Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1260,2,Mod(361,1260)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1260, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1260.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1260.s (of order \(3\), degree \(2\), 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: | \(10.0611506547\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 140) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1260.361 |
Dual form | 1260.2.s.c.541.1 |
$q$-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 \(\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times\).
\(n\) | \(281\) | \(631\) | \(757\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.50000 | − | 0.866025i | 0.944911 | − | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.00000 | − | 5.19615i | 0.904534 | − | 1.56670i | 0.0829925 | − | 0.996550i | \(-0.473552\pi\) |
0.821541 | − | 0.570149i | \(-0.193114\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.00000 | + | 5.19615i | −0.727607 | + | 1.26025i | 0.230285 | + | 0.973123i | \(0.426034\pi\) |
−0.957892 | + | 0.287129i | \(0.907299\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.00000 | − | 6.92820i | −0.917663 | − | 1.58944i | −0.802955 | − | 0.596040i | \(-0.796740\pi\) |
−0.114708 | − | 0.993399i | \(-0.536593\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.50000 | + | 2.59808i | 0.312772 | + | 0.541736i | 0.978961 | − | 0.204046i | \(-0.0654092\pi\) |
−0.666190 | + | 0.745782i | \(0.732076\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.00000 | −0.557086 | −0.278543 | − | 0.960424i | \(-0.589851\pi\) | ||||
−0.278543 | + | 0.960424i | \(0.589851\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | + | 1.73205i | −0.179605 | + | 0.311086i | −0.941745 | − | 0.336327i | \(-0.890815\pi\) |
0.762140 | + | 0.647412i | \(0.224149\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00000 | − | 1.73205i | −0.338062 | − | 0.292770i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | − | 6.92820i | −0.657596 | − | 1.13899i | −0.981236 | − | 0.192809i | \(-0.938240\pi\) |
0.323640 | − | 0.946180i | \(-0.395093\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.00000 | 0.468521 | 0.234261 | − | 0.972174i | \(-0.424733\pi\) | ||||
0.234261 | + | 0.972174i | \(0.424733\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.00000 | 0.762493 | 0.381246 | − | 0.924473i | \(-0.375495\pi\) | ||||
0.381246 | + | 0.924473i | \(0.375495\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | − | 10.3923i | 0.824163 | − | 1.42749i | −0.0783936 | − | 0.996922i | \(-0.524979\pi\) |
0.902557 | − | 0.430570i | \(-0.141688\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.00000 | −0.809040 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.500000 | + | 0.866025i | 0.0640184 | + | 0.110883i | 0.896258 | − | 0.443533i | \(-0.146275\pi\) |
−0.832240 | + | 0.554416i | \(0.812942\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | − | 1.73205i | −0.124035 | − | 0.214834i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.50000 | − | 6.06218i | 0.427593 | − | 0.740613i | −0.569066 | − | 0.822292i | \(-0.692695\pi\) |
0.996659 | + | 0.0816792i | \(0.0260283\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.00000 | − | 8.66025i | 0.585206 | − | 1.01361i | −0.409644 | − | 0.912245i | \(-0.634347\pi\) |
0.994850 | − | 0.101361i | \(-0.0323196\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.00000 | − | 15.5885i | 0.341882 | − | 1.77647i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00000 | + | 3.46410i | 0.225018 | + | 0.389742i | 0.956325 | − | 0.292306i | \(-0.0944227\pi\) |
−0.731307 | + | 0.682048i | \(0.761089\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.00000 | −0.329293 | −0.164646 | − | 0.986353i | \(-0.552648\pi\) | ||||
−0.164646 | + | 0.986353i | \(0.552648\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.00000 | 0.650791 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.50000 | − | 2.59808i | −0.159000 | − | 0.275396i | 0.775509 | − | 0.631337i | \(-0.217494\pi\) |
−0.934508 | + | 0.355942i | \(0.884160\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.00000 | − | 1.73205i | 0.524142 | − | 0.181568i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.00000 | + | 6.92820i | −0.410391 | + | 0.710819i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.0000 | −1.01535 | −0.507673 | − | 0.861550i | \(-0.669494\pi\) | ||||
−0.507673 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.50000 | + | 2.59808i | −0.149256 | + | 0.258518i | −0.930953 | − | 0.365140i | \(-0.881021\pi\) |
0.781697 | + | 0.623658i | \(0.214354\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.50000 | + | 6.06218i | 0.344865 | + | 0.597324i | 0.985329 | − | 0.170664i | \(-0.0545913\pi\) |
−0.640464 | + | 0.767988i | \(0.721258\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.50000 | − | 2.59808i | −0.145010 | − | 0.251166i | 0.784366 | − | 0.620298i | \(-0.212988\pi\) |
−0.929377 | + | 0.369132i | \(0.879655\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.50000 | + | 14.7224i | −0.814152 | + | 1.41015i | 0.0957826 | + | 0.995402i | \(0.469465\pi\) |
−0.909935 | + | 0.414751i | \(0.863869\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.0000 | 1.12887 | 0.564433 | − | 0.825479i | \(-0.309095\pi\) | ||||
