Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6080,2,Mod(1,6080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6080, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6080.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6080 = 2^{6} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6080.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: | \(48.5490444289\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.11344.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4x^{2} + 4x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 95) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.552409\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6080.1 |
$q$-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 | ||||||||
\(3\) | −2.87834 | −1.66181 | −0.830907 | − | 0.556412i | \(-0.812178\pi\) | ||||
−0.830907 | + | 0.556412i | \(0.812178\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.10482 | −1.17351 | −0.586756 | − | 0.809764i | \(-0.699595\pi\) | ||||
−0.586756 | + | 0.809764i | \(0.699595\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.28487 | 1.76162 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.10482 | −0.333115 | −0.166558 | − | 0.986032i | \(-0.553265\pi\) | ||||
−0.166558 | + | 0.986032i | \(0.553265\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.77353 | −0.491888 | −0.245944 | − | 0.969284i | \(-0.579098\pi\) | ||||
−0.245944 | + | 0.969284i | \(0.579098\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.87834 | −0.743185 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.75669 | 1.88127 | 0.940637 | − | 0.339415i | \(-0.110229\pi\) | ||||
0.940637 | + | 0.339415i | \(0.110229\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.93674 | 1.95016 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.65187 | 1.38701 | 0.693505 | − | 0.720451i | \(-0.256065\pi\) | ||||
0.693505 | + | 0.720451i | \(0.256065\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −6.57664 | −1.26567 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.75669 | −1.44038 | −0.720191 | − | 0.693776i | \(-0.755946\pi\) | ||||
−0.720191 | + | 0.693776i | \(0.755946\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.57664 | −1.18120 | −0.590600 | − | 0.806965i | \(-0.701109\pi\) | ||||
−0.590600 | + | 0.806965i | \(0.701109\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.18005 | 0.553576 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.10482 | −0.524810 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.40652 | 0.231231 | 0.115616 | − | 0.993294i | \(-0.463116\pi\) | ||||
0.115616 | + | 0.993294i | \(0.463116\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.10482 | 0.817425 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.81995 | 0.440402 | 0.220201 | − | 0.975454i | \(-0.429329\pi\) | ||||
0.220201 | + | 0.975454i | \(0.429329\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.10482 | 0.473480 | 0.236740 | − | 0.971573i | \(-0.423921\pi\) | ||||
0.236740 | + | 0.971573i | \(0.423921\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.28487 | 0.787822 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.46492 | −0.213680 | −0.106840 | − | 0.994276i | \(-0.534073\pi\) | ||||
−0.106840 | + | 0.994276i | \(0.534073\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.63990 | 0.377129 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −22.3264 | −3.12633 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.59348 | 0.356241 | 0.178121 | − | 0.984009i | \(-0.442998\pi\) | ||||
0.178121 | + | 0.984009i | \(0.442998\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.10482 | −0.148974 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.87834 | −0.381246 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.38969 | −0.701678 | −0.350839 | − | 0.936436i | \(-0.614103\pi\) | ||||
−0.350839 | + | 0.936436i | \(0.614103\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.07523 | −0.521780 | −0.260890 | − | 0.965369i | \(-0.584016\pi\) | ||||
−0.260890 | + | 0.965369i | \(0.584016\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −16.4086 | −2.06728 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.77353 | −0.219979 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.8151 | −1.93212 | −0.966060 | − | 0.258318i | \(-0.916832\pi\) | ||||
−0.966060 | + | 0.258318i | \(0.916832\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −19.1464 | −2.30495 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.14638 | −0.848119 | −0.424059 | − | 0.905634i | \(-0.639395\pi\) | ||||
−0.424059 | + | 0.905634i | \(0.639395\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.243310 | 0.0284773 | 0.0142387 | − | 0.999899i | \(-0.495468\pi\) | ||||
0.0142387 | + | 0.999899i | \(0.495468\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.87834 | −0.332363 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.43026 | 0.390915 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.38969 | 1.05642 | 0.528211 | − | 0.849113i | \(-0.322863\pi\) | ||||
0.528211 | + | 0.849113i | \(0.322863\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.07523 | 0.341692 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.86151 | 0.972677 | 0.486338 | − | 0.873771i | \(-0.338332\pi\) | ||||
0.486338 | + | 0.873771i | \(0.338332\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.75669 | 0.841331 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 22.3264 | 2.39364 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.813048 | 0.0861829 | 0.0430914 | − | 0.999071i | \(-0.486279\pi\) | ||||
0.0430914 | + | 0.999071i | \(0.486279\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.50648 | 0.577236 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 18.9298 | 1.96293 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.00000 | 0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.19689 | 0.324595 | 0.162297 | − | 0.986742i | \(-0.448110\pi\) | ||||
0.162297 | + | 0.986742i | \(0.448110\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.83882 | −0.586824 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.01887 | 0.300389 | 0.150195 | − | 0.988656i | \(-0.452010\pi\) | ||||
0.150195 | + | 0.988656i | \(0.452010\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.05839 | −0.596951 | −0.298476 | − | 0.954417i | \(-0.596478\pi\) | ||||
−0.298476 | + | 0.954417i | \(0.596478\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.93674 | 0.872136 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 20.3848 | 1.97068 | 0.985338 | − | 0.170616i | \(-0.0545759\pi\) | ||||
