Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,2,Mod(289,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.r (of order \(6\), degree \(2\), 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: | \(13.7981494693\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 16x^{8} - 24x^{7} + 96x^{5} + 304x^{4} + 384x^{3} + 288x^{2} + 144x + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 576) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1441.3 | ||
Root | \(-1.50511 - 0.403293i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.1441 |
Dual form | 1728.2.r.e.289.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(5\) | −1.50000 | − | 0.866025i | −0.670820 | − | 0.387298i | 0.125567 | − | 0.992085i | \(-0.459925\pi\) |
−0.796387 | + | 0.604787i | \(0.793258\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.495361 | − | 0.857990i | −0.187229 | − | 0.324290i | 0.757097 | − | 0.653303i | \(-0.226617\pi\) |
−0.944325 | + | 0.329013i | \(0.893284\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.81937 | + | 1.05042i | −0.548561 | + | 0.316712i | −0.748542 | − | 0.663088i | \(-0.769246\pi\) |
0.199980 | + | 0.979800i | \(0.435912\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.50924 | + | 3.18076i | 1.52799 | + | 0.882184i | 0.999446 | + | 0.0332758i | \(0.0105940\pi\) |
0.528541 | + | 0.848908i | \(0.322739\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.81681 | −0.925712 | −0.462856 | − | 0.886433i | \(-0.653175\pi\) | ||||
−0.462856 | + | 0.886433i | \(0.653175\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000i | 0.458831i | 0.973329 | + | 0.229416i | \(0.0736815\pi\) | ||||
−0.973329 | + | 0.229416i | \(0.926318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.55142 | − | 6.15125i | 0.740523 | − | 1.28262i | −0.211734 | − | 0.977327i | \(-0.567911\pi\) |
0.952257 | − | 0.305296i | \(-0.0987555\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | − | 1.73205i | −0.200000 | − | 0.346410i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.22522 | − | 4.17148i | 1.34169 | − | 0.774624i | 0.354634 | − | 0.935005i | \(-0.384606\pi\) |
0.987055 | + | 0.160381i | \(0.0512723\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.07804 | − | 1.86723i | 0.193622 | − | 0.335364i | −0.752826 | − | 0.658220i | \(-0.771310\pi\) |
0.946448 | + | 0.322856i | \(0.104643\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.71598i | 0.290054i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.62947i | 0.761080i | 0.924765 | + | 0.380540i | \(0.124262\pi\) | ||||
−0.924765 | + | 0.380540i | \(0.875738\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.408405 | − | 0.707378i | 0.0637822 | − | 0.110474i | −0.832371 | − | 0.554219i | \(-0.813017\pi\) |
0.896153 | + | 0.443745i | \(0.146350\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.97802 | − | 1.14201i | 0.301645 | − | 0.174155i | −0.341537 | − | 0.939868i | \(-0.610947\pi\) |
0.643182 | + | 0.765714i | \(0.277614\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.39278 | − | 5.87646i | −0.494887 | − | 0.857170i | 0.505095 | − | 0.863064i | \(-0.331457\pi\) |
−0.999983 | + | 0.00589362i | \(0.998124\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00924 | − | 5.21215i | 0.429891 | − | 0.744593i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 3.14681i | − | 0.432247i | −0.976366 | − | 0.216124i | \(-0.930659\pi\) | ||
0.976366 | − | 0.216124i | \(-0.0693414\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.63875 | 0.490648 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.3210 | − | 5.95882i | −1.34368 | − | 0.775772i | −0.356332 | − | 0.934359i | \(-0.615973\pi\) |
−0.987345 | + | 0.158587i | \(0.949306\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.22522 | − | 2.43943i | 0.540983 | − | 0.312337i | −0.204494 | − | 0.978868i | \(-0.565555\pi\) |
0.745477 | + | 0.666531i | \(0.232222\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.50924 | − | 9.54228i | −0.683337 | − | 1.18357i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.8944 | − | 6.86723i | −1.45313 | − | 0.838965i | −0.454473 | − | 0.890761i | \(-0.650172\pi\) |
−0.998658 | + | 0.0517956i | \(0.983506\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.5391 | −1.60680 | −0.803399 | − | 0.595442i | \(-0.796977\pi\) | ||||
−0.803399 | + | 0.595442i | \(0.796977\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.0185 | 1.17257 | 0.586287 | − | 0.810104i | \(-0.300589\pi\) | ||||
0.586287 | + | 0.810104i | \(0.300589\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.80249 | + | 1.04067i | 0.205413 | + | 0.118595i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.54214 | − | 7.86723i | −0.511031 | − | 0.885132i | −0.999918 | − | 0.0127849i | \(-0.995930\pi\) |
0.488887 | − | 0.872347i | \(-0.337403\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.71007 | − | 2.14201i | 0.407233 | − | 0.235116i | −0.282367 | − | 0.959306i | \(-0.591120\pi\) |
0.689600 | + | 0.724190i | \(0.257786\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.72522 | + | 3.30545i | 0.620987 | + | 0.358527i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.0185 | 1.48595 | 0.742977 | − | 0.669316i | \(-0.233413\pi\) | ||||
0.742977 | + | 0.669316i | \(0.233413\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 6.30249i | − | 0.660681i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.73205 | − | 3.00000i | 0.177705 | − | 0.307794i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.22522 | − | 10.7824i | −0.632075 | − | 1.09479i | −0.987127 | − | 0.159939i | \(-0.948870\pi\) |
0.355052 | − | 0.934847i | \(-0.384463\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.8025 | − | 7.96887i | 1.37340 | − | 0.792932i | 0.382045 | − | 0.924144i | \(-0.375220\pi\) |
0.991354 | + | 0.131211i | \(0.0418867\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.58893 | − | 14.8765i | 0.846292 | − | 1.46582i | −0.0382019 | − | 0.999270i | \(-0.512163\pi\) |
0.884494 | − | 0.466551i | \(-0.154504\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.2017i | 1.56627i | 0.621849 | + | 0.783137i | \(0.286382\pi\) | ||||
