Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [288,2,Mod(47,288)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(288, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("288.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 288 = 2^{5} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 288.p (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.29969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 7 x^{14} - 12 x^{13} + 16 x^{12} - 12 x^{11} - 8 x^{10} + 36 x^{9} - 68 x^{8} + 72 x^{7} - 32 x^{6} - 96 x^{5} + 256 x^{4} - 384 x^{3} + 448 x^{2} - 384 x + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 239.5 | ||
Root | \(-0.409484 + 1.35363i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 288.239 |
Dual form | 288.2.p.b.47.5 |
$q$-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 \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | 1.12774 | + | 1.31461i | 0.651100 | + | 0.758992i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.565188 | + | 0.978934i | −0.252760 | + | 0.437793i | −0.964285 | − | 0.264868i | \(-0.914672\pi\) |
0.711525 | + | 0.702661i | \(0.248005\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.71499 | + | 2.14485i | −1.40413 | + | 0.810677i | −0.994814 | − | 0.101714i | \(-0.967567\pi\) |
−0.409320 | + | 0.912391i | \(0.634234\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.456412 | + | 2.96508i | −0.152137 | + | 0.988359i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00953 | + | 0.582853i | −0.304385 | + | 0.175737i | −0.644411 | − | 0.764679i | \(-0.722897\pi\) |
0.340026 | + | 0.940416i | \(0.389564\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.64466 | + | 1.52689i | 0.733496 | + | 0.423484i | 0.819700 | − | 0.572793i | \(-0.194140\pi\) |
−0.0862038 | + | 0.996278i | \(0.527474\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.92430 | + | 0.360979i | −0.496853 | + | 0.0932043i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.49654i | − | 0.362963i | −0.983394 | − | 0.181482i | \(-0.941911\pi\) | ||
0.983394 | − | 0.181482i | \(-0.0580893\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.42378 | 0.785468 | 0.392734 | − | 0.919652i | \(-0.371529\pi\) | ||||
0.392734 | + | 0.919652i | \(0.371529\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.00918 | − | 2.46494i | −1.52953 | − | 0.537894i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.85938 | − | 6.68464i | 0.804736 | − | 1.39384i | −0.111733 | − | 0.993738i | \(-0.535640\pi\) |
0.916469 | − | 0.400106i | \(-0.131027\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.86113 | + | 3.22356i | 0.372225 | + | 0.644713i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.41264 | + | 2.74383i | −0.849213 | + | 0.528050i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.709580 | − | 1.22903i | −0.131766 | − | 0.228225i | 0.792592 | − | 0.609753i | \(-0.208731\pi\) |
−0.924357 | + | 0.381528i | \(0.875398\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.66408 | + | 2.69281i | 0.837694 | + | 0.483643i | 0.856480 | − | 0.516181i | \(-0.172647\pi\) |
−0.0187859 | + | 0.999824i | \(0.505980\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.90471 | − | 0.669837i | −0.331568 | − | 0.116604i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 4.84897i | − | 0.819625i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.97201i | 0.488596i | 0.969700 | + | 0.244298i | \(0.0785575\pi\) | ||||
−0.969700 | + | 0.244298i | \(0.921443\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.975209 | + | 5.19864i | 0.156158 | + | 0.832448i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.23339 | − | 2.44415i | −0.661144 | − | 0.381712i | 0.131569 | − | 0.991307i | \(-0.457999\pi\) |
−0.792713 | + | 0.609595i | \(0.791332\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.74292 | + | 3.01882i | 0.265793 | + | 0.460366i | 0.967771 | − | 0.251832i | \(-0.0810330\pi\) |
−0.701978 | + | 0.712198i | \(0.747700\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.64466 | − | 2.12262i | −0.394242 | − | 0.316422i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.77991 | + | 3.08289i | 0.259627 | + | 0.449686i | 0.966142 | − | 0.258011i | \(-0.0830672\pi\) |
−0.706515 | + | 0.707698i | \(0.749734\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.70075 | − | 9.87399i | 0.814393 | − | 1.41057i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.96737 | − | 1.68770i | 0.275486 | − | 0.236326i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.2786 | 1.54923 | 0.774616 | − | 0.632432i | \(-0.217943\pi\) | ||||
0.774616 | + | 0.632432i | \(0.217943\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.31769i | − | 0.177677i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.86113 | + | 4.50094i | 0.511419 | + | 0.596164i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.50935 | − | 4.33553i | −0.977634 | − | 0.564437i | −0.0760791 | − | 0.997102i | \(-0.524240\pi\) |
−0.901555 | + | 0.432664i | \(0.857573\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.16057 | + | 1.82476i | −0.404670 | + | 0.233636i | −0.688497 | − | 0.725239i | \(-0.741729\pi\) |
0.283827 | + | 0.958875i | \(0.408396\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.66408 | − | 11.9942i | −0.587619 | − | 1.51112i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.98946 | + | 1.72596i | −0.370796 | + | 0.214079i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.58255 | − | 9.66925i | 0.682017 | − | 1.18129i | −0.292348 | − | 0.956312i | \(-0.594437\pi\) |
0.974364 | − | 0.224975i | \(-0.0722301\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13.1401 | − | 2.46494i | 1.58188 | − | 0.296744i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.54954 | −0.302574 | −0.151287 | − | 0.988490i | \(-0.548342\pi\) | ||||
−0.151287 | + | 0.988490i | \(0.548342\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.06491 | −0.826885 | −0.413442 | − | 0.910530i | \(-0.635674\pi\) | ||||
−0.413442 | + | 0.910530i | \(0.635674\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.13887 | + | 6.08200i | −0.246976 | + | 0.702288i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.50026 | − | 4.33059i | 0.284932 | − | 0.493516i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.24998 | − | 1.29902i | 0.253142 | − | 0.146152i | −0.368060 | − | 0.929802i | \(-0.619978\pi\) |
0.621202 | + | 0.783650i | \(0.286645\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.58338 | − | 2.70659i | −0.953709 | − | 0.300732i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.98482 | − | 2.30064i | 0.437391 | − | 0.252528i | −0.265099 | − | 0.964221i | \(-0.585405\pi\) |
0.702490 | + | 0.711693i | \(0.252071\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.46501 | + | 0.845824i | 0.158903 | + | 0.0917425i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.815476 | − | 2.31885i | 0.0874282 | − | 0.248606i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 8.63803i | − | 0.915630i | −0.889048 | − | 0.457815i | \(-0.848632\pi\) | ||
0.889048 | − | 0.457815i | \(-0.151368\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.0998 | −1.37323 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.71986 | + | 9.16824i | 0.178342 | + | 0.950702i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.93508 | + | 3.35165i | −0.198535 | + | 0.343872i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.35869 | + | 5.81742i | 0.341023 | + | 0.590670i | 0.984623 | − | 0.174693i | \(-0.0558931\pi\) |
−0.643600 | + | 0.765362i | \(0.722560\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.26744 | − | 3.25936i | −0.127383 | − | 0.327578i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.86479 | − | 11.8902i | −0.683072 | − | 1.18312i | −0.974039 | − | 0.226382i | \(-0.927310\pi\) |
0.290967 | − | 0.956733i | \(-0.406023\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.48137 | + | 3.16467i | 0.540095 | + | 0.311824i | 0.745118 | − | 0.666933i | \(-0.232393\pi\) |
−0.205022 | + | 0.978757i | \(0.565727\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.37451 | − | 5.46837i | 0.622089 | − | 0.533658i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.4483i | 1.01007i | 0.863097 | + | 0.505037i | \(0.168521\pi\) | ||||
