Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,2,Mod(97,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, 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("576.97");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.r (of order \(6\), 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: | \(4.59938315643\) |
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: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 481.2 | ||
Root | \(-1.50511 + 0.403293i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 576.481 |
Dual form | 576.2.r.f.97.2 |
$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.10182 | + | 1.33641i | −0.636135 | + | 0.771578i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.50000 | + | 0.866025i | 0.670820 | + | 0.387298i | 0.796387 | − | 0.604787i | \(-0.206742\pi\) |
−0.125567 | + | 0.992085i | \(0.540075\pi\) | |||||||
\(6\) | 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 | ||||||||
\(9\) | −0.571993 | − | 2.94497i | −0.190664 | − | 0.981655i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.81937 | − | 1.05042i | 0.548561 | − | 0.316712i | −0.199980 | − | 0.979800i | \(-0.564088\pi\) |
0.748542 | + | 0.663088i | \(0.230754\pi\) | |||||||
\(12\) | 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 | ||||||||
\(15\) | −2.81009 | + | 1.05042i | −0.725563 | + | 0.271216i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.81681 | 0.925712 | 0.462856 | − | 0.886433i | \(-0.346825\pi\) | ||||
0.462856 | + | 0.886433i | \(0.346825\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000i | 0.458831i | 0.973329 | + | 0.229416i | \(0.0736815\pi\) | ||||
−0.973329 | + | 0.229416i | \(0.926318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.69243 | + | 0.283343i | 0.369317 | + | 0.0618305i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.55142 | + | 6.15125i | −0.740523 | + | 1.28262i | 0.211734 | + | 0.977327i | \(0.432089\pi\) |
−0.952257 | + | 0.305296i | \(0.901245\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | − | 1.73205i | −0.200000 | − | 0.346410i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.56592 | + | 2.48040i | 0.878712 | + | 0.477353i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.22522 | + | 4.17148i | −1.34169 | + | 0.774624i | −0.987055 | − | 0.160381i | \(-0.948728\pi\) |
−0.354634 | + | 0.935005i | \(0.615394\pi\) | |||||||
\(30\) | 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 | ||||||||
\(33\) | −0.600830 | + | 3.58880i | −0.104591 | + | 0.624729i | ||||
\(34\) | 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 | ||||||||
\(39\) | −10.3210 | + | 3.85799i | −1.65268 | + | 0.617773i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.408405 | + | 0.707378i | −0.0637822 | + | 0.110474i | −0.896153 | − | 0.443745i | \(-0.853650\pi\) |
0.832371 | + | 0.554219i | \(0.186983\pi\) | |||||||
\(42\) | 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 | ||||||||
\(45\) | 1.69243 | − | 4.91281i | 0.252292 | − | 0.732358i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.39278 | + | 5.87646i | 0.494887 | + | 0.857170i | 0.999983 | − | 0.00589362i | \(-0.00187601\pi\) |
−0.505095 | + | 0.863064i | \(0.668543\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00924 | − | 5.21215i | 0.429891 | − | 0.744593i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.20543 | + | 5.10083i | −0.588878 | + | 0.714259i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.14681i | 0.432247i | 0.976366 | + | 0.216124i | \(0.0693414\pi\) | ||||
−0.976366 | + | 0.216124i | \(0.930659\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.63875 | 0.490648 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.67282 | − | 2.20364i | −0.354024 | − | 0.291879i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.3210 | + | 5.95882i | 1.34368 | + | 0.775772i | 0.987345 | − | 0.158587i | \(-0.0506938\pi\) |
0.356332 | + | 0.934359i | \(0.384027\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | −2.24341 | + | 1.94958i | −0.282643 | + | 0.245625i | ||||
\(64\) | 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 | ||||||||
\(69\) | −4.30757 | − | 11.5237i | −0.518571 | − | 1.38729i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.5391 | 1.60680 | 0.803399 | − | 0.595442i | \(-0.203023\pi\) | ||||
0.803399 | + | 0.595442i | \(0.203023\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.0185 | 1.17257 | 0.586287 | − | 0.810104i | \(-0.300589\pi\) | ||||
0.586287 | + | 0.810104i | \(0.300589\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.41655 | + | 0.571993i | 0.394509 | + | 0.0660481i | ||||
\(76\) | 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 | ||||||||
\(81\) | −8.34565 | + | 3.36900i | −0.927294 | + | 0.374333i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.71007 | + | 2.14201i | −0.407233 | + | 0.235116i | −0.689600 | − | 0.724190i | \(-0.742214\pi\) |
0.282367 | + | 0.959306i | \(0.408880\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.72522 | + | 3.30545i | 0.620987 | + | 0.358527i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.38606 | − | 14.2521i | 0.255812 | − | 1.52798i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.0185 | −1.48595 | −0.742977 | − | 0.669316i | \(-0.766587\pi\) | ||||
−0.742977 | + | 0.669316i | \(0.766587\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 6.30249i | − | 0.660681i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.30757 | + | 3.49805i | 0.135589 | + | 0.362731i | ||||
\(94\) | 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 | ||||||||
\(99\) | −4.13411 | − | 4.75716i | −0.415493 | − | 0.478113i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.8025 | + | 7.96887i | −1.37340 | + | 0.792932i | −0.991354 | − | 0.131211i | \(-0.958113\pi\) |
−0.382045 | + | 0.924144i | \(0.624780\pi\) | |||||||
\(102\) | 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 | ||||||||
