Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8400,2,Mod(1,8400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8400.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8400 = 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8400.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: | \(67.0743376979\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 840) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.311108\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8400.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.05086 | 1.52289 | 0.761445 | − | 0.648229i | \(-0.224490\pi\) | ||||
0.761445 | + | 0.648229i | \(0.224490\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.37778 | 0.936829 | 0.468414 | − | 0.883509i | \(-0.344825\pi\) | ||||
0.468414 | + | 0.883509i | \(0.344825\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.18421 | 1.74243 | 0.871213 | − | 0.490905i | \(-0.163334\pi\) | ||||
0.871213 | + | 0.490905i | \(0.163334\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.23506 | −1.88925 | −0.944627 | − | 0.328147i | \(-0.893576\pi\) | ||||
−0.944627 | + | 0.328147i | \(0.893576\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.23506 | 1.30010 | 0.650050 | − | 0.759891i | \(-0.274748\pi\) | ||||
0.650050 | + | 0.759891i | \(0.274748\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.62222 | 0.830174 | 0.415087 | − | 0.909782i | \(-0.363751\pi\) | ||||
0.415087 | + | 0.909782i | \(0.363751\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.05086 | 0.879241 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.85728 | −0.798532 | −0.399266 | − | 0.916835i | \(-0.630735\pi\) | ||||
−0.399266 | + | 0.916835i | \(0.630735\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.37778 | 0.540878 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.37778 | −0.527521 | −0.263761 | − | 0.964588i | \(-0.584963\pi\) | ||||
−0.263761 | + | 0.964588i | \(0.584963\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.24443 | −0.189774 | −0.0948870 | − | 0.995488i | \(-0.530249\pi\) | ||||
−0.0948870 | + | 0.995488i | \(0.530249\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.18421 | 1.00599 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.62222 | 0.634910 | 0.317455 | − | 0.948273i | \(-0.397172\pi\) | ||||
0.317455 | + | 0.948273i | \(0.397172\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.23506 | −1.09076 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.6128 | 1.51186 | 0.755932 | − | 0.654650i | \(-0.227184\pi\) | ||||
0.755932 | + | 0.654650i | \(0.227184\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.488863 | 0.0625924 | 0.0312962 | − | 0.999510i | \(-0.490036\pi\) | ||||
0.0312962 | + | 0.999510i | \(0.490036\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.61285 | −0.441380 | −0.220690 | − | 0.975344i | \(-0.570831\pi\) | ||||
−0.220690 | + | 0.975344i | \(0.570831\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.23506 | 0.750613 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.2953 | 1.22183 | 0.610913 | − | 0.791698i | \(-0.290803\pi\) | ||||
0.610913 | + | 0.791698i | \(0.290803\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.2351 | 1.90017 | 0.950085 | − | 0.311991i | \(-0.100996\pi\) | ||||
0.950085 | + | 0.311991i | \(0.100996\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.05086 | 0.575598 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.24443 | −0.140009 | −0.0700047 | − | 0.997547i | \(-0.522301\pi\) | ||||
−0.0700047 | + | 0.997547i | \(0.522301\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.6128 | −1.27468 | −0.637338 | − | 0.770585i | \(-0.719964\pi\) | ||||
−0.637338 | + | 0.770585i | \(0.719964\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.00000 | −0.214423 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.99063 | 0.741006 | 0.370503 | − | 0.928831i | \(-0.379185\pi\) | ||||
0.370503 | + | 0.928831i | \(0.379185\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.37778 | 0.354088 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.62222 | 0.479301 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.23506 | −0.836144 | −0.418072 | − | 0.908414i | \(-0.637294\pi\) | ||||
−0.418072 | + | 0.908414i | \(0.637294\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.05086 | 0.507630 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.47949 | −0.943245 | −0.471622 | − | 0.881801i | \(-0.656331\pi\) | ||||
−0.471622 | + | 0.881801i | \(0.656331\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.8573 | −1.66100 | −0.830499 | − | 0.557021i | \(-0.811944\pi\) | ||||
−0.830499 | + | 0.557021i | \(0.811944\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.4795 | −1.49646 | −0.748230 | − | 0.663440i | \(-0.769096\pi\) | ||||
−0.748230 | + | 0.663440i | \(0.769096\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.61285 | −0.154483 | −0.0772414 | − | 0.997012i | \(-0.524611\pi\) | ||||
−0.0772414 | + | 0.997012i | \(0.524611\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.85728 | −0.461033 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.86665 | 0.175599 | 0.0877997 | − | 0.996138i | \(-0.472016\pi\) | ||||
0.0877997 | + | 0.996138i | \(0.472016\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.37778 | 0.312276 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.18421 | 0.658575 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.5111 | 1.31919 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.37778 | −0.304565 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.8573 | −1.14090 | −0.570450 | − | 0.821333i | \(-0.693231\pi\) | ||||
