Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4864,2,Mod(1,4864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4864, 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("4864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4864 = 2^{8} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4864.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: | \(38.8392355432\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 13x^{6} + 24x^{5} + 48x^{4} - 68x^{3} - 62x^{2} + 32x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 152) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(2.25259\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4864.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.91886 | 1.10785 | 0.553926 | − | 0.832566i | \(-0.313129\pi\) | ||||
0.553926 | + | 0.832566i | \(0.313129\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.51356 | 0.676885 | 0.338442 | − | 0.940987i | \(-0.390100\pi\) | ||||
0.338442 | + | 0.940987i | \(0.390100\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.580162 | −0.219281 | −0.109640 | − | 0.993971i | \(-0.534970\pi\) | ||||
−0.109640 | + | 0.993971i | \(0.534970\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.682013 | 0.227338 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.31799 | −0.397388 | −0.198694 | − | 0.980062i | \(-0.563670\pi\) | ||||
−0.198694 | + | 0.980062i | \(0.563670\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.89230 | −1.07953 | −0.539765 | − | 0.841816i | \(-0.681487\pi\) | ||||
−0.539765 | + | 0.841816i | \(0.681487\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.90431 | 0.749889 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.20142 | −0.291388 | −0.145694 | − | 0.989330i | \(-0.546541\pi\) | ||||
−0.145694 | + | 0.989330i | \(0.546541\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.11325 | −0.242931 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.85527 | −1.22091 | −0.610454 | − | 0.792052i | \(-0.709013\pi\) | ||||
−0.610454 | + | 0.792052i | \(0.709013\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.70913 | −0.541827 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.44789 | −0.855996 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.29188 | −0.239896 | −0.119948 | − | 0.992780i | \(-0.538273\pi\) | ||||
−0.119948 | + | 0.992780i | \(0.538273\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.96413 | 0.532374 | 0.266187 | − | 0.963921i | \(-0.414236\pi\) | ||||
0.266187 | + | 0.963921i | \(0.414236\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.52903 | −0.440248 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.878110 | −0.148428 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.18418 | −0.194677 | −0.0973387 | − | 0.995251i | \(-0.531033\pi\) | ||||
−0.0973387 | + | 0.995251i | \(0.531033\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.46877 | −1.19596 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.04577 | 1.41271 | 0.706356 | − | 0.707856i | \(-0.250338\pi\) | ||||
0.706356 | + | 0.707856i | \(0.250338\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.38816 | 1.27918 | 0.639592 | − | 0.768715i | \(-0.279104\pi\) | ||||
0.639592 | + | 0.768715i | \(0.279104\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.03227 | 0.153881 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.8560 | −1.87524 | −0.937620 | − | 0.347661i | \(-0.886976\pi\) | ||||
−0.937620 | + | 0.347661i | \(0.886976\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.66341 | −0.951916 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.30536 | −0.322815 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.07183 | −0.421949 | −0.210974 | − | 0.977492i | \(-0.567664\pi\) | ||||
−0.210974 | + | 0.977492i | \(0.567664\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.99485 | −0.268986 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.91886 | −0.254159 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.258163 | 0.0336100 | 0.0168050 | − | 0.999859i | \(-0.494651\pi\) | ||||
0.0168050 | + | 0.999859i | \(0.494651\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.7200 | −1.88470 | −0.942352 | − | 0.334623i | \(-0.891391\pi\) | ||||
−0.942352 | + | 0.334623i | \(0.891391\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.395678 | −0.0498507 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.89123 | −0.730717 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.54884 | 1.16658 | 0.583288 | − | 0.812265i | \(-0.301766\pi\) | ||||
0.583288 | + | 0.812265i | \(0.301766\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.2354 | −1.35259 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.93697 | 0.823267 | 0.411634 | − | 0.911349i | \(-0.364958\pi\) | ||||
0.411634 | + | 0.911349i | \(0.364958\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.2934 | −1.78996 | −0.894978 | − | 0.446110i | \(-0.852809\pi\) | ||||
−0.894978 | + | 0.446110i | \(0.852809\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.19844 | −0.600264 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.764646 | 0.0871395 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.1332 | −1.47760 | −0.738798 | − | 0.673927i | \(-0.764606\pi\) | ||||
−0.738798 | + | 0.673927i | \(0.764606\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.5809 | −1.17566 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.70615 | 0.406803 | 0.203402 | − | 0.979095i | \(-0.434800\pi\) | ||||
0.203402 | + | 0.979095i | \(0.434800\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.81843 | −0.197236 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.47893 | −0.265769 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.36653 | 0.886850 | 0.443425 | − | 0.896311i | \(-0.353763\pi\) | ||||
0.443425 | + | 0.896311i | \(0.353763\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.25816 | 0.236720 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.68774 | 0.589792 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.51356 | −0.155288 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.0442 | 1.73057 | 0.865286 | − | 0.501278i | \(-0.167137\pi\) | ||||
0.865286 | + | 0.501278i | \(0.167137\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.898884 | −0.0903412 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.97721 | −0.196739 | −0.0983697 | − | 0.995150i | \(-0.531363\pi\) | ||||
−0.0983697 | + | 0.995150i | \(0.531363\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.30853 | 0.227466 | 0.113733 | − | 0.993511i | \(-0.463719\pi\) | ||||
