Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8036,2,Mod(1,8036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8036, 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("8036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8036.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: | \(64.1677830643\) |
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: | \( x^{8} - 14x^{6} - 4x^{5} + 60x^{4} + 31x^{3} - 75x^{2} - 60x - 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1148) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.24904\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8036.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.24904 | −1.29848 | −0.649241 | − | 0.760582i | \(-0.724914\pi\) | ||||
−0.649241 | + | 0.760582i | \(0.724914\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.47097 | 0.657839 | 0.328919 | − | 0.944358i | \(-0.393316\pi\) | ||||
0.328919 | + | 0.944358i | \(0.393316\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.05817 | 0.686058 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.494253 | −0.149023 | −0.0745114 | − | 0.997220i | \(-0.523740\pi\) | ||||
−0.0745114 | + | 0.997220i | \(0.523740\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.52254 | −1.53168 | −0.765838 | − | 0.643033i | \(-0.777676\pi\) | ||||
−0.765838 | + | 0.643033i | \(0.777676\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.30827 | −0.854193 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.25624 | 1.03229 | 0.516145 | − | 0.856501i | \(-0.327367\pi\) | ||||
0.516145 | + | 0.856501i | \(0.327367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.960935 | 0.220454 | 0.110227 | − | 0.993906i | \(-0.464842\pi\) | ||||
0.110227 | + | 0.993906i | \(0.464842\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.30001 | −0.479585 | −0.239793 | − | 0.970824i | \(-0.577079\pi\) | ||||
−0.239793 | + | 0.970824i | \(0.577079\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.83624 | −0.567248 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.11820 | 0.407648 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.25851 | 0.233699 | 0.116850 | − | 0.993150i | \(-0.462720\pi\) | ||||
0.116850 | + | 0.993150i | \(0.462720\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.26477 | 1.48440 | 0.742198 | − | 0.670181i | \(-0.233783\pi\) | ||||
0.742198 | + | 0.670181i | \(0.233783\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.11159 | 0.193504 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.22617 | −1.35237 | −0.676187 | − | 0.736730i | \(-0.736369\pi\) | ||||
−0.676187 | + | 0.736730i | \(0.736369\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 12.4204 | 1.98886 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.33579 | 0.813700 | 0.406850 | − | 0.913495i | \(-0.366627\pi\) | ||||
0.406850 | + | 0.913495i | \(0.366627\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.02752 | 0.451316 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.66765 | −0.534982 | −0.267491 | − | 0.963560i | \(-0.586195\pi\) | ||||
−0.267491 | + | 0.963560i | \(0.586195\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.57245 | −1.34041 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.54635 | 1.17393 | 0.586966 | − | 0.809612i | \(-0.300322\pi\) | ||||
0.586966 | + | 0.809612i | \(0.300322\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.727033 | −0.0980331 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.16118 | −0.286255 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.47245 | −0.191696 | −0.0958481 | − | 0.995396i | \(-0.530556\pi\) | ||||
−0.0958481 | + | 0.995396i | \(0.530556\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.23371 | 0.798145 | 0.399072 | − | 0.916919i | \(-0.369332\pi\) | ||||
0.399072 | + | 0.916919i | \(0.369332\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.12350 | −1.00760 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.91517 | 0.478314 | 0.239157 | − | 0.970981i | \(-0.423129\pi\) | ||||
0.239157 | + | 0.970981i | \(0.423129\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.17281 | 0.622733 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.1617 | −1.20597 | −0.602987 | − | 0.797751i | \(-0.706023\pi\) | ||||
−0.602987 | + | 0.797751i | \(0.706023\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.775836 | −0.0908048 | −0.0454024 | − | 0.998969i | \(-0.514457\pi\) | ||||
−0.0454024 | + | 0.998969i | \(0.514457\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.37881 | 0.736562 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.98543 | −1.12345 | −0.561724 | − | 0.827325i | \(-0.689862\pi\) | ||||
−0.561724 | + | 0.827325i | \(0.689862\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.9384 | −1.21538 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.68368 | 0.843393 | 0.421697 | − | 0.906737i | \(-0.361435\pi\) | ||||
0.421697 | + | 0.906737i | \(0.361435\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.26081 | 0.679080 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.83043 | −0.303454 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.83079 | 0.724063 | 0.362031 | − | 0.932166i | \(-0.382083\pi\) | ||||
0.362031 | + | 0.932166i | \(0.382083\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −18.5878 | −1.92746 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.41351 | 0.145023 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.83506 | 0.693995 | 0.346998 | − | 0.937866i | \(-0.387201\pi\) | ||||
0.346998 | + | 0.937866i | \(0.387201\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.01726 | −0.102238 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.49543 | −0.248305 | −0.124152 | − | 0.992263i | \(-0.539621\pi\) | ||||
−0.124152 | + | 0.992263i | \(0.539621\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.27911 | 0.224567 | 0.112284 | − | 0.993676i | \(-0.464183\pi\) | ||||
