Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(80,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.80");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.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: | \(26.0198423125\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 215.16 | ||
Character | \(\chi\) | \(=\) | 441.215 |
Dual form | 441.4.p.d.80.16 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.40358 | + | 0.810356i | 0.496240 | + | 0.286504i | 0.727159 | − | 0.686469i | \(-0.240840\pi\) |
−0.230920 | + | 0.972973i | \(0.574173\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.68665 | − | 4.65341i | −0.335831 | − | 0.581676i | ||||
\(5\) | 2.35993 | − | 4.08752i | 0.211079 | − | 0.365599i | −0.740974 | − | 0.671534i | \(-0.765636\pi\) |
0.952052 | + | 0.305935i | \(0.0989691\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 21.6743i | − | 0.957876i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.62469 | − | 3.82477i | 0.209491 | − | 0.120950i | ||||
\(11\) | −25.9801 | + | 14.9996i | −0.712118 | + | 0.411142i | −0.811845 | − | 0.583873i | \(-0.801536\pi\) |
0.0997267 | + | 0.995015i | \(0.468203\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 27.1586i | − | 0.579417i | −0.957115 | − | 0.289709i | \(-0.906442\pi\) | ||
0.957115 | − | 0.289709i | \(-0.0935584\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.92932 | + | 6.80578i | −0.0613956 | + | 0.106340i | ||||
\(17\) | 8.92464 | + | 15.4579i | 0.127326 | + | 0.220535i | 0.922640 | − | 0.385663i | \(-0.126027\pi\) |
−0.795314 | + | 0.606198i | \(0.792694\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −107.297 | − | 61.9477i | −1.29555 | − | 0.747988i | −0.315921 | − | 0.948786i | \(-0.602313\pi\) |
−0.979633 | + | 0.200797i | \(0.935647\pi\) | |||||||
\(20\) | −25.3612 | −0.283547 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −48.6201 | −0.471175 | ||||||||
\(23\) | 71.0802 | + | 41.0382i | 0.644402 | + | 0.372046i | 0.786308 | − | 0.617835i | \(-0.211990\pi\) |
−0.141906 | + | 0.989880i | \(0.545323\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 51.3615 | + | 88.9606i | 0.410892 | + | 0.711685i | ||||
\(26\) | 22.0081 | − | 38.1191i | 0.166005 | − | 0.287530i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 88.2194i | − | 0.564894i | −0.959283 | − | 0.282447i | \(-0.908854\pi\) | ||
0.959283 | − | 0.282447i | \(-0.0911462\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −220.389 | + | 127.242i | −1.27687 | + | 0.737203i | −0.976272 | − | 0.216548i | \(-0.930520\pi\) |
−0.300600 | + | 0.953750i | \(0.597187\pi\) | |||||||
\(32\) | −161.194 | + | 93.0653i | −0.890479 | + | 0.514118i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 28.9285i | 0.145918i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −107.695 | + | 186.533i | −0.478511 | + | 0.828805i | −0.999696 | − | 0.0246385i | \(-0.992157\pi\) |
0.521186 | + | 0.853443i | \(0.325490\pi\) | |||||||
\(38\) | −100.399 | − | 173.897i | −0.428603 | − | 0.742363i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −88.5939 | − | 51.1497i | −0.350198 | − | 0.202187i | ||||
\(41\) | −427.760 | −1.62939 | −0.814695 | − | 0.579890i | \(-0.803095\pi\) | ||||
−0.814695 | + | 0.579890i | \(0.803095\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 62.4602 | 0.221514 | 0.110757 | − | 0.993848i | \(-0.464673\pi\) | ||||
0.110757 | + | 0.993848i | \(0.464673\pi\) | |||||||
\(44\) | 139.599 | + | 80.5974i | 0.478303 | + | 0.276148i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 66.5110 | + | 115.200i | 0.213185 | + | 0.369247i | ||||
\(47\) | 211.787 | − | 366.825i | 0.657282 | − | 1.13845i | −0.324035 | − | 0.946045i | \(-0.605040\pi\) |
0.981317 | − | 0.192400i | \(-0.0616271\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 166.484i | 0.470888i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −126.380 | + | 72.9654i | −0.337033 | + | 0.194586i | ||||
\(53\) | −587.234 | + | 339.039i | −1.52194 | + | 0.878692i | −0.522274 | + | 0.852778i | \(0.674916\pi\) |
−0.999664 | + | 0.0259140i | \(0.991750\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 141.592i | 0.347133i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 71.4891 | − | 123.823i | 0.161844 | − | 0.280323i | ||||
\(59\) | −383.719 | − | 664.621i | −0.846711 | − | 1.46655i | −0.884127 | − | 0.467246i | \(-0.845246\pi\) |
0.0374163 | − | 0.999300i | \(-0.488087\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −313.156 | − | 180.801i | −0.657303 | − | 0.379494i | 0.133946 | − | 0.990989i | \(-0.457235\pi\) |
−0.791249 | + | 0.611495i | \(0.790569\pi\) | |||||||
\(62\) | −412.444 | −0.844846 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −238.795 | −0.466396 | ||||||||
\(65\) | −111.011 | − | 64.0923i | −0.211834 | − | 0.122303i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 323.947 | + | 561.093i | 0.590694 | + | 1.02311i | 0.994139 | + | 0.108108i | \(0.0344791\pi\) |
−0.403446 | + | 0.915004i | \(0.632188\pi\) | |||||||
\(68\) | 47.9547 | − | 83.0600i | 0.0855200 | − | 0.148125i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 536.663i | − | 0.897045i | −0.893772 | − | 0.448522i | \(-0.851950\pi\) | ||
0.893772 | − | 0.448522i | \(-0.148050\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −547.293 | + | 315.980i | −0.877477 | + | 0.506612i | −0.869826 | − | 0.493359i | \(-0.835769\pi\) |
−0.00765130 | + | 0.999971i | \(0.502436\pi\) | |||||||
\(74\) | −302.316 | + | 174.542i | −0.474912 | + | 0.274190i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 665.726i | 1.00479i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 298.709 | − | 517.379i | 0.425410 | − | 0.736832i | −0.571049 | − | 0.820916i | \(-0.693463\pi\) |
0.996459 | + | 0.0840844i | \(0.0267965\pi\) | |||||||
\(80\) | 18.5458 | + | 32.1223i | 0.0259186 | + | 0.0448923i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −600.395 | − | 346.638i | −0.808567 | − | 0.466827i | ||||
\(83\) | 591.773 | 0.782597 | 0.391299 | − | 0.920264i | \(-0.372026\pi\) | ||||
0.391299 | + | 0.920264i | \(0.372026\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 84.2461 | 0.107503 | ||||||||
\(86\) | 87.6677 | + | 50.6150i | 0.109924 | + | 0.0634646i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 325.106 | + | 563.100i | 0.393823 | + | 0.682121i | ||||
\(89\) | 769.502 | − | 1332.82i | 0.916484 | − | 1.58740i | 0.111769 | − | 0.993734i | \(-0.464348\pi\) |
0.804714 | − | 0.593662i | \(-0.202318\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 441.020i | − | 0.499778i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 594.517 | − | 343.245i | 0.652338 | − | 0.376628i | ||||
\(95\) | −506.425 | + | 292.385i | −0.546927 | + | 0.315769i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 654.102i | 0.684680i | 0.939576 | + | 0.342340i | \(0.111219\pi\) | ||||
−0.939576 | + | 0.342340i | \(0.888781\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 275.980 | − | 478.012i | 0.275980 | − | 0.478012i | ||||
\(101\) | −148.389 | − | 257.018i | −0.146191 | − | 0.253210i | 0.783626 | − | 0.621233i | \(-0.213368\pi\) |
−0.929817 | + | 0.368023i | \(0.880035\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 387.255 | + | 223.582i | 0.370460 | + | 0.213885i | 0.673660 | − | 0.739042i | \(-0.264721\pi\) |
−0.303199 | + | 0.952927i | \(0.598055\pi\) | |||||||
\(104\) | −588.641 | −0.555010 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1098.97 | −1.00699 | ||||||||
\(107\) | −655.418 | − | 378.406i | −0.592165 | − | 0.341887i | 0.173788 | − | 0.984783i | \(-0.444399\pi\) |