0.113733 | + | 0.993511i | \(0.463719\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.68497 | −0.164436 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.0396 | −1.45393 | −0.726965 | − | 0.686675i | \(-0.759070\pi\) | ||||
−0.726965 | + | 0.686675i | \(0.759070\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.4002 | 1.28351 | 0.641753 | − | 0.766911i | \(-0.278207\pi\) | ||||
0.641753 | + | 0.766911i | \(0.278207\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.27227 | −0.215674 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.89717 | 0.460687 | 0.230343 | − | 0.973109i | \(-0.426015\pi\) | ||||
0.230343 | + | 0.973109i | \(0.426015\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.86230 | −0.826414 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.65460 | −0.245418 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.697020 | 0.0638957 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.26291 | −0.842083 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 17.3575 | 1.56508 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.6682 | −1.04364 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.61625 | −0.232155 | −0.116078 | − | 0.993240i | \(-0.537032\pi\) | ||||
−0.116078 | + | 0.993240i | \(0.537032\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 16.0957 | 1.41715 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.64498 | −0.231093 | −0.115547 | − | 0.993302i | \(-0.536862\pi\) | ||||
−0.115547 | + | 0.993302i | \(0.536862\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.580162 | 0.0503064 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.73215 | −0.579411 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.88035 | −0.416957 | −0.208478 | − | 0.978027i | \(-0.566851\pi\) | ||||
−0.208478 | + | 0.978027i | \(0.566851\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.3334 | 0.876468 | 0.438234 | − | 0.898861i | \(-0.355604\pi\) | ||||
0.438234 | + | 0.898861i | \(0.355604\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −24.6688 | −2.07749 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.13000 | 0.428992 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.95533 | −0.162382 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.7861 | −1.05458 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.35324 | −0.684324 | −0.342162 | − | 0.939641i | \(-0.611159\pi\) | ||||
−0.342162 | + | 0.939641i | \(0.611159\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.84941 | 0.476019 | 0.238009 | − | 0.971263i | \(-0.423505\pi\) | ||||
0.238009 | + | 0.971263i | \(0.423505\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.819386 | −0.0662434 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.48639 | 0.360356 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.361645 | 0.0288624 | 0.0144312 | − | 0.999896i | \(-0.495406\pi\) | ||||
0.0144312 | + | 0.999896i | \(0.495406\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.89441 | −0.467457 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.39700 | 0.267721 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.146029 | −0.0114379 | −0.00571894 | − | 0.999984i | \(-0.501820\pi\) | ||||
−0.00571894 | + | 0.999984i | \(0.501820\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.82784 | −0.297997 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.406603 | −0.0314639 | −0.0157319 | − | 0.999876i | \(-0.505008\pi\) | ||||
−0.0157319 | + | 0.999876i | \(0.505008\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.14999 | 0.165384 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.682013 | −0.0521548 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.6466 | −0.961507 | −0.480753 | − | 0.876856i | \(-0.659637\pi\) | ||||
−0.480753 | + | 0.876856i | \(0.659637\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.57174 | 0.118812 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.495378 | 0.0372349 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.55598 | 0.415274 | 0.207637 | − | 0.978206i | \(-0.433423\pi\) | ||||
0.207637 | + | 0.978206i | \(0.433423\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.13401 | −0.678926 | −0.339463 | − | 0.940619i | \(-0.610245\pi\) | ||||
−0.339463 | + | 0.940619i | \(0.610245\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −28.2456 | −2.08797 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.79232 | −0.131774 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.58346 | 0.115794 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.58049 | 0.187703 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.47532 | 0.396180 | 0.198090 | − | 0.980184i | \(-0.436526\pi\) | ||||
0.198090 | + | 0.980184i | \(0.436526\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.9697 | 1.22151 | 0.610753 | − | 0.791821i | \(-0.290867\pi\) | ||||
0.610753 | + | 0.791821i | \(0.290867\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −11.3044 | −0.809527 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −23.7727 | −1.69374 | −0.846868 | − | 0.531803i | \(-0.821515\pi\) | ||||
−0.846868 | + | 0.531803i | \(0.821515\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.5747 | 1.24584 | 0.622918 | − | 0.782287i | \(-0.285947\pi\) | ||||
0.622918 | + | 0.782287i | \(0.285947\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 18.3229 | 1.29239 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.749498 | 0.0526044 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.6913 | 0.956244 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.99337 | −0.277558 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.31799 | 0.0911671 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.2804 | −1.18963 | −0.594815 | − | 0.803863i | \(-0.702775\pi\) | ||||
−0.594815 | + | 0.803863i | \(0.702775\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.3111 | 0.912059 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.6960 | 0.865860 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.71968 | −0.116739 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −29.3458 | −1.98301 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.67630 | 0.314562 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.6027 | 0.776973 | 0.388487 | − | 0.921454i | \(-0.372998\pi\) | ||||
0.388487 | + | 0.921454i | \(0.372998\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.84766 | −0.123178 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 27.4484 | 1.82182 | 0.910908 | − | 0.412609i | \(-0.135382\pi\) | ||||
0.910908 | + | 0.412609i | \(0.135382\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.8680 | −1.44508 | −0.722540 | − | 0.691329i | \(-0.757025\pi\) | ||||