−0.621849 | + | 0.783137i | \(0.713618\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 0.816078i | − | 0.0781661i | −0.999236 | − | 0.0390830i | \(-0.987556\pi\) | ||
0.999236 | − | 0.0390830i | \(-0.0124437\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.21598 | + | 5.57024i | −0.302534 | + | 0.524004i | −0.976709 | − | 0.214567i | \(-0.931166\pi\) |
0.674175 | + | 0.738571i | \(0.264499\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.6543 | + | 6.15125i | −0.993516 | + | 0.573607i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.89070 | + | 3.27478i | 0.173320 | + | 0.300199i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.29326 | + | 5.70409i | −0.299387 | + | 0.518553i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1244i | 1.08444i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.1871 | 1.43638 | 0.718188 | − | 0.695849i | \(-0.244972\pi\) | ||||
0.718188 | + | 0.695849i | \(0.244972\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.68223 | + | 3.85799i | 0.583830 | + | 0.337074i | 0.762654 | − | 0.646807i | \(-0.223896\pi\) |
−0.178824 | + | 0.983881i | \(0.557229\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.71598 | − | 0.990721i | 0.148794 | − | 0.0859064i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.30757 | − | 7.46094i | −0.368021 | − | 0.637431i | 0.621235 | − | 0.783624i | \(-0.286631\pi\) |
−0.989256 | + | 0.146193i | \(0.953298\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.95018 | + | 2.85799i | 0.419869 | + | 0.242412i | 0.695021 | − | 0.718989i | \(-0.255395\pi\) |
−0.275152 | + | 0.961401i | \(0.588728\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.3645 | −1.11759 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.4504 | −1.20004 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.22522 | + | 0.707378i | 0.100374 | + | 0.0579507i | 0.549346 | − | 0.835595i | \(-0.314877\pi\) |
−0.448973 | + | 0.893545i | \(0.648210\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.64473 | + | 2.84875i | 0.133846 | + | 0.231828i | 0.925156 | − | 0.379587i | \(-0.123934\pi\) |
−0.791310 | + | 0.611415i | \(0.790601\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.23413 | + | 1.86723i | −0.259772 | + | 0.149979i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.78402 | − | 3.33941i | −0.461615 | − | 0.266514i | 0.251108 | − | 0.967959i | \(-0.419205\pi\) |
−0.712723 | + | 0.701445i | \(0.752538\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.03694 | −0.554589 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 7.43196i | − | 0.582116i | −0.956705 | − | 0.291058i | \(-0.905993\pi\) | ||
0.956705 | − | 0.291058i | \(-0.0940073\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.95018 | − | 8.57397i | 0.383057 | − | 0.663474i | −0.608441 | − | 0.793599i | \(-0.708205\pi\) |
0.991498 | + | 0.130126i | \(0.0415380\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.7345 | + | 23.7888i | 1.05650 | + | 1.82991i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.5000 | − | 6.06218i | 0.798300 | − | 0.460899i | −0.0445762 | − | 0.999006i | \(-0.514194\pi\) |
0.842876 | + | 0.538107i | \(0.180860\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.990721 | + | 1.71598i | −0.0748915 | + | 0.129716i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 6.00000i | − | 0.448461i | −0.974536 | − | 0.224231i | \(-0.928013\pi\) | ||
0.974536 | − | 0.224231i | \(-0.0719869\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 4.62947i | − | 0.344106i | −0.985088 | − | 0.172053i | \(-0.944960\pi\) | ||
0.985088 | − | 0.172053i | \(-0.0550400\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.00924 | − | 6.94420i | 0.294765 | − | 0.510548i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.94420 | − | 4.00924i | 0.507810 | − | 0.293184i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.58893 | + | 14.8765i | 0.621473 | + | 1.07642i | 0.989212 | + | 0.146494i | \(0.0467988\pi\) |
−0.367739 | + | 0.929929i | \(0.619868\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.79326 | − | 10.0342i | 0.417008 | − | 0.722278i | −0.578629 | − | 0.815591i | \(-0.696412\pi\) |
0.995637 | + | 0.0933122i | \(0.0297455\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.6698i | 1.25892i | 0.777033 | + | 0.629460i | \(0.216724\pi\) | ||||
−0.777033 | + | 0.629460i | \(0.783276\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.5044 | −1.16997 | −0.584984 | − | 0.811045i | \(-0.698899\pi\) | ||||
−0.584984 | + | 0.811045i | \(0.698899\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.15818 | − | 4.13277i | −0.502405 | − | 0.290064i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.22522 | + | 0.707378i | −0.0855728 | + | 0.0494055i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.10083 | − | 3.63875i | −0.145317 | − | 0.251697i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.1623 | + | 5.86723i | 0.699604 | + | 0.403916i | 0.807200 | − | 0.590278i | \(-0.200982\pi\) |
−0.107596 | + | 0.994195i | \(0.534315\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.95604 | −0.269800 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.13608 | −0.145007 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.0277 | − | 12.1404i | −1.41448 | − | 0.816648i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.670004 | + | 1.16048i | 0.0448668 | + | 0.0777116i | 0.887587 | − | 0.460641i | \(-0.152380\pi\) |
−0.842720 | + | 0.538352i | \(0.819047\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.37678 | + | 1.94958i | −0.224125 | + | 0.129398i | −0.607859 | − | 0.794045i | \(-0.707971\pi\) |
0.383734 | + | 0.923444i | \(0.374638\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.93196 | − | 1.11542i | −0.127667 | − | 0.0737089i | 0.434806 | − | 0.900524i | \(-0.356817\pi\) |
−0.562474 | + | 0.826815i | \(0.690150\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.26724 | 0.607117 | 0.303559 | − | 0.952813i | \(-0.401825\pi\) | ||||