−0.765953 | + | 0.642896i | \(0.777733\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −59.2503 | − | 102.625i | −0.0520656 | − | 0.0901803i | 0.838818 | − | 0.544412i | \(-0.183247\pi\) |
−0.890884 | + | 0.454232i | \(0.849914\pi\) | |||||||
\(110\) | −114.740 | + | 198.736i | −0.0994550 | + | 0.172261i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 90.4761i | − | 0.0753210i | −0.999291 | − | 0.0376605i | \(-0.988009\pi\) | ||
0.999291 | − | 0.0376605i | \(-0.0119905\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 335.489 | − | 193.694i | 0.272039 | − | 0.157062i | ||||
\(116\) | −410.521 | + | 237.014i | −0.328586 | + | 0.189709i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 1243.80i | − | 0.970344i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −215.522 | + | 373.296i | −0.161925 | + | 0.280463i | ||||
\(122\) | −293.026 | − | 507.535i | −0.217453 | − | 0.376640i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1184.22 | + | 683.707i | 0.857626 | + | 0.495151i | ||||
\(125\) | 1074.82 | 0.769079 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 324.991 | 0.227073 | 0.113536 | − | 0.993534i | \(-0.463782\pi\) | ||||
0.113536 | + | 0.993534i | \(0.463782\pi\) | |||||||
\(128\) | 954.384 | + | 551.014i | 0.659034 | + | 0.380494i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −103.875 | − | 179.917i | −0.0700804 | − | 0.121383i | ||||
\(131\) | 338.925 | − | 587.035i | 0.226046 | − | 0.391523i | −0.730587 | − | 0.682820i | \(-0.760753\pi\) |
0.956633 | + | 0.291297i | \(0.0940868\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1050.05i | 0.676944i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 335.039 | − | 193.435i | 0.211245 | − | 0.121963i | ||||
\(137\) | 1866.23 | − | 1077.47i | 1.16381 | − | 0.671928i | 0.211598 | − | 0.977357i | \(-0.432133\pi\) |
0.952215 | + | 0.305429i | \(0.0987998\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 719.518i | 0.439055i | 0.975606 | + | 0.219528i | \(0.0704516\pi\) | ||||
−0.975606 | + | 0.219528i | \(0.929548\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 434.888 | − | 753.248i | 0.257007 | − | 0.445149i | ||||
\(143\) | 407.368 | + | 705.582i | 0.238223 | + | 0.412614i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −360.599 | − | 208.192i | −0.206525 | − | 0.119237i | ||||
\(146\) | −1024.22 | −0.580585 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1157.35 | 0.642795 | ||||||||
\(149\) | −1034.65 | − | 597.357i | −0.568873 | − | 0.328439i | 0.187826 | − | 0.982202i | \(-0.439856\pi\) |
−0.756699 | + | 0.653763i | \(0.773189\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −536.066 | − | 928.494i | −0.288904 | − | 0.500396i | 0.684645 | − | 0.728877i | \(-0.259957\pi\) |
−0.973548 | + | 0.228481i | \(0.926624\pi\) | |||||||
\(152\) | −1342.67 | + | 2325.57i | −0.716480 | + | 1.24098i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1201.13i | 0.622431i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2022.12 | + | 1167.47i | −1.02792 | + | 0.593468i | −0.916387 | − | 0.400293i | \(-0.868908\pi\) |
−0.111530 | + | 0.993761i | \(0.535575\pi\) | |||||||
\(158\) | 838.523 | − | 484.121i | 0.422211 | − | 0.243763i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 878.511i | 0.434077i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1803.42 | + | 3123.61i | −0.866592 | + | 1.50098i | −0.00113428 | + | 0.999999i | \(0.500361\pi\) |
−0.865458 | + | 0.500982i | \(0.832972\pi\) | |||||||
\(164\) | 1149.24 | + | 1990.54i | 0.547199 | + | 0.947777i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 830.600 | + | 479.547i | 0.388356 | + | 0.224217i | ||||
\(167\) | 2249.44 | 1.04232 | 0.521159 | − | 0.853460i | \(-0.325500\pi\) | ||||
0.521159 | + | 0.853460i | \(0.325500\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1459.41 | 0.664275 | ||||||||
\(170\) | 118.246 | + | 68.2693i | 0.0533473 | + | 0.0308001i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −167.809 | − | 290.653i | −0.0743912 | − | 0.128849i | ||||
\(173\) | −2022.40 | + | 3502.90i | −0.888788 | + | 1.53943i | −0.0474778 | + | 0.998872i | \(0.515118\pi\) |
−0.841310 | + | 0.540553i | \(0.818215\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 235.753i | − | 0.100969i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2160.11 | − | 1247.14i | 0.909591 | − | 0.525153i | ||||
\(179\) | 1843.22 | − | 1064.18i | 0.769658 | − | 0.444362i | −0.0630946 | − | 0.998008i | \(-0.520097\pi\) |
0.832753 | + | 0.553645i | \(0.186764\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 4272.10i | − | 1.75438i | −0.480143 | − | 0.877190i | \(-0.659415\pi\) | ||
0.480143 | − | 0.877190i | \(-0.340585\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 889.472 | − | 1540.61i | 0.356373 | − | 0.617257i | ||||
\(185\) | 508.304 | + | 880.408i | 0.202007 | + | 0.349886i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −463.726 | − | 267.732i | −0.181342 | − | 0.104698i | ||||
\(188\) | −2275.98 | −0.882942 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −947.742 | −0.361876 | ||||||||
\(191\) | −670.762 | − | 387.265i | −0.254108 | − | 0.146709i | 0.367536 | − | 0.930009i | \(-0.380202\pi\) |
−0.621644 | + | 0.783300i | \(0.713535\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2456.61 | − | 4254.97i | −0.916221 | − | 1.58694i | −0.805104 | − | 0.593134i | \(-0.797890\pi\) |
−0.111117 | − | 0.993807i | \(-0.535443\pi\) | |||||||
\(194\) | −530.055 | + | 918.082i | −0.196164 | + | 0.339765i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1004.44i | 0.363265i | 0.983366 | + | 0.181632i | \(0.0581381\pi\) | ||||
−0.983366 | + | 0.181632i | \(0.941862\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1734.53 | − | 1001.43i | 0.617878 | − | 0.356732i | −0.158164 | − | 0.987413i | \(-0.550558\pi\) |
0.776042 | + | 0.630681i | \(0.217224\pi\) | |||||||
\(200\) | 1928.16 | − | 1113.22i | 0.681706 | − | 0.393583i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 480.992i | − | 0.167537i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1009.49 | + | 1748.48i | −0.343929 | + | 0.595703i | ||||
\(206\) | 362.362 | + | 627.629i | 0.122558 | + | 0.212277i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 184.835 | + | 106.715i | 0.0616154 | + | 0.0355737i | ||||
\(209\) | 3716.77 | 1.23012 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2630.90 | 0.858383 | 0.429191 | − | 0.903214i | \(-0.358799\pi\) | ||||
0.429191 | + | 0.903214i | \(0.358799\pi\) | |||||||
\(212\) | 3155.38 | + | 1821.76i | 1.02223 | + | 0.590184i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −613.287 | − | 1062.24i | −0.195904 | − | 0.339315i | ||||
\(215\) | 147.402 | − | 255.307i | 0.0467568 | − | 0.0809852i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 192.055i | − | 0.0596680i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 658.887 | − | 380.409i | 0.201919 | − | 0.116578i | ||||
\(221\) | 419.815 | − | 242.380i | 0.127782 | − | 0.0737749i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 4972.20i | − | 1.49311i | −0.665324 | − | 0.746555i | \(-0.731707\pi\) | ||
0.665324 | − | 0.746555i | \(-0.268293\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 73.3178 | − | 126.990i | 0.0215798 | − | 0.0373773i | ||||
\(227\) | 1710.26 | + | 2962.26i | 0.500062 | + | 0.866133i | 1.00000 | 7.18991e-5i | \(2.28862e-5\pi\) | |
−0.499938 | + | 0.866061i | \(0.666644\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2770.81 | + | 1599.73i | 0.799566 | + | 0.461629i | 0.843319 | − | 0.537413i | \(-0.180598\pi\) |
−0.0437537 | + | 0.999042i | \(0.513932\pi\) | |||||||