−0.722540 | + | 0.691329i | \(0.757025\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.46725 | 0.0965377 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.1975 | 1.45421 | 0.727103 | − | 0.686528i | \(-0.240866\pi\) | ||||
0.727103 | + | 0.686528i | \(0.240866\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −19.4583 | −1.26932 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −25.2007 | −1.63696 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.1350 | 1.36711 | 0.683555 | − | 0.729899i | \(-0.260433\pi\) | ||||
0.683555 | + | 0.729899i | \(0.260433\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.2437 | −1.11076 | −0.555382 | − | 0.831595i | \(-0.687428\pi\) | ||||
−0.555382 | + | 0.831595i | \(0.687428\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.95957 | −0.446457 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.0855 | −0.644338 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.89230 | 0.247661 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.11158 | 0.450678 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.08851 | −0.384303 | −0.192152 | − | 0.981365i | \(-0.561547\pi\) | ||||
−0.192152 | + | 0.981365i | \(0.561547\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.71717 | 0.485174 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.48930 | −0.218509 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.1741 | 0.634643 | 0.317322 | − | 0.948318i | \(-0.397217\pi\) | ||||
0.317322 | + | 0.948318i | \(0.397217\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.687014 | 0.0426890 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.881077 | −0.0545373 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.8414 | 0.976822 | 0.488411 | − | 0.872614i | \(-0.337577\pi\) | ||||
0.488411 | + | 0.872614i | \(0.337577\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.64940 | −0.285611 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.0542 | 0.982500 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.8533 | −1.39339 | −0.696695 | − | 0.717367i | \(-0.745347\pi\) | ||||
−0.696695 | + | 0.717367i | \(0.745347\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.2830 | 0.746142 | 0.373071 | − | 0.927803i | \(-0.378305\pi\) | ||||
0.373071 | + | 0.927803i | \(0.378305\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.33309 | 0.262251 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.57060 | 0.215316 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.643776 | 0.0386808 | 0.0193404 | − | 0.999813i | \(-0.493843\pi\) | ||||
0.0193404 | + | 0.999813i | \(0.493843\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.02157 | 0.121029 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.93027 | 0.532735 | 0.266368 | − | 0.963872i | \(-0.414177\pi\) | ||||
0.266368 | + | 0.963872i | \(0.414177\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.7397 | 0.876187 | 0.438094 | − | 0.898929i | \(-0.355654\pi\) | ||||
0.438094 | + | 0.898929i | \(0.355654\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.90431 | −0.172036 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.24801 | −0.309780 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.5566 | −0.915093 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 32.7053 | 1.91722 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.9816 | 1.40102 | 0.700509 | − | 0.713643i | \(-0.252956\pi\) | ||||
0.700509 | + | 0.713643i | \(0.252956\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.390746 | 0.0227501 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.86226 | 0.340163 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 22.7905 | 1.31801 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.86649 | −0.280500 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.79398 | −0.217958 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −22.2796 | −1.27573 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.82132 | 0.103948 | 0.0519740 | − | 0.998648i | \(-0.483449\pi\) | ||||
0.0519740 | + | 0.998648i | \(0.483449\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.42974 | 0.251999 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.53302 | 0.257044 | 0.128522 | − | 0.991707i | \(-0.458977\pi\) | ||||
0.128522 | + | 0.991707i | \(0.458977\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.4149 | −0.701730 | −0.350865 | − | 0.936426i | \(-0.614112\pi\) | ||||
−0.350865 | + | 0.936426i | \(0.614112\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.598882 | −0.0337432 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −23.0948 | −1.29713 | −0.648567 | − | 0.761157i | \(-0.724632\pi\) | ||||
−0.648567 | + | 0.761157i | \(0.724632\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.70268 | 0.0953317 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −28.8588 | −1.61074 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.20142 | 0.0668490 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.5448 | 0.584918 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 25.7131 | 1.42194 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.45856 | 0.411204 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.3743 | −1.44966 | −0.724831 | − | 0.688927i | \(-0.758082\pi\) | ||||
−0.724831 | + | 0.688927i | \(0.758082\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.807623 | −0.0442575 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.4527 | 0.789638 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.82102 | 0.208144 | 0.104072 | − | 0.994570i | \(-0.466813\pi\) | ||||
0.104072 | + | 0.994570i | \(0.466813\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.39697 | 0.510373 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.90669 | −0.211559 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.92699 | 0.428017 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −17.0055 | −0.915545 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 29.8808 | 1.60408 | 0.802042 | − | 0.597268i | \(-0.203747\pi\) | ||||
0.802042 | + | 0.597268i | \(0.203747\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.7016 | −0.679902 | −0.339951 | − | 0.940443i | \(-0.610411\pi\) | ||||
−0.339951 | + | 0.940443i | \(0.610411\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 17.3125 | 0.924073 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.8398 | 1.21564 | 0.607820 | − | 0.794074i | \(-0.292044\pi\) | ||||
0.607820 | + | 0.794074i | \(0.292044\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.4995 | 0.557257 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.33748 | 0.0707870 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −35.4003 | −1.86835 | −0.934177 | − | 0.356810i | \(-0.883864\pi\) | ||||
