Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,4,Mod(865,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.865");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(101.955300490\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1731891456.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 865.7 | ||
Root | \(-2.21837 + 1.28078i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.865 |
Dual form | 1728.4.d.g.865.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 10.3923i | 0.929516i | 0.885438 | + | 0.464758i | \(0.153859\pi\) | ||||
−0.885438 | + | 0.464758i | \(0.846141\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 21.4243 | 1.15680 | 0.578401 | − | 0.815752i | \(-0.303677\pi\) | ||||
0.578401 | + | 0.815752i | \(0.303677\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 24.7386i | − 0.678089i | −0.940770 | − | 0.339044i | \(-0.889896\pi\) | ||||
0.940770 | − | 0.339044i | \(-0.110104\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 21.4243i | − 0.457079i | −0.973535 | − | 0.228540i | \(-0.926605\pi\) | ||||
0.973535 | − | 0.228540i | \(-0.0733950\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 123.693 | 1.76471 | 0.882353 | − | 0.470588i | \(-0.155958\pi\) | ||||
0.882353 | + | 0.470588i | \(0.155958\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 7.00000i | − 0.0845216i | −0.999107 | − | 0.0422608i | \(-0.986544\pi\) | ||||
0.999107 | − | 0.0422608i | \(-0.0134560\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −114.315 | −1.03637 | −0.518183 | − | 0.855270i | \(-0.673391\pi\) | ||||
−0.518183 | + | 0.855270i | \(0.673391\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 17.0000 | 0.136000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 270.200i | − 1.73017i | −0.501627 | − | 0.865084i | \(-0.667265\pi\) | ||||
0.501627 | − | 0.865084i | \(-0.332735\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 214.243 | 1.24126 | 0.620631 | − | 0.784102i | \(-0.286876\pi\) | ||||
0.620631 | + | 0.784102i | \(0.286876\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 222.648i | 1.07527i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 235.667i | − 1.04712i | −0.851989 | − | 0.523560i | \(-0.824604\pi\) | ||||
0.851989 | − | 0.523560i | \(-0.175396\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −395.818 | −1.50772 | −0.753859 | − | 0.657037i | \(-0.771810\pi\) | ||||
−0.753859 | + | 0.657037i | \(0.771810\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 92.0000i | − 0.326276i | −0.986603 | − | 0.163138i | \(-0.947838\pi\) | ||||
0.986603 | − | 0.163138i | \(-0.0521616\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −114.315 | −0.354779 | −0.177389 | − | 0.984141i | \(-0.556765\pi\) | ||||
−0.177389 | + | 0.984141i | \(0.556765\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 116.000 | 0.338192 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 20.7846i | 0.0538677i | 0.999637 | + | 0.0269338i | \(0.00857434\pi\) | ||||
−0.999637 | + | 0.0269338i | \(0.991426\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 257.091 | 0.630295 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 173.170i | − 0.382116i | −0.981579 | − | 0.191058i | \(-0.938808\pi\) | ||||
0.981579 | − | 0.191058i | \(-0.0611919\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 449.910i | − 0.944345i | −0.881506 | − | 0.472173i | \(-0.843470\pi\) | ||||
0.881506 | − | 0.472173i | \(-0.156530\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 222.648 | 0.424862 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 353.000i | − 0.643669i | −0.946796 | − | 0.321834i | \(-0.895701\pi\) | ||||
0.946796 | − | 0.321834i | \(-0.104299\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −789.815 | −1.32019 | −0.660097 | − | 0.751180i | \(-0.729485\pi\) | ||||
−0.660097 | + | 0.751180i | \(0.729485\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 425.000 | 0.681404 | 0.340702 | − | 0.940171i | \(-0.389335\pi\) | ||||
0.340702 | + | 0.940171i | \(0.389335\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 530.008i | − 0.784415i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1306.88 | −1.86121 | −0.930605 | − | 0.366024i | \(-0.880719\pi\) | ||||
−0.930605 | + | 0.366024i | \(0.880719\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 593.727i | − 0.785181i | −0.919713 | − | 0.392591i | \(-0.871579\pi\) | ||||
0.919713 | − | 0.392591i | \(-0.128421\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1285.46i | 1.64032i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 74.2159 | 0.0883918 | 0.0441959 | − | 0.999023i | \(-0.485927\pi\) | ||||
0.0441959 | + | 0.999023i | \(0.485927\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 459.000i | − 0.528750i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 72.7461 | 0.0785642 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 799.000 | 0.836352 | 0.418176 | − | 0.908366i | \(-0.362670\pi\) | ||||
0.418176 | + | 0.908366i | \(0.362670\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 228.631i | − 0.225244i | −0.993638 | − | 0.112622i | \(-0.964075\pi\) | ||||
