Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2960,2,Mod(1,2960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2960, 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("2960.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2960 = 2^{4} \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2960.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: | \(23.6357189983\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.583504.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 8x^{3} - 2x^{2} + 15x + 8 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1480) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.44679\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2960.1 |
$q$-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 | ||||||||
\(3\) | 2.44679 | 1.41265 | 0.706326 | − | 0.707886i | \(-0.250351\pi\) | ||||
0.706326 | + | 0.707886i | \(0.250351\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.02963 | 1.52306 | 0.761529 | − | 0.648131i | \(-0.224449\pi\) | ||||
0.761529 | + | 0.648131i | \(0.224449\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.98676 | 0.995587 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.17769 | −0.355088 | −0.177544 | − | 0.984113i | \(-0.556815\pi\) | ||||
−0.177544 | + | 0.984113i | \(0.556815\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.60200 | 1.55371 | 0.776857 | − | 0.629677i | \(-0.216813\pi\) | ||||
0.776857 | + | 0.629677i | \(0.216813\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.44679 | 0.631757 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.00455 | −0.728711 | −0.364356 | − | 0.931260i | \(-0.618711\pi\) | ||||
−0.364356 | + | 0.931260i | \(0.618711\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.62448 | −0.372681 | −0.186341 | − | 0.982485i | \(-0.559663\pi\) | ||||
−0.186341 | + | 0.982485i | \(0.559663\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.85964 | 2.15155 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.296128 | 0.0617469 | 0.0308735 | − | 0.999523i | \(-0.490171\pi\) | ||||
0.0308735 | + | 0.999523i | \(0.490171\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.0323921 | −0.00623386 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.296128 | 0.0549896 | 0.0274948 | − | 0.999622i | \(-0.491247\pi\) | ||||
0.0274948 | + | 0.999622i | \(0.491247\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.77199 | 0.318258 | 0.159129 | − | 0.987258i | \(-0.449131\pi\) | ||||
0.159129 | + | 0.987258i | \(0.449131\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.88157 | −0.501616 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.02963 | 0.681132 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 13.7069 | 2.19486 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.17769 | −0.183925 | −0.0919625 | − | 0.995762i | \(-0.529314\pi\) | ||||
−0.0919625 | + | 0.995762i | \(0.529314\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.07995 | 0.774685 | 0.387343 | − | 0.921936i | \(-0.373393\pi\) | ||||
0.387343 | + | 0.921936i | \(0.373393\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.98676 | 0.445240 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.94968 | 0.721985 | 0.360993 | − | 0.932569i | \(-0.382438\pi\) | ||||
0.360993 | + | 0.932569i | \(0.382438\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.23792 | 1.31970 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.35150 | −1.02942 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.75086 | −1.20202 | −0.601012 | − | 0.799240i | \(-0.705236\pi\) | ||||
−0.601012 | + | 0.799240i | \(0.705236\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.17769 | −0.158800 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.97476 | −0.526469 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.72482 | −0.875497 | −0.437748 | − | 0.899098i | \(-0.644224\pi\) | ||||
−0.437748 | + | 0.899098i | \(0.644224\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.22469 | −1.05306 | −0.526532 | − | 0.850156i | \(-0.676508\pi\) | ||||
−0.526532 | + | 0.850156i | \(0.676508\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 12.0355 | 1.51634 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.60200 | 0.694842 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.5238 | 1.65220 | 0.826100 | − | 0.563523i | \(-0.190555\pi\) | ||||
0.826100 | + | 0.563523i | \(0.190555\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.724561 | 0.0872269 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.2719 | −1.45641 | −0.728206 | − | 0.685359i | \(-0.759646\pi\) | ||||
−0.728206 | + | 0.685359i | \(0.759646\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.74015 | −0.320711 | −0.160355 | − | 0.987059i | \(-0.551264\pi\) | ||||
−0.160355 | + | 0.987059i | \(0.551264\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.44679 | 0.282531 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.74568 | −0.540820 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.18305 | −0.695647 | −0.347824 | − | 0.937560i | \(-0.613079\pi\) | ||||
−0.347824 | + | 0.937560i | \(0.613079\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.03954 | −1.00439 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.4851 | 1.58995 | 0.794973 | − | 0.606645i | \(-0.207485\pi\) | ||||
0.794973 | + | 0.606645i | \(0.207485\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.00455 | −0.325890 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.724561 | 0.0776811 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.13921 | −0.544755 | −0.272378 | − | 0.962190i | \(-0.587810\pi\) | ||||
−0.272378 | + | 0.962190i | \(0.587810\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 22.5740 | 2.36640 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.33567 | 0.449588 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.62448 | −0.166668 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.32201 | −0.337299 | −0.168649 | − | 0.985676i | \(-0.553941\pi\) | ||||
−0.168649 | + | 0.985676i | \(0.553941\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.51749 | −0.353521 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.9694 | −1.39001 | −0.695003 | − | 0.719007i | \(-0.744597\pi\) | ||||
−0.695003 | + | 0.719007i | \(0.744597\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.19489 | 0.708933 | 0.354467 | − | 0.935069i | \(-0.384662\pi\) | ||||
0.354467 | + | 0.935069i | \(0.384662\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.85964 | 0.962203 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.11468 | 0.204434 | 0.102217 | − | 0.994762i | \(-0.467406\pi\) | ||||