−0.570450 | + | 0.821333i | \(0.693231\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.24443 | −0.109566 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21.7146 | −1.89721 | −0.948605 | − | 0.316463i | \(-0.897505\pi\) | ||||
−0.948605 | + | 0.316463i | \(0.897505\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.23506 | −0.714071 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.47949 | 0.809888 | 0.404944 | − | 0.914342i | \(-0.367291\pi\) | ||||
0.404944 | + | 0.914342i | \(0.367291\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.1334 | −0.859500 | −0.429750 | − | 0.902948i | \(-0.641398\pi\) | ||||
−0.429750 | + | 0.902948i | \(0.641398\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17.0607 | 1.42669 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.24443 | 0.593487 | 0.296743 | − | 0.954957i | \(-0.404099\pi\) | ||||
0.296743 | + | 0.954957i | \(0.404099\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.85728 | 0.720795 | 0.360398 | − | 0.932799i | \(-0.382641\pi\) | ||||
0.360398 | + | 0.932799i | \(0.382641\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.18421 | 0.580809 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.4795 | 1.07578 | 0.537890 | − | 0.843015i | \(-0.319221\pi\) | ||||
0.537890 | + | 0.843015i | \(0.319221\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.62222 | 0.366566 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.23506 | 0.491392 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.00000 | −0.313304 | −0.156652 | − | 0.987654i | \(-0.550070\pi\) | ||||
−0.156652 | + | 0.987654i | \(0.550070\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.10171 | −0.162635 | −0.0813176 | − | 0.996688i | \(-0.525913\pi\) | ||||
−0.0813176 | + | 0.996688i | \(0.525913\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.59057 | −0.122352 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.23506 | −0.629751 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.1842 | 0.850320 | 0.425160 | − | 0.905118i | \(-0.360218\pi\) | ||||
0.425160 | + | 0.905118i | \(0.360218\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.6128 | 0.872875 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.6637 | −1.54448 | −0.772239 | − | 0.635332i | \(-0.780863\pi\) | ||||
−0.772239 | + | 0.635332i | \(0.780863\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.9590 | 1.85519 | 0.927594 | − | 0.373591i | \(-0.121874\pi\) | ||||
0.927594 | + | 0.373591i | \(0.121874\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.488863 | 0.0361378 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 36.2864 | 2.65352 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.52098 | −0.688914 | −0.344457 | − | 0.938802i | \(-0.611937\pi\) | ||||
−0.344457 | + | 0.938802i | \(0.611937\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −22.9590 | −1.65262 | −0.826312 | − | 0.563212i | \(-0.809565\pi\) | ||||
−0.826312 | + | 0.563212i | \(0.809565\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.8479 | −1.41411 | −0.707053 | − | 0.707161i | \(-0.749976\pi\) | ||||
−0.707053 | + | 0.707161i | \(0.749976\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.23506 | 0.583768 | 0.291884 | − | 0.956454i | \(-0.405718\pi\) | ||||
0.291884 | + | 0.956454i | \(0.405718\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.61285 | −0.254831 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.00000 | −0.140372 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.23506 | 0.433367 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −41.5941 | −2.87712 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.6128 | 0.799461 | 0.399731 | − | 0.916633i | \(-0.369104\pi\) | ||||
0.399731 | + | 0.916633i | \(0.369104\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.2953 | 0.705421 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.62222 | 0.313776 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.2351 | 1.09706 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 24.2667 | 1.63236 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.48886 | −0.166667 | −0.0833333 | − | 0.996522i | \(-0.526557\pi\) | ||||
−0.0833333 | + | 0.996522i | \(0.526557\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.857279 | 0.0568996 | 0.0284498 | − | 0.999595i | \(-0.490943\pi\) | ||||
0.0284498 | + | 0.999595i | \(0.490943\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.4701 | −0.956213 | −0.478106 | − | 0.878302i | \(-0.658677\pi\) | ||||
−0.478106 | + | 0.878302i | \(0.658677\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.05086 | 0.332322 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.96836 | −0.259976 | −0.129988 | − | 0.991516i | \(-0.541494\pi\) | ||||
−0.129988 | + | 0.991516i | \(0.541494\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.24443 | −0.0808345 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.90813 | −0.123427 | −0.0617135 | − | 0.998094i | \(-0.519656\pi\) | ||||
−0.0617135 | + | 0.998094i | \(0.519656\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.755569 | 0.0486705 | 0.0243352 | − | 0.999704i | \(-0.492253\pi\) | ||||