0.112284 | + | 0.993676i | \(0.464183\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.05987 | −0.585830 | −0.292915 | − | 0.956138i | \(-0.594625\pi\) | ||||
−0.292915 | + | 0.956138i | \(0.594625\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.55318 | −0.531898 | −0.265949 | − | 0.963987i | \(-0.585685\pi\) | ||||
−0.265949 | + | 0.963987i | \(0.585685\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 18.5010 | 1.75603 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.60020 | 0.903111 | 0.451555 | − | 0.892243i | \(-0.350869\pi\) | ||||
0.451555 | + | 0.892243i | \(0.350869\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.38325 | −0.315490 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −11.3663 | −1.05082 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7557 | −0.977792 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.24904 | 0.202789 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.5269 | −1.03100 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.29583 | 0.381193 | 0.190596 | − | 0.981668i | \(-0.438958\pi\) | ||||
0.190596 | + | 0.981668i | \(0.438958\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.0004 | −1.05658 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.8643 | −1.12396 | −0.561981 | − | 0.827150i | \(-0.689961\pi\) | ||||
−0.561981 | + | 0.827150i | \(0.689961\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.11582 | 0.268167 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.8399 | −1.69504 | −0.847520 | − | 0.530764i | \(-0.821905\pi\) | ||||
−0.847520 | + | 0.530764i | \(0.821905\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.3831 | −0.880685 | −0.440342 | − | 0.897830i | \(-0.645143\pi\) | ||||
−0.440342 | + | 0.897830i | \(0.645143\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.24869 | 0.694665 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.72953 | 0.228255 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.85123 | 0.153736 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.3985 | −1.34342 | −0.671710 | − | 0.740815i | \(-0.734440\pi\) | ||||
−0.671710 | + | 0.740815i | \(0.734440\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.89266 | −0.235402 | −0.117701 | − | 0.993049i | \(-0.537552\pi\) | ||||
−0.117701 | + | 0.993049i | \(0.537552\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.76008 | 0.708211 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.1572 | 0.976494 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.5181 | 1.71733 | 0.858665 | − | 0.512537i | \(-0.171294\pi\) | ||||
0.858665 | + | 0.512537i | \(0.171294\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −19.2211 | −1.52433 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.03732 | 0.316228 | 0.158114 | − | 0.987421i | \(-0.449459\pi\) | ||||
0.158114 | + | 0.987421i | \(0.449459\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.63512 | 0.127294 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.8080 | 1.22326 | 0.611630 | − | 0.791144i | \(-0.290514\pi\) | ||||
0.611630 | + | 0.791144i | \(0.290514\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.4984 | 1.34603 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.97777 | 0.151244 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.9471 | −1.06038 | −0.530190 | − | 0.847879i | \(-0.677879\pi\) | ||||
−0.530190 | + | 0.847879i | \(0.677879\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.31159 | 0.248914 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.4518 | 1.22967 | 0.614833 | − | 0.788657i | \(-0.289223\pi\) | ||||
0.614833 | + | 0.788657i | \(0.289223\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.78054 | −0.132347 | −0.0661733 | − | 0.997808i | \(-0.521079\pi\) | ||||
−0.0661733 | + | 0.997808i | \(0.521079\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.0198 | −1.03638 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12.1005 | −0.889644 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.10366 | −0.153835 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.2536 | 1.61021 | 0.805107 | − | 0.593130i | \(-0.202108\pi\) | ||||
0.805107 | + | 0.593130i | \(0.202108\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.34825 | −0.312994 | −0.156497 | − | 0.987678i | \(-0.550020\pi\) | ||||
−0.156497 | + | 0.987678i | \(0.550020\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 18.2701 | 1.30835 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.5511 | −1.32171 | −0.660854 | − | 0.750514i | \(-0.729806\pi\) | ||||
−0.660854 | + | 0.750514i | \(0.729806\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.02988 | 0.427447 | 0.213724 | − | 0.976894i | \(-0.431441\pi\) | ||||
0.213724 | + | 0.976894i | \(0.431441\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.80536 | −0.621082 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.47097 | −0.102737 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.73382 | −0.329023 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.474945 | −0.0328526 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.97038 | −0.548704 | −0.274352 | − | 0.961629i | \(-0.588463\pi\) | ||||
−0.274352 | + | 0.961629i | \(0.588463\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 22.8541 | 1.56594 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.84880 | 0.535284 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.74489 | 0.117908 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −23.5052 | −1.58113 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.1994 | 1.21872 | 0.609360 | − | 0.792894i | \(-0.291427\pi\) | ||||
0.609360 | + | 0.792894i | \(0.291427\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.83748 | −0.389165 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.57940 | 0.171201 | 0.0856004 | − | 0.996330i | \(-0.472719\pi\) | ||||