\(105\) | 2.29326 | + | 1.89070i | 0.223799 | + | 0.184513i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 16.2017i | − | 1.56627i | −0.621849 | − | 0.783137i | \(-0.713618\pi\) | ||
0.621849 | − | 0.783137i | \(-0.286382\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 0.816078i | − | 0.0781661i | −0.999236 | − | 0.0390830i | \(-0.987556\pi\) | ||
0.999236 | − | 0.0390830i | \(-0.0124437\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.18687 | − | 5.10083i | −0.587232 | − | 0.484149i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.21598 | − | 5.57024i | 0.302534 | − | 0.524004i | −0.674175 | − | 0.738571i | \(-0.735501\pi\) |
0.976709 | + | 0.214567i | \(0.0688341\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.6543 | + | 6.15125i | −0.993516 | + | 0.573607i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.21598 | − | 18.0439i | 0.574668 | − | 1.66816i | ||||
\(118\) | 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 | ||||||||
\(123\) | −0.495361 | − | 1.32520i | −0.0446652 | − | 0.119489i | ||||
\(124\) | 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 | ||||||||
\(129\) | −0.653222 | + | 3.90174i | −0.0575130 | + | 0.343529i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.68223 | − | 3.85799i | −0.583830 | − | 0.337074i | 0.178824 | − | 0.983881i | \(-0.442771\pi\) |
−0.762654 | + | 0.646807i | \(0.776104\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.71598 | − | 0.990721i | 0.148794 | − | 0.0859064i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.70079 | + | 7.67480i | 0.404580 | + | 0.660542i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.30757 | + | 7.46094i | 0.368021 | + | 0.637431i | 0.989256 | − | 0.146193i | \(-0.0467021\pi\) |
−0.621235 | + | 0.783624i | \(0.713369\pi\) | |||||||
\(138\) | 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 | ||||||||
\(141\) | −11.5916 | − | 1.94065i | −0.976188 | − | 0.163432i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.3645 | 1.11759 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.4504 | −1.20004 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.64995 | + | 9.76442i | 0.301043 | + | 0.805356i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.22522 | − | 0.707378i | −0.100374 | − | 0.0579507i | 0.448973 | − | 0.893545i | \(-0.351790\pi\) |
−0.549346 | + | 0.835595i | \(0.685123\pi\) | |||||||
\(150\) | 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 | ||||||||
\(153\) | −2.18319 | − | 11.2404i | −0.176500 | − | 0.908731i | ||||
\(154\) | 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 | ||||||||
\(159\) | −4.20543 | − | 3.46721i | −0.333512 | − | 0.274968i | ||||
\(160\) | 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 | ||||||||
\(165\) | −4.00924 | + | 4.86286i | −0.312119 | + | 0.378573i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.95018 | + | 8.57397i | −0.383057 | + | 0.663474i | −0.991498 | − | 0.130126i | \(-0.958462\pi\) |
0.608441 | + | 0.793599i | \(0.291795\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.7345 | + | 23.7888i | 1.05650 | + | 1.82991i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.88993 | − | 1.14399i | 0.450414 | − | 0.0874828i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.5000 | + | 6.06218i | −0.798300 | + | 0.460899i | −0.842876 | − | 0.538107i | \(-0.819140\pi\) |
0.0445762 | + | 0.999006i | \(0.485806\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.990721 | + | 1.71598i | −0.0748915 | + | 0.129716i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −19.3353 | + | 7.22754i | −1.45333 | + | 0.543255i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.00000i | 0.448461i | 0.974536 | + | 0.224231i | \(0.0719869\pi\) | ||||
−0.974536 | + | 0.224231i | \(0.928013\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 4.62947i | − | 0.344106i | −0.985088 | − | 0.172053i | \(-0.944960\pi\) | ||
0.985088 | − | 0.172053i | \(-0.0550400\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.39534 | + | 8.33444i | −0.103146 | + | 0.616099i | ||||
\(184\) | 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 | ||||||||
\(189\) | −0.133620 | − | 5.14620i | −0.00971946 | − | 0.374331i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.58893 | − | 14.8765i | −0.621473 | − | 1.07642i | −0.989212 | − | 0.146494i | \(-0.953201\pi\) |
0.367739 | − | 0.929929i | \(-0.380132\pi\) | |||||||
\(192\) | 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 | ||||||||
\(195\) | −18.8226 | − | 3.15125i | −1.34791 | − | 0.225665i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 17.6698i | − | 1.25892i | −0.777033 | − | 0.629460i | \(-0.783276\pi\) | ||
0.777033 | − | 0.629460i | \(-0.216724\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.5044 | −1.16997 | −0.584984 | − | 0.811045i | \(-0.698899\pi\) | ||||
−0.584984 | + | 0.811045i | \(0.698899\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 22.2829 | − | 8.32936i | 1.57171 | − | 0.587508i | ||||
\(202\) | 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 | ||||||||
\(207\) | 20.1466 | + | 6.94035i | 1.40029 | + | 0.482388i | ||||
\(208\) | 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 | ||||||||
\(213\) | −14.9176 | + | 18.0938i | −1.02214 | + | 1.23977i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.95604 | 0.269800 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.13608 | −0.145007 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.0385 | + | 13.3888i | −0.745915 | + | 0.904731i | ||||
\(220\) | 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 | ||||||||
\(225\) | −4.52884 | + | 3.93569i | −0.301922 | + | 0.262379i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.37678 | − | 1.94958i | 0.224125 | − | 0.129398i | −0.383734 | − | 0.923444i | \(-0.625362\pi\) |
0.607859 | + | 0.794045i | \(0.292029\pi\) | |||||||
\(228\) | 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 | ||||||||