0.985338 | + | 0.170616i | \(0.0545759\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.72710 | −0.452774 | −0.226387 | − | 0.974037i | \(-0.572691\pi\) | ||||
−0.226387 | + | 0.974037i | \(0.572691\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.04846 | −0.384263 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.98316 | −0.750993 | −0.375496 | − | 0.926824i | \(-0.622528\pi\) | ||||
−0.375496 | + | 0.926824i | \(0.622528\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.65187 | 0.620290 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.37285 | −0.866520 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −24.0831 | −2.20770 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.77938 | −0.889034 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.11679 | −0.731866 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.63503 | −0.411293 | −0.205646 | − | 0.978626i | \(-0.565930\pi\) | ||||
−0.205646 | + | 0.978626i | \(0.565930\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.93674 | −0.786836 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.5134 | 1.35541 | 0.677705 | − | 0.735334i | \(-0.262975\pi\) | ||||
0.677705 | + | 0.735334i | \(0.262975\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.10482 | −0.269222 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.57664 | −0.566027 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.813048 | −0.0694634 | −0.0347317 | − | 0.999397i | \(-0.511058\pi\) | ||||
−0.0347317 | + | 0.999397i | \(0.511058\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.7687 | −1.08302 | −0.541512 | − | 0.840693i | \(-0.682148\pi\) | ||||
−0.541512 | + | 0.840693i | \(0.682148\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.21654 | 0.355097 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.95942 | 0.163855 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.75669 | −0.644158 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.59854 | −0.626717 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.7982 | 1.13040 | 0.565198 | − | 0.824955i | \(-0.308800\pi\) | ||||
0.565198 | + | 0.824955i | \(0.308800\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.02269 | −0.408740 | −0.204370 | − | 0.978894i | \(-0.565515\pi\) | ||||
−0.204370 | + | 0.978894i | \(0.565515\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 40.9931 | 3.31409 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.57664 | −0.528248 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.18695 | −0.573581 | −0.286791 | − | 0.957993i | \(-0.592588\pi\) | ||||
−0.286791 | + | 0.957993i | \(0.592588\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.46492 | −0.592007 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.6529 | −1.62767 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.25528 | 0.568277 | 0.284139 | − | 0.958783i | \(-0.408292\pi\) | ||||
0.284139 | + | 0.958783i | \(0.408292\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.18005 | 0.247567 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.33129 | 0.567312 | 0.283656 | − | 0.958926i | \(-0.408453\pi\) | ||||
0.283656 | + | 0.958926i | \(0.408453\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.85461 | −0.758047 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.28487 | 0.404144 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.77353 | 0.438953 | 0.219477 | − | 0.975618i | \(-0.429565\pi\) | ||||
0.219477 | + | 0.975618i | \(0.429565\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.10482 | −0.234702 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 15.5134 | 1.16606 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.48379 | −0.335134 | −0.167567 | − | 0.985861i | \(-0.553591\pi\) | ||||
−0.167567 | + | 0.985861i | \(0.553591\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.73400 | 0.203217 | 0.101608 | − | 0.994824i | \(-0.467601\pi\) | ||||
0.101608 | + | 0.994824i | \(0.467601\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.7299 | 0.867101 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.40652 | 0.103410 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.56974 | −0.626681 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 20.4193 | 1.48528 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.7230 | 1.28239 | 0.641196 | − | 0.767377i | \(-0.278438\pi\) | ||||
0.641196 | + | 0.767377i | \(0.278438\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.5371 | −0.974423 | −0.487212 | − | 0.873284i | \(-0.661986\pi\) | ||||
−0.487212 | + | 0.873284i | \(0.661986\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.10482 | 0.365564 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.5134 | 1.53276 | 0.766382 | − | 0.642385i | \(-0.222055\pi\) | ||||
0.766382 | + | 0.642385i | \(0.222055\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.09410 | −0.502888 | −0.251444 | − | 0.967872i | \(-0.580905\pi\) | ||||
−0.251444 | + | 0.967872i | \(0.580905\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 45.5213 | 3.21082 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 24.0831 | 1.69030 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.81995 | 0.196954 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 35.1543 | 2.44339 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.10482 | −0.0764219 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.0604 | 0.761431 | 0.380716 | − | 0.924692i | \(-0.375678\pi\) | ||||
0.380716 | + | 0.924692i | \(0.375678\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 20.5697 | 1.40942 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.10482 | 0.211747 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.4193 | 1.38615 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.700331 | −0.0473240 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.7567 | −0.925375 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.6350 | 0.846104 | 0.423052 | − | 0.906105i | \(-0.360959\pi\) | ||||
0.423052 | + | 0.906105i | \(0.360959\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.28487 | 0.352325 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.62813 | −0.439925 | −0.219962 | − | 0.975508i | \(-0.570593\pi\) | ||||
−0.219962 | + | 0.975508i | \(0.570593\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.0752308 | 0.00497139 | 0.00248570 | − | 0.999997i | \(-0.499209\pi\) | ||||
0.00248570 | + | 0.999997i | \(0.499209\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.87348 | −0.649627 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.51338 | 0.623242 | 0.311621 | − | 0.950206i | \(-0.399128\pi\) | ||||
