 | −0.456263 | −0.228132 | − | 0.973630i | \(-0.573262\pi\) | ||||
−0.228132 | + | 0.973630i | \(0.573262\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.1211 | −0.424915 | ||||||||
\(686\) | −2.70451 | −0.103259 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −128.204 | −4.88772 | ||||||||
\(689\) | −43.6798 | −1.66407 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.7809 | −1.47529 | −0.737647 | − | 0.675187i | \(-0.764063\pi\) | ||||
−0.737647 | + | 0.675187i | \(0.764063\pi\) | |||||||
\(692\) | 42.3846 | 1.61122 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −54.8288 | −2.08127 | ||||||||
\(695\) | 14.1919 | 0.538330 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.5382 | −0.702183 | ||||||||
\(698\) | −11.0065 | −0.416601 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 17.0712 | 0.645233 | ||||||||
\(701\) | −17.9182 | −0.676761 | −0.338381 | − | 0.941009i | \(-0.609879\pi\) | ||||
−0.338381 | + | 0.941009i | \(0.609879\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22.3824 | −0.844167 | ||||||||
\(704\) | 134.172 | 5.05681 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −62.7456 | −2.36146 | ||||||||
\(707\) | −16.7322 | −0.629279 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.4343 | 1.10543 | 0.552715 | − | 0.833371i | \(-0.313592\pi\) | ||||
0.552715 | + | 0.833371i | \(0.313592\pi\) | |||||||
\(710\) | 48.1972 | 1.80881 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −74.0485 | −2.77509 | ||||||||
\(713\) | 53.6506 | 2.00923 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 27.3691 | 1.02355 | ||||||||
\(716\) | 8.43973 | 0.315407 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 16.8700 | 0.629583 | ||||||||
\(719\) | 47.0977 | 1.75645 | 0.878224 | − | 0.478249i | \(-0.158729\pi\) | ||||
0.878224 | + | 0.478249i | \(0.158729\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.76048 | −0.214532 | ||||||||
\(722\) | −28.6049 | −1.06456 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.49393 | 0.278510 | ||||||||
\(725\) | −13.6748 | −0.507869 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34.1781 | −1.26760 | −0.633798 | − | 0.773499i | \(-0.718505\pi\) | ||||
−0.633798 | + | 0.773499i | \(0.718505\pi\) | |||||||
\(728\) | −32.6347 | −1.20952 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −43.2389 | −1.60034 | ||||||||
\(731\) | −59.2042 | −2.18975 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −40.1865 | −1.48432 | −0.742162 | − | 0.670221i | \(-0.766199\pi\) | ||||
−0.742162 | + | 0.670221i | \(0.766199\pi\) | |||||||
\(734\) | −30.6591 | −1.13165 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −110.220 | −4.06276 | ||||||||
\(737\) | −1.98001 | −0.0729346 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.2533 | 0.965742 | 0.482871 | − | 0.875691i | \(-0.339594\pi\) | ||||
0.482871 | + | 0.875691i | \(0.339594\pi\) | |||||||
\(740\) | −54.7984 | −2.01443 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 32.4474 | 1.19118 | ||||||||
\(743\) | −15.6848 | −0.575421 | −0.287711 | − | 0.957717i | \(-0.592894\pi\) | ||||
−0.287711 | + | 0.957717i | \(0.592894\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.346995 | 0.0127129 | ||||||||
\(746\) | −1.99037 | −0.0728728 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 187.848 | 6.86841 | ||||||||
\(749\) | −4.24934 | −0.155267 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.5963 | −0.678588 | −0.339294 | − | 0.940680i | \(-0.610188\pi\) | ||||
−0.339294 | + | 0.940680i | \(0.610188\pi\) | |||||||
\(752\) | −25.4713 | −0.928842 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 41.9166 | 1.52651 | ||||||||
\(755\) | −18.3168 | −0.666617 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.8501 | −0.576083 | −0.288042 | − | 0.957618i | \(-0.593004\pi\) | ||||
−0.288042 | + | 0.957618i | \(0.593004\pi\) | |||||||
\(758\) | −28.4531 | −1.03346 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 34.7841 | 1.26175 | ||||||||
\(761\) | 24.2645 | 0.879588 | 0.439794 | − | 0.898099i | \(-0.355051\pi\) | ||||
0.439794 | + | 0.898099i | \(0.355051\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.0625 | 0.545300 | ||||||||