−0.934177 | + | 0.356810i | \(0.883864\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −17.7742 | −0.932904 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −23.1475 | −1.21159 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.2148 | −0.898608 | −0.449304 | − | 0.893379i | \(-0.648328\pi\) | ||||
−0.449304 | + | 0.893379i | \(0.648328\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.16933 | 0.321163 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.78216 | 0.0925251 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.3506 | −1.05372 | −0.526858 | − | 0.849953i | \(-0.676630\pi\) | ||||
−0.526858 | + | 0.849953i | \(0.676630\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −22.3897 | −1.15620 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.02837 | 0.258974 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.22765 | 0.217160 | 0.108580 | − | 0.994088i | \(-0.465370\pi\) | ||||
0.108580 | + | 0.994088i | \(0.465370\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.02022 | −0.257194 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.71281 | 0.496301 | 0.248151 | − | 0.968721i | \(-0.420177\pi\) | ||||
0.248151 | + | 0.968721i | \(0.420177\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.15734 | 0.0589834 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.72083 | 0.290806 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.3291 | −1.13213 | −0.566064 | − | 0.824361i | \(-0.691534\pi\) | ||||
−0.566064 | + | 0.824361i | \(0.691534\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.03466 | 0.355758 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.07534 | −0.256017 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −19.8778 | −1.00016 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.9210 | 1.20056 | 0.600281 | − | 0.799789i | \(-0.295055\pi\) | ||||
0.600281 | + | 0.799789i | \(0.295055\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.11325 | 0.0557321 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.5237 | −0.825154 | −0.412577 | − | 0.910923i | \(-0.635371\pi\) | ||||
−0.412577 | + | 0.910923i | \(0.635371\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.5373 | −0.574713 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −16.0148 | −0.795783 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.56073 | 0.0773625 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.0228 | −0.792278 | −0.396139 | − | 0.918191i | \(-0.629650\pi\) | ||||
−0.396139 | + | 0.918191i | \(0.629650\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.36470 | −0.461926 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.149776 | −0.00737002 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.60949 | 0.275359 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 19.8283 | 0.970998 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.7496 | −0.622858 | −0.311429 | − | 0.950269i | \(-0.600808\pi\) | ||||
−0.311429 | + | 0.950269i | \(0.600808\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.89293 | 0.0922560 | 0.0461280 | − | 0.998936i | \(-0.485312\pi\) | ||||
0.0461280 | + | 0.998936i | \(0.485312\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.76796 | −0.426313 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.25482 | 0.157882 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.53999 | 0.413279 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.84374 | 0.475260 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 37.2166 | 1.79266 | 0.896331 | − | 0.443386i | \(-0.146223\pi\) | ||||
0.896331 | + | 0.443386i | \(0.146223\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −36.0314 | −1.73156 | −0.865780 | − | 0.500425i | \(-0.833177\pi\) | ||||
−0.865780 | + | 0.500425i | \(0.833177\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.75201 | −0.179895 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.85527 | 0.280095 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.6188 | 0.888629 | 0.444315 | − | 0.895871i | \(-0.353447\pi\) | ||||
0.444315 | + | 0.895871i | \(0.353447\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.54453 | −0.216406 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.26887 | 0.107797 | 0.0538987 | − | 0.998546i | \(-0.482835\pi\) | ||||
0.0538987 | + | 0.998546i | \(0.482835\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.6633 | 0.600296 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.0287 | −0.758130 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.248909 | 0.0117467 | 0.00587337 | − | 0.999983i | \(-0.498130\pi\) | ||||
0.00587337 | + | 0.999983i | \(0.498130\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.9222 | −0.561395 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.2242 | 0.527358 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.41787 | 0.160232 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.98767 | 0.326869 | 0.163435 | − | 0.986554i | \(-0.447743\pi\) | ||||
0.163435 | + | 0.986554i | \(0.447743\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.34379 | 0.249427 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 34.1624 | 1.59110 | 0.795550 | − | 0.605888i | \(-0.207182\pi\) | ||||
0.795550 | + | 0.605888i | \(0.207182\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.5311 | 1.60480 | 0.802399 | − | 0.596788i | \(-0.203556\pi\) | ||||
0.802399 | + | 0.596788i | \(0.203556\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.60875 | 0.399221 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −39.6496 | −1.83476 | −0.917382 | − | 0.398008i | \(-0.869702\pi\) | ||||
−0.917382 | + | 0.398008i | \(0.869702\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.53987 | −0.255808 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.693945 | 0.0319753 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.0555 | −0.508332 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.70913 | 0.124304 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.09503 | −0.0959247 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.8669 | −1.13620 | −0.568098 | − | 0.822961i | \(-0.692321\pi\) | ||||
−0.568098 | + | 0.822961i | \(0.692321\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.60917 | 0.210160 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.51836 | 0.296596 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 25.7974 | 1.17140 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.7320 | 1.80043 | 0.900214 | − | 0.435448i | \(-0.143410\pi\) | ||||
0.900214 | + | 0.435448i | \(0.143410\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.280209 | −0.0126715 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.45561 | −0.155949 | −0.0779747 | − | 0.996955i | \(-0.524845\pi\) | ||||