0.993638 | − | 0.112622i | \(-0.0359249\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1092.64 | 1.04525 | 0.522626 | − | 0.852562i | \(-0.324953\pi\) | ||||
0.522626 | + | 0.852562i | \(0.324953\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 766.898i | − 0.692886i | −0.938071 | − | 0.346443i | \(-0.887389\pi\) | ||||
0.938071 | − | 0.346443i | \(-0.112611\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 685.577i | 0.602444i | 0.953554 | + | 0.301222i | \(0.0973945\pi\) | ||||
−0.953554 | + | 0.301222i | \(0.902606\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 519.511 | 0.432491 | 0.216246 | − | 0.976339i | \(-0.430619\pi\) | ||||
0.216246 | + | 0.976339i | \(0.430619\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 1188.00i | − 0.963318i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2650.04 | 2.04142 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 719.000 | 0.540195 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1475.71i | 1.05593i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2013.88 | −1.40711 | −0.703556 | − | 0.710640i | \(-0.748406\pi\) | ||||
−0.703556 | + | 0.710640i | \(0.748406\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2523.34i | 1.68294i | 0.540303 | + | 0.841471i | \(0.318310\pi\) | ||||
−0.540303 | + | 0.841471i | \(0.681690\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 149.970i | − 0.0977748i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −24.7386 | −0.0154275 | −0.00771374 | − | 0.999970i | \(-0.502455\pi\) | ||||
−0.00771374 | + | 0.999970i | \(0.502455\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 2185.00i | − 1.33330i | −0.745369 | − | 0.666652i | \(-0.767727\pi\) | ||||
0.745369 | − | 0.666652i | \(-0.232273\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −530.008 | −0.309940 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2808.00 | 1.60822 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3242.40i | 1.78274i | 0.453280 | + | 0.891368i | \(0.350254\pi\) | ||||
−0.453280 | + | 0.891368i | \(0.649746\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 192.819 | 0.103916 | 0.0519581 | − | 0.998649i | \(-0.483454\pi\) | ||||
0.0519581 | + | 0.998649i | \(0.483454\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2226.48i | 1.15377i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1371.15i | 0.697007i | 0.937308 | + | 0.348503i | \(0.113310\pi\) | ||||
−0.937308 | + | 0.348503i | \(0.886690\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2449.12 | −1.19887 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 1321.00i | − 0.634777i | −0.948296 | − | 0.317389i | \(-0.897194\pi\) | ||||
0.948296 | − | 0.317389i | \(-0.102806\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −571.577 | −0.264850 | −0.132425 | − | 0.991193i | \(-0.542276\pi\) | ||||
−0.132425 | + | 0.991193i | \(0.542276\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1738.00 | 0.791079 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 3450.25i | − 1.51628i | −0.652089 | − | 0.758142i | \(-0.726107\pi\) | ||||
0.652089 | − | 0.758142i | \(-0.273893\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 364.213 | 0.157325 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 1484.32i | − 0.619794i | −0.950770 | − | 0.309897i | \(-0.899705\pi\) | ||||
0.950770 | − | 0.309897i | \(-0.100295\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 1949.61i | − 0.800626i | −0.916378 | − | 0.400313i | \(-0.868901\pi\) | ||||
0.916378 | − | 0.400313i | \(-0.131099\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2449.12 | 0.973315 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 3060.00i | − 1.19663i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2047.28 | 0.775583 | 0.387791 | − | 0.921747i | \(-0.373238\pi\) | ||||
0.387791 | + | 0.921747i | \(0.373238\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2459.00 | 0.917112 | 0.458556 | − | 0.888665i | \(-0.348367\pi\) | ||||
0.458556 | + | 0.888665i | \(0.348367\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3959.47i | 1.43198i | 0.698110 | + | 0.715991i | \(0.254025\pi\) | ||||
−0.698110 | + | 0.715991i | \(0.745975\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2977.98 | 1.06082 | 0.530410 | − | 0.847741i | \(-0.322038\pi\) | ||||
0.530410 | + | 0.847741i | \(0.322038\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 5788.84i | − 2.00146i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 4113.46i | − 1.40145i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −173.170 | −0.0573132 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 4763.00i | − 1.55402i | −0.629488 | − | 0.777011i | \(-0.716735\pi\) | ||||
0.629488 | − | 0.777011i | \(-0.283265\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 956.092 | 0.303279 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4590.00 | 1.43590 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 2650.04i | − 0.806610i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1842.49 | 0.553283 | 0.276642 | − | 0.960973i | \(-0.410779\pi\) | ||||
0.276642 | + | 0.960973i | \(0.410779\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 2572.82i | − 0.752264i | −0.926566 | − | 0.376132i | \(-0.877254\pi\) | ||||