\(231\) | 3.37678 | − | 1.26224i | 0.222176 | − | 0.0830495i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.26724 | −0.607117 | −0.303559 | − | 0.952813i | \(-0.598175\pi\) | ||||
−0.303559 | + | 0.952813i | \(0.598175\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.7529i | 0.766676i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.5185 | + | 2.59808i | 1.00803 | + | 0.168763i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.4796 | + | 18.1512i | −0.677871 | + | 1.17411i | 0.297750 | + | 0.954644i | \(0.403764\pi\) |
−0.975621 | + | 0.219463i | \(0.929570\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | 4.69301 | − | 14.8652i | 0.301057 | − | 0.953606i | ||||
\(244\) | 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 | ||||||||
\(249\) | 1.22522 | − | 7.31829i | 0.0776449 | − | 0.463778i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 0.164719i | − | 0.0103969i | −0.999986 | − | 0.00519847i | \(-0.998345\pi\) | ||
0.999986 | − | 0.00519847i | \(-0.00165473\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.9219i | 0.938130i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.7256 | + | 4.00924i | −0.671663 | + | 0.251068i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.4176 | − | 23.2400i | 0.836969 | − | 1.44967i | −0.0554474 | − | 0.998462i | \(-0.517659\pi\) |
0.892417 | − | 0.451212i | \(-0.149008\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.97204 | − | 2.29326i | 0.246810 | − | 0.142496i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16.4176 | + | 18.8920i | 1.01623 | + | 1.16938i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.98769 | − | 17.2992i | −0.615867 | − | 1.06671i | −0.990232 | − | 0.139432i | \(-0.955472\pi\) |
0.374364 | − | 0.927282i | \(-0.377861\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.72522 | + | 4.72021i | −0.167409 | + | 0.289960i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.4458 | − | 18.7345i | 0.945268 | − | 1.14653i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.666581i | 0.0406422i | 0.999794 | + | 0.0203211i | \(0.00646884\pi\) | ||||
−0.999794 | + | 0.0203211i | \(0.993531\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.0352 | −1.03482 | −0.517408 | − | 0.855739i | \(-0.673103\pi\) | ||||
−0.517408 | + | 0.855739i | \(0.673103\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.42272 | + | 6.94420i | 0.509766 | + | 0.420282i | ||||
\(274\) | 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 | ||||||||
\(279\) | −6.11555 | − | 2.10676i | −0.366128 | − | 0.126128i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.5277 | − | 23.4307i | −0.806995 | − | 1.39776i | −0.914936 | − | 0.403600i | \(-0.867759\pi\) |
0.107940 | − | 0.994157i | \(-0.465574\pi\) | |||||||
\(282\) | 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 | ||||||||
\(285\) | −2.10083 | − | 5.62019i | −0.124442 | − | 0.332911i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.809231 | 0.0477674 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.43196 | −0.143056 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 21.2688 | + | 3.56078i | 1.24680 | + | 0.208737i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.8025 | + | 13.1650i | 1.33214 | + | 0.769109i | 0.985627 | − | 0.168938i | \(-0.0540337\pi\) |
0.346509 | + | 0.938047i | \(0.387367\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.3210 | + | 17.8765i | 0.600911 | + | 1.04081i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 10.9126 | − | 0.283343i | 0.633211 | − | 0.0164412i | ||||
\(298\) | 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 | ||||||||
\(303\) | 4.55814 | − | 27.2261i | 0.261858 | − | 1.56410i | ||||
\(304\) | 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 | ||||||||
\(309\) | 10.4176 | + | 27.8695i | 0.592639 | + | 1.58544i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.96618 | − | 8.60168i | 0.281606 | − | 0.487756i | −0.690174 | − | 0.723643i | \(-0.742466\pi\) |
0.971781 | + | 0.235887i | \(0.0757995\pi\) | |||||||
\(312\) | 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 | ||||||||
\(315\) | −5.05350 | + | 0.981529i | −0.284733 | + | 0.0553029i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.52771 | − | 4.34612i | 0.422798 | − | 0.244103i | −0.273476 | − | 0.961879i | \(-0.588173\pi\) |
0.696274 | + | 0.717776i | \(0.254840\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.76357 | + | 15.1790i | −0.490666 | + | 0.849858i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 21.6521 | + | 17.8513i | 1.20850 | + | 0.996362i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.63362i | 0.424746i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 12.7230i | − | 0.705747i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.09062 | + | 0.899170i | 0.0603112 | + | 0.0497242i | ||||
\(328\) | 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 | ||||||||
\(333\) | 13.6336 | − | 2.64802i | 0.747118 | − | 0.145111i | ||||
\(334\) | 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 | ||||||||
\(339\) | 3.90071 | + | 10.4353i | 0.211857 | + | 0.566766i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 4.52957i | − | 0.245290i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.8977 | −0.696409 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.51847 | − | 21.0160i | 0.189428 | − | 1.13147i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.2373 | + | 11.6840i | 1.08640 | + | 0.627232i | 0.932615 | − | 0.360873i | \(-0.117521\pi\) |
0.153782 | + | 0.988105i | \(0.450854\pi\) | |||||||
\(348\) | 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 | ||||||||
\(351\) | 17.2652 | + | 28.1882i | 0.921547 | + | 1.50457i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.6924 | + | 18.5198i | 0.569100 | + | 0.985711i | 0.996655 | + | 0.0817214i | \(0.0260418\pi\) |
−0.427555 | + | 0.903989i | \(0.640625\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.3087 | + | 11.7252i | 1.07787 | + | 0.622310i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.45967 | + | 1.08147i | 0.341882 | + | 0.0572373i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.9634 | −1.26474 | −0.632370 | − | 0.774666i | \(-0.717918\pi\) | ||||