0.0856004 | + | 0.996330i | \(0.472719\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.5532 | −1.49036 | −0.745180 | − | 0.666863i | \(-0.767637\pi\) | ||||
−0.745180 | + | 0.666863i | \(0.767637\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.54988 | −0.101536 | −0.0507682 | − | 0.998710i | \(-0.516167\pi\) | ||||
−0.0507682 | + | 0.998710i | \(0.516167\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.39502 | −0.351932 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 22.4576 | 1.45878 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.3710 | 1.05895 | 0.529477 | − | 0.848324i | \(-0.322388\pi\) | ||||
0.529477 | + | 0.848324i | \(0.322388\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.7603 | −0.757546 | −0.378773 | − | 0.925490i | \(-0.623654\pi\) | ||||
−0.378773 | + | 0.925490i | \(0.623654\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 18.2464 | 1.17051 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.30680 | −0.337663 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −17.2809 | −1.09513 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.1858 | −0.958517 | −0.479259 | − | 0.877674i | \(-0.659094\pi\) | ||||
−0.479259 | + | 0.877674i | \(0.659094\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.13679 | 0.0714692 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −14.0808 | −0.881774 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.0946877 | −0.00590645 | −0.00295323 | − | 0.999996i | \(-0.500940\pi\) | ||||
−0.00295323 | + | 0.999996i | \(0.500940\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.59023 | 0.160331 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.9175 | 1.10484 | 0.552420 | − | 0.833566i | \(-0.313705\pi\) | ||||
0.552420 | + | 0.833566i | \(0.313705\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.5714 | 0.772258 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.3627 | −0.940183 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −32.3561 | −1.97279 | −0.986393 | − | 0.164406i | \(-0.947429\pi\) | ||||
−0.986393 | + | 0.164406i | \(0.947429\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.9810 | 1.03152 | 0.515762 | − | 0.856732i | \(-0.327509\pi\) | ||||
0.515762 | + | 0.856732i | \(0.327509\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.40182 | 0.0845329 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.422608 | −0.0253921 | −0.0126960 | − | 0.999919i | \(-0.504041\pi\) | ||||
−0.0126960 | + | 0.999919i | \(0.504041\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 17.0103 | 1.01838 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.4772 | −0.625016 | −0.312508 | − | 0.949915i | \(-0.601169\pi\) | ||||
−0.312508 | + | 0.949915i | \(0.601169\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.5343 | 1.63674 | 0.818372 | − | 0.574689i | \(-0.194877\pi\) | ||||
0.818372 | + | 0.574689i | \(0.194877\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.17904 | −0.188310 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.11558 | 0.0656225 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −15.3723 | −0.901141 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −22.6387 | −1.32257 | −0.661283 | − | 0.750137i | \(-0.729988\pi\) | ||||
−0.661283 | + | 0.750137i | \(0.729988\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.16593 | −0.126105 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.04693 | −0.0607489 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.7019 | 0.734570 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.61233 | 0.322420 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.16961 | 0.525051 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.00706 | 0.514060 | 0.257030 | − | 0.966403i | \(-0.417256\pi\) | ||||
0.257030 | + | 0.966403i | \(0.417256\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.12580 | −0.291597 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 25.8029 | 1.46315 | 0.731573 | − | 0.681763i | \(-0.238787\pi\) | ||||
0.731573 | + | 0.681763i | \(0.238787\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.30641 | 0.299936 | 0.149968 | − | 0.988691i | \(-0.452083\pi\) | ||||
0.149968 | + | 0.988691i | \(0.452083\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.73715 | 0.153734 | 0.0768668 | − | 0.997041i | \(-0.475508\pi\) | ||||
0.0768668 | + | 0.997041i | \(0.475508\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.622022 | −0.0348265 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.6289 | 0.760690 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.08997 | 0.227572 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.6632 | 0.868840 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.4893 | 0.690660 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.5489 | −0.634787 | −0.317394 | − | 0.948294i | \(-0.602808\pi\) | ||||
−0.317394 | + | 0.948294i | \(0.602808\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −16.9309 | −0.927807 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.75910 | 0.314653 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −31.6744 | −1.72541 | −0.862706 | − | 0.505705i | \(-0.831232\pi\) | ||||
−0.862706 | + | 0.505705i | \(0.831232\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −21.5912 | −1.17267 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.08489 | −0.221209 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.60906 | 0.409658 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.14098 | −0.437031 | −0.218515 | − | 0.975833i | \(-0.570121\pi\) | ||||
−0.218515 | + | 0.975833i | \(0.570121\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.07115 | −0.217924 | −0.108962 | − | 0.994046i | \(-0.534753\pi\) | ||||
−0.108962 | + | 0.994046i | \(0.534753\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.6979 | −0.624385 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.5592 | −1.62650 | −0.813252 | − | 0.581912i | \(-0.802305\pi\) | ||||
