Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(199,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.c (of order \(2\), degree \(1\), not 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: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.4 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.199 |
Dual form | 825.2.c.c.199.1 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.73205i | 1.22474i | 0.790569 | + | 0.612372i | \(0.209785\pi\) | ||||
−0.790569 | + | 0.612372i | \(0.790215\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.73205 | −0.707107 | ||||||||
\(7\) | − 2.00000i | − 0.755929i | −0.925820 | − | 0.377964i | \(-0.876624\pi\) | ||||
0.925820 | − | 0.377964i | \(-0.123376\pi\) | |||||||
\(8\) | 1.73205i | 0.612372i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | − 1.00000i | − 0.288675i | ||||||||
\(13\) | 5.46410i | 1.51547i | 0.652563 | + | 0.757735i | \(0.273694\pi\) | ||||
−0.652563 | + | 0.757735i | \(0.726306\pi\) | |||||||
\(14\) | 3.46410 | 0.925820 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.00000 | −1.25000 | ||||||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | − 1.73205i | − 0.408248i | ||||||||
\(19\) | −5.46410 | −1.25355 | −0.626775 | − | 0.779200i | \(-0.715626\pi\) | ||||
−0.626775 | + | 0.779200i | \(0.715626\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | 0.436436 | ||||||||
\(22\) | − 1.73205i | − 0.369274i | ||||||||
\(23\) | 6.92820i | 1.44463i | 0.691564 | + | 0.722315i | \(0.256922\pi\) | ||||
−0.691564 | + | 0.722315i | \(0.743078\pi\) | |||||||
\(24\) | −1.73205 | −0.353553 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −9.46410 | −1.85606 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | 2.00000i | 0.377964i | ||||||||
\(29\) | 3.46410 | 0.643268 | 0.321634 | − | 0.946864i | \(-0.395768\pi\) | ||||
0.321634 | + | 0.946864i | \(0.395768\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.9282 | −1.96276 | −0.981382 | − | 0.192068i | \(-0.938481\pi\) | ||||
−0.981382 | + | 0.192068i | \(0.938481\pi\) | |||||||
\(32\) | − 5.19615i | − 0.918559i | ||||||||
\(33\) | − 1.00000i | − 0.174078i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 4.92820i | 0.810192i | 0.914274 | + | 0.405096i | \(0.132762\pi\) | ||||
−0.914274 | + | 0.405096i | \(0.867238\pi\) | |||||||
\(38\) | − 9.46410i | − 1.53528i | ||||||||
\(39\) | −5.46410 | −0.874957 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.46410 | 0.541002 | 0.270501 | − | 0.962720i | \(-0.412811\pi\) | ||||
0.270501 | + | 0.962720i | \(0.412811\pi\) | |||||||
\(42\) | 3.46410i | 0.534522i | ||||||||
\(43\) | − 4.92820i | − 0.751544i | −0.926712 | − | 0.375772i | \(-0.877378\pi\) | ||||
0.926712 | − | 0.375772i | \(-0.122622\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12.0000 | −1.76930 | ||||||||
\(47\) | 6.92820i | 1.01058i | 0.862949 | + | 0.505291i | \(0.168615\pi\) | ||||
−0.862949 | + | 0.505291i | \(0.831385\pi\) | |||||||
\(48\) | − 5.00000i | − 0.721688i | ||||||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 5.46410i | − 0.757735i | ||||||||
\(53\) | 0.928203i | 0.127499i | 0.997966 | + | 0.0637493i | \(0.0203058\pi\) | ||||
−0.997966 | + | 0.0637493i | \(0.979694\pi\) | |||||||
\(54\) | 1.73205 | 0.235702 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.46410 | 0.462910 | ||||||||
\(57\) | − 5.46410i | − 0.723738i | ||||||||
\(58\) | 6.00000i | 0.787839i | ||||||||
\(59\) | 6.92820 | 0.901975 | 0.450988 | − | 0.892530i | \(-0.351072\pi\) | ||||
0.450988 | + | 0.892530i | \(0.351072\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | − 18.9282i | − 2.40388i | ||||||||
\(63\) | 2.00000i | 0.251976i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.73205 | 0.213201 | ||||||||
\(67\) | − 8.00000i | − 0.977356i | −0.872464 | − | 0.488678i | \(-0.837479\pi\) | ||||
0.872464 | − | 0.488678i | \(-0.162521\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.92820 | −0.834058 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.8564 | 1.64445 | 0.822226 | − | 0.569160i | \(-0.192732\pi\) | ||||
0.822226 | + | 0.569160i | \(0.192732\pi\) | |||||||
\(72\) | − 1.73205i | − 0.204124i | ||||||||
\(73\) | − 8.39230i | − 0.982245i | −0.871091 | − | 0.491122i | \(-0.836587\pi\) | ||||
0.871091 | − | 0.491122i | \(-0.163413\pi\) | |||||||
\(74\) | −8.53590 | −0.992278 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.46410 | 0.626775 | ||||||||
\(77\) | 2.00000i | 0.227921i | ||||||||
\(78\) | − 9.46410i | − 1.07160i | ||||||||
\(79\) | 6.53590 | 0.735346 | 0.367673 | − | 0.929955i | \(-0.380155\pi\) | ||||
0.367673 | + | 0.929955i | \(0.380155\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.00000i | 0.662589i | ||||||||
\(83\) | 8.53590i | 0.936937i | 0.883480 | + | 0.468468i | \(0.155194\pi\) | ||||
−0.883480 | + | 0.468468i | \(0.844806\pi\) | |||||||
\(84\) | −2.00000 | −0.218218 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.53590 | 0.920450 | ||||||||
\(87\) | 3.46410i | 0.371391i | ||||||||
\(88\) | − 1.73205i | − 0.184637i | ||||||||
\(89\) | −0.928203 | −0.0983893 | −0.0491947 | − | 0.998789i | \(-0.515665\pi\) | ||||
−0.0491947 | + | 0.998789i | \(0.515665\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.9282 | 1.14559 | ||||||||
\(92\) | − 6.92820i | − 0.722315i | ||||||||
\(93\) | − 10.9282i | − 1.13320i | ||||||||
\(94\) | −12.0000 | −1.23771 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.19615 | 0.530330 | ||||||||
\(97\) | 10.0000i | 1.01535i | 0.861550 | + | 0.507673i | \(0.169494\pi\) | ||||
−0.861550 | + | 0.507673i | \(0.830506\pi\) | |||||||
\(98\) | 5.19615i | 0.524891i | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.3923 | −1.03407 | −0.517036 | − | 0.855963i | \(-0.672965\pi\) | ||||
−0.517036 | + | 0.855963i | \(0.672965\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000i | 0.788263i | 0.919054 | + | 0.394132i | \(0.128955\pi\) | ||||
−0.919054 | + | 0.394132i | \(0.871045\pi\) | |||||||
\(104\) | −9.46410 | −0.928032 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.60770 | −0.156153 | ||||||||
\(107\) | − 8.53590i | − 0.825196i | −0.910913 | − | 0.412598i | \(-0.864621\pi\) | ||||
0.910913 | − | 0.412598i | \(-0.135379\pi\) | |||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | 10.0000 | 0.957826 | 0.478913 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.92820 | −0.467764 | ||||||||
\(112\) | 10.0000i | 0.944911i | ||||||||
\(113\) | − 12.9282i | − 1.21618i | −0.793867 | − | 0.608092i | \(-0.791935\pi\) | ||||
0.793867 | − | 0.608092i | \(-0.208065\pi\) | |||||||
\(114\) | 9.46410 | 0.886394 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.46410 | −0.321634 | ||||||||
\(117\) | − 5.46410i | − 0.505156i | ||||||||
\(118\) | 12.0000i | 1.10469i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 3.46410i | 0.313625i | ||||||||
\(123\) | 3.46410i | 0.312348i | ||||||||