0.102217 | + | 0.994762i | \(0.467406\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.97352 | −0.189029 | −0.0945146 | − | 0.995523i | \(-0.530130\pi\) | ||||
−0.0945146 | + | 0.995523i | \(0.530130\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.44679 | −0.232239 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.7969 | 1.39197 | 0.695987 | − | 0.718054i | \(-0.254967\pi\) | ||||
0.695987 | + | 0.718054i | \(0.254967\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.296128 | 0.0276141 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 16.7318 | 1.54686 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.1072 | −1.10987 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.61304 | −0.873912 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.88157 | −0.259822 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.20633 | −0.195780 | −0.0978902 | − | 0.995197i | \(-0.531209\pi\) | ||||
−0.0978902 | + | 0.995197i | \(0.531209\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.4296 | 1.09436 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.4433 | 1.17455 | 0.587273 | − | 0.809389i | \(-0.300202\pi\) | ||||
0.587273 | + | 0.809389i | \(0.300202\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.54606 | −0.567615 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.0323921 | −0.00278787 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.0328 | −1.54064 | −0.770322 | − | 0.637655i | \(-0.779905\pi\) | ||||
−0.770322 | + | 0.637655i | \(0.779905\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.5238 | −1.31671 | −0.658356 | − | 0.752707i | \(-0.728748\pi\) | ||||
−0.658356 | + | 0.752707i | \(0.728748\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.1108 | 1.01991 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.59744 | −0.551706 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.296128 | 0.0245921 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 22.6032 | 1.86428 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.75322 | −0.553245 | −0.276622 | − | 0.960979i | \(-0.589215\pi\) | ||||
−0.276622 | + | 0.960979i | \(0.589215\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.547291 | 0.0445379 | 0.0222690 | − | 0.999752i | \(-0.492911\pi\) | ||||
0.0222690 | + | 0.999752i | \(0.492911\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.97389 | −0.725496 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.77199 | 0.142329 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.34338 | 0.187022 | 0.0935112 | − | 0.995618i | \(-0.470191\pi\) | ||||
0.0935112 | + | 0.995618i | \(0.470191\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −21.4115 | −1.69804 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.19329 | 0.0940441 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.1218 | 1.81104 | 0.905521 | − | 0.424301i | \(-0.139480\pi\) | ||||
0.905521 | + | 0.424301i | \(0.139480\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.88157 | −0.224330 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.38127 | −0.106886 | −0.0534428 | − | 0.998571i | \(-0.517019\pi\) | ||||
−0.0534428 | + | 0.998571i | \(0.517019\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18.3824 | 1.41403 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.85194 | −0.371037 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.55956 | −0.118571 | −0.0592856 | − | 0.998241i | \(-0.518882\pi\) | ||||
−0.0592856 | + | 0.998241i | \(0.518882\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.02963 | 0.304611 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −16.4542 | −1.23677 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.8075 | −1.25625 | −0.628127 | − | 0.778111i | \(-0.716178\pi\) | ||||
−0.628127 | + | 0.778111i | \(0.716178\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.7267 | −1.09463 | −0.547315 | − | 0.836927i | \(-0.684350\pi\) | ||||
−0.547315 | + | 0.836927i | \(0.684350\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.1240 | −1.48761 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.00000 | −0.0735215 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.53845 | 0.258757 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.130528 | −0.00949453 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.1417 | 1.45740 | 0.728700 | − | 0.684833i | \(-0.240125\pi\) | ||||
0.728700 | + | 0.684833i | \(0.240125\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.9057 | 1.72077 | 0.860384 | − | 0.509647i | \(-0.170224\pi\) | ||||
0.860384 | + | 0.509647i | \(0.170224\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 13.7069 | 0.981571 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.44623 | −0.245533 | −0.122767 | − | 0.992436i | \(-0.539177\pi\) | ||||
−0.122767 | + | 0.992436i | \(0.539177\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.3788 | 1.72816 | 0.864082 | − | 0.503351i | \(-0.167900\pi\) | ||||
0.864082 | + | 0.503351i | \(0.167900\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 33.0899 | 2.33398 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.19329 | 0.0837522 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.17769 | −0.0822538 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.884463 | 0.0614744 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.91314 | 0.132335 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.98579 | 0.480922 | 0.240461 | − | 0.970659i | \(-0.422701\pi\) | ||||
0.240461 | + | 0.970659i | \(0.422701\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −30.0268 | −2.05740 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.07995 | 0.346450 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.14045 | 0.484725 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.70457 | −0.453053 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.8315 | −1.13221 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.545824 | −0.0365511 | −0.0182755 | − | 0.999833i | \(-0.505818\pi\) | ||||
−0.0182755 | + | 0.999833i | \(0.505818\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.98676 | 0.199117 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.650399 | 0.0431685 | 0.0215842 | − | 0.999767i | \(-0.493129\pi\) | ||||
0.0215842 | + | 0.999767i | \(0.493129\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 28.8995 | 1.90973 | 0.954865 | − | 0.297041i | \(-0.0959998\pi\) | ||||