0.926566 | − | 0.376132i | \(-0.122746\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 4027.77i | − 1.16228i | −0.813803 | − | 0.581140i | \(-0.802607\pi\) | ||||
0.813803 | − | 0.581140i | \(-0.197393\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3512.89 | 0.987712 | 0.493856 | − | 0.869544i | \(-0.335587\pi\) | ||||
0.493856 | + | 0.869544i | \(0.335587\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 1188.00i | − 0.329773i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2265.52 | 0.613157 | 0.306578 | − | 0.951845i | \(-0.400816\pi\) | ||||
0.306578 | + | 0.951845i | \(0.400816\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4709.00 | 1.25864 | 0.629322 | − | 0.777144i | \(-0.283333\pi\) | ||||
0.629322 | + | 0.777144i | \(0.283333\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1205.51i | 0.314355i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −149.970 | −0.0386330 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7025.77i | 1.76678i | 0.468635 | + | 0.883392i | \(0.344746\pi\) | ||||
−0.468635 | + | 0.883392i | \(0.655254\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2828.01i | 0.702748i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4205.57 | −1.02076 | −0.510382 | − | 0.859948i | \(-0.670496\pi\) | ||||
−0.510382 | + | 0.859948i | \(0.670496\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 5049.00i | − 1.21131i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5300.08 | −1.24265 | −0.621324 | − | 0.783553i | \(-0.713405\pi\) | ||||
−0.621324 | + | 0.783553i | \(0.713405\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −216.000 | −0.0500708 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 4458.30i | − 1.01051i | −0.862970 | − | 0.505255i | \(-0.831398\pi\) | ||||
0.862970 | − | 0.505255i | \(-0.168602\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 449.910 | 0.100849 | 0.0504245 | − | 0.998728i | \(-0.483943\pi\) | ||||
0.0504245 | + | 0.998728i | \(0.483943\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 420.557i | − 0.0922201i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7027.17i | 1.52427i | 0.647421 | + | 0.762133i | \(0.275848\pi\) | ||||
−0.647421 | + | 0.762133i | \(0.724152\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6382.57 | −1.35499 | −0.677495 | − | 0.735528i | \(-0.736934\pi\) | ||||
−0.677495 | + | 0.735528i | \(0.736934\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 8116.00i | − 1.70476i | −0.522926 | − | 0.852378i | \(-0.675159\pi\) | ||||
0.522926 | − | 0.852378i | \(-0.324841\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8480.12 | −1.74413 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10387.0 | 2.11419 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 3813.98i | − 0.760460i | −0.924892 | − | 0.380230i | \(-0.875845\pi\) | ||||
0.924892 | − | 0.380230i | \(-0.124155\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1799.64 | 0.355183 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2449.12i | 0.473701i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 1971.03i | − 0.377437i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4675.60 | 0.877784 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 628.000i | 0.116749i | 0.998295 | + | 0.0583744i | \(0.0185917\pi\) | ||||
−0.998295 | + | 0.0583744i | \(0.981408\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5310.47 | −0.968260 | −0.484130 | − | 0.874996i | \(-0.660864\pi\) | ||||
−0.484130 | + | 0.874996i | \(0.660864\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 745.000 | 0.134536 | 0.0672682 | − | 0.997735i | \(-0.478572\pi\) | ||||
0.0672682 | + | 0.997735i | \(0.478572\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 249.415i | 0.0441910i | 0.999756 | + | 0.0220955i | \(0.00703379\pi\) | ||||
−0.999756 | + | 0.0220955i | \(0.992966\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6684.38 | −1.17321 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 865.852i | − 0.149156i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 364.213i | − 0.0621628i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2449.12 | −0.410409 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 4057.00i | − 0.673695i | −0.941559 | − | 0.336847i | \(-0.890639\pi\) | ||||
0.941559 | − | 0.336847i | \(-0.109361\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3668.48 | 0.598301 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2023.00 | 0.327002 | 0.163501 | − | 0.986543i | \(-0.447721\pi\) | ||||
0.163501 | + | 0.986543i | \(0.447721\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 5300.08i | − 0.841687i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4863.31 | −0.765581 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6283.61i | 0.972110i | 0.873928 | + | 0.486055i | \(0.161564\pi\) | ||||
−0.873928 | + | 0.486055i | \(0.838436\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7991.26i | 1.22568i | 0.790207 | + | 0.612840i | \(0.209973\pi\) | ||||
−0.790207 | + | 0.612840i | \(0.790027\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12121.9 | 1.82772 | 0.913860 | − | 0.406029i | \(-0.133087\pi\) | ||||