\(764\) | 59.8199 | 2.16421 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −74.6660 | −2.69779 | ||||||||
\(767\) | −20.9652 | −0.757009 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.6349 | 0.816236 | 0.408118 | − | 0.912929i | \(-0.366185\pi\) | ||||
0.408118 | + | 0.912929i | \(0.366185\pi\) | |||||||
\(770\) | −20.3311 | −0.732682 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −24.9627 | −0.898428 | ||||||||
\(773\) | −13.3581 | −0.480459 | −0.240230 | − | 0.970716i | \(-0.577223\pi\) | ||||
−0.240230 | + | 0.970716i | \(0.577223\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.5385 | 1.06105 | ||||||||
\(776\) | 27.0499 | 0.971034 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −59.9968 | −2.15099 | ||||||||
\(779\) | −8.55805 | −0.306624 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 74.9385 | 2.68151 | ||||||||
\(782\) | −99.2020 | −3.54746 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 13.6138 | 0.486209 | ||||||||
\(785\) | 23.3914 | 0.834873 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −39.0191 | −1.39088 | −0.695439 | − | 0.718585i | \(-0.744790\pi\) | ||||
−0.695439 | + | 0.718585i | \(0.744790\pi\) | |||||||
\(788\) | 46.6105 | 1.66043 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.0305151 | 0.00108568 | ||||||||
\(791\) | 11.1372 | 0.395993 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.56063 | 0.126442 | ||||||||
\(794\) | −4.17975 | −0.148334 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 15.4911 | 0.549066 | ||||||||
\(797\) | 49.7364 | 1.76175 | 0.880877 | − | 0.473345i | \(-0.156954\pi\) | ||||
0.880877 | + | 0.473345i | \(0.156954\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.7626 | −0.416131 | ||||||||
\(800\) | −60.6839 | −2.14550 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 40.5780 | 1.43286 | ||||||||
\(803\) | −67.2292 | −2.37247 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.80098 | 0.274949 | ||||||||
\(806\) | −90.5427 | −3.18923 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 149.983 | 5.27640 | ||||||||
\(809\) | −47.5739 | −1.67261 | −0.836304 | − | 0.548266i | \(-0.815288\pi\) | ||||
−0.836304 | + | 0.548266i | \(0.815288\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.6412 | −0.479008 | −0.239504 | − | 0.970895i | \(-0.576985\pi\) | ||||
−0.239504 | + | 0.970895i | \(0.576985\pi\) | |||||||
\(812\) | −22.6235 | −0.793930 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −117.267 | −4.11021 | ||||||||
\(815\) | 18.3074 | 0.641281 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −27.3313 | −0.956201 | ||||||||
\(818\) | 7.50403 | 0.262372 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −20.9525 | −0.731695 | ||||||||
\(821\) | −2.47458 | −0.0863635 | −0.0431818 | − | 0.999067i | \(-0.513749\pi\) | ||||
−0.0431818 | + | 0.999067i | \(0.513749\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.220843 | 0.00769810 | 0.00384905 | − | 0.999993i | \(-0.498775\pi\) | ||||
0.00384905 | + | 0.999993i | \(0.498775\pi\) | |||||||
\(824\) | 51.6356 | 1.79881 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 15.5739 | 0.541886 | ||||||||
\(827\) | 43.5850 | 1.51560 | 0.757799 | − | 0.652488i | \(-0.226275\pi\) | ||||
0.757799 | + | 0.652488i | \(0.226275\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.2871 | −0.530944 | −0.265472 | − | 0.964119i | \(-0.585528\pi\) | ||||
−0.265472 | + | 0.964119i | \(0.585528\pi\) | |||||||
\(830\) | −0.361494 | −0.0125476 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 86.8821 | 3.01209 | ||||||||
\(833\) | 6.28684 | 0.217826 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.53026 | −0.122170 | ||||||||
\(836\) | 86.7191 | 2.99924 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.21967 | 0.0421328 | ||||||||
\(839\) | 33.9366 | 1.17162 | 0.585811 | − | 0.810448i | \(-0.300776\pi\) | ||||
0.585811 | + | 0.810448i | \(0.300776\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.8776 | −0.375089 | ||||||||
\(842\) | 82.3467 | 2.83785 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.92316 | 0.238305 | ||||||||