\(230\) | 627.846 | 0.179995 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1912.09 | −0.541099 | ||||||||
\(233\) | −1859.97 | − | 1073.85i | −0.522964 | − | 0.301933i | 0.215183 | − | 0.976574i | \(-0.430965\pi\) |
−0.738146 | + | 0.674641i | \(0.764299\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −999.603 | − | 1731.36i | −0.277476 | − | 0.480603i | ||||
\(236\) | −2061.83 | + | 3571.20i | −0.568703 | + | 0.985023i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 2853.29i | − | 0.772236i | −0.922449 | − | 0.386118i | \(-0.873816\pi\) | ||
0.922449 | − | 0.386118i | \(-0.126184\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 340.988 | − | 196.869i | 0.0911409 | − | 0.0526202i | −0.453737 | − | 0.891136i | \(-0.649909\pi\) |
0.544878 | + | 0.838516i | \(0.316576\pi\) | |||||||
\(242\) | −605.005 | + | 349.300i | −0.160707 | + | 0.0927844i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1942.99i | 0.509783i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1682.41 | + | 2914.02i | −0.433397 | + | 0.750666i | ||||
\(248\) | 2757.87 | + | 4776.77i | 0.706149 | + | 1.22309i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1508.59 | + | 870.987i | 0.381647 | + | 0.220344i | ||||
\(251\) | 2520.34 | 0.633794 | 0.316897 | − | 0.948460i | \(-0.397359\pi\) | ||||
0.316897 | + | 0.948460i | \(0.397359\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2462.23 | −0.611854 | ||||||||
\(254\) | 456.150 | + | 263.358i | 0.112683 | + | 0.0650573i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1848.21 | + | 3201.20i | 0.451224 | + | 0.781543i | ||||
\(257\) | 2125.96 | − | 3682.26i | 0.516006 | − | 0.893748i | −0.483822 | − | 0.875167i | \(-0.660752\pi\) |
0.999827 | − | 0.0185815i | \(-0.00591500\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 688.774i | 0.164292i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 951.414 | − | 549.299i | 0.224346 | − | 0.129526i | ||||
\(263\) | 6145.87 | − | 3548.32i | 1.44095 | − | 0.831935i | 0.443040 | − | 0.896502i | \(-0.353900\pi\) |
0.997913 | + | 0.0645666i | \(0.0205665\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3200.44i | 0.741892i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1740.66 | − | 3014.92i | 0.396746 | − | 0.687185i | ||||
\(269\) | −2180.43 | − | 3776.61i | −0.494212 | − | 0.856000i | 0.505766 | − | 0.862671i | \(-0.331210\pi\) |
−0.999978 | + | 0.00667106i | \(0.997877\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3737.79 | − | 2158.02i | −0.837841 | − | 0.483727i | 0.0186891 | − | 0.999825i | \(-0.494051\pi\) |
−0.856530 | + | 0.516098i | \(0.827384\pi\) | |||||||
\(272\) | −140.271 | −0.0312690 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3492.52 | 0.770040 | ||||||||
\(275\) | −2668.75 | − | 1540.81i | −0.585207 | − | 0.337869i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1319.46 | + | 2285.38i | 0.286205 | + | 0.495722i | 0.972901 | − | 0.231223i | \(-0.0742728\pi\) |
−0.686696 | + | 0.726945i | \(0.740939\pi\) | |||||||
\(278\) | −583.065 | + | 1009.90i | −0.125791 | + | 0.217877i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5925.56i | 1.25797i | 0.777417 | + | 0.628985i | \(0.216529\pi\) | ||||
−0.777417 | + | 0.628985i | \(0.783471\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2663.30 | + | 1537.65i | −0.559422 | + | 0.322983i | −0.752914 | − | 0.658119i | \(-0.771352\pi\) |
0.193491 | + | 0.981102i | \(0.438019\pi\) | |||||||
\(284\) | −2497.31 | + | 1441.82i | −0.521789 | + | 0.301255i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1320.45i | 0.273007i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2297.20 | − | 3978.87i | 0.467576 | − | 0.809866i | ||||
\(290\) | −337.419 | − | 584.426i | −0.0683238 | − | 0.118340i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2940.77 | + | 1697.85i | 0.589368 | + | 0.340272i | ||||
\(293\) | −1557.31 | −0.310509 | −0.155254 | − | 0.987875i | \(-0.549620\pi\) | ||||
−0.155254 | + | 0.987875i | \(0.549620\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3622.20 | −0.714890 | ||||||||
\(296\) | 4042.96 | + | 2334.20i | 0.793892 | + | 0.458354i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −968.144 | − | 1676.87i | −0.188198 | − | 0.325969i | ||||
\(299\) | 1114.54 | − | 1930.43i | 0.215570 | − | 0.373378i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 1737.62i | − | 0.331088i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 843.205 | − | 486.825i | 0.159083 | − | 0.0918464i | ||||
\(305\) | −1478.05 | + | 853.353i | −0.277485 | + | 0.160206i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1802.67i | − | 0.335127i | −0.985861 | − | 0.167563i | \(-0.946410\pi\) | ||
0.985861 | − | 0.167563i | \(-0.0535898\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −973.340 | + | 1685.87i | −0.178329 | + | 0.308875i | ||||
\(311\) | −4769.98 | − | 8261.85i | −0.869714 | − | 1.50639i | −0.862289 | − | 0.506416i | \(-0.830970\pi\) |
−0.00742422 | − | 0.999972i | \(-0.502363\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1095.23 | − | 632.332i | −0.197783 | − | 0.114190i | 0.397838 | − | 0.917456i | \(-0.369761\pi\) |
−0.595621 | + | 0.803266i | \(0.703094\pi\) | |||||||
\(314\) | −3784.27 | −0.680124 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3210.10 | −0.571463 | ||||||||
\(317\) | −8265.68 | − | 4772.19i | −1.46450 | − | 0.845530i | −0.465287 | − | 0.885160i | \(-0.654049\pi\) |
−0.999214 | + | 0.0396301i | \(0.987382\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1323.26 | + | 2291.95i | 0.232252 | + | 0.402271i | ||||
\(320\) | −563.539 | + | 976.079i | −0.0984463 | + | 0.170514i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 2211.44i | − | 0.380954i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2416.04 | − | 1394.90i | 0.412363 | − | 0.238078i | ||||
\(326\) | −5062.47 | + | 2922.82i | −0.860074 | + | 0.496564i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9271.39i | 1.56075i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1353.22 | − | 2343.85i | 0.224712 | − | 0.389213i | −0.731521 | − | 0.681819i | \(-0.761189\pi\) |
0.956233 | + | 0.292606i | \(0.0945225\pi\) | |||||||
\(332\) | −1589.89 | − | 2753.76i | −0.262820 | − | 0.455218i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3157.27 | + | 1822.85i | 0.517239 | + | 0.298628i | ||||
\(335\) | 3057.97 | 0.498731 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10550.8 | 1.70545 | 0.852727 | − | 0.522357i | \(-0.174947\pi\) | ||||
0.852727 | + | 0.522357i | \(0.174947\pi\) | |||||||
\(338\) | 2048.40 | + | 1182.64i | 0.329640 | + | 0.190318i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −226.340 | − | 392.032i | −0.0361029 | − | 0.0625321i | ||||
\(341\) | 3817.16 | − | 6611.51i | 0.606189 | − | 1.04995i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 1353.78i | − | 0.212183i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5677.19 | + | 3277.73i | −0.882103 | + | 0.509283i | ||||
\(347\) | −8636.09 | + | 4986.05i | −1.33605 | + | 0.771369i | −0.986219 | − | 0.165444i | \(-0.947094\pi\) |
−0.349831 | + | 0.936813i | \(0.613761\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1653.11i | 0.253549i | 0.991932 | + | 0.126775i | \(0.0404625\pi\) | ||||
−0.991932 | + | 0.126775i | \(0.959537\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2791.89 | − | 4835.69i | 0.422751 | − | 0.732226i | ||||
\(353\) | −1677.25 | − | 2905.09i | −0.252893 | − | 0.438024i | 0.711428 | − | 0.702759i | \(-0.248049\pi\) |
−0.964321 | + | 0.264735i | \(0.914715\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2193.62 | − | 1266.49i | −0.327959 | − | 0.189347i | ||||