0.303559 | + | 0.952813i | \(0.401825\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.7529i | 0.766676i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.4796 | − | 18.1512i | 0.677871 | − | 1.17411i | −0.297750 | − | 0.954644i | \(-0.596236\pi\) |
0.975621 | − | 0.219463i | \(-0.0704304\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.51847 | − | 13.0224i | −0.484307 | − | 0.838845i | 0.515530 | − | 0.856871i | \(-0.327595\pi\) |
−0.999838 | + | 0.0180266i | \(0.994262\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.02771 | + | 5.21215i | −0.576759 | + | 0.332992i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.36152 | + | 11.0185i | −0.404774 | + | 0.701089i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.164719i | 0.0103969i | 0.999986 | + | 0.00519847i | \(0.00165473\pi\) | ||||
−0.999986 | + | 0.00519847i | \(0.998345\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.9219i | 0.938130i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.4176 | + | 23.2400i | −0.836969 | + | 1.44967i | 0.0554474 | + | 0.998462i | \(0.482341\pi\) |
−0.892417 | + | 0.451212i | \(0.850992\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.97204 | − | 2.29326i | 0.246810 | − | 0.142496i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.98769 | + | 17.2992i | 0.615867 | + | 1.06671i | 0.990232 | + | 0.139432i | \(0.0445276\pi\) |
−0.374364 | + | 0.927282i | \(0.622139\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.72522 | + | 4.72021i | −0.167409 | + | 0.289960i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 0.666581i | − | 0.0406422i | −0.999794 | − | 0.0203211i | \(-0.993531\pi\) | ||
0.999794 | − | 0.0203211i | \(-0.00646884\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.0352 | −1.03482 | −0.517408 | − | 0.855739i | \(-0.673103\pi\) | ||||
−0.517408 | + | 0.855739i | \(0.673103\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.63875 | + | 2.10083i | 0.219425 | + | 0.126685i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.21598 | + | 1.85675i | −0.193229 | + | 0.111561i | −0.593494 | − | 0.804839i | \(-0.702252\pi\) |
0.400264 | + | 0.916400i | \(0.368918\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.5277 | + | 23.4307i | 0.806995 | + | 1.39776i | 0.914936 | + | 0.403600i | \(0.132241\pi\) |
−0.107940 | + | 0.994157i | \(0.534426\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.994145 | − | 0.573970i | −0.0590958 | − | 0.0341190i | 0.470161 | − | 0.882581i | \(-0.344196\pi\) |
−0.529257 | + | 0.848462i | \(0.677529\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.809231 | −0.0477674 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.43196 | −0.143056 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −22.8025 | − | 13.1650i | −1.33214 | − | 0.769109i | −0.346509 | − | 0.938047i | \(-0.612633\pi\) |
−0.985627 | + | 0.168938i | \(0.945966\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.3210 | + | 17.8765i | 0.600911 | + | 1.04081i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 39.1313 | − | 22.5924i | 2.26302 | − | 1.30655i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.95967 | − | 1.13141i | −0.112953 | − | 0.0652136i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.45043 | −0.483870 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.43196i | 0.424164i | 0.977252 | + | 0.212082i | \(0.0680244\pi\) | ||||
−0.977252 | + | 0.212082i | \(0.931976\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.96618 | + | 8.60168i | −0.281606 | + | 0.487756i | −0.971781 | − | 0.235887i | \(-0.924201\pi\) |
0.690174 | + | 0.723643i | \(0.257534\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.51847 | + | 7.82622i | 0.255399 | + | 0.442364i | 0.965004 | − | 0.262236i | \(-0.0844598\pi\) |
−0.709605 | + | 0.704600i | \(0.751126\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.52771 | + | 4.34612i | −0.422798 | + | 0.244103i | −0.696274 | − | 0.717776i | \(-0.745160\pi\) |
0.273476 | + | 0.961879i | \(0.411827\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.76357 | + | 15.1790i | −0.490666 | + | 0.849858i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 7.63362i | − | 0.424746i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 12.7230i | − | 0.705747i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.36130 | + | 5.82194i | −0.185314 | + | 0.320974i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.1462 | + | 6.43527i | −0.612651 | + | 0.353714i | −0.774002 | − | 0.633183i | \(-0.781748\pi\) |
0.161351 | + | 0.986897i | \(0.448415\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.8944 | + | 20.6017i | 0.649860 | + | 1.12559i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.21598 | − | 2.10614i | 0.0662386 | − | 0.114729i | −0.831004 | − | 0.556266i | \(-0.812233\pi\) |
0.897243 | + | 0.441538i | \(0.145567\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.52957i | 0.245290i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.8977 | −0.696409 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.2373 | − | 11.6840i | −1.08640 | − | 0.627232i | −0.153782 | − | 0.988105i | \(-0.549146\pi\) |
−0.932615 | + | 0.360873i | \(0.882479\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.66641 | + | 5.00355i | −0.463902 | + | 0.267834i | −0.713684 | − | 0.700468i | \(-0.752975\pi\) |
0.249781 | + | 0.968302i | \(0.419641\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.6924 | − | 18.5198i | −0.569100 | − | 0.985711i | −0.996655 | − | 0.0817214i | \(-0.973958\pi\) |
0.427555 | − | 0.903989i | \(-0.359375\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.3087 | + | 11.7252i | 1.07787 | + | 0.622310i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.9634 | 1.26474 | 0.632370 | − | 0.774666i | \(-0.282082\pi\) | ||||
0.632370 | + | 0.774666i | \(0.282082\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | 0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.0277 | − | 8.67625i | −0.786586 | − | 0.454136i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.25564 | + | 14.2992i | 0.430941 | + | 0.746411i | 0.996955 | − | 0.0779844i | \(-0.0248484\pi\) |