0.913860 | + | 0.406029i | \(0.133087\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 8208.00i | − 1.22714i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10090.9 | 1.48351 | 0.741753 | − | 0.670673i | \(-0.233995\pi\) | ||||
0.741753 | + | 0.670673i | \(0.233995\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6810.00 | 0.992856 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4416.73i | 0.633376i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2892.28 | 0.411378 | 0.205689 | − | 0.978617i | \(-0.434056\pi\) | ||||
0.205689 | + | 0.978617i | \(0.434056\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 445.295i | 0.0623142i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 4520.52i | − 0.627517i | −0.949503 | − | 0.313759i | \(-0.898412\pi\) | ||||
0.949503 | − | 0.313759i | \(-0.101588\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5788.84 | −0.790823 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4759.00i | 0.644996i | 0.946570 | + | 0.322498i | \(0.104523\pi\) | ||||
−0.946570 | + | 0.322498i | \(0.895477\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1101.58 | −0.146967 | −0.0734835 | − | 0.997296i | \(-0.523412\pi\) | ||||
−0.0734835 | + | 0.997296i | \(0.523412\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5508.00 | 0.729126 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1236.68i | 0.161189i | 0.996747 | + | 0.0805943i | \(0.0256818\pi\) | ||||
−0.996747 | + | 0.0805943i | \(0.974318\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14140.0 | −1.82888 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 13581.5i | − 1.73003i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 856.971i | 0.108338i | 0.998532 | + | 0.0541690i | \(0.0172510\pi\) | ||||
−0.998532 | + | 0.0541690i | \(0.982749\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8064.79 | 1.00433 | 0.502165 | − | 0.864772i | \(-0.332537\pi\) | ||||
0.502165 | + | 0.864772i | \(0.332537\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 4590.00i | − 0.567355i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5830.08 | −0.710041 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10555.0 | −1.27607 | −0.638033 | − | 0.770009i | \(-0.720252\pi\) | ||||
−0.638033 | + | 0.770009i | \(0.720252\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 3710.05i | − 0.442033i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6170.19 | 0.729838 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 1706.97i | − 0.199023i | −0.995036 | − | 0.0995116i | \(-0.968272\pi\) | ||||
0.995036 | − | 0.0995116i | \(-0.0317280\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9662.35i | 1.11856i | 0.828978 | + | 0.559281i | \(0.188923\pi\) | ||||
−0.828978 | + | 0.559281i | \(0.811077\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2102.78 | 0.240000 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 9639.00i | − 1.09242i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2359.05 | 0.263646 | 0.131823 | − | 0.991273i | \(-0.457917\pi\) | ||||
0.131823 | + | 0.991273i | \(0.457917\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16450.0 | 1.82572 | 0.912860 | − | 0.408273i | \(-0.133869\pi\) | ||||
0.912860 | + | 0.408273i | \(0.133869\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 800.207i | 0.0875952i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5784.56 | −0.628888 | −0.314444 | − | 0.949276i | \(-0.601818\pi\) | ||||
−0.314444 | + | 0.949276i | \(0.601818\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 11627.2i | − 1.24700i | −0.781822 | − | 0.623502i | \(-0.785709\pi\) | ||||
0.781822 | − | 0.623502i | \(-0.214291\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 771.274i | 0.0821616i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14670.0 | −1.54192 | −0.770958 | − | 0.636886i | \(-0.780222\pi\) | ||||
−0.770958 | + | 0.636886i | \(0.780222\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9792.00i | 1.02237i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4770.07 | 0.491482 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9574.00 | −0.979984 | −0.489992 | − | 0.871727i | \(-0.663000\pi\) | ||||
−0.489992 | + | 0.871727i | \(0.663000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14310.2i | 1.44575i | 0.690977 | + | 0.722877i | \(0.257181\pi\) | ||||
−0.690977 | + | 0.722877i | \(0.742819\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18103.5 | 1.81715 | 0.908577 | − | 0.417718i | \(-0.137170\pi\) | ||||
0.908577 | + | 0.417718i | \(0.137170\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6852.60i | 0.679016i | 0.940603 | + | 0.339508i | \(0.110261\pi\) | ||||
−0.940603 | + | 0.339508i | \(0.889739\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 7562.77i | − 0.744598i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2275.95 | −0.221244 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 119.000i | − 0.0114949i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13156.7 | −1.25500 | −0.627498 | − | 0.778618i | \(-0.715921\pi\) | ||||