−0.813252 | + | 0.581912i | \(0.802305\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.9476 | −0.793337 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −29.0102 | −1.53110 | −0.765550 | − | 0.643376i | \(-0.777533\pi\) | ||||
−0.765550 | + | 0.643376i | \(0.777533\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0766 | −0.951400 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 24.1900 | 1.26965 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.14123 | −0.0597349 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.4440 | −0.858369 | −0.429185 | − | 0.903217i | \(-0.641199\pi\) | ||||
−0.429185 | + | 0.903217i | \(0.641199\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.05817 | −0.107144 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.4364 | 1.36883 | 0.684413 | − | 0.729095i | \(-0.260059\pi\) | ||||
0.684413 | + | 0.729095i | \(0.260059\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 25.9244 | 1.33873 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.95016 | −0.357951 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.6085 | −0.801756 | −0.400878 | − | 0.916132i | \(-0.631295\pi\) | ||||
−0.400878 | + | 0.916132i | \(0.631295\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.66148 | −0.494973 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.36472 | 0.171929 | 0.0859645 | − | 0.996298i | \(-0.472603\pi\) | ||||
0.0859645 | + | 0.996298i | \(0.472603\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.9820 | 0.558246 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.22512 | −0.0621159 | −0.0310579 | − | 0.999518i | \(-0.509888\pi\) | ||||
−0.0310579 | + | 0.999518i | \(0.509888\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.78940 | −0.495071 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 28.9324 | 1.45945 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.6883 | −0.739048 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −36.5319 | −1.83348 | −0.916742 | − | 0.399481i | \(-0.869190\pi\) | ||||
−0.916742 | + | 0.399481i | \(0.869190\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −29.9865 | −1.49746 | −0.748728 | − | 0.662877i | \(-0.769335\pi\) | ||||
−0.748728 | + | 0.662877i | \(0.769335\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −45.6425 | −2.27361 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −16.0901 | −0.799526 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.06581 | 0.201535 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 37.0251 | 1.83077 | 0.915386 | − | 0.402578i | \(-0.131886\pi\) | ||||
0.915386 | + | 0.402578i | \(0.131886\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 44.6208 | 2.20098 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.3025 | 0.554817 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 23.3520 | 1.14355 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.4042 | −1.19222 | −0.596112 | − | 0.802901i | \(-0.703289\pi\) | ||||
−0.596112 | + | 0.802901i | \(0.703289\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.51451 | −0.122550 | −0.0612750 | − | 0.998121i | \(-0.519517\pi\) | ||||
−0.0612750 | + | 0.998121i | \(0.519517\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.54867 | −0.367029 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.0717 | −0.585564 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.13882 | −0.296385 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.8325 | 0.858961 | 0.429481 | − | 0.903076i | \(-0.358697\pi\) | ||||
0.429481 | + | 0.903076i | \(0.358697\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.2172 | 1.25992 | 0.629960 | − | 0.776628i | \(-0.283071\pi\) | ||||
0.629960 | + | 0.776628i | \(0.283071\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.16349 | −0.199624 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.21016 | −0.105726 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.0661 | −0.575881 | −0.287941 | − | 0.957648i | \(-0.592971\pi\) | ||||
−0.287941 | + | 0.957648i | \(0.592971\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −31.1899 | −1.48187 | −0.740937 | − | 0.671574i | \(-0.765619\pi\) | ||||
−0.740937 | + | 0.671574i | \(0.765619\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.0479 | 0.476316 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 36.8809 | 1.74441 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.5606 | −0.592770 | −0.296385 | − | 0.955069i | \(-0.595781\pi\) | ||||
−0.296385 | + | 0.955069i | \(0.595781\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.494253 | 0.0232735 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.50571 | 0.305665 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.209051 | −0.00977900 | −0.00488950 | − | 0.999988i | \(-0.501556\pi\) | ||||
−0.00488950 | + | 0.999988i | \(0.501556\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9.01558 | 0.420811 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.3033 | 0.479873 | 0.239936 | − | 0.970789i | \(-0.422873\pi\) | ||||
0.239936 | + | 0.970789i | \(0.422873\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.65140 | −0.402065 | −0.201032 | − | 0.979585i | \(-0.564430\pi\) | ||||
−0.201032 | + | 0.979585i | \(0.564430\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −27.3421 | −1.26796 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.7584 | −1.05313 | −0.526566 | − | 0.850134i | \(-0.676521\pi\) | ||||
−0.526566 | + | 0.850134i | \(0.676521\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −48.3950 | −2.22992 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.63723 | −0.121260 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.72544 | −0.125052 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 17.5899 | 0.805385 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.76991 | −0.0808691 | −0.0404345 | − | 0.999182i | \(-0.512874\pi\) | ||||