−0.566014 | + | 0.824396i | \(0.691515\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.69993 | + | 1.55880i | −0.140173 | + | 0.0809291i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.2437 | − | 12.2650i | −1.09996 | − | 0.635060i | −0.163747 | − | 0.986502i | \(-0.552358\pi\) |
−0.936210 | + | 0.351442i | \(0.885691\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 53.0739 | 2.73344 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 10.8824i | − | 0.558991i | −0.960147 | − | 0.279495i | \(-0.909833\pi\) | ||
0.960147 | − | 0.279495i | \(-0.0901672\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.66073 | + | 2.87646i | −0.0848591 | + | 0.146980i | −0.905331 | − | 0.424706i | \(-0.860377\pi\) |
0.820472 | + | 0.571687i | \(0.193711\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.80249 | − | 3.12201i | −0.0918635 | − | 0.159112i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.19751 | − | 0.691382i | 0.0607161 | − | 0.0350545i | −0.469335 | − | 0.883020i | \(-0.655506\pi\) |
0.530051 | + | 0.847966i | \(0.322173\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.5551 | + | 23.4781i | −0.685511 | + | 1.18734i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.7345i | 0.791686i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 19.9685i | − | 1.00219i | −0.865392 | − | 0.501096i | \(-0.832930\pi\) | ||
0.865392 | − | 0.501096i | \(-0.167070\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.326046 | + | 0.564728i | −0.0162819 | + | 0.0282012i | −0.874052 | − | 0.485833i | \(-0.838516\pi\) |
0.857770 | + | 0.514034i | \(0.171850\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.8784 | − | 6.85799i | 0.591705 | − | 0.341621i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.86286 | − | 8.42272i | −0.241043 | − | 0.417499i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.51847 | + | 13.0224i | −0.371764 | + | 0.643915i | −0.989837 | − | 0.142206i | \(-0.954580\pi\) |
0.618073 | + | 0.786121i | \(0.287914\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.8071i | 0.580988i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.42014 | −0.364240 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.4024 | − | 6.58321i | −0.557046 | − | 0.321611i | 0.194913 | − | 0.980821i | \(-0.437558\pi\) |
−0.751959 | + | 0.659210i | \(0.770891\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.36130 | − | 1.94065i | 0.163820 | − | 0.0945813i | −0.415849 | − | 0.909434i | \(-0.636515\pi\) |
0.579668 | + | 0.814853i | \(0.303182\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.81681 | + | 6.61091i | 0.185142 | + | 0.320676i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.18601 | − | 2.41679i | −0.202575 | − | 0.116957i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.81339 | −0.183684 | −0.0918422 | − | 0.995774i | \(-0.529276\pi\) | ||||
−0.0918422 | + | 0.995774i | \(0.529276\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.0185 | −0.481457 | −0.240728 | − | 0.970592i | \(-0.577386\pi\) | ||||
−0.240728 | + | 0.970592i | \(0.577386\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.3025 | + | 7.10285i | 0.588508 | + | 0.339775i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.2117 | − | 21.1512i | −0.582832 | − | 1.00949i | −0.995142 | − | 0.0984504i | \(-0.968611\pi\) |
0.412310 | − | 0.911043i | \(-0.364722\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.3799 | − | 12.3437i | 1.01579 | − | 0.586466i | 0.102907 | − | 0.994691i | \(-0.467186\pi\) |
0.912881 | + | 0.408225i | \(0.133852\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −21.0277 | − | 12.1404i | −0.996809 | − | 0.575508i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.6521 | −1.02183 | −0.510913 | − | 0.859633i | \(-0.670692\pi\) | ||||
−0.510913 | + | 0.859633i | \(0.670692\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.71598i | 0.0808023i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.45812 | + | 9.45374i | −0.255880 | + | 0.443198i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.2437 | + | 19.4746i | 0.525957 | + | 0.910985i | 0.999543 | + | 0.0302371i | \(0.00962623\pi\) |
−0.473585 | + | 0.880748i | \(0.657040\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.6756 | + | 12.5144i | −1.00954 | + | 0.582856i | −0.911056 | − | 0.412283i | \(-0.864731\pi\) |
−0.0984799 | + | 0.995139i | \(0.531398\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.73830 | + | 16.8672i | −0.452577 | + | 0.783886i | −0.998545 | − | 0.0539194i | \(-0.982829\pi\) |
0.545968 | + | 0.837806i | \(0.316162\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.40332i | 0.111212i | 0.998453 | + | 0.0556062i | \(0.0177091\pi\) | ||||
−0.998453 | + | 0.0556062i | \(0.982291\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.6070i | 0.628314i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.39917 | + | 4.15548i | −0.110314 | + | 0.191069i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.46410 | − | 2.00000i | 0.158944 | − | 0.0917663i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.6543 | + | 18.4537i | 0.486806 | + | 0.843173i | 0.999885 | − | 0.0151687i | \(-0.00482852\pi\) |
−0.513079 | + | 0.858341i | \(0.671495\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.7252 | + | 25.5048i | −0.671412 | + | 1.16292i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.5648i | 0.979206i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 40.7851 | 1.84815 | 0.924075 | − | 0.382210i | \(-0.124837\pi\) | ||||
0.924075 | + | 0.382210i | \(0.124837\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.6776 | + | 17.7117i | 1.38446 | + | 0.799320i | 0.992684 | − | 0.120740i | \(-0.0385267\pi\) |
0.391778 | + | 0.920060i | \(0.371860\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27.5773 | + | 15.9217i | −1.24202 | + | 0.717079i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.70674 | + | 11.6164i | 0.300839 | + | 0.521068i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.74206 | + | 2.16048i | 0.167518 | + | 0.0967164i | 0.581415 | − | 0.813607i | \(-0.302499\pi\) |