−0.627498 | + | 0.778618i | \(0.715921\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5049.00 | −0.478617 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8303.45i | 0.777403i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3706.40 | 0.344873 | 0.172436 | − | 0.985021i | \(-0.444836\pi\) | ||||
0.172436 | + | 0.985021i | \(0.444836\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19024.0i | 1.74856i | 0.485425 | + | 0.874279i | \(0.338665\pi\) | ||||
−0.485425 | + | 0.874279i | \(0.661335\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 33421.9i | − 3.05324i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16921.2 | −1.52720 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 3944.00i | − 0.353823i | −0.984227 | − | 0.176912i | \(-0.943389\pi\) | ||||
0.984227 | − | 0.176912i | \(-0.0566106\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20898.9 | 1.85256 | 0.926279 | − | 0.376838i | \(-0.122989\pi\) | ||||
0.926279 | + | 0.376838i | \(0.122989\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2376.00 | 0.209368 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 51.9615i | 0.00452486i | 0.999997 | + | 0.00226243i | \(0.000720155\pi\) | ||||
−0.999997 | + | 0.00226243i | \(0.999280\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9105.32 | 0.788250 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11355.0i | 0.971578i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2828.01i | 0.240572i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9920.19 | 0.834187 | 0.417094 | − | 0.908864i | \(-0.363049\pi\) | ||||
0.417094 | + | 0.908864i | \(0.363049\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20923.0i | 1.74933i | 0.484729 | + | 0.874664i | \(0.338918\pi\) | ||||
−0.484729 | + | 0.874664i | \(0.661082\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 26500.4 | 2.19046 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 901.000 | 0.0740528 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8480.12i | 0.689146i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7969.83 | 0.644049 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 2869.68i | − 0.229325i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19946.0i | 1.58511i | 0.609799 | + | 0.792556i | \(0.291250\pi\) | ||||
−0.609799 | + | 0.792556i | \(0.708750\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7124.73 | −0.559981 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 875.000i | 0.0683954i | 0.999415 | + | 0.0341977i | \(0.0108876\pi\) | ||||
−0.999415 | + | 0.0341977i | \(0.989112\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1891.40 | −0.146237 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −27999.0 | −2.15305 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 467.654i | − 0.0355747i | −0.999842 | − | 0.0177874i | \(-0.994338\pi\) | ||||
0.999842 | − | 0.0177874i | \(-0.00566219\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1971.03 | −0.149134 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 17119.1i | − 1.28150i | −0.767749 | − | 0.640751i | \(-0.778623\pi\) | ||||
0.767749 | − | 0.640751i | \(-0.221377\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5398.92i | 0.402008i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17094.4 | 1.25946 | 0.629731 | − | 0.776813i | \(-0.283165\pi\) | ||||
0.629731 | + | 0.776813i | \(0.283165\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 12823.0i | − 0.939800i | −0.882720 | − | 0.469900i | \(-0.844290\pi\) | ||||
0.882720 | − | 0.469900i | \(-0.155710\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1943.36 | −0.140946 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17773.0 | 1.28232 | 0.641161 | − | 0.767406i | \(-0.278453\pi\) | ||||
0.641161 | + | 0.767406i | \(0.278453\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 12720.2i | − 0.908300i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 514.183 | 0.0365271 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 4032.40i | − 0.283535i | −0.989900 | − | 0.141767i | \(-0.954722\pi\) | ||||
0.989900 | − | 0.141767i | \(-0.0452785\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 1499.70i | − 0.104914i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18108.7 | 1.25402 | 0.627010 | − | 0.779011i | \(-0.284278\pi\) | ||||
0.627010 | + | 0.779011i | \(0.284278\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 27540.0i | 1.89753i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22967.0 | −1.56662 | −0.783310 | − | 0.621631i | \(-0.786470\pi\) | ||||
−0.783310 | + | 0.621631i | \(0.786470\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21562.0 | −1.46345 | −0.731724 | − | 0.681601i | \(-0.761284\pi\) | ||||
−0.731724 | + | 0.681601i | \(0.761284\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7472.07i | 0.502120i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2078.16 | 0.138962 | 0.0694808 | − | 0.997583i | \(-0.477866\pi\) | ||||
0.0694808 | + | 0.997583i | \(0.477866\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2449.12i | 0.162162i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 25902.0i | − 1.70664i | −0.521388 | − | 0.853320i | \(-0.674585\pi\) | ||||
0.521388 | − | 0.853320i | \(-0.325415\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4922.99 | 0.321219 | 0.160609 | − | 0.987018i | \(-0.448654\pi\) | ||||
