Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(442,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.442");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.f (of order \(3\), 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: | \(10.5642081874\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{5} \) |
Twist minimal: | no (minimal twist has level 441) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 883.1 | ||
Root | \(-0.474636 + 0.274031i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1323.883 |
Dual form | 1323.2.f.g.442.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.849814 | + | 1.47192i | −0.600909 | + | 1.04081i | 0.391774 | + | 0.920061i | \(0.371861\pi\) |
−0.992684 | + | 0.120744i | \(0.961472\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.444368 | − | 0.769668i | −0.222184 | − | 0.384834i | ||||
\(5\) | −0.474636 | − | 0.822093i | −0.212263 | − | 0.367651i | 0.740159 | − | 0.672432i | \(-0.234750\pi\) |
−0.952423 | + | 0.304781i | \(0.901417\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.88874 | −0.667769 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.61341 | 0.510204 | ||||||||
\(11\) | −0.294182 | + | 0.509538i | −0.0886992 | + | 0.153632i | −0.906962 | − | 0.421213i | \(-0.861604\pi\) |
0.818262 | + | 0.574845i | \(0.194938\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.50987 | + | 4.34722i | 0.696112 | + | 1.20570i | 0.969804 | + | 0.243885i | \(0.0784218\pi\) |
−0.273692 | + | 0.961817i | \(0.588245\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.49381 | − | 4.31941i | 0.623453 | − | 1.07985i | ||||
\(17\) | 7.58242 | 1.83901 | 0.919503 | − | 0.393083i | \(-0.128591\pi\) | ||||
0.919503 | + | 0.393083i | \(0.128591\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.46122 | −1.02347 | −0.511737 | − | 0.859142i | \(-0.670998\pi\) | ||||
−0.511737 | + | 0.859142i | \(0.670998\pi\) | |||||||
\(20\) | −0.421826 | + | 0.730623i | −0.0943231 | + | 0.163372i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.500000 | − | 0.866025i | −0.106600 | − | 0.184637i | ||||
\(23\) | 1.23855 | + | 2.14523i | 0.258256 | + | 0.447312i | 0.965775 | − | 0.259382i | \(-0.0835190\pi\) |
−0.707519 | + | 0.706694i | \(0.750186\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.04944 | − | 3.54974i | 0.409888 | − | 0.709948i | ||||
\(26\) | −8.53169 | −1.67320 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.73855 | − | 4.74331i | 0.508536 | − | 0.880810i | −0.491415 | − | 0.870925i | \(-0.663520\pi\) |
0.999951 | − | 0.00988468i | \(-0.00314644\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.03731 | + | 5.26078i | 0.545518 | + | 0.944865i | 0.998574 | + | 0.0533826i | \(0.0170003\pi\) |
−0.453056 | + | 0.891482i | \(0.649666\pi\) | |||||||
\(32\) | 2.34981 | + | 4.07000i | 0.415392 | + | 0.719481i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.44364 | + | 11.1607i | −1.10508 | + | 1.91405i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.98762 | −1.14876 | −0.574379 | − | 0.818590i | \(-0.694756\pi\) | ||||
−0.574379 | + | 0.818590i | \(0.694756\pi\) | |||||||
\(38\) | 3.79121 | − | 6.56657i | 0.615015 | − | 1.06524i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.896461 | + | 1.55272i | 0.141743 | + | 0.245506i | ||||
\(41\) | −0.527445 | − | 0.913562i | −0.0823731 | − | 0.142674i | 0.821896 | − | 0.569638i | \(-0.192917\pi\) |
−0.904269 | + | 0.426964i | \(0.859583\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.49381 | + | 6.05146i | −0.532801 | + | 0.922838i | 0.466465 | + | 0.884540i | \(0.345527\pi\) |
−0.999266 | + | 0.0382990i | \(0.987806\pi\) | |||||||
\(44\) | 0.522900 | 0.0788302 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.21015 | −0.620753 | ||||||||
\(47\) | −3.73840 | + | 6.47510i | −0.545301 | + | 0.944490i | 0.453286 | + | 0.891365i | \(0.350251\pi\) |
−0.998588 | + | 0.0531249i | \(0.983082\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.48329 | + | 6.03323i | 0.492612 | + | 0.853228i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.23061 | − | 3.86353i | 0.309330 | − | 0.535775i | ||||
\(53\) | −6.92216 | −0.950831 | −0.475416 | − | 0.879761i | \(-0.657702\pi\) | ||||
−0.475416 | + | 0.879761i | \(0.657702\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.558517 | 0.0753104 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.65452 | + | 8.06186i | 0.611168 | + | 1.05857i | ||||
\(59\) | 5.21512 | + | 9.03284i | 0.678950 | + | 1.17598i | 0.975297 | + | 0.220896i | \(0.0708981\pi\) |
−0.296347 | + | 0.955080i | \(0.595769\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.82644 | + | 10.0917i | −0.745999 | + | 1.29211i | 0.203727 | + | 0.979028i | \(0.434695\pi\) |
−0.949726 | + | 0.313081i | \(0.898639\pi\) | |||||||
\(62\) | −10.3246 | −1.31123 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.98762 | 0.248453 | ||||||||
\(65\) | 2.38255 | − | 4.12669i | 0.295518 | − | 0.511853i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.93199 | + | 10.2745i | 0.724708 | + | 1.25523i | 0.959094 | + | 0.283087i | \(0.0913585\pi\) |
−0.234387 | + | 0.972143i | \(0.575308\pi\) | |||||||
\(68\) | −3.36938 | − | 5.83594i | −0.408598 | − | 0.707712i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.30037 | −0.510360 | −0.255180 | − | 0.966894i | \(-0.582135\pi\) | ||||
−0.255180 | + | 0.966894i | \(0.582135\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.46122 | 0.522146 | 0.261073 | − | 0.965319i | \(-0.415924\pi\) | ||||
0.261073 | + | 0.965319i | \(0.415924\pi\) | |||||||
\(74\) | 5.93818 | − | 10.2852i | 0.690299 | − | 1.19563i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.98242 | + | 3.43366i | 0.227400 | + | 0.393868i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.666896 | − | 1.15510i | 0.0750317 | − | 0.129959i | −0.826068 | − | 0.563570i | \(-0.809428\pi\) |
0.901100 | + | 0.433611i | \(0.142761\pi\) | |||||||
\(80\) | −4.73460 | −0.529345 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.79292 | 0.197995 | ||||||||
\(83\) | −2.84194 | + | 4.92238i | −0.311943 | + | 0.540301i | −0.978783 | − | 0.204900i | \(-0.934313\pi\) |
0.666840 | + | 0.745201i | \(0.267647\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.59888 | − | 6.23345i | −0.390354 | − | 0.676113i | ||||
\(86\) | −5.93818 | − | 10.2852i | −0.640330 | − | 1.10908i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.555632 | − | 0.962383i | 0.0592306 | − | 0.102590i | ||||
\(89\) | −0.843651 | −0.0894269 | −0.0447134 | − | 0.999000i | \(-0.514237\pi\) | ||||
−0.0447134 | + | 0.999000i | \(0.514237\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.10074 | − | 1.90654i | 0.114760 | − | 0.198771i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.35389 | − | 11.0053i | −0.655353 | − | 1.13511i | ||||
\(95\) | 2.11745 | + | 3.66754i | 0.217246 | + | 0.376281i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.70317 | − | 2.94997i | 0.172930 | − | 0.299524i | −0.766513 | − | 0.642229i | \(-0.778010\pi\) |
0.939443 | + | 0.342705i | \(0.111343\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.64283 | −0.364283 | ||||||||
\(101\) | −4.79329 | + | 8.30222i | −0.476950 | + | 0.826102i | −0.999651 | − | 0.0264143i | \(-0.991591\pi\) |
0.522701 | + | 0.852516i | \(0.324924\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.82644 | + | 10.0917i | 0.574096 | + | 0.994364i | 0.996139 | + | 0.0877882i | \(0.0279799\pi\) |
−0.422043 | + | 0.906576i | \(0.638687\pi\) | |||||||
\(104\) | −4.74048 | − | 8.21075i | −0.464842 | − | 0.805130i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.88255 | − | 10.1889i | 0.571363 | − | 0.989630i | ||||
\(107\) | 3.79851 | 0.367216 | 0.183608 | − | 0.983000i | \(-0.441222\pi\) | ||||
0.183608 | + | 0.983000i | \(0.441222\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.8640 | −1.23215 | −0.616073 | − | 0.787689i | \(-0.711277\pi\) | ||||