0.564433 | + | 0.825479i | \(0.309095\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.50000 | − | 2.59808i | 0.139876 | − | 0.242272i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.00000 | + | 15.5885i | −0.275010 | + | 1.42899i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.5000 | − | 21.6506i | −1.13636 | − | 1.96824i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.00000 | + | 10.3923i | 0.524222 | + | 0.907980i | 0.999602 | + | 0.0281993i | \(0.00897729\pi\) |
−0.475380 | + | 0.879781i | \(0.657689\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.0000 | − | 13.8564i | −1.38738 | − | 1.20150i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.00000 | + | 10.3923i | −0.512615 | + | 0.887875i | 0.487278 | + | 0.873247i | \(0.337990\pi\) |
−0.999893 | + | 0.0146279i | \(0.995344\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.00000 | 0.169638 | 0.0848189 | − | 0.996396i | \(-0.472969\pi\) | ||||
0.0848189 | + | 0.996396i | \(0.472969\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.00000 | − | 10.3923i | 0.501745 | − | 0.869048i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.50000 | + | 2.59808i | 0.124568 | + | 0.215758i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.50000 | − | 12.9904i | −0.614424 | − | 1.06421i | −0.990485 | − | 0.137619i | \(-0.956055\pi\) |
0.376061 | − | 0.926595i | \(-0.377278\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.00000 | − | 8.66025i | 0.406894 | − | 0.704761i | −0.587646 | − | 0.809118i | \(-0.699945\pi\) |
0.994540 | + | 0.104357i | \(0.0332784\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.00000 | 0.160644 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.00000 | + | 12.1244i | −0.558661 | + | 0.967629i | 0.438948 | + | 0.898513i | \(0.355351\pi\) |
−0.997609 | + | 0.0691164i | \(0.977982\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.00000 | + | 5.19615i | 0.472866 | + | 0.409514i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.00000 | + | 13.8564i | 0.626608 | + | 1.08532i | 0.988227 | + | 0.152992i | \(0.0488907\pi\) |
−0.361619 | + | 0.932326i | \(0.617776\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.0000 | 1.62503 | 0.812514 | − | 0.582941i | \(-0.198098\pi\) | ||||
0.812514 | + | 0.582941i | \(0.198098\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.500000 | + | 2.59808i | −0.0377964 | + | 0.196396i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.00000 | + | 5.19615i | −0.224231 | + | 0.388379i | −0.956088 | − | 0.293079i | \(-0.905320\pi\) |
0.731858 | + | 0.681457i | \(0.238654\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.0000 | 1.26360 | 0.631800 | − | 0.775131i | \(-0.282316\pi\) | ||||
0.631800 | + | 0.775131i | \(0.282316\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.00000 | + | 6.92820i | −0.294086 | + | 0.509372i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.0000 | + | 31.1769i | 1.31629 | + | 2.27988i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.00000 | − | 15.5885i | −0.651217 | − | 1.12794i | −0.982828 | − | 0.184525i | \(-0.940925\pi\) |
0.331611 | − | 0.943416i | \(-0.392408\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.00000 | + | 1.73205i | −0.0719816 | + | 0.124676i | −0.899770 | − | 0.436365i | \(-0.856266\pi\) |
0.827788 | + | 0.561041i | \(0.189599\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.0000 | + | 17.3205i | −0.708881 | + | 1.22782i | 0.256391 | + | 0.966573i | \(0.417466\pi\) |
−0.965272 | + | 0.261245i | \(0.915867\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.50000 | + | 2.59808i | −0.526397 | + | 0.182349i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.50000 | − | 2.59808i | −0.104765 | − | 0.181458i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −48.0000 | −3.32023 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.50000 | − | 4.33013i | −0.170499 | − | 0.295312i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.00000 | + | 5.19615i | −0.0678844 | + | 0.352738i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.00000 | + | 10.3923i | −0.403604 | + | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.00000 | 0.535720 | 0.267860 | − | 0.963458i | \(-0.413684\pi\) | ||||
0.267860 | + | 0.963458i | \(0.413684\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.00000 | + | 10.3923i | −0.398234 | + | 0.689761i | −0.993508 | − | 0.113761i | \(-0.963710\pi\) |
0.595274 | + | 0.803523i | \(0.297043\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.00000 | − | 1.73205i | −0.0660819 | − | 0.114457i | 0.831092 | − | 0.556136i | \(-0.187717\pi\) |
−0.897173 | + | 0.441679i | \(0.854383\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.00000 | + | 5.19615i | 0.196537 | + | 0.340411i | 0.947403 | − | 0.320043i | \(-0.103697\pi\) |
−0.750867 | + | 0.660454i | \(0.770364\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.00000 | −0.388108 | −0.194054 | − | 0.980991i | \(-0.562164\pi\) | ||||
−0.194054 | + | 0.980991i | \(0.562164\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.0000 | + | 22.5167i | −0.837404 | + | 1.45043i | 0.0546547 | + | 0.998505i | \(0.482594\pi\) |
−0.892058 | + | 0.451920i | \(0.850739\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.50000 | − | 2.59808i | −0.415270 | − | 0.165985i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.00000 | − | 13.8564i | −0.509028 | − | 0.881662i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.0000 | 1.13615 | 0.568075 | − | 0.822977i | \(-0.307688\pi\) | ||||
0.568075 | + | 0.822977i | \(0.307688\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.0000 | 1.13165 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.0000 | − | 20.7846i | −0.748539 | − | 1.29651i | −0.948523 | − | 0.316709i | \(-0.897422\pi\) |