0.160609 | + | 0.987018i | \(0.448654\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12917.0i | 0.838737i | 0.907816 | + | 0.419368i | \(0.137748\pi\) | ||||
−0.907816 | + | 0.419368i | \(0.862252\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1590.02 | 0.102252 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13211.0 | −0.845504 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 29150.4i | − 1.84786i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17632.2 | −1.11240 | −0.556201 | − | 0.831047i | \(-0.687742\pi\) | ||||
−0.556201 | + | 0.831047i | \(0.687742\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 20928.9i | − 1.30793i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 2485.22i | − 0.154581i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −494.773 | −0.0304873 | −0.0152436 | − | 0.999884i | \(-0.504852\pi\) | ||||
−0.0152436 | + | 0.999884i | \(0.504852\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1564.00i | − 0.0959225i | −0.998849 | − | 0.0479612i | \(-0.984728\pi\) | ||||
0.998849 | − | 0.0479612i | \(-0.0152724\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20493.6 | −1.24527 | −0.622633 | − | 0.782514i | \(-0.713937\pi\) | ||||
−0.622633 | + | 0.782514i | \(0.713937\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4284.00 | −0.259109 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19579.1i | 1.17334i | 0.809827 | + | 0.586669i | \(0.199561\pi\) | ||||
−0.809827 | + | 0.586669i | \(0.800439\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −26223.3 | −1.56432 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14991.6i | 0.886176i | 0.896478 | + | 0.443088i | \(0.146117\pi\) | ||||
−0.896478 | + | 0.443088i | \(0.853883\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27058.9i | 1.59224i | 0.605141 | + | 0.796118i | \(0.293117\pi\) | ||||
−0.605141 | + | 0.796118i | \(0.706883\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1558.53 | 0.0908832 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30888.0i | 1.79309i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11130.2 | −0.640350 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5231.00 | −0.299614 | −0.149807 | − | 0.988715i | \(-0.547865\pi\) | ||||
−0.149807 | + | 0.988715i | \(0.547865\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 19631.1i | − 1.11445i | −0.830361 | − | 0.557225i | \(-0.811866\pi\) | ||||
0.830361 | − | 0.557225i | \(-0.188134\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17118.0 | 0.967494 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27855.7i | 1.56057i | 0.625425 | + | 0.780285i | \(0.284926\pi\) | ||||
−0.625425 | + | 0.780285i | \(0.715074\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 257.091i | − 0.0143401i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 445.295 | 0.0246218 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4556.00i | 0.250823i | 0.992105 | + | 0.125411i | \(0.0400250\pi\) | ||||
−0.992105 | + | 0.125411i | \(0.959975\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 22707.2 | 1.23933 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −48960.0 | −2.66068 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19360.9i | 1.04315i | 0.853205 | + | 0.521576i | \(0.174656\pi\) | ||||
−0.853205 | + | 0.521576i | \(0.825344\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1649.67 | −0.0885042 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 4898.25i | − 0.260562i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 10305.1i | − 0.545861i | −0.962034 | − | 0.272930i | \(-0.912007\pi\) | ||||
0.962034 | − | 0.272930i | \(-0.0879929\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24491.2 | −1.28640 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 5508.00i | − 0.288094i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9353.07 | −0.485133 | −0.242567 | − | 0.970135i | \(-0.577989\pi\) | ||||
−0.242567 | + | 0.970135i | \(0.577989\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23409.0 | 1.20915 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 4593.40i | − 0.235303i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2956.55 | −0.150829 | −0.0754143 | − | 0.997152i | \(-0.524028\pi\) | ||||
−0.0754143 | + | 0.997152i | \(0.524028\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 11379.8i | − 0.575781i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31536.5i | 1.58913i | 0.607182 | + | 0.794563i | \(0.292300\pi\) | ||||
−0.607182 | + | 0.794563i | \(0.707700\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8732.74 | −0.436465 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33892.0i | 1.68706i | 0.537082 | + | 0.843530i | \(0.319527\pi\) | ||||
−0.537082 | + | 0.843530i | \(0.680473\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17095.3 | −0.844101 | −0.422051 | − | 0.906572i | \(-0.638690\pi\) | ||||
−0.422051 | + | 0.906572i | \(0.638690\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −33696.0 | −1.65708 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 16430.2i | − 0.801532i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31215.2 | −1.51672 | −0.758361 | − | 0.651835i | \(-0.774000\pi\) | ||||