\(845\) | 0.340889 | 0.0117269 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.6114 | −0.708216 | ||||||||
\(848\) | −163.332 | −5.60885 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −54.6178 | −1.87338 | ||||||||
\(851\) | 44.9951 | 1.54241 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.144164 | 0.00493609 | 0.00246804 | − | 0.999997i | \(-0.499214\pi\) | ||||
0.00246804 | + | 0.999997i | \(0.499214\pi\) | |||||||
\(854\) | −2.64500 | −0.0905101 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 38.0900 | 1.30189 | ||||||||
\(857\) | −18.4457 | −0.630093 | −0.315047 | − | 0.949076i | \(-0.602020\pi\) | ||||
−0.315047 | + | 0.949076i | \(0.602020\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.4383 | −1.00442 | −0.502210 | − | 0.864746i | \(-0.667480\pi\) | ||||
−0.502210 | + | 0.864746i | \(0.667480\pi\) | |||||||
\(860\) | −66.9148 | −2.28178 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 70.1231 | 2.38840 | ||||||||
\(863\) | 32.8559 | 1.11843 | 0.559214 | − | 0.829023i | \(-0.311103\pi\) | ||||
0.559214 | + | 0.829023i | \(0.311103\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.6636 | 0.362575 | ||||||||
\(866\) | −88.0426 | −2.99181 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 48.8684 | 1.65870 | ||||||||
\(869\) | 0.0474458 | 0.00160949 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.28214 | −0.0434435 | ||||||||
\(872\) | −135.017 | −4.57225 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −45.7961 | −1.54908 | ||||||||
\(875\) | 10.9803 | 0.371201 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.3527 | 0.822332 | 0.411166 | − | 0.911561i | \(-0.365122\pi\) | ||||
0.411166 | + | 0.911561i | \(0.365122\pi\) | |||||||
\(878\) | −35.8354 | −1.20939 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 102.342 | 3.44994 | ||||||||
\(881\) | 23.4022 | 0.788439 | 0.394219 | − | 0.919016i | \(-0.371015\pi\) | ||||
0.394219 | + | 0.919016i | \(0.371015\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.2982 | −1.12057 | −0.560287 | − | 0.828299i | \(-0.689309\pi\) | ||||
−0.560287 | + | 0.828299i | \(0.689309\pi\) | |||||||
\(884\) | 121.639 | 4.09117 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.88120 | 0.264774 | ||||||||
\(887\) | 5.13157 | 0.172301 | 0.0861507 | − | 0.996282i | \(-0.472543\pi\) | ||||
0.0861507 | + | 0.996282i | \(0.472543\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −29.8720 | −1.00131 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 14.6344 | 0.489996 | ||||||||
\(893\) | −5.43014 | −0.181713 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.12337 | 0.0709765 | ||||||||
\(896\) | −26.7576 | −0.893909 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −85.4867 | −2.85273 | ||||||||
\(899\) | −39.1457 | −1.30558 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −75.4265 | −2.51282 | ||||||||
\(902\) | −44.8379 | −1.49294 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −99.8313 | −3.32034 | ||||||||
\(905\) | 1.88542 | 0.0626734 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.5415 | 1.21334 | 0.606670 | − | 0.794954i | \(-0.292505\pi\) | ||||
0.606670 | + | 0.794954i | \(0.292505\pi\) | |||||||
\(908\) | 59.4304 | 1.97227 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −13.1652 | −0.436423 | ||||||||
\(911\) | −15.3920 | −0.509961 | −0.254980 | − | 0.966946i | \(-0.582069\pi\) | ||||
−0.254980 | + | 0.966946i | \(0.582069\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.562061 | −0.0186015 | ||||||||
\(914\) | −5.44435 | −0.180083 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −100.383 | −3.31676 | ||||||||
\(917\) | −10.4598 | −0.345414 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.7665 | −0.586061 | −0.293031 | − | 0.956103i | \(-0.594664\pi\) | ||||
−0.293031 | + | 0.956103i | \(0.594664\pi\) | |||||||
\(920\) | −69.9262 | −2.30540 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −48.8412 | −1.60850 | ||||||||
\(923\) | 48.5258 | 1.59724 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.7730 | 0.814532 | ||||||||