−0.863097 | + | 0.505037i | \(0.831479\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 9.67531i | − | 0.926727i | −0.886168 | − | 0.463364i | \(-0.846642\pi\) | ||
0.886168 | − | 0.463364i | \(-0.153358\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.90704 | + | 3.35165i | −0.370840 | + | 0.318125i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.15149 | + | 4.12891i | 0.672756 | + | 0.388416i | 0.797120 | − | 0.603821i | \(-0.206356\pi\) |
−0.124364 | + | 0.992237i | \(0.539689\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.36255 | + | 7.55615i | 0.406810 | + | 0.704615i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.73441 | + | 7.14472i | −0.530146 | + | 0.660530i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.20984 | + | 5.55961i | 0.294246 | + | 0.509649i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.82056 | + | 8.34946i | −0.438233 | + | 0.759042i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.56105 | − | 8.32162i | −0.140755 | − | 0.750335i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.85942 | −0.881853 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.78757i | − | 0.247357i | −0.992322 | − | 0.123678i | \(-0.960531\pi\) | ||
0.992322 | − | 0.123678i | \(-0.0394691\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.00303 | + | 5.69571i | −0.176357 | + | 0.501479i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.0529 | + | 7.53612i | 1.14044 | + | 0.658434i | 0.946540 | − | 0.322587i | \(-0.104553\pi\) |
0.193901 | + | 0.981021i | \(0.437886\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.7193 | + | 7.34348i | −1.10290 | + | 0.636761i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.192056 | − | 5.87046i | −0.0165295 | − | 0.505249i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.55211 | − | 4.36021i | 0.645220 | − | 0.372518i | −0.141402 | − | 0.989952i | \(-0.545161\pi\) |
0.786623 | + | 0.617434i | \(0.211828\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.18897 | + | 2.05935i | −0.100847 | + | 0.174672i | −0.912034 | − | 0.410115i | \(-0.865489\pi\) |
0.811187 | + | 0.584787i | \(0.198822\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.04554 | + | 5.81659i | −0.172265 | + | 0.489845i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.55982 | −0.297687 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.60418 | 0.133220 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 19.4094 | − | 3.64100i | 1.60086 | − | 0.300305i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.94426 | + | 15.4919i | −0.732742 | + | 1.26915i | 0.222965 | + | 0.974826i | \(0.428426\pi\) |
−0.955707 | + | 0.294320i | \(0.904907\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.39162 | + | 1.38080i | −0.194627 | + | 0.112368i | −0.594147 | − | 0.804357i | \(-0.702510\pi\) |
0.399520 | + | 0.916725i | \(0.369177\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.43735 | + | 0.683037i | 0.358738 | + | 0.0552202i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.27216 | + | 3.04388i | −0.423470 | + | 0.244491i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.21148 | + | 1.27680i | 0.176495 | + | 0.101900i | 0.585645 | − | 0.810568i | \(-0.300841\pi\) |
−0.409150 | + | 0.912467i | \(0.634175\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.7193 | + | 14.8270i | 1.00871 | + | 1.17585i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 33.1111i | 2.60952i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.93355 | −0.543077 | −0.271539 | − | 0.962428i | \(-0.587532\pi\) | ||||
−0.271539 | + | 0.962428i | \(0.587532\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.73225 | − | 1.48601i | 0.134855 | − | 0.115685i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.36829 | + | 14.4943i | −0.647558 | + | 1.12160i | 0.336146 | + | 0.941810i | \(0.390876\pi\) |
−0.983704 | + | 0.179794i | \(0.942457\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.83719 | − | 3.18211i | −0.141322 | − | 0.244778i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.56265 | + | 10.1518i | −0.119499 | + | 0.776325i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.2190 | + | 17.6999i | 0.776938 | + | 1.34570i | 0.933699 | + | 0.358059i | \(0.116562\pi\) |
−0.156761 | + | 0.987637i | \(0.550105\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.8281 | − | 7.98367i | −1.04531 | − | 0.603508i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.76905 | − | 14.7612i | −0.208134 | − | 1.10952i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 4.07982i | − | 0.304940i | −0.988308 | − | 0.152470i | \(-0.951277\pi\) | ||
0.988308 | − | 0.152470i | \(-0.0487227\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 22.3226i | − | 1.65923i | −0.558337 | − | 0.829614i | \(-0.688560\pi\) | ||
0.558337 | − | 0.829614i | \(-0.311440\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.96315 | − | 2.09708i | −0.440809 | − | 0.155021i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.90940 | − | 1.67974i | −0.213904 | − | 0.123497i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.872261 | + | 1.51080i | 0.0637861 | + | 0.110481i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.5078 | − | 19.6577i | 0.764331 | − | 1.42989i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.27481 | − | 12.6003i | −0.526387 | − | 0.911728i | −0.999527 | − | 0.0307415i | \(-0.990213\pi\) |
0.473141 | − | 0.880987i | \(-0.343120\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.19526 | − | 3.80230i | 0.158018 | − | 0.273696i | −0.776136 | − | 0.630566i | \(-0.782823\pi\) |
0.934154 | + | 0.356870i | \(0.116156\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.64030 | − | 1.98354i | −0.403910 | − | 0.142044i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.69721 | −0.548404 | −0.274202 | − | 0.961672i | \(-0.588414\pi\) | ||||
−0.274202 | + | 0.961672i | \(0.588414\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 20.9790i | − | 1.48716i | −0.668646 | − | 0.743580i | \(-0.733126\pi\) | ||
0.668646 | − | 0.743580i | \(-0.266874\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 19.0070 | − | 3.56551i | 1.34065 | − | 0.251491i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.27216 | + | 3.04388i | 0.370033 | + | 0.213639i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.78532 | − | 2.76280i | 0.334221 | − | 0.192963i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 18.0590 | + | 14.4943i | 1.25519 | + | 1.00742i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.45641 | + | 1.99556i | −0.239085 | + | 0.138036i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.38482 | + | 4.13063i | −0.164178 | + | 0.284364i | −0.936363 | − | 0.351033i | \(-0.885830\pi\) |
0.772185 | + | 0.635397i | \(0.219164\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.87521 | − | 3.35165i | −0.197006 | − | 0.229651i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.94031 | −0.268727 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −23.1027 | −1.56831 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.96737 | − | 9.28761i | −0.538385 | − | 0.627599i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.28505 | − | 3.95783i | 0.153709 | − | 0.266232i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.5272 | + | 7.23260i | −0.838886 | + | 0.484331i | −0.856885 | − | 0.515507i | \(-0.827604\pi\) |
0.0179997 | + | 0.999838i | \(0.494270\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.4076 | + | 4.04711i | −0.693837 | + | 0.269807i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.561821 | + | 0.324367i | −0.0372894 | + | 0.0215290i | −0.518529 | − | 0.855060i | \(-0.673520\pi\) |
0.481239 | + | 0.876589i | \(0.340187\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.0007 | + | 6.92863i | 0.793032 | + | 0.457857i | 0.841029 | − | 0.540990i | \(-0.181950\pi\) |
−0.0479971 | + | 0.998847i | \(0.515284\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.51269 | − | 1.59689i | 0.560094 | − | 0.105068i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 23.1276i | − | 1.51514i | −0.652755 | − | 0.757569i | \(-0.726387\pi\) | ||