−0.0404345 | + | 0.999182i | \(0.512874\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 45.4293 | 2.07140 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.0542 | 0.456537 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.1322 | −1.22948 | −0.614738 | − | 0.788731i | \(-0.710738\pi\) | ||||
−0.614738 | + | 0.788731i | \(0.710738\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.08010 | −0.410616 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.410698 | −0.0185345 | −0.00926727 | − | 0.999957i | \(-0.502950\pi\) | ||||
−0.00926727 | + | 0.999957i | \(0.502950\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.35651 | 0.241245 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.49636 | −0.0672564 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.2052 | −0.904509 | −0.452255 | − | 0.891889i | \(-0.649380\pi\) | ||||
−0.452255 | + | 0.891889i | \(0.649380\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −35.5528 | −1.58838 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 38.0193 | 1.69520 | 0.847599 | − | 0.530638i | \(-0.178048\pi\) | ||||
0.847599 | + | 0.530638i | \(0.178048\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.67071 | −0.163345 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −39.3546 | −1.74780 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −43.2599 | −1.91746 | −0.958730 | − | 0.284317i | \(-0.908233\pi\) | ||||
−0.958730 | + | 0.284317i | \(0.908233\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.03545 | 0.0898675 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.35251 | 0.147729 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.81275 | 0.0797246 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 31.3676 | 1.37689 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.70419 | −0.206094 | −0.103047 | − | 0.994676i | \(-0.532859\pi\) | ||||
−0.103047 | + | 0.994676i | \(0.532859\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.1882 | −0.751588 | −0.375794 | − | 0.926703i | \(-0.622630\pi\) | ||||
−0.375794 | + | 0.926703i | \(0.622630\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 35.1768 | 1.53233 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.7100 | −0.769998 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.03055 | −0.131515 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.52254 | 0.239208 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.91391 | −0.385382 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −37.0008 | −1.59670 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.4343 | −0.835545 | −0.417772 | − | 0.908552i | \(-0.637189\pi\) | ||||
−0.417772 | + | 0.908552i | \(0.637189\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.00451 | 0.171850 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.16857 | −0.349903 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.8699 | −1.06336 | −0.531681 | − | 0.846945i | \(-0.678439\pi\) | ||||
−0.531681 | + | 0.846945i | \(0.678439\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.8301 | 0.547573 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.20934 | 0.0515198 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 27.2144 | 1.15519 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.7680 | 0.922338 | 0.461169 | − | 0.887312i | \(-0.347430\pi\) | ||||
0.461169 | + | 0.887312i | \(0.347430\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −29.4671 | −1.24633 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.73121 | 0.199752 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −34.7390 | −1.46407 | −0.732036 | − | 0.681265i | \(-0.761430\pi\) | ||||
−0.732036 | + | 0.681265i | \(0.761430\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.1216 | 0.594101 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −38.2133 | −1.60199 | −0.800993 | − | 0.598674i | \(-0.795695\pi\) | ||||
−0.800993 | + | 0.598674i | \(0.795695\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −45.6458 | −1.91022 | −0.955109 | − | 0.296256i | \(-0.904262\pi\) | ||||
−0.955109 | + | 0.296256i | \(0.904262\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −50.0492 | −2.09083 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.52338 | 0.272044 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.19932 | 0.216451 | 0.108225 | − | 0.994126i | \(-0.465483\pi\) | ||||
0.108225 | + | 0.994126i | \(0.465483\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.77938 | 0.406417 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.22406 | −0.174943 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −16.7196 | −0.691269 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.2599 | 0.506020 | 0.253010 | − | 0.967464i | \(-0.418579\pi\) | ||||
0.253010 | + | 0.967464i | \(0.418579\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.94190 | 0.327240 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 41.7220 | 1.71622 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.4659 | −0.511914 | −0.255957 | − | 0.966688i | \(-0.582391\pi\) | ||||
−0.255957 | + | 0.966688i | \(0.582391\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.5614 | −0.555033 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −42.8908 | −1.75247 | −0.876235 | − | 0.481884i | \(-0.839953\pi\) | ||||
−0.876235 | + | 0.481884i | \(0.839953\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.40756 | −0.0982066 | −0.0491033 | − | 0.998794i | \(-0.515636\pi\) | ||||
−0.0491033 | + | 0.998794i | \(0.515636\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.05809 | 0.328151 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.8214 | −0.643230 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.03651 | 0.285603 | 0.142802 | − | 0.989751i | \(-0.454389\pi\) | ||||
0.142802 | + | 0.989751i | \(0.454389\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.2547 | 0.819419 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.5473 | 1.23379 | 0.616897 | − | 0.787044i | \(-0.288390\pi\) | ||||