−0.0779747 | + | 0.996955i | \(0.524845\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.55209 | 0.0699027 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.36052 | −0.0611506 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.02457 | −0.180527 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.5837 | −0.787156 | −0.393578 | − | 0.919291i | \(-0.628763\pi\) | ||||
−0.393578 | + | 0.919291i | \(0.628763\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.780212 | −0.0348573 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.72712 | −0.121596 | −0.0607981 | − | 0.998150i | \(-0.519365\pi\) | ||||
−0.0607981 | + | 0.998150i | \(0.519365\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.99262 | −0.133170 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.12553 | 0.183221 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.73123 | 0.298356 | 0.149178 | − | 0.988810i | \(-0.452337\pi\) | ||||
0.149178 | + | 0.988810i | \(0.452337\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.87264 | 0.392503 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.44789 | 0.196379 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.49410 | 0.153968 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.9441 | 0.745198 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −24.2671 | −1.06521 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −38.2190 | −1.67440 | −0.837202 | − | 0.546894i | \(-0.815810\pi\) | ||||
−0.837202 | + | 0.546894i | \(0.815810\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.37182 | −0.234893 | −0.117447 | − | 0.993079i | \(-0.537471\pi\) | ||||
−0.117447 | + | 0.993079i | \(0.537471\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.01594 | 0.131626 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.56118 | −0.155127 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.2842 | 0.490616 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.176071 | 0.00764081 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −35.2089 | −1.52506 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −22.7633 | −0.984143 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.6611 | 0.460062 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.78229 | 0.378280 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.3497 | −1.47681 | −0.738404 | − | 0.674359i | \(-0.764420\pi\) | ||||
−0.738404 | + | 0.674359i | \(0.764420\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −17.5269 | −0.752150 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 20.2820 | 0.868786 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.58358 | 0.110466 | 0.0552330 | − | 0.998473i | \(-0.482410\pi\) | ||||
0.0552330 | + | 0.998473i | \(0.482410\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.0392 | −0.428464 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.29188 | 0.0550358 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.61936 | 0.324008 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.43921 | −0.145986 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.498941 | 0.0211408 | 0.0105704 | − | 0.999944i | \(-0.496635\pi\) | ||||
0.0105704 | + | 0.999944i | \(0.496635\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −32.6492 | −1.38092 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.03843 | 0.128283 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −32.5553 | −1.37204 | −0.686021 | − | 0.727581i | \(-0.740644\pi\) | ||||
−0.686021 | + | 0.727581i | \(0.740644\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.41216 | 0.311832 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.13863 | 0.257798 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.6834 | −0.573636 | −0.286818 | − | 0.957985i | \(-0.592598\pi\) | ||||
−0.286818 | + | 0.957985i | \(0.592598\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.2520 | 0.512732 | 0.256366 | − | 0.966580i | \(-0.417475\pi\) | ||||
0.256366 | + | 0.966580i | \(0.417475\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.5064 | 0.438909 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15.8627 | 0.661521 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.6672 | 0.610605 | 0.305302 | − | 0.952255i | \(-0.401242\pi\) | ||||
0.305302 | + | 0.952255i | \(0.401242\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 32.5624 | 1.35325 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.15017 | −0.0892040 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.04864 | 0.167677 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.01789 | −0.166119 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.53206 | −0.228333 | −0.114166 | − | 0.993462i | \(-0.536420\pi\) | ||||
−0.114166 | + | 0.993462i | \(0.536420\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.96413 | −0.122135 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −45.6165 | −1.87641 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.5870 | 0.886470 | 0.443235 | − | 0.896405i | \(-0.353831\pi\) | ||||
0.443235 | + | 0.896405i | \(0.353831\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.05498 | 0.0432500 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 33.7233 | 1.38020 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 28.3513 | 1.15840 | 0.579202 | − | 0.815184i | \(-0.303364\pi\) | ||||
0.579202 | + | 0.815184i | \(0.303364\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.9758 | 0.896410 | 0.448205 | − | 0.893931i | \(-0.352064\pi\) | ||||
0.448205 | + | 0.893931i | \(0.352064\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.51243 | 0.265207 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.0200 | −0.569993 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.89484 | −0.320441 | −0.160221 | − | 0.987081i | \(-0.551221\pi\) | ||||
−0.160221 | + | 0.987081i | \(0.551221\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.43818 | 0.0582780 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 50.0394 | 2.02438 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.5174 | −1.19220 | −0.596098 | − | 0.802912i | \(-0.703283\pi\) | ||||
−0.596098 | + | 0.802912i | \(0.703283\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 26.2717 | 1.05938 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.08379 | −0.124149 | −0.0620744 | − | 0.998072i | \(-0.519772\pi\) | ||||
−0.0620744 | + | 0.998072i | \(0.519772\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.9487 | 0.440066 | 0.220033 | − | 0.975492i | \(-0.429384\pi\) | ||||