−0.616073 | + | 0.787689i | \(0.711277\pi\) | |||||||
\(110\) | −0.474636 | + | 0.822093i | −0.0452547 | + | 0.0783835i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.51052 | + | 7.81245i | 0.424314 | + | 0.734934i | 0.996356 | − | 0.0852908i | \(-0.0271819\pi\) |
−0.572042 | + | 0.820224i | \(0.693849\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.17572 | − | 2.03641i | 0.109636 | − | 0.189896i | ||||
\(116\) | −4.86769 | −0.451954 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −17.7275 | −1.63195 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.32691 | + | 9.22649i | 0.484265 | + | 0.838771i | ||||
\(122\) | −9.90278 | − | 17.1521i | −0.896556 | − | 1.55288i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.69937 | − | 4.67545i | 0.242411 | − | 0.419867i | ||||
\(125\) | −8.63731 | −0.772544 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.43268 | 0.570808 | 0.285404 | − | 0.958407i | \(-0.407872\pi\) | ||||
0.285404 | + | 0.958407i | \(0.407872\pi\) | |||||||
\(128\) | −6.38874 | + | 11.0656i | −0.564690 | + | 0.978071i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.04944 | + | 7.01384i | 0.355160 | + | 0.615154i | ||||
\(131\) | 3.31657 | + | 5.74447i | 0.289770 | + | 0.501897i | 0.973755 | − | 0.227600i | \(-0.0730877\pi\) |
−0.683984 | + | 0.729497i | \(0.739754\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −20.1643 | −1.74193 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −14.3212 | −1.22803 | ||||||||
\(137\) | 7.01671 | − | 12.1533i | 0.599478 | − | 1.03833i | −0.393420 | − | 0.919359i | \(-0.628708\pi\) |
0.992898 | − | 0.118968i | \(-0.0379585\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.40254 | − | 7.62541i | −0.373418 | − | 0.646779i | 0.616671 | − | 0.787221i | \(-0.288481\pi\) |
−0.990089 | + | 0.140442i | \(0.955148\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.65452 | − | 6.32981i | 0.306680 | − | 0.531186i | ||||
\(143\) | −2.95343 | −0.246978 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.19925 | −0.431774 | ||||||||
\(146\) | −3.79121 | + | 6.56657i | −0.313763 | + | 0.543453i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.10507 | + | 5.37815i | 0.255236 | + | 0.442081i | ||||
\(149\) | −2.18292 | − | 3.78092i | −0.178832 | − | 0.309745i | 0.762649 | − | 0.646813i | \(-0.223898\pi\) |
−0.941481 | + | 0.337067i | \(0.890565\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.32691 | − | 10.9585i | 0.514877 | − | 0.891793i | −0.484974 | − | 0.874529i | \(-0.661171\pi\) |
0.999851 | − | 0.0172645i | \(-0.00549573\pi\) | |||||||
\(152\) | 8.42607 | 0.683444 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.88323 | − | 4.99391i | 0.231587 | − | 0.401120i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.63694 | − | 9.76347i | −0.449877 | − | 0.779210i | 0.548501 | − | 0.836150i | \(-0.315199\pi\) |
−0.998378 | + | 0.0569405i | \(0.981865\pi\) | |||||||
\(158\) | 1.13348 | + | 1.96324i | 0.0901745 | + | 0.156187i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.23061 | − | 3.86353i | 0.176345 | − | 0.305439i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.66621 | −0.130507 | −0.0652537 | − | 0.997869i | \(-0.520786\pi\) | ||||
−0.0652537 | + | 0.997869i | \(0.520786\pi\) | |||||||
\(164\) | −0.468760 | + | 0.811916i | −0.0366040 | + | 0.0634000i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.83024 | − | 8.36622i | −0.374899 | − | 0.649344i | ||||
\(167\) | 1.95135 | + | 3.37984i | 0.151000 | + | 0.261540i | 0.931595 | − | 0.363497i | \(-0.118417\pi\) |
−0.780595 | + | 0.625037i | \(0.785084\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.09888 | + | 10.5636i | −0.469145 | + | 0.812583i | ||||
\(170\) | 12.2335 | 0.938269 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.21015 | 0.473519 | ||||||||
\(173\) | 8.05705 | − | 13.9552i | 0.612566 | − | 1.06100i | −0.378240 | − | 0.925708i | \(-0.623471\pi\) |
0.990806 | − | 0.135288i | \(-0.0431961\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.46727 | + | 2.54138i | 0.110599 | + | 0.191564i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.716947 | − | 1.24179i | 0.0537374 | − | 0.0930760i | ||||
\(179\) | −14.2880 | −1.06793 | −0.533967 | − | 0.845505i | \(-0.679299\pi\) | ||||
−0.533967 | + | 0.845505i | \(0.679299\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.8873 | 0.957905 | 0.478952 | − | 0.877841i | \(-0.341017\pi\) | ||||
0.478952 | + | 0.877841i | \(0.341017\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.33929 | − | 4.05178i | −0.172455 | − | 0.298701i | ||||
\(185\) | 3.31657 | + | 5.74447i | 0.243839 | + | 0.422342i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.23061 | + | 3.86353i | −0.163118 | + | 0.282529i | ||||
\(188\) | 6.64490 | 0.484629 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.19777 | −0.522181 | ||||||||
\(191\) | −1.08217 | + | 1.87438i | −0.0783034 | + | 0.135625i | −0.902518 | − | 0.430652i | \(-0.858284\pi\) |
0.824215 | + | 0.566277i | \(0.191617\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.21565 | − | 9.03377i | −0.375431 | − | 0.650265i | 0.614961 | − | 0.788558i | \(-0.289172\pi\) |
−0.990391 | + | 0.138293i | \(0.955839\pi\) | |||||||
\(194\) | 2.89475 | + | 5.01385i | 0.207831 | + | 0.359973i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.7848 | 1.33836 | 0.669179 | − | 0.743101i | \(-0.266646\pi\) | ||||
0.669179 | + | 0.743101i | \(0.266646\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.42607 | 0.597308 | 0.298654 | − | 0.954361i | \(-0.403462\pi\) | ||||
0.298654 | + | 0.954361i | \(0.403462\pi\) | |||||||
\(200\) | −3.87085 | + | 6.70452i | −0.273711 | + | 0.474081i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.14681 | − | 14.1107i | −0.573208 | − | 0.992825i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.500689 | + | 0.867218i | −0.0349696 | + | 0.0605692i | ||||
\(206\) | −19.8056 | −1.37992 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 25.0365 | 1.73597 | ||||||||
\(209\) | 1.31241 | − | 2.27316i | 0.0907814 | − | 0.157238i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.61126 | − | 9.71899i | −0.386295 | − | 0.669083i | 0.605653 | − | 0.795729i | \(-0.292912\pi\) |
−0.991948 | + | 0.126646i | \(0.959579\pi\) | |||||||
\(212\) | 3.07598 | + | 5.32776i | 0.211259 | + | 0.365912i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.22803 | + | 5.59111i | −0.220664 | + | 0.382200i | ||||
\(215\) | 6.63315 | 0.452377 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 10.9320 | − | 18.9348i | 0.740408 | − | 1.28242i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.248187 | − | 0.429872i | −0.0167328 | − | 0.0289820i | ||||
\(221\) | 19.0309 | + | 32.9624i | 1.28016 | + | 2.21729i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.3774 | − | 17.9742i | 0.694923 | − | 1.20364i | −0.275283 | − | 0.961363i | \(-0.588772\pi\) |
0.970206 | − | 0.242279i | \(-0.0778951\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −15.3324 | −1.01990 | ||||||||
\(227\) | −5.21512 | + | 9.03284i | −0.346139 | + | 0.599531i | −0.985560 | − | 0.169326i | \(-0.945841\pi\) |
0.639421 | + | 0.768857i | \(0.279174\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.52961 | − | 13.0417i | −0.497570 | − | 0.861817i | 0.502426 | − | 0.864620i | \(-0.332441\pi\) |
−0.999996 | + | 0.00280316i | \(0.999108\pi\) | |||||||
\(230\) | 1.99829 | + | 3.46113i | 0.131763 | + | 0.228220i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.17240 | + | 8.95886i | −0.339585 | + | 0.588178i | ||||
\(233\) | −4.38688 | −0.287394 | −0.143697 | − | 0.989622i | \(-0.545899\pi\) | ||||
−0.143697 | + | 0.989622i | \(0.545899\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.09751 | 0.462990 | ||||||||
\(236\) | 4.63486 | − | 8.02781i | 0.301704 | − | 0.522566i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.77561 | − | 8.27160i | −0.308909 | − | 0.535046i | 0.669215 | − | 0.743069i | \(-0.266630\pi\) |