−0.632370 | + | 0.774666i | \(0.717918\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | 0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.99444 | − | 10.6860i | −0.209654 | − | 0.560870i | ||||
\(364\) | 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 | ||||||||
\(369\) | 2.31681 | + | 0.798123i | 0.120608 | + | 0.0415486i | ||||
\(370\) | 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 | ||||||||
\(375\) | 16.2031 | + | 13.3588i | 0.836726 | + | 0.689847i | ||||
\(376\) | 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 | ||||||||
\(381\) | −17.8353 | + | 21.6327i | −0.913729 | + | 1.10828i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.66073 | − | 2.87646i | 0.0848591 | − | 0.146980i | −0.820472 | − | 0.571687i | \(-0.806289\pi\) |
0.905331 | + | 0.424706i | \(0.139623\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.80249 | − | 3.12201i | −0.0918635 | − | 0.159112i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.49459 | − | 5.17198i | −0.228473 | − | 0.262906i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.19751 | + | 0.691382i | −0.0607161 | + | 0.0350545i | −0.530051 | − | 0.847966i | \(-0.677827\pi\) |
0.469335 | + | 0.883020i | \(0.344494\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.5551 | + | 23.4781i | −0.685511 | + | 1.18734i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.5185 | − | 4.67941i | 0.631473 | − | 0.236045i | ||||
\(394\) | 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 | ||||||||
\(399\) | −0.566686 | + | 3.38485i | −0.0283698 | + | 0.169454i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.326046 | − | 0.564728i | 0.0162819 | − | 0.0282012i | −0.857770 | − | 0.514034i | \(-0.828150\pi\) |
0.874052 | + | 0.485833i | \(0.161484\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.8784 | − | 6.85799i | 0.591705 | − | 0.341621i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −15.4361 | − | 2.17404i | −0.767027 | − | 0.108029i | ||||
\(406\) | 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 | ||||||||
\(411\) | −14.7171 | − | 2.46390i | −0.725939 | − | 0.121535i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 11.8071i | − | 0.580988i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.42014 | −0.364240 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.27365 | + | 3.46650i | −0.454133 | + | 0.169755i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.4024 | + | 6.58321i | 0.557046 | + | 0.321611i | 0.751959 | − | 0.659210i | \(-0.229109\pi\) |
−0.194913 | + | 0.980821i | \(0.562442\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | 15.3653 | − | 13.3529i | 0.747088 | − | 0.649241i | ||||
\(424\) | 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 | ||||||||
\(429\) | −14.7252 | + | 17.8604i | −0.710940 | + | 0.862310i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.81339 | 0.183684 | 0.0918422 | − | 0.995774i | \(-0.470724\pi\) | ||||
0.0918422 | + | 0.995774i | \(0.470724\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.0185 | −0.481457 | −0.240728 | − | 0.970592i | \(-0.577386\pi\) | ||||
−0.240728 | + | 0.970592i | \(0.577386\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 15.9217 | − | 19.3117i | 0.763389 | − | 0.925926i | ||||
\(436\) | 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 | ||||||||
\(441\) | −17.0709 | − | 5.88078i | −0.812898 | − | 0.280037i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.3799 | + | 12.3437i | −1.01579 | + | 0.586466i | −0.912881 | − | 0.408225i | \(-0.866148\pi\) |
−0.102907 | + | 0.994691i | \(0.532814\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −21.0277 | − | 12.1404i | −0.996809 | − | 0.575508i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.29531 | − | 0.857990i | 0.108565 | − | 0.0405815i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.6521 | 1.02183 | 0.510913 | − | 0.859633i | \(-0.329308\pi\) | ||||
0.510913 | + | 0.859633i | \(0.329308\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.71598i | 0.0808023i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.61930 | − | 0.940774i | −0.264018 | − | 0.0442014i | ||||
\(454\) | 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 | ||||||||
\(459\) | 17.4272 | + | 9.46721i | 0.813434 | + | 0.441892i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.6756 | − | 12.5144i | 1.00954 | − | 0.582856i | 0.0984799 | − | 0.995139i | \(-0.468602\pi\) |
0.911056 | + | 0.412283i | \(0.135269\pi\) | |||||||
\(462\) | 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 | ||||||||
\(465\) | −1.06804 | + | 6.37947i | −0.0495292 | + | 0.295841i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 2.40332i | − | 0.111212i | −0.998453 | − | 0.0556062i | \(-0.982291\pi\) | ||
0.998453 | − | 0.0556062i | \(-0.0177091\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.6070i | 0.628314i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.8358 | − | 4.05042i | 0.499285 | − | 0.186633i | ||||
\(472\) | 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 | ||||||||
\(477\) | 9.26724 | − | 1.79995i | 0.424318 | − | 0.0824142i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.6543 | − | 18.4537i | −0.486806 | − | 0.843173i | 0.513079 | − | 0.858341i | \(-0.328505\pi\) |
−0.999885 | + | 0.0151687i | \(0.995171\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.7252 | + | 25.5048i | −0.671412 | + | 1.16292i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.75343 | + | 9.40425i | −0.352793 | + | 0.427908i | ||||
\(484\) | 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 | ||||||||
\(489\) | 9.93216 | + | 8.18867i | 0.449148 | + | 0.370304i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.6776 | − | 17.7117i | −1.38446 | − | 0.799320i | −0.391778 | − | 0.920060i | \(-0.628140\pi\) |