0.311621 | + | 0.950206i | \(0.399128\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.46492 | −0.0955607 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −27.0268 | −1.75558 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.92984 | 0.189515 | 0.0947577 | − | 0.995500i | \(-0.469792\pi\) | ||||
0.0947577 | + | 0.995500i | \(0.469792\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.42743 | −0.607274 | −0.303637 | − | 0.952788i | \(-0.598201\pi\) | ||||
−0.303637 | + | 0.952788i | \(0.598201\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.8783 | 0.697846 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.63990 | 0.168657 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.77353 | −0.112847 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −25.5065 | −1.61641 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.9298 | −0.942363 | −0.471181 | − | 0.882036i | \(-0.656172\pi\) | ||||
−0.471181 | + | 0.882036i | \(0.656172\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.34911 | −0.462035 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −22.3264 | −1.39814 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.1295 | −0.943755 | −0.471877 | − | 0.881664i | \(-0.656424\pi\) | ||||
−0.471877 | + | 0.881664i | \(0.656424\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.36700 | −0.271352 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −40.9931 | −2.53741 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.2216 | 0.938605 | 0.469302 | − | 0.883038i | \(-0.344505\pi\) | ||||
0.469302 | + | 0.883038i | \(0.344505\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.59348 | 0.159316 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.34023 | −0.143220 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.5203 | −0.702404 | −0.351202 | − | 0.936300i | \(-0.614227\pi\) | ||||
−0.351202 | + | 0.936300i | \(0.614227\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.16118 | −0.131282 | −0.0656411 | − | 0.997843i | \(-0.520909\pi\) | ||||
−0.0656411 | + | 0.997843i | \(0.520909\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −15.8495 | −0.959258 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.10482 | −0.0666231 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.4205 | −1.40720 | −0.703602 | − | 0.710595i | \(-0.748426\pi\) | ||||
−0.703602 | + | 0.710595i | \(0.748426\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −34.7567 | −2.08083 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.6824 | 1.53209 | 0.766043 | − | 0.642789i | \(-0.222223\pi\) | ||||
0.766043 | + | 0.642789i | \(0.222223\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.38587 | 0.439045 | 0.219522 | − | 0.975607i | \(-0.429550\pi\) | ||||
0.219522 | + | 0.975607i | \(0.429550\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.87834 | −0.170498 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.75543 | −0.516817 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 43.1662 | 2.53919 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.20174 | −0.539416 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.1522 | 1.41099 | 0.705494 | − | 0.708716i | \(-0.250725\pi\) | ||||
0.705494 | + | 0.708716i | \(0.250725\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.38969 | −0.313800 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.26600 | 0.421616 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.7973 | −0.682253 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.63990 | −0.555635 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.68936 | −0.499190 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.07523 | −0.233347 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.38482 | 0.250255 | 0.125127 | − | 0.992141i | \(-0.460066\pi\) | ||||
0.125127 | + | 0.992141i | \(0.460066\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.4381 | 0.992022 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.7123 | 0.890963 | 0.445481 | − | 0.895291i | \(-0.353033\pi\) | ||||
0.445481 | + | 0.895291i | \(0.353033\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.7794 | 1.40061 | 0.700307 | − | 0.713842i | \(-0.253047\pi\) | ||||
0.700307 | + | 0.713842i | \(0.253047\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −16.4086 | −0.924518 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 27.3798 | 1.53780 | 0.768900 | − | 0.639369i | \(-0.220804\pi\) | ||||
0.768900 | + | 0.639369i | \(0.220804\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.56974 | 0.479813 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −58.6745 | −3.27489 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.75669 | 0.431594 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.77353 | −0.0983775 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.6062 | 0.752426 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.54831 | 0.250756 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.70033 | 0.258354 | 0.129177 | − | 0.991622i | \(-0.458767\pi\) | ||||
0.129177 | + | 0.991622i | \(0.458767\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.43329 | 0.407342 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −15.8151 | −0.864070 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.6360 | −1.12412 | −0.562058 | − | 0.827098i | \(-0.689990\pi\) | ||||
−0.562058 | + | 0.827098i | \(0.689990\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 22.9783 | 1.24801 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.26600 | 0.393476 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.5373 | 0.730947 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −19.1464 | −1.03081 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 30.0148 | 1.61128 | 0.805639 | − | 0.592407i | \(-0.201822\pi\) | ||||
0.805639 | + | 0.592407i | \(0.201822\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.7340 | 0.788693 | 0.394347 | − | 0.918962i | \(-0.370971\pi\) | ||||
0.394347 | + | 0.918962i | \(0.370971\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.6638 | 0.622570 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −29.6302 | −1.57705 | −0.788527 | − | 0.615000i | \(-0.789156\pi\) | ||||
−0.788527 | + | 0.615000i | \(0.789156\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.14638 | −0.379290 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 69.3195 | 3.66878 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.7577 | −1.14833 | −0.574163 | − | 0.818741i | \(-0.694672\pi\) | ||||