−0.978124 | + | 0.208023i | \(0.933297\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.26792 | + | 9.12431i | −0.339337 | + | 0.587749i | −0.984308 | − | 0.176458i | \(-0.943536\pi\) |
0.644971 | + | 0.764207i | \(0.276869\pi\) | |||||||
\(242\) | −18.1075 | −1.16400 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.3563 | 0.662996 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.1971 | − | 19.3939i | −0.712453 | − | 1.23401i | ||||
\(248\) | −5.73668 | − | 9.93623i | −0.364280 | − | 0.630951i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.34011 | − | 12.7134i | 0.464229 | − | 0.804068i | ||||
\(251\) | 24.4346 | 1.54230 | 0.771148 | − | 0.636656i | \(-0.219683\pi\) | ||||
0.771148 | + | 0.636656i | \(0.219683\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.45744 | −0.0916282 | ||||||||
\(254\) | −5.46658 | + | 9.46839i | −0.343004 | + | 0.594100i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.87085 | − | 15.3648i | −0.554428 | − | 0.960298i | ||||
\(257\) | 2.00416 | + | 3.47131i | 0.125016 | + | 0.216534i | 0.921739 | − | 0.387810i | \(-0.126768\pi\) |
−0.796723 | + | 0.604345i | \(0.793435\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4.23491 | −0.262638 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −11.2739 | −0.696503 | ||||||||
\(263\) | 8.84362 | − | 15.3176i | 0.545321 | − | 0.944524i | −0.453265 | − | 0.891376i | \(-0.649741\pi\) |
0.998587 | − | 0.0531485i | \(-0.0169257\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.28550 | + | 5.69066i | 0.201827 | + | 0.349574i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.27197 | − | 9.13132i | 0.322037 | − | 0.557784i | ||||
\(269\) | 14.2273 | 0.867455 | 0.433727 | − | 0.901044i | \(-0.357198\pi\) | ||||
0.433727 | + | 0.901044i | \(0.357198\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.39874 | −0.327950 | −0.163975 | − | 0.986464i | \(-0.552432\pi\) | ||||
−0.163975 | + | 0.986464i | \(0.552432\pi\) | |||||||
\(272\) | 18.9091 | − | 32.7515i | 1.14653 | − | 1.98585i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.9258 | + | 20.6561i | 0.720464 | + | 1.24788i | ||||
\(275\) | 1.20582 | + | 2.08854i | 0.0727136 | + | 0.125944i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.83310 | + | 6.63913i | −0.230309 | + | 0.398907i | −0.957899 | − | 0.287105i | \(-0.907307\pi\) |
0.727590 | + | 0.686012i | \(0.240640\pi\) | |||||||
\(278\) | 14.9653 | 0.897562 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.3312 | + | 19.6263i | −0.675965 | + | 1.17081i | 0.300220 | + | 0.953870i | \(0.402940\pi\) |
−0.976186 | + | 0.216936i | \(0.930394\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.9246 | + | 27.5822i | 0.946619 | + | 1.63959i | 0.752476 | + | 0.658620i | \(0.228859\pi\) |
0.194144 | + | 0.980973i | \(0.437807\pi\) | |||||||
\(284\) | 1.91095 | + | 3.30986i | 0.113394 | + | 0.196404i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.50987 | − | 4.34722i | 0.148412 | − | 0.257057i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 40.4930 | 2.38194 | ||||||||
\(290\) | 4.41840 | − | 7.65289i | 0.259457 | − | 0.449393i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.98242 | − | 3.43366i | −0.116013 | − | 0.200940i | ||||
\(293\) | 13.7468 | + | 23.8102i | 0.803097 | + | 1.39100i | 0.917568 | + | 0.397578i | \(0.130149\pi\) |
−0.114472 | + | 0.993427i | \(0.536517\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.95056 | − | 8.57462i | 0.288233 | − | 0.499234i | ||||
\(296\) | 13.1978 | 0.767105 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.42030 | 0.429846 | ||||||||
\(299\) | −6.21720 | + | 10.7685i | −0.359550 | + | 0.622758i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 10.7534 | + | 18.6254i | 0.618789 | + | 1.07177i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −11.1254 | + | 19.2698i | −0.638088 | + | 1.10520i | ||||
\(305\) | 11.0617 | 0.633394 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.8176 | 0.845683 | 0.422841 | − | 0.906204i | \(-0.361033\pi\) | ||||
0.422841 | + | 0.906204i | \(0.361033\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.90043 | + | 8.48779i | 0.278326 | + | 0.482074i | ||||
\(311\) | 14.5318 | + | 25.1698i | 0.824021 | + | 1.42725i | 0.902665 | + | 0.430343i | \(0.141608\pi\) |
−0.0786442 | + | 0.996903i | \(0.525059\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.2390 | − | 21.1986i | 0.691790 | − | 1.19822i | −0.279461 | − | 0.960157i | \(-0.590156\pi\) |
0.971251 | − | 0.238058i | \(-0.0765110\pi\) | |||||||
\(314\) | 19.1614 | 1.08134 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.18539 | −0.0666834 | ||||||||
\(317\) | −3.69344 | + | 6.39722i | −0.207444 | + | 0.359304i | −0.950909 | − | 0.309472i | \(-0.899848\pi\) |
0.743465 | + | 0.668775i | \(0.233181\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.61126 | + | 2.79079i | 0.0902135 | + | 0.156254i | ||||
\(320\) | −0.943395 | − | 1.63401i | −0.0527374 | − | 0.0913438i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −33.8268 | −1.88218 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 20.5753 | 1.14131 | ||||||||
\(326\) | 1.41597 | − | 2.45253i | 0.0784231 | − | 0.135833i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.996205 | + | 1.72548i | 0.0550062 | + | 0.0952736i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.0309 | + | 17.3740i | −0.551347 | + | 0.954960i | 0.446831 | + | 0.894618i | \(0.352552\pi\) |
−0.998178 | + | 0.0603420i | \(0.980781\pi\) | |||||||
\(332\) | 5.05146 | 0.277235 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.63315 | −0.362950 | ||||||||
\(335\) | 5.63106 | − | 9.75329i | 0.307658 | − | 0.532879i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.20327 | − | 5.54823i | −0.174493 | − | 0.302231i | 0.765493 | − | 0.643445i | \(-0.222495\pi\) |
−0.939986 | + | 0.341214i | \(0.889162\pi\) | |||||||
\(338\) | −10.3658 | − | 17.9542i | −0.563827 | − | 0.976577i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.19846 | + | 5.53989i | −0.173461 | + | 0.300443i | ||||
\(341\) | −3.57409 | −0.193548 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6.59888 | − | 11.4296i | 0.355788 | − | 0.616243i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13.6940 | + | 23.7187i | 0.736194 | + | 1.27512i | ||||
\(347\) | −14.5963 | − | 25.2816i | −0.783572 | − | 1.35719i | −0.929848 | − | 0.367943i | \(-0.880062\pi\) |
0.146276 | − | 0.989244i | \(-0.453271\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.17192 | − | 3.76188i | 0.116260 | − | 0.201369i | −0.802022 | − | 0.597294i | \(-0.796243\pi\) |
0.918283 | + | 0.395925i | \(0.129576\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.76509 | −0.147380 | ||||||||
\(353\) | 12.8503 | − | 22.2574i | 0.683955 | − | 1.18464i | −0.289809 | − | 0.957084i | \(-0.593592\pi\) |
0.973764 | − | 0.227560i | \(-0.0730747\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.04111 | + | 3.53530i | 0.108331 | + | 0.187635i | ||||
\(356\) | 0.374892 | + | 0.649331i | 0.0198692 | + | 0.0344145i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.1421 | − | 21.0308i | 0.641732 | − | 1.11151i | ||||
\(359\) | −20.6872 | −1.09183 | −0.545916 | − | 0.837840i | \(-0.683818\pi\) | ||||
−0.545916 | + | 0.837840i | \(0.683818\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.902493 | 0.0474996 | ||||||||
\(362\) | −10.9518 | + | 18.9691i | −0.575614 | + | 0.996992i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.11745 | − | 3.66754i | −0.110833 | − | 0.191968i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.42391 | − | 2.46628i | 0.0743273 | − | 0.128739i | −0.826466 | − | 0.562986i | \(-0.809652\pi\) |
0.900794 | + | 0.434248i | \(0.142986\pi\) | |||||||
\(368\) | 12.3548 | 0.644040 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −11.2739 | −0.586101 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.7163 | − | 18.5612i | −0.554871 | − | 0.961065i | −0.997914 | − | 0.0645641i | \(-0.979434\pi\) |