−0.413897 | + | 0.910324i | \(0.635833\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.24550 | −0.323061 | −0.161530 | − | 0.986868i | \(-0.551643\pi\) | ||||
−0.161530 | + | 0.986868i | \(0.551643\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27.6050 | −1.22841 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.22522 | + | 4.17148i | 0.320252 | + | 0.184898i | 0.651505 | − | 0.758644i | \(-0.274138\pi\) |
−0.331253 | + | 0.943542i | \(0.607471\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.96276 | − | 8.59575i | −0.219539 | − | 0.380253i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −25.7668 | + | 14.8765i | −1.13542 | + | 0.655535i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.3454 | + | 7.12765i | 0.542952 | + | 0.313474i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.9714 | −0.743529 | −0.371764 | − | 0.928327i | \(-0.621247\pi\) | ||||
−0.371764 | + | 0.928327i | \(0.621247\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.0554i | 1.75150i | 0.482764 | + | 0.875750i | \(0.339633\pi\) | ||||
−0.482764 | + | 0.875750i | \(0.660367\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.11469 | + | 7.12685i | −0.179239 | + | 0.310450i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.7252 | − | 23.7728i | −0.596748 | − | 1.03360i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.50000 | − | 2.59808i | 0.194917 | − | 0.112535i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.0310 | − | 24.3025i | 0.606615 | − | 1.05069i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.6438i | 0.544606i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 25.5956i | − | 1.10044i | −0.835020 | − | 0.550220i | \(-0.814544\pi\) | ||
0.835020 | − | 0.550220i | \(-0.185456\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.706744 | + | 1.22412i | −0.0302736 | + | 0.0524354i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.2469 | − | 16.8857i | 1.25051 | − | 0.721980i | 0.279296 | − | 0.960205i | \(-0.409899\pi\) |
0.971210 | + | 0.238225i | \(0.0765655\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.34296 | + | 14.4504i | 0.355422 | + | 0.615609i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.50000 | + | 7.79423i | −0.191359 | + | 0.331444i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.3364i | 0.776937i | 0.921462 | + | 0.388469i | \(0.126996\pi\) | ||||
−0.921462 | + | 0.388469i | \(0.873004\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.5298 | 0.614546 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 35.8258 | + | 20.6840i | 1.50988 | + | 0.871728i | 0.999934 | + | 0.0115205i | \(0.00366716\pi\) |
0.509944 | + | 0.860208i | \(0.329666\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.64794 | − | 5.57024i | 0.405892 | − | 0.234342i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.683190 | − | 1.18332i | −0.0286408 | − | 0.0496073i | 0.851350 | − | 0.524599i | \(-0.175785\pi\) |
−0.879991 | + | 0.474991i | \(0.842451\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.3585 | − | 8.86723i | −0.642733 | − | 0.371082i | 0.142934 | − | 0.989732i | \(-0.454346\pi\) |
−0.785666 | + | 0.618650i | \(0.787680\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.2057 | −0.592418 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.5865 | 0.857028 | 0.428514 | − | 0.903535i | \(-0.359037\pi\) | ||||
0.428514 | + | 0.903535i | \(0.359037\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.67565 | − | 2.12214i | −0.152491 | − | 0.0880410i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.30545 | + | 5.72522i | 0.136898 | + | 0.237114i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.5450 | − | 7.24284i | 0.517786 | − | 0.298944i | −0.218242 | − | 0.975895i | \(-0.570032\pi\) |
0.736028 | + | 0.676951i | \(0.236699\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.73445 | + | 2.15609i | 0.153875 | + | 0.0888400i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.58651 | −0.188345 | −0.0941727 | − | 0.995556i | \(-0.530021\pi\) | ||||
−0.0941727 | + | 0.995556i | \(0.530021\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 6.54957i | − | 0.268506i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.31144 | + | 2.27148i | −0.0535839 | + | 0.0928101i | −0.891573 | − | 0.452877i | \(-0.850398\pi\) |
0.837989 | + | 0.545687i | \(0.183731\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.50924 | − | 6.07817i | −0.143145 | − | 0.247934i | 0.785535 | − | 0.618818i | \(-0.212388\pi\) |
−0.928679 | + | 0.370884i | \(0.879055\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.87977 | − | 5.70409i | 0.401670 | − | 0.231904i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.5892 | − | 32.1974i | 0.754512 | − | 1.30685i | −0.191105 | − | 0.981570i | \(-0.561207\pi\) |
0.945617 | − | 0.325283i | \(-0.105460\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 43.1664i | − | 1.74633i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 10.7096i | − | 0.432557i | −0.976332 | − | 0.216278i | \(-0.930608\pi\) | ||
0.976332 | − | 0.216278i | \(-0.0693919\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.6101 | − | 28.7695i | 0.668696 | − | 1.15822i | −0.309573 | − | 0.950876i | \(-0.600186\pi\) |
0.978269 | − | 0.207340i | \(-0.0664806\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.8106 | + | 13.1697i | −0.916836 | + | 0.529336i | −0.882624 | − | 0.470079i | \(-0.844225\pi\) |
−0.0342118 | + | 0.999415i | \(0.510892\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.94420 | − | 12.0277i | −0.278213 | − | 0.481880i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50000 | − | 9.52628i | 0.220000 | − | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 17.6698i | − | 0.704541i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.6327 | −0.861183 | −0.430592 | − | 0.902547i | \(-0.641695\pi\) | ||||
−0.430592 | + | 0.902547i | \(0.641695\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −24.2807 | − | 14.0185i | −0.963550 | − | 0.556306i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 33.1572 | − | 19.1433i | 1.31374 | − | 0.758485i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.88485 | + | 3.26466i | 0.0744471 | + | 0.128946i | 0.900846 | − | 0.434139i | \(-0.142947\pi\) |