0.199983 | − | 0.979799i | \(-0.435911\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.0000 | − | 13.8564i | −0.994192 | − | 0.860995i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.50000 | + | 2.59808i | −0.0924940 | + | 0.160204i | −0.908560 | − | 0.417755i | \(-0.862817\pi\) |
0.816066 | + | 0.577959i | \(0.196151\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.0000 | −0.737154 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.50000 | + | 12.9904i | −0.457283 | + | 0.792038i | −0.998816 | − | 0.0486418i | \(-0.984511\pi\) |
0.541533 | + | 0.840679i | \(0.317844\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | + | 13.8564i | 0.485965 | + | 0.841717i | 0.999870 | − | 0.0161307i | \(-0.00513477\pi\) |
−0.513905 | + | 0.857847i | \(0.671801\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.00000 | + | 5.19615i | 0.180907 | + | 0.313340i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.0000 | − | 19.0526i | 0.660926 | − | 1.14476i | −0.319447 | − | 0.947604i | \(-0.603497\pi\) |
0.980373 | − | 0.197153i | \(-0.0631696\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.0000 | + | 17.3205i | −0.594438 | + | 1.02960i | 0.399188 | + | 0.916869i | \(0.369292\pi\) |
−0.993626 | + | 0.112728i | \(0.964041\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.50000 | − | 2.59808i | 0.442711 | − | 0.153360i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.50000 | − | 16.4545i | −0.558824 | − | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.0000 | 0.701047 | 0.350524 | − | 0.936554i | \(-0.386004\pi\) | ||||
0.350524 | + | 0.936554i | \(0.386004\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.00000 | + | 5.19615i | 0.173494 | + | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.5000 | − | 4.33013i | 0.720488 | − | 0.249584i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.500000 | − | 0.866025i | 0.0286299 | − | 0.0495885i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.0000 | −1.08439 | −0.542194 | − | 0.840254i | \(-0.682406\pi\) | ||||
−0.542194 | + | 0.840254i | \(0.682406\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.00000 | + | 3.46410i | 0.113047 | + | 0.195803i | 0.916997 | − | 0.398894i | \(-0.130606\pi\) |
−0.803951 | + | 0.594696i | \(0.797272\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.00000 | + | 15.5885i | 0.505490 | + | 0.875535i | 0.999980 | + | 0.00635137i | \(0.00202172\pi\) |
−0.494489 | + | 0.869184i | \(0.664645\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.00000 | + | 15.5885i | −0.503903 | + | 0.872786i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 48.0000 | 2.67079 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | + | 1.73205i | −0.0554700 | + | 0.0960769i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.0000 | + | 19.0526i | 0.604615 | + | 1.04722i | 0.992112 | + | 0.125353i | \(0.0400062\pi\) |
−0.387498 | + | 0.921871i | \(0.626660\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.00000 | −0.382451 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.0000 | 1.08947 | 0.544735 | − | 0.838608i | \(-0.316630\pi\) | ||||
0.544735 | + | 0.838608i | \(0.316630\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.00000 | + | 10.3923i | 0.324918 | + | 0.562775i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.5000 | + | 23.3827i | −0.724718 | + | 1.25525i | 0.234372 | + | 0.972147i | \(0.424697\pi\) |
−0.959090 | + | 0.283101i | \(0.908637\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.00000 | −0.0535288 | −0.0267644 | − | 0.999642i | \(-0.508520\pi\) | ||||
−0.0267644 | + | 0.999642i | \(0.508520\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.00000 | + | 10.3923i | −0.319348 | + | 0.553127i | −0.980352 | − | 0.197256i | \(-0.936797\pi\) |
0.661004 | + | 0.750382i | \(0.270130\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.00000 | + | 5.19615i | 0.158334 | + | 0.274242i | 0.934268 | − | 0.356572i | \(-0.116054\pi\) |
−0.775934 | + | 0.630814i | \(0.782721\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −22.5000 | + | 38.9711i | −1.18421 | + | 2.05111i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.0000 | −0.523424 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.50000 | + | 4.33013i | −0.130499 | + | 0.226031i | −0.923869 | − | 0.382709i | \(-0.874991\pi\) |
0.793370 | + | 0.608740i | \(0.208325\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.00000 | − | 31.1769i | 0.311504 | − | 1.61862i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.00000 | + | 13.8564i | 0.414224 | + | 0.717458i | 0.995347 | − | 0.0963587i | \(-0.0307196\pi\) |
−0.581122 | + | 0.813816i | \(0.697386\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.00000 | −0.309016 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.00000 | 0.410932 | 0.205466 | − | 0.978664i | \(-0.434129\pi\) | ||||
0.205466 | + | 0.978664i | \(0.434129\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.50000 | + | 2.59808i | 0.0766464 | + | 0.132755i | 0.901801 | − | 0.432151i | \(-0.142245\pi\) |
−0.825155 | + | 0.564907i | \(0.808912\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −15.0000 | + | 5.19615i | −0.764471 | + | 0.264820i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.00000 | − | 5.19615i | 0.152106 | − | 0.263455i | −0.779895 | − | 0.625910i | \(-0.784728\pi\) |
0.932002 | + | 0.362454i | \(0.118061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.0000 | −0.910299 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.00000 | − | 3.46410i | 0.100631 | − | 0.174298i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.0000 | − | 22.5167i | −0.652451 | − | 1.13008i | −0.982526 | − | 0.186124i | \(-0.940407\pi\) |