0.443043 | − | 0.896501i | \(-0.353899\pi\) | |||||||
\(374\) | −3.79121 | − | 6.56657i | −0.196039 | − | 0.339549i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.06085 | − | 12.2297i | 0.364135 | − | 0.630701i | ||||
\(377\) | 27.4936 | 1.41599 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.0494 | 1.38943 | 0.694716 | − | 0.719284i | \(-0.255530\pi\) | ||||
0.694716 | + | 0.719284i | \(0.255530\pi\) | |||||||
\(380\) | 1.88186 | − | 3.25947i | 0.0965372 | − | 0.167207i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.83929 | − | 3.18575i | −0.0941064 | − | 0.162997i | ||||
\(383\) | −7.21340 | − | 12.4940i | −0.368588 | − | 0.638412i | 0.620757 | − | 0.784003i | \(-0.286825\pi\) |
−0.989345 | + | 0.145590i | \(0.953492\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.7293 | 0.902399 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.02733 | −0.153689 | ||||||||
\(389\) | −3.05377 | + | 5.28929i | −0.154832 | + | 0.268178i | −0.932998 | − | 0.359882i | \(-0.882817\pi\) |
0.778166 | + | 0.628059i | \(0.216150\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.39120 | + | 16.2660i | 0.474933 | + | 0.822609i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −15.9635 | + | 27.6497i | −0.804232 | + | 1.39297i | ||||
\(395\) | −1.26613 | −0.0637059 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.8873 | −0.646794 | −0.323397 | − | 0.946263i | \(-0.604825\pi\) | ||||
−0.323397 | + | 0.946263i | \(0.604825\pi\) | |||||||
\(398\) | −7.16059 | + | 12.4025i | −0.358928 | + | 0.621682i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −10.2218 | − | 17.7047i | −0.511092 | − | 0.885237i | ||||
\(401\) | 4.19530 | + | 7.26647i | 0.209503 | + | 0.362870i | 0.951558 | − | 0.307469i | \(-0.0994820\pi\) |
−0.742055 | + | 0.670339i | \(0.766149\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.2465 | + | 26.4078i | −0.759483 | + | 1.31546i | ||||
\(404\) | 8.51994 | 0.423883 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.05563 | − | 3.56046i | 0.101894 | − | 0.176485i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.40633 | − | 5.89994i | −0.168432 | − | 0.291733i | 0.769437 | − | 0.638723i | \(-0.220537\pi\) |
−0.937869 | + | 0.346990i | \(0.887204\pi\) | |||||||
\(410\) | −0.850985 | − | 1.47395i | −0.0420271 | − | 0.0727931i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.17817 | − | 8.96885i | 0.255110 | − | 0.441864i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.39554 | 0.264857 | ||||||||
\(416\) | −11.7955 | + | 20.4303i | −0.578320 | + | 1.00168i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.23061 | + | 3.86353i | 0.109103 | + | 0.188971i | ||||
\(419\) | −5.16231 | − | 8.94137i | −0.252195 | − | 0.436815i | 0.711935 | − | 0.702246i | \(-0.247819\pi\) |
−0.964130 | + | 0.265431i | \(0.914486\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.56801 | + | 2.71588i | −0.0764202 | + | 0.132364i | −0.901703 | − | 0.432356i | \(-0.857682\pi\) |
0.825283 | + | 0.564720i | \(0.191016\pi\) | |||||||
\(422\) | 19.0741 | 0.928514 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 13.0741 | 0.634936 | ||||||||
\(425\) | 15.5397 | − | 26.9156i | 0.753787 | − | 1.30560i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.68794 | − | 2.92359i | −0.0815895 | − | 0.141317i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.63694 | + | 9.76347i | −0.271837 | + | 0.470836i | ||||
\(431\) | −31.8726 | −1.53525 | −0.767625 | − | 0.640899i | \(-0.778562\pi\) | ||||
−0.767625 | + | 0.640899i | \(0.778562\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.48855 | 0.359877 | 0.179938 | − | 0.983678i | \(-0.442410\pi\) | ||||
0.179938 | + | 0.983678i | \(0.442410\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.71634 | + | 9.90099i | 0.273763 | + | 0.474171i | ||||
\(437\) | −5.52544 | − | 9.57035i | −0.264318 | − | 0.457812i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.14465 | + | 1.98259i | −0.0546311 | + | 0.0946238i | −0.892048 | − | 0.451941i | \(-0.850732\pi\) |
0.837417 | + | 0.546565i | \(0.184065\pi\) | |||||||
\(440\) | −1.05489 | −0.0502900 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −64.6908 | −3.07703 | ||||||||
\(443\) | 18.6749 | − | 32.3458i | 0.887270 | − | 1.53680i | 0.0441800 | − | 0.999024i | \(-0.485933\pi\) |
0.843090 | − | 0.537773i | \(-0.180734\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.400427 | + | 0.693560i | 0.0189821 | + | 0.0328779i | ||||
\(446\) | 17.6378 | + | 30.5495i | 0.835172 | + | 1.44656i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.20286 | 0.292731 | 0.146366 | − | 0.989231i | \(-0.453242\pi\) | ||||
0.146366 | + | 0.989231i | \(0.453242\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.620660 | 0.0292257 | ||||||||
\(452\) | 4.00866 | − | 6.94320i | 0.188552 | − | 0.326581i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8.86376 | − | 15.3525i | −0.415997 | − | 0.720527i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.0858 | + | 17.4691i | −0.471795 | + | 0.817172i | −0.999479 | − | 0.0322682i | \(-0.989727\pi\) |
0.527685 | + | 0.849440i | \(0.323060\pi\) | |||||||
\(458\) | 25.5951 | 1.19598 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.08981 | −0.0974378 | ||||||||
\(461\) | −11.2680 | + | 19.5168i | −0.524803 | + | 0.908986i | 0.474780 | + | 0.880105i | \(0.342528\pi\) |
−0.999583 | + | 0.0288813i | \(0.990806\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.8145 | + | 23.9275i | 0.642016 | + | 1.11200i | 0.984982 | + | 0.172656i | \(0.0552350\pi\) |
−0.342966 | + | 0.939348i | \(0.611432\pi\) | |||||||
\(464\) | −13.6588 | − | 23.6578i | −0.634096 | − | 1.09829i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.72803 | − | 6.45714i | 0.172698 | − | 0.299121i | ||||
\(467\) | −20.1224 | −0.931155 | −0.465577 | − | 0.885007i | \(-0.654153\pi\) | ||||
−0.465577 | + | 0.885007i | \(0.654153\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −6.03156 | + | 10.4470i | −0.278215 | + | 0.481883i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.84997 | − | 17.0607i | −0.453382 | − | 0.785280i | ||||
\(473\) | −2.05563 | − | 3.56046i | −0.0945181 | − | 0.163710i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.14301 | + | 15.8362i | −0.419510 | + | 0.726613i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 16.2335 | 0.742504 | ||||||||
\(479\) | −4.79329 | + | 8.30222i | −0.219011 | + | 0.379338i | −0.954506 | − | 0.298192i | \(-0.903616\pi\) |
0.735495 | + | 0.677530i | \(0.236950\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.5380 | − | 30.3767i | −0.799664 | − | 1.38506i | ||||
\(482\) | −8.95351 | − | 15.5079i | −0.407821 | − | 0.706367i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.73422 | − | 8.19991i | 0.215192 | − | 0.372723i | ||||
\(485\) | −3.23353 | −0.146827 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.0741 | 0.592445 | 0.296223 | − | 0.955119i | \(-0.404273\pi\) | ||||
0.296223 | + | 0.955119i | \(0.404273\pi\) | |||||||
\(488\) | 11.0046 | − | 19.0605i | 0.498155 | − | 0.862830i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.67054 | + | 13.2858i | 0.346167 | + | 0.599578i | 0.985565 | − | 0.169298i | \(-0.0541499\pi\) |
−0.639398 | + | 0.768876i | \(0.720817\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.7648 | − | 35.9657i | 0.935201 | − | 1.61982i | ||||
\(494\) | 38.0617 | 1.71248 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 30.2979 | 1.36042 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.43268 | − | 4.21352i | −0.108902 | − | 0.188623i | 0.806424 | − | 0.591338i | \(-0.201400\pi\) |
−0.915326 | + | 0.402715i | \(0.868067\pi\) | |||||||
\(500\) | 3.83814 | + | 6.64786i | 0.171647 | + | 0.297301i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −20.7648 | + | 35.9657i | −0.926780 | + | 1.60523i | ||||
\(503\) | −16.0085 | −0.713783 | −0.356892 | − | 0.934146i | \(-0.616163\pi\) | ||||