−0.826399 | + | 0.563086i | \(0.809614\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.2469 | − | 16.8857i | −1.15338 | − | 0.665907i | −0.203675 | − | 0.979039i | \(-0.565289\pi\) |
−0.949710 | + | 0.313132i | \(0.898622\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15.7020 | −0.617311 | −0.308656 | − | 0.951174i | \(-0.599879\pi\) | ||||
−0.308656 | + | 0.951174i | \(0.599879\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 25.0369 | 0.982786 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.4009 | + | 15.8199i | 1.07228 | + | 0.619080i | 0.928803 | − | 0.370574i | \(-0.120839\pi\) |
0.143475 | + | 0.989654i | \(0.454172\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.68223 | − | 11.5740i | −0.261097 | − | 0.452232i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.4389 | + | 18.1512i | −1.22468 | + | 0.707072i | −0.965913 | − | 0.258866i | \(-0.916651\pi\) |
−0.258772 | + | 0.965939i | \(0.583318\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.6479 | − | 7.30229i | −0.491948 | − | 0.284026i | 0.233434 | − | 0.972373i | \(-0.425004\pi\) |
−0.725382 | + | 0.688346i | \(0.758337\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.43196 | −0.133086 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 59.2588i | − | 2.29451i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.12483 | + | 8.87646i | −0.197842 | + | 0.342672i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.79326 | + | 3.10601i | 0.0691249 | + | 0.119728i | 0.898516 | − | 0.438940i | \(-0.144646\pi\) |
−0.829391 | + | 0.558668i | \(0.811313\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.25292 | − | 0.723375i | 0.0481537 | − | 0.0278016i | −0.475730 | − | 0.879591i | \(-0.657816\pi\) |
0.523884 | + | 0.851790i | \(0.324483\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.16745 | + | 10.6823i | −0.236685 | + | 0.409951i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.9714i | 0.649391i | 0.945819 | + | 0.324696i | \(0.105262\pi\) | ||||
−0.945819 | + | 0.324696i | \(0.894738\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.9219i | 0.570136i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.0092 | − | 17.3365i | 0.381322 | − | 0.660468i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.44628 | + | 4.87646i | −0.321312 | + | 0.185509i | −0.651977 | − | 0.758239i | \(-0.726060\pi\) |
0.330665 | + | 0.943748i | \(0.392727\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.95018 | − | 8.57397i | −0.187771 | − | 0.325229i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.55880 | + | 2.69993i | −0.0590439 | + | 0.102267i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 33.3398i | − | 1.25923i | −0.776908 | − | 0.629614i | \(-0.783213\pi\) | ||
0.776908 | − | 0.629614i | \(-0.216787\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.25893 | −0.349207 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13.6744 | − | 7.89493i | −0.514280 | − | 0.296919i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −44.5369 | + | 25.7134i | −1.67262 | + | 0.965688i | −0.706457 | + | 0.707756i | \(0.749708\pi\) |
−0.966163 | + | 0.257931i | \(0.916959\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.65717 | − | 13.2626i | −0.286763 | − | 0.496689i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.0467 | + | 11.5740i | 0.749704 | + | 0.432842i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.1178 | 0.824854 | 0.412427 | − | 0.910991i | \(-0.364681\pi\) | ||||
0.412427 | + | 0.910991i | \(0.364681\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.0185 | −0.633801 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −14.4504 | − | 8.34296i | −0.536676 | − | 0.309850i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.2930 | + | 24.7562i | 0.530099 | + | 0.918158i | 0.999383 | + | 0.0351108i | \(0.0111784\pi\) |
−0.469285 | + | 0.883047i | \(0.655488\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.54973 | + | 4.35884i | −0.279237 | + | 0.161217i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.4167 | + | 22.7572i | 1.45589 | + | 0.840558i | 0.998805 | − | 0.0488654i | \(-0.0155605\pi\) |
0.457084 | + | 0.889424i | \(0.348894\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 28.8538 | 1.06284 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.9815i | 0.735032i | 0.930017 | + | 0.367516i | \(0.119792\pi\) | ||||
−0.930017 | + | 0.367516i | \(0.880208\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.8386 | − | 32.6294i | 0.691121 | − | 1.19706i | −0.280350 | − | 0.959898i | \(-0.590451\pi\) |
0.971471 | − | 0.237158i | \(-0.0762160\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.22522 | − | 2.12214i | −0.0448884 | − | 0.0777490i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.9009 | − | 8.02567i | 0.507926 | − | 0.293251i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.25820 | − | 10.8395i | 0.228365 | − | 0.395540i | −0.728959 | − | 0.684558i | \(-0.759995\pi\) |
0.957324 | + | 0.289018i | \(0.0933287\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 5.69751i | − | 0.207354i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.5872i | 0.457491i | 0.973486 | + | 0.228745i | \(0.0734623\pi\) | ||||
−0.973486 | + | 0.228745i | \(0.926538\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.94120 | + | 10.2905i | −0.215368 | + | 0.373029i | −0.953386 | − | 0.301752i | \(-0.902428\pi\) |
0.738018 | + | 0.674781i | \(0.235762\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.700187 | + | 0.404253i | −0.0253485 | + | 0.0146349i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −37.9071 | − | 65.6571i | −1.36875 | − | 2.37074i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.5369 | − | 39.0351i | 0.812703 | − | 1.40764i | −0.0982627 | − | 0.995161i | \(-0.531329\pi\) |
0.910966 | − | 0.412482i | \(-0.135338\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 34.0384i | − | 1.22428i | −0.790751 | − | 0.612138i | \(-0.790310\pi\) | ||