0.220033 | + | 0.975492i | \(0.429384\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 26.0436 | 1.04509 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.85394 | −0.194469 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.11492 | −0.164597 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.52903 | 0.101000 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.42270 | 0.0567267 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.7432 | 0.825773 | 0.412886 | − | 0.910783i | \(-0.364521\pi\) | ||||
0.412886 | + | 0.910783i | \(0.364521\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −33.1586 | −1.31794 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.95986 | −0.157142 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 25.9360 | 1.02762 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.73110 | 0.187160 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −34.5310 | −1.36389 | −0.681946 | − | 0.731403i | \(-0.738866\pi\) | ||||
−0.681946 | + | 0.731403i | \(0.738866\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.5300 | 0.849062 | 0.424531 | − | 0.905413i | \(-0.360439\pi\) | ||||
0.424531 | + | 0.905413i | \(0.360439\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 24.3618 | 0.959245 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.7527 | −0.894502 | −0.447251 | − | 0.894409i | \(-0.647597\pi\) | ||||
−0.447251 | + | 0.894409i | \(0.647597\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.340256 | −0.0133562 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.29981 | −0.129330 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −35.6805 | −1.39629 | −0.698143 | − | 0.715958i | \(-0.745990\pi\) | ||||
−0.698143 | + | 0.715958i | \(0.745990\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.00334 | −0.156423 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.4303 | −0.406924 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −35.8589 | −1.39686 | −0.698432 | − | 0.715676i | \(-0.746119\pi\) | ||||
−0.698432 | + | 0.715676i | \(0.746119\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.4409 | 0.989537 | 0.494769 | − | 0.869025i | \(-0.335253\pi\) | ||||
0.494769 | + | 0.869025i | \(0.335253\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.97315 | 0.348488 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.878110 | 0.0340516 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.56429 | 0.292890 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 22.2639 | 0.860772 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.4008 | 0.748959 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.2142 | 1.31886 | 0.659431 | − | 0.751765i | \(-0.270797\pi\) | ||||
0.659431 | + | 0.751765i | \(0.270797\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12.0499 | 0.463802 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −37.9103 | −1.45701 | −0.728505 | − | 0.685040i | \(-0.759785\pi\) | ||||
−0.728505 | + | 0.685040i | \(0.759785\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.88837 | −0.379481 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 52.6696 | 2.01830 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30.3542 | −1.16147 | −0.580736 | − | 0.814092i | \(-0.697235\pi\) | ||||
−0.580736 | + | 0.814092i | \(0.697235\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.38671 | −0.282232 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −41.9616 | −1.60094 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.9565 | 0.455506 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.50694 | 0.133410 | 0.0667052 | − | 0.997773i | \(-0.478751\pi\) | ||||
0.0667052 | + | 0.997773i | \(0.478751\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.521498 | 0.0198101 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.6402 | 0.593268 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.8678 | −0.411647 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 42.5938 | 1.61105 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.2168 | 0.499190 | 0.249595 | − | 0.968350i | \(-0.419703\pi\) | ||||
0.249595 | + | 0.968350i | \(0.419703\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.18418 | 0.0446621 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −37.3378 | −1.40622 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.14710 | 0.0431411 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.2882 | 0.874605 | 0.437302 | − | 0.899314i | \(-0.355934\pi\) | ||||
0.437302 | + | 0.899314i | \(0.355934\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.95699 | −0.335913 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17.3558 | −0.649979 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.76457 | 0.290378 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 40.5551 | 1.51456 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.192843 | 0.00719184 | 0.00359592 | − | 0.999994i | \(-0.498855\pi\) | ||||
0.00359592 | + | 0.999994i | \(0.498855\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.33932 | −0.0498789 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −33.0882 | −1.23056 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.49987 | 0.129982 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.5604 | −0.540014 | −0.270007 | − | 0.962858i | \(-0.587026\pi\) | ||||
−0.270007 | + | 0.962858i | \(0.587026\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18.3883 | 0.681047 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.0777 | −0.372739 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.0856 | 1.07430 | 0.537150 | − | 0.843487i | \(-0.319501\pi\) | ||||
0.537150 | + | 0.843487i | \(0.319501\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −19.3526 | −0.713831 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.5853 | −0.463584 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.8090 | −1.05975 | −0.529877 | − | 0.848074i | \(-0.677762\pi\) | ||||
−0.529877 | + | 0.848074i | \(0.677762\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.46877 | 0.274372 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −42.2025 | −1.54826 | −0.774129 | − | 0.633027i | \(-0.781812\pi\) | ||||
−0.774129 | + | 0.633027i | \(0.781812\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.6431 | −0.463208 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.52764 | 0.0924816 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.72538 | 0.318818 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.64036 | 0.0963483 | 0.0481741 | − | 0.998839i | \(-0.484660\pi\) | ||||
0.0481741 | + | 0.998839i | \(0.484660\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.6830 | −0.425751 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.85344 | 0.322210 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.51764 | 0.164197 | 0.0820983 | − | 0.996624i | \(-0.473838\pi\) | ||||