−0.356892 | + | 0.934146i | \(0.616163\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.10026 | 0.404956 | ||||||||
\(506\) | 1.23855 | − | 2.14523i | 0.0550603 | − | 0.0953672i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.85848 | − | 4.95102i | −0.126824 | − | 0.219666i | ||||
\(509\) | −15.5925 | − | 27.0071i | −0.691127 | − | 1.19707i | −0.971469 | − | 0.237167i | \(-0.923781\pi\) |
0.280342 | − | 0.959900i | \(-0.409552\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 4.59937 | 0.203265 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.81266 | −0.300494 | ||||||||
\(515\) | 5.53087 | − | 9.57975i | 0.243719 | − | 0.422134i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.19954 | − | 3.80971i | −0.0967356 | − | 0.167551i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.50000 | + | 7.79423i | −0.197338 | + | 0.341800i | ||||
\(521\) | −20.9661 | −0.918541 | −0.459270 | − | 0.888297i | \(-0.651889\pi\) | ||||
−0.459270 | + | 0.888297i | \(0.651889\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 43.5642 | 1.90493 | 0.952465 | − | 0.304647i | \(-0.0985383\pi\) | ||||
0.952465 | + | 0.304647i | \(0.0985383\pi\) | |||||||
\(524\) | 2.94756 | − | 5.10532i | 0.128765 | − | 0.223027i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.0309 | + | 26.0342i | 0.655377 | + | 1.13515i | ||||
\(527\) | 23.0302 | + | 39.8894i | 1.00321 | + | 1.73761i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.43199 | − | 14.6046i | 0.366608 | − | 0.634984i | ||||
\(530\) | −11.1683 | −0.485118 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.64764 | − | 4.58584i | 0.114682 | − | 0.198635i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.80291 | − | 3.12273i | −0.0779466 | − | 0.135007i | ||||
\(536\) | −11.2040 | − | 19.4058i | −0.483937 | − | 0.838204i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −12.0906 | + | 20.9415i | −0.521262 | + | 0.902852i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.86535 | 0.424145 | 0.212072 | − | 0.977254i | \(-0.431979\pi\) | ||||
0.212072 | + | 0.977254i | \(0.431979\pi\) | |||||||
\(542\) | 4.58793 | − | 7.94652i | 0.197068 | − | 0.341332i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 17.8173 | + | 30.8604i | 0.763909 | + | 1.32313i | ||||
\(545\) | 6.10570 | + | 10.5754i | 0.261539 | + | 0.453000i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.284350 | + | 0.492509i | −0.0121579 | + | 0.0210582i | −0.872040 | − | 0.489434i | \(-0.837203\pi\) |
0.859882 | + | 0.510492i | \(0.170537\pi\) | |||||||
\(548\) | −12.4720 | −0.532778 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.09888 | −0.174777 | ||||||||
\(551\) | −12.2173 | + | 21.1609i | −0.520473 | + | 0.901487i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −6.51485 | − | 11.2841i | −0.276789 | − | 0.479413i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.91269 | + | 6.77698i | −0.165935 | + | 0.287408i | ||||
\(557\) | 2.58699 | 0.109614 | 0.0548071 | − | 0.998497i | \(-0.482546\pi\) | ||||
0.0548071 | + | 0.998497i | \(0.482546\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −35.0760 | −1.48356 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −19.2589 | − | 33.3574i | −0.812388 | − | 1.40710i | ||||
\(563\) | −16.6416 | − | 28.8240i | −0.701358 | − | 1.21479i | −0.967990 | − | 0.250989i | \(-0.919244\pi\) |
0.266632 | − | 0.963798i | \(-0.414089\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.28171 | − | 7.41613i | 0.180133 | − | 0.311999i | ||||
\(566\) | −54.1318 | −2.27533 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.12227 | 0.340803 | ||||||||
\(569\) | −2.67673 | + | 4.63623i | −0.112214 | + | 0.194361i | −0.916663 | − | 0.399662i | \(-0.869128\pi\) |
0.804448 | + | 0.594022i | \(0.202461\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.45056 | − | 4.24449i | −0.102553 | − | 0.177626i | 0.810183 | − | 0.586177i | \(-0.199368\pi\) |
−0.912736 | + | 0.408551i | \(0.866034\pi\) | |||||||
\(572\) | 1.31241 | + | 2.27316i | 0.0548747 | + | 0.0950457i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.1533 | 0.423424 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.0757 | −1.50185 | −0.750925 | − | 0.660387i | \(-0.770392\pi\) | ||||
−0.750925 | + | 0.660387i | \(0.770392\pi\) | |||||||
\(578\) | −34.4116 | + | 59.6026i | −1.43133 | + | 2.47914i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.31038 | + | 4.00170i | 0.0959333 | + | 0.166161i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.03637 | − | 3.52710i | 0.0843380 | − | 0.146078i | ||||
\(584\) | −8.42607 | −0.348673 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −46.7289 | −1.93035 | ||||||||
\(587\) | 0.527445 | − | 0.913562i | 0.0217700 | − | 0.0377068i | −0.854935 | − | 0.518735i | \(-0.826403\pi\) |
0.876705 | + | 0.481028i | \(0.159737\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.5501 | − | 23.4695i | −0.558323 | − | 0.967045i | ||||
\(590\) | 8.41411 | + | 14.5737i | 0.346403 | + | 0.599988i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −17.4258 | + | 30.1824i | −0.716196 | + | 1.24049i | ||||
\(593\) | 15.0710 | 0.618890 | 0.309445 | − | 0.950917i | \(-0.399857\pi\) | ||||
0.309445 | + | 0.950917i | \(0.399857\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.94004 | + | 3.36024i | −0.0794670 | + | 0.137641i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −10.5669 | − | 18.3024i | −0.432114 | − | 0.748443i | ||||
\(599\) | 21.0283 | + | 36.4221i | 0.859194 | + | 1.48817i | 0.872699 | + | 0.488259i | \(0.162368\pi\) |
−0.0135047 | + | 0.999909i | \(0.504299\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.44989 | + | 16.3677i | −0.385469 | + | 0.667652i | −0.991834 | − | 0.127534i | \(-0.959294\pi\) |
0.606365 | + | 0.795186i | \(0.292627\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11.2459 | −0.457590 | ||||||||
\(605\) | 5.05669 | − | 8.75844i | 0.205583 | − | 0.356081i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.7213 | + | 25.4980i | 0.597518 | + | 1.03493i | 0.993186 | + | 0.116538i | \(0.0371796\pi\) |
−0.395668 | + | 0.918393i | \(0.629487\pi\) | |||||||
\(608\) | −10.4830 | − | 18.1572i | −0.425143 | − | 0.736370i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.40043 | + | 16.2820i | −0.380612 | + | 0.659240i | ||||
\(611\) | −37.5316 | −1.51836 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.6676 | −0.471249 | −0.235625 | − | 0.971844i | \(-0.575714\pi\) | ||||
−0.235625 | + | 0.971844i | \(0.575714\pi\) | |||||||
\(614\) | −12.5922 | + | 21.8103i | −0.508179 | + | 0.880191i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.4054 | − | 28.4151i | −0.660458 | − | 1.14395i | −0.980495 | − | 0.196542i | \(-0.937029\pi\) |
0.320037 | − | 0.947405i | \(-0.396305\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.0806 | − | 20.9242i | 0.485560 | − | 0.841014i | −0.514303 | − | 0.857609i | \(-0.671949\pi\) |
0.999862 | + | 0.0165947i | \(0.00528250\pi\) | |||||||
\(620\) | −5.12487 | −0.205820 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −49.3972 | −1.98065 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.14764 | − | 10.6480i | −0.245906 | − | 0.425921i | ||||
\(626\) | 20.8018 | + | 36.0297i | 0.831406 | + | 1.44004i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.00975 | + | 8.67714i | −0.199911 | + | 0.346256i | ||||
\(629\) | −52.9830 | −2.11257 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.1003 | −0.441894 | −0.220947 | − | 0.975286i | \(-0.570915\pi\) | ||||
−0.220947 | + | 0.975286i | \(0.570915\pi\) | |||||||
\(632\) | −1.25959 | + | 2.18168i | −0.0501038 | + | 0.0867824i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6.27747 | − | 10.8729i | −0.249310 | − | 0.431818i | ||||
\(635\) | −3.05318 | − | 5.28826i | −0.121162 | − | 0.209858i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.47710 | −0.216840 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 12.1293 | 0.479452 | ||||||||