0.652755 | − | 0.757569i | \(-0.273613\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.02393 | −0.262492 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.24510 | + | 1.49289i | 0.275749 | + | 0.0969734i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.44075 | − | 12.8878i | 0.481302 | − | 0.833640i | −0.518468 | − | 0.855097i | \(-0.673497\pi\) |
0.999770 | + | 0.0214576i | \(0.00683070\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.87960 | − | 10.1838i | −0.378738 | − | 0.655994i | 0.612141 | − | 0.790749i | \(-0.290309\pi\) |
−0.990879 | + | 0.134755i | \(0.956975\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.12169 | − | 14.3361i | −0.392706 | − | 0.919664i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.44399 | + | 11.1613i | 0.411691 | + | 0.713071i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.05472 | + | 5.22774i | 0.576138 | + | 0.332633i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.51829 | + | 2.64398i | 0.476452 | + | 0.167555i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.51619i | 0.348179i | 0.984730 | + | 0.174089i | \(0.0556981\pi\) | ||||
−0.984730 | + | 0.174089i | \(0.944302\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.99781i | 0.565687i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.540218 | + | 2.87979i | 0.0338298 | + | 0.180339i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.9194 | + | 9.76841i | 1.05540 | + | 0.609337i | 0.924157 | − | 0.382013i | \(-0.124769\pi\) |
0.131245 | + | 0.991350i | \(0.458102\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.37451 | − | 11.0410i | −0.396093 | − | 0.686053i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.96803 | − | 1.54302i | 0.245615 | − | 0.0955104i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.62576 | − | 9.74411i | −0.346899 | − | 0.600847i | 0.638798 | − | 0.769375i | \(-0.279432\pi\) |
−0.985697 | + | 0.168527i | \(0.946099\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.37451 | + | 11.0410i | −0.391583 | + | 0.678242i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.3557 | − | 9.74144i | 0.694955 | − | 0.596167i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.1600 | −0.863350 | −0.431675 | − | 0.902029i | \(-0.642077\pi\) | ||||
−0.431675 | + | 0.902029i | \(0.642077\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.91574i | 0.237864i | 0.992902 | + | 0.118932i | \(0.0379471\pi\) | ||||
−0.992902 | + | 0.118932i | \(0.962053\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −14.7732 | − | 17.2212i | −0.894113 | − | 1.04227i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.75773 | − | 2.16953i | −0.226600 | − | 0.130827i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.9537 | − | 13.2523i | 1.37915 | − | 0.796253i | 0.387094 | − | 0.922040i | \(-0.373479\pi\) |
0.992057 | + | 0.125787i | \(0.0401455\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.1131 | + | 12.6003i | −0.605457 | + | 0.754362i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.923368 | + | 0.533106i | −0.0550835 | + | 0.0318025i | −0.527289 | − | 0.849686i | \(-0.676791\pi\) |
0.472205 | + | 0.881489i | \(0.343458\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.77840 | + | 3.08028i | −0.105715 | + | 0.183103i | −0.914030 | − | 0.405647i | \(-0.867046\pi\) |
0.808315 | + | 0.588750i | \(0.200380\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.58838 | + | 1.23591i | −0.390262 | + | 0.0732090i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 20.9693 | 1.23778 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.7604 | 0.868258 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.85993 | + | 10.9759i | −0.226273 | + | 0.643419i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.78958 | − | 13.4919i | 0.455072 | − | 0.788208i | −0.543620 | − | 0.839331i | \(-0.682947\pi\) |
0.998692 | + | 0.0511233i | \(0.0162802\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.48839 | − | 4.90077i | 0.494213 | − | 0.285334i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.85545 | − | 5.34190i | 0.165690 | − | 0.309969i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 20.4135 | − | 11.7857i | 1.18054 | − | 0.681586i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.9498 | − | 7.47659i | −0.746416 | − | 0.430944i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.88927 | − | 22.4335i | 0.453227 | − | 1.28877i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 4.12532i | − | 0.236215i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.960690 | 0.0548295 | 0.0274147 | − | 0.999624i | \(-0.491273\pi\) | ||||
0.0274147 | + | 0.999624i | \(0.491273\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.02124 | + | 10.7748i | 0.114984 | + | 0.612957i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.49539 | + | 7.78624i | −0.254910 | + | 0.441517i | −0.964871 | − | 0.262724i | \(-0.915379\pi\) |
0.709961 | + | 0.704241i | \(0.248713\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.55885 | + | 14.8244i | 0.483775 | + | 0.837923i | 0.999826 | − | 0.0186349i | \(-0.00593201\pi\) |
−0.516051 | + | 0.856558i | \(0.672599\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 14.3776 | + | 2.21313i | 0.810084 | + | 0.124696i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.96528 | − | 6.86806i | −0.222712 | − | 0.385749i | 0.732919 | − | 0.680316i | \(-0.238158\pi\) |
−0.955631 | + | 0.294568i | \(0.904824\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.43269 | + | 0.827162i | 0.0802151 | + | 0.0463122i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.7355 | + | 11.7829i | −0.766639 | + | 0.657660i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 5.12381i | − | 0.285096i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.3670i | 0.630526i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.7193 | − | 10.9112i | 0.703378 | − | 0.603392i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.2247 | − | 7.63528i | −0.729101 | − | 0.420946i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.78348 | − | 8.28523i | −0.262924 | − | 0.455397i | 0.704094 | − | 0.710107i | \(-0.251353\pi\) |
−0.967018 | + | 0.254710i | \(0.918020\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.81225 | − | 1.35646i | −0.482908 | − | 0.0743336i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.31037 | + | 10.9299i | 0.344773 | + | 0.597164i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.0727 | − | 29.5707i | 0.930007 | − | 1.61082i | 0.146702 | − | 0.989181i | \(-0.453134\pi\) |
0.783305 | − | 0.621638i | \(-0.213532\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.63709 | + | 14.0578i | 0.143227 | + | 0.763514i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.27805 | −0.339975 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.8811i | 1.01949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.01360 | + | 14.2564i | −0.269923 | + | 0.767540i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.9431 | − | 12.0915i | −1.12428 | − | 0.649105i | −0.181792 | − | 0.983337i | \(-0.558190\pi\) |
−0.942491 | + | 0.334232i | \(0.891523\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.71845 | + | 5.61095i | −0.520217 | + | 0.300347i | −0.737023 | − | 0.675867i | \(-0.763769\pi\) |
0.216807 | + | 0.976215i | \(0.430436\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.8595 | + | 0.518852i | −0.846515 | + | 0.0276943i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.85176 | + | 3.37852i | −0.311458 | + | 0.179820i | −0.647579 | − | 0.761999i | \(-0.724218\pi\) |
0.336121 | + | 0.941819i | \(0.390885\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.44097 | − | 2.49583i | 0.0764786 | − | 0.132465i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.68887 | + | 10.4895i | −0.195236 | + | 0.555163i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.3395 | 1.07348 | 0.536739 | − | 0.843748i | \(-0.319656\pi\) | ||||
0.536739 | + | 0.843748i | \(0.319656\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.27775 | −0.383039 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −16.4126 | + | 3.07884i | −0.861440 | + | 0.161597i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.99300 | − | 6.91608i | 0.209003 | − | 0.362004i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.7198 | − | 6.76642i | 0.611767 | − | 0.353204i | −0.161889 | − | 0.986809i | \(-0.551759\pi\) |