−0.574163 | + | 0.818741i | \(0.694672\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 28.1484 | 1.47741 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.243310 | 0.0127355 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.0347 | −1.56780 | −0.783898 | − | 0.620889i | \(-0.786772\pi\) | ||||
−0.783898 | + | 0.620889i | \(0.786772\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 14.9031 | 0.775823 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.05227 | −0.418053 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 37.3055 | 1.93161 | 0.965803 | − | 0.259277i | \(-0.0834843\pi\) | ||||
0.965803 | + | 0.259277i | \(0.0834843\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.87834 | −0.148637 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.7567 | 0.708506 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.7794 | −0.759166 | −0.379583 | − | 0.925158i | \(-0.623932\pi\) | ||||
−0.379583 | + | 0.925158i | \(0.623932\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.3412 | 0.683492 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 29.0020 | 1.48193 | 0.740967 | − | 0.671541i | \(-0.234367\pi\) | ||||
0.740967 | + | 0.671541i | \(0.234367\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.43026 | 0.174822 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 16.4086 | 0.834094 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −21.1987 | −1.07481 | −0.537407 | − | 0.843323i | \(-0.680596\pi\) | ||||
−0.537407 | + | 0.843323i | \(0.680596\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 51.5965 | 2.60935 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −44.6529 | −2.25244 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.38969 | 0.472446 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.3856 | −0.521238 | −0.260619 | − | 0.965442i | \(-0.583927\pi\) | ||||
−0.260619 | + | 0.965442i | \(0.583927\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.93674 | 0.447397 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.6638 | 1.28159 | 0.640796 | − | 0.767712i | \(-0.278605\pi\) | ||||
0.640796 | + | 0.767712i | \(0.278605\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.6638 | 0.581017 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.07523 | 0.152809 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.55395 | −0.0770266 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.71611 | 0.282644 | 0.141322 | − | 0.989964i | \(-0.454865\pi\) | ||||
0.141322 | + | 0.989964i | \(0.454865\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.34023 | 0.115435 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16.7340 | 0.823427 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.86151 | 0.434994 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 36.7526 | 1.79978 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.4303 | 0.753818 | 0.376909 | − | 0.926250i | \(-0.376987\pi\) | ||||
0.376909 | + | 0.926250i | \(0.376987\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.18005 | 0.0575121 | 0.0287561 | − | 0.999586i | \(-0.490845\pi\) | ||||
0.0287561 | + | 0.999586i | \(0.490845\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.74190 | −0.376424 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.75669 | 0.376255 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.6529 | 0.612315 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.63990 | −0.272297 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.0255 | 0.675585 | 0.337792 | − | 0.941221i | \(-0.390320\pi\) | ||||
0.337792 | + | 0.941221i | \(0.390320\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.5894 | 1.22975 | 0.614874 | − | 0.788625i | \(-0.289207\pi\) | ||||
0.614874 | + | 0.788625i | \(0.289207\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 22.3264 | 1.07047 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.65187 | 0.318202 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.9732 | 1.04873 | 0.524363 | − | 0.851495i | \(-0.324304\pi\) | ||||
0.524363 | + | 0.851495i | \(0.324304\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.9515 | 0.664358 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.3721 | −0.920395 | −0.460197 | − | 0.887817i | \(-0.652221\pi\) | ||||
−0.460197 | + | 0.887817i | \(0.652221\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.813048 | 0.0385422 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −39.7161 | −1.87851 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.1841 | −0.905355 | −0.452677 | − | 0.891674i | \(-0.649531\pi\) | ||||
−0.452677 | + | 0.891674i | \(0.649531\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.11553 | −0.146705 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.4570 | 0.679250 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.50648 | 0.258148 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.36010 | 0.391069 | 0.195534 | − | 0.980697i | \(-0.437356\pi\) | ||||
0.195534 | + | 0.980697i | \(0.437356\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −51.0130 | −2.38108 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.0268 | 1.16561 | 0.582806 | − | 0.812611i | \(-0.301955\pi\) | ||||
0.582806 | + | 0.812611i | \(0.301955\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −32.3749 | −1.50459 | −0.752294 | − | 0.658827i | \(-0.771053\pi\) | ||||
−0.752294 | + | 0.658827i | \(0.771053\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 18.9298 | 0.877850 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.2216 | 0.704372 | 0.352186 | − | 0.935930i | \(-0.385438\pi\) | ||||
0.352186 | + | 0.935930i | \(0.385438\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 49.1030 | 2.26736 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 20.6865 | 0.953185 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.43026 | −0.157724 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.7062 | 0.627563 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.0485 | 0.916038 | 0.458019 | − | 0.888943i | \(-0.348559\pi\) | ||||
0.458019 | + | 0.888943i | \(0.348559\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.49451 | −0.113740 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 59.4460 | 2.70489 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.19689 | 0.145163 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.6508 | 1.43424 | 0.717118 | − | 0.696952i | \(-0.245461\pi\) | ||||
0.717118 | + | 0.696952i | \(0.245461\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −20.8832 | −0.944371 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.8033 | 1.11936 | 0.559679 | − | 0.828710i | \(-0.310924\pi\) | ||||