0.330075 | − | 0.943955i | \(-0.392926\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.50000 | + | 2.59808i | 0.0749064 | + | 0.129742i | 0.901046 | − | 0.433724i | \(-0.142801\pi\) |
−0.826139 | + | 0.563466i | \(0.809468\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.00000 | + | 3.46410i | −0.0996271 | + | 0.172559i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −48.0000 | −2.37927 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.50000 | + | 9.52628i | −0.271957 | + | 0.471044i | −0.969363 | − | 0.245633i | \(-0.921004\pi\) |
0.697406 | + | 0.716677i | \(0.254338\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.50000 | + | 2.59808i | 0.0736321 | + | 0.127535i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.0000 | −1.17248 | −0.586238 | − | 0.810139i | \(-0.699392\pi\) | ||||
−0.586238 | + | 0.810139i | \(0.699392\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.0000 | 1.12095 | 0.560476 | − | 0.828171i | \(-0.310618\pi\) | ||||
0.560476 | + | 0.828171i | \(0.310618\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.00000 | − | 5.19615i | −0.145521 | − | 0.252050i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.00000 | + | 1.73205i | 0.0967868 | + | 0.0838198i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.0000 | − | 25.9808i | 0.722525 | − | 1.25145i | −0.237460 | − | 0.971397i | \(-0.576315\pi\) |
0.959985 | − | 0.280052i | \(-0.0903517\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.0000 | −1.34559 | −0.672797 | − | 0.739827i | \(-0.734907\pi\) | ||||
−0.672797 | + | 0.739827i | \(0.734907\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.0000 | − | 20.7846i | 0.574038 | − | 0.994263i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.0000 | + | 24.2487i | 0.668184 | + | 1.15733i | 0.978412 | + | 0.206666i | \(0.0662612\pi\) |
−0.310228 | + | 0.950662i | \(0.600405\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.50000 | + | 7.79423i | 0.213801 | + | 0.370315i | 0.952901 | − | 0.303281i | \(-0.0980821\pi\) |
−0.739100 | + | 0.673596i | \(0.764749\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.50000 | + | 2.59808i | −0.0711068 | + | 0.123161i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.00000 | 0.424736 | 0.212368 | − | 0.977190i | \(-0.431882\pi\) | ||||
0.212368 | + | 0.977190i | \(0.431882\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.00000 | − | 15.5885i | 0.423793 | − | 0.734032i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.00000 | − | 3.46410i | −0.187523 | − | 0.162400i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.00000 | + | 3.46410i | 0.0935561 | + | 0.162044i | 0.909005 | − | 0.416785i | \(-0.136843\pi\) |
−0.815449 | + | 0.578829i | \(0.803510\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.0000 | −1.39724 | −0.698620 | − | 0.715493i | \(-0.746202\pi\) | ||||
−0.698620 | + | 0.715493i | \(0.746202\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.0000 | 1.34774 | 0.673872 | − | 0.738848i | \(-0.264630\pi\) | ||||
0.673872 | + | 0.738848i | \(0.264630\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.5000 | + | 28.5788i | 0.763529 | + | 1.32247i | 0.941021 | + | 0.338349i | \(0.109868\pi\) |
−0.177492 | + | 0.984122i | \(0.556798\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.50000 | − | 18.1865i | 0.161615 | − | 0.839776i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.0000 | − | 25.9808i | 0.689701 | − | 1.19460i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.00000 | 0.367065 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.0000 | + | 25.9808i | −0.685367 | + | 1.18709i | 0.287954 | + | 0.957644i | \(0.407025\pi\) |
−0.973321 | + | 0.229447i | \(0.926308\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.00000 | − | 13.8564i | −0.364769 | − | 0.631798i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.00000 | + | 8.66025i | 0.227038 | + | 0.393242i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.00000 | + | 6.92820i | −0.181257 | + | 0.313947i | −0.942309 | − | 0.334744i | \(-0.891350\pi\) |
0.761052 | + | 0.648691i | \(0.224683\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.00000 | −0.270776 | −0.135388 | − | 0.990793i | \(-0.543228\pi\) | ||||
−0.135388 | + | 0.990793i | \(0.543228\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.00000 | − | 15.5885i | 0.405340 | − | 0.702069i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.00000 | − | 1.73205i | −0.0447661 | − | 0.0775372i | 0.842774 | − | 0.538267i | \(-0.180921\pi\) |
−0.887540 | + | 0.460730i | \(0.847588\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.00000 | 0.401290 | 0.200645 | − | 0.979664i | \(-0.435696\pi\) | ||||
0.200645 | + | 0.979664i | \(0.435696\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.00000 | 0.133498 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.5000 | + | 33.7750i | 0.864322 | + | 1.49705i | 0.867719 | + | 0.497056i | \(0.165586\pi\) |
−0.00339621 | + | 0.999994i | \(0.501081\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.00000 | − | 25.9808i | 0.221187 | − | 1.14932i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.50000 | − | 6.06218i | 0.154228 | − | 0.267131i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.0000 | − | 25.9808i | 0.657162 | − | 1.13824i | −0.324185 | − | 0.945994i | \(-0.605090\pi\) |
0.981347 | − | 0.192244i | \(-0.0615766\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.0000 | − | 38.1051i | −0.961993 | − | 1.66622i | −0.717486 | − | 0.696573i | \(-0.754707\pi\) |