−0.992684 | + | 0.120740i | \(0.961473\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27.5773 | + | 15.9217i | −1.24202 | + | 0.717079i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.08134 | − | 10.7160i | −0.0935492 | − | 0.481647i | ||||
\(496\) | 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 | ||||||||
\(501\) | −6.00415 | − | 16.0624i | −0.268246 | − | 0.717617i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.24550 | 0.323061 | 0.161530 | − | 0.986868i | \(-0.448357\pi\) | ||||
0.161530 | + | 0.986868i | \(0.448357\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27.6050 | −1.22841 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −46.9245 | − | 7.85601i | −2.08399 | − | 0.348898i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.22522 | − | 4.17148i | −0.320252 | − | 0.184898i | 0.331253 | − | 0.943542i | \(-0.392529\pi\) |
−0.651505 | + | 0.758644i | \(0.725862\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.96276 | − | 8.59575i | −0.219539 | − | 0.380253i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.96080 | + | 9.13184i | −0.219025 | + | 0.403181i | ||||
\(514\) | 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 | ||||||||
\(519\) | 3.46752 | − | 20.7117i | 0.152207 | − | 0.909145i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.9714 | 0.743529 | 0.371764 | − | 0.928327i | \(-0.378753\pi\) | ||||
0.371764 | + | 0.928327i | \(0.378753\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.0554i | 1.75150i | 0.482764 | + | 0.875750i | \(0.339633\pi\) | ||||
−0.482764 | + | 0.875750i | \(0.660367\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.20166 | − | 3.21471i | −0.0524448 | − | 0.140301i | ||||
\(526\) | 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 | ||||||||
\(531\) | 11.6450 | − | 33.8033i | 0.505350 | − | 1.46694i | ||||
\(532\) | 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 | ||||||||
\(537\) | −8.01847 | − | 6.61091i | −0.346023 | − | 0.285282i | ||||
\(538\) | 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 | ||||||||
\(543\) | 6.18687 | + | 5.10083i | 0.265504 | + | 0.218898i | ||||
\(544\) | 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 | ||||||||
\(549\) | −9.60083 | − | 11.0478i | −0.409753 | − | 0.471508i | ||||
\(550\) | 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 | ||||||||
\(555\) | −4.86286 | − | 13.0092i | −0.206417 | − | 0.552211i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 18.3364i | − | 0.776937i | −0.921462 | − | 0.388469i | \(-0.873004\pi\) | ||
0.921462 | − | 0.388469i | \(-0.126996\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.5298 | 0.614546 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.29326 | + | 13.6978i | −0.0968213 | + | 0.578320i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −35.8258 | − | 20.6840i | −1.50988 | − | 0.871728i | −0.999934 | − | 0.0115205i | \(-0.996333\pi\) |
−0.509944 | − | 0.860208i | \(-0.670334\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.64794 | − | 5.57024i | 0.405892 | − | 0.234342i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.02467 | + | 5.49161i | 0.295009 | + | 0.230626i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.683190 | + | 1.18332i | 0.0286408 | + | 0.0496073i | 0.879991 | − | 0.474991i | \(-0.157549\pi\) |
−0.851350 | + | 0.524599i | \(0.824215\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | 29.3445 | + | 4.91281i | 1.22588 | + | 0.205236i | ||||
\(574\) | 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 | ||||||||
\(579\) | 7.02673 | + | 18.7981i | 0.292021 | + | 0.781220i | ||||
\(580\) | 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 | ||||||||
\(585\) | 24.9504 | − | 21.6826i | 1.03157 | − | 0.896466i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.5450 | + | 7.24284i | −0.517786 | + | 0.298944i | −0.736028 | − | 0.676951i | \(-0.763301\pi\) |
0.218242 | + | 0.975895i | \(0.429968\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.73445 | + | 2.15609i | 0.153875 | + | 0.0888400i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 23.6141 | + | 19.4689i | 0.971355 | + | 0.800844i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.58651 | 0.188345 | 0.0941727 | − | 0.995556i | \(-0.469979\pi\) | ||||
0.0941727 | + | 0.995556i | \(0.469979\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 6.54957i | − | 0.268506i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.1849 | − | 22.0567i | 0.744258 | − | 0.902721i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.31144 | − | 2.27148i | 0.0535839 | − | 0.0928101i | −0.837989 | − | 0.545687i | \(-0.816269\pi\) |
0.891573 | + | 0.452877i | \(0.149602\pi\) | |||||||
\(600\) | 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 | ||||||||
\(603\) | −13.4202 | + | 38.9566i | −0.546514 | + | 1.58643i | ||||
\(604\) | 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 | ||||||||
\(609\) | −13.4101 | + | 5.01270i | −0.543405 | + | 0.203125i | ||||
\(610\) | 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 | ||||||||
\(615\) | 0.404616 | − | 2.41679i | 0.0163157 | − | 0.0974546i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.6101 | + | 28.7695i | −0.668696 | + | 1.15822i | 0.309573 | + | 0.950876i | \(0.399814\pi\) |
−0.978269 | + | 0.207340i | \(0.933519\pi\) | |||||||
\(618\) | 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 | ||||||||
\(621\) | −31.4731 | + | 19.2771i | −1.26297 | + | 0.773565i | ||||
\(622\) | 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 | ||||||||
\(627\) | −7.17760 | − | 1.20166i | −0.286646 | − | 0.0479897i | ||||
\(628\) | 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 | ||||||||
\(633\) | −19.0381 | + | 7.11645i | −0.756695 | + | 0.282853i | ||||
\(634\) | 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 | ||||||||
\(639\) | −7.74428 | − | 39.8722i | −0.306359 | − | 1.57732i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.88485 | − | 3.26466i | −0.0744471 | − | 0.128946i | 0.826399 | − | 0.563086i | \(-0.190386\pi\) |