0.773657 | + | 0.633605i | \(0.218425\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.17925 | − | 11.4368i | 0.477853 | − | 0.595375i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −41.8998 | + | 24.1908i | −2.17533 | + | 1.25593i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.0364 | − | 13.3001i | −1.19278 | − | 0.688651i | −0.233843 | − | 0.972274i | \(-0.575130\pi\) |
−0.958936 | + | 0.283623i | \(0.908464\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.1188 | − | 12.9613i | −0.574175 | − | 0.669319i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 4.33381i | − | 0.223203i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.5030 | 1.46410 | 0.732050 | − | 0.681251i | \(-0.238564\pi\) | ||||
0.732050 | + | 0.681251i | \(0.238564\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.66457 | − | 3.14365i | 0.187742 | − | 0.161054i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.0515 | + | 17.4097i | −0.513606 | + | 0.889592i | 0.486269 | + | 0.873809i | \(0.338357\pi\) |
−0.999875 | + | 0.0157832i | \(0.994976\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.82624 | + | 4.89519i | 0.144038 | + | 0.249482i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.74654 | + | 3.79006i | −0.495444 | + | 0.192660i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.08110 | + | 1.87253i | 0.0548142 | + | 0.0949409i | 0.892130 | − | 0.451778i | \(-0.149210\pi\) |
−0.837316 | + | 0.546719i | \(0.815877\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.0038 | − | 5.77570i | −0.505914 | − | 0.292090i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.81323 | + | 25.6583i | 0.242795 | + | 1.29429i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.93677i | 0.147765i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.8504i | 0.946076i | 0.881042 | + | 0.473038i | \(0.156843\pi\) | ||||
−0.881042 | + | 0.473038i | \(0.843157\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −23.9979 | − | 8.43940i | −1.20140 | − | 0.422499i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.0668 | − | 8.69883i | −0.752401 | − | 0.434399i | 0.0741601 | − | 0.997246i | \(-0.476372\pi\) |
−0.826561 | + | 0.562848i | \(0.809706\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.22326 | + | 14.2431i | 0.409630 | + | 0.709500i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.50079 | − | 6.87283i | 0.372717 | − | 0.341513i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.73225 | − | 3.00034i | −0.0858643 | − | 0.148721i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.2872 | + | 17.8179i | −0.508667 | + | 0.881037i | 0.491282 | + | 0.871000i | \(0.336528\pi\) |
−0.999950 | + | 0.0100370i | \(0.996805\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.2488 | + | 5.01092i | 0.702841 | + | 0.247170i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 37.1962 | 1.83030 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.20117i | 0.255316i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.04810 | + | 0.759379i | −0.198236 | + | 0.0371870i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.1959 | + | 13.9695i | 1.18205 | + | 0.682455i | 0.956487 | − | 0.291774i | \(-0.0942454\pi\) |
0.225560 | + | 0.974229i | \(0.427579\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.27826 | + | 3.62475i | −0.305983 | + | 0.176660i | −0.645128 | − | 0.764075i | \(-0.723196\pi\) |
0.339144 | + | 0.940734i | \(0.389863\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.95340 | + | 3.87050i | −0.483951 | + | 0.188190i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.82418 | − | 2.78524i | 0.234007 | − | 0.135104i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.82766 | − | 13.5579i | 0.378807 | − | 0.656113i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.01455 | − | 4.67978i | −0.193824 | − | 0.225942i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −37.7004 | −1.81596 | −0.907982 | − | 0.419009i | \(-0.862377\pi\) | ||||
−0.907982 | + | 0.419009i | \(0.862377\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.1185 | 1.73575 | 0.867873 | − | 0.496787i | \(-0.165487\pi\) | ||||
0.867873 | + | 0.496787i | \(0.165487\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.80910 | + | 2.10888i | 0.0867397 | + | 0.101113i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.2137 | − | 22.8867i | 0.632095 | − | 1.09482i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.02239 | + | 5.20908i | −0.430615 | + | 0.248616i | −0.699609 | − | 0.714526i | \(-0.746642\pi\) |
0.268993 | + | 0.963142i | \(0.413309\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 26.6753 | + | 21.4098i | 1.27025 | + | 1.01951i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.7905 | − | 17.7769i | 1.46290 | − | 0.844606i | 0.463756 | − | 0.885963i | \(-0.346502\pi\) |
0.999144 | + | 0.0413574i | \(0.0131682\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.45606 | + | 4.88211i | 0.400856 | + | 0.231434i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −30.4526 | + | 5.71259i | −1.44036 | + | 0.270196i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.7750i | 0.791662i | 0.918323 | + | 0.395831i | \(0.129543\pi\) | ||||
−0.918323 | + | 0.395831i | \(0.870457\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.69832 | 0.268323 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.51234 | − | 1.58687i | −0.212008 | − | 0.0745575i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.40386 | − | 12.8239i | 0.347098 | − | 0.601192i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.679436 | − | 1.17682i | −0.0317827 | − | 0.0550492i | 0.849697 | − | 0.527272i | \(-0.176785\pi\) |
−0.881479 | + | 0.472223i | \(0.843452\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.10624 | + | 6.60368i | 0.191663 | + | 0.308233i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.07410 | − | 8.78860i | −0.236324 | − | 0.409326i | 0.723332 | − | 0.690500i | \(-0.242609\pi\) |
−0.959657 | + | 0.281174i | \(0.909276\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.2656 | + | 13.4324i | 1.08124 | + | 0.624256i | 0.931232 | − | 0.364428i | \(-0.118735\pi\) |
0.150012 | + | 0.988684i | \(0.452069\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.94715 | − | 3.49814i | −0.461288 | − | 0.162223i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 31.4118i | − | 1.45356i | −0.686868 | − | 0.726782i | \(-0.741015\pi\) | ||
0.686868 | − | 0.726782i | \(-0.258985\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 47.8949i | 2.21158i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.815476 | + | 4.34713i | 0.0375751 | + | 0.200305i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.51906 | − | 2.03173i | −0.161807 | − | 0.0934191i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.37208 | + | 11.0368i | 0.292371 | + | 0.506402i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.14767 | + | 33.4419i | −0.235696 | + | 1.53120i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.42488 | − | 4.20001i | −0.110796 | − | 0.191904i | 0.805296 | − | 0.592873i | \(-0.202007\pi\) |
−0.916091 | + | 0.400970i | \(0.868673\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.53794 | + | 7.85995i | −0.206912 | + | 0.358383i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −43.5283 | + | 37.3407i | −1.98061 | + | 1.69906i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.59316 | −0.344788 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.2664i | 1.05430i | 0.849772 | + | 0.527150i | \(0.176739\pi\) | ||||
−0.849772 | + | 0.527150i | \(0.823261\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.81923 | − | 9.11493i | −0.353598 | − | 0.412191i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.48139 | − | 5.47408i | −0.427889 | − | 0.247042i | 0.270558 | − | 0.962704i | \(-0.412792\pi\) |
−0.698447 | + | 0.715662i | \(0.746125\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.83929 | + | 1.06191i | −0.0828373 | + | 0.0478262i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.90704 | + | 0.601407i | 0.175609 | + | 0.0270312i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.47149 | − | 5.46837i | 0.424855 | − | 0.245290i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.4409 | + | 33.6726i | −0.870293 | + | 1.50739i | −0.00859924 | + | 0.999963i | \(0.502737\pi\) |