0.790751 | − | 0.612138i | \(-0.209690\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.31217 | −0.154898 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.41476 | + | 0.816810i | 0.0506889 | + | 0.0292653i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.6327 | − | 14.2217i | 0.881427 | − | 0.508892i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.78402 | + | 10.0182i | 0.206441 | + | 0.357565i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.67808 | + | 2.12354i | 0.131109 | + | 0.0756960i | 0.564120 | − | 0.825693i | \(-0.309215\pi\) |
−0.433011 | + | 0.901389i | \(0.642549\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.37228 | 0.226572 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31.0369 | 1.10215 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 37.2806 | + | 21.5240i | 1.32055 | + | 0.762419i | 0.983816 | − | 0.179182i | \(-0.0573451\pi\) |
0.336732 | + | 0.941601i | \(0.390678\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.9496 | + | 22.4293i | 0.458123 | + | 0.793493i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.2273 | + | 10.5236i | −0.643229 | + | 0.371368i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.5554 | + | 6.09417i | 0.372029 | + | 0.214791i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −25.2488 | −0.887699 | −0.443850 | − | 0.896101i | \(-0.646388\pi\) | ||||
−0.443850 | + | 0.896101i | \(0.646388\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.9378i | 1.29706i | 0.761188 | + | 0.648531i | \(0.224616\pi\) | ||||
−0.761188 | + | 0.648531i | \(0.775384\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.43627 | + | 11.1479i | −0.225453 | + | 0.390495i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.28402 | + | 3.95604i | 0.0799078 | + | 0.138404i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.7748 | + | 6.22082i | −0.376043 | + | 0.217108i | −0.676095 | − | 0.736814i | \(-0.736329\pi\) |
0.300052 | + | 0.953923i | \(0.402996\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.760749 | − | 1.31766i | 0.0265180 | − | 0.0459306i | −0.852462 | − | 0.522789i | \(-0.824891\pi\) |
0.878980 | + | 0.476859i | \(0.158225\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 10.0369i | − | 0.349019i | −0.984656 | − | 0.174509i | \(-0.944166\pi\) | ||
0.984656 | − | 0.174509i | \(-0.0558339\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 43.7824i | 1.52063i | 0.649556 | + | 0.760314i | \(0.274955\pi\) | ||||
−0.649556 | + | 0.760314i | \(0.725045\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.4857 | + | 19.8938i | −0.397955 | + | 0.689279i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.8506 | + | 8.57397i | −0.513925 | + | 0.296714i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.0626 | − | 36.4814i | −0.727161 | − | 1.25948i | −0.958078 | − | 0.286506i | \(-0.907506\pi\) |
0.230918 | − | 0.972973i | \(-0.425827\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.3025 | − | 35.1649i | 0.700086 | − | 1.21258i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 47.5775i | − | 1.63672i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.52540 | 0.224215 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 28.4770 | + | 16.4412i | 0.976178 | + | 0.563597i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.7748 | − | 13.1490i | 0.779794 | − | 0.450214i | −0.0565634 | − | 0.998399i | \(-0.518014\pi\) |
0.836357 | + | 0.548185i | \(0.184681\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.24369 | − | 16.0105i | −0.315758 | − | 0.546909i | 0.663840 | − | 0.747875i | \(-0.268926\pi\) |
−0.979598 | + | 0.200965i | \(0.935592\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.8954 | − | 23.0336i | −1.36121 | − | 0.785898i | −0.371429 | − | 0.928461i | \(-0.621132\pi\) |
−0.989786 | + | 0.142564i | \(0.954465\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 46.0812 | 1.56862 | 0.784311 | − | 0.620368i | \(-0.213017\pi\) | ||||
0.784311 | + | 0.620368i | \(0.213017\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.0000 | −0.714021 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.5277 | + | 9.54228i | 0.560664 | + | 0.323700i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −43.6860 | − | 75.6663i | −1.48024 | − | 2.56386i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.4026 | − | 6.00593i | 0.351671 | − | 0.203037i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.5396 | + | 16.4773i | 0.963713 | + | 0.556400i | 0.897314 | − | 0.441393i | \(-0.145516\pi\) |
0.0663989 | + | 0.997793i | \(0.478849\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.9815 | −0.740577 | −0.370288 | − | 0.928917i | \(-0.620741\pi\) | ||||
−0.370288 | + | 0.928917i | \(0.620741\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 10.0000i | − | 0.336527i | −0.985742 | − | 0.168263i | \(-0.946184\pi\) | ||
0.985742 | − | 0.168263i | \(-0.0538159\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.67672 | − | 2.90417i | 0.0562988 | − | 0.0975124i | −0.836502 | − | 0.547963i | \(-0.815403\pi\) |
0.892801 | + | 0.450451i | \(0.148737\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.01847 | − | 13.8884i | −0.268931 | − | 0.465802i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.7529 | − | 6.78555i | 0.393297 | − | 0.227070i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.19615 | + | 9.00000i | −0.173688 | + | 0.300837i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 17.9881i | − | 0.599938i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.0108i | 0.400137i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.00924 | + | 6.94420i | −0.133271 | + | 0.230833i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.87423 | − | 5.12354i | 0.294664 | − | 0.170124i | −0.345379 | − | 0.938463i | \(-0.612250\pi\) |
0.640043 | + | 0.768339i | \(0.278916\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.7036 | − | 22.0033i | −0.420890 | − | 0.729002i | 0.575137 | − | 0.818057i | \(-0.304949\pi\) |