0.0243352 | + | 0.999704i | \(0.492253\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −27.8163 | −1.76991 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.6128 | −0.735934 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.12399 | 0.575901 | 0.287950 | − | 0.957645i | \(-0.407026\pi\) | ||||
0.287950 | + | 0.957645i | \(0.407026\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 31.4924 | 1.97991 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.28592 | −0.0802134 | −0.0401067 | − | 0.999195i | \(-0.512770\pi\) | ||||
−0.0401067 | + | 0.999195i | \(0.512770\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.85728 | −0.301817 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.00000 | −0.123797 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.00937 | −0.432216 | −0.216108 | − | 0.976369i | \(-0.569336\pi\) | ||||
−0.216108 | + | 0.976369i | \(0.569336\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.99063 | 0.427820 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 23.1941 | 1.41417 | 0.707083 | − | 0.707130i | \(-0.250011\pi\) | ||||
0.707083 | + | 0.707130i | \(0.250011\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.11108 | −0.431967 | −0.215984 | − | 0.976397i | \(-0.569296\pi\) | ||||
−0.215984 | + | 0.976397i | \(0.569296\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.37778 | 0.204433 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.34614 | 0.441387 | 0.220693 | − | 0.975343i | \(-0.429168\pi\) | ||||
0.220693 | + | 0.975343i | \(0.429168\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.62222 | 0.276725 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.9813 | −1.19198 | −0.595991 | − | 0.802991i | \(-0.703241\pi\) | ||||
−0.595991 | + | 0.802991i | \(0.703241\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.85728 | −0.288735 | −0.144368 | − | 0.989524i | \(-0.546115\pi\) | ||||
−0.144368 | + | 0.989524i | \(0.546115\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.37778 | −0.199384 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 34.6128 | 2.03605 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.23506 | −0.482748 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.1842 | −0.653388 | −0.326694 | − | 0.945130i | \(-0.605935\pi\) | ||||
−0.326694 | + | 0.945130i | \(0.605935\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.05086 | 0.293080 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 21.0607 | 1.21797 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.24443 | −0.0717278 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.47949 | −0.544583 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.3461 | 1.33243 | 0.666217 | − | 0.745758i | \(-0.267912\pi\) | ||||
0.666217 | + | 0.745758i | \(0.267912\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.8573 | −0.958977 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 32.8573 | 1.86317 | 0.931583 | − | 0.363530i | \(-0.118428\pi\) | ||||
0.931583 | + | 0.363530i | \(0.118428\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.8256 | 1.62932 | 0.814661 | − | 0.579938i | \(-0.196923\pi\) | ||||
0.814661 | + | 0.579938i | \(0.196923\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.3590 | 1.42431 | 0.712153 | − | 0.702024i | \(-0.247720\pi\) | ||||
0.712153 | + | 0.702024i | \(0.247720\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.1017 | −0.565587 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.4795 | −0.863981 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −59.1624 | −3.29188 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.61285 | −0.0891907 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.89829 | −0.104339 | −0.0521697 | − | 0.998638i | \(-0.516614\pi\) | ||||
−0.0521697 | + | 0.998638i | \(0.516614\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.85728 | −0.266177 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.2257 | 1.26518 | 0.632592 | − | 0.774485i | \(-0.281991\pi\) | ||||
0.632592 | + | 0.774485i | \(0.281991\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.86665 | 0.101382 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 23.3461 | 1.26426 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.47949 | −0.401520 | −0.200760 | − | 0.979640i | \(-0.564341\pi\) | ||||
−0.200760 | + | 0.979640i | \(0.564341\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.2257 | 1.56442 | 0.782208 | − | 0.623018i | \(-0.214094\pi\) | ||||
0.782208 | + | 0.623018i | \(0.214094\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.37778 | 0.180293 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.4099 | −1.61856 | −0.809278 | − | 0.587426i | \(-0.800141\pi\) | ||||
−0.809278 | + | 0.587426i | \(0.800141\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.18421 | 0.380229 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.1936 | 0.854664 | 0.427332 | − | 0.904095i | \(-0.359454\pi\) | ||||
0.427332 | + | 0.904095i | \(0.359454\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 48.8163 | 2.56928 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 14.5111 | 0.761637 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.51114 | 0.287679 | 0.143840 | − | 0.989601i | \(-0.454055\pi\) | ||||
0.143840 | + | 0.989601i | \(0.454055\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.37778 | −0.175840 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.62222 | 0.239973 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.63158 | 0.0844802 | 0.0422401 | − | 0.999107i | \(-0.486551\pi\) | ||||