−0.861694 | + | 0.507429i | \(0.830596\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −28.4916 | + | 5.34473i | −1.27291 | + | 0.238785i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.97588 | 0.444803 | 0.222401 | − | 0.974955i | \(-0.428610\pi\) | ||||
0.222401 | + | 0.974955i | \(0.428610\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.5196 | 0.690612 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.11137 | − | 6.00378i | 0.0937692 | − | 0.266637i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.82922 | + | 13.5606i | −0.347024 | + | 0.601063i | −0.985719 | − | 0.168396i | \(-0.946141\pi\) |
0.638695 | + | 0.769460i | \(0.279474\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 26.2460 | − | 15.1532i | 1.16106 | − | 0.670336i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −15.1079 | + | 9.39426i | −0.667030 | + | 0.414767i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.19601 | + | 3.57727i | −0.273029 | + | 0.157633i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.59375 | − | 2.07485i | −0.158053 | − | 0.0912519i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11.7441 | + | 33.3949i | −0.515508 | + | 1.46587i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 9.78813i | − | 0.428826i | −0.976743 | − | 0.214413i | \(-0.931216\pi\) | ||
0.976743 | − | 0.214413i | \(-0.0687838\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.9015 | 1.43868 | 0.719342 | − | 0.694656i | \(-0.244443\pi\) | ||||
0.719342 | + | 0.694656i | \(0.244443\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.09907 | − | 27.1821i | −0.222542 | − | 1.18632i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.02989 | − | 6.97997i | 0.175545 | − | 0.304052i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.2896 | − | 31.6786i | −0.795201 | − | 1.37733i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 16.2825 | − | 20.2870i | 0.706601 | − | 0.880382i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.46391 | − | 12.9279i | −0.323298 | − | 0.559968i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.2282 | − | 5.90525i | −0.442203 | − | 0.255306i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.36338 | − | 4.60097i | 0.231447 | − | 0.198546i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.2908i | 0.572476i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 26.4228i | − | 1.13601i | −0.823027 | − | 0.568003i | \(-0.807716\pi\) | ||
0.823027 | − | 0.568003i | \(-0.192284\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 29.3456 | − | 25.1741i | 1.25934 | − | 1.08032i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.47149 | + | 5.46837i | 0.405714 | + | 0.234239i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.7776 | − | 30.7917i | −0.760116 | − | 1.31656i | −0.942790 | − | 0.333387i | \(-0.891809\pi\) |
0.182674 | − | 0.983174i | \(-0.441525\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.96803 | − | 10.2042i | −0.169351 | − | 0.435504i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.42944 | − | 4.20792i | −0.103498 | − | 0.179263i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.57242 | + | 9.65172i | −0.236964 | + | 0.410433i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.07283 | − | 5.71905i | −0.0455392 | − | 0.242760i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.4413 | 0.781384 | 0.390692 | − | 0.920522i | \(-0.372236\pi\) | ||||
0.390692 | + | 0.920522i | \(0.372236\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.6450i | 0.450236i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.00244 | + | 2.85047i | −0.0423228 | + | 0.120347i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −35.4943 | − | 20.4926i | −1.49591 | − | 0.863661i | −0.495917 | − | 0.868370i | \(-0.665168\pi\) |
−0.999989 | + | 0.00470871i | \(0.998501\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.08387 | + | 4.66722i | −0.340091 | + | 0.196352i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 37.6924 | − | 8.35509i | 1.58293 | − | 0.350881i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.72340 | + | 2.14971i | −0.156093 | + | 0.0901205i | −0.576012 | − | 0.817441i | \(-0.695392\pi\) |
0.419919 | + | 0.907562i | \(0.362059\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.17462 | − | 3.76656i | 0.0910052 | − | 0.157626i | −0.816929 | − | 0.576738i | \(-0.804325\pi\) |
0.907934 | + | 0.419112i | \(0.137659\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.36048 | − | 23.7734i | 0.349264 | − | 0.993150i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 28.7312 | 1.19817 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.5475 | 0.522361 | 0.261180 | − | 0.965290i | \(-0.415888\pi\) | ||||
0.261180 | + | 0.965290i | \(0.415888\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.47423 | − | 1.40209i | 0.310619 | − | 0.0582687i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.86905 | + | 17.0937i | −0.409437 | + | 0.709166i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.3861 | + | 6.57376i | −0.471563 | + | 0.272257i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.75319 | − | 9.65172i | −0.155175 | − | 0.399049i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.02388 | − | 4.63259i | 0.331181 | − | 0.191207i | −0.325184 | − | 0.945651i | \(-0.605426\pi\) |
0.656365 | + | 0.754443i | \(0.272093\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.9688 | + | 9.21958i | 0.657982 | + | 0.379886i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.68044 | − | 10.1188i | −0.357066 | − | 0.416234i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 11.1342i | − | 0.457228i | −0.973517 | − | 0.228614i | \(-0.926581\pi\) | ||
0.973517 | − | 0.228614i | \(-0.0734193\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.25666 | −0.297494 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 27.5792 | − | 23.6588i | 1.12874 | − | 0.968291i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.8693 | − | 39.6108i | 0.934415 | − | 1.61845i | 0.158740 | − | 0.987320i | \(-0.449257\pi\) |
0.775675 | − | 0.631133i | \(-0.217410\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.2521 | − | 19.4892i | −0.458982 | − | 0.794980i | 0.539925 | − | 0.841713i | \(-0.318453\pi\) |
−0.998907 | + | 0.0467325i | \(0.985119\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 26.1222 | + | 20.9658i | 1.06378 | + | 0.853795i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.44905 | − | 9.43803i | −0.221535 | − | 0.383710i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.7306 | − | 14.2782i | −1.00378 | − | 0.579535i | −0.0944185 | − | 0.995533i | \(-0.530099\pi\) |
−0.909366 | + | 0.415997i | \(0.863433\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.94409 | + | 10.3636i | 0.0787786 | + | 0.419953i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.8709i | 0.439791i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 40.4574i | − | 1.63406i | −0.576596 | − | 0.817030i | \(-0.695619\pi\) | ||
0.576596 | − | 0.817030i | \(-0.304381\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.02860 | + | 3.17512i | 0.364068 | + | 0.128033i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.6715 | − | 18.2855i | −1.27505 | − | 0.736148i | −0.299112 | − | 0.954218i | \(-0.596691\pi\) |
−0.975933 | + | 0.218070i | \(0.930024\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.3697 | − | 35.2814i | −0.818727 | − | 1.41808i | −0.906620 | − | 0.421948i | \(-0.861347\pi\) |
0.0878927 | − | 0.996130i | \(-0.471987\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.31145 | + | 40.0864i | 0.0526267 | + | 1.60861i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.5273 | + | 32.0902i | 0.742279 | + | 1.28567i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.73321 | + | 6.46610i | −0.149328 | + | 0.258644i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.52132 | − | 2.29337i | −0.260436 | − | 0.0915884i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.44772 | 0.177342 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 15.0916i | − | 0.600788i | −0.953815 | − | 0.300394i | \(-0.902882\pi\) | ||