0.559679 | + | 0.828710i | \(0.310924\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −60.1662 | −2.70975 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.83882 | −0.262436 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 22.1882 | 0.995277 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.0237 | −1.47834 | −0.739171 | − | 0.673518i | \(-0.764783\pi\) | ||||
−0.739171 | + | 0.673518i | \(0.764783\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21.1020 | −0.942767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.54396 | 0.158017 | 0.0790087 | − | 0.996874i | \(-0.474825\pi\) | ||||
0.0790087 | + | 0.996874i | \(0.474825\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.01887 | 0.134338 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 28.3650 | 1.25973 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.11679 | 0.0938250 | 0.0469125 | − | 0.998899i | \(-0.485062\pi\) | ||||
0.0469125 | + | 0.998899i | \(0.485062\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.755435 | −0.0334185 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.57664 | −0.290366 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.05839 | −0.266965 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.61847 | 0.0711802 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.6182 | −0.729458 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.60748 | −0.377101 | −0.188550 | − | 0.982064i | \(-0.560379\pi\) | ||||
−0.188550 | + | 0.982064i | \(0.560379\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.8349 | 1.61068 | 0.805340 | − | 0.592814i | \(-0.201983\pi\) | ||||
0.805340 | + | 0.592814i | \(0.201983\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.93674 | 0.390031 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −51.0130 | −2.22216 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.2474 | 0.923799 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −28.4838 | −1.23609 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.00125 | −0.216628 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 20.3848 | 0.881313 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.9059 | 0.556931 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.91661 | −0.125627 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.0079 | 1.37613 | 0.688063 | − | 0.725651i | \(-0.258461\pi\) | ||||
0.688063 | + | 0.725651i | \(0.258461\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.86941 | −0.337709 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.72710 | −0.202487 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.6240 | 0.753550 | 0.376775 | − | 0.926305i | \(-0.377033\pi\) | ||||
0.376775 | + | 0.926305i | \(0.377033\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −21.5371 | −0.919179 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.75669 | −0.330446 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −29.1533 | −1.23972 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.04846 | −0.171848 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 34.6865 | 1.46972 | 0.734858 | − | 0.678221i | \(-0.237249\pi\) | ||||
0.734858 | + | 0.678221i | \(0.237249\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.50648 | −0.232899 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.6667 | 1.04143 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.5073 | 0.569263 | 0.284632 | − | 0.958637i | \(-0.408129\pi\) | ||||
0.284632 | + | 0.958637i | \(0.408129\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.98316 | −0.335854 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.54803 | −0.400980 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 32.3588 | 1.35655 | 0.678276 | − | 0.734807i | \(-0.262727\pi\) | ||||
0.678276 | + | 0.734807i | \(0.262727\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.93293 | −0.373831 | −0.186916 | − | 0.982376i | \(-0.559849\pi\) | ||||
−0.186916 | + | 0.982376i | \(0.559849\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −51.0130 | −2.13110 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.65187 | 0.277402 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.9059 | 0.620541 | 0.310270 | − | 0.950648i | \(-0.399580\pi\) | ||||
0.310270 | + | 0.950648i | \(0.399580\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 38.9645 | 1.61931 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −27.5134 | −1.14145 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.86532 | −0.118669 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.37285 | −0.387520 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.37207 | 0.304278 | 0.152139 | − | 0.988359i | \(-0.451384\pi\) | ||||
0.152139 | + | 0.988359i | \(0.451384\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.57664 | −0.270986 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −61.9229 | −2.54717 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.6853 | −0.726247 | −0.363124 | − | 0.931741i | \(-0.618290\pi\) | ||||
−0.363124 | + | 0.931741i | \(0.618290\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −24.0831 | −0.987312 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.4193 | 0.835705 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.30657 | −0.216821 | −0.108410 | − | 0.994106i | \(-0.534576\pi\) | ||||
−0.108410 | + | 0.994106i | \(0.534576\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 43.7875 | 1.78613 | 0.893065 | − | 0.449927i | \(-0.148550\pi\) | ||||
0.893065 | + | 0.449927i | \(0.148550\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −83.5806 | −3.40367 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.77938 | −0.397588 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.24535 | 0.294080 | 0.147040 | − | 0.989131i | \(-0.453025\pi\) | ||||
0.147040 | + | 0.989131i | \(0.453025\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −69.3195 | −2.80897 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.59807 | 0.105107 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.8962 | −0.843988 | −0.421994 | − | 0.906599i | \(-0.638670\pi\) | ||||
−0.421994 | + | 0.906599i | \(0.638670\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.11679 | −0.327301 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.0494 | −0.887677 | −0.443839 | − | 0.896107i | \(-0.646384\pi\) | ||||
−0.443839 | + | 0.896107i | \(0.646384\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.0484607 | −0.00194780 | −0.000973900 | − | 1.00000i | \(-0.500310\pi\) | ||||