−0.900846 | + | 0.434139i | \(0.857053\pi\) | |||||||
\(642\) | 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 | ||||||||
\(645\) | −4.35884 | + | 5.28690i | −0.171629 | + | 0.208171i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.7020 | 0.617311 | 0.308656 | − | 0.951174i | \(-0.400121\pi\) | ||||
0.308656 | + | 0.951174i | \(0.400121\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 25.0369 | 0.982786 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.35357 | − | 2.85468i | 0.0922438 | − | 0.111884i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −27.4009 | − | 15.8199i | −1.07228 | − | 0.619080i | −0.143475 | − | 0.989654i | \(-0.545828\pi\) |
−0.928803 | + | 0.370574i | \(0.879161\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.68223 | − | 11.5740i | −0.261097 | − | 0.452232i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.73050 | − | 29.5041i | −0.223568 | − | 1.15106i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 31.4389 | − | 18.1512i | 1.22468 | − | 0.707072i | 0.258772 | − | 0.965939i | \(-0.416682\pi\) |
0.965913 | + | 0.258866i | \(0.0833489\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | −39.3932 | + | 14.7252i | −1.52991 | + | 0.571880i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.43196 | 0.133086 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 59.2588i | − | 2.29451i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.28910 | − | 0.383238i | −0.0885019 | − | 0.0148168i | ||||
\(670\) | 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 | ||||||||
\(675\) | −0.269744 | − | 10.3888i | −0.0103824 | − | 0.399865i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.25292 | + | 0.723375i | −0.0481537 | + | 0.0278016i | −0.523884 | − | 0.851790i | \(-0.675517\pi\) |
0.475730 | + | 0.879591i | \(0.342184\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.16745 | + | 10.6823i | −0.236685 | + | 0.409951i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.11515 | + | 6.66086i | −0.0427326 | + | 0.255245i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 16.9714i | − | 0.649391i | −0.945819 | − | 0.324696i | \(-0.894738\pi\) | ||
0.945819 | − | 0.324696i | \(-0.105262\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.9219i | 0.570136i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.61933 | − | 1.35291i | 0.138086 | − | 0.0516166i | ||||
\(688\) | 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 | ||||||||
\(693\) | −2.03372 | + | 5.90353i | −0.0772547 | + | 0.224257i | ||||
\(694\) | 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 | ||||||||
\(699\) | 10.2108 | − | 12.3849i | 0.386208 | − | 0.468438i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.3398i | 1.25923i | 0.776908 | + | 0.629614i | \(0.216787\pi\) | ||||
−0.776908 | + | 0.629614i | \(0.783213\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.25893 | −0.349207 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −15.7067 | − | 12.9496i | −0.591550 | − | 0.487710i | ||||
\(706\) | 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 | ||||||||
\(711\) | −20.5706 | + | 17.8765i | −0.771459 | + | 0.670420i | ||||
\(712\) | 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 | ||||||||
\(717\) | −12.7109 | − | 34.0045i | −0.474697 | − | 1.26992i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.1178 | −0.824854 | −0.412427 | − | 0.910991i | \(-0.635319\pi\) | ||||
−0.412427 | + | 0.910991i | \(0.635319\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.0185 | −0.633801 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 25.6872 | + | 4.30051i | 0.955319 | + | 0.159938i | ||||
\(724\) | 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 | ||||||||
\(729\) | 14.6952 | + | 22.6506i | 0.544268 | + | 0.838911i | ||||
\(730\) | 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 | ||||||||
\(735\) | −2.98131 | + | 17.8076i | −0.109967 | + | 0.656842i | ||||
\(736\) | 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 | ||||||||
\(741\) | −7.71598 | − | 20.6420i | −0.283454 | − | 0.758301i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.8386 | + | 32.6294i | −0.691121 | + | 1.19706i | 0.280350 | + | 0.959898i | \(0.409549\pi\) |
−0.971471 | + | 0.237158i | \(0.923784\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.22522 | − | 2.12214i | −0.0448884 | − | 0.0777490i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.43028 | + | 9.70081i | 0.308448 | + | 0.354934i | ||||
\(748\) | 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 | ||||||||
\(753\) | 0.220132 | + | 0.181490i | 0.00802205 | + | 0.00661386i | ||||
\(754\) | 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 | ||||||||
\(759\) | −19.9418 | − | 16.4412i | −0.723840 | − | 0.596778i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.94120 | − | 10.2905i | 0.215368 | − | 0.373029i | −0.738018 | − | 0.674781i | \(-0.764238\pi\) |
0.953386 | + | 0.301752i | \(0.0975715\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.700187 | + | 0.404253i | −0.0253485 | + | 0.0146349i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.45967 | − | 18.7513i | 0.233550 | − | 0.677953i | ||||
\(766\) | 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 | ||||||||
\(771\) | 16.2745 | + | 43.5378i | 0.586110 | + | 1.56798i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 34.0384i | 1.22428i | 0.790751 | + | 0.612138i | \(0.209690\pi\) | ||||
−0.790751 | + | 0.612138i | \(0.790310\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.31217 | −0.154898 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.31173 | + | 7.83503i | −0.0470579 | + | 0.281080i | ||||
\(778\) | 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 | ||||||||
\(783\) | −43.3367 | + | 1.12523i | −1.54873 | + | 0.0402125i | ||||
\(784\) | 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 | ||||||||