−0.244507 | − | 0.969648i | \(-0.578626\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.00000 | − | 10.3923i | −0.261364 | − | 0.452696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | − | 12.1244i | 0.304348 | − | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.00000 | 0.259889 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.50000 | + | 2.59808i | −0.0648507 | + | 0.112325i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.00000 | − | 41.5692i | −0.258438 | − | 1.79051i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.50000 | − | 14.7224i | −0.365444 | − | 0.632967i | 0.623404 | − | 0.781900i | \(-0.285749\pi\) |
−0.988847 | + | 0.148933i | \(0.952416\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 17.0000 | 0.728200 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.0000 | −0.812381 | −0.406191 | − | 0.913788i | \(-0.633143\pi\) | ||||
−0.406191 | + | 0.913788i | \(0.633143\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.0000 | + | 20.7846i | 0.511217 | + | 0.885454i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.00000 | + | 6.92820i | 0.340195 | + | 0.294617i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.0000 | − | 25.9808i | 0.635570 | − | 1.10084i | −0.350824 | − | 0.936442i | \(-0.614098\pi\) |
0.986394 | − | 0.164399i | \(-0.0525683\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.0000 | 0.422955 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.50000 | + | 7.79423i | −0.189652 | + | 0.328488i | −0.945134 | − | 0.326682i | \(-0.894069\pi\) |
0.755482 | + | 0.655169i | \(0.227403\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.00000 | − | 10.3923i | −0.252422 | − | 0.437208i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.00000 | − | 15.5885i | −0.377300 | − | 0.653502i | 0.613369 | − | 0.789797i | \(-0.289814\pi\) |
−0.990668 | + | 0.136295i | \(0.956481\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.00000 | − | 13.8564i | 0.334790 | − | 0.579873i | −0.648655 | − | 0.761083i | \(-0.724668\pi\) |
0.983444 | + | 0.181210i | \(0.0580014\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.00000 | −0.125109 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.00000 | − | 8.66025i | 0.208153 | − | 0.360531i | −0.742980 | − | 0.669314i | \(-0.766588\pi\) |
0.951133 | + | 0.308783i | \(0.0999216\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.50000 | + | 2.59808i | −0.311152 | + | 0.107786i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −36.0000 | − | 62.3538i | −1.49097 | − | 2.58243i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.0000 | −0.495293 | −0.247647 | − | 0.968850i | \(-0.579657\pi\) | ||||
−0.247647 | + | 0.968850i | \(0.579657\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.0000 | 0.659269 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.00000 | − | 10.3923i | −0.246390 | − | 0.426761i | 0.716131 | − | 0.697966i | \(-0.245911\pi\) |
−0.962522 | + | 0.271205i | \(0.912578\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.0000 | − | 5.19615i | 0.614940 | − | 0.213021i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.0000 | −0.897399 | −0.448699 | − | 0.893683i | \(-0.648113\pi\) | ||||
−0.448699 | + | 0.893683i | \(0.648113\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12.5000 | + | 21.6506i | −0.508197 | + | 0.880223i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.5000 | + | 37.2391i | 0.872658 | + | 1.51149i | 0.859237 | + | 0.511578i | \(0.170939\pi\) |
0.0134214 | + | 0.999910i | \(0.495728\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.00000 | + | 1.73205i | −0.0403896 | + | 0.0699569i | −0.885514 | − | 0.464614i | \(-0.846193\pi\) |
0.845124 | + | 0.534570i | \(0.179527\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.0000 | 0.483102 | 0.241551 | − | 0.970388i | \(-0.422344\pi\) | ||||
0.241551 | + | 0.970388i | \(0.422344\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.00000 | + | 12.1244i | −0.281354 | + | 0.487319i | −0.971718 | − | 0.236143i | \(-0.924117\pi\) |
0.690365 | + | 0.723462i | \(0.257450\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.00000 | − | 5.19615i | −0.240385 | − | 0.208179i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 48.0000 | 1.91389 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.0000 | 1.51276 | 0.756378 | − | 0.654135i | \(-0.226967\pi\) | ||||
0.756378 | + | 0.654135i | \(0.226967\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.00000 | − | 6.92820i | −0.158735 | − | 0.274937i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.0000 | − | 8.66025i | 0.435836 | − | 0.343132i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.5000 | + | 33.7750i | −0.770204 | + | 1.33403i | 0.167247 | + | 0.985915i | \(0.446512\pi\) |
−0.937451 | + | 0.348117i | \(0.886821\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.0000 | 0.788723 | 0.394362 | − | 0.918955i | \(-0.370966\pi\) | ||||
0.394362 | + | 0.918955i | \(0.370966\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.5000 | − | 18.1865i | 0.412798 | − | 0.714986i | −0.582397 | − | 0.812905i | \(-0.697885\pi\) |
0.995194 | + | 0.0979182i | \(0.0312184\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.0000 | − | 36.3731i | −0.821794 | − | 1.42339i | −0.904345 | − | 0.426801i | \(-0.859640\pi\) |
0.0825519 | − | 0.996587i | \(-0.473693\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.00000 | − | 10.3923i | 0.234439 | − | 0.406061i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.0000 | −0.467454 | −0.233727 | − | 0.972302i | \(-0.575092\pi\) | ||||