−0.000973900 | 1.00000i | \(0.500310\pi\) | ||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −43.7470 | −1.75550 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.52437 | −0.101137 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.18005 | 0.126999 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.9100 | 0.435009 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.6182 | 1.29851 | 0.649255 | − | 0.760571i | \(-0.275081\pi\) | ||||
0.649255 | + | 0.760571i | \(0.275081\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −31.8357 | −1.26536 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.63503 | −0.183936 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.68193 | −0.185505 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −37.7677 | −1.49407 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.4136 | −0.529806 | −0.264903 | − | 0.964275i | \(-0.585340\pi\) | ||||
−0.264903 | + | 0.964275i | \(0.585340\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.8052 | 0.938783 | 0.469392 | − | 0.882990i | \(-0.344473\pi\) | ||||
0.469392 | + | 0.882990i | \(0.344473\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.93674 | −0.351884 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 48.4580 | 1.90508 | 0.952540 | − | 0.304412i | \(-0.0984601\pi\) | ||||
0.952540 | + | 0.304412i | \(0.0984601\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.95463 | 0.233740 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −58.7737 | −2.30352 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.2351 | −0.870128 | −0.435064 | − | 0.900399i | \(-0.643274\pi\) | ||||
−0.435064 | + | 0.900399i | \(0.643274\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.5134 | 0.606158 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.28586 | 0.0501663 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.7072 | −0.417095 | −0.208547 | − | 0.978012i | \(-0.566874\pi\) | ||||
−0.208547 | + | 0.978012i | \(0.566874\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 44.7980 | 1.74244 | 0.871220 | − | 0.490893i | \(-0.163330\pi\) | ||||
0.871220 | + | 0.490893i | \(0.163330\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 39.5965 | 1.53780 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.10482 | −0.120400 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −51.5965 | −1.99782 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −36.3680 | −1.40607 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.50239 | 0.173813 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −43.2772 | −1.66821 | −0.834106 | − | 0.551604i | \(-0.814016\pi\) | ||||
−0.834106 | + | 0.551604i | \(0.814016\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.57664 | −0.253135 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.5330 | −0.443251 | −0.221625 | − | 0.975132i | \(-0.571136\pi\) | ||||
−0.221625 | + | 0.975132i | \(0.571136\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.92575 | −0.380915 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.0780 | 0.731072 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.916090 | 0.0350532 | 0.0175266 | − | 0.999846i | \(-0.494421\pi\) | ||||
0.0175266 | + | 0.999846i | \(0.494421\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.813048 | −0.0310650 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.216540 | −0.00826153 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.59960 | −0.175231 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.8278 | 0.564077 | 0.282039 | − | 0.959403i | \(-0.408989\pi\) | ||||
0.282039 | + | 0.959403i | \(0.408989\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 18.1285 | 0.688644 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.7687 | −0.484343 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21.8735 | 0.828517 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −27.3828 | −1.03571 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.1722 | −1.36620 | −0.683102 | − | 0.730323i | \(-0.739369\pi\) | ||||
−0.683102 | + | 0.730323i | \(0.739369\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.40652 | 0.0530481 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.21654 | 0.158804 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.37305 | −0.352510 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.4331 | −0.391823 | −0.195911 | − | 0.980622i | \(-0.562766\pi\) | ||||
−0.195911 | + | 0.980622i | \(0.562766\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 49.6233 | 1.86102 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −43.7470 | −1.63834 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.95942 | 0.0732783 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.43308 | −0.314939 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.73373 | −0.288420 | −0.144210 | − | 0.989547i | \(-0.546064\pi\) | ||||
−0.144210 | + | 0.989547i | \(0.546064\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.8102 | 0.700529 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 27.1354 | 1.00918 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.75669 | −0.288076 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.5241 | 1.46587 | 0.732934 | − | 0.680300i | \(-0.238151\pi\) | ||||
0.732934 | + | 0.680300i | \(0.238151\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −40.5373 | −1.50138 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.0831 | 0.890746 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −50.7498 | −1.87449 | −0.937243 | − | 0.348677i | \(-0.886631\pi\) | ||||
−0.937243 | + | 0.348677i | \(0.886631\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.59854 | −0.280277 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.4728 | 0.643619 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.419276 | 0.0154233 | 0.00771165 | − | 0.999970i | \(-0.497545\pi\) | ||||
0.00771165 | + | 0.999970i | \(0.497545\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.10482 | 0.187530 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.5511 | −0.717259 | −0.358630 | − | 0.933480i | \(-0.616756\pi\) | ||||
−0.358630 | + | 0.933480i | \(0.616756\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.7982 | 0.505529 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 46.8319 | 1.71349 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −63.2912 | −2.31261 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.76768 | −0.319937 | −0.159969 | − | 0.987122i | \(-0.551139\pi\) | ||||
−0.159969 | + | 0.987122i | \(0.551139\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 42.9732 | 1.56603 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.02269 | −0.182794 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 48.0535 | 1.74653 | 0.873267 | − | 0.487241i | \(-0.161997\pi\) | ||||