0.0422401 | + | 0.999107i | \(0.486551\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.75557 | −0.347929 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.8573 | −1.07137 | −0.535683 | − | 0.844419i | \(-0.679946\pi\) | ||||
−0.535683 | + | 0.844419i | \(0.679946\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.8573 | −0.658698 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.0830 | −1.02619 | −0.513096 | − | 0.858331i | \(-0.671502\pi\) | ||||
−0.513096 | + | 0.858331i | \(0.671502\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.24443 | −0.0632580 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 33.2257 | 1.68461 | 0.842305 | − | 0.539001i | \(-0.181198\pi\) | ||||
0.842305 | + | 0.539001i | \(0.181198\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 44.7940 | 2.26533 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −21.7146 | −1.09535 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.7239 | 1.14048 | 0.570241 | − | 0.821478i | \(-0.306850\pi\) | ||||
0.570241 | + | 0.821478i | \(0.306850\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.23506 | −0.412269 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.7556 | 0.636983 | 0.318491 | − | 0.947926i | \(-0.396824\pi\) | ||||
0.318491 | + | 0.947926i | \(0.396824\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.6128 | 0.777731 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.5334 | −1.21608 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.4479 | 1.35721 | 0.678604 | − | 0.734504i | \(-0.262585\pi\) | ||||
0.678604 | + | 0.734504i | \(0.262585\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.47949 | 0.467589 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.6128 | 0.571431 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.1334 | −0.496232 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.36842 | −0.115705 | −0.0578524 | − | 0.998325i | \(-0.518425\pi\) | ||||
−0.0578524 | + | 0.998325i | \(0.518425\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 39.3274 | 1.91670 | 0.958350 | − | 0.285596i | \(-0.0921914\pi\) | ||||
0.958350 | + | 0.285596i | \(0.0921914\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.488863 | 0.0236577 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 17.0607 | 0.823698 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.19358 | −0.394671 | −0.197335 | − | 0.980336i | \(-0.563229\pi\) | ||||
−0.197335 | + | 0.980336i | \(0.563229\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.6035 | −0.701798 | −0.350899 | − | 0.936413i | \(-0.614124\pi\) | ||||
−0.350899 | + | 0.936413i | \(0.614124\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −51.3461 | −2.45622 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.27607 | −0.251813 | −0.125907 | − | 0.992042i | \(-0.540184\pi\) | ||||
−0.125907 | + | 0.992042i | \(0.540184\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.5018 | −0.879046 | −0.439523 | − | 0.898231i | \(-0.644852\pi\) | ||||
−0.439523 | + | 0.898231i | \(0.644852\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.24443 | 0.342650 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.7146 | 0.552844 | 0.276422 | − | 0.961036i | \(-0.410851\pi\) | ||||
0.276422 | + | 0.961036i | \(0.410851\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.0607 | −0.803357 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.85728 | 0.416151 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.9590 | −0.886864 | −0.443432 | − | 0.896308i | \(-0.646239\pi\) | ||||
−0.443432 | + | 0.896308i | \(0.646239\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.18421 | 0.335330 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.1111 | −0.703793 | −0.351897 | − | 0.936039i | \(-0.614463\pi\) | ||||
−0.351897 | + | 0.936039i | \(0.614463\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.5718 | 1.04900 | 0.524501 | − | 0.851410i | \(-0.324252\pi\) | ||||
0.524501 | + | 0.851410i | \(0.324252\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.3684 | 1.03509 | 0.517543 | − | 0.855657i | \(-0.326847\pi\) | ||||
0.517543 | + | 0.855657i | \(0.326847\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.61285 | −0.166826 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.4795 | 0.621102 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.28544 | −0.289005 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.62222 | 0.211637 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 32.8573 | 1.50129 | 0.750644 | − | 0.660707i | \(-0.229744\pi\) | ||||
0.750644 | + | 0.660707i | \(0.229744\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.4068 | −0.748088 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.23506 | 0.283705 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.40943 | −0.154496 | −0.0772479 | − | 0.997012i | \(-0.524613\pi\) | ||||
−0.0772479 | + | 0.997012i | \(0.524613\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.00000 | −0.180886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.7877 | 1.52482 | 0.762409 | − | 0.647096i | \(-0.224017\pi\) | ||||
0.762409 | + | 0.647096i | \(0.224017\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.3684 | −0.647121 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.2953 | 0.461807 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.6316 | −0.610233 | −0.305117 | − | 0.952315i | \(-0.598695\pi\) | ||||