−0.758361 | + | 0.651835i | \(0.774000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2003.83i | 0.0965918i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23973.8i | 1.15105i | 0.817786 | + | 0.575523i | \(0.195201\pi\) | ||||
−0.817786 | + | 0.575523i | \(0.804799\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5120.90 | −0.243932 | −0.121966 | − | 0.992534i | \(-0.538920\pi\) | ||||
−0.121966 | + | 0.992534i | \(0.538920\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14688.0i | 0.696909i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3710.05 | −0.174657 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15649.0 | −0.733833 | −0.366916 | − | 0.930254i | \(-0.619586\pi\) | ||||
−0.366916 | + | 0.930254i | \(0.619586\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 8646.40i | − 0.402315i | −0.979559 | − | 0.201157i | \(-0.935530\pi\) | ||||
0.979559 | − | 0.201157i | \(-0.0644703\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3642.13 | 0.168812 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2770.73i | 0.127435i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19538.9i | 0.895209i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14249.5 | −0.647879 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10217.0i | 0.462766i | 0.972863 | + | 0.231383i | \(0.0743250\pi\) | ||||
−0.972863 | + | 0.231383i | \(0.925675\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11130.2 | 0.500307 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9639.00 | −0.431641 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 32070.7i | − 1.42535i | −0.701496 | − | 0.712673i | \(-0.747484\pi\) | ||||
0.701496 | − | 0.712673i | \(-0.252516\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14140.0 | −0.626080 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 10513.9i | − 0.462052i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 25452.1i | − 1.11437i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26816.7 | −1.16542 | −0.582710 | − | 0.812680i | \(-0.698008\pi\) | ||||
−0.582710 | + | 0.812680i | \(0.698008\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45556.0i | 1.97249i | 0.165297 | + | 0.986244i | \(0.447142\pi\) | ||||
−0.165297 | + | 0.986244i | \(0.552858\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13728.2 | 0.590036 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −644.000 | −0.0275774 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 24744.1i | − 1.05186i | −0.850529 | − | 0.525928i | \(-0.823718\pi\) | ||||
0.850529 | − | 0.525928i | \(-0.176282\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31129.5 | 1.31848 | 0.659238 | − | 0.751934i | \(-0.270879\pi\) | ||||
0.659238 | + | 0.751934i | \(0.270879\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 23378.0i | − 0.982990i | −0.870880 | − | 0.491495i | \(-0.836451\pi\) | ||||
0.870880 | − | 0.491495i | \(-0.163549\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 5120.40i | − 0.214522i | −0.994231 | − | 0.107261i | \(-0.965792\pi\) | ||||
0.994231 | − | 0.107261i | \(-0.0342081\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14348.4 | 0.596810 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 5940.00i | − 0.246182i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28204.7 | −1.16059 | −0.580295 | − | 0.814406i | \(-0.697063\pi\) | ||||
−0.580295 | + | 0.814406i | \(0.697063\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −48619.0 | −1.99348 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18061.8i | 0.735320i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15404.1 | 0.624899 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 26940.4i | 1.08520i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 13175.9i | − 0.528881i | −0.964402 | − | 0.264440i | \(-0.914813\pi\) | ||||
0.964402 | − | 0.264440i | \(-0.0851873\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24936.5 | 0.993951 | 0.496976 | − | 0.867765i | \(-0.334444\pi\) | ||||
0.496976 | + | 0.867765i | \(0.334444\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 25031.0i | − 0.994234i | −0.867684 | − | 0.497117i | \(-0.834392\pi\) | ||||
0.867684 | − | 0.497117i | \(-0.165608\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −46464.0 | −1.83274 | −0.916369 | − | 0.400335i | \(-0.868894\pi\) | ||||
−0.916369 | + | 0.400335i | \(0.868894\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 35856.0 | 1.40941 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 32330.5i | 1.26207i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7562.77 | −0.294208 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 31616.0i | 1.22150i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 30315.4i | − 1.16725i | −0.812024 | − | 0.583624i | \(-0.801634\pi\) | ||||
0.812024 | − | 0.583624i | \(-0.198366\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28127.8 | 1.07565 | 0.537827 | − | 0.843055i | \(-0.319245\pi\) | ||||
0.537827 | + | 0.843055i | \(0.319245\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34931.0i | 1.33128i | 0.746272 | + | 0.665641i | \(0.231842\pi\) | ||||