0.873267 | + | 0.487241i | \(0.161997\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 21.1533 | 0.767815 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.3947 | 1.06556 | 0.532779 | − | 0.846254i | \(-0.321148\pi\) | ||||
0.532779 | + | 0.846254i | \(0.321148\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.6768 | 0.531336 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 40.9931 | 1.48211 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.55875 | 0.345146 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.3790 | −0.482458 | −0.241229 | − | 0.970468i | \(-0.577551\pi\) | ||||
−0.241229 | + | 0.970468i | \(0.577551\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 43.5480 | 1.56834 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.133625 | −0.00480617 | −0.00240309 | − | 0.999997i | \(-0.500765\pi\) | ||||
−0.00240309 | + | 0.999997i | \(0.500765\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.57664 | −0.236240 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12.5697 | 0.450937 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.81995 | 0.101035 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.89545 | 0.282522 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 51.0130 | 1.82305 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.18695 | −0.256513 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.84060 | −0.172549 | −0.0862744 | − | 0.996271i | \(-0.527496\pi\) | ||||
−0.0862744 | + | 0.996271i | \(0.527496\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −43.8130 | −1.55979 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.7863 | 0.881299 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.22753 | 0.256657 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.46492 | −0.264753 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.6993 | −0.414410 | −0.207205 | − | 0.978298i | \(-0.566437\pi\) | ||||
−0.207205 | + | 0.978298i | \(0.566437\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.3629 | −0.401991 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.29685 | 0.151822 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.268814 | −0.00948624 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20.6529 | −0.727917 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 33.1593 | 1.16726 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −33.1987 | −1.16720 | −0.583601 | − | 0.812040i | \(-0.698357\pi\) | ||||
−0.583601 | + | 0.812040i | \(0.698357\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26.5766 | −0.933232 | −0.466616 | − | 0.884460i | \(-0.654527\pi\) | ||||
−0.466616 | + | 0.884460i | \(0.654527\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.22061 | 0.218166 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.25528 | 0.254141 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.10482 | 0.108624 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 29.1010 | 1.01687 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.5807 | −0.892773 | −0.446387 | − | 0.894840i | \(-0.647289\pi\) | ||||
−0.446387 | + | 0.894840i | \(0.647289\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.9783 | −0.452395 | −0.226198 | − | 0.974081i | \(-0.572629\pi\) | ||||
−0.226198 | + | 0.974081i | \(0.572629\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.18005 | 0.110715 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.5167 | −0.435248 | −0.217624 | − | 0.976033i | \(-0.569831\pi\) | ||||
−0.217624 | + | 0.976033i | \(0.569831\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.4391 | 0.675149 | 0.337574 | − | 0.941299i | \(-0.390394\pi\) | ||||
0.337574 | + | 0.941299i | \(0.390394\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 67.4124 | 2.33851 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.4769 | 0.709482 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.33129 | 0.253710 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 43.2522 | 1.49501 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 43.9972 | 1.51895 | 0.759475 | − | 0.650536i | \(-0.225456\pi\) | ||||
0.759475 | + | 0.650536i | \(0.225456\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31.1662 | 1.07470 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −73.9229 | −2.54604 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.85461 | −0.339009 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30.3632 | 1.04329 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −21.2591 | −0.729610 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.35601 | 0.320720 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.30374 | −0.113118 | −0.0565590 | − | 0.998399i | \(-0.518013\pi\) | ||||
−0.0565590 | + | 0.998399i | \(0.518013\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.28487 | 0.180739 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.02374 | 0.205767 | 0.102883 | − | 0.994693i | \(-0.467193\pi\) | ||||
0.102883 | + | 0.994693i | \(0.467193\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.0158 | −1.22884 | −0.614421 | − | 0.788978i | \(-0.710610\pi\) | ||||
−0.614421 | + | 0.788978i | \(0.710610\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 25.2012 | 0.858853 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −29.9250 | −1.01866 | −0.509329 | − | 0.860572i | \(-0.670106\pi\) | ||||
−0.509329 | + | 0.860572i | \(0.670106\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.77353 | 0.196306 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −124.247 | −4.21966 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.3739 | −0.351911 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.0485 | 0.950386 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16.8951 | 0.571813 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.10482 | −0.104962 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.618980 | −0.0209015 | −0.0104507 | − | 0.999945i | \(-0.503327\pi\) | ||||
−0.0104507 | + | 0.999945i | \(0.503327\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −69.5184 | −2.34480 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.2423 | −0.715672 | −0.357836 | − | 0.933784i | \(-0.616485\pi\) | ||||
−0.357836 | + | 0.933784i | \(0.616485\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48.8971 | −1.64552 | −0.822760 | − | 0.568389i | \(-0.807567\pi\) | ||||
−0.822760 | + | 0.568389i | \(0.807567\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15.5134 | 0.521477 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −58.2797 | −1.95684 | −0.978421 | − | 0.206622i | \(-0.933753\pi\) | ||||