\(641\) | 3.65019 | − | 6.32231i | 0.144174 | − | 0.249716i | −0.784891 | − | 0.619634i | \(-0.787281\pi\) |
0.929064 | + | 0.369918i | \(0.120614\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.6256 | − | 18.4041i | −0.419033 | − | 0.725787i | 0.576809 | − | 0.816879i | \(-0.304298\pi\) |
−0.995842 | + | 0.0910922i | \(0.970964\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 28.7465 | − | 49.7904i | 1.13102 | − | 1.95898i | ||||
\(647\) | −16.9460 | −0.666216 | −0.333108 | − | 0.942889i | \(-0.608097\pi\) | ||||
−0.333108 | + | 0.942889i | \(0.608097\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.13677 | −0.240889 | ||||||||
\(650\) | −17.4852 | + | 30.2853i | −0.685826 | + | 1.18789i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.740409 | + | 1.28243i | 0.0289967 | + | 0.0502237i | ||||
\(653\) | −1.86652 | − | 3.23292i | −0.0730427 | − | 0.126514i | 0.827191 | − | 0.561921i | \(-0.189938\pi\) |
−0.900233 | + | 0.435408i | \(0.856604\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.14833 | − | 5.45306i | 0.123015 | − | 0.213069i | ||||
\(656\) | −5.26140 | −0.205423 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.7992 | + | 20.4368i | −0.459632 | + | 0.796105i | −0.998941 | − | 0.0460022i | \(-0.985352\pi\) |
0.539310 | + | 0.842107i | \(0.318685\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.2588 | − | 29.8930i | −0.671288 | − | 1.16270i | −0.977539 | − | 0.210754i | \(-0.932408\pi\) |
0.306252 | − | 0.951951i | \(-0.400925\pi\) | |||||||
\(662\) | −17.0488 | − | 29.5293i | −0.662619 | − | 1.14769i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.36767 | − | 9.29708i | 0.208306 | − | 0.360796i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.5673 | 0.525329 | ||||||||
\(668\) | 1.73424 | − | 3.00379i | 0.0670996 | − | 0.116220i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9.57072 | + | 16.5770i | 0.369749 | + | 0.640424i | ||||
\(671\) | −3.42807 | − | 5.93759i | −0.132339 | − | 0.229218i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.2287 | − | 21.1808i | 0.471382 | − | 0.816458i | −0.528082 | − | 0.849194i | \(-0.677088\pi\) |
0.999464 | + | 0.0327353i | \(0.0104218\pi\) | |||||||
\(674\) | 10.8887 | 0.419418 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.8406 | 0.416946 | ||||||||
\(677\) | −4.16022 | + | 7.20572i | −0.159890 | + | 0.276938i | −0.934829 | − | 0.355098i | \(-0.884447\pi\) |
0.774939 | + | 0.632037i | \(0.217781\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 6.79734 | + | 11.7733i | 0.260666 | + | 0.451487i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.03731 | − | 5.26078i | 0.116305 | − | 0.201446i | ||||
\(683\) | 42.4624 | 1.62478 | 0.812389 | − | 0.583116i | \(-0.198167\pi\) | ||||
0.812389 | + | 0.583116i | \(0.198167\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.3215 | −0.508989 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 17.4258 | + | 30.1824i | 0.664352 | + | 1.15069i | ||||
\(689\) | −17.3737 | − | 30.0921i | −0.661885 | − | 1.14642i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.6964 | + | 30.6511i | −0.673204 | + | 1.16602i | 0.303786 | + | 0.952740i | \(0.401749\pi\) |
−0.976990 | + | 0.213284i | \(0.931584\pi\) | |||||||
\(692\) | −14.3212 | −0.544410 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 49.6167 | 1.88342 | ||||||||
\(695\) | −4.17920 | + | 7.23859i | −0.158526 | + | 0.274575i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.99931 | − | 6.92701i | −0.151485 | − | 0.262379i | ||||
\(698\) | 3.69146 | + | 6.39380i | 0.139724 | + | 0.242009i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.00372 | 0.264527 | 0.132263 | − | 0.991215i | \(-0.457776\pi\) | ||||
0.132263 | + | 0.991215i | \(0.457776\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31.1733 | 1.17572 | ||||||||
\(704\) | −0.584722 | + | 1.01277i | −0.0220375 | + | 0.0381701i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21.8408 | + | 37.8294i | 0.821989 | + | 1.42373i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.11126 | − | 1.92477i | 0.0417344 | − | 0.0722861i | −0.844404 | − | 0.535707i | \(-0.820045\pi\) |
0.886138 | + | 0.463421i | \(0.153378\pi\) | |||||||
\(710\) | −6.93825 | −0.260388 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.59343 | 0.0597165 | ||||||||
\(713\) | −7.52373 | + | 13.0315i | −0.281766 | + | 0.488033i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.40180 | + | 2.42800i | 0.0524245 | + | 0.0908019i | ||||
\(716\) | 6.34913 | + | 10.9970i | 0.237278 | + | 0.410977i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 17.5803 | − | 30.4500i | 0.656092 | − | 1.13638i | ||||
\(719\) | −26.0175 | −0.970291 | −0.485145 | − | 0.874434i | \(-0.661233\pi\) | ||||
−0.485145 | + | 0.874434i | \(0.661233\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.766951 | + | 1.32840i | −0.0285430 | + | 0.0494379i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.72670 | − | 9.91893i | −0.212831 | − | 0.368634i | ||||
\(725\) | −11.2250 | − | 19.4423i | −0.416886 | − | 0.722068i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.685875 | − | 1.18797i | 0.0254377 | − | 0.0440594i | −0.853026 | − | 0.521868i | \(-0.825235\pi\) |
0.878464 | + | 0.477809i | \(0.158569\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.19777 | 0.266401 | ||||||||
\(731\) | −26.4915 | + | 45.8847i | −0.979824 | + | 1.69711i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.400087 | + | 0.692971i | 0.0147776 | + | 0.0255955i | 0.873320 | − | 0.487148i | \(-0.161963\pi\) |
−0.858542 | + | 0.512743i | \(0.828629\pi\) | |||||||
\(734\) | 2.42011 | + | 4.19176i | 0.0893280 | + | 0.154721i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.82072 | + | 10.0818i | −0.214555 | + | 0.371620i | ||||
\(737\) | −6.98034 | −0.257124 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.37093 | 0.197573 | 0.0987865 | − | 0.995109i | \(-0.468504\pi\) | ||||
0.0987865 | + | 0.995109i | \(0.468504\pi\) | |||||||
\(740\) | 2.94756 | − | 5.10532i | 0.108354 | − | 0.187675i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.63162 | − | 11.4863i | −0.243290 | − | 0.421391i | 0.718359 | − | 0.695672i | \(-0.244893\pi\) |
−0.961650 | + | 0.274281i | \(0.911560\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.07218 | + | 3.58912i | −0.0759188 | + | 0.131495i | ||||
\(746\) | 36.4276 | 1.33371 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.96485 | 0.144969 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.77816 | − | 4.81191i | −0.101377 | − | 0.175589i | 0.810875 | − | 0.585219i | \(-0.198991\pi\) |
−0.912252 | + | 0.409629i | \(0.865658\pi\) | |||||||
\(752\) | 18.6457 | + | 32.2953i | 0.679939 | + | 1.17769i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −23.3645 | + | 40.4684i | −0.850883 | + | 1.47377i | ||||
\(755\) | −12.0119 | −0.437158 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.3942 | −0.486819 | −0.243410 | − | 0.969924i | \(-0.578266\pi\) | ||||
−0.243410 | + | 0.969924i | \(0.578266\pi\) | |||||||
\(758\) | −22.9869 | + | 39.8145i | −0.834923 | + | 1.44613i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.99931 | − | 6.92701i | −0.145070 | − | 0.251269i | ||||
\(761\) | −6.42191 | − | 11.1231i | −0.232794 | − | 0.403211i | 0.725835 | − | 0.687868i | \(-0.241453\pi\) |
−0.958629 | + | 0.284658i | \(0.908120\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.92353 | 0.0695910 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.5202 | 0.885951 | ||||||||
\(767\) | −26.1785 | + | 45.3425i | −0.945251 | + | 1.63722i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.48259 | − | 2.56793i | −0.0534636 | − | 0.0926018i | 0.838055 | − | 0.545586i | \(-0.183693\pi\) |
−0.891519 | + | 0.452984i | \(0.850359\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.63533 | + | 8.02864i | −0.166829 | + | 0.288957i | ||||