−0.996027 | + | 0.0890549i | \(0.971615\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.50000 | + | 7.79423i | −0.148928 | + | 0.257951i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 7.64439i | − | 0.252440i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.1134 | 1.45517 | 0.727584 | − | 0.686019i | \(-0.240643\pi\) | ||||
0.727584 | + | 0.686019i | \(0.240643\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −74.5902 | − | 43.0646i | −2.45517 | − | 1.41749i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.01847 | − | 4.62947i | 0.263646 | − | 0.152216i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.8117 | − | 30.8508i | −0.584384 | − | 1.01218i | −0.994952 | − | 0.100353i | \(-0.968003\pi\) |
0.410568 | − | 0.911830i | \(-0.365330\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.4243 | + | 6.01847i | 0.341643 | + | 0.197247i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13.8884 | −0.454199 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.4135 | −0.503537 | −0.251768 | − | 0.967788i | \(-0.581012\pi\) | ||||
−0.251768 | + | 0.967788i | \(0.581012\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.55541 | − | 4.36212i | −0.246299 | − | 0.142201i | 0.371769 | − | 0.928325i | \(-0.378751\pi\) |
−0.618069 | + | 0.786124i | \(0.712085\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.90084 | − | 5.02440i | −0.0944643 | − | 0.163617i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.7691 | + | 7.94958i | −0.447435 | + | 0.258327i | −0.706746 | − | 0.707467i | \(-0.749838\pi\) |
0.259311 | + | 0.965794i | \(0.416504\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 55.1941 | + | 31.8663i | 1.79168 | + | 1.03443i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.6890 | −0.832149 | −0.416075 | − | 0.909330i | \(-0.636595\pi\) | ||||
−0.416075 | + | 0.909330i | \(0.636595\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 29.7529i | − | 0.962782i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.26761 | + | 7.39171i | −0.137808 | + | 0.238691i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.1756 | + | 22.8209i | 0.425021 | + | 0.736158i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.3798 | + | 10.0342i | −0.559475 | + | 0.323013i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.3585 | − | 26.6017i | 0.493896 | − | 0.855452i | −0.506080 | − | 0.862487i | \(-0.668906\pi\) |
0.999975 | + | 0.00703449i | \(0.00223917\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40.0924i | 1.28662i | 0.765604 | + | 0.643312i | \(0.222440\pi\) | ||||
−0.765604 | + | 0.643312i | \(0.777560\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 5.66294i | − | 0.181546i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24.4361 | − | 42.3246i | 0.781780 | − | 1.35408i | −0.149123 | − | 0.988819i | \(-0.547645\pi\) |
0.930904 | − | 0.365265i | \(-0.119022\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25.5048 | + | 14.7252i | −0.815138 | + | 0.470620i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.60077 | + | 9.70081i | 0.178637 | + | 0.309408i | 0.941414 | − | 0.337254i | \(-0.109498\pi\) |
−0.762777 | + | 0.646662i | \(0.776165\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.3025 | − | 26.5047i | 0.487578 | − | 0.844510i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 16.2230i | − | 0.515863i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.7020 | −0.498792 | −0.249396 | − | 0.968402i | \(-0.580232\pi\) | ||||
−0.249396 | + | 0.968402i | \(0.580232\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.7566 | + | 14.2933i | 0.784838 | + | 0.453127i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.0984 | − | 12.1811i | 0.668192 | − | 0.385781i | −0.127199 | − | 0.991877i | \(-0.540599\pi\) |
0.795391 | + | 0.606096i | \(0.207265\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1728.2.r.e.1441.3 | 12 | ||
3.2 | odd | 2 | 576.2.r.f.481.2 | yes | 12 | ||
4.3 | odd | 2 | inner | 1728.2.r.e.1441.4 | 12 | ||
8.3 | odd | 2 | 1728.2.r.f.1441.4 | 12 | |||
8.5 | even | 2 | 1728.2.r.f.1441.3 | 12 | |||
9.2 | odd | 6 | 576.2.r.e.97.5 | yes | 12 | ||
9.4 | even | 3 | 5184.2.d.r.2593.10 | 12 | |||
9.5 | odd | 6 | 5184.2.d.q.2593.4 | 12 | |||
9.7 | even | 3 | 1728.2.r.f.289.3 | 12 | |||
12.11 | even | 2 | 576.2.r.f.481.5 | yes | 12 | ||
24.5 | odd | 2 | 576.2.r.e.481.5 | yes | 12 | ||
24.11 | even | 2 | 576.2.r.e.481.2 | yes | 12 | ||
36.7 | odd | 6 | 1728.2.r.f.289.4 | 12 | |||
36.11 | even | 6 | 576.2.r.e.97.2 | ✓ | 12 | ||
36.23 | even | 6 | 5184.2.d.q.2593.3 | 12 | |||
36.31 | odd | 6 | 5184.2.d.r.2593.9 | 12 | |||
72.5 | odd | 6 | 5184.2.d.q.2593.10 | 12 | |||
72.11 | even | 6 | 576.2.r.f.97.5 | yes | 12 | ||
72.13 | even | 6 | 5184.2.d.r.2593.4 | 12 | |||
72.29 | odd | 6 | 576.2.r.f.97.2 | yes | 12 | ||
72.43 | odd | 6 | inner | 1728.2.r.e.289.4 | 12 | ||
72.59 | even | 6 | 5184.2.d.q.2593.9 | 12 | |||
72.61 | even | 6 | inner | 1728.2.r.e.289.3 | 12 | ||
72.67 | odd | 6 | 5184.2.d.r.2593.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
576.2.r.e.97.2 | ✓ | 12 | 36.11 | even | 6 | ||
576.2.r.e.97.5 | yes | 12 | 9.2 | odd | 6 | ||
576.2.r.e.481.2 | yes | 12 | 24.11 | even | 2 | ||
576.2.r.e.481.5 | yes | 12 | 24.5 | odd | 2 | ||
576.2.r.f.97.2 | yes | 12 | 72.29 | odd | 6 | ||
576.2.r.f.97.5 | yes | 12 | 72.11 | even | 6 | ||
576.2.r.f.481.2 | yes | 12 | 3.2 | odd | 2 | ||
576.2.r.f.481.5 | yes | 12 | 12.11 | even | 2 | ||
1728.2.r.e.289.3 | 12 | 72.61 | even | 6 | inner | ||
1728.2.r.e.289.4 | 12 | 72.43 | odd | 6 | inner | ||
1728.2.r.e.1441.3 | 12 | 1.1 | even | 1 | trivial | ||
1728.2.r.e.1441.4 | 12 | 4.3 | odd | 2 | inner | ||
1728.2.r.f.289.3 | 12 | 9.7 | even | 3 | |||
1728.2.r.f.289.4 | 12 | 36.7 | odd | 6 | |||
1728.2.r.f.1441.3 | 12 | 8.5 | even | 2 | |||
1728.2.r.f.1441.4 | 12 | 8.3 | odd | 2 | |||
5184.2.d.q.2593.3 | 12 | 36.23 | even | 6 | |||
5184.2.d.q.2593.4 | 12 | 9.5 | odd | 6 | |||
5184.2.d.q.2593.9 | 12 | 72.59 | even | 6 | |||
5184.2.d.q.2593.10 | 12 | 72.5 | odd | 6 | |||
5184.2.d.r.2593.3 | 12 | 72.67 | odd | 6 | |||
5184.2.d.r.2593.4 | 12 | 72.13 | even | 6 | |||
5184.2.d.r.2593.9 | 12 | 36.31 | odd | 6 | |||
5184.2.d.r.2593.10 | 12 | 9.4 | even | 3 |