−0.305117 | + | 0.952315i | \(0.598695\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.10171 | −0.0938975 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.34614 | −0.327548 | −0.163774 | − | 0.986498i | \(-0.552367\pi\) | ||||
−0.163774 | + | 0.986498i | \(0.552367\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.59057 | −0.0706398 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.9684 | −0.707785 | −0.353892 | − | 0.935286i | \(-0.615142\pi\) | ||||
−0.353892 | + | 0.935286i | \(0.615142\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.2351 | 0.718197 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.23506 | −0.363587 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.1842 | 0.490932 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.09234 | −0.0478564 | −0.0239282 | − | 0.999714i | \(-0.507617\pi\) | ||||
−0.0239282 | + | 0.999714i | \(0.507617\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.5111 | −0.765709 | −0.382854 | − | 0.923809i | \(-0.625059\pi\) | ||||
−0.382854 | + | 0.923809i | \(0.625059\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 33.2070 | 1.44652 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.8760 | 0.690262 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.6128 | 0.503955 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11.4094 | −0.494197 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −20.6637 | −0.891705 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.05086 | 0.217556 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.3274 | −0.658977 | −0.329488 | − | 0.944160i | \(-0.606876\pi\) | ||||
−0.329488 | + | 0.944160i | \(0.606876\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 24.9590 | 1.07109 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.32741 | 0.227783 | 0.113892 | − | 0.993493i | \(-0.463668\pi\) | ||||
0.113892 | + | 0.993493i | \(0.463668\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.488863 | 0.0208641 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.4701 | 0.701651 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.24443 | −0.0529186 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.355509 | −0.0150634 | −0.00753171 | − | 0.999972i | \(-0.502397\pi\) | ||||
−0.00753171 | + | 0.999972i | \(0.502397\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.20342 | −0.177786 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 36.2864 | 1.53201 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16.4701 | −0.694133 | −0.347067 | − | 0.937841i | \(-0.612822\pi\) | ||||
−0.347067 | + | 0.937841i | \(0.612822\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.9590 | −0.878647 | −0.439323 | − | 0.898329i | \(-0.644782\pi\) | ||||
−0.439323 | + | 0.898329i | \(0.644782\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.5111 | −0.732818 | −0.366409 | − | 0.930454i | \(-0.619413\pi\) | ||||
−0.366409 | + | 0.930454i | \(0.619413\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.52098 | −0.397745 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.152089 | −0.00633155 | −0.00316577 | − | 0.999995i | \(-0.501008\pi\) | ||||
−0.00316577 | + | 0.999995i | \(0.501008\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −22.9590 | −0.954143 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.6128 | −0.481782 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.3461 | 0.966898 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 34.1847 | 1.41095 | 0.705476 | − | 0.708733i | \(-0.250733\pi\) | ||||
0.705476 | + | 0.708733i | \(0.250733\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −38.0642 | −1.56841 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19.8479 | −0.816434 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.3047 | −0.792747 | −0.396374 | − | 0.918089i | \(-0.629731\pi\) | ||||
−0.396374 | + | 0.918089i | \(0.629731\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.23506 | 0.337039 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.9081 | 1.05858 | 0.529289 | − | 0.848442i | \(-0.322459\pi\) | ||||
0.529289 | + | 0.848442i | \(0.322459\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.7368 | −0.927455 | −0.463727 | − | 0.885978i | \(-0.653488\pi\) | ||||
−0.463727 | + | 0.885978i | \(0.653488\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.61285 | −0.147127 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.9403 | −1.33700 | −0.668502 | − | 0.743711i | \(-0.733064\pi\) | ||||
−0.668502 | + | 0.743711i | \(0.733064\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.00000 | −0.0810441 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.1240 | 0.530073 | 0.265036 | − | 0.964238i | \(-0.414616\pi\) | ||||
0.265036 | + | 0.964238i | \(0.414616\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.2538 | −0.734870 | −0.367435 | − | 0.930049i | \(-0.619764\pi\) | ||||
−0.367435 | + | 0.930049i | \(0.619764\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.64449 | −0.307258 | −0.153629 | − | 0.988129i | \(-0.549096\pi\) | ||||
−0.153629 | + | 0.988129i | \(0.549096\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.23506 | 0.250204 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.99063 | 0.280074 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −41.5941 | −1.66111 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −34.8957 | −1.39138 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.6735 | −1.14148 | −0.570738 | − | 0.821132i | \(-0.693343\pi\) | ||||