−0.233727 | + | 0.972302i | \(0.575092\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.5000 | − | 21.6506i | 0.486194 | − | 0.842112i | −0.513680 | − | 0.857982i | \(-0.671718\pi\) |
0.999874 | + | 0.0158695i | \(0.00505163\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.00000 | + | 20.7846i | −0.155113 | + | 0.805993i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.50000 | − | 7.79423i | −0.174241 | − | 0.301794i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.00000 | 0.231627 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.0000 | 1.23351 | 0.616755 | − | 0.787155i | \(-0.288447\pi\) | ||||
0.616755 | + | 0.787155i | \(0.288447\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.00000 | − | 15.5885i | −0.345898 | − | 0.599113i | 0.639618 | − | 0.768693i | \(-0.279092\pi\) |
−0.985517 | + | 0.169580i | \(0.945759\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25.0000 | + | 8.66025i | −0.959412 | + | 0.332350i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.50000 | + | 12.9904i | −0.286980 | + | 0.497063i | −0.973087 | − | 0.230437i | \(-0.925985\pi\) |
0.686108 | + | 0.727500i | \(0.259318\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.0000 | 0.458496 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.0000 | − | 20.7846i | 0.457164 | − | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.00000 | − | 12.1244i | −0.266293 | − | 0.461232i | 0.701609 | − | 0.712562i | \(-0.252465\pi\) |
−0.967901 | + | 0.251330i | \(0.919132\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.00000 | − | 1.73205i | −0.0379322 | − | 0.0657004i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.00000 | + | 15.5885i | −0.340899 | + | 0.590455i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.0000 | −1.01978 | −0.509888 | − | 0.860241i | \(-0.670313\pi\) | ||||
−0.509888 | + | 0.860241i | \(0.670313\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −32.0000 | + | 55.4256i | −1.20690 | + | 2.09042i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.50000 | + | 7.79423i | −0.0564133 | + | 0.293132i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.500000 | + | 0.866025i | 0.0187779 | + | 0.0325243i | 0.875262 | − | 0.483650i | \(-0.160689\pi\) |
−0.856484 | + | 0.516174i | \(0.827356\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.00000 | −0.224702 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.0000 | −0.448775 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.0000 | − | 25.9808i | −0.559406 | − | 0.968919i | −0.997546 | − | 0.0700124i | \(-0.977696\pi\) |
0.438141 | − | 0.898906i | \(-0.355637\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.0000 | + | 12.1244i | 0.521387 | + | 0.451535i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.50000 | − | 2.59808i | 0.0557086 | − | 0.0964901i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.0000 | 0.853023 | 0.426511 | − | 0.904482i | \(-0.359742\pi\) | ||||
0.426511 | + | 0.904482i | \(0.359742\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.0000 | + | 25.9808i | −0.554795 | + | 0.960933i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.00000 | − | 1.73205i | −0.0369358 | − | 0.0639748i | 0.846967 | − | 0.531646i | \(-0.178426\pi\) |
−0.883902 | + | 0.467671i | \(0.845093\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −21.0000 | − | 36.3731i | −0.773545 | − | 1.33982i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.0000 | − | 39.8372i | 0.846069 | − | 1.46543i | −0.0386212 | − | 0.999254i | \(-0.512297\pi\) |
0.884690 | − | 0.466180i | \(-0.154370\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 39.0000 | 1.43077 | 0.715386 | − | 0.698730i | \(-0.246251\pi\) | ||||
0.715386 | + | 0.698730i | \(0.246251\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.50000 | + | 12.9904i | −0.274779 | + | 0.475931i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.00000 | − | 5.19615i | −0.219235 | − | 0.189863i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.0000 | − | 17.3205i | −0.364905 | − | 0.632034i | 0.623856 | − | 0.781540i | \(-0.285565\pi\) |
−0.988761 | + | 0.149505i | \(0.952232\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.0000 | −0.363937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.00000 | 0.0726912 | 0.0363456 | − | 0.999339i | \(-0.488428\pi\) | ||||
0.0363456 | + | 0.999339i | \(0.488428\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.0000 | + | 25.9808i | 0.543750 | + | 0.941802i | 0.998684 | + | 0.0512772i | \(0.0163292\pi\) |
−0.454935 | + | 0.890525i | \(0.650337\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.50000 | + | 44.1673i | −0.307721 | + | 1.59896i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.0000 | −1.22607 | −0.613036 | − | 0.790055i | \(-0.710052\pi\) | ||||
−0.613036 | + | 0.790055i | \(0.710052\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.0000 | + | 36.3731i | −0.755318 | + | 1.30825i | 0.189899 | + | 0.981804i | \(0.439184\pi\) |
−0.945216 | + | 0.326445i | \(0.894149\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.00000 | − | 1.73205i | −0.0359211 | − | 0.0622171i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.0000 | − | 20.7846i | −0.429945 | − | 0.744686i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.0000 | 0.499681 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.5000 | − | 26.8468i | 0.552515 | − | 0.956985i | −0.445577 | − | 0.895244i | \(-0.647001\pi\) |