0.0820983 | + | 0.996624i | \(0.473838\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14.8081 | 0.537502 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.5124 | 0.852323 | 0.426162 | − | 0.904647i | \(-0.359866\pi\) | ||||
0.426162 | + | 0.904647i | \(0.359866\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.77428 | −0.281448 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.24019 | −0.0448392 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.00485 | −0.0362830 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.6727 | −1.07002 | −0.535012 | − | 0.844845i | \(-0.679693\pi\) | ||||
−0.535012 | + | 0.844845i | \(0.679693\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.5227 | 0.703091 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.1647 | −0.365598 | −0.182799 | − | 0.983150i | \(-0.558516\pi\) | ||||
−0.182799 | + | 0.983150i | \(0.558516\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.03023 | −0.288454 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.31828 | 0.0472931 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.04577 | −0.324098 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.14285 | −0.327157 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.74612 | 0.205350 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.547372 | 0.0195365 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.8481 | −0.671863 | −0.335931 | − | 0.941886i | \(-0.609051\pi\) | ||||
−0.335931 | + | 0.941886i | \(0.609051\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 30.3974 | 1.08217 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.84115 | −0.101020 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 57.2947 | 2.03459 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.92154 | −0.316414 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.9098 | 0.492709 | 0.246355 | − | 0.969180i | \(-0.420767\pi\) | ||||
0.246355 | + | 0.969180i | \(0.420767\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.4455 | 0.546423 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.70608 | 0.201614 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.1565 | 0.711308 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.14157 | 0.181217 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −43.8522 | −1.54367 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.7630 | −0.694831 | −0.347415 | − | 0.937711i | \(-0.612941\pi\) | ||||
−0.347415 | + | 0.937711i | \(0.612941\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30.1099 | −1.05730 | −0.528651 | − | 0.848839i | \(-0.677302\pi\) | ||||
−0.528651 | + | 0.848839i | \(0.677302\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 23.5694 | 0.826615 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.221024 | −0.00774213 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.38816 | −0.293465 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.54010 | 0.0538153 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.1788 | −0.913645 | −0.456823 | − | 0.889558i | \(-0.651013\pi\) | ||||
−0.456823 | + | 0.889558i | \(0.651013\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −41.9817 | −1.46339 | −0.731696 | − | 0.681631i | \(-0.761271\pi\) | ||||
−0.731696 | + | 0.681631i | \(0.761271\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.85148 | 0.238538 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.6394 | 0.717703 | 0.358851 | − | 0.933395i | \(-0.383168\pi\) | ||||
0.358851 | + | 0.933395i | \(0.383168\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −36.6292 | −1.27218 | −0.636092 | − | 0.771613i | \(-0.719450\pi\) | ||||
−0.636092 | + | 0.771613i | \(0.719450\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.23531 | 0.0428526 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.00558 | 0.277377 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.615418 | −0.0212974 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −13.1841 | −0.455710 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.71855 | −0.128379 | −0.0641893 | − | 0.997938i | \(-0.520446\pi\) | ||||
−0.0641893 | + | 0.997938i | \(0.520446\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.3311 | −0.942450 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17.1359 | 0.590192 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.25414 | 0.111946 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.37399 | 0.184652 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 28.2835 | 0.970686 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.93367 | 0.237683 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 49.7965 | 1.70500 | 0.852501 | − | 0.522726i | \(-0.175085\pi\) | ||||
0.852501 | + | 0.522726i | \(0.175085\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.03227 | −0.0353028 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −35.6409 | −1.21747 | −0.608735 | − | 0.793374i | \(-0.708323\pi\) | ||||
−0.608735 | + | 0.793374i | \(0.708323\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −43.5752 | −1.48677 | −0.743383 | − | 0.668866i | \(-0.766780\pi\) | ||||
−0.743383 | + | 0.668866i | \(0.766780\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.0702 | −0.343191 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −43.6579 | −1.48613 | −0.743067 | − | 0.669217i | \(-0.766630\pi\) | ||||
−0.743067 | + | 0.669217i | \(0.766630\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.1415 | −0.650829 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −29.8509 | −1.01379 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.3093 | 0.587179 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37.1669 | −1.25935 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.6243 | 0.393424 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.76947 | 0.228850 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.23078 | 0.176631 | 0.0883154 | − | 0.996093i | \(-0.471852\pi\) | ||||
0.0883154 | + | 0.996093i | \(0.471852\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 46.0172 | 1.55212 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.0358 | −0.742405 | −0.371203 | − | 0.928552i | \(-0.621054\pi\) | ||||
−0.371203 | + | 0.928552i | \(0.621054\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 56.9658 | 1.91705 | 0.958525 | − | 0.285008i | \(-0.0919962\pi\) | ||||
0.958525 | + | 0.285008i | \(0.0919962\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.749785 | 0.0252038 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.28694 | −0.110365 | −0.0551823 | − | 0.998476i | \(-0.517574\pi\) | ||||