−0.570738 | + | 0.821132i | \(0.693343\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.6128 | 0.461569 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.37778 | 0.133833 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.2953 | 0.407275 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.4479 | 0.610153 | 0.305077 | − | 0.952328i | \(-0.401318\pi\) | ||||
0.305077 | + | 0.952328i | \(0.401318\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.8350 | 1.01883 | 0.509417 | − | 0.860520i | \(-0.329861\pi\) | ||||
0.509417 | + | 0.860520i | \(0.329861\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.6128 | −0.928317 | −0.464158 | − | 0.885752i | \(-0.653643\pi\) | ||||
−0.464158 | + | 0.885752i | \(0.653643\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 58.6548 | 2.30240 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.62222 | 0.181159 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −36.7052 | −1.43639 | −0.718193 | − | 0.695844i | \(-0.755030\pi\) | ||||
−0.718193 | + | 0.695844i | \(0.755030\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.2351 | 0.633390 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −37.9911 | −1.47992 | −0.739962 | − | 0.672649i | \(-0.765156\pi\) | ||||
−0.739962 | + | 0.672649i | \(0.765156\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −49.2257 | −1.91466 | −0.957329 | − | 0.289001i | \(-0.906677\pi\) | ||||
−0.957329 | + | 0.289001i | \(0.906677\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 24.2667 | 0.942441 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.4701 | −0.482845 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.48886 | −0.0962250 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.46917 | 0.0953214 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.2257 | 0.432719 | 0.216359 | − | 0.976314i | \(-0.430582\pi\) | ||||
0.216359 | + | 0.976314i | \(0.430582\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.55262 | −0.367137 | −0.183569 | − | 0.983007i | \(-0.558765\pi\) | ||||
−0.183569 | + | 0.983007i | \(0.558765\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.23506 | −0.316033 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.857279 | 0.0328510 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.9684 | −0.687540 | −0.343770 | − | 0.939054i | \(-0.611704\pi\) | ||||
−0.343770 | + | 0.939054i | \(0.611704\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.4701 | −0.552070 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.6128 | 0.594802 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.355509 | −0.0135242 | −0.00676211 | − | 0.999977i | \(-0.502152\pi\) | ||||
−0.00676211 | + | 0.999977i | \(0.502152\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.05086 | 0.191866 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.2667 | −0.919167 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.96836 | −0.150097 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.2257 | 0.499528 | 0.249764 | − | 0.968307i | \(-0.419647\pi\) | ||||
0.249764 | + | 0.968307i | \(0.419647\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 40.0000 | 1.50863 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.47949 | −0.356513 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.9777 | −0.412277 | −0.206139 | − | 0.978523i | \(-0.566090\pi\) | ||||
−0.206139 | + | 0.978523i | \(0.566090\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.24443 | −0.0466698 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 28.8198 | 1.07931 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.90813 | −0.0712606 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.9813 | 0.819763 | 0.409881 | − | 0.912139i | \(-0.365570\pi\) | ||||
0.409881 | + | 0.912139i | \(0.365570\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.8573 | −0.627798 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.755569 | 0.0280999 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.0607 | −0.484395 | −0.242197 | − | 0.970227i | \(-0.577868\pi\) | ||||
−0.242197 | + | 0.970227i | \(0.577868\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.94025 | −0.330667 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.5625 | −0.500941 | −0.250471 | − | 0.968124i | \(-0.580585\pi\) | ||||
−0.250471 | + | 0.968124i | \(0.580585\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.2480 | −0.672173 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.2854 | −0.378356 | −0.189178 | − | 0.981943i | \(-0.560582\pi\) | ||||
−0.189178 | + | 0.981943i | \(0.560582\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −27.8163 | −1.02186 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.4608 | 0.787319 | 0.393659 | − | 0.919256i | \(-0.371209\pi\) | ||||
0.393659 | + | 0.919256i | \(0.371209\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11.6128 | −0.424892 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.4795 | −0.565608 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −46.0642 | −1.68091 | −0.840454 | − | 0.541883i | \(-0.817712\pi\) | ||||
−0.840454 | + | 0.541883i | \(0.817712\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.12399 | 0.332497 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.1052 | −0.985157 | −0.492579 | − | 0.870268i | \(-0.663946\pi\) | ||||
−0.492579 | + | 0.870268i | \(0.663946\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 31.4924 | 1.14310 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 39.4608 | 1.43045 | 0.715226 | − | 0.698894i | \(-0.246324\pi\) | ||||