\(789\) | 34.1235 | + | 5.71289i | 1.21483 | + | 0.203384i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.37228 | −0.226572 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31.0369 | 1.10215 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.30545 | − | 8.84283i | −0.117232 | − | 0.313623i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −37.2806 | − | 21.5240i | −1.32055 | − | 0.762419i | −0.336732 | − | 0.941601i | \(-0.609322\pi\) |
−0.983816 | + | 0.179182i | \(0.942655\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.9496 | + | 22.4293i | 0.458123 | + | 0.793493i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.01847 | + | 41.2839i | 0.283319 | + | 1.45870i | ||||
\(802\) | 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 | ||||||||
\(807\) | −0.890827 | − | 0.734451i | −0.0313586 | − | 0.0258539i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.2488 | 0.887699 | 0.443850 | − | 0.896101i | \(-0.353612\pi\) | ||||
0.443850 | + | 0.896101i | \(0.353612\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.9378i | 1.29706i | 0.761188 | + | 0.648531i | \(0.224616\pi\) | ||||
−0.761188 | + | 0.648531i | \(0.775384\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.7697 | − | 22.7661i | 0.658282 | − | 0.798440i | ||||
\(814\) | 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 | ||||||||
\(819\) | −18.5606 | + | 3.60498i | −0.648561 | + | 0.125968i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.7748 | − | 6.22082i | 0.376043 | − | 0.217108i | −0.300052 | − | 0.953923i | \(-0.597004\pi\) |
0.676095 | + | 0.736814i | \(0.263671\pi\) | |||||||
\(822\) | 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 | ||||||||
\(825\) | 6.81681 | − | 2.54813i | 0.237331 | − | 0.0887145i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.0369i | 0.349019i | 0.984656 | + | 0.174509i | \(0.0558339\pi\) | ||||
−0.984656 | + | 0.174509i | \(0.944166\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 43.7824i | 1.52063i | 0.649556 | + | 0.760314i | \(0.274955\pi\) | ||||
−0.649556 | + | 0.760314i | \(0.725045\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.06205 | − | 6.34367i | 0.0368420 | − | 0.220060i | ||||
\(832\) | 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 | ||||||||
\(837\) | 9.55372 | − | 5.85163i | 0.330225 | − | 0.202262i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.0626 | + | 36.4814i | 0.727161 | + | 1.25948i | 0.958078 | + | 0.286506i | \(0.0924938\pi\) |
−0.230918 | + | 0.972973i | \(0.574173\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.3025 | − | 35.1649i | 0.700086 | − | 1.21258i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 46.2181 | + | 7.73776i | 1.59184 | + | 0.266503i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 47.5775i | 1.63672i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.52540 | 0.224215 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.86243 | − | 0.696176i | 0.0639183 | − | 0.0238927i | ||||
\(850\) | 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 | ||||||||
\(855\) | 9.82562 | + | 3.38485i | 0.336029 | + | 0.115759i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.24369 | + | 16.0105i | 0.315758 | + | 0.546909i | 0.979598 | − | 0.200965i | \(-0.0644078\pi\) |
−0.663840 | + | 0.747875i | \(0.731074\pi\) | |||||||
\(858\) | 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 | ||||||||
\(861\) | −0.891626 | + | 1.08147i | −0.0303865 | + | 0.0368563i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −46.0812 | −1.56862 | −0.784311 | − | 0.620368i | \(-0.786983\pi\) | ||||
−0.784311 | + | 0.620368i | \(0.786983\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.0000 | −0.714021 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.67958 | − | 3.25010i | 0.0910032 | − | 0.110379i | ||||
\(868\) | 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 | ||||||||
\(873\) | −28.1930 | + | 24.5005i | −0.954188 | + | 0.829216i | ||||
\(874\) | 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 | ||||||||
\(879\) | −42.7181 | + | 15.9681i | −1.44085 | + | 0.538589i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.9815 | 0.740577 | 0.370288 | − | 0.928917i | \(-0.379259\pi\) | ||||
0.370288 | + | 0.928917i | \(0.379259\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 10.0000i | − | 0.336527i | −0.985742 | − | 0.168263i | \(-0.946184\pi\) | ||
0.985742 | − | 0.168263i | \(-0.0538159\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −35.2622 | − | 5.90353i | −1.18532 | − | 0.198445i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.67672 | + | 2.90417i | −0.0562988 | + | 0.0975124i | −0.892801 | − | 0.450451i | \(-0.851263\pi\) |
0.836502 | + | 0.547963i | \(0.184597\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.01847 | − | 13.8884i | −0.268931 | − | 0.465802i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.6450 | + | 14.8959i | −0.390122 | + | 0.499030i | ||||
\(892\) | 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 | ||||||||
\(897\) | 12.9227 | − | 77.1882i | 0.431477 | − | 2.57724i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.9881i | 0.599938i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.0108i | 0.400137i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.67123 | − | 1.37231i | 0.122171 | − | 0.0456676i | ||||
\(904\) | 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 | ||||||||
\(909\) | 31.3630 | + | 36.0897i | 1.04024 | + | 1.19702i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.7036 | + | 22.0033i | 0.420890 | + | 0.729002i | 0.996027 | − | 0.0890549i | \(-0.0283847\pi\) |
−0.575137 | + | 0.818057i | \(0.695051\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.50000 | + | 7.79423i | −0.148928 | + | 0.257951i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.31084 | + | 11.2933i | −0.307807 | + | 0.373344i | ||||
\(916\) | 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 | ||||||||
\(921\) | −9.93216 | − | 8.18867i | −0.327276 | − | 0.269826i | ||||