0.954865 | + | 0.297041i | \(0.0959998\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.6117 | −0.763991 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.8787 | 0.843710 | 0.421855 | − | 0.906663i | \(-0.361379\pi\) | ||||
0.421855 | + | 0.906663i | \(0.361379\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.94968 | 0.322882 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.1286 | −0.982708 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.05982 | 0.456662 | 0.228331 | − | 0.973584i | \(-0.426673\pi\) | ||||
0.228331 | + | 0.973584i | \(0.426673\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0328 | −0.646268 | −0.323134 | − | 0.946353i | \(-0.604737\pi\) | ||||
−0.323134 | + | 0.946353i | \(0.604737\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.0206 | −1.41263 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.23792 | 0.590189 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.10034 | −0.579041 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 35.4419 | 2.24604 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.3965 | −1.53989 | −0.769945 | − | 0.638110i | \(-0.779717\pi\) | ||||
−0.769945 | + | 0.638110i | \(0.779717\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.348748 | −0.0219256 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.35150 | −0.460369 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.4001 | 0.898255 | 0.449127 | − | 0.893468i | \(-0.351735\pi\) | ||||
0.449127 | + | 0.893468i | \(0.351735\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.02963 | −0.250389 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.884463 | 0.0547469 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.6475 | −1.02653 | −0.513263 | − | 0.858231i | \(-0.671564\pi\) | ||||
−0.513263 | + | 0.858231i | \(0.671564\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.75086 | −0.537561 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.5746 | −0.769550 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.76410 | −0.412415 | −0.206207 | − | 0.978508i | \(-0.566112\pi\) | ||||
−0.206207 | + | 0.978508i | \(0.566112\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −29.2728 | −1.77820 | −0.889098 | − | 0.457717i | \(-0.848667\pi\) | ||||
−0.889098 | + | 0.457717i | \(0.848667\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 55.2337 | 3.34290 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.17769 | −0.0710177 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.96046 | 0.117793 | 0.0588963 | − | 0.998264i | \(-0.481242\pi\) | ||||
0.0588963 | + | 0.998264i | \(0.481242\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.29250 | 0.316854 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −32.1268 | −1.91652 | −0.958261 | − | 0.285894i | \(-0.907709\pi\) | ||||
−0.958261 | + | 0.285894i | \(0.907709\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.0540 | −1.48931 | −0.744653 | − | 0.667452i | \(-0.767385\pi\) | ||||
−0.744653 | + | 0.667452i | \(0.767385\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.97476 | −0.235444 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.74568 | −0.280128 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.97265 | −0.468980 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.12824 | −0.476486 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.674408 | 0.0393994 | 0.0196997 | − | 0.999806i | \(-0.493729\pi\) | ||||
0.0196997 | + | 0.999806i | \(0.493729\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.72482 | −0.391534 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.0381480 | 0.00221357 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.65891 | 0.0959371 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.4703 | 1.17989 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −34.1801 | −1.96360 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.22469 | −0.470944 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.87824 | −0.506708 | −0.253354 | − | 0.967374i | \(-0.581534\pi\) | ||||
−0.253354 | + | 0.967374i | \(0.581534\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.6044 | 1.00148 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.3016 | −0.584149 | −0.292074 | − | 0.956396i | \(-0.594345\pi\) | ||||
−0.292074 | + | 0.956396i | \(0.594345\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.2633 | −0.862730 | −0.431365 | − | 0.902177i | \(-0.641968\pi\) | ||||
−0.431365 | + | 0.902177i | \(0.641968\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 12.0355 | 0.678126 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.2751 | 0.970266 | 0.485133 | − | 0.874440i | \(-0.338771\pi\) | ||||
0.485133 | + | 0.874440i | \(0.338771\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.348748 | −0.0195261 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.17417 | 0.288794 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.88084 | 0.271577 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.60200 | 0.310743 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.82879 | −0.267033 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 19.9454 | 1.09962 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.17696 | 0.449446 | 0.224723 | − | 0.974423i | \(-0.427852\pi\) | ||||
0.224723 | + | 0.974423i | \(0.427852\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.98676 | −0.163674 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 13.5238 | 0.738886 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.2723 | 0.886407 | 0.443204 | − | 0.896421i | \(-0.353842\pi\) | ||||
0.443204 | + | 0.896421i | \(0.353842\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 36.2048 | 1.96638 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.08686 | −0.113010 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.01801 | 0.486927 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.724561 | 0.0390091 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 32.2492 | 1.73123 | 0.865614 | − | 0.500712i | \(-0.166928\pi\) | ||||
0.865614 | + | 0.500712i | \(0.166928\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.6373 | 1.37233 | 0.686165 | − | 0.727446i | \(-0.259293\pi\) | ||||
0.686165 | + | 0.727446i | \(0.259293\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.181461 | −0.00968565 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.408344 | −0.0217340 | −0.0108670 | − | 0.999941i | \(-0.503459\pi\) | ||||