−0.0551823 | + | 0.998476i | \(0.517574\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.51785 | 0.0509071 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.9455 | 0.467191 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.8560 | 0.430210 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.40932 | 0.281092 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 43.7316 | 1.46016 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.82929 | −0.127714 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.69057 | 0.122951 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.33810 | −0.310753 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13.8249 | −0.459555 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.0491571 | 0.00163223 | 0.000816117 | − | 1.00000i | \(-0.499740\pi\) | ||||
0.000816117 | 1.00000i | \(0.499740\pi\) | ||||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.34848 | −0.0447263 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.4990 | 1.07674 | 0.538370 | − | 0.842708i | \(-0.319040\pi\) | ||||
0.538370 | + | 0.842708i | \(0.319040\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.88466 | −0.161659 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −42.7514 | −1.41332 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.53452 | 0.0506742 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.8145 | 0.653619 | 0.326810 | − | 0.945090i | \(-0.394026\pi\) | ||||
0.326810 | + | 0.945090i | \(0.394026\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.49485 | 0.115159 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −27.0008 | −0.888742 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.20809 | 0.105481 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.57445 | 0.0517116 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 43.9293 | 1.44127 | 0.720637 | − | 0.693313i | \(-0.243850\pi\) | ||||
0.720637 | + | 0.693313i | \(0.243850\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.66341 | 0.218385 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.69822 | 0.284767 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.39666 | 0.0783793 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.9026 | 0.780863 | 0.390431 | − | 0.920632i | \(-0.372326\pi\) | ||||
0.390431 | + | 0.920632i | \(0.372326\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23.8224 | −0.777413 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.4109 | −0.665375 | −0.332688 | − | 0.943037i | \(-0.607955\pi\) | ||||
−0.332688 | + | 0.943037i | \(0.607955\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −52.9654 | −1.72479 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.90573 | 0.127054 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.72706 | −0.0886176 | −0.0443088 | − | 0.999018i | \(-0.514109\pi\) | ||||
−0.0443088 | + | 0.999018i | \(0.514109\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 59.5265 | 1.93231 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −44.3157 | −1.43703 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.7679 | 1.06146 | 0.530729 | − | 0.847542i | \(-0.321918\pi\) | ||||
0.530729 | + | 0.847542i | \(0.321918\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.28723 | 0.268168 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.26720 | 0.105613 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.83139 | 0.0914305 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.2139 | −0.716578 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.2572 | −0.330533 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25.6847 | 0.826818 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36.4163 | −1.17107 | −0.585535 | − | 0.810647i | \(-0.699115\pi\) | ||||
−0.585535 | + | 0.810647i | \(0.699115\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.30536 | 0.0740588 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.40329 | 0.205491 | 0.102746 | − | 0.994708i | \(-0.467237\pi\) | ||||
0.102746 | + | 0.994708i | \(0.467237\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.99505 | −0.192192 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 20.2339 | 0.648003 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.6473 | 0.372629 | 0.186315 | − | 0.982490i | \(-0.440346\pi\) | ||||
0.186315 | + | 0.982490i | \(0.440346\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.0270 | −0.352424 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.13910 | 0.291789 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 34.7061 | 1.10695 | 0.553477 | − | 0.832864i | \(-0.313301\pi\) | ||||
0.553477 | + | 0.832864i | \(0.313301\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −35.9815 | −1.14646 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 14.3119 | 0.455553 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −49.1150 | −1.56176 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.30503 | 0.104988 | 0.0524939 | − | 0.998621i | \(-0.483283\pi\) | ||||
0.0524939 | + | 0.998621i | \(0.483283\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −50.6085 | −1.60601 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 26.6003 | 0.843288 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.9009 | 0.503586 | 0.251793 | − | 0.967781i | \(-0.418980\pi\) | ||||
0.251793 | + | 0.967781i | \(0.418980\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.26708 | 0.166643 |
(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 | 4864.2.a.bo.1.6 | 8 | ||
4.3 | odd | 2 | 4864.2.a.bn.1.3 | 8 | |||
8.3 | odd | 2 | 4864.2.a.bp.1.6 | 8 | |||
8.5 | even | 2 | 4864.2.a.bq.1.3 | 8 | |||
16.3 | odd | 4 | 608.2.c.b.305.5 | 16 | |||
16.5 | even | 4 | 152.2.c.b.77.11 | ✓ | 16 | ||
16.11 | odd | 4 | 608.2.c.b.305.12 | 16 | |||
16.13 | even | 4 | 152.2.c.b.77.12 | yes | 16 | ||
48.5 | odd | 4 | 1368.2.g.b.685.6 | 16 | |||
48.11 | even | 4 | 5472.2.g.b.2737.7 | 16 | |||
48.29 | odd | 4 | 1368.2.g.b.685.5 | 16 | |||
48.35 | even | 4 | 5472.2.g.b.2737.10 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.2.c.b.77.11 | ✓ | 16 | 16.5 | even | 4 | ||
152.2.c.b.77.12 | yes | 16 | 16.13 | even | 4 | ||
608.2.c.b.305.5 | 16 | 16.3 | odd | 4 | |||
608.2.c.b.305.12 | 16 | 16.11 | odd | 4 | |||
1368.2.g.b.685.5 | 16 | 48.29 | odd | 4 | |||
1368.2.g.b.685.6 | 16 | 48.5 | odd | 4 | |||
4864.2.a.bn.1.3 | 8 | 4.3 | odd | 2 | |||
4864.2.a.bo.1.6 | 8 | 1.1 | even | 1 | trivial | ||
4864.2.a.bp.1.6 | 8 | 8.3 | odd | 2 | |||
4864.2.a.bq.1.3 | 8 | 8.5 | even | 2 | |||
5472.2.g.b.2737.7 | 16 | 48.11 | even | 4 | |||
5472.2.g.b.2737.10 | 16 | 48.35 | even | 4 |