0.616897 | + | 0.787044i | \(0.288390\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.30827 | 0.133402 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.2455 | −0.654018 | −0.327009 | − | 0.945021i | \(-0.606041\pi\) | ||||
−0.327009 | + | 0.945021i | \(0.606041\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.3140 | −1.05765 | −0.528825 | − | 0.848731i | \(-0.677367\pi\) | ||||
−0.528825 | + | 0.848731i | \(0.677367\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.87189 | −0.195502 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.77454 | −0.110982 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.06817 | 0.0426586 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −35.0126 | −1.39604 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.3206 | 1.32647 | 0.663237 | − | 0.748410i | \(-0.269182\pi\) | ||||
0.663237 | + | 0.748410i | \(0.269182\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.9257 | 0.712483 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.31904 | 0.250764 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −20.9146 | −0.827368 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.2462 | 1.35264 | 0.676322 | − | 0.736606i | \(-0.263573\pi\) | ||||
0.676322 | + | 0.736606i | \(0.263573\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.7446 | −0.699777 | −0.349889 | − | 0.936791i | \(-0.613781\pi\) | ||||
−0.349889 | + | 0.936791i | \(0.613781\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −17.6523 | −0.695057 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.3513 | −0.564209 | −0.282104 | − | 0.959384i | \(-0.591032\pi\) | ||||
−0.282104 | + | 0.959384i | \(0.591032\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.727761 | 0.0285671 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 31.0966 | 1.21690 | 0.608452 | − | 0.793591i | \(-0.291791\pi\) | ||||
0.608452 | + | 0.793591i | \(0.291791\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.9231 | −0.739386 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.59681 | −0.0622973 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.5409 | −0.955980 | −0.477990 | − | 0.878365i | \(-0.658634\pi\) | ||||
−0.477990 | + | 0.878365i | \(0.658634\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.5985 | −1.03456 | −0.517281 | − | 0.855816i | \(-0.673056\pi\) | ||||
−0.517281 | + | 0.855816i | \(0.673056\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 52.8642 | 2.05308 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.89458 | −0.112079 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −40.9311 | −1.58249 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.08103 | −0.118942 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.9351 | −0.806988 | −0.403494 | − | 0.914982i | \(-0.632204\pi\) | ||||
−0.403494 | + | 0.914982i | \(0.632204\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.00773 | −0.231238 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.82687 | 0.108645 | 0.0543227 | − | 0.998523i | \(-0.482700\pi\) | ||||
0.0543227 | + | 0.998523i | \(0.482700\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.80117 | −0.222301 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.7116 | 0.562922 | 0.281461 | − | 0.959573i | \(-0.409181\pi\) | ||||
0.281461 | + | 0.959573i | \(0.409181\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −29.1840 | −1.11506 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 50.7231 | 1.93521 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −47.1975 | −1.79808 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.48370 | −0.360777 | −0.180388 | − | 0.983595i | \(-0.557735\pi\) | ||||
−0.180388 | + | 0.983595i | \(0.557735\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.2733 | −0.579349 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.25624 | −0.161217 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.48575 | 0.131843 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.62883 | 0.250367 | 0.125184 | − | 0.992134i | \(-0.460048\pi\) | ||||
0.125184 | + | 0.992134i | \(0.460048\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.90481 | −0.298136 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.1336 | 0.456978 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.4597 | −1.10638 | −0.553191 | − | 0.833054i | \(-0.686590\pi\) | ||||
−0.553191 | + | 0.833054i | \(0.686590\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.5517 | −0.770751 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −19.0091 | −0.711895 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.01506 | 0.150155 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −36.8191 | −1.37503 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.0532 | −0.598682 | −0.299341 | − | 0.954146i | \(-0.596767\pi\) | ||||
−0.299341 | + | 0.954146i | \(0.596767\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 26.4493 | 0.983661 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.56943 | −0.132565 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −41.7494 | −1.54840 | −0.774199 | − | 0.632942i | \(-0.781847\pi\) | ||||
−0.774199 | + | 0.632942i | \(0.781847\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.22146 | −0.304498 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22.7104 | 0.839975 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.2698 | −0.564003 | −0.282002 | − | 0.959414i | \(-0.590998\pi\) | ||||
−0.282002 | + | 0.959414i | \(0.590998\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.93508 | −0.0712797 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 51.4608 | 1.89302 | 0.946508 | − | 0.322680i | \(-0.104584\pi\) | ||||
0.946508 | + | 0.322680i | \(0.104584\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.9352 | 0.438450 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.2055 | −0.521148 | −0.260574 | − | 0.965454i | \(-0.583912\pi\) | ||||