−0.978421 | + | 0.206622i | \(0.933753\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.3909 | 0.482657 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.39757 | −0.113823 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.46492 | −0.0490216 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.48379 | −0.149877 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 33.9566 | 1.13378 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 51.0130 | 1.70138 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.1168 | 0.670187 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 27.7470 | 0.923361 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.73400 | 0.0908814 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.5154 | −1.21247 | −0.606237 | − | 0.795284i | \(-0.707322\pi\) | ||||
−0.606237 | + | 0.795284i | \(0.707322\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.9543 | 0.529172 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.62735 | −0.219574 | −0.109787 | − | 0.993955i | \(-0.535017\pi\) | ||||
−0.109787 | + | 0.993955i | \(0.535017\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.79036 | −0.324014 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.7299 | 0.387779 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −48.1662 | −1.59059 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.91688 | −0.261154 | −0.130577 | − | 0.991438i | \(-0.541683\pi\) | ||||
−0.130577 | + | 0.991438i | \(0.541683\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.6210 | −0.415877 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.6743 | 0.417179 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.40652 | 0.0462462 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −32.0178 | −1.05160 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35.8597 | 1.17652 | 0.588259 | − | 0.808673i | \(-0.299814\pi\) | ||||
0.588259 | + | 0.808673i | \(0.299814\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.63990 | 0.0865192 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −45.2254 | −1.48061 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.56974 | −0.280260 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.4420 | −0.373793 | −0.186896 | − | 0.982380i | \(-0.559843\pi\) | ||||
−0.186896 | + | 0.982380i | \(0.559843\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −71.3236 | −2.32756 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.360100 | 0.0117389 | 0.00586945 | − | 0.999983i | \(-0.498132\pi\) | ||||
0.00586945 | + | 0.999983i | \(0.498132\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.7579 | 0.610843 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 20.4193 | 0.664239 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.63807 | 0.0857256 | 0.0428628 | − | 0.999081i | \(-0.486352\pi\) | ||||
0.0428628 | + | 0.999081i | \(0.486352\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.431517 | −0.0140076 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −78.8084 | −2.55554 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.4430 | 0.338282 | 0.169141 | − | 0.985592i | \(-0.445901\pi\) | ||||
0.169141 | + | 0.985592i | \(0.445901\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.7230 | 0.573503 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −24.6667 | −0.797360 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.52437 | 0.0815160 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.2522 | 0.395232 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 107.731 | 3.47159 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13.5371 | −0.435775 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −33.2732 | −1.06999 | −0.534996 | − | 0.844854i | \(-0.679687\pi\) | ||||
−0.534996 | + | 0.844854i | \(0.679687\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −22.3264 | −0.717228 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.5657 | 0.756258 | 0.378129 | − | 0.925753i | \(-0.376568\pi\) | ||||
0.378129 | + | 0.925753i | \(0.376568\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 39.6444 | 1.27094 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.10482 | 0.163485 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.402439 | 0.0128752 | 0.00643759 | − | 0.999979i | \(-0.497951\pi\) | ||||
0.00643759 | + | 0.999979i | \(0.497951\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.898271 | −0.0287089 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −24.9821 | −0.797617 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.4927 | −0.366561 | −0.183281 | − | 0.983061i | \(-0.558672\pi\) | ||||
−0.183281 | + | 0.983061i | \(0.558672\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.5134 | 0.685473 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −13.0916 | −0.416710 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.6529 | 0.656723 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.05761 | −0.192426 | −0.0962132 | − | 0.995361i | \(-0.530673\pi\) | ||||
−0.0962132 | + | 0.995361i | \(0.530673\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.5292 | −0.429335 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.09410 | −0.224898 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 48.1086 | 1.52362 | 0.761808 | − | 0.647803i | \(-0.224312\pi\) | ||||
0.761808 | + | 0.647803i | \(0.224312\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.25020 | −0.292663 |
(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 | 6080.2.a.ch.1.1 | 4 | ||
4.3 | odd | 2 | 6080.2.a.cc.1.4 | 4 | |||
8.3 | odd | 2 | 95.2.a.b.1.2 | ✓ | 4 | ||
8.5 | even | 2 | 1520.2.a.t.1.4 | 4 | |||
24.11 | even | 2 | 855.2.a.m.1.3 | 4 | |||
40.3 | even | 4 | 475.2.b.e.324.7 | 8 | |||
40.19 | odd | 2 | 475.2.a.i.1.3 | 4 | |||
40.27 | even | 4 | 475.2.b.e.324.2 | 8 | |||
40.29 | even | 2 | 7600.2.a.cf.1.1 | 4 | |||
56.27 | even | 2 | 4655.2.a.y.1.2 | 4 | |||
120.59 | even | 2 | 4275.2.a.bo.1.2 | 4 | |||
152.75 | even | 2 | 1805.2.a.p.1.3 | 4 | |||
760.379 | even | 2 | 9025.2.a.bf.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.a.b.1.2 | ✓ | 4 | 8.3 | odd | 2 | ||
475.2.a.i.1.3 | 4 | 40.19 | odd | 2 | |||
475.2.b.e.324.2 | 8 | 40.27 | even | 4 | |||
475.2.b.e.324.7 | 8 | 40.3 | even | 4 | |||
855.2.a.m.1.3 | 4 | 24.11 | even | 2 | |||
1520.2.a.t.1.4 | 4 | 8.5 | even | 2 | |||
1805.2.a.p.1.3 | 4 | 152.75 | even | 2 | |||
4275.2.a.bo.1.2 | 4 | 120.59 | even | 2 | |||
4655.2.a.y.1.2 | 4 | 56.27 | even | 2 | |||
6080.2.a.cc.1.4 | 4 | 4.3 | odd | 2 | |||
6080.2.a.ch.1.1 | 4 | 1.1 | even | 1 | trivial | ||
7600.2.a.cf.1.1 | 4 | 40.29 | even | 2 | |||
9025.2.a.bf.1.2 | 4 | 760.379 | even | 2 |