\(124\) | 10.9282 | 0.981382 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3.46410 | −0.308607 | ||||||||
\(127\) | − 8.92820i | − 0.792250i | −0.918197 | − | 0.396125i | \(-0.870355\pi\) | ||||
0.918197 | − | 0.396125i | \(-0.129645\pi\) | |||||||
\(128\) | − 12.1244i | − 1.07165i | ||||||||
\(129\) | 4.92820 | 0.433904 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.9282 | 1.65376 | 0.826882 | − | 0.562375i | \(-0.190112\pi\) | ||||
0.826882 | + | 0.562375i | \(0.190112\pi\) | |||||||
\(132\) | 1.00000i | 0.0870388i | ||||||||
\(133\) | 10.9282i | 0.947595i | ||||||||
\(134\) | 13.8564 | 1.19701 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.0000i | 1.53784i | 0.639343 | + | 0.768922i | \(0.279207\pi\) | ||||
−0.639343 | + | 0.768922i | \(0.720793\pi\) | |||||||
\(138\) | − 12.0000i | − 1.02151i | ||||||||
\(139\) | −12.3923 | −1.05110 | −0.525551 | − | 0.850762i | \(-0.676141\pi\) | ||||
−0.525551 | + | 0.850762i | \(0.676141\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.92820 | −0.583460 | ||||||||
\(142\) | 24.0000i | 2.01404i | ||||||||
\(143\) | − 5.46410i | − 0.456931i | ||||||||
\(144\) | 5.00000 | 0.416667 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 14.5359 | 1.20300 | ||||||||
\(147\) | 3.00000i | 0.247436i | ||||||||
\(148\) | − 4.92820i | − 0.405096i | ||||||||
\(149\) | 15.4641 | 1.26687 | 0.633434 | − | 0.773796i | \(-0.281645\pi\) | ||||
0.633434 | + | 0.773796i | \(0.281645\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.3923 | −1.65950 | −0.829751 | − | 0.558134i | \(-0.811518\pi\) | ||||
−0.829751 | + | 0.558134i | \(0.811518\pi\) | |||||||
\(152\) | − 9.46410i | − 0.767640i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.46410 | −0.279145 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 5.46410 | 0.437478 | ||||||||
\(157\) | 3.07180i | 0.245156i | 0.992459 | + | 0.122578i | \(0.0391162\pi\) | ||||
−0.992459 | + | 0.122578i | \(0.960884\pi\) | |||||||
\(158\) | 11.3205i | 0.900611i | ||||||||
\(159\) | −0.928203 | −0.0736113 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.8564 | 1.09204 | ||||||||
\(162\) | 1.73205i | 0.136083i | ||||||||
\(163\) | 9.85641i | 0.772013i | 0.922496 | + | 0.386007i | \(0.126146\pi\) | ||||
−0.922496 | + | 0.386007i | \(0.873854\pi\) | |||||||
\(164\) | −3.46410 | −0.270501 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.7846 | −1.14751 | ||||||||
\(167\) | 10.3923i | 0.804181i | 0.915600 | + | 0.402090i | \(0.131716\pi\) | ||||
−0.915600 | + | 0.402090i | \(0.868284\pi\) | |||||||
\(168\) | 3.46410i | 0.267261i | ||||||||
\(169\) | −16.8564 | −1.29665 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.46410 | 0.417850 | ||||||||
\(172\) | 4.92820i | 0.375772i | ||||||||
\(173\) | − 12.0000i | − 0.912343i | −0.889892 | − | 0.456172i | \(-0.849220\pi\) | ||||
0.889892 | − | 0.456172i | \(-0.150780\pi\) | |||||||
\(174\) | −6.00000 | −0.454859 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.00000 | 0.376889 | ||||||||
\(177\) | 6.92820i | 0.520756i | ||||||||
\(178\) | − 1.60770i | − 0.120502i | ||||||||
\(179\) | −6.92820 | −0.517838 | −0.258919 | − | 0.965899i | \(-0.583366\pi\) | ||||
−0.258919 | + | 0.965899i | \(0.583366\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.8564 | 1.17860 | 0.589299 | − | 0.807915i | \(-0.299404\pi\) | ||||
0.589299 | + | 0.807915i | \(0.299404\pi\) | |||||||
\(182\) | 18.9282i | 1.40305i | ||||||||
\(183\) | 2.00000i | 0.147844i | ||||||||
\(184\) | −12.0000 | −0.884652 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 18.9282 | 1.38788 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − 6.92820i | − 0.505291i | ||||||||
\(189\) | −2.00000 | −0.145479 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.9282 | −1.36960 | −0.684798 | − | 0.728733i | \(-0.740110\pi\) | ||||
−0.684798 | + | 0.728733i | \(0.740110\pi\) | |||||||
\(192\) | − 1.00000i | − 0.0721688i | ||||||||
\(193\) | 24.3923i | 1.75580i | 0.478847 | + | 0.877898i | \(0.341055\pi\) | ||||
−0.478847 | + | 0.877898i | \(0.658945\pi\) | |||||||
\(194\) | −17.3205 | −1.24354 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | 12.0000i | 0.854965i | 0.904024 | + | 0.427482i | \(0.140599\pi\) | ||||
−0.904024 | + | 0.427482i | \(0.859401\pi\) | |||||||
\(198\) | 1.73205i | 0.123091i | ||||||||
\(199\) | 24.7846 | 1.75693 | 0.878467 | − | 0.477803i | \(-0.158567\pi\) | ||||
0.878467 | + | 0.477803i | \(0.158567\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.00000 | 0.564276 | ||||||||
\(202\) | − 18.0000i | − 1.26648i | ||||||||
\(203\) | − 6.92820i | − 0.486265i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −13.8564 | −0.965422 | ||||||||
\(207\) | − 6.92820i | − 0.481543i | ||||||||
\(208\) | − 27.3205i | − 1.89434i | ||||||||
\(209\) | 5.46410 | 0.377960 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.39230 | −0.577750 | −0.288875 | − | 0.957367i | \(-0.593281\pi\) | ||||
−0.288875 | + | 0.957367i | \(0.593281\pi\) | |||||||
\(212\) | − 0.928203i | − 0.0637493i | ||||||||
\(213\) | 13.8564i | 0.949425i | ||||||||
\(214\) | 14.7846 | 1.01066 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.73205 | 0.117851 | ||||||||
\(217\) | 21.8564i | 1.48371i | ||||||||
\(218\) | 17.3205i | 1.17309i | ||||||||
\(219\) | 8.39230 | 0.567099 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | − 8.53590i | − 0.572892i | ||||||||
\(223\) | 9.85641i | 0.660034i | 0.943975 | + | 0.330017i | \(0.107054\pi\) | ||||
−0.943975 | + | 0.330017i | \(0.892946\pi\) | |||||||
\(224\) | −10.3923 | −0.694365 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 22.3923 | 1.48951 | ||||||||
\(227\) | − 15.4641i | − 1.02639i | −0.858272 | − | 0.513194i | \(-0.828462\pi\) | ||||
0.858272 | − | 0.513194i | \(-0.171538\pi\) | |||||||
\(228\) | 5.46410i | 0.361869i | ||||||||
\(229\) | 23.8564 | 1.57648 | 0.788238 | − | 0.615371i | \(-0.210994\pi\) | ||||
0.788238 | + | 0.615371i | \(0.210994\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.00000 | −0.131590 | ||||||||
\(232\) | 6.00000i | 0.393919i | ||||||||
\(233\) | 12.0000i | 0.786146i | 0.919507 | + | 0.393073i | \(0.128588\pi\) | ||||
−0.919507 | + | 0.393073i | \(0.871412\pi\) | |||||||
\(234\) | 9.46410 | 0.618688 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.92820 | −0.450988 | ||||||||
\(237\) | 6.53590i | 0.424552i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.0000 | 0.776215 | 0.388108 | − | 0.921614i | \(-0.373129\pi\) | ||||
0.388108 | + | 0.921614i | \(0.373129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.143594 | 0.00924967 | 0.00462484 | − | 0.999989i | \(-0.498528\pi\) | ||||
0.00462484 | + | 0.999989i | \(0.498528\pi\) | |||||||
\(242\) | 1.73205i | 0.111340i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −2.00000 | −0.128037 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.00000 | −0.382546 | ||||||||
\(247\) | − 29.8564i | − 1.89972i | ||||||||