0.953815 | − | 0.300394i | \(-0.0971182\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.11963 | + | 1.52316i | −0.322726 | + | 0.0605400i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.72884 | + | 1.57550i | 0.108291 | + | 0.0625218i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 30.1531 | − | 17.4089i | 1.19471 | − | 0.689765i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.16364 | − | 7.55957i | 0.0460328 | − | 0.299052i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.9377 | + | 15.5525i | −1.06398 | + | 0.614287i | −0.926529 | − | 0.376222i | \(-0.877223\pi\) |
−0.137447 | + | 0.990509i | \(0.543890\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.93125 | − | 3.34503i | 0.0761612 | − | 0.131915i | −0.825429 | − | 0.564505i | \(-0.809067\pi\) |
0.901591 | + | 0.432590i | \(0.142400\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.44363 | − | 5.17997i | −0.174968 | − | 0.203961i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.1359 | −0.948879 | −0.474440 | − | 0.880288i | \(-0.657349\pi\) | ||||
−0.474440 | + | 0.880288i | \(0.657349\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.1079 | 0.396770 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −26.0538 | − | 30.3711i | −1.02113 | − | 1.19034i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.2083 | + | 28.0736i | −0.634279 | + | 1.09860i | 0.352388 | + | 0.935854i | \(0.385370\pi\) |
−0.986667 | + | 0.162750i | \(0.947964\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.7547 | + | 8.51864i | −0.576515 | + | 0.332851i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.22450 | − | 20.9480i | 0.125800 | − | 0.817259i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.7202 | + | 11.3855i | −0.768191 | + | 0.443515i | −0.832229 | − | 0.554432i | \(-0.812936\pi\) |
0.0640377 | + | 0.997947i | \(0.479602\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.6004 | + | 14.7804i | 0.995740 | + | 0.574891i | 0.906985 | − | 0.421163i | \(-0.138378\pi\) |
0.0887549 | + | 0.996053i | \(0.471711\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.77995 | − | 1.45944i | 0.302148 | − | 0.0566798i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 16.6018i | − | 0.643790i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.9542 | −0.424147 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −23.6355 | − | 8.31197i | −0.913802 | − | 0.321359i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.12713 | − | 3.68430i | 0.0821171 | − | 0.142231i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.89907 | + | 15.4136i | 0.343034 | + | 0.594152i | 0.984995 | − | 0.172585i | \(-0.0552121\pi\) |
−0.641961 | + | 0.766738i | \(0.721879\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −17.0574 | − | 9.11782i | −0.656539 | − | 0.350945i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.9383 | + | 39.7303i | 0.881591 | + | 1.52696i | 0.849572 | + | 0.527473i | \(0.176860\pi\) |
0.0320192 | + | 0.999487i | \(0.489806\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.9550 | − | 14.4078i | −0.957684 | − | 0.552919i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.06000 | − | 0.372775i | −0.0406195 | − | 0.0142848i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.20513i | 0.0843769i | 0.999110 | + | 0.0421884i | \(0.0134330\pi\) | ||||
−0.999110 | + | 0.0421884i | \(0.986567\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.85735i | 0.376630i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.42524 | + | 23.5900i | 0.168833 | + | 0.900015i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 29.8280 | + | 17.2212i | 1.13636 | + | 0.656075i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.2512 | + | 17.7556i | 0.389975 | + | 0.675457i | 0.992446 | − | 0.122684i | \(-0.0391503\pi\) |
−0.602471 | + | 0.798141i | \(0.705817\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.6994 | + | 9.39001i | 0.444422 | + | 0.356697i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.34398 | − | 2.32784i | −0.0509801 | − | 0.0883001i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.65776 | + | 6.33542i | −0.138547 | + | 0.239971i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 30.4038 | − | 26.0819i | 1.14998 | − | 0.986506i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.6854 | −1.00789 | −0.503947 | − | 0.863734i | \(-0.668119\pi\) | ||||
−0.503947 | + | 0.863734i | \(0.668119\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.1755i | 0.383776i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.53794 | − | 5.28991i | −0.170909 | − | 0.199230i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 51.0052 | + | 29.4479i | 1.91825 | + | 1.10750i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.8684 | − | 21.8633i | 1.42218 | − | 0.821095i | 0.425693 | − | 0.904868i | \(-0.360030\pi\) |
0.996485 | + | 0.0837727i | \(0.0266970\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.82479 | + | 7.26425i | 0.105938 | + | 0.272431i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 36.0009 | − | 20.7851i | 1.34825 | − | 0.778410i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.01197 | − | 3.48483i | 0.0752433 | − | 0.130325i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 25.3336 | − | 4.75232i | 0.946101 | − | 0.177479i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.9253 | −0.519327 | −0.259663 | − | 0.965699i | \(-0.583612\pi\) | ||||
−0.259663 | + | 0.965699i | \(0.583612\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −27.1510 | −1.01115 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.75705 | − | 19.2140i | 0.251297 | − | 0.714577i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.64124 | − | 4.57475i | 0.0980930 | − | 0.169902i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.9380 | − | 17.8621i | 1.14743 | − | 0.662468i | 0.199169 | − | 0.979965i | \(-0.436176\pi\) |
0.948259 | + | 0.317497i | \(0.102842\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 11.9428 | − | 24.2151i | 0.442326 | − | 0.896854i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.51778 | − | 2.60834i | 0.167096 | − | 0.0964730i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.2141 | − | 17.4441i | −1.11598 | − | 0.644312i | −0.175610 | − | 0.984460i | \(-0.556190\pi\) |
−0.940372 | + | 0.340148i | \(0.889523\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.40567 | + | 21.0584i | −0.273162 | + | 0.776751i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.0152i | 0.479422i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.1128 | −0.482361 | −0.241181 | − | 0.970480i | \(-0.577535\pi\) | ||||
−0.241181 | + | 0.970480i | \(0.577535\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.33890 | + | 17.7990i | 0.122657 | + | 0.653862i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.1665 | + | 19.3410i | −0.409660 | + | 0.709551i | −0.994851 | − | 0.101344i | \(-0.967686\pi\) |
0.585192 | + | 0.810895i | \(0.301019\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.1104 | − | 17.5117i | −0.370415 | − | 0.641578i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.00286 | + | 12.8654i | 0.183045 | + | 0.470719i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −22.4100 | − | 38.8153i | −0.818844 | − | 1.41828i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.99545 | − | 4.03882i | −0.255267 | − | 0.147379i | 0.366906 | − | 0.930258i | \(-0.380417\pi\) |
−0.622174 | + | 0.782879i | \(0.713750\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.25165 | + | 6.22082i | −0.264265 | + | 0.226699i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 3.12165i | − | 0.113608i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.7751i | 0.464319i | 0.972678 | + | 0.232160i | \(0.0745792\pi\) | ||||
−0.972678 | + | 0.232160i | \(0.925421\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11.8286 | + | 10.1472i | −0.429352 | + | 0.368319i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 43.2325 | + | 24.9603i | 1.56718 | + | 0.904809i | 0.996496 | + | 0.0836361i | \(0.0266533\pi\) |
0.570679 | + | 0.821173i | \(0.306680\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.7521 | + | 35.9437i | 0.751276 | + | 1.30125i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.17658 | + | 3.95783i | −0.114850 | + | 0.143096i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13.2398 | − | 22.9320i | −0.478060 | − | 0.828025i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.2517 | + | 24.6846i | −0.513929 | + | 0.890150i | 0.485941 | + | 0.873992i | \(0.338477\pi\) |