−0.0108670 | + | 0.999941i | \(0.503459\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.2719 | −0.651327 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −29.6238 | −1.56786 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.3792 | 1.49780 | 0.748899 | − | 0.662684i | \(-0.230583\pi\) | ||||
0.748899 | + | 0.662684i | \(0.230583\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.3611 | −0.861109 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −23.5210 | −1.23453 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.74015 | −0.143426 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −27.3615 | −1.42826 | −0.714129 | − | 0.700015i | \(-0.753177\pi\) | ||||
−0.714129 | + | 0.700015i | \(0.753177\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.51749 | −0.183113 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −35.2627 | −1.83075 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.74534 | −0.452817 | −0.226408 | − | 0.974032i | \(-0.572698\pi\) | ||||
−0.226408 | + | 0.974032i | \(0.572698\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.44679 | 0.126351 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.65891 | 0.0854381 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.13879 | 0.109862 | 0.0549311 | − | 0.998490i | \(-0.482506\pi\) | ||||
0.0549311 | + | 0.998490i | \(0.482506\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.39843 | −0.276570 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.8905 | 0.658674 | 0.329337 | − | 0.944212i | \(-0.393175\pi\) | ||||
0.329337 | + | 0.944212i | \(0.393175\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.74568 | −0.241862 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 15.1726 | 0.771267 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.6843 | −1.15014 | −0.575070 | − | 0.818104i | \(-0.695025\pi\) | ||||
−0.575070 | + | 0.818104i | \(0.695025\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.889732 | −0.0449957 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 32.8929 | 1.65922 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.18305 | −0.311103 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.2430 | 0.915590 | 0.457795 | − | 0.889058i | \(-0.348639\pi\) | ||||
0.457795 | + | 0.889058i | \(0.348639\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −16.0168 | −0.801843 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.9586 | −0.796936 | −0.398468 | − | 0.917182i | \(-0.630458\pi\) | ||||
−0.398468 | + | 0.917182i | \(0.630458\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.92666 | 0.494482 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.03954 | −0.449178 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.17769 | 0.0583762 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.8296 | 1.22775 | 0.613873 | − | 0.789405i | \(-0.289611\pi\) | ||||
0.613873 | + | 0.789405i | \(0.289611\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −44.1224 | −2.17640 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −27.0985 | −1.33343 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.4851 | 0.711045 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −37.9834 | −1.86006 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 37.6102 | 1.83738 | 0.918690 | − | 0.394979i | \(-0.129248\pi\) | ||||
0.918690 | + | 0.394979i | \(0.129248\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.1100 | 0.736417 | 0.368209 | − | 0.929743i | \(-0.379971\pi\) | ||||
0.368209 | + | 0.929743i | \(0.379971\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 14.7835 | 0.718799 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.00455 | −0.145742 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −33.1424 | −1.60388 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −16.1425 | −0.779369 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.865719 | 0.0417002 | 0.0208501 | − | 0.999783i | \(-0.493363\pi\) | ||||
0.0208501 | + | 0.999783i | \(0.493363\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.55956 | −0.267175 | −0.133588 | − | 0.991037i | \(-0.542650\pi\) | ||||
−0.133588 | + | 0.991037i | \(0.542650\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.724561 | 0.0347401 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.481054 | −0.0230119 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.2925 | −1.01624 | −0.508118 | − | 0.861288i | \(-0.669659\pi\) | ||||
−0.508118 | + | 0.861288i | \(0.669659\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 27.5915 | 1.31388 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.1283 | 1.24139 | 0.620697 | − | 0.784051i | \(-0.286850\pi\) | ||||
0.620697 | + | 0.784051i | \(0.286850\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.13921 | −0.243622 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.5237 | −0.781543 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.2599 | −0.767354 | −0.383677 | − | 0.923467i | \(-0.625342\pi\) | ||||
−0.383677 | + | 0.923467i | \(0.625342\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.38696 | 0.0653096 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.33910 | 0.0629166 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 22.5740 | 1.05828 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.1519 | −1.08300 | −0.541500 | − | 0.840701i | \(-0.682143\pi\) | ||||
−0.541500 | + | 0.840701i | \(0.682143\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.0973239 | 0.00454269 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.8787 | −0.972417 | −0.486208 | − | 0.873843i | \(-0.661620\pi\) | ||||
−0.486208 | + | 0.873843i | \(0.661620\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.7785 | −0.826239 | −0.413120 | − | 0.910677i | \(-0.635561\pi\) | ||||
−0.413120 | + | 0.910677i | \(0.635561\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.33567 | 0.201062 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 31.6443 | 1.46432 | 0.732161 | − | 0.681132i | \(-0.238512\pi\) | ||||
0.732161 | + | 0.681132i | \(0.238512\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 54.4961 | 2.51640 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.73376 | 0.264198 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.98263 | −0.275082 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.62448 | −0.0745363 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −26.1367 | −1.19672 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 28.2547 | 1.29099 | 0.645495 | − | 0.763764i | \(-0.276651\pi\) | ||||