\(248\) | − 18.9282i | − 1.20194i | ||||||||
\(249\) | −8.53590 | −0.540941 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.85641 | −0.117175 | −0.0585877 | − | 0.998282i | \(-0.518660\pi\) | ||||
−0.0585877 | + | 0.998282i | \(0.518660\pi\) | |||||||
\(252\) | − 2.00000i | − 0.125988i | ||||||||
\(253\) | − 6.92820i | − 0.435572i | ||||||||
\(254\) | 15.4641 | 0.970304 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.0000 | 1.18750 | ||||||||
\(257\) | 19.8564i | 1.23861i | 0.785151 | + | 0.619304i | \(0.212585\pi\) | ||||
−0.785151 | + | 0.619304i | \(0.787415\pi\) | |||||||
\(258\) | 8.53590i | 0.531422i | ||||||||
\(259\) | 9.85641 | 0.612447 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.46410 | −0.214423 | ||||||||
\(262\) | 32.7846i | 2.02544i | ||||||||
\(263\) | 20.5359i | 1.26630i | 0.774030 | + | 0.633149i | \(0.218238\pi\) | ||||
−0.774030 | + | 0.633149i | \(0.781762\pi\) | |||||||
\(264\) | 1.73205 | 0.106600 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −18.9282 | −1.16056 | ||||||||
\(267\) | − 0.928203i | − 0.0568051i | ||||||||
\(268\) | 8.00000i | 0.488678i | ||||||||
\(269\) | −19.8564 | −1.21067 | −0.605333 | − | 0.795972i | \(-0.706960\pi\) | ||||
−0.605333 | + | 0.795972i | \(0.706960\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.6077 | −0.705117 | −0.352559 | − | 0.935790i | \(-0.614688\pi\) | ||||
−0.352559 | + | 0.935790i | \(0.614688\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.9282i | 0.661405i | ||||||||
\(274\) | −31.1769 | −1.88347 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.92820 | 0.417029 | ||||||||
\(277\) | − 29.4641i | − 1.77033i | −0.465281 | − | 0.885163i | \(-0.654047\pi\) | ||||
0.465281 | − | 0.885163i | \(-0.345953\pi\) | |||||||
\(278\) | − 21.4641i | − 1.28733i | ||||||||
\(279\) | 10.9282 | 0.654254 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.46410 | 0.206651 | 0.103325 | − | 0.994648i | \(-0.467052\pi\) | ||||
0.103325 | + | 0.994648i | \(0.467052\pi\) | |||||||
\(282\) | − 12.0000i | − 0.714590i | ||||||||
\(283\) | − 4.92820i | − 0.292951i | −0.989214 | − | 0.146476i | \(-0.953207\pi\) | ||||
0.989214 | − | 0.146476i | \(-0.0467930\pi\) | |||||||
\(284\) | −13.8564 | −0.822226 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.46410 | 0.559624 | ||||||||
\(287\) | − 6.92820i | − 0.408959i | ||||||||
\(288\) | 5.19615i | 0.306186i | ||||||||
\(289\) | 17.0000 | 1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.0000 | −0.586210 | ||||||||
\(292\) | 8.39230i | 0.491122i | ||||||||
\(293\) | − 13.8564i | − 0.809500i | −0.914427 | − | 0.404750i | \(-0.867359\pi\) | ||||
0.914427 | − | 0.404750i | \(-0.132641\pi\) | |||||||
\(294\) | −5.19615 | −0.303046 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8.53590 | −0.496139 | ||||||||
\(297\) | 1.00000i | 0.0580259i | ||||||||
\(298\) | 26.7846i | 1.55159i | ||||||||
\(299\) | −37.8564 | −2.18929 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.85641 | −0.568114 | ||||||||
\(302\) | − 35.3205i | − 2.03247i | ||||||||
\(303\) | − 10.3923i | − 0.597022i | ||||||||
\(304\) | 27.3205 | 1.56694 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 14.0000i | − 0.799022i | −0.916728 | − | 0.399511i | \(-0.869180\pi\) | ||||
0.916728 | − | 0.399511i | \(-0.130820\pi\) | |||||||
\(308\) | − 2.00000i | − 0.113961i | ||||||||
\(309\) | −8.00000 | −0.455104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.07180 | 0.287595 | 0.143798 | − | 0.989607i | \(-0.454069\pi\) | ||||
0.143798 | + | 0.989607i | \(0.454069\pi\) | |||||||
\(312\) | − 9.46410i | − 0.535799i | ||||||||
\(313\) | 20.9282i | 1.18293i | 0.806330 | + | 0.591466i | \(0.201451\pi\) | ||||
−0.806330 | + | 0.591466i | \(0.798549\pi\) | |||||||
\(314\) | −5.32051 | −0.300254 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.53590 | −0.367673 | ||||||||
\(317\) | 24.9282i | 1.40011i | 0.714090 | + | 0.700054i | \(0.246841\pi\) | ||||
−0.714090 | + | 0.700054i | \(0.753159\pi\) | |||||||
\(318\) | − 1.60770i | − 0.0901551i | ||||||||
\(319\) | −3.46410 | −0.193952 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.53590 | 0.476427 | ||||||||
\(322\) | 24.0000i | 1.33747i | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −17.0718 | −0.945519 | ||||||||
\(327\) | 10.0000i | 0.553001i | ||||||||
\(328\) | 6.00000i | 0.331295i | ||||||||
\(329\) | 13.8564 | 0.763928 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.85641 | 0.541757 | 0.270879 | − | 0.962614i | \(-0.412686\pi\) | ||||
0.270879 | + | 0.962614i | \(0.412686\pi\) | |||||||
\(332\) | − 8.53590i | − 0.468468i | ||||||||
\(333\) | − 4.92820i | − 0.270064i | ||||||||
\(334\) | −18.0000 | −0.984916 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −10.0000 | −0.545545 | ||||||||
\(337\) | − 33.1769i | − 1.80726i | −0.428312 | − | 0.903631i | \(-0.640892\pi\) | ||||
0.428312 | − | 0.903631i | \(-0.359108\pi\) | |||||||
\(338\) | − 29.1962i | − 1.58806i | ||||||||
\(339\) | 12.9282 | 0.702164 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.9282 | 0.591795 | ||||||||
\(342\) | 9.46410i | 0.511760i | ||||||||
\(343\) | − 20.0000i | − 1.07990i | ||||||||
\(344\) | 8.53590 | 0.460225 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 20.7846 | 1.11739 | ||||||||
\(347\) | − 22.3923i | − 1.20208i | −0.799218 | − | 0.601041i | \(-0.794753\pi\) | ||||
0.799218 | − | 0.601041i | \(-0.205247\pi\) | |||||||
\(348\) | − 3.46410i | − 0.185695i | ||||||||
\(349\) | 8.14359 | 0.435917 | 0.217958 | − | 0.975958i | \(-0.430060\pi\) | ||||
0.217958 | + | 0.975958i | \(0.430060\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.46410 | 0.291652 | ||||||||
\(352\) | 5.19615i | 0.276956i | ||||||||
\(353\) | 12.9282i | 0.688099i | 0.938952 | + | 0.344049i | \(0.111799\pi\) | ||||
−0.938952 | + | 0.344049i | \(0.888201\pi\) | |||||||
\(354\) | −12.0000 | −0.637793 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.928203 | 0.0491947 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 12.0000i | − 0.634220i | ||||||||
\(359\) | 20.7846 | 1.09697 | 0.548485 | − | 0.836160i | \(-0.315205\pi\) | ||||
0.548485 | + | 0.836160i | \(0.315205\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.8564 | 0.571390 | ||||||||
\(362\) | 27.4641i | 1.44348i | ||||||||
\(363\) | 1.00000i | 0.0524864i | ||||||||
\(364\) | −10.9282 | −0.572793 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.46410 | −0.181071 | ||||||||
\(367\) | − 20.0000i | − 1.04399i | −0.852948 | − | 0.521996i | \(-0.825188\pi\) | ||||
0.852948 | − | 0.521996i | \(-0.174812\pi\) | |||||||
\(368\) | − 34.6410i | − 1.80579i | ||||||||
\(369\) | −3.46410 | −0.180334 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.85641 | 0.0963798 | ||||||||
\(372\) | 10.9282i | 0.566601i | ||||||||
\(373\) | − 20.3923i | − 1.05587i | −0.849284 | − | 0.527937i | \(-0.822966\pi\) | ||||