−0.260574 | + | 0.965454i | \(0.583912\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −24.1218 | −0.883753 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 15.8143 | 0.578617 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 48.1537 | 1.75715 | 0.878576 | − | 0.477602i | \(-0.158494\pi\) | ||||
0.878576 | + | 0.477602i | \(0.158494\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 34.1534 | 1.24462 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.25503 | −0.154856 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.7677 | −0.754816 | −0.377408 | − | 0.926047i | \(-0.623185\pi\) | ||||
−0.377408 | + | 0.926047i | \(0.623185\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.55668 | −0.0928015 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.80893 | 0.283073 | 0.141537 | − | 0.989933i | \(-0.454796\pi\) | ||||
0.141537 | + | 0.989933i | \(0.454796\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 12.8858 | 0.465889 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.13164 | 0.293617 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.74705 | 0.243305 | 0.121652 | − | 0.992573i | \(-0.461181\pi\) | ||||
0.121652 | + | 0.992573i | \(0.461181\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.212956 | 0.00766943 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.0422 | 0.864738 | 0.432369 | − | 0.901697i | \(-0.357678\pi\) | ||||
0.432369 | + | 0.901697i | \(0.357678\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −23.4409 | −0.842021 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.960935 | −0.0344291 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.02246 | 0.179718 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.66578 | 0.0952671 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 31.6525 | 1.12973 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32.7427 | −1.16715 | −0.583576 | − | 0.812059i | \(-0.698347\pi\) | ||||
−0.583576 | + | 0.812059i | \(0.698347\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −40.2971 | −1.43462 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −34.4259 | −1.22250 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −28.2737 | −1.00276 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 50.3514 | 1.78354 | 0.891769 | − | 0.452491i | \(-0.149465\pi\) | ||||
0.891769 | + | 0.452491i | \(0.149465\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.6104 | −0.552257 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.0590 | 0.496749 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.383459 | 0.0135320 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 72.7701 | 2.56163 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 40.3726 | 1.41942 | 0.709712 | − | 0.704492i | \(-0.248825\pi\) | ||||
0.709712 | + | 0.704492i | \(0.248825\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −46.0779 | −1.61801 | −0.809007 | − | 0.587799i | \(-0.799994\pi\) | ||||
−0.809007 | + | 0.587799i | \(0.799994\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −38.1910 | −1.33942 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.93879 | 0.208027 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.12735 | 0.179383 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.1739 | 0.564471 | 0.282236 | − | 0.959345i | \(-0.408924\pi\) | ||||
0.282236 | + | 0.959345i | \(0.408924\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.62680 | 0.196138 | 0.0980689 | − | 0.995180i | \(-0.468733\pi\) | ||||
0.0980689 | + | 0.995180i | \(0.468733\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.15275 | −0.109765 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.75878 | −0.304573 | −0.152286 | − | 0.988336i | \(-0.548664\pi\) | ||||
−0.152286 | + | 0.988336i | \(0.548664\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.6059 | −0.680942 | −0.340471 | − | 0.940255i | \(-0.610587\pi\) | ||||
−0.340471 | + | 0.940255i | \(0.610587\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.950462 | 0.0329712 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.2531 | 0.804708 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 17.5065 | 0.605112 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.03213 | −0.311824 | −0.155912 | − | 0.987771i | \(-0.549832\pi\) | ||||
−0.155912 | + | 0.987771i | \(0.549832\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.4162 | −0.945385 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 23.5636 | 0.811573 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 25.7397 | 0.885472 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −61.9257 | −2.12528 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.9203 | 0.648579 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.1999 | 0.794348 | 0.397174 | − | 0.917743i | \(-0.369991\pi\) | ||||
0.397174 | + | 0.917743i | \(0.369991\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.90925 | 0.0994941 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.56663 | −0.190153 | −0.0950763 | − | 0.995470i | \(-0.530309\pi\) | ||||
−0.0950763 | + | 0.995470i | \(0.530309\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.6041 | 0.907719 | 0.453860 | − | 0.891073i | \(-0.350047\pi\) | ||||
0.453860 | + | 0.891073i | \(0.350047\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.26472 | −0.179213 | −0.0896066 | − | 0.995977i | \(-0.528561\pi\) | ||||
−0.0896066 | + | 0.995977i | \(0.528561\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.5158 | −0.697559 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.50899 | −0.0852097 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.93533 | 0.167420 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.6217 | −0.732622 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.0677 | 0.476121 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.8920 | 1.00938 | 0.504691 | − | 0.863300i | \(-0.331606\pi\) | ||||