0.645495 | + | 0.763764i | \(0.276651\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.60200 | −0.255429 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.91971 | 0.132852 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.32201 | −0.150844 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.75156 | 0.260628 | 0.130314 | − | 0.991473i | \(-0.458401\pi\) | ||||
0.130314 | + | 0.991473i | \(0.458401\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 56.5742 | 2.55837 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.55420 | 0.160399 | 0.0801994 | − | 0.996779i | \(-0.474444\pi\) | ||||
0.0801994 | + | 0.996779i | \(0.474444\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.889732 | −0.0400715 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.51749 | −0.158100 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −49.4514 | −2.21820 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.1842 | 0.724503 | 0.362251 | − | 0.932080i | \(-0.382008\pi\) | ||||
0.362251 | + | 0.932080i | \(0.382008\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.37966 | −0.150992 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13.1447 | −0.586095 | −0.293047 | − | 0.956098i | \(-0.594669\pi\) | ||||
−0.293047 | + | 0.956098i | \(0.594669\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.9694 | −0.621630 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 44.9778 | 1.99753 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −26.1677 | −1.15986 | −0.579932 | − | 0.814665i | \(-0.696921\pi\) | ||||
−0.579932 | + | 0.814665i | \(0.696921\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.0418 | −0.488461 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.0526204 | 0.00232325 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.19489 | 0.317045 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.82921 | −0.256368 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.81591 | −0.167500 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.98369 | 0.437393 | 0.218697 | − | 0.975793i | \(-0.429819\pi\) | ||||
0.218697 | + | 0.975793i | \(0.429819\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −32.1916 | −1.40764 | −0.703819 | − | 0.710379i | \(-0.748523\pi\) | ||||
−0.703819 | + | 0.710379i | \(0.748523\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.85964 | 0.430310 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.32403 | −0.231918 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9123 | −0.996187 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −20.0854 | −0.871633 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.59744 | −0.285767 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.11468 | 0.0914256 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −41.1244 | −1.77465 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.8795 | −0.468611 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.3904 | −1.26359 | −0.631795 | − | 0.775135i | \(-0.717682\pi\) | ||||
−0.631795 | + | 0.775135i | \(0.717682\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −36.0332 | −1.54633 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.97352 | −0.0845364 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.6104 | 1.35156 | 0.675781 | − | 0.737102i | \(-0.263806\pi\) | ||||
0.675781 | + | 0.737102i | \(0.263806\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −24.5652 | −1.04842 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.481054 | −0.0204936 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24.9154 | −1.05951 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.44679 | −0.103860 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −39.6014 | −1.67796 | −0.838982 | − | 0.544158i | \(-0.816849\pi\) | ||||
−0.838982 | + | 0.544158i | \(0.816849\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 28.4579 | 1.20364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.65782 | 0.365534 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 37.9329 | 1.59868 | 0.799341 | − | 0.600878i | \(-0.205182\pi\) | ||||
0.799341 | + | 0.600878i | \(0.205182\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.7969 | 0.622510 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −36.4260 | −1.52975 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.36977 | 0.141268 | 0.0706341 | − | 0.997502i | \(-0.477498\pi\) | ||||
0.0706341 | + | 0.997502i | \(0.477498\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.53861 | 0.315481 | 0.157740 | − | 0.987481i | \(-0.449579\pi\) | ||||
0.157740 | + | 0.987481i | \(0.449579\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 49.2824 | 2.05880 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.296128 | 0.0123494 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.5226 | −1.39556 | −0.697781 | − | 0.716311i | \(-0.745829\pi\) | ||||
−0.697781 | + | 0.716311i | \(0.745829\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 58.4920 | 2.43085 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 58.3696 | 2.42158 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.3058 | 0.426825 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 16.7318 | 0.691776 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.3785 | −0.510917 | −0.255458 | − | 0.966820i | \(-0.582226\pi\) | ||||
−0.255458 | + | 0.966820i | \(0.582226\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.87856 | −0.118609 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.43218 | −0.346853 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 32.6703 | 1.34161 | 0.670805 | − | 0.741634i | \(-0.265949\pi\) | ||||
0.670805 | + | 0.741634i | \(0.265949\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.1072 | −0.496349 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 59.6496 | 2.44130 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.1132 | −0.821801 | −0.410901 | − | 0.911680i | \(-0.634786\pi\) | ||||
−0.410901 | + | 0.911680i | \(0.634786\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.58291 | −0.105359 | −0.0526796 | − | 0.998611i | \(-0.516776\pi\) | ||||
−0.0526796 | + | 0.998611i | \(0.516776\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 40.3925 | 1.64491 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.61304 | −0.390825 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.1629 | −0.615443 | −0.307721 | − | 0.951477i | \(-0.599566\pi\) | ||||
−0.307721 | + | 0.951477i | \(0.599566\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.91971 | 0.118313 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 27.7281 | 1.12176 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −38.2949 | −1.54672 | −0.773358 | − | 0.633970i | \(-0.781424\pi\) | ||||