−0.746272 | + | 0.665641i | \(0.768158\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29056.9 | 1.09993 | 0.549963 | − | 0.835189i | \(-0.314642\pi\) | ||||
0.549963 | + | 0.835189i | \(0.314642\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −43146.0 | −1.62775 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 800.207i | 0.0299865i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15425.5 | 0.576109 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 57888.4i | − 2.14759i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2570.91i | 0.0950606i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20260.9 | 0.744195 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30283.0i | 1.10863i | 0.832306 | + | 0.554317i | \(0.187020\pi\) | ||||
−0.832306 | + | 0.554317i | \(0.812980\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32964.4 | 1.19886 | 0.599429 | − | 0.800428i | \(-0.295395\pi\) | ||||
0.599429 | + | 0.800428i | \(0.295395\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14688.0 | −0.532423 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 54060.8i | 1.94683i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26866.1 | 0.964341 | 0.482170 | − | 0.876077i | \(-0.339849\pi\) | ||||
0.482170 | + | 0.876077i | \(0.339849\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16921.2i | 0.603433i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 4006.34i | − 0.142408i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 52099.6 | 1.83997 | 0.919985 | − | 0.391955i | \(-0.128201\pi\) | ||||
0.919985 | + | 0.391955i | \(0.128201\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 812.000i | − 0.0285846i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 31800.5 | 1.11228 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13367.0 | −0.466041 | −0.233021 | − | 0.972472i | \(-0.574861\pi\) | ||||
−0.233021 | + | 0.972472i | \(0.574861\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 4354.38i | − 0.150849i | −0.997152 | − | 0.0754243i | \(-0.975969\pi\) | ||||
0.997152 | − | 0.0754243i | \(-0.0240311\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 45248.1 | 1.56255 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 38419.1i | − 1.31832i | −0.752001 | − | 0.659162i | \(-0.770911\pi\) | ||||
0.752001 | − | 0.659162i | \(-0.229089\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 9105.32i | − 0.311455i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35598.9 | −1.21003 | −0.605016 | − | 0.796213i | \(-0.706833\pi\) | ||||
−0.605016 | + | 0.796213i | \(0.706833\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21276.0i | 0.720916i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −530.008 | −0.0178465 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16109.0 | 0.540734 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25554.7i | 0.852471i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34900.2 | −1.16061 | −0.580307 | − | 0.814398i | \(-0.697067\pi\) | ||||
−0.580307 | + | 0.814398i | \(0.697067\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 222.648i | 0.00735850i | 0.999993 | + | 0.00367925i | \(0.00117114\pi\) | ||||
−0.999993 | + | 0.00367925i | \(0.998829\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 46812.1i | − 1.54237i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14645.3 | −0.479574 | −0.239787 | − | 0.970826i | \(-0.577078\pi\) | ||||
−0.239787 | + | 0.970826i | \(0.577078\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1836.00i | − 0.0599375i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 38004.7 | 1.23312 | 0.616562 | − | 0.787307i | \(-0.288525\pi\) | ||||
0.616562 | + | 0.787307i | \(0.288525\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −41148.0 | −1.33105 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10517.0i | 0.338141i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45955.1 | −1.47307 | −0.736535 | − | 0.676400i | \(-0.763539\pi\) | ||||
−0.736535 | + | 0.676400i | \(0.763539\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 30948.0i | 0.986049i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32393.5i | 1.02900i | 0.857490 | + | 0.514500i | \(0.172022\pi\) | ||||
−0.857490 | + | 0.514500i | \(0.827978\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1728.4.d.g.865.7 | yes | 8 | |
3.2 | odd | 2 | inner | 1728.4.d.g.865.3 | yes | 8 | |
4.3 | odd | 2 | inner | 1728.4.d.g.865.5 | yes | 8 | |
8.3 | odd | 2 | inner | 1728.4.d.g.865.2 | yes | 8 | |
8.5 | even | 2 | inner | 1728.4.d.g.865.4 | yes | 8 | |
12.11 | even | 2 | inner | 1728.4.d.g.865.1 | ✓ | 8 | |
24.5 | odd | 2 | inner | 1728.4.d.g.865.8 | yes | 8 | |
24.11 | even | 2 | inner | 1728.4.d.g.865.6 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1728.4.d.g.865.1 | ✓ | 8 | 12.11 | even | 2 | inner | |
1728.4.d.g.865.2 | yes | 8 | 8.3 | odd | 2 | inner | |
1728.4.d.g.865.3 | yes | 8 | 3.2 | odd | 2 | inner | |
1728.4.d.g.865.4 | yes | 8 | 8.5 | even | 2 | inner | |
1728.4.d.g.865.5 | yes | 8 | 4.3 | odd | 2 | inner | |
1728.4.d.g.865.6 | yes | 8 | 24.11 | even | 2 | inner | |
1728.4.d.g.865.7 | yes | 8 | 1.1 | even | 1 | trivial | |
1728.4.d.g.865.8 | yes | 8 | 24.5 | odd | 2 | inner |