0.715226 | + | 0.698894i | \(0.246324\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.61285 | −0.0583890 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 39.2257 | 1.41636 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.51114 | −0.270859 | −0.135429 | − | 0.990787i | \(-0.543241\pi\) | ||||
−0.135429 | + | 0.990787i | \(0.543241\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.28592 | −0.0463112 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.46965 | −0.0528596 | −0.0264298 | − | 0.999651i | \(-0.508414\pi\) | ||||
−0.0264298 | + | 0.999651i | \(0.508414\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.85728 | −0.174254 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 27.8163 | 0.996621 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 52.0000 | 1.86071 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.00000 | −0.0714742 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.2034 | −0.577590 | −0.288795 | − | 0.957391i | \(-0.593255\pi\) | ||||
−0.288795 | + | 0.957391i | \(0.593255\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.00937 | −0.249540 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.86665 | 0.0663703 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.65127 | 0.0586384 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.161933 | 0.00573597 | 0.00286799 | − | 0.999996i | \(-0.499087\pi\) | ||||
0.00286799 | + | 0.999996i | \(0.499087\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.99063 | 0.247002 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 82.0010 | 2.89375 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23.1941 | 0.816469 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −42.9403 | −1.50970 | −0.754849 | − | 0.655898i | \(-0.772290\pi\) | ||||
−0.754849 | + | 0.655898i | \(0.772290\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.2958 | 1.45009 | 0.725045 | − | 0.688701i | \(-0.241819\pi\) | ||||
0.725045 | + | 0.688701i | \(0.241819\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.11108 | −0.249396 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.2480 | 0.358531 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.37778 | 0.118029 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −43.2070 | −1.50793 | −0.753967 | − | 0.656913i | \(-0.771862\pi\) | ||||
−0.753967 | + | 0.656913i | \(0.771862\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.1427 | 0.388411 | 0.194205 | − | 0.980961i | \(-0.437787\pi\) | ||||
0.194205 | + | 0.980961i | \(0.437787\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.9906 | −1.28629 | −0.643145 | − | 0.765744i | \(-0.722371\pi\) | ||||
−0.643145 | + | 0.765744i | \(0.722371\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.6735 | −0.787485 | −0.393742 | − | 0.919221i | \(-0.628820\pi\) | ||||
−0.393742 | + | 0.919221i | \(0.628820\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.34614 | 0.254835 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.18421 | 0.248918 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.62222 | 0.159767 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.8983 | 0.756013 | 0.378006 | − | 0.925803i | \(-0.376610\pi\) | ||||
0.378006 | + | 0.925803i | \(0.376610\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19.9813 | −0.688191 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.5111 | 0.498609 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.85728 | −0.166701 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −30.2854 | −1.03817 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 52.4010 | 1.79418 | 0.897088 | − | 0.441851i | \(-0.145678\pi\) | ||||
0.897088 | + | 0.441851i | \(0.145678\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.5116 | −0.837301 | −0.418650 | − | 0.908147i | \(-0.637497\pi\) | ||||
−0.418650 | + | 0.908147i | \(0.637497\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −57.4795 | −1.96118 | −0.980588 | − | 0.196082i | \(-0.937178\pi\) | ||||
−0.980588 | + | 0.196082i | \(0.937178\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.37778 | −0.115115 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21.1941 | −0.721454 | −0.360727 | − | 0.932671i | \(-0.617471\pi\) | ||||
−0.360727 | + | 0.932671i | \(0.617471\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 34.6128 | 1.17551 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.28544 | −0.213219 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.2034 | −0.413497 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.23506 | −0.278715 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.38715 | 0.283214 | 0.141607 | − | 0.989923i | \(-0.454773\pi\) | ||||
0.141607 | + | 0.989923i | \(0.454773\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −11.1842 | −0.377234 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.1753 | 0.982941 | 0.491471 | − | 0.870894i | \(-0.336459\pi\) | ||||
0.491471 | + | 0.870894i | \(0.336459\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.8796 | 0.669000 | 0.334500 | − | 0.942396i | \(-0.391433\pi\) | ||||
0.334500 | + | 0.942396i | \(0.391433\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.6923 | −0.493319 | −0.246659 | − | 0.969102i | \(-0.579333\pi\) | ||||