\(356\) | −8269.52 | −1.23113 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3449.47 | 0.509246 | ||||||||
\(359\) | 937.988 | + | 541.548i | 0.137897 | + | 0.0796150i | 0.567361 | − | 0.823469i | \(-0.307964\pi\) |
−0.429464 | + | 0.903084i | \(0.641298\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4245.53 | + | 7353.48i | 0.618973 | + | 1.07209i | ||||
\(362\) | 3461.92 | − | 5996.23i | 0.502637 | − | 0.870593i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2982.76i | 0.427739i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1823.53 | + | 1052.81i | −0.259366 | + | 0.149745i | −0.624045 | − | 0.781388i | \(-0.714512\pi\) |
0.364679 | + | 0.931133i | \(0.381179\pi\) | |||||||
\(368\) | −558.594 | + | 322.504i | −0.0791269 | + | 0.0456839i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1647.63i | 0.231503i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1867.35 | + | 3234.34i | −0.259216 | + | 0.448975i | −0.966032 | − | 0.258422i | \(-0.916797\pi\) |
0.706816 | + | 0.707397i | \(0.250131\pi\) | |||||||
\(374\) | −433.917 | − | 751.567i | −0.0599928 | − | 0.103911i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7950.66 | − | 4590.31i | −1.09049 | − | 0.629594i | ||||
\(377\) | −2395.91 | −0.327310 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13141.6 | −1.78111 | −0.890555 | − | 0.454876i | \(-0.849684\pi\) | ||||
−0.890555 | + | 0.454876i | \(0.849684\pi\) | |||||||
\(380\) | 2721.17 | + | 1571.07i | 0.367350 | + | 0.212090i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −627.645 | − | 1087.11i | −0.0840657 | − | 0.145606i | ||||
\(383\) | 2671.88 | − | 4627.84i | 0.356467 | − | 0.617419i | −0.630901 | − | 0.775863i | \(-0.717315\pi\) |
0.987368 | + | 0.158444i | \(0.0506479\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 7962.91i | − | 1.05000i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3043.80 | − | 1757.34i | 0.398262 | − | 0.229937i | ||||
\(389\) | −1624.29 | + | 937.783i | −0.211709 | + | 0.122230i | −0.602105 | − | 0.798417i | \(-0.705671\pi\) |
0.390397 | + | 0.920647i | \(0.372338\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1465.00i | 0.189484i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −813.951 | + | 1409.81i | −0.104077 | + | 0.180266i | ||||
\(395\) | −1409.87 | − | 2441.96i | −0.179590 | − | 0.311059i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8327.97 | − | 4808.16i | −1.05282 | − | 0.607845i | −0.129381 | − | 0.991595i | \(-0.541299\pi\) |
−0.923437 | + | 0.383750i | \(0.874633\pi\) | |||||||
\(398\) | 3246.07 | 0.408821 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −807.262 | −0.100908 | ||||||||
\(401\) | −562.762 | − | 324.911i | −0.0700823 | − | 0.0404620i | 0.464549 | − | 0.885547i | \(-0.346216\pi\) |
−0.534632 | + | 0.845085i | \(0.679550\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3455.70 | + | 5985.45i | 0.427148 | + | 0.739842i | ||||
\(404\) | −797.339 | + | 1381.03i | −0.0981908 | + | 0.170072i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 6461.52i | − | 0.786943i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13491.6 | + | 7789.38i | −1.63109 | + | 0.941711i | −0.647334 | + | 0.762206i | \(0.724116\pi\) |
−0.983757 | + | 0.179505i | \(0.942550\pi\) | |||||||
\(410\) | −2833.78 | + | 1636.08i | −0.341343 | + | 0.197074i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 2402.74i | − | 0.287317i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1396.54 | − | 2418.89i | 0.165190 | − | 0.286117i | ||||
\(416\) | 2527.52 | + | 4377.79i | 0.297889 | + | 0.515959i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5216.77 | + | 3011.91i | 0.610432 | + | 0.352433i | ||||
\(419\) | −5391.59 | −0.628631 | −0.314315 | − | 0.949319i | \(-0.601775\pi\) | ||||
−0.314315 | + | 0.949319i | \(0.601775\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12506.0 | −1.44776 | −0.723879 | − | 0.689927i | \(-0.757642\pi\) | ||||
−0.723879 | + | 0.689927i | \(0.757642\pi\) | |||||||
\(422\) | 3692.67 | + | 2131.97i | 0.425963 | + | 0.245930i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7348.43 | + | 12727.8i | 0.841677 | + | 1.45783i | ||||
\(425\) | −916.765 | + | 1587.88i | −0.104634 | + | 0.181232i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4066.57i | 0.459264i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 413.780 | − | 238.896i | 0.0464052 | − | 0.0267920i | ||||
\(431\) | −7648.94 | + | 4416.12i | −0.854841 | + | 0.493543i | −0.862281 | − | 0.506430i | \(-0.830965\pi\) |
0.00744041 | + | 0.999972i | \(0.497632\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 5550.41i | − | 0.616017i | −0.951384 | − | 0.308009i | \(-0.900337\pi\) | ||
0.951384 | − | 0.308009i | \(-0.0996626\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −318.369 | + | 551.432i | −0.0349705 | + | 0.0605707i | ||||
\(437\) | −5084.44 | − | 8806.51i | −0.556571 | − | 0.964010i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9848.19 | − | 5685.86i | −1.07068 | − | 0.618157i | −0.142313 | − | 0.989822i | \(-0.545454\pi\) |
−0.928367 | + | 0.371664i | \(0.878787\pi\) | |||||||
\(440\) | 3068.91 | 0.332510 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 785.657 | 0.0845473 | ||||||||
\(443\) | 6944.93 | + | 4009.66i | 0.744839 | + | 0.430033i | 0.823826 | − | 0.566843i | \(-0.191835\pi\) |
−0.0789873 | + | 0.996876i | \(0.525169\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3631.94 | − | 6290.71i | −0.386900 | − | 0.670131i | ||||
\(446\) | 4029.25 | − | 6978.87i | 0.427782 | − | 0.740940i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 1039.67i | − | 0.109276i | −0.998506 | − | 0.0546379i | \(-0.982600\pi\) | ||
0.998506 | − | 0.0546379i | \(-0.0174005\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11113.3 | − | 6416.25i | 1.16032 | − | 0.669910i | ||||
\(452\) | −421.022 | + | 243.077i | −0.0438124 | + | 0.0252951i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5543.69i | 0.573079i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7151.36 | + | 12386.5i | −0.732005 | + | 1.26787i | 0.224019 | + | 0.974585i | \(0.428082\pi\) |
−0.956025 | + | 0.293286i | \(0.905251\pi\) | |||||||
\(458\) | 2592.70 | + | 4490.69i | 0.264517 | + | 0.458158i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1802.68 | − | 1040.78i | −0.182718 | − | 0.105492i | ||||
\(461\) | −12732.1 | −1.28632 | −0.643159 | − | 0.765733i | \(-0.722377\pi\) | ||||
−0.643159 | + | 0.765733i | \(0.722377\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12358.7 | 1.24051 | 0.620256 | − | 0.784400i | \(-0.287029\pi\) | ||||
0.620256 | + | 0.784400i | \(0.287029\pi\) | |||||||
\(464\) | 600.402 | + | 346.642i | 0.0600711 | + | 0.0346820i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1740.41 | − | 3014.47i | −0.173010 | − | 0.299662i | ||||
\(467\) | 6288.06 | − | 10891.2i | 0.623077 | − | 1.07920i | −0.365833 | − | 0.930681i | \(-0.619216\pi\) |
0.988909 | − | 0.148520i | \(-0.0474509\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 3240.14i | − | 0.317992i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −14405.2 | + | 8316.82i | −1.40477 | + | 0.811044i | ||||
\(473\) | −1622.72 | + | 936.880i | −0.157744 | + | 0.0910735i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 12726.9i | − | 1.22937i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2312.18 | − | 4004.82i | 0.221249 | − | 0.383214i | ||||
\(479\) | 6137.19 | + | 10629.9i | 0.585418 | + | 1.01397i | 0.994823 | + | 0.101621i | \(0.0324030\pi\) |