−0.773358 | + | 0.633970i | \(0.781424\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.88157 | −0.116196 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.89672 | 0.398427 | 0.199213 | − | 0.979956i | \(-0.436161\pi\) | ||||
0.199213 | + | 0.979956i | \(0.436161\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −35.3052 | −1.41904 | −0.709519 | − | 0.704686i | \(-0.751088\pi\) | ||||
−0.709519 | + | 0.704686i | \(0.751088\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.00959221 | −0.000384922 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −20.7091 | −0.829694 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.68105 | 0.186943 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.00455 | 0.119799 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.03196 | −0.160510 | −0.0802549 | − | 0.996774i | \(-0.525573\pi\) | ||||
−0.0802549 | + | 0.996774i | \(0.525573\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.0927 | 0.679375 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.20633 | −0.0875557 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 51.7508 | 2.05044 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −36.6534 | −1.44998 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.6080 | −0.497985 | −0.248992 | − | 0.968505i | \(-0.580099\pi\) | ||||
−0.248992 | + | 0.968505i | \(0.580099\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.9553 | 0.432035 | 0.216017 | − | 0.976390i | \(-0.430693\pi\) | ||||
0.216017 | + | 0.976390i | \(0.430693\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.4296 | 0.489413 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.3667 | −0.682755 | −0.341378 | − | 0.939926i | \(-0.610894\pi\) | ||||
−0.341378 | + | 0.939926i | \(0.610894\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.91978 | 0.310879 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17.4711 | 0.684748 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 43.5326 | 1.70356 | 0.851780 | − | 0.523899i | \(-0.175523\pi\) | ||||
0.851780 | + | 0.523899i | \(0.175523\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.4433 | 0.525273 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.18418 | −0.319295 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.21899 | −0.164348 | −0.0821742 | − | 0.996618i | \(-0.526186\pi\) | ||||
−0.0821742 | + | 0.996618i | \(0.526186\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 44.6587 | 1.73702 | 0.868511 | − | 0.495671i | \(-0.165078\pi\) | ||||
0.868511 | + | 0.495671i | \(0.165078\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −41.1831 | −1.59942 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.54606 | −0.253845 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.0876917 | 0.00339544 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.33551 | −0.0516340 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.68617 | 0.373930 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.7726 | 1.03201 | 0.516004 | − | 0.856586i | \(-0.327419\pi\) | ||||
0.516004 | + | 0.856586i | \(0.327419\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.0323921 | −0.00124677 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.5201 | −0.442752 | −0.221376 | − | 0.975189i | \(-0.571055\pi\) | ||||
−0.221376 | + | 0.975189i | \(0.571055\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.3865 | −0.513725 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.59139 | 0.0609820 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.1654 | 0.618553 | 0.309276 | − | 0.950972i | \(-0.399913\pi\) | ||||
0.309276 | + | 0.950972i | \(0.399913\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.0328 | −0.688997 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 70.7108 | 2.69778 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −49.0223 | −1.86760 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.9079 | −1.40404 | −0.702021 | − | 0.712156i | \(-0.747719\pi\) | ||||
−0.702021 | + | 0.712156i | \(0.747719\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −14.1742 | −0.538433 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.5238 | −0.588851 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.53845 | 0.134028 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 31.5114 | 1.19187 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.93275 | −0.224077 | −0.112038 | − | 0.993704i | \(-0.535738\pi\) | ||||
−0.112038 | + | 0.993704i | \(0.535738\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.62448 | 0.0612684 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.1108 | 0.456119 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −56.2915 | −2.11706 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.9746 | −0.449717 | −0.224859 | − | 0.974391i | \(-0.572192\pi\) | ||||
−0.224859 | + | 0.974391i | \(0.572192\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −18.4673 | −0.692578 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.524734 | 0.0196514 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.59744 | −0.246730 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 17.2739 | 0.645105 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.2521 | 0.494221 | 0.247110 | − | 0.968987i | \(-0.420519\pi\) | ||||
0.247110 | + | 0.968987i | \(0.420519\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28.9927 | 1.07975 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −24.5481 | −0.912953 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.296128 | 0.0109979 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.62112 | −0.245564 | −0.122782 | − | 0.992434i | \(-0.539182\pi\) | ||||
−0.122782 | + | 0.992434i | \(0.539182\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.7612 | −0.991155 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.2630 | −0.564522 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.5783 | −1.05556 | −0.527782 | − | 0.849380i | \(-0.676976\pi\) | ||||
−0.527782 | + | 0.849380i | \(0.676976\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 22.6032 | 0.833732 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15.9270 | −0.586677 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.4227 | 1.19269 | 0.596345 | − | 0.802728i | \(-0.296619\pi\) | ||||
0.596345 | + | 0.802728i | \(0.296619\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −22.2666 | −0.817983 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −37.1096 | −1.36142 | −0.680709 | − | 0.732554i | \(-0.738328\pi\) | ||||