−0.999869 | + | 0.0161588i | \(0.994856\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.23897 | + | 33.2586i | 0.224691 | + | 1.19778i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.8254 | 0.749037 | 0.374518 | − | 0.927220i | \(-0.377808\pi\) | ||||
0.374518 | + | 0.927220i | \(0.377808\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.0466i | 0.720096i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.32583 | − | 20.8314i | 0.262813 | − | 0.747321i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14.4942 | − | 8.36822i | −0.519308 | − | 0.299822i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.57384 | − | 1.48601i | 0.0920991 | − | 0.0531735i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.50337 | + | 3.47630i | 0.232411 | + | 0.124233i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.49980 | + | 1.44326i | −0.0892218 | + | 0.0515122i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.4386 | + | 18.0802i | −0.372096 | + | 0.644488i | −0.989888 | − | 0.141853i | \(-0.954694\pi\) |
0.617792 | + | 0.786341i | \(0.288027\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.46533 | − | 18.3845i | 0.230172 | − | 0.654506i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −35.4236 | −1.25952 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.1448 | −0.395765 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −21.7034 | + | 4.07133i | −0.769740 | + | 0.144395i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.4238 | + | 24.9828i | −0.510918 | + | 0.884935i | 0.489002 | + | 0.872283i | \(0.337361\pi\) |
−0.999920 | + | 0.0126529i | \(0.995972\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.61367 | − | 2.66370i | 0.163220 | − | 0.0942350i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 25.6124 | + | 3.94250i | 0.904971 | + | 0.139301i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.13225 | − | 4.11780i | 0.251691 | − | 0.145314i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −32.4136 | − | 18.7140i | −1.14243 | − | 0.659582i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15.9688 | − | 18.6149i | −0.562128 | − | 0.655276i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 43.6746i | 1.53552i | 0.640739 | + | 0.767759i | \(0.278628\pi\) | ||||
−0.640739 | + | 0.767759i | \(0.721372\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.3445 | −1.48692 | −0.743458 | − | 0.668782i | \(-0.766816\pi\) | ||||
−0.743458 | + | 0.668782i | \(0.766816\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.14767 | + | 4.41593i | −0.180537 | + | 0.154873i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.91876 | − | 6.78749i | 0.137268 | − | 0.237755i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.96737 | + | 10.3358i | 0.208772 | + | 0.361603i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.97891 | − | 38.8420i | 0.208920 | − | 1.35725i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.40953 | − | 2.44138i | −0.0491930 | − | 0.0852047i | 0.840380 | − | 0.541997i | \(-0.182332\pi\) |
−0.889573 | + | 0.456792i | \(0.848998\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.46763 | − | 2.57939i | −0.155732 | − | 0.0899118i | 0.420109 | − | 0.907474i | \(-0.361992\pi\) |
−0.575841 | + | 0.817562i | \(0.695325\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.38565 | − | 7.38662i | −0.0482422 | − | 0.257169i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21.8630i | 0.760251i | 0.924935 | + | 0.380125i | \(0.124119\pi\) | ||||
−0.924935 | + | 0.380125i | \(0.875881\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.0815i | 0.766924i | 0.923557 | + | 0.383462i | \(0.125268\pi\) | ||||
−0.923557 | + | 0.383462i | \(0.874732\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 43.3074 | + | 15.2300i | 1.50232 | + | 0.528324i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.7768 | − | 8.53139i | −0.511986 | − | 0.295595i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.45931 | − | 16.3840i | −0.327353 | − | 0.566992i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −27.9695 | + | 0.915040i | −0.966768 | + | 0.0316284i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25.4035 | + | 44.0002i | 0.877026 | + | 1.51905i | 0.854588 | + | 0.519306i | \(0.173809\pi\) |
0.0224378 | + | 0.999748i | \(0.492857\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.4930 | − | 23.3705i | 0.465276 | − | 0.805881i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.74215 | − | 0.612666i | −0.0600027 | − | 0.0211013i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.15343 | 0.142882 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 41.3575i | − | 1.42106i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.05494 | + | 1.13584i | −0.207805 | + | 0.0389820i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.8668 | + | 11.4701i | 0.681026 | + | 0.393191i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −45.4891 | + | 26.2631i | −1.55752 | + | 0.899233i | −0.560023 | + | 0.828477i | \(0.689208\pi\) |
−0.997494 | + | 0.0707558i | \(0.977459\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.05472 | − | 7.26739i | −0.309665 | − | 0.248539i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −48.4564 | + | 27.9763i | −1.65524 | + | 0.955653i | −0.680372 | + | 0.732867i | \(0.738182\pi\) |
−0.974867 | + | 0.222786i | \(0.928485\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.4078 | + | 26.6871i | −0.525708 | + | 0.910554i | 0.473843 | + | 0.880609i | \(0.342866\pi\) |
−0.999552 | + | 0.0299443i | \(0.990467\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 23.6479 | + | 27.5665i | 0.805918 | + | 0.939464i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25.1750 | −0.856966 | −0.428483 | − | 0.903550i | \(-0.640952\pi\) | ||||
−0.428483 | + | 0.903550i | \(0.640952\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23.1027 | −0.785514 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.6458 | + | 19.4042i | 0.565323 | + | 0.659000i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.51428 | + | 2.62281i | −0.0513685 | + | 0.0889728i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29.5278 | − | 17.0479i | 1.00051 | − | 0.577646i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −18.7821 | + | 7.30364i | −0.635676 | + | 0.247191i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 36.6276 | − | 21.1470i | 1.23824 | − | 0.714898i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.8486 | − | 18.3878i | −1.07545 | − | 0.620913i | −0.145786 | − | 0.989316i | \(-0.546571\pi\) |
−0.929666 | + | 0.368404i | \(0.879904\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 26.5213 | − | 4.97511i | 0.894541 | − | 0.167806i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.15439i | 0.274728i | 0.990521 | + | 0.137364i | \(0.0438631\pi\) | ||||
−0.990521 | + | 0.137364i | \(0.956137\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.3792 | 0.685814 | 0.342907 | − | 0.939369i | \(-0.388588\pi\) | ||||
0.342907 | + | 0.939369i | \(0.388588\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 16.0153 | + | 5.63215i | 0.538348 | + | 0.189323i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.3561 | + | 38.7220i | −0.750646 | + | 1.30016i | 0.196864 | + | 0.980431i | \(0.436924\pi\) |
−0.947510 | + | 0.319726i | \(0.896409\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.97891 | + | 10.3558i | 0.200526 | + | 0.347322i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.2427 | − | 2.27046i | 0.343145 | − | 0.0760633i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.09402 | + | 10.5551i | 0.203928 | + | 0.353214i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.99387 | + | 2.30586i | 0.133500 | + | 0.0770765i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 38.5147 | + | 13.5446i | 1.28597 | + | 0.452241i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 7.64305i | − | 0.254910i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 16.8788i | − | 0.562315i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.77521 | − | 25.4557i | −0.158909 | − | 0.847112i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21.8524 | + | 12.6165i | 0.726398 | + | 0.419386i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.99519 | − | 13.8481i | −0.265476 | − | 0.459818i | 0.702212 | − | 0.711968i | \(-0.252196\pi\) |