0.849284 | − | 0.527937i | \(-0.177034\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −12.0000 | −0.618853 | ||||||||
\(377\) | 18.9282i | 0.974852i | ||||||||
\(378\) | − 3.46410i | − 0.178174i | ||||||||
\(379\) | 17.8564 | 0.917222 | 0.458611 | − | 0.888637i | \(-0.348347\pi\) | ||||
0.458611 | + | 0.888637i | \(0.348347\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.92820 | 0.457406 | ||||||||
\(382\) | − 32.7846i | − 1.67741i | ||||||||
\(383\) | − 13.8564i | − 0.708029i | −0.935240 | − | 0.354015i | \(-0.884816\pi\) | ||||
0.935240 | − | 0.354015i | \(-0.115184\pi\) | |||||||
\(384\) | 12.1244 | 0.618718 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −42.2487 | −2.15040 | ||||||||
\(387\) | 4.92820i | 0.250515i | ||||||||
\(388\) | − 10.0000i | − 0.507673i | ||||||||
\(389\) | −11.0718 | −0.561362 | −0.280681 | − | 0.959801i | \(-0.590560\pi\) | ||||
−0.280681 | + | 0.959801i | \(0.590560\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 5.19615i | 0.262445i | ||||||||
\(393\) | 18.9282i | 0.954802i | ||||||||
\(394\) | −20.7846 | −1.04711 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.00000 | −0.0502519 | ||||||||
\(397\) | − 2.00000i | − 0.100377i | −0.998740 | − | 0.0501886i | \(-0.984018\pi\) | ||||
0.998740 | − | 0.0501886i | \(-0.0159822\pi\) | |||||||
\(398\) | 42.9282i | 2.15180i | ||||||||
\(399\) | −10.9282 | −0.547094 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.85641 | −0.392330 | −0.196165 | − | 0.980571i | \(-0.562849\pi\) | ||||
−0.196165 | + | 0.980571i | \(0.562849\pi\) | |||||||
\(402\) | 13.8564i | 0.691095i | ||||||||
\(403\) | − 59.7128i | − 2.97451i | ||||||||
\(404\) | 10.3923 | 0.517036 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12.0000 | 0.595550 | ||||||||
\(407\) | − 4.92820i | − 0.244282i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.78461 | 0.335477 | 0.167739 | − | 0.985831i | \(-0.446354\pi\) | ||||
0.167739 | + | 0.985831i | \(0.446354\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.0000 | −0.887875 | ||||||||
\(412\) | − 8.00000i | − 0.394132i | ||||||||
\(413\) | − 13.8564i | − 0.681829i | ||||||||
\(414\) | 12.0000 | 0.589768 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 28.3923 | 1.39205 | ||||||||
\(417\) | − 12.3923i | − 0.606854i | ||||||||
\(418\) | 9.46410i | 0.462904i | ||||||||
\(419\) | −30.9282 | −1.51094 | −0.755471 | − | 0.655182i | \(-0.772592\pi\) | ||||
−0.755471 | + | 0.655182i | \(0.772592\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.00000 | 0.0974740 | 0.0487370 | − | 0.998812i | \(-0.484480\pi\) | ||||
0.0487370 | + | 0.998812i | \(0.484480\pi\) | |||||||
\(422\) | − 14.5359i | − 0.707596i | ||||||||
\(423\) | − 6.92820i | − 0.336861i | ||||||||
\(424\) | −1.60770 | −0.0780766 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −24.0000 | −1.16280 | ||||||||
\(427\) | − 4.00000i | − 0.193574i | ||||||||
\(428\) | 8.53590i | 0.412598i | ||||||||
\(429\) | 5.46410 | 0.263809 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.78461 | 0.423140 | 0.211570 | − | 0.977363i | \(-0.432142\pi\) | ||||
0.211570 | + | 0.977363i | \(0.432142\pi\) | |||||||
\(432\) | 5.00000i | 0.240563i | ||||||||
\(433\) | 0.143594i | 0.00690067i | 0.999994 | + | 0.00345033i | \(0.00109828\pi\) | ||||
−0.999994 | + | 0.00345033i | \(0.998902\pi\) | |||||||
\(434\) | −37.8564 | −1.81717 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.0000 | −0.478913 | ||||||||
\(437\) | − 37.8564i | − 1.81092i | ||||||||
\(438\) | 14.5359i | 0.694552i | ||||||||
\(439\) | −33.1769 | −1.58345 | −0.791724 | − | 0.610879i | \(-0.790816\pi\) | ||||
−0.791724 | + | 0.610879i | \(0.790816\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.0000i | 0.570137i | 0.958507 | + | 0.285069i | \(0.0920164\pi\) | ||||
−0.958507 | + | 0.285069i | \(0.907984\pi\) | |||||||
\(444\) | 4.92820 | 0.233882 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −17.0718 | −0.808373 | ||||||||
\(447\) | 15.4641i | 0.731427i | ||||||||
\(448\) | 2.00000i | 0.0944911i | ||||||||
\(449\) | 26.7846 | 1.26404 | 0.632022 | − | 0.774950i | \(-0.282225\pi\) | ||||
0.632022 | + | 0.774950i | \(0.282225\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.46410 | −0.163118 | ||||||||
\(452\) | 12.9282i | 0.608092i | ||||||||
\(453\) | − 20.3923i | − 0.958114i | ||||||||
\(454\) | 26.7846 | 1.25706 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 9.46410 | 0.443197 | ||||||||
\(457\) | − 12.3923i | − 0.579688i | −0.957074 | − | 0.289844i | \(-0.906397\pi\) | ||||
0.957074 | − | 0.289844i | \(-0.0936034\pi\) | |||||||
\(458\) | 41.3205i | 1.93078i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 36.2487 | 1.68827 | 0.844135 | − | 0.536130i | \(-0.180114\pi\) | ||||
0.844135 | + | 0.536130i | \(0.180114\pi\) | |||||||
\(462\) | − 3.46410i | − 0.161165i | ||||||||
\(463\) | − 28.0000i | − 1.30127i | −0.759390 | − | 0.650635i | \(-0.774503\pi\) | ||||
0.759390 | − | 0.650635i | \(-0.225497\pi\) | |||||||
\(464\) | −17.3205 | −0.804084 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.7846 | −0.962828 | ||||||||
\(467\) | − 5.07180i | − 0.234695i | −0.993091 | − | 0.117347i | \(-0.962561\pi\) | ||||
0.993091 | − | 0.117347i | \(-0.0374391\pi\) | |||||||
\(468\) | 5.46410i | 0.252578i | ||||||||
\(469\) | −16.0000 | −0.738811 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.07180 | −0.141541 | ||||||||
\(472\) | 12.0000i | 0.552345i | ||||||||
\(473\) | 4.92820i | 0.226599i | ||||||||
\(474\) | −11.3205 | −0.519968 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 0.928203i | − 0.0424995i | ||||||||
\(478\) | 20.7846i | 0.950666i | ||||||||
\(479\) | −12.0000 | −0.548294 | −0.274147 | − | 0.961688i | \(-0.588395\pi\) | ||||
−0.274147 | + | 0.961688i | \(0.588395\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.9282 | −1.22782 | ||||||||
\(482\) | 0.248711i | 0.0113285i | ||||||||
\(483\) | 13.8564i | 0.630488i | ||||||||
\(484\) | −1.00000 | −0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.73205 | −0.0785674 | ||||||||
\(487\) | 31.7128i | 1.43704i | 0.695504 | + | 0.718522i | \(0.255181\pi\) | ||||
−0.695504 | + | 0.718522i | \(0.744819\pi\) | |||||||
\(488\) | 3.46410i | 0.156813i | ||||||||
\(489\) | −9.85641 | −0.445722 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.9282 | −1.39577 | −0.697885 | − | 0.716210i | \(-0.745875\pi\) | ||||
−0.697885 | + | 0.716210i | \(0.745875\pi\) | |||||||
\(492\) | − 3.46410i | − 0.156174i | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 51.7128 | 2.32667 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 54.6410 | 2.45345 | ||||||||
\(497\) | − 27.7128i | − 1.24309i | ||||||||
\(498\) | − 14.7846i | − 0.662514i | ||||||||
\(499\) | −28.7846 | −1.28858 | −0.644288 | − | 0.764783i | \(-0.722846\pi\) | ||||
−0.644288 | + | 0.764783i | \(0.722846\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.3923 | −0.464294 | ||||||||
\(502\) | − 3.21539i | − 0.143510i | ||||||||