0.998092 | − | 0.0617409i | \(-0.0196653\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 30.0000 | − | 10.3923i | 1.06668 | − | 0.369508i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.00000 | + | 1.73205i | 0.0355110 | + | 0.0615069i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.0000 | 0.425062 | 0.212531 | − | 0.977154i | \(-0.431829\pi\) | ||||
0.212531 | + | 0.977154i | \(0.431829\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −30.0000 | − | 51.9615i | −1.05868 | − | 1.83368i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.50000 | − | 7.79423i | 0.0528681 | − | 0.274710i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −25.5000 | + | 44.1673i | −0.896532 | + | 1.55284i | −0.0646355 | + | 0.997909i | \(0.520588\pi\) |
−0.831897 | + | 0.554930i | \(0.812745\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.00000 | 0.0702295 | 0.0351147 | − | 0.999383i | \(-0.488820\pi\) | ||||
0.0351147 | + | 0.999383i | \(0.488820\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.00000 | − | 13.8564i | 0.280228 | − | 0.485369i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.0000 | − | 34.6410i | −0.699711 | − | 1.21194i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.00000 | + | 15.5885i | 0.314102 | + | 0.544041i | 0.979246 | − | 0.202674i | \(-0.0649632\pi\) |
−0.665144 | + | 0.746715i | \(0.731630\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.5000 | − | 42.4352i | 0.854016 | − | 1.47920i | −0.0235383 | − | 0.999723i | \(-0.507493\pi\) |
0.877555 | − | 0.479477i | \(-0.159174\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 45.0000 | 1.56480 | 0.782402 | − | 0.622774i | \(-0.213994\pi\) | ||||
0.782402 | + | 0.622774i | \(0.213994\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.00000 | − | 8.66025i | 0.173657 | − | 0.300783i | −0.766039 | − | 0.642795i | \(-0.777775\pi\) |
0.939696 | + | 0.342012i | \(0.111108\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.00000 | + | 41.5692i | 0.207888 | + | 1.44029i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.5000 | − | 18.1865i | −0.363367 | − | 0.629371i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 42.0000 | 1.45000 | 0.725001 | − | 0.688748i | \(-0.241839\pi\) | ||||
0.725001 | + | 0.688748i | \(0.241839\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.50000 | + | 7.79423i | 0.154805 | + | 0.268130i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −50.0000 | − | 43.3013i | −1.71802 | − | 1.48785i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.0000 | − | 20.7846i | 0.411355 | − | 0.712487i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.0000 | 1.09566 | 0.547830 | − | 0.836590i | \(-0.315454\pi\) | ||||
0.547830 | + | 0.836590i | \(0.315454\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.0000 | − | 36.3731i | 0.717346 | − | 1.24248i | −0.244701 | − | 0.969599i | \(-0.578690\pi\) |
0.962048 | − | 0.272882i | \(-0.0879768\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.00000 | + | 3.46410i | 0.0682391 | + | 0.118194i | 0.898126 | − | 0.439738i | \(-0.144929\pi\) |
−0.829887 | + | 0.557931i | \(0.811595\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.5000 | + | 28.5788i | 0.561667 | + | 0.972835i | 0.997351 | + | 0.0727356i | \(0.0231729\pi\) |
−0.435685 | + | 0.900099i | \(0.643494\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.0000 | 0.814144 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.00000 | − | 12.1244i | 0.237186 | − | 0.410818i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.50000 | − | 0.866025i | 0.0845154 | − | 0.0292770i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.0000 | + | 34.6410i | 0.675352 | + | 1.16974i | 0.976366 | + | 0.216124i | \(0.0693416\pi\) |
−0.301014 | + | 0.953620i | \(0.597325\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.00000 | −0.303218 | −0.151609 | − | 0.988441i | \(-0.548445\pi\) | ||||
−0.151609 | + | 0.988441i | \(0.548445\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.0000 | −0.942275 | −0.471138 | − | 0.882060i | \(-0.656156\pi\) | ||||
−0.471138 | + | 0.882060i | \(0.656156\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28.5000 | + | 49.3634i | 0.956936 | + | 1.65746i | 0.729873 | + | 0.683582i | \(0.239579\pi\) |
0.227063 | + | 0.973880i | \(0.427088\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.0000 | − | 6.92820i | 0.670778 | − | 0.232364i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.00000 | 0.200558 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.00000 | − | 5.19615i | 0.100056 | − | 0.173301i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.0000 | + | 62.3538i | 1.19933 | + | 2.07731i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.50000 | − | 14.7224i | −0.282550 | − | 0.489390i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.5000 | + | 19.9186i | −0.381851 | + | 0.661386i | −0.991327 | − | 0.131419i | \(-0.958047\pi\) |
0.609476 | + | 0.792805i | \(0.291380\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.0000 | −0.993944 | −0.496972 | − | 0.867766i | \(-0.665555\pi\) | ||||
−0.496972 | + | 0.867766i | \(0.665555\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.00000 | + | 15.5885i | −0.297857 | + | 0.515903i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 24.0000 | + | 20.7846i | 0.792550 | + | 0.686368i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.00000 | − | 6.92820i | −0.131948 | − | 0.228540i | 0.792480 | − | 0.609898i | \(-0.208790\pi\) |
−0.924427 | + | 0.381358i | \(0.875456\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.00000 | 0.263038 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.5000 | − | 38.9711i | −0.738201 | − | 1.27860i | −0.953305 | − | 0.302010i | \(-0.902342\pi\) |