−0.409405 | + | 0.912353i | \(0.634264\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5065.96 | + | 2924.83i | 0.480224 | + | 0.277257i | ||||
\(482\) | 638.137 | 0.0603036 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2316.13 | 0.217518 | ||||||||
\(485\) | 2673.65 | + | 1543.63i | 0.250318 | + | 0.144521i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3769.96 | − | 6529.76i | −0.350787 | − | 0.607581i | 0.635601 | − | 0.772018i | \(-0.280753\pi\) |
−0.986388 | + | 0.164437i | \(0.947419\pi\) | |||||||
\(488\) | −3918.72 | + | 6787.42i | −0.363508 | + | 0.629614i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 406.618i | 0.0373735i | 0.999825 | + | 0.0186868i | \(0.00594853\pi\) | ||||
−0.999825 | + | 0.0186868i | \(0.994051\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1363.69 | − | 787.326i | 0.124579 | − | 0.0719258i | ||||
\(494\) | −4722.78 | + | 2726.70i | −0.430138 | + | 0.248340i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 1999.89i | − | 0.181044i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2752.48 | + | 4767.44i | −0.246930 | + | 0.427695i | −0.962672 | − | 0.270669i | \(-0.912755\pi\) |
0.715742 | + | 0.698364i | \(0.246088\pi\) | |||||||
\(500\) | −2887.66 | − | 5001.58i | −0.258280 | − | 0.447355i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3537.49 | + | 2042.37i | 0.314514 | + | 0.181585i | ||||
\(503\) | 6535.76 | 0.579354 | 0.289677 | − | 0.957124i | \(-0.406452\pi\) | ||||
0.289677 | + | 0.957124i | \(0.406452\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1400.75 | −0.123431 | ||||||||
\(506\) | −3455.93 | − | 1995.28i | −0.303626 | − | 0.175299i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −873.135 | − | 1512.31i | −0.0762581 | − | 0.132083i | ||||
\(509\) | −8953.46 | + | 15507.9i | −0.779677 | + | 1.35044i | 0.152452 | + | 0.988311i | \(0.451283\pi\) |
−0.932128 | + | 0.362128i | \(0.882050\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 2825.37i | − | 0.243877i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5967.89 | − | 3445.56i | 0.512125 | − | 0.295675i | ||||
\(515\) | 1827.79 | − | 1055.28i | 0.156392 | − | 0.0902932i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12706.9i | 1.08094i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1389.15 | + | 2406.08i | −0.117151 | + | 0.202911i | ||||
\(521\) | −5445.98 | − | 9432.71i | −0.457951 | − | 0.793195i | 0.540901 | − | 0.841086i | \(-0.318083\pi\) |
−0.998853 | + | 0.0478914i | \(0.984750\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2311.20 | + | 1334.37i | 0.193235 | + | 0.111564i | 0.593496 | − | 0.804837i | \(-0.297747\pi\) |
−0.400261 | + | 0.916401i | \(0.631081\pi\) | |||||||
\(524\) | −3642.28 | −0.303652 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11501.6 | 0.953411 | ||||||||
\(527\) | −3933.79 | − | 2271.17i | −0.325158 | − | 0.187730i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2715.24 | − | 4702.93i | −0.223164 | − | 0.386532i | ||||
\(530\) | −2593.49 | + | 4492.06i | −0.212555 | + | 0.368156i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11617.4i | 0.944097i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3093.48 | + | 1786.02i | −0.249987 | + | 0.144330i | ||||
\(536\) | 12161.3 | − | 7021.32i | 0.980013 | − | 0.565811i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 7067.68i | − | 0.566374i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5388.29 | − | 9332.80i | 0.428209 | − | 0.741679i | −0.568506 | − | 0.822679i | \(-0.692478\pi\) |
0.996714 | + | 0.0810005i | \(0.0258115\pi\) | |||||||
\(542\) | −3497.52 | − | 6057.89i | −0.277180 | − | 0.480089i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2877.19 | − | 1661.15i | −0.226762 | − | 0.130921i | ||||
\(545\) | −559.307 | −0.0439598 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6796.09 | −0.531225 | −0.265612 | − | 0.964080i | \(-0.585574\pi\) | ||||
−0.265612 | + | 0.964080i | \(0.585574\pi\) | |||||||
\(548\) | −10027.8 | − | 5789.54i | −0.781689 | − | 0.451308i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2497.20 | − | 4325.28i | −0.193602 | − | 0.335328i | ||||
\(551\) | −5464.99 | + | 9465.64i | −0.422534 | + | 0.731851i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 4276.94i | 0.327996i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3348.21 | − | 1933.09i | 0.255388 | − | 0.147448i | ||||
\(557\) | 15641.9 | − | 9030.85i | 1.18989 | − | 0.686983i | 0.231608 | − | 0.972809i | \(-0.425601\pi\) |
0.958282 | + | 0.285826i | \(0.0922680\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1696.33i | − | 0.128349i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4801.82 | + | 8316.99i | −0.360413 | + | 0.624254i | ||||
\(563\) | 10523.3 | + | 18227.0i | 0.787755 | + | 1.36443i | 0.927339 | + | 0.374221i | \(0.122090\pi\) |
−0.139585 | + | 0.990210i | \(0.544577\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −369.823 | − | 213.517i | −0.0275373 | − | 0.0158986i | ||||
\(566\) | −4984.19 | −0.370143 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11631.8 | −0.859257 | ||||||||
\(569\) | 10497.9 | + | 6060.98i | 0.773455 | + | 0.446554i | 0.834106 | − | 0.551605i | \(-0.185984\pi\) |
−0.0606509 | + | 0.998159i | \(0.519318\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1472.07 | + | 2549.70i | 0.107888 | + | 0.186868i | 0.914915 | − | 0.403647i | \(-0.132258\pi\) |
−0.807026 | + | 0.590516i | \(0.798924\pi\) | |||||||
\(572\) | 2188.91 | − | 3791.30i | 0.160005 | − | 0.277137i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8431.12i | 0.611482i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4495.86 | − | 2595.69i | 0.324376 | − | 0.187279i | −0.328965 | − | 0.944342i | \(-0.606700\pi\) |
0.653342 | + | 0.757063i | \(0.273367\pi\) | |||||||
\(578\) | 6448.60 | − | 3723.10i | 0.464060 | − | 0.267925i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2237.35i | 0.160174i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10170.9 | − | 17616.6i | 0.722533 | − | 1.25146i | ||||
\(584\) | 6848.63 | + | 11862.2i | 0.485271 | + | 0.840514i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2185.81 | − | 1261.98i | −0.154087 | − | 0.0889620i | ||||
\(587\) | 21918.4 | 1.54118 | 0.770588 | − | 0.637334i | \(-0.219963\pi\) | ||||
0.770588 | + | 0.637334i | \(0.219963\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 31529.3 | 2.20568 | ||||||||
\(590\) | −5084.04 | − | 2935.27i | −0.354757 | − | 0.204819i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −846.334 | − | 1465.89i | −0.0587569 | − | 0.101770i | ||||
\(593\) | −10119.7 | + | 17527.9i | −0.700788 | + | 1.21380i | 0.267402 | + | 0.963585i | \(0.413835\pi\) |
−0.968190 | + | 0.250216i | \(0.919499\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6419.55i | 0.441200i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3128.68 | − | 1806.34i | 0.213948 | − | 0.123523i | ||||
\(599\) | 7376.06 | − | 4258.57i | 0.503135 | − | 0.290485i | −0.226872 | − | 0.973925i | \(-0.572850\pi\) |
0.730007 | + | 0.683439i | \(0.239517\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5040.33i | 0.342096i | 0.985263 | + | 0.171048i | \(0.0547152\pi\) | ||||
−0.985263 | + | 0.171048i | \(0.945285\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2880.44 | + | 4989.07i | −0.194046 | + | 0.336097i | ||||
\(605\) | 1017.24 | + | 1761.90i | 0.0683579 | + | 0.118399i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23489.5 | + | 13561.6i | 1.57069 | + | 0.906837i | 0.996085 | + | 0.0884057i | \(0.0281772\pi\) |
0.574604 | + | 0.818432i | \(0.305156\pi\) | |||||||
\(608\) | 23060.7 | 1.53822 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2766.08 | −0.183599 | ||||||||