\(773\) | 19.2788 | 0.693409 | 0.346705 | − | 0.937974i | \(-0.387301\pi\) | ||||
0.346705 | + | 0.937974i | \(0.387301\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24.8992 | 0.894406 | ||||||||
\(776\) | −3.21683 | + | 5.57171i | −0.115477 | + | 0.200013i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.19028 | − | 8.98983i | −0.186080 | − | 0.322301i | ||||
\(779\) | 2.35305 | + | 4.07560i | 0.0843068 | + | 0.146024i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.26509 | − | 2.19120i | 0.0452685 | − | 0.0784074i | ||||
\(782\) | −31.9231 | −1.14157 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.35098 | + | 9.26818i | −0.190985 | + | 0.330795i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.82265 | − | 11.8172i | −0.243201 | − | 0.421237i | 0.718423 | − | 0.695606i | \(-0.244864\pi\) |
−0.961624 | + | 0.274370i | \(0.911531\pi\) | |||||||
\(788\) | −8.34734 | − | 14.4580i | −0.297362 | − | 0.515046i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.07598 | − | 1.86364i | 0.0382815 | − | 0.0663055i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −58.4944 | −2.07720 | ||||||||
\(794\) | 10.9518 | − | 18.9691i | 0.388665 | − | 0.673187i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.74427 | − | 6.48527i | −0.132712 | − | 0.229864i | ||||
\(797\) | −11.4792 | − | 19.8826i | −0.406616 | − | 0.704279i | 0.587892 | − | 0.808939i | \(-0.299958\pi\) |
−0.994508 | + | 0.104660i | \(0.966625\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −28.3461 | + | 49.0969i | −1.00281 | + | 1.73692i | ||||
\(800\) | 19.2632 | 0.681058 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −14.2609 | −0.503570 | ||||||||
\(803\) | −1.31241 | + | 2.27316i | −0.0463140 | + | 0.0802182i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −25.9134 | − | 44.8834i | −0.912761 | − | 1.58095i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.05326 | − | 15.6807i | 0.318492 | − | 0.551645i | ||||
\(809\) | −39.4582 | −1.38728 | −0.693639 | − | 0.720323i | \(-0.743994\pi\) | ||||
−0.693639 | + | 0.720323i | \(0.743994\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.496374 | −0.0174300 | −0.00871502 | − | 0.999962i | \(-0.502774\pi\) | ||||
−0.00871502 | + | 0.999962i | \(0.502774\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.49381 | + | 6.05146i | 0.122458 | + | 0.212103i | ||||
\(815\) | 0.790841 | + | 1.36978i | 0.0277020 | + | 0.0479812i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.5867 | − | 26.9969i | 0.545308 | − | 0.944501i | ||||
\(818\) | 11.5790 | 0.404850 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.889960 | 0.0310788 | ||||||||
\(821\) | 23.5519 | − | 40.7931i | 0.821967 | − | 1.42369i | −0.0822476 | − | 0.996612i | \(-0.526210\pi\) |
0.904215 | − | 0.427077i | \(-0.140457\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.09888 | + | 1.90332i | 0.0383047 | + | 0.0663457i | 0.884542 | − | 0.466460i | \(-0.154471\pi\) |
−0.846237 | + | 0.532806i | \(0.821138\pi\) | |||||||
\(824\) | −11.0046 | − | 19.0605i | −0.383364 | − | 0.664005i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 55.3360 | 1.92422 | 0.962110 | − | 0.272661i | \(-0.0879036\pi\) | ||||
0.962110 | + | 0.272661i | \(0.0879036\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.3206 | −0.705764 | −0.352882 | − | 0.935668i | \(-0.614798\pi\) | ||||
−0.352882 | + | 0.935668i | \(0.614798\pi\) | |||||||
\(830\) | −4.58520 | + | 7.94181i | −0.159155 | + | 0.275664i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.98867 | + | 8.64062i | 0.172951 | + | 0.299560i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.85236 | − | 3.20839i | 0.0641036 | − | 0.111031i | ||||
\(836\) | −2.33277 | −0.0806806 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 17.5480 | 0.606186 | ||||||||
\(839\) | 12.2760 | − | 21.2626i | 0.423813 | − | 0.734066i | −0.572496 | − | 0.819908i | \(-0.694025\pi\) |
0.996309 | + | 0.0858417i | \(0.0273579\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.499311 | − | 0.864833i | −0.0172176 | − | 0.0298218i | ||||
\(842\) | −2.66504 | − | 4.61598i | −0.0918432 | − | 0.159077i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.98693 | + | 8.63762i | −0.171657 | + | 0.297319i | ||||
\(845\) | 11.5790 | 0.398329 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −17.2625 | + | 29.8996i | −0.592798 | + | 1.02676i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 26.4118 | + | 45.7465i | 0.905916 | + | 1.56909i | ||||
\(851\) | −8.65452 | − | 14.9901i | −0.296673 | − | 0.513853i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.7708 | + | 46.3684i | −0.916614 | + | 1.58762i | −0.112093 | + | 0.993698i | \(0.535756\pi\) |
−0.804521 | + | 0.593925i | \(0.797578\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.17439 | −0.245215 | ||||||||
\(857\) | 27.0777 | − | 46.8999i | 0.924955 | − | 1.60207i | 0.133322 | − | 0.991073i | \(-0.457436\pi\) |
0.791633 | − | 0.610996i | \(-0.209231\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.896461 | + | 1.55272i | 0.0305869 | + | 0.0529780i | 0.880914 | − | 0.473277i | \(-0.156929\pi\) |
−0.850327 | + | 0.526255i | \(0.823596\pi\) | |||||||
\(860\) | −2.94756 | − | 5.10532i | −0.100511 | − | 0.174090i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27.0858 | − | 46.9140i | 0.922547 | − | 1.59790i | ||||
\(863\) | 32.5709 | 1.10873 | 0.554363 | − | 0.832275i | \(-0.312962\pi\) | ||||
0.554363 | + | 0.832275i | \(0.312962\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.2967 | −0.520102 | ||||||||
\(866\) | −6.36387 | + | 11.0226i | −0.216253 | + | 0.374562i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.392378 | + | 0.679618i | 0.0133105 | + | 0.0230545i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29.7770 | + | 51.5753i | −1.00896 | + | 1.74756i | ||||
\(872\) | 24.2967 | 0.822789 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 18.7824 | 0.635324 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.3647 | + | 31.8085i | 0.620131 | + | 1.07410i | 0.989461 | + | 0.144800i | \(0.0462538\pi\) |
−0.369330 | + | 0.929298i | \(0.620413\pi\) | |||||||
\(878\) | −1.94548 | − | 3.36966i | −0.0656566 | − | 0.113721i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.39284 | − | 2.41246i | 0.0469525 | − | 0.0813241i | ||||
\(881\) | 25.3721 | 0.854807 | 0.427403 | − | 0.904061i | \(-0.359428\pi\) | ||||
0.427403 | + | 0.904061i | \(0.359428\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.9381 | −0.570012 | −0.285006 | − | 0.958526i | \(-0.591996\pi\) | ||||
−0.285006 | + | 0.958526i | \(0.591996\pi\) | |||||||
\(884\) | 16.9134 | − | 29.2949i | 0.568860 | − | 0.985294i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 31.7403 | + | 54.9759i | 1.06634 | + | 1.84695i | ||||
\(887\) | 24.0069 | + | 41.5811i | 0.806071 | + | 1.39616i | 0.915566 | + | 0.402169i | \(0.131744\pi\) |
−0.109494 | + | 0.993987i | \(0.534923\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1.36115 | −0.0456260 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −18.4456 | −0.617603 | ||||||||
\(893\) | 16.6778 | − | 28.8868i | 0.558102 | − | 0.966661i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.78159 | + | 11.7461i | 0.226684 | + | 0.392627i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.27128 | + | 9.13013i | −0.175905 | + | 0.304676i | ||||
\(899\) | 33.2713 | 1.10966 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −52.4867 | −1.74858 | ||||||||
\(902\) | −0.527445 | + | 0.913562i | −0.0175620 | + | 0.0304183i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.51918 | − | 14.7557i | −0.283344 | − | 0.490766i | ||||
\(905\) | −6.11677 | − | 10.5945i | −0.203328 | − | 0.352175i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.3887 | − | 21.4579i | 0.411361 | − | 0.712499i | −0.583678 | − | 0.811985i | \(-0.698387\pi\) |
0.995039 | + | 0.0994869i | \(0.0317201\pi\) | |||||||