−0.680709 | + | 0.732554i | \(0.738328\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.75322 | −0.247419 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 43.2635 | 1.58293 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.52138 | 0.311364 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −46.4524 | −1.69507 | −0.847537 | − | 0.530736i | \(-0.821915\pi\) | ||||
−0.847537 | + | 0.530736i | \(0.821915\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −59.6929 | −2.17533 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.547291 | 0.0199180 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.2429 | 0.554013 | 0.277006 | − | 0.960868i | \(-0.410658\pi\) | ||||
0.277006 | + | 0.960868i | \(0.410658\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.853312 | −0.0309733 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.4577 | −1.39409 | −0.697046 | − | 0.717027i | \(-0.745502\pi\) | ||||
−0.697046 | + | 0.717027i | \(0.745502\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.95257 | −0.287902 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.97389 | −0.324452 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −37.6724 | −1.36027 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 52.5072 | 1.89346 | 0.946728 | − | 0.322033i | \(-0.104366\pi\) | ||||
0.946728 | + | 0.322033i | \(0.104366\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 35.2340 | 1.26892 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.4944 | 0.485361 | 0.242680 | − | 0.970106i | \(-0.421973\pi\) | ||||
0.242680 | + | 0.970106i | \(0.421973\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.77199 | 0.0636516 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.85964 | −0.353713 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.91314 | 0.0685454 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.4526 | 0.517155 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.00959221 | −0.000342797 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.34338 | 0.0836390 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.5231 | 1.62272 | 0.811362 | − | 0.584545i | \(-0.198727\pi\) | ||||
0.811362 | + | 0.584545i | \(0.198727\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −40.7328 | −1.45013 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 59.6260 | 2.12006 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −46.0747 | −1.63616 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −21.4115 | −0.759387 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.3244 | −0.684504 | −0.342252 | − | 0.939608i | \(-0.611190\pi\) | ||||
−0.342252 | + | 0.939608i | \(0.611190\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.8716 | −0.526119 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.3496 | −0.542351 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.22706 | 0.113881 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.19329 | 0.0420578 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.5503 | −0.582598 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.79985 | 0.0632795 | 0.0316398 | − | 0.999499i | \(-0.489927\pi\) | ||||
0.0316398 | + | 0.999499i | \(0.489927\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.0856 | −0.494611 | −0.247306 | − | 0.968938i | \(-0.579545\pi\) | ||||
−0.247306 | + | 0.968938i | \(0.579545\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −71.6243 | −2.51197 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 23.1218 | 0.809923 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.25228 | −0.288711 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 67.4231 | 2.35595 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.1677 | −0.354856 | −0.177428 | − | 0.984134i | \(-0.556778\pi\) | ||||
−0.177428 | + | 0.984134i | \(0.556778\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.4606 | −0.922359 | −0.461179 | − | 0.887307i | \(-0.652574\pi\) | ||||
−0.461179 | + | 0.887307i | \(0.652574\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.88157 | −0.100323 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34.6037 | −1.20329 | −0.601645 | − | 0.798764i | \(-0.705488\pi\) | ||||
−0.601645 | + | 0.798764i | \(0.705488\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.0945 | −0.628448 | −0.314224 | − | 0.949349i | \(-0.601744\pi\) | ||||
−0.314224 | + | 0.949349i | \(0.601744\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.79682 | 0.166400 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −27.7558 | −0.961683 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.38127 | −0.0478007 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.0573983 | −0.00198398 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.7290 | −0.577549 | −0.288775 | − | 0.957397i | \(-0.593248\pi\) | ||||
−0.288775 | + | 0.957397i | \(0.593248\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9123 | −0.996976 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −78.6073 | −2.70738 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18.3824 | 0.632373 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −38.7370 | −1.33102 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −61.3017 | −2.10387 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.296128 | −0.0101511 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 44.7962 | 1.53379 | 0.766896 | − | 0.641772i | \(-0.221800\pi\) | ||||
0.766896 | + | 0.641772i | \(0.221800\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.85194 | −0.165933 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −34.0394 | −1.16276 | −0.581382 | − | 0.813631i | \(-0.697488\pi\) | ||||
−0.581382 | + | 0.813631i | \(0.697488\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.7341 | 1.15099 | 0.575497 | − | 0.817804i | \(-0.304809\pi\) | ||||
0.575497 | + | 0.817804i | \(0.304809\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.6117 | −0.395724 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −48.1190 | −1.63799 | −0.818995 | − | 0.573801i | \(-0.805468\pi\) | ||||
−0.818995 | + | 0.573801i | \(0.805468\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.55956 | −0.0530267 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −19.5074 | −0.662505 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.28175 | 0.247016 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 75.7605 | 2.56705 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.92204 | −0.335810 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.02963 | 0.136226 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44.5082 | 1.50293 | 0.751467 | − | 0.659771i | \(-0.229347\pi\) | ||||