−0.246659 | + | 0.969102i | \(0.579333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.8573 | −0.431219 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.05086 | 0.169210 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 21.0607 | 0.703196 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.24443 | −0.308319 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33.2070 | 1.10628 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.24443 | −0.0414121 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.8796 | 0.660090 | 0.330045 | − | 0.943965i | \(-0.392936\pi\) | ||||
0.330045 | + | 0.943965i | \(0.392936\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.47949 | −0.314415 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 53.3372 | 1.76714 | 0.883571 | − | 0.468297i | \(-0.155132\pi\) | ||||
0.883571 | + | 0.468297i | \(0.155132\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −58.6548 | −1.94119 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −21.7146 | −0.717078 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.1240 | 0.696816 | 0.348408 | − | 0.937343i | \(-0.386722\pi\) | ||||
0.348408 | + | 0.937343i | \(0.386722\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23.3461 | 0.769282 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 34.7753 | 1.14464 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.8573 | −0.553666 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.72393 | 0.0893691 | 0.0446846 | − | 0.999001i | \(-0.485772\pi\) | ||||
0.0446846 | + | 0.999001i | \(0.485772\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.23506 | −0.269893 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 32.8573 | 1.07570 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.3145 | −0.500303 | −0.250151 | − | 0.968207i | \(-0.580480\pi\) | ||||
−0.250151 | + | 0.968207i | \(0.580480\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 28.8256 | 0.940689 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.6035 | −0.997645 | −0.498822 | − | 0.866704i | \(-0.666234\pi\) | ||||
−0.498822 | + | 0.866704i | \(0.666234\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.0607 | −0.685831 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.74266 | 0.0891245 | 0.0445623 | − | 0.999007i | \(-0.485811\pi\) | ||||
0.0445623 | + | 0.999007i | \(0.485811\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 54.8385 | 1.78013 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.3590 | 0.822323 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −47.8479 | −1.54995 | −0.774973 | − | 0.631994i | \(-0.782237\pi\) | ||||
−0.774973 | + | 0.631994i | \(0.782237\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.1017 | −0.326542 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.47949 | 0.306109 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.63512 | −0.310810 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.4795 | −0.498820 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38.7181 | 1.24509 | 0.622545 | − | 0.782584i | \(-0.286099\pi\) | ||||
0.622545 | + | 0.782584i | \(0.286099\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −59.1624 | −1.90057 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.7778 | −0.442152 | −0.221076 | − | 0.975257i | \(-0.570957\pi\) | ||||
−0.221076 | + | 0.975257i | \(0.570957\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.1334 | −0.324860 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.03164 | 0.128984 | 0.0644918 | − | 0.997918i | \(-0.479457\pi\) | ||||
0.0644918 | + | 0.997918i | \(0.479457\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35.3087 | 1.12847 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.61285 | −0.0514943 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −47.4924 | −1.51477 | −0.757386 | − | 0.652967i | \(-0.773524\pi\) | ||||
−0.757386 | + | 0.652967i | \(0.773524\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.75911 | −0.246725 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.16146 | −0.0368949 | −0.0184474 | − | 0.999830i | \(-0.505872\pi\) | ||||
−0.0184474 | + | 0.999830i | \(0.505872\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.89829 | −0.0602404 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.4572 | −0.584546 | −0.292273 | − | 0.956335i | \(-0.594412\pi\) | ||||
−0.292273 | + | 0.956335i | \(0.594412\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.85728 | −0.153678 |
(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 | 8400.2.a.dl.1.3 | 3 | ||
4.3 | odd | 2 | 4200.2.a.bn.1.1 | 3 | |||
5.2 | odd | 4 | 1680.2.t.j.1009.2 | 6 | |||
5.3 | odd | 4 | 1680.2.t.j.1009.5 | 6 | |||
5.4 | even | 2 | 8400.2.a.di.1.3 | 3 | |||
15.2 | even | 4 | 5040.2.t.z.1009.4 | 6 | |||
15.8 | even | 4 | 5040.2.t.z.1009.3 | 6 | |||
20.3 | even | 4 | 840.2.t.d.169.2 | ✓ | 6 | ||
20.7 | even | 4 | 840.2.t.d.169.5 | yes | 6 | ||
20.19 | odd | 2 | 4200.2.a.bp.1.1 | 3 | |||
60.23 | odd | 4 | 2520.2.t.k.1009.3 | 6 | |||
60.47 | odd | 4 | 2520.2.t.k.1009.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.t.d.169.2 | ✓ | 6 | 20.3 | even | 4 | ||
840.2.t.d.169.5 | yes | 6 | 20.7 | even | 4 | ||
1680.2.t.j.1009.2 | 6 | 5.2 | odd | 4 | |||
1680.2.t.j.1009.5 | 6 | 5.3 | odd | 4 | |||
2520.2.t.k.1009.3 | 6 | 60.23 | odd | 4 | |||
2520.2.t.k.1009.4 | 6 | 60.47 | odd | 4 | |||
4200.2.a.bn.1.1 | 3 | 4.3 | odd | 2 | |||
4200.2.a.bp.1.1 | 3 | 20.19 | odd | 2 | |||
5040.2.t.z.1009.3 | 6 | 15.8 | even | 4 | |||
5040.2.t.z.1009.4 | 6 | 15.2 | even | 4 | |||
8400.2.a.di.1.3 | 3 | 5.4 | even | 2 | |||
8400.2.a.dl.1.3 | 3 | 1.1 | even | 1 | trivial |