\(908\) | 9.26972 | 0.307626 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.7916 | − | 27.3519i | 0.523200 | − | 0.906209i | −0.476435 | − | 0.879210i | \(-0.658071\pi\) |
0.999635 | − | 0.0269997i | \(-0.00859533\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.67209 | − | 2.89615i | −0.0553382 | − | 0.0958486i | ||||
\(914\) | −17.1421 | − | 29.6911i | −0.567011 | − | 0.982093i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.69183 | + | 11.5906i | −0.221104 | + | 0.382964i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.59208 | 0.0525180 | 0.0262590 | − | 0.999655i | \(-0.491641\pi\) | ||||
0.0262590 | + | 0.999655i | \(0.491641\pi\) | |||||||
\(920\) | −2.22062 | + | 3.84623i | −0.0732118 | + | 0.126807i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −19.1514 | − | 33.1712i | −0.630718 | − | 1.09244i | ||||
\(923\) | −10.7934 | − | 18.6947i | −0.355268 | − | 0.615342i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.3207 | + | 24.8042i | −0.470863 | + | 0.815558i | ||||
\(926\) | −46.9591 | −1.54317 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 25.7403 | 0.844968 | ||||||||
\(929\) | 13.5356 | − | 23.4443i | 0.444087 | − | 0.769182i | −0.553901 | − | 0.832583i | \(-0.686861\pi\) |
0.997988 | + | 0.0634007i | \(0.0201946\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.94939 | + | 3.37644i | 0.0638543 | + | 0.110599i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 17.1003 | − | 29.6186i | 0.559540 | − | 0.969151i | ||||
\(935\) | 4.23491 | 0.138496 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.6624 | 1.06704 | 0.533518 | − | 0.845789i | \(-0.320870\pi\) | ||||
0.533518 | + | 0.845789i | \(0.320870\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.15390 | − | 5.46272i | −0.102869 | − | 0.178174i | ||||
\(941\) | 2.36143 | + | 4.09011i | 0.0769803 | + | 0.133334i | 0.901946 | − | 0.431849i | \(-0.142139\pi\) |
−0.824965 | + | 0.565183i | \(0.808805\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.30654 | − | 2.26299i | 0.0425466 | − | 0.0736929i | ||||
\(944\) | 52.0220 | 1.69317 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.98762 | 0.227187 | ||||||||
\(947\) | 28.3905 | − | 49.1738i | 0.922568 | − | 1.59793i | 0.127141 | − | 0.991885i | \(-0.459420\pi\) |
0.795427 | − | 0.606050i | \(-0.207247\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.1971 | + | 19.3939i | 0.363473 | + | 0.629553i | ||||
\(950\) | −15.5397 | − | 26.9156i | −0.504175 | − | 0.873257i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 47.1693 | 1.52796 | 0.763982 | − | 0.645238i | \(-0.223242\pi\) | ||||
0.763982 | + | 0.645238i | \(0.223242\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.05455 | 0.0664838 | ||||||||
\(956\) | −4.24426 | + | 7.35127i | −0.137269 | + | 0.237757i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.14681 | − | 14.1107i | −0.263211 | − | 0.455896i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.95056 | + | 5.11052i | −0.0951793 | + | 0.164855i | ||||
\(962\) | 59.6162 | 1.92210 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.36359 | 0.301581 | ||||||||
\(965\) | −4.95107 | + | 8.57550i | −0.159380 | + | 0.276055i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.6985 | − | 41.0469i | −0.762091 | − | 1.31998i | −0.941771 | − | 0.336255i | \(-0.890840\pi\) |
0.179680 | − | 0.983725i | \(-0.442494\pi\) | |||||||
\(968\) | −10.0611 | − | 17.4264i | −0.323377 | − | 0.560106i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.74790 | − | 4.75950i | 0.0882297 | − | 0.152818i | ||||
\(971\) | −22.7473 | −0.729994 | −0.364997 | − | 0.931009i | \(-0.618930\pi\) | ||||
−0.364997 | + | 0.931009i | \(0.618930\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −11.1106 | + | 19.2441i | −0.356006 | + | 0.616620i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 29.0601 | + | 50.3335i | 0.930190 | + | 1.61114i | ||||
\(977\) | 17.8425 | + | 30.9040i | 0.570831 | + | 0.988708i | 0.996481 | + | 0.0838200i | \(0.0267121\pi\) |
−0.425650 | + | 0.904888i | \(0.639955\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.248187 | − | 0.429872i | 0.00793209 | − | 0.0137388i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −26.0741 | −0.832059 | ||||||||
\(983\) | 12.0067 | − | 20.7962i | 0.382954 | − | 0.663296i | −0.608529 | − | 0.793532i | \(-0.708240\pi\) |
0.991483 | + | 0.130236i | \(0.0415735\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.91591 | − | 15.4428i | −0.284085 | − | 0.492049i | ||||
\(986\) | 35.2925 | + | 61.1284i | 1.12394 | + | 1.94672i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9.95125 | + | 17.2361i | −0.316591 | + | 0.548352i | ||||
\(989\) | −17.3090 | −0.550395 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44.4189 | −1.41101 | −0.705507 | − | 0.708703i | \(-0.749281\pi\) | ||||
−0.705507 | + | 0.708703i | \(0.749281\pi\) | |||||||
\(992\) | −14.2742 | + | 24.7237i | −0.453208 | + | 0.784979i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.99931 | − | 6.92701i | −0.126787 | − | 0.219601i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.52336 | + | 7.83470i | −0.143256 | + | 0.248127i | −0.928721 | − | 0.370779i | \(-0.879091\pi\) |
0.785465 | + | 0.618906i | \(0.212424\pi\) | |||||||
\(998\) | 8.26929 | 0.261760 | ||||||||
\(999\) | 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 | 1323.2.f.g.883.1 | 12 | ||
3.2 | odd | 2 | 441.2.f.g.295.6 | yes | 12 | ||
7.2 | even | 3 | 1323.2.h.g.802.5 | 12 | |||
7.3 | odd | 6 | 1323.2.g.g.667.1 | 12 | |||
7.4 | even | 3 | 1323.2.g.g.667.2 | 12 | |||
7.5 | odd | 6 | 1323.2.h.g.802.6 | 12 | |||
7.6 | odd | 2 | inner | 1323.2.f.g.883.2 | 12 | ||
9.2 | odd | 6 | 3969.2.a.be.1.1 | 6 | |||
9.4 | even | 3 | inner | 1323.2.f.g.442.1 | 12 | ||
9.5 | odd | 6 | 441.2.f.g.148.6 | yes | 12 | ||
9.7 | even | 3 | 3969.2.a.bd.1.6 | 6 | |||
21.2 | odd | 6 | 441.2.h.g.214.2 | 12 | |||
21.5 | even | 6 | 441.2.h.g.214.1 | 12 | |||
21.11 | odd | 6 | 441.2.g.g.79.5 | 12 | |||
21.17 | even | 6 | 441.2.g.g.79.6 | 12 | |||
21.20 | even | 2 | 441.2.f.g.295.5 | yes | 12 | ||
63.4 | even | 3 | 1323.2.h.g.226.5 | 12 | |||
63.5 | even | 6 | 441.2.g.g.67.6 | 12 | |||
63.13 | odd | 6 | inner | 1323.2.f.g.442.2 | 12 | ||
63.20 | even | 6 | 3969.2.a.be.1.2 | 6 | |||
63.23 | odd | 6 | 441.2.g.g.67.5 | 12 | |||
63.31 | odd | 6 | 1323.2.h.g.226.6 | 12 | |||
63.32 | odd | 6 | 441.2.h.g.373.2 | 12 | |||
63.34 | odd | 6 | 3969.2.a.bd.1.5 | 6 | |||
63.40 | odd | 6 | 1323.2.g.g.361.1 | 12 | |||
63.41 | even | 6 | 441.2.f.g.148.5 | ✓ | 12 | ||
63.58 | even | 3 | 1323.2.g.g.361.2 | 12 | |||
63.59 | even | 6 | 441.2.h.g.373.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.g.148.5 | ✓ | 12 | 63.41 | even | 6 | ||
441.2.f.g.148.6 | yes | 12 | 9.5 | odd | 6 | ||
441.2.f.g.295.5 | yes | 12 | 21.20 | even | 2 | ||
441.2.f.g.295.6 | yes | 12 | 3.2 | odd | 2 | ||
441.2.g.g.67.5 | 12 | 63.23 | odd | 6 | |||
441.2.g.g.67.6 | 12 | 63.5 | even | 6 | |||
441.2.g.g.79.5 | 12 | 21.11 | odd | 6 | |||
441.2.g.g.79.6 | 12 | 21.17 | even | 6 | |||
441.2.h.g.214.1 | 12 | 21.5 | even | 6 | |||
441.2.h.g.214.2 | 12 | 21.2 | odd | 6 | |||
441.2.h.g.373.1 | 12 | 63.59 | even | 6 | |||
441.2.h.g.373.2 | 12 | 63.32 | odd | 6 | |||
1323.2.f.g.442.1 | 12 | 9.4 | even | 3 | inner | ||
1323.2.f.g.442.2 | 12 | 63.13 | odd | 6 | inner | ||
1323.2.f.g.883.1 | 12 | 1.1 | even | 1 | trivial | ||
1323.2.f.g.883.2 | 12 | 7.6 | odd | 2 | inner | ||
1323.2.g.g.361.1 | 12 | 63.40 | odd | 6 | |||
1323.2.g.g.361.2 | 12 | 63.58 | even | 3 | |||
1323.2.g.g.667.1 | 12 | 7.3 | odd | 6 | |||
1323.2.g.g.667.2 | 12 | 7.4 | even | 3 | |||
1323.2.h.g.226.5 | 12 | 63.4 | even | 3 | |||
1323.2.h.g.226.6 | 12 | 63.31 | odd | 6 | |||
1323.2.h.g.802.5 | 12 | 7.2 | even | 3 | |||
1323.2.h.g.802.6 | 12 | 7.5 | odd | 6 | |||
3969.2.a.bd.1.5 | 6 | 63.34 | odd | 6 | |||
3969.2.a.bd.1.6 | 6 | 9.7 | even | 3 | |||
3969.2.a.be.1.1 | 6 | 9.2 | odd | 6 | |||
3969.2.a.be.1.2 | 6 | 63.20 | even | 6 |