\(611\) | −9962.44 | − | 5751.81i | −0.659635 | − | 0.380840i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1467.22 | − | 2541.30i | −0.0966730 | − | 0.167443i | 0.813633 | − | 0.581379i | \(-0.197487\pi\) |
−0.910306 | + | 0.413937i | \(0.864153\pi\) | |||||||
\(614\) | 1460.80 | − | 2530.19i | 0.0960151 | − | 0.166303i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 2908.86i | − | 0.189799i | −0.995487 | − | 0.0948996i | \(-0.969747\pi\) | ||
0.995487 | − | 0.0948996i | \(-0.0302530\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13814.4 | − | 7975.77i | 0.897010 | − | 0.517889i | 0.0207811 | − | 0.999784i | \(-0.493385\pi\) |
0.876229 | + | 0.481895i | \(0.160051\pi\) | |||||||
\(620\) | 5589.33 | − | 3227.00i | 0.362053 | − | 0.209032i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 15461.5i | − | 0.996706i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3883.68 | + | 6726.73i | −0.248556 | + | 0.430511i | ||||
\(626\) | −1024.83 | − | 1775.05i | −0.0654319 | − | 0.113331i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10865.5 | + | 6273.18i | 0.690412 | + | 0.398610i | ||||
\(629\) | −3844.54 | −0.243707 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31218.8 | −1.96957 | −0.984786 | − | 0.173771i | \(-0.944405\pi\) | ||||
−0.984786 | + | 0.173771i | \(0.944405\pi\) | |||||||
\(632\) | −11213.8 | − | 6474.30i | −0.705793 | − | 0.407490i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7734.35 | − | 13396.3i | −0.484496 | − | 0.839171i | ||||
\(635\) | 766.955 | − | 1328.41i | 0.0479302 | − | 0.0830176i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4289.24i | 0.266164i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4504.56 | − | 2600.71i | 0.278216 | − | 0.160628i | ||||
\(641\) | 4720.80 | − | 2725.55i | 0.290890 | − | 0.167945i | −0.347453 | − | 0.937697i | \(-0.612953\pi\) |
0.638343 | + | 0.769752i | \(0.279620\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15700.8i | 0.962956i | 0.876458 | + | 0.481478i | \(0.159900\pi\) | ||||
−0.876458 | + | 0.481478i | \(0.840100\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1792.06 | − | 3103.93i | 0.109145 | − | 0.189044i | ||||
\(647\) | 11372.0 | + | 19696.9i | 0.691006 | + | 1.19686i | 0.971509 | + | 0.237004i | \(0.0761656\pi\) |
−0.280502 | + | 0.959853i | \(0.590501\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19938.1 | + | 11511.3i | 1.20592 | + | 0.696236i | ||||
\(650\) | 4521.47 | 0.272841 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 19380.6 | 1.16411 | ||||||||
\(653\) | 4984.17 | + | 2877.61i | 0.298691 | + | 0.172450i | 0.641855 | − | 0.766826i | \(-0.278165\pi\) |
−0.343163 | + | 0.939276i | \(0.611498\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1599.68 | − | 2770.72i | −0.0954268 | − | 0.165284i | ||||
\(656\) | 1680.81 | − | 2911.24i | 0.100037 | − | 0.173270i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 24579.2i | − | 1.45292i | −0.687211 | − | 0.726458i | \(-0.741165\pi\) | ||
0.687211 | − | 0.726458i | \(-0.258835\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4251.57 | − | 2454.64i | 0.250177 | − | 0.144440i | −0.369669 | − | 0.929164i | \(-0.620529\pi\) |
0.619845 | + | 0.784724i | \(0.287195\pi\) | |||||||
\(662\) | 3798.70 | − | 2193.18i | 0.223022 | − | 0.128762i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 12826.2i | − | 0.749631i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3620.36 | − | 6270.65i | 0.210166 | − | 0.364019i | ||||
\(668\) | −6043.46 | − | 10467.6i | −0.350043 | − | 0.606291i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4292.10 | + | 2478.05i | 0.247490 | + | 0.142888i | ||||
\(671\) | 10847.8 | 0.624103 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2635.70 | 0.150964 | 0.0754819 | − | 0.997147i | \(-0.475950\pi\) | ||||
0.0754819 | + | 0.997147i | \(0.475950\pi\) | |||||||
\(674\) | 14808.8 | + | 8549.89i | 0.846314 | + | 0.488619i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3920.93 | − | 6791.25i | −0.223084 | − | 0.386393i | ||||
\(677\) | 3191.45 | − | 5527.76i | 0.181178 | − | 0.313809i | −0.761104 | − | 0.648630i | \(-0.775342\pi\) |
0.942282 | + | 0.334821i | \(0.108676\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − | 1825.97i | − | 0.102975i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 10715.3 | − | 6186.51i | 0.601630 | − | 0.347351i | ||||
\(683\) | 11952.8 | − | 6900.95i | 0.669636 | − | 0.386614i | −0.126303 | − | 0.991992i | \(-0.540311\pi\) |
0.795939 | + | 0.605377i | \(0.206978\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 10171.0i | − | 0.567318i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −245.426 | + | 425.091i | −0.0136000 | + | 0.0235559i | ||||
\(689\) | 9207.82 | + | 15948.4i | 0.509129 | + | 0.881838i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1516.12 | − | 875.333i | −0.0834674 | − | 0.0481899i | 0.457685 | − | 0.889114i | \(-0.348679\pi\) |
−0.541153 | + | 0.840924i | \(0.682012\pi\) | |||||||
\(692\) | 21733.9 | 1.19393 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16161.9 | −0.884001 | ||||||||
\(695\) | 2941.04 | + | 1698.01i | 0.160518 | + | 0.0926752i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3817.61 | − | 6612.29i | −0.207464 | − | 0.359338i | ||||
\(698\) | −1339.60 | + | 2320.26i | −0.0726429 | + | 0.125821i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26927.8i | 1.45085i | 0.688300 | + | 0.725426i | \(0.258357\pi\) | ||||
−0.688300 | + | 0.725426i | \(0.741643\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23110.5 | − | 13342.9i | 1.23987 | − | 0.715841i | ||||
\(704\) | 6203.92 | − | 3581.83i | 0.332129 | − | 0.191755i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 5436.69i | − | 0.289819i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5801.80 | − | 10049.0i | 0.307322 | − | 0.532297i | −0.670454 | − | 0.741952i | \(-0.733900\pi\) |
0.977776 | + | 0.209654i | \(0.0672338\pi\) | |||||||
\(710\) | −2052.61 | − | 3555.23i | −0.108497 | − | 0.187923i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −28887.8 | − | 16678.4i | −1.52053 | − | 0.877877i | ||||
\(713\) | −20887.1 | −1.09709 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3845.44 | 0.201135 | ||||||||
\(716\) | −9904.17 | − | 5718.17i | −0.516950 | − | 0.298461i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 877.693 | + | 1520.21i | 0.0456201 | + | 0.0790163i | ||||
\(719\) | −6750.67 | + | 11692.5i | −0.350150 | + | 0.606477i | −0.986275 | − | 0.165108i | \(-0.947203\pi\) |
0.636126 | + | 0.771585i | \(0.280536\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 13761.6i | 0.709353i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −19879.8 | + | 11477.6i | −1.02048 | + | 0.589175i | ||||
\(725\) | 7848.06 | − | 4531.08i | 0.402027 | − | 0.232110i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1116.75i | − | 0.0569708i | −0.999594 | − | 0.0284854i | \(-0.990932\pi\) | ||
0.999594 | − | 0.0284854i | \(-0.00906842\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2417.10 | + | 4186.54i | −0.122549 | + | 0.212261i | ||||
\(731\) | 557.435 | + | 965.505i | 0.0282045 | + | 0.0488516i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25019.4 | + | 14444.9i | 1.26072 | + | 0.727879i | 0.973215 | − | 0.229898i | \(-0.0738394\pi\) |
0.287510 | + | 0.957778i | \(0.407173\pi\) | |||||||
\(734\) | −3412.62 | −0.171610 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −15276.9 | −0.765101 | ||||||||