\(922\) | 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 | ||||||||
\(927\) | −48.7235 | − | 16.7849i | −1.60029 | − | 0.551287i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.8117 | + | 30.8508i | 0.584384 | + | 1.01218i | 0.994952 | + | 0.100353i | \(0.0319971\pi\) |
−0.410568 | + | 0.911830i | \(0.634670\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.4243 | + | 6.01847i | 0.341643 | + | 0.197247i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.02355 | + | 16.1143i | 0.197202 | + | 0.527560i | ||||
\(934\) | 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 | ||||||||
\(939\) | −15.4376 | − | 2.58454i | −0.503787 | − | 0.0843431i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.55541 | + | 4.36212i | 0.246299 | + | 0.142201i | 0.618069 | − | 0.786124i | \(-0.287915\pi\) |
−0.371769 | + | 0.928325i | \(0.621249\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.90084 | − | 5.02440i | −0.0944643 | − | 0.163617i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.25631 | − | 7.83503i | 0.138458 | − | 0.254873i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.7691 | − | 7.94958i | 0.447435 | − | 0.258327i | −0.259311 | − | 0.965794i | \(-0.583496\pi\) |
0.706746 | + | 0.707467i | \(0.250162\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 55.1941 | + | 31.8663i | 1.79168 | + | 1.03443i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.48595 | + | 14.8488i | −0.0806126 | + | 0.481504i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.6890 | 0.832149 | 0.416075 | − | 0.909330i | \(-0.363405\pi\) | ||||
0.416075 | + | 0.909330i | \(0.363405\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 29.7529i | − | 0.962782i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.6295 | − | 28.4362i | −0.343602 | − | 0.919211i | ||||
\(958\) | 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 | ||||||||
\(963\) | −47.7133 | + | 9.26724i | −1.53754 | + | 0.298633i | ||||
\(964\) | 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 | ||||||||
\(969\) | −10.2017 | − | 8.41086i | −0.327725 | − | 0.270196i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 40.0924i | − | 1.28662i | −0.765604 | − | 0.643312i | \(-0.777560\pi\) | ||
0.765604 | − | 0.643312i | \(-0.222440\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 5.66294i | − | 0.181546i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 17.0032 | + | 14.0185i | 0.544539 | + | 0.448950i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24.4361 | + | 42.3246i | −0.781780 | + | 1.35408i | 0.149123 | + | 0.988819i | \(0.452355\pi\) |
−0.930904 | + | 0.365265i | \(0.880978\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25.5048 | + | 14.7252i | −0.815138 | + | 0.470620i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.40332 | + | 0.466791i | −0.0767322 | + | 0.0149035i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.60077 | − | 9.70081i | −0.178637 | − | 0.309408i | 0.762777 | − | 0.646662i | \(-0.223835\pi\) |
−0.941414 | + | 0.337254i | \(0.890502\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.3025 | − | 26.5047i | 0.487578 | − | 0.844510i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.07697 | + | 10.9068i | 0.129771 | + | 0.347167i | ||||
\(988\) | 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 | ||||||||
\(993\) | 3.68093 | − | 21.9864i | 0.116811 | − | 0.697718i | ||||
\(994\) | 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 | ||||||||
\(999\) | −11.4829 | + | 21.1378i | −0.363304 | + | 0.668770i |
(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 | 576.2.r.f.481.2 | yes | 12 | |
3.2 | odd | 2 | 1728.2.r.e.1441.3 | 12 | |||
4.3 | odd | 2 | inner | 576.2.r.f.481.5 | yes | 12 | |
8.3 | odd | 2 | 576.2.r.e.481.2 | yes | 12 | ||
8.5 | even | 2 | 576.2.r.e.481.5 | yes | 12 | ||
9.2 | odd | 6 | 1728.2.r.f.289.3 | 12 | |||
9.4 | even | 3 | 5184.2.d.q.2593.4 | 12 | |||
9.5 | odd | 6 | 5184.2.d.r.2593.10 | 12 | |||
9.7 | even | 3 | 576.2.r.e.97.5 | yes | 12 | ||
12.11 | even | 2 | 1728.2.r.e.1441.4 | 12 | |||
24.5 | odd | 2 | 1728.2.r.f.1441.3 | 12 | |||
24.11 | even | 2 | 1728.2.r.f.1441.4 | 12 | |||
36.7 | odd | 6 | 576.2.r.e.97.2 | ✓ | 12 | ||
36.11 | even | 6 | 1728.2.r.f.289.4 | 12 | |||
36.23 | even | 6 | 5184.2.d.r.2593.9 | 12 | |||
36.31 | odd | 6 | 5184.2.d.q.2593.3 | 12 | |||
72.5 | odd | 6 | 5184.2.d.r.2593.4 | 12 | |||
72.11 | even | 6 | 1728.2.r.e.289.4 | 12 | |||
72.13 | even | 6 | 5184.2.d.q.2593.10 | 12 | |||
72.29 | odd | 6 | 1728.2.r.e.289.3 | 12 | |||
72.43 | odd | 6 | inner | 576.2.r.f.97.5 | yes | 12 | |
72.59 | even | 6 | 5184.2.d.r.2593.3 | 12 | |||
72.61 | even | 6 | inner | 576.2.r.f.97.2 | yes | 12 | |
72.67 | odd | 6 | 5184.2.d.q.2593.9 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
576.2.r.e.97.2 | ✓ | 12 | 36.7 | odd | 6 | ||
576.2.r.e.97.5 | yes | 12 | 9.7 | even | 3 | ||
576.2.r.e.481.2 | yes | 12 | 8.3 | odd | 2 | ||
576.2.r.e.481.5 | yes | 12 | 8.5 | even | 2 | ||
576.2.r.f.97.2 | yes | 12 | 72.61 | even | 6 | inner | |
576.2.r.f.97.5 | yes | 12 | 72.43 | odd | 6 | inner | |
576.2.r.f.481.2 | yes | 12 | 1.1 | even | 1 | trivial | |
576.2.r.f.481.5 | yes | 12 | 4.3 | odd | 2 | inner | |
1728.2.r.e.289.3 | 12 | 72.29 | odd | 6 | |||
1728.2.r.e.289.4 | 12 | 72.11 | even | 6 | |||
1728.2.r.e.1441.3 | 12 | 3.2 | odd | 2 | |||
1728.2.r.e.1441.4 | 12 | 12.11 | even | 2 | |||
1728.2.r.f.289.3 | 12 | 9.2 | odd | 6 | |||
1728.2.r.f.289.4 | 12 | 36.11 | even | 6 | |||
1728.2.r.f.1441.3 | 12 | 24.5 | odd | 2 | |||
1728.2.r.f.1441.4 | 12 | 24.11 | even | 2 | |||
5184.2.d.q.2593.3 | 12 | 36.31 | odd | 6 | |||
5184.2.d.q.2593.4 | 12 | 9.4 | even | 3 | |||
5184.2.d.q.2593.9 | 12 | 72.67 | odd | 6 | |||
5184.2.d.q.2593.10 | 12 | 72.13 | even | 6 | |||
5184.2.d.r.2593.3 | 12 | 72.59 | even | 6 | |||
5184.2.d.r.2593.4 | 12 | 72.5 | odd | 6 | |||
5184.2.d.r.2593.9 | 12 | 36.23 | even | 6 | |||
5184.2.d.r.2593.10 | 12 | 9.5 | odd | 6 |