\(503\) | 31.1769i | 1.39011i | 0.718957 | + | 0.695055i | \(0.244620\pi\) | ||||
−0.718957 | + | 0.695055i | \(0.755380\pi\) | |||||||
\(504\) | −3.46410 | −0.154303 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 12.0000 | 0.533465 | ||||||||
\(507\) | − 16.8564i | − 0.748619i | ||||||||
\(508\) | 8.92820i | 0.396125i | ||||||||
\(509\) | −19.8564 | −0.880120 | −0.440060 | − | 0.897968i | \(-0.645043\pi\) | ||||
−0.440060 | + | 0.897968i | \(0.645043\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.7846 | −0.742507 | ||||||||
\(512\) | 8.66025i | 0.382733i | ||||||||
\(513\) | 5.46410i | 0.241246i | ||||||||
\(514\) | −34.3923 | −1.51698 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.92820 | −0.216952 | ||||||||
\(517\) | − 6.92820i | − 0.304702i | ||||||||
\(518\) | 17.0718i | 0.750092i | ||||||||
\(519\) | 12.0000 | 0.526742 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.00000 | 0.262865 | 0.131432 | − | 0.991325i | \(-0.458042\pi\) | ||||
0.131432 | + | 0.991325i | \(0.458042\pi\) | |||||||
\(522\) | − 6.00000i | − 0.262613i | ||||||||
\(523\) | − 22.0000i | − 0.961993i | −0.876723 | − | 0.480996i | \(-0.840275\pi\) | ||||
0.876723 | − | 0.480996i | \(-0.159725\pi\) | |||||||
\(524\) | −18.9282 | −0.826882 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −35.5692 | −1.55089 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 5.00000i | 0.217597i | ||||||||
\(529\) | −25.0000 | −1.08696 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.92820 | −0.300658 | ||||||||
\(532\) | − 10.9282i | − 0.473798i | ||||||||
\(533\) | 18.9282i | 0.819871i | ||||||||
\(534\) | 1.60770 | 0.0695718 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 13.8564 | 0.598506 | ||||||||
\(537\) | − 6.92820i | − 0.298974i | ||||||||
\(538\) | − 34.3923i | − 1.48276i | ||||||||
\(539\) | −3.00000 | −0.129219 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.8564 | 1.19764 | 0.598820 | − | 0.800883i | \(-0.295636\pi\) | ||||
0.598820 | + | 0.800883i | \(0.295636\pi\) | |||||||
\(542\) | − 20.1051i | − 0.863589i | ||||||||
\(543\) | 15.8564i | 0.680464i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −18.9282 | −0.810052 | ||||||||
\(547\) | − 2.00000i | − 0.0855138i | −0.999086 | − | 0.0427569i | \(-0.986386\pi\) | ||||
0.999086 | − | 0.0427569i | \(-0.0136141\pi\) | |||||||
\(548\) | − 18.0000i | − 0.768922i | ||||||||
\(549\) | −2.00000 | −0.0853579 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −18.9282 | −0.806369 | ||||||||
\(552\) | − 12.0000i | − 0.510754i | ||||||||
\(553\) | − 13.0718i | − 0.555869i | ||||||||
\(554\) | 51.0333 | 2.16820 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12.3923 | 0.525551 | ||||||||
\(557\) | − 3.21539i | − 0.136240i | −0.997677 | − | 0.0681202i | \(-0.978300\pi\) | ||||
0.997677 | − | 0.0681202i | \(-0.0217001\pi\) | |||||||
\(558\) | 18.9282i | 0.801295i | ||||||||
\(559\) | 26.9282 | 1.13894 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.00000i | 0.253095i | ||||||||
\(563\) | 10.3923i | 0.437983i | 0.975727 | + | 0.218992i | \(0.0702768\pi\) | ||||
−0.975727 | + | 0.218992i | \(0.929723\pi\) | |||||||
\(564\) | 6.92820 | 0.291730 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 8.53590 | 0.358791 | ||||||||
\(567\) | − 2.00000i | − 0.0839921i | ||||||||
\(568\) | 24.0000i | 1.00702i | ||||||||
\(569\) | −5.32051 | −0.223047 | −0.111524 | − | 0.993762i | \(-0.535573\pi\) | ||||
−0.111524 | + | 0.993762i | \(0.535573\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.60770 | 0.150977 | 0.0754887 | − | 0.997147i | \(-0.475948\pi\) | ||||
0.0754887 | + | 0.997147i | \(0.475948\pi\) | |||||||
\(572\) | 5.46410i | 0.228466i | ||||||||
\(573\) | − 18.9282i | − 0.790737i | ||||||||
\(574\) | 12.0000 | 0.500870 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 18.7846i | 0.782014i | 0.920388 | + | 0.391007i | \(0.127873\pi\) | ||||
−0.920388 | + | 0.391007i | \(0.872127\pi\) | |||||||
\(578\) | 29.4449i | 1.22474i | ||||||||
\(579\) | −24.3923 | −1.01371 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.0718 | 0.708257 | ||||||||
\(582\) | − 17.3205i | − 0.717958i | ||||||||
\(583\) | − 0.928203i | − 0.0384422i | ||||||||
\(584\) | 14.5359 | 0.601500 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.0000 | 0.991431 | ||||||||
\(587\) | 18.9282i | 0.781251i | 0.920550 | + | 0.390625i | \(0.127741\pi\) | ||||
−0.920550 | + | 0.390625i | \(0.872259\pi\) | |||||||
\(588\) | − 3.00000i | − 0.123718i | ||||||||
\(589\) | 59.7128 | 2.46042 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.0000 | −0.493614 | ||||||||
\(592\) | − 24.6410i | − 1.01274i | ||||||||
\(593\) | 8.78461i | 0.360741i | 0.983599 | + | 0.180370i | \(0.0577296\pi\) | ||||
−0.983599 | + | 0.180370i | \(0.942270\pi\) | |||||||
\(594\) | −1.73205 | −0.0710669 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −15.4641 | −0.633434 | ||||||||
\(597\) | 24.7846i | 1.01437i | ||||||||
\(598\) | − 65.5692i | − 2.68132i | ||||||||
\(599\) | 37.8564 | 1.54677 | 0.773385 | − | 0.633936i | \(-0.218562\pi\) | ||||
0.773385 | + | 0.633936i | \(0.218562\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.6410 | −1.33145 | −0.665727 | − | 0.746195i | \(-0.731879\pi\) | ||||
−0.665727 | + | 0.746195i | \(0.731879\pi\) | |||||||
\(602\) | − 17.0718i | − 0.695794i | ||||||||
\(603\) | 8.00000i | 0.325785i | ||||||||
\(604\) | 20.3923 | 0.829751 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 18.0000 | 0.731200 | ||||||||
\(607\) | 18.7846i | 0.762444i | 0.924484 | + | 0.381222i | \(0.124497\pi\) | ||||
−0.924484 | + | 0.381222i | \(0.875503\pi\) | |||||||
\(608\) | 28.3923i | 1.15146i | ||||||||
\(609\) | 6.92820 | 0.280745 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −37.8564 | −1.53151 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 20.3923i | − 0.823637i | −0.911266 | − | 0.411819i | \(-0.864894\pi\) | ||||
0.911266 | − | 0.411819i | \(-0.135106\pi\) | |||||||
\(614\) | 24.2487 | 0.978598 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.46410 | −0.139573 | ||||||||
\(617\) | 36.9282i | 1.48667i | 0.668917 | + | 0.743337i | \(0.266758\pi\) | ||||
−0.668917 | + | 0.743337i | \(0.733242\pi\) | |||||||
\(618\) | − 13.8564i | − 0.557386i | ||||||||
\(619\) | −20.0000 | −0.803868 | −0.401934 | − | 0.915669i | \(-0.631662\pi\) | ||||
−0.401934 | + | 0.915669i | \(0.631662\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.92820 | 0.278019 | ||||||||
\(622\) | 8.78461i | 0.352231i | ||||||||
\(623\) | 1.85641i | 0.0743754i | ||||||||
\(624\) | 27.3205 | 1.09370 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −36.2487 | −1.44879 | ||||||||
\(627\) | 5.46410i | 0.218215i | ||||||||
\(628\) | − 3.07180i | − 0.122578i | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.0718 | −0.838855 | −0.419427 | − | 0.907789i | \(-0.637769\pi\) | ||||
−0.419427 | + | 0.907789i | \(0.637769\pi\) | |||||||