0.215104 | − | 0.976591i | \(-0.430991\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −52.0000 | − | 20.7846i | −1.70423 | − | 0.681188i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18.0000 | − | 31.1769i | 0.588663 | − | 1.01959i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.0000 | 1.43742 | 0.718709 | − | 0.695311i | \(-0.244734\pi\) | ||||
0.718709 | + | 0.695311i | \(0.244734\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.0000 | − | 46.7654i | 0.880175 | − | 1.52451i | 0.0290288 | − | 0.999579i | \(-0.490759\pi\) |
0.851146 | − | 0.524929i | \(-0.175908\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.50000 | + | 7.79423i | 0.146540 | + | 0.253815i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.50000 | + | 7.79423i | 0.146230 | + | 0.253278i | 0.929831 | − | 0.367986i | \(-0.119953\pi\) |
−0.783601 | + | 0.621264i | \(0.786619\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.0000 | − | 17.3205i | 0.324614 | − | 0.562247i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −36.0000 | −1.16615 | −0.583077 | − | 0.812417i | \(-0.698151\pi\) | ||||
−0.583077 | + | 0.812417i | \(0.698151\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.00000 | + | 15.5885i | −0.291233 | + | 0.504431i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.00000 | + | 31.1769i | −0.193750 | + | 1.00676i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | + | 23.3827i | 0.435484 | + | 0.754280i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.00000 | 0.0643823 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.00000 | −0.225105 | −0.112552 | − | 0.993646i | \(-0.535903\pi\) | ||||
−0.112552 | + | 0.993646i | \(0.535903\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.00000 | − | 10.3923i | −0.192549 | − | 0.333505i | 0.753545 | − | 0.657396i | \(-0.228342\pi\) |
−0.946094 | + | 0.323891i | \(0.895009\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.00000 | − | 1.73205i | 0.160293 | − | 0.0555270i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −27.0000 | + | 46.7654i | −0.863807 | + | 1.49616i | 0.00442082 | + | 0.999990i | \(0.498593\pi\) |
−0.868227 | + | 0.496167i | \(0.834741\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.0000 | −0.575282 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −19.5000 | + | 33.7750i | −0.621953 | + | 1.07725i | 0.367168 | + | 0.930155i | \(0.380327\pi\) |
−0.989122 | + | 0.147100i | \(0.953006\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.00000 | − | 15.5885i | −0.286764 | − | 0.496690i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.50000 | + | 12.9904i | 0.238486 | + | 0.413070i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.0000 | + | 22.5167i | −0.412959 | + | 0.715265i | −0.995212 | − | 0.0977423i | \(-0.968838\pi\) |
0.582253 | + | 0.813008i | \(0.302171\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.0000 | 0.634043 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.0000 | + | 27.7128i | −0.506725 | + | 0.877674i | 0.493245 | + | 0.869891i | \(0.335811\pi\) |
−0.999970 | + | 0.00778294i | \(0.997523\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1260.2.s.c.361.1 | 2 | ||
3.2 | odd | 2 | 140.2.i.a.81.1 | ✓ | 2 | ||
7.2 | even | 3 | inner | 1260.2.s.c.541.1 | 2 | ||
7.3 | odd | 6 | 8820.2.a.a.1.1 | 1 | |||
7.4 | even | 3 | 8820.2.a.p.1.1 | 1 | |||
12.11 | even | 2 | 560.2.q.f.81.1 | 2 | |||
15.2 | even | 4 | 700.2.r.a.249.2 | 4 | |||
15.8 | even | 4 | 700.2.r.a.249.1 | 4 | |||
15.14 | odd | 2 | 700.2.i.b.501.1 | 2 | |||
21.2 | odd | 6 | 140.2.i.a.121.1 | yes | 2 | ||
21.5 | even | 6 | 980.2.i.f.961.1 | 2 | |||
21.11 | odd | 6 | 980.2.a.g.1.1 | 1 | |||
21.17 | even | 6 | 980.2.a.e.1.1 | 1 | |||
21.20 | even | 2 | 980.2.i.f.361.1 | 2 | |||
84.11 | even | 6 | 3920.2.a.k.1.1 | 1 | |||
84.23 | even | 6 | 560.2.q.f.401.1 | 2 | |||
84.59 | odd | 6 | 3920.2.a.w.1.1 | 1 | |||
105.2 | even | 12 | 700.2.r.a.149.1 | 4 | |||
105.17 | odd | 12 | 4900.2.e.n.2549.2 | 2 | |||
105.23 | even | 12 | 700.2.r.a.149.2 | 4 | |||
105.32 | even | 12 | 4900.2.e.m.2549.1 | 2 | |||
105.38 | odd | 12 | 4900.2.e.n.2549.1 | 2 | |||
105.44 | odd | 6 | 700.2.i.b.401.1 | 2 | |||
105.53 | even | 12 | 4900.2.e.m.2549.2 | 2 | |||
105.59 | even | 6 | 4900.2.a.q.1.1 | 1 | |||
105.74 | odd | 6 | 4900.2.a.i.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
140.2.i.a.81.1 | ✓ | 2 | 3.2 | odd | 2 | ||
140.2.i.a.121.1 | yes | 2 | 21.2 | odd | 6 | ||
560.2.q.f.81.1 | 2 | 12.11 | even | 2 | |||
560.2.q.f.401.1 | 2 | 84.23 | even | 6 | |||
700.2.i.b.401.1 | 2 | 105.44 | odd | 6 | |||
700.2.i.b.501.1 | 2 | 15.14 | odd | 2 | |||
700.2.r.a.149.1 | 4 | 105.2 | even | 12 | |||
700.2.r.a.149.2 | 4 | 105.23 | even | 12 | |||
700.2.r.a.249.1 | 4 | 15.8 | even | 4 | |||
700.2.r.a.249.2 | 4 | 15.2 | even | 4 | |||
980.2.a.e.1.1 | 1 | 21.17 | even | 6 | |||
980.2.a.g.1.1 | 1 | 21.11 | odd | 6 | |||
980.2.i.f.361.1 | 2 | 21.20 | even | 2 | |||
980.2.i.f.961.1 | 2 | 21.5 | even | 6 | |||
1260.2.s.c.361.1 | 2 | 1.1 | even | 1 | trivial | ||
1260.2.s.c.541.1 | 2 | 7.2 | even | 3 | inner | ||
3920.2.a.k.1.1 | 1 | 84.11 | even | 6 | |||
3920.2.a.w.1.1 | 1 | 84.59 | odd | 6 | |||
4900.2.a.i.1.1 | 1 | 105.74 | odd | 6 | |||
4900.2.a.q.1.1 | 1 | 105.59 | even | 6 | |||
4900.2.e.m.2549.1 | 2 | 105.32 | even | 12 | |||
4900.2.e.m.2549.2 | 2 | 105.53 | even | 12 | |||
4900.2.e.n.2549.1 | 2 | 105.38 | odd | 12 | |||
4900.2.e.n.2549.2 | 2 | 105.17 | odd | 12 | |||
8820.2.a.a.1.1 | 1 | 7.3 | odd | 6 | |||
8820.2.a.p.1.1 | 1 | 7.4 | even | 3 |