\(737\) | −16832.4 | − | 9718.18i | −0.841287 | − | 0.485717i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 996.244 | + | 1725.55i | 0.0495906 | + | 0.0858934i | 0.889755 | − | 0.456438i | \(-0.150875\pi\) |
−0.840165 | + | 0.542332i | \(0.817542\pi\) | |||||||
\(740\) | 2731.27 | − | 4730.69i | 0.135680 | − | 0.235005i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 32395.7i | − | 1.59957i | −0.600284 | − | 0.799787i | \(-0.704946\pi\) | ||
0.600284 | − | 0.799787i | \(-0.295054\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4883.42 | + | 2819.44i | −0.240154 | + | 0.138653i | ||||
\(746\) | −5241.93 | + | 3026.43i | −0.257266 | + | 0.148533i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2877.21i | 0.140643i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3796.22 | − | 6575.24i | 0.184455 | − | 0.319486i | −0.758937 | − | 0.651163i | \(-0.774281\pi\) |
0.943393 | + | 0.331677i | \(0.107615\pi\) | |||||||
\(752\) | 1664.35 | + | 2882.75i | 0.0807084 | + | 0.139791i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3362.85 | − | 1941.54i | −0.162424 | − | 0.0937755i | ||||
\(755\) | −5060.32 | −0.243926 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29398.9 | 1.41152 | 0.705760 | − | 0.708451i | \(-0.250605\pi\) | ||||
0.705760 | + | 0.708451i | \(0.250605\pi\) | |||||||
\(758\) | −18445.3 | − | 10649.4i | −0.883857 | − | 0.510295i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6337.22 | + | 10976.4i | 0.302467 | + | 0.523888i | ||||
\(761\) | −16277.5 | + | 28193.4i | −0.775373 | + | 1.34299i | 0.159212 | + | 0.987244i | \(0.449105\pi\) |
−0.934585 | + | 0.355741i | \(0.884229\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4161.78i | 0.197078i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7500.39 | − | 4330.35i | 0.353786 | − | 0.204258i | ||||
\(767\) | −18050.1 | + | 10421.2i | −0.849742 | + | 0.490599i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34767.8i | 1.63038i | 0.579195 | + | 0.815189i | \(0.303367\pi\) | ||||
−0.579195 | + | 0.815189i | \(0.696633\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −13200.1 | + | 22863.2i | −0.615391 | + | 1.06589i | ||||
\(773\) | −2994.63 | − | 5186.85i | −0.139339 | − | 0.241343i | 0.787907 | − | 0.615794i | \(-0.211165\pi\) |
−0.927247 | + | 0.374451i | \(0.877831\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −22639.0 | − | 13070.6i | −1.04931 | − | 0.605821i | ||||
\(776\) | 14177.2 | 0.655838 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3039.75 | −0.140078 | ||||||||
\(779\) | 45897.2 | + | 26498.8i | 2.11096 | + | 1.21876i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8049.74 | + | 13942.6i | 0.368812 | + | 0.638802i | ||||
\(782\) | −1187.17 | + | 2056.25i | −0.0542880 | + | 0.0940296i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11020.6i | 0.501074i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36037.5 | + | 20806.3i | −1.63227 | + | 0.942393i | −0.648882 | + | 0.760889i | \(0.724763\pi\) |
−0.983390 | + | 0.181504i | \(0.941903\pi\) | |||||||
\(788\) | 4674.06 | − | 2698.57i | 0.211302 | − | 0.121996i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 4569.97i | − | 0.205813i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4910.28 | + | 8504.86i | −0.219885 | + | 0.380853i | ||||
\(794\) | −7792.64 | − | 13497.2i | −0.348300 | − | 0.603274i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9320.15 | − | 5380.99i | −0.415005 | − | 0.239603i | ||||
\(797\) | −2077.70 | −0.0923412 | −0.0461706 | − | 0.998934i | \(-0.514702\pi\) | ||||
−0.0461706 | + | 0.998934i | \(0.514702\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7560.47 | 0.334756 | ||||||||
\(800\) | −16558.3 | − | 9559.94i | −0.731780 | − | 0.422494i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −526.587 | − | 912.075i | −0.0231851 | − | 0.0401577i | ||||
\(803\) | 9479.16 | − | 16418.4i | 0.416578 | − | 0.721535i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11201.4i | 0.489519i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5570.67 | + | 3216.23i | −0.242544 | + | 0.140033i | ||||
\(809\) | −21392.6 | + | 12351.0i | −0.929697 | + | 0.536761i | −0.886716 | − | 0.462315i | \(-0.847019\pi\) |
−0.0429815 | + | 0.999076i | \(0.513686\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 30991.5i | − | 1.34187i | −0.741516 | − | 0.670936i | \(-0.765893\pi\) | ||
0.741516 | − | 0.670936i | \(-0.234107\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5236.13 | − | 9069.24i | 0.225462 | − | 0.390512i | ||||
\(815\) | 8511.88 | + | 14743.0i | 0.365838 | + | 0.633650i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6701.77 | − | 3869.27i | −0.286983 | − | 0.165690i | ||||
\(818\) | −25248.7 | −1.07922 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10848.5 | 0.462008 | ||||||||
\(821\) | 24401.5 | + | 14088.2i | 1.03730 | + | 0.598883i | 0.919066 | − | 0.394103i | \(-0.128945\pi\) |
0.118230 | + | 0.992986i | \(0.462278\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8539.10 | − | 14790.2i | −0.361670 | − | 0.626431i | 0.626566 | − | 0.779368i | \(-0.284460\pi\) |
−0.988236 | + | 0.152938i | \(0.951127\pi\) | |||||||
\(824\) | 4845.97 | − | 8393.47i | 0.204876 | − | 0.354855i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 19778.2i | − | 0.831626i | −0.909450 | − | 0.415813i | \(-0.863497\pi\) | ||
0.909450 | − | 0.415813i | \(-0.136503\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10941.2 | + | 6316.89i | −0.458387 | + | 0.264650i | −0.711366 | − | 0.702822i | \(-0.751923\pi\) |
0.252979 | + | 0.967472i | \(0.418590\pi\) | |||||||
\(830\) | 3920.32 | − | 2263.40i | 0.163947 | − | 0.0946549i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6485.32i | 0.270238i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5308.53 | − | 9194.64i | 0.220011 | − | 0.381070i | ||||
\(836\) | −9985.65 | − | 17295.6i | −0.413111 | − | 0.715529i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7567.51 | − | 4369.10i | −0.311951 | − | 0.180105i | ||||
\(839\) | −39650.4 | −1.63157 | −0.815784 | − | 0.578357i | \(-0.803694\pi\) | ||||
−0.815784 | + | 0.578357i | \(0.803694\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16606.3 | 0.680894 | ||||||||
\(842\) | −17553.2 | − | 10134.3i | −0.718434 | − | 0.414788i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7068.30 | − | 12242.7i | −0.288271 | − | 0.499301i | ||||
\(845\) | 3444.11 | − | 5965.38i | 0.140214 | − | 0.242858i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 5328.78i | − | 0.215791i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2573.50 | + | 1485.81i | −0.103847 | + | 0.0599564i | ||||
\(851\) | −15309.9 | + | 8839.18i | −0.616706 | + | 0.356056i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27542.7i | 1.10556i | 0.833327 | + | 0.552780i | \(0.186433\pi\) | ||||
−0.833327 | + | 0.552780i | \(0.813567\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8201.67 | + | 14205.7i | −0.327485 | + | 0.567221i | ||||
\(857\) | −20097.4 | − | 34809.8i | −0.801068 | − | 1.38749i | −0.918914 | − | 0.394458i | \(-0.870932\pi\) |
0.117846 | − | 0.993032i | \(-0.462401\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10338.3 | + | 5968.81i | 0.410638 | + | 0.237082i | 0.691064 | − | 0.722794i | \(-0.257142\pi\) |
−0.280426 | + | 0.959876i | \(0.590476\pi\) | |||||||
\(860\) | −1584.07 | −0.0628095 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −14314.5 | −0.565608 | ||||||||
\(863\) | 28785.5 | + | 16619.3i | 1.13542 | + | 0.655536i | 0.945293 | − | 0.326223i | \(-0.105776\pi\) |
0.190129 | + | 0.981759i | \(0.439109\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9545.45 | + | 16533.2i | 0.375208 | + | 0.649880i | ||||