\(632\) | 11.3205i | 0.450306i | ||||||||
\(633\) | − 8.39230i | − 0.333564i | ||||||||
\(634\) | −43.1769 | −1.71477 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.928203 | 0.0368057 | ||||||||
\(637\) | 16.3923i | 0.649487i | ||||||||
\(638\) | − 6.00000i | − 0.237542i | ||||||||
\(639\) | −13.8564 | −0.548151 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.9282 | −0.510633 | −0.255317 | − | 0.966857i | \(-0.582180\pi\) | ||||
−0.255317 | + | 0.966857i | \(0.582180\pi\) | |||||||
\(642\) | 14.7846i | 0.583502i | ||||||||
\(643\) | 37.5692i | 1.48159i | 0.671734 | + | 0.740793i | \(0.265550\pi\) | ||||
−0.671734 | + | 0.740793i | \(0.734450\pi\) | |||||||
\(644\) | −13.8564 | −0.546019 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 27.7128i | − 1.08950i | −0.838597 | − | 0.544752i | \(-0.816624\pi\) | ||||
0.838597 | − | 0.544752i | \(-0.183376\pi\) | |||||||
\(648\) | 1.73205i | 0.0680414i | ||||||||
\(649\) | −6.92820 | −0.271956 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −21.8564 | −0.856620 | ||||||||
\(652\) | − 9.85641i | − 0.386007i | ||||||||
\(653\) | 19.8564i | 0.777041i | 0.921440 | + | 0.388521i | \(0.127014\pi\) | ||||
−0.921440 | + | 0.388521i | \(0.872986\pi\) | |||||||
\(654\) | −17.3205 | −0.677285 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −17.3205 | −0.676252 | ||||||||
\(657\) | 8.39230i | 0.327415i | ||||||||
\(658\) | 24.0000i | 0.935617i | ||||||||
\(659\) | 15.7128 | 0.612084 | 0.306042 | − | 0.952018i | \(-0.400995\pi\) | ||||
0.306042 | + | 0.952018i | \(0.400995\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.0000 | 0.544537 | 0.272268 | − | 0.962221i | \(-0.412226\pi\) | ||||
0.272268 | + | 0.962221i | \(0.412226\pi\) | |||||||
\(662\) | 17.0718i | 0.663514i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −14.7846 | −0.573754 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.53590 | 0.330759 | ||||||||
\(667\) | 24.0000i | 0.929284i | ||||||||
\(668\) | − 10.3923i | − 0.402090i | ||||||||
\(669\) | −9.85641 | −0.381071 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.00000 | −0.0772091 | ||||||||
\(672\) | − 10.3923i | − 0.400892i | ||||||||
\(673\) | − 3.32051i | − 0.127996i | −0.997950 | − | 0.0639981i | \(-0.979615\pi\) | ||||
0.997950 | − | 0.0639981i | \(-0.0203852\pi\) | |||||||
\(674\) | 57.4641 | 2.21343 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.8564 | 0.648323 | ||||||||
\(677\) | − 8.78461i | − 0.337620i | −0.985649 | − | 0.168810i | \(-0.946008\pi\) | ||||
0.985649 | − | 0.168810i | \(-0.0539924\pi\) | |||||||
\(678\) | 22.3923i | 0.859971i | ||||||||
\(679\) | 20.0000 | 0.767530 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.4641 | 0.592586 | ||||||||
\(682\) | 18.9282i | 0.724798i | ||||||||
\(683\) | − 32.7846i | − 1.25447i | −0.778831 | − | 0.627234i | \(-0.784187\pi\) | ||||
0.778831 | − | 0.627234i | \(-0.215813\pi\) | |||||||
\(684\) | −5.46410 | −0.208925 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 34.6410 | 1.32260 | ||||||||
\(687\) | 23.8564i | 0.910179i | ||||||||
\(688\) | 24.6410i | 0.939430i | ||||||||
\(689\) | −5.07180 | −0.193220 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 47.7128 | 1.81508 | 0.907540 | − | 0.419965i | \(-0.137958\pi\) | ||||
0.907540 | + | 0.419965i | \(0.137958\pi\) | |||||||
\(692\) | 12.0000i | 0.456172i | ||||||||
\(693\) | − 2.00000i | − 0.0759737i | ||||||||
\(694\) | 38.7846 | 1.47224 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −6.00000 | −0.227429 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 14.1051i | 0.533887i | ||||||||
\(699\) | −12.0000 | −0.453882 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.4641 | 1.49054 | 0.745269 | − | 0.666764i | \(-0.232321\pi\) | ||||
0.745269 | + | 0.666764i | \(0.232321\pi\) | |||||||
\(702\) | 9.46410i | 0.357199i | ||||||||
\(703\) | − 26.9282i | − 1.01562i | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −22.3923 | −0.842746 | ||||||||
\(707\) | 20.7846i | 0.781686i | ||||||||
\(708\) | − 6.92820i | − 0.260378i | ||||||||
\(709\) | 11.8564 | 0.445277 | 0.222638 | − | 0.974901i | \(-0.428533\pi\) | ||||
0.222638 | + | 0.974901i | \(0.428533\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.53590 | −0.245115 | ||||||||
\(712\) | − 1.60770i | − 0.0602509i | ||||||||
\(713\) | − 75.7128i | − 2.83547i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.92820 | 0.258919 | ||||||||
\(717\) | 12.0000i | 0.448148i | ||||||||
\(718\) | 36.0000i | 1.34351i | ||||||||
\(719\) | 5.07180 | 0.189146 | 0.0945731 | − | 0.995518i | \(-0.469851\pi\) | ||||
0.0945731 | + | 0.995518i | \(0.469851\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.0000 | 0.595871 | ||||||||
\(722\) | 18.8038i | 0.699807i | ||||||||
\(723\) | 0.143594i | 0.00534030i | ||||||||
\(724\) | −15.8564 | −0.589299 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.73205 | −0.0642824 | ||||||||
\(727\) | − 8.00000i | − 0.296704i | −0.988935 | − | 0.148352i | \(-0.952603\pi\) | ||||
0.988935 | − | 0.148352i | \(-0.0473968\pi\) | |||||||
\(728\) | 18.9282i | 0.701526i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | − 2.00000i | − 0.0739221i | ||||||||
\(733\) | 53.9615i | 1.99311i | 0.0829082 | + | 0.996557i | \(0.473579\pi\) | ||||
−0.0829082 | + | 0.996557i | \(0.526421\pi\) | |||||||
\(734\) | 34.6410 | 1.27862 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 36.0000 | 1.32698 | ||||||||
\(737\) | 8.00000i | 0.294684i | ||||||||
\(738\) | − 6.00000i | − 0.220863i | ||||||||
\(739\) | −17.4641 | −0.642427 | −0.321214 | − | 0.947007i | \(-0.604091\pi\) | ||||
−0.321214 | + | 0.947007i | \(0.604091\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 29.8564 | 1.09680 | ||||||||
\(742\) | 3.21539i | 0.118041i | ||||||||
\(743\) | 25.6077i | 0.939455i | 0.882811 | + | 0.469728i | \(0.155648\pi\) | ||||
−0.882811 | + | 0.469728i | \(0.844352\pi\) | |||||||
\(744\) | 18.9282 | 0.693942 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 35.3205 | 1.29318 | ||||||||
\(747\) | − 8.53590i | − 0.312312i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17.0718 | −0.623790 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.9282 | 0.982624 | 0.491312 | − | 0.870984i | \(-0.336517\pi\) | ||||
0.491312 | + | 0.870984i | \(0.336517\pi\) | |||||||
\(752\) | − 34.6410i | − 1.26323i | ||||||||
\(753\) | − 1.85641i | − 0.0676512i | ||||||||
\(754\) | −32.7846 | −1.19395 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.00000 | 0.0727393 | ||||||||
\(757\) | − 34.7846i | − 1.26427i | −0.774859 | − | 0.632134i | \(-0.782179\pi\) | ||||
0.774859 | − | 0.632134i | \(-0.217821\pi\) | |||||||
\(758\) | 30.9282i | 1.12336i | ||||||||
\(759\) | 6.92820 | 0.251478 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32.5359 | −1.17943 | −0.589713 | − | 0.807613i | \(-0.700759\pi\) | ||||
−0.589713 | + | 0.807613i | \(0.700759\pi\) | |||||||