0.751467 | + | 0.659771i | \(0.229347\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.65013 | 0.0556576 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −42.8253 | −1.44282 | −0.721411 | − | 0.692507i | \(-0.756506\pi\) | ||||
−0.721411 | + | 0.692507i | \(0.756506\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.1555 | −0.510023 | −0.255011 | − | 0.966938i | \(-0.582079\pi\) | ||||
−0.255011 | + | 0.966938i | \(0.582079\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16.4542 | −0.553102 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.2381 | −0.545221 | −0.272611 | − | 0.962124i | \(-0.587887\pi\) | ||||
−0.272611 | + | 0.962124i | \(0.587887\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.89071 | −0.298185 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.6458 | 0.356648 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.04066 | −0.269070 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.8075 | −0.561814 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.05899 | 0.135526 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.524734 | 0.0175009 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 26.2924 | 0.875928 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 50.0865 | 1.66677 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14.7267 | −0.489533 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.6804 | 1.31757 | 0.658783 | − | 0.752333i | \(-0.271072\pi\) | ||||
0.658783 | + | 0.752333i | \(0.271072\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −41.7232 | −1.38387 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.68438 | 0.287726 | 0.143863 | − | 0.989598i | \(-0.454047\pi\) | ||||
0.143863 | + | 0.989598i | \(0.454047\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.0590 | −0.564571 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −20.1240 | −0.665280 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 54.1715 | 1.78890 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.0577 | −0.430732 | −0.215366 | − | 0.976533i | \(-0.569094\pi\) | ||||
−0.215366 | + | 0.976533i | \(0.569094\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.7231 | −0.715802 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −68.7474 | −2.26285 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.00000 | −0.0328798 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 21.4894 | 0.705805 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.0027 | 0.918739 | 0.459369 | − | 0.888245i | \(-0.348075\pi\) | ||||
0.459369 | + | 0.888245i | \(0.348075\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.0068 | −0.491829 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −25.2057 | −0.825199 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.53845 | 0.115720 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39.3559 | −1.28570 | −0.642851 | − | 0.765991i | \(-0.722249\pi\) | ||||
−0.642851 | + | 0.765991i | \(0.722249\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −37.3459 | −1.21874 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.58139 | −0.0515520 | −0.0257760 | − | 0.999668i | \(-0.508206\pi\) | ||||
−0.0257760 | + | 0.999668i | \(0.508206\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.348748 | −0.0113568 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.130528 | −0.00424608 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.6564 | −0.476268 | −0.238134 | − | 0.971232i | \(-0.576536\pi\) | ||||
−0.238134 | + | 0.971232i | \(0.576536\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.3503 | −0.498293 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 42.2684 | 1.37065 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.57726 | −0.180665 | −0.0903327 | − | 0.995912i | \(-0.528793\pi\) | ||||
−0.0903327 | + | 0.995912i | \(0.528793\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.1417 | 0.651769 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.853312 | −0.0275837 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −72.6655 | −2.34649 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.8601 | −0.898712 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.31604 | 0.203532 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 23.9057 | 0.769551 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.2964 | −0.427583 | −0.213792 | − | 0.976879i | \(-0.568581\pi\) | ||||
−0.213792 | + | 0.976879i | \(0.568581\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.9424 | 0.383644 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.69118 | −0.311005 | −0.155502 | − | 0.987836i | \(-0.549700\pi\) | ||||
−0.155502 | + | 0.987836i | \(0.549700\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −62.5552 | −2.00543 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13.7069 | 0.438972 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −36.9029 | −1.18063 | −0.590315 | − | 0.807173i | \(-0.700996\pi\) | ||||
−0.590315 | + | 0.807173i | \(0.700996\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.05242 | 0.193436 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.89444 | −0.188195 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10.0346 | −0.320055 | −0.160028 | − | 0.987113i | \(-0.551158\pi\) | ||||
−0.160028 | + | 0.987113i | \(0.551158\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.44623 | −0.109806 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 48.8021 | 1.55339 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.50431 | 0.0478344 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.7094 | −0.435492 | −0.217746 | − | 0.976005i | \(-0.569870\pi\) | ||||
−0.217746 | + | 0.976005i | \(0.569870\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20.0073 | 0.634912 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.3788 | 0.772858 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45.3620 | 1.43663 | 0.718314 | − | 0.695719i | \(-0.244914\pi\) | ||||
0.718314 | + | 0.695719i | \(0.244914\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.0323921 | 0.00102484 |
(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 | 2960.2.a.bb.1.4 | 5 | ||
4.3 | odd | 2 | 1480.2.a.g.1.2 | ✓ | 5 | ||
20.19 | odd | 2 | 7400.2.a.r.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1480.2.a.g.1.2 | ✓ | 5 | 4.3 | odd | 2 | ||
2960.2.a.bb.1.4 | 5 | 1.1 | even | 1 | trivial | ||
7400.2.a.r.1.4 | 5 | 20.19 | odd | 2 |