\(926\) | 52.5166 | 1.72580 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 80.4208 | 2.63994 | ||||||||
\(929\) | 39.8633 | 1.30787 | 0.653936 | − | 0.756550i | \(-0.273117\pi\) | ||||
0.653936 | + | 0.756550i | \(0.273117\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.90229 | 0.0951186 | ||||||||
\(932\) | −112.000 | −3.66868 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 69.2026 | 2.26438 | ||||||||
\(935\) | 47.2612 | 1.54561 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.0762 | −0.492518 | −0.246259 | − | 0.969204i | \(-0.579201\pi\) | ||||
−0.246259 | + | 0.969204i | \(0.579201\pi\) | |||||||
\(938\) | 0.952432 | 0.0310980 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −13.2945 | −0.433619 | ||||||||
\(941\) | 1.47329 | 0.0480279 | 0.0240140 | − | 0.999712i | \(-0.492355\pi\) | ||||
0.0240140 | + | 0.999712i | \(0.492355\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.2042 | 0.560245 | ||||||||
\(944\) | −78.3953 | −2.55155 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −143.196 | −4.65570 | ||||||||
\(947\) | 5.38384 | 0.174951 | 0.0874756 | − | 0.996167i | \(-0.472120\pi\) | ||||
0.0874756 | + | 0.996167i | \(0.472120\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −43.5337 | −1.41316 | ||||||||
\(950\) | −25.2140 | −0.818051 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −56.3538 | −1.82644 | ||||||||
\(953\) | −38.9729 | −1.26246 | −0.631228 | − | 0.775598i | \(-0.717449\pi\) | ||||
−0.631228 | + | 0.775598i | \(0.717449\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.0502 | 0.487014 | ||||||||
\(956\) | 124.960 | 4.04151 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 69.2800 | 2.23833 | ||||||||
\(959\) | 8.31758 | 0.268589 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 53.5573 | 1.72766 | ||||||||
\(962\) | −75.9353 | −2.44825 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 33.5128 | 1.07938 | ||||||||
\(965\) | −6.28044 | −0.202174 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39.5360 | −1.27139 | −0.635696 | − | 0.771940i | \(-0.719287\pi\) | ||||
−0.635696 | + | 0.771940i | \(0.719287\pi\) | |||||||
\(968\) | 184.756 | 5.93827 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10.9122 | 0.350371 | ||||||||
\(971\) | 3.27748 | 0.105179 | 0.0525896 | − | 0.998616i | \(-0.483252\pi\) | ||||
0.0525896 | + | 0.998616i | \(0.483252\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.6143 | −0.340278 | ||||||||
\(974\) | −55.9964 | −1.79424 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.3143 | 0.426180 | ||||||||
\(977\) | 23.4451 | 0.750075 | 0.375037 | − | 0.927010i | \(-0.377630\pi\) | ||||
0.375037 | + | 0.927010i | \(0.377630\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −46.4460 | −1.48442 | ||||||||
\(980\) | 7.10563 | 0.226981 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 67.1224 | 2.14196 | ||||||||
\(983\) | 45.8347 | 1.46190 | 0.730950 | − | 0.682431i | \(-0.239077\pi\) | ||||
0.730950 | + | 0.682431i | \(0.239077\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.7269 | 0.373649 | ||||||||
\(986\) | 72.3818 | 2.30511 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 56.1541 | 1.78650 | ||||||||
\(989\) | 54.9438 | 1.74711 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.15029 | −0.290669 | −0.145334 | − | 0.989383i | \(-0.546426\pi\) | ||||
−0.145334 | + | 0.989383i | \(0.546426\pi\) | |||||||
\(992\) | −173.715 | −5.51544 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −36.0472 | −1.14335 | ||||||||
\(995\) | 3.89744 | 0.123557 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.9523 | −0.378532 | −0.189266 | − | 0.981926i | \(-0.560611\pi\) | ||||
−0.189266 | + | 0.981926i | \(0.560611\pi\) | |||||||
\(998\) | 101.898 | 3.22554 | ||||||||
\(999\) | 0 | 0 |
(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 | 8001.2.a.t.1.16 | 16 | ||
3.2 | odd | 2 | 889.2.a.c.1.1 | ✓ | 16 | ||
21.20 | even | 2 | 6223.2.a.k.1.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
889.2.a.c.1.1 | ✓ | 16 | 3.2 | odd | 2 | ||
6223.2.a.k.1.1 | 16 | 21.20 | even | 2 | |||
8001.2.a.t.1.16 | 16 | 1.1 | even | 1 | trivial |