\(762\) | 15.4641i | 0.560205i | ||||||||
\(763\) | − 20.0000i | − 0.724049i | ||||||||
\(764\) | 18.9282 | 0.684798 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.0000 | 0.867155 | ||||||||
\(767\) | 37.8564i | 1.36692i | ||||||||
\(768\) | 19.0000i | 0.685603i | ||||||||
\(769\) | −50.4974 | −1.82098 | −0.910492 | − | 0.413527i | \(-0.864297\pi\) | ||||
−0.910492 | + | 0.413527i | \(0.864297\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.8564 | −0.715111 | ||||||||
\(772\) | − 24.3923i | − 0.877898i | ||||||||
\(773\) | − 4.14359i | − 0.149035i | −0.997220 | − | 0.0745174i | \(-0.976258\pi\) | ||||
0.997220 | − | 0.0745174i | \(-0.0237416\pi\) | |||||||
\(774\) | −8.53590 | −0.306817 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −17.3205 | −0.621770 | ||||||||
\(777\) | 9.85641i | 0.353597i | ||||||||
\(778\) | − 19.1769i | − 0.687526i | ||||||||
\(779\) | −18.9282 | −0.678173 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.8564 | −0.495821 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 3.46410i | − 0.123797i | ||||||||
\(784\) | −15.0000 | −0.535714 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −32.7846 | −1.16939 | ||||||||
\(787\) | − 22.7846i | − 0.812184i | −0.913832 | − | 0.406092i | \(-0.866891\pi\) | ||||
0.913832 | − | 0.406092i | \(-0.133109\pi\) | |||||||
\(788\) | − 12.0000i | − 0.427482i | ||||||||
\(789\) | −20.5359 | −0.731097 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −25.8564 | −0.919348 | ||||||||
\(792\) | 1.73205i | 0.0615457i | ||||||||
\(793\) | 10.9282i | 0.388072i | ||||||||
\(794\) | 3.46410 | 0.122936 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −24.7846 | −0.878467 | ||||||||
\(797\) | 52.6410i | 1.86464i | 0.361634 | + | 0.932320i | \(0.382219\pi\) | ||||
−0.361634 | + | 0.932320i | \(0.617781\pi\) | |||||||
\(798\) | − 18.9282i | − 0.670051i | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.928203 | 0.0327964 | ||||||||
\(802\) | − 13.6077i | − 0.480504i | ||||||||
\(803\) | 8.39230i | 0.296158i | ||||||||
\(804\) | −8.00000 | −0.282138 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 103.426 | 3.64301 | ||||||||
\(807\) | − 19.8564i | − 0.698979i | ||||||||
\(808\) | − 18.0000i | − 0.633238i | ||||||||
\(809\) | 15.4641 | 0.543689 | 0.271844 | − | 0.962341i | \(-0.412366\pi\) | ||||
0.271844 | + | 0.962341i | \(0.412366\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.3923 | 0.435153 | 0.217576 | − | 0.976043i | \(-0.430185\pi\) | ||||
0.217576 | + | 0.976043i | \(0.430185\pi\) | |||||||
\(812\) | 6.92820i | 0.243132i | ||||||||
\(813\) | − 11.6077i | − 0.407100i | ||||||||
\(814\) | 8.53590 | 0.299183 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.9282i | 0.942099i | ||||||||
\(818\) | 11.7513i | 0.410874i | ||||||||
\(819\) | −10.9282 | −0.381862 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.5359 | 0.716708 | 0.358354 | − | 0.933586i | \(-0.383338\pi\) | ||||
0.358354 | + | 0.933586i | \(0.383338\pi\) | |||||||
\(822\) | − 31.1769i | − 1.08742i | ||||||||
\(823\) | − 33.5692i | − 1.17015i | −0.810979 | − | 0.585075i | \(-0.801065\pi\) | ||||
0.810979 | − | 0.585075i | \(-0.198935\pi\) | |||||||
\(824\) | −13.8564 | −0.482711 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 24.0000 | 0.835067 | ||||||||
\(827\) | − 22.3923i | − 0.778657i | −0.921099 | − | 0.389328i | \(-0.872707\pi\) | ||||
0.921099 | − | 0.389328i | \(-0.127293\pi\) | |||||||
\(828\) | 6.92820i | 0.240772i | ||||||||
\(829\) | −29.7128 | −1.03197 | −0.515984 | − | 0.856598i | \(-0.672574\pi\) | ||||
−0.515984 | + | 0.856598i | \(0.672574\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.4641 | 1.02210 | ||||||||
\(832\) | − 5.46410i | − 0.189434i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 21.4641 | 0.743241 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −5.46410 | −0.188980 | ||||||||
\(837\) | 10.9282i | 0.377734i | ||||||||
\(838\) | − 53.5692i | − 1.85052i | ||||||||
\(839\) | −56.7846 | −1.96042 | −0.980211 | − | 0.197954i | \(-0.936570\pi\) | ||||
−0.980211 | + | 0.197954i | \(0.936570\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.0000 | −0.586207 | ||||||||
\(842\) | 3.46410i | 0.119381i | ||||||||
\(843\) | 3.46410i | 0.119310i | ||||||||
\(844\) | 8.39230 | 0.288875 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 12.0000 | 0.412568 | ||||||||
\(847\) | − 2.00000i | − 0.0687208i | ||||||||
\(848\) | − 4.64102i | − 0.159373i | ||||||||
\(849\) | 4.92820 | 0.169135 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −34.1436 | −1.17043 | ||||||||
\(852\) | − 13.8564i | − 0.474713i | ||||||||
\(853\) | 3.60770i | 0.123525i | 0.998091 | + | 0.0617626i | \(0.0196722\pi\) | ||||
−0.998091 | + | 0.0617626i | \(0.980328\pi\) | |||||||
\(854\) | 6.92820 | 0.237078 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14.7846 | 0.505328 | ||||||||
\(857\) | 37.8564i | 1.29315i | 0.762850 | + | 0.646575i | \(0.223799\pi\) | ||||
−0.762850 | + | 0.646575i | \(0.776201\pi\) | |||||||
\(858\) | 9.46410i | 0.323099i | ||||||||
\(859\) | 7.71281 | 0.263158 | 0.131579 | − | 0.991306i | \(-0.457995\pi\) | ||||
0.131579 | + | 0.991306i | \(0.457995\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.92820 | 0.236113 | ||||||||
\(862\) | 15.2154i | 0.518238i | ||||||||
\(863\) | − 37.8564i | − 1.28865i | −0.764753 | − | 0.644324i | \(-0.777139\pi\) | ||||
0.764753 | − | 0.644324i | \(-0.222861\pi\) | |||||||
\(864\) | −5.19615 | −0.176777 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −0.248711 | −0.00845155 | ||||||||
\(867\) | 17.0000i | 0.577350i | ||||||||
\(868\) | − 21.8564i | − 0.741855i | ||||||||
\(869\) | −6.53590 | −0.221715 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 43.7128 | 1.48115 | ||||||||
\(872\) | 17.3205i | 0.586546i | ||||||||
\(873\) | − 10.0000i | − 0.338449i | ||||||||
\(874\) | 65.5692 | 2.21791 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.39230 | −0.283550 | ||||||||
\(877\) | 34.2487i | 1.15650i | 0.815861 | + | 0.578248i | \(0.196264\pi\) | ||||
−0.815861 | + | 0.578248i | \(0.803736\pi\) | |||||||
\(878\) | − 57.4641i | − 1.93932i | ||||||||
\(879\) | 13.8564 | 0.467365 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.928203 | −0.0312720 | −0.0156360 | − | 0.999878i | \(-0.504977\pi\) | ||||
−0.0156360 | + | 0.999878i | \(0.504977\pi\) | |||||||
\(882\) | − 5.19615i | − 0.174964i | ||||||||
\(883\) | − 4.00000i | − 0.134611i | −0.997732 | − | 0.0673054i | \(-0.978560\pi\) | ||||
0.997732 | − | 0.0673054i | \(-0.0214402\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −20.7846 | −0.698273 | ||||||||
\(887\) | − 12.2487i | − 0.411271i | −0.978629 | − | 0.205636i | \(-0.934074\pi\) | ||||
0.978629 | − | 0.205636i | \(-0.0659262\pi\) | |||||||
\(888\) | − 8.53590i | − 0.286446i | ||||||||
\(889\) | −17.8564 | −0.598885 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | − 9.85641i | − 0.330017i | ||||||||