−0.967688 | + | 0.252150i | \(0.918862\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 38.3884 | − | 14.9278i | 1.27326 | − | 0.495125i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.1609 | − | 24.5275i | −0.469173 | − | 0.812631i | 0.530206 | − | 0.847869i | \(-0.322115\pi\) |
−0.999379 | + | 0.0352377i | \(0.988781\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.68187 | + | 4.64514i | −0.0887570 | + | 0.153732i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.42320 | − | 4.65229i | 0.179286 | − | 0.153800i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −64.6553 | −2.13511 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 17.1474i | − | 0.565642i | −0.959173 | − | 0.282821i | \(-0.908730\pi\) | ||
0.959173 | − | 0.282821i | \(-0.0912702\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.08341 | + | 1.26294i | 0.0356995 | + | 0.0416151i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.74265 | − | 3.89287i | −0.221937 | − | 0.128135i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.58047 | + | 5.53129i | −0.315004 | + | 0.181868i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.8853 | + | 14.8083i | −0.390363 | + | 0.486368i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 38.0670 | − | 21.9780i | 1.24894 | − | 0.721075i | 0.278040 | − | 0.960569i | \(-0.410315\pi\) |
0.970898 | + | 0.239495i | \(0.0769818\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.5181 | − | 33.8064i | 0.639680 | − | 1.10796i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15.3055 | + | 2.87115i | −0.501080 | + | 0.0939972i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.97197 | −0.0644902 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.5845 | −0.443786 | −0.221893 | − | 0.975071i | \(-0.571223\pi\) | ||||
−0.221893 | + | 0.975071i | \(0.571223\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.83615 | + | 27.9696i | −0.320991 | + | 0.912753i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.5116 | − | 23.4028i | 0.440466 | − | 0.762909i | −0.557258 | − | 0.830339i | \(-0.688147\pi\) |
0.997724 | + | 0.0674301i | \(0.0214800\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −32.6765 | + | 18.8658i | −1.06409 | + | 0.614354i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.3047 | + | 21.3968i | 0.432803 | + | 0.696037i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34.5376 | + | 19.9403i | −1.12232 | + | 0.647972i | −0.941992 | − | 0.335634i | \(-0.891049\pi\) |
−0.180328 | + | 0.983607i | \(0.557716\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.6843 | − | 10.7874i | −0.606516 | − | 0.350172i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.55704 | − | 12.9582i | 0.147772 | − | 0.420198i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 14.0999i | − | 0.456741i | −0.973574 | − | 0.228371i | \(-0.926660\pi\) | ||
0.973574 | − | 0.228371i | \(-0.0733398\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.4465 | 0.532197 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.528299 | + | 2.81625i | 0.0170775 | + | 0.0910365i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18.7040 | + | 32.3963i | −0.603983 | + | 1.04613i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.997565 | − | 1.72783i | −0.0321795 | − | 0.0557366i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −30.9800 | − | 4.76872i | −0.998317 | − | 0.153670i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.48147 | + | 4.29803i | 0.0798813 | + | 0.138358i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.4687 | + | 26.2514i | 1.46217 | + | 0.844187i | 0.999112 | − | 0.0421387i | \(-0.0134171\pi\) |
0.463063 | + | 0.886326i | \(0.346750\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.73582 | − | 5.77832i | 0.216386 | − | 0.185626i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 61.3864i | 1.96998i | 0.172599 | + | 0.984992i | \(0.444784\pi\) | ||||
−0.172599 | + | 0.984992i | \(0.555216\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 10.2006i | − | 0.327017i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −14.9432 | + | 12.8190i | −0.478564 | + | 0.410535i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −25.9568 | − | 14.9862i | −0.830431 | − | 0.479450i | 0.0235691 | − | 0.999722i | \(-0.492497\pi\) |
−0.854000 | + | 0.520273i | \(0.825830\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.03471 | + | 8.72037i | 0.160910 | + | 0.278704i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 28.6881 | + | 4.41593i | 0.915939 | + | 0.140990i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.1703 | + | 36.6681i | 0.675228 | + | 1.16953i | 0.976402 | + | 0.215961i | \(0.0692883\pi\) |
−0.301174 | + | 0.953569i | \(0.597378\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.35037 | − | 7.53506i | 0.138614 | − | 0.240087i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.87656 | − | 25.9959i | −0.155223 | − | 0.827460i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 26.9063 | 0.855572 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 12.3787i | − | 0.393222i | −0.980482 | − | 0.196611i | \(-0.937006\pi\) | ||
0.980482 | − | 0.196611i | \(-0.0629937\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.49735 | − | 15.6320i | 0.174453 | − | 0.496066i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.5370 | + | 11.8571i | 0.651068 | + | 0.375894i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.20535 | + | 3.58266i | −0.196525 | + | 0.113464i | −0.595034 | − | 0.803701i | \(-0.702861\pi\) |
0.398508 | + | 0.917165i | \(0.369528\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.15469 | − | 13.1144i | −0.258003 | − | 0.414922i |
(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 | 288.2.p.b.239.5 | 16 | ||
3.2 | odd | 2 | 864.2.p.b.719.5 | 16 | |||
4.3 | odd | 2 | 72.2.l.b.59.6 | yes | 16 | ||
8.3 | odd | 2 | inner | 288.2.p.b.239.6 | 16 | ||
8.5 | even | 2 | 72.2.l.b.59.8 | yes | 16 | ||
9.2 | odd | 6 | inner | 288.2.p.b.47.6 | 16 | ||
9.4 | even | 3 | 2592.2.f.b.1295.9 | 16 | |||
9.5 | odd | 6 | 2592.2.f.b.1295.7 | 16 | |||
9.7 | even | 3 | 864.2.p.b.143.4 | 16 | |||
12.11 | even | 2 | 216.2.l.b.179.3 | 16 | |||
24.5 | odd | 2 | 216.2.l.b.179.1 | 16 | |||
24.11 | even | 2 | 864.2.p.b.719.4 | 16 | |||
36.7 | odd | 6 | 216.2.l.b.35.1 | 16 | |||
36.11 | even | 6 | 72.2.l.b.11.8 | yes | 16 | ||
36.23 | even | 6 | 648.2.f.b.323.5 | 16 | |||
36.31 | odd | 6 | 648.2.f.b.323.12 | 16 | |||
72.5 | odd | 6 | 648.2.f.b.323.11 | 16 | |||
72.11 | even | 6 | inner | 288.2.p.b.47.5 | 16 | ||
72.13 | even | 6 | 648.2.f.b.323.6 | 16 | |||
72.29 | odd | 6 | 72.2.l.b.11.6 | ✓ | 16 | ||
72.43 | odd | 6 | 864.2.p.b.143.5 | 16 | |||
72.59 | even | 6 | 2592.2.f.b.1295.10 | 16 | |||
72.61 | even | 6 | 216.2.l.b.35.3 | 16 | |||
72.67 | odd | 6 | 2592.2.f.b.1295.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.2.l.b.11.6 | ✓ | 16 | 72.29 | odd | 6 | ||
72.2.l.b.11.8 | yes | 16 | 36.11 | even | 6 | ||
72.2.l.b.59.6 | yes | 16 | 4.3 | odd | 2 | ||
72.2.l.b.59.8 | yes | 16 | 8.5 | even | 2 | ||
216.2.l.b.35.1 | 16 | 36.7 | odd | 6 | |||
216.2.l.b.35.3 | 16 | 72.61 | even | 6 | |||
216.2.l.b.179.1 | 16 | 24.5 | odd | 2 | |||
216.2.l.b.179.3 | 16 | 12.11 | even | 2 | |||
288.2.p.b.47.5 | 16 | 72.11 | even | 6 | inner | ||
288.2.p.b.47.6 | 16 | 9.2 | odd | 6 | inner | ||
288.2.p.b.239.5 | 16 | 1.1 | even | 1 | trivial | ||
288.2.p.b.239.6 | 16 | 8.3 | odd | 2 | inner | ||
648.2.f.b.323.5 | 16 | 36.23 | even | 6 | |||
648.2.f.b.323.6 | 16 | 72.13 | even | 6 | |||
648.2.f.b.323.11 | 16 | 72.5 | odd | 6 | |||
648.2.f.b.323.12 | 16 | 36.31 | odd | 6 | |||
864.2.p.b.143.4 | 16 | 9.7 | even | 3 | |||
864.2.p.b.143.5 | 16 | 72.43 | odd | 6 | |||
864.2.p.b.719.4 | 16 | 24.11 | even | 2 | |||
864.2.p.b.719.5 | 16 | 3.2 | odd | 2 | |||
2592.2.f.b.1295.7 | 16 | 9.5 | odd | 6 | |||
2592.2.f.b.1295.8 | 16 | 72.67 | odd | 6 | |||
2592.2.f.b.1295.9 | 16 | 9.4 | even | 3 | |||
2592.2.f.b.1295.10 | 16 | 72.59 | even | 6 |