0.504691 | + | 0.863300i | \(0.331606\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 50.9153 | 1.71733 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.34231 | 0.213678 | 0.106839 | − | 0.994276i | \(-0.465927\pi\) | ||||
0.106839 | + | 0.994276i | \(0.465927\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.9746 | −0.537587 | −0.268794 | − | 0.963198i | \(-0.586625\pi\) | ||||
−0.268794 | + | 0.963198i | \(0.586625\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.87126 | 0.163745 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.5568 | 0.455192 | 0.227596 | − | 0.973756i | \(-0.426913\pi\) | ||||
0.227596 | + | 0.973756i | \(0.426913\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.40636 | 0.181120 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.52437 | −0.117939 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.2002 | 0.808923 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −28.5670 | −0.953826 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.4013 | 0.346902 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.3753 | 1.21184 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.61913 | −0.0870627 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.4506 | 0.944688 | 0.472344 | − | 0.881414i | \(-0.343408\pi\) | ||||
0.472344 | + | 0.881414i | \(0.343408\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.13604 | −0.170352 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.8892 | 0.924011 | 0.462006 | − | 0.886877i | \(-0.347130\pi\) | ||||
0.462006 | + | 0.886877i | \(0.347130\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.79768 | −0.125685 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −20.6228 | −0.681769 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.3422 | 0.967910 | 0.483955 | − | 0.875093i | \(-0.339200\pi\) | ||||
0.483955 | + | 0.875093i | \(0.339200\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.2572 | −0.667499 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 56.1185 | 1.84716 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 23.3314 | 0.767132 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.69080 | 0.154066 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −45.7393 | −1.50066 | −0.750329 | − | 0.661064i | \(-0.770105\pi\) | ||||
−0.750329 | + | 0.661064i | \(0.770105\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −58.0316 | −1.89987 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.09443 | −0.101199 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.24433 | −0.269331 | −0.134665 | − | 0.990891i | \(-0.542996\pi\) | ||||
−0.134665 | + | 0.990891i | \(0.542996\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.9343 | −0.389462 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.2362 | 0.333691 | 0.166846 | − | 0.985983i | \(-0.446642\pi\) | ||||
0.166846 | + | 0.985983i | \(0.446642\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.30001 | 0.0748986 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.0375 | 0.358669 | 0.179335 | − | 0.983788i | \(-0.442606\pi\) | ||||
0.179335 | + | 0.983788i | \(0.442606\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.28459 | 0.139084 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.15595 | −0.199620 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.620938 | 0.0201141 | 0.0100571 | − | 0.999949i | \(-0.496799\pi\) | ||||
0.0100571 | + | 0.999949i | \(0.496799\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 32.7344 | 1.05926 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.39895 | 0.0452216 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.3064 | 1.20343 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.4723 | −0.401913 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.39616 | −0.205900 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.9164 | 0.511836 | 0.255918 | − | 0.966698i | \(-0.417622\pi\) | ||||
0.255918 | + | 0.966698i | \(0.417622\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.19850 | −0.295498 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34.7069 | 1.11380 | 0.556899 | − | 0.830580i | \(-0.311991\pi\) | ||||
0.556899 | + | 0.830580i | \(0.311991\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −35.2272 | −1.12817 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24.1455 | −0.772484 | −0.386242 | − | 0.922397i | \(-0.626227\pi\) | ||||
−0.386242 | + | 0.922397i | \(0.626227\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.37614 | −0.107902 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.4294 | −0.364913 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.08919 | −0.226110 | −0.113055 | − | 0.993589i | \(-0.536064\pi\) | ||||
−0.113055 | + | 0.993589i | \(0.536064\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27.2881 | −0.869471 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.2724 | −0.390239 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 49.1063 | 1.55991 | 0.779956 | − | 0.625834i | \(-0.215241\pi\) | ||||
0.779956 | + | 0.625834i | \(0.215241\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 25.9740 | 0.824260 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.86979 | 0.281191 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.8456 | 0.755198 | 0.377599 | − | 0.925969i | \(-0.376750\pi\) | ||||
0.377599 | + | 0.925969i | \(0.376750\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −17.4247 | −0.551293 |
(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 | 8036.2.a.n.1.2 | 8 | ||
7.3 | odd | 6 | 1148.2.i.d.821.2 | yes | 16 | ||
7.5 | odd | 6 | 1148.2.i.d.165.2 | ✓ | 16 | ||
7.6 | odd | 2 | 8036.2.a.m.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.i.d.165.2 | ✓ | 16 | 7.5 | odd | 6 | ||
1148.2.i.d.821.2 | yes | 16 | 7.3 | odd | 6 | ||
8036.2.a.m.1.7 | 8 | 7.6 | odd | 2 | |||
8036.2.a.n.1.2 | 8 | 1.1 | even | 1 | trivial |