\(893\) | − 37.8564i | − 1.26682i | ||||||||
\(894\) | −26.7846 | −0.895811 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −24.2487 | −0.810093 | ||||||||
\(897\) | − 37.8564i | − 1.26399i | ||||||||
\(898\) | 46.3923i | 1.54813i | ||||||||
\(899\) | −37.8564 | −1.26258 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | − 6.00000i | − 0.199778i | ||||||||
\(903\) | − 9.85641i | − 0.328001i | ||||||||
\(904\) | 22.3923 | 0.744757 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 35.3205 | 1.17345 | ||||||||
\(907\) | − 18.1436i | − 0.602448i | −0.953553 | − | 0.301224i | \(-0.902605\pi\) | ||||
0.953553 | − | 0.301224i | \(-0.0973952\pi\) | |||||||
\(908\) | 15.4641i | 0.513194i | ||||||||
\(909\) | 10.3923 | 0.344691 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.9282 | 0.627119 | 0.313560 | − | 0.949568i | \(-0.398478\pi\) | ||||
0.313560 | + | 0.949568i | \(0.398478\pi\) | |||||||
\(912\) | 27.3205i | 0.904672i | ||||||||
\(913\) | − 8.53590i | − 0.282497i | ||||||||
\(914\) | 21.4641 | 0.709969 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −23.8564 | −0.788238 | ||||||||
\(917\) | − 37.8564i | − 1.25013i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.3923 | 1.06852 | 0.534262 | − | 0.845319i | \(-0.320590\pi\) | ||||
0.534262 | + | 0.845319i | \(0.320590\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.0000 | 0.461316 | ||||||||
\(922\) | 62.7846i | 2.06770i | ||||||||
\(923\) | 75.7128i | 2.49212i | ||||||||
\(924\) | 2.00000 | 0.0657952 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 48.4974 | 1.59372 | ||||||||
\(927\) | − 8.00000i | − 0.262754i | ||||||||
\(928\) | − 18.0000i | − 0.590879i | ||||||||
\(929\) | −2.78461 | −0.0913601 | −0.0456800 | − | 0.998956i | \(-0.514545\pi\) | ||||
−0.0456800 | + | 0.998956i | \(0.514545\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.3923 | −0.537236 | ||||||||
\(932\) | − 12.0000i | − 0.393073i | ||||||||
\(933\) | 5.07180i | 0.166043i | ||||||||
\(934\) | 8.78461 | 0.287441 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9.46410 | 0.309344 | ||||||||
\(937\) | 20.3923i | 0.666188i | 0.942894 | + | 0.333094i | \(0.108093\pi\) | ||||
−0.942894 | + | 0.333094i | \(0.891907\pi\) | |||||||
\(938\) | − 27.7128i | − 0.904855i | ||||||||
\(939\) | −20.9282 | −0.682966 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.4641 | 0.895304 | 0.447652 | − | 0.894208i | \(-0.352260\pi\) | ||||
0.447652 | + | 0.894208i | \(0.352260\pi\) | |||||||
\(942\) | − 5.32051i | − 0.173352i | ||||||||
\(943\) | 24.0000i | 0.781548i | ||||||||
\(944\) | −34.6410 | −1.12747 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.53590 | −0.277526 | ||||||||
\(947\) | 18.9282i | 0.615084i | 0.951535 | + | 0.307542i | \(0.0995065\pi\) | ||||
−0.951535 | + | 0.307542i | \(0.900494\pi\) | |||||||
\(948\) | − 6.53590i | − 0.212276i | ||||||||
\(949\) | 45.8564 | 1.48856 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.9282 | −0.808352 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 3.21539i | − 0.104157i | −0.998643 | − | 0.0520784i | \(-0.983415\pi\) | ||||
0.998643 | − | 0.0520784i | \(-0.0165846\pi\) | |||||||
\(954\) | 1.60770 | 0.0520511 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −12.0000 | −0.388108 | ||||||||
\(957\) | − 3.46410i | − 0.111979i | ||||||||
\(958\) | − 20.7846i | − 0.671520i | ||||||||
\(959\) | 36.0000 | 1.16250 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 88.4256 | 2.85244 | ||||||||
\(962\) | − 46.6410i | − 1.50377i | ||||||||
\(963\) | 8.53590i | 0.275065i | ||||||||
\(964\) | −0.143594 | −0.00462484 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −24.0000 | −0.772187 | ||||||||
\(967\) | − 22.7846i | − 0.732704i | −0.930476 | − | 0.366352i | \(-0.880607\pi\) | ||||
0.930476 | − | 0.366352i | \(-0.119393\pi\) | |||||||
\(968\) | 1.73205i | 0.0556702i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.8564 | 0.829772 | 0.414886 | − | 0.909873i | \(-0.363822\pi\) | ||||
0.414886 | + | 0.909873i | \(0.363822\pi\) | |||||||
\(972\) | − 1.00000i | − 0.0320750i | ||||||||
\(973\) | 24.7846i | 0.794558i | ||||||||
\(974\) | −54.9282 | −1.76001 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.0000 | −0.320092 | ||||||||
\(977\) | − 47.5692i | − 1.52187i | −0.648826 | − | 0.760937i | \(-0.724740\pi\) | ||||
0.648826 | − | 0.760937i | \(-0.275260\pi\) | |||||||
\(978\) | − 17.0718i | − 0.545896i | ||||||||
\(979\) | 0.928203 | 0.0296655 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.0000 | −0.319275 | ||||||||
\(982\) | − 53.5692i | − 1.70946i | ||||||||
\(983\) | 24.0000i | 0.765481i | 0.923856 | + | 0.382741i | \(0.125020\pi\) | ||||
−0.923856 | + | 0.382741i | \(0.874980\pi\) | |||||||
\(984\) | −6.00000 | −0.191273 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13.8564i | 0.441054i | ||||||||
\(988\) | 29.8564i | 0.949859i | ||||||||
\(989\) | 34.1436 | 1.08570 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.21539 | −0.229204 | −0.114602 | − | 0.993411i | \(-0.536559\pi\) | ||||
−0.114602 | + | 0.993411i | \(0.536559\pi\) | |||||||
\(992\) | 56.7846i | 1.80291i | ||||||||
\(993\) | 9.85641i | 0.312784i | ||||||||
\(994\) | 48.0000 | 1.52247 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 8.53590 | 0.270470 | ||||||||
\(997\) | − 27.6077i | − 0.874344i | −0.899378 | − | 0.437172i | \(-0.855980\pi\) | ||||
0.899378 | − | 0.437172i | \(-0.144020\pi\) | |||||||
\(998\) | − 49.8564i | − 1.57818i | ||||||||
\(999\) | 4.92820 | 0.155921 |
(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 | 825.2.c.c.199.4 | 4 | ||
3.2 | odd | 2 | 2475.2.c.n.199.1 | 4 | |||
5.2 | odd | 4 | 165.2.a.b.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 825.2.a.e.1.2 | 2 | |||
5.4 | even | 2 | inner | 825.2.c.c.199.1 | 4 | ||
15.2 | even | 4 | 495.2.a.c.1.2 | 2 | |||
15.8 | even | 4 | 2475.2.a.r.1.1 | 2 | |||
15.14 | odd | 2 | 2475.2.c.n.199.4 | 4 | |||
20.7 | even | 4 | 2640.2.a.x.1.2 | 2 | |||
35.27 | even | 4 | 8085.2.a.bd.1.1 | 2 | |||
55.32 | even | 4 | 1815.2.a.i.1.2 | 2 | |||
55.43 | even | 4 | 9075.2.a.bh.1.1 | 2 | |||
60.47 | odd | 4 | 7920.2.a.bz.1.2 | 2 | |||
165.32 | odd | 4 | 5445.2.a.s.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.a.b.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
495.2.a.c.1.2 | 2 | 15.2 | even | 4 | |||
825.2.a.e.1.2 | 2 | 5.3 | odd | 4 | |||
825.2.c.c.199.1 | 4 | 5.4 | even | 2 | inner | ||
825.2.c.c.199.4 | 4 | 1.1 | even | 1 | trivial | ||
1815.2.a.i.1.2 | 2 | 55.32 | even | 4 | |||
2475.2.a.r.1.1 | 2 | 15.8 | even | 4 | |||
2475.2.c.n.199.1 | 4 | 3.2 | odd | 2 | |||
2475.2.c.n.199.4 | 4 | 15.14 | odd | 2 | |||
2640.2.a.x.1.2 | 2 | 20.7 | even | 4 | |||
5445.2.a.s.1.1 | 2 | 165.32 | odd | 4 | |||
7920.2.a.bz.1.2 | 2 | 60.47 | odd | 4 | |||
8085.2.a.bd.1.1 | 2 | 35.27 | even | 4 | |||
9075.2.a.bh.1.1 | 2 | 55.43 | even | 4 |