\(866\) | 4497.80 | − | 7790.43i | 0.176491 | − | 0.305692i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17922.1i | 0.699615i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15238.5 | − | 8797.94i | 0.592809 | − | 0.342258i | ||||
\(872\) | −2224.31 | + | 1284.21i | −0.0863815 | + | 0.0498724i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 16480.8i | − | 0.637840i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10709.6 | + | 18549.6i | −0.412358 | + | 0.714226i | −0.995147 | − | 0.0983981i | \(-0.968628\pi\) |
0.582789 | + | 0.812624i | \(0.301961\pi\) | |||||||
\(878\) | −9215.13 | − | 15961.1i | −0.354209 | − | 0.613508i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −963.646 | − | 556.362i | −0.0369142 | − | 0.0213124i | ||||
\(881\) | −31353.3 | −1.19900 | −0.599501 | − | 0.800374i | \(-0.704634\pi\) | ||||
−0.599501 | + | 0.800374i | \(0.704634\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35483.7 | −1.35235 | −0.676173 | − | 0.736743i | \(-0.736363\pi\) | ||||
−0.676173 | + | 0.736743i | \(0.736363\pi\) | |||||||
\(884\) | −2255.79 | − | 1302.38i | −0.0858262 | − | 0.0495518i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6498.50 | + | 11255.7i | 0.246412 | + | 0.426799i | ||||
\(887\) | 10127.6 | − | 17541.6i | 0.383374 | − | 0.664024i | −0.608168 | − | 0.793808i | \(-0.708095\pi\) |
0.991542 | + | 0.129785i | \(0.0414286\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 11772.7i | − | 0.443394i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −23137.7 | + | 13358.6i | −0.868506 | + | 0.501432i | ||||
\(893\) | −45447.9 | + | 26239.4i | −1.70309 | + | 0.983278i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 10045.6i | − | 0.375182i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 842.499 | − | 1459.25i | 0.0313080 | − | 0.0542270i | ||||
\(899\) | 11225.2 | + | 19442.6i | 0.416442 | + | 0.721298i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10481.7 | − | 6051.61i | −0.387565 | − | 0.223761i | ||||
\(902\) | 20797.8 | 0.767727 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1961.00 | −0.0721481 | ||||||||
\(905\) | −17462.3 | − | 10081.9i | −0.641400 | − | 0.370312i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12848.0 | + | 22253.5i | 0.470355 | + | 0.814680i | 0.999425 | − | 0.0338987i | \(-0.0107924\pi\) |
−0.529070 | + | 0.848578i | \(0.677459\pi\) | |||||||
\(908\) | 9189.75 | − | 15917.1i | 0.335873 | − | 0.581749i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 33200.2i | − | 1.20743i | −0.797199 | − | 0.603716i | \(-0.793686\pi\) | ||
0.797199 | − | 0.603716i | \(-0.206314\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15374.3 | + | 8876.38i | −0.557302 | + | 0.321758i | ||||
\(914\) | −20075.0 | + | 11590.3i | −0.726500 | + | 0.419445i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 17191.6i | − | 0.620118i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1068.12 | + | 1850.03i | −0.0383394 | + | 0.0664058i | −0.884558 | − | 0.466429i | \(-0.845540\pi\) |
0.846219 | + | 0.532835i | \(0.178873\pi\) | |||||||
\(920\) | −4198.18 | − | 7271.46i | −0.150446 | − | 0.260579i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −17870.5 | − | 10317.5i | −0.638322 | − | 0.368535i | ||||
\(923\) | −14575.0 | −0.519763 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22125.4 | −0.786464 | ||||||||
\(926\) | 17346.4 | + | 10014.9i | 0.615591 | + | 0.355412i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8210.17 | + | 14220.4i | 0.290422 | + | 0.503026i | ||||
\(929\) | 526.275 | − | 911.535i | 0.0185861 | − | 0.0321921i | −0.856583 | − | 0.516010i | \(-0.827417\pi\) |
0.875169 | + | 0.483818i | \(0.160750\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 11540.3i | 0.405594i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 17651.6 | − | 10191.1i | 0.618391 | − | 0.357028i | ||||
\(935\) | −2188.72 | + | 1263.66i | −0.0765550 | + | 0.0441990i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14333.0i | 0.499721i | 0.968282 | + | 0.249861i | \(0.0803848\pi\) | ||||
−0.968282 | + | 0.249861i | \(0.919615\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5371.16 | + | 9303.12i | −0.186370 | + | 0.322803i | ||||
\(941\) | −6563.30 | − | 11368.0i | −0.227372 | − | 0.393821i | 0.729656 | − | 0.683814i | \(-0.239680\pi\) |
−0.957029 | + | 0.289994i | \(0.906347\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30405.3 | − | 17554.5i | −1.04998 | − | 0.606207i | ||||
\(944\) | 6031.02 | 0.207937 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3036.82 | −0.104372 | ||||||||
\(947\) | 7602.28 | + | 4389.18i | 0.260867 | + | 0.150611i | 0.624730 | − | 0.780841i | \(-0.285209\pi\) |
−0.363863 | + | 0.931452i | \(0.618542\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8581.56 | + | 14863.7i | 0.293540 | + | 0.508425i | ||||
\(950\) | 10313.3 | − | 17863.2i | 0.352219 | − | 0.610061i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 4130.75i | − | 0.140407i | −0.997533 | − | 0.0702036i | \(-0.977635\pi\) | ||
0.997533 | − | 0.0702036i | \(-0.0223649\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3165.91 | + | 1827.84i | −0.107274 | + | 0.0619344i | ||||
\(956\) | −13277.5 | + | 7665.80i | −0.449191 | + | 0.259341i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 19893.2i | 0.670899i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17485.4 | − | 30285.6i | 0.586936 | − | 1.01660i | ||||
\(962\) | 4740.31 | + | 8210.45i | 0.158871 | + | 0.275172i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1832.23 | − | 1057.84i | −0.0612158 | − | 0.0353430i | ||||
\(965\) | −23189.7 | −0.773579 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2697.99 | 0.0897222 | 0.0448611 | − | 0.998993i | \(-0.485715\pi\) | ||||
0.0448611 | + | 0.998993i | \(0.485715\pi\) | |||||||
\(968\) | 8090.91 | + | 4671.29i | 0.268648 | + | 0.155104i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2501.79 | + | 4333.22i | 0.0828119 | + | 0.143434i | ||||
\(971\) | 8411.94 | − | 14569.9i | 0.278014 | − | 0.481535i | −0.692877 | − | 0.721056i | \(-0.743657\pi\) |
0.970891 | + | 0.239521i | \(0.0769904\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 12220.0i | − | 0.402007i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2460.98 | − | 1420.85i | 0.0807110 | − | 0.0465985i | ||||
\(977\) | 33352.8 | − | 19256.3i | 1.09217 | − | 0.630565i | 0.158017 | − | 0.987436i | \(-0.449490\pi\) |
0.934154 | + | 0.356871i | \(0.116157\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 46169.0i | 1.50722i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −329.505 | + | 570.719i | −0.0107077 | + | 0.0185462i | ||||
\(983\) | 13465.4 | + | 23322.7i | 0.436905 | + | 0.756742i | 0.997449 | − | 0.0713826i | \(-0.0227411\pi\) |
−0.560544 | + | 0.828125i | \(0.689408\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4105.66 | + | 2370.40i | 0.132809 | + | 0.0766774i | ||||
\(986\) | 2552.06 | 0.0824281 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18080.2 | 0.582193 | ||||||||
\(989\) | 4439.68 | + | 2563.25i | 0.142744 | + | 0.0824132i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5796.70 | + | 10040.2i | 0.185810 | + | 0.321833i | 0.943849 | − | 0.330376i | \(-0.107176\pi\) |
−0.758039 | + | 0.652209i | \(0.773842\pi\) | |||||||
\(992\) | 23683.6 | − | 41021.2i | 0.758018 | − | 1.31293i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 9453.25i | − | 0.301194i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −43168.7 | + | 24923.4i | −1.37128 | + | 0.791708i | −0.991089 | − | 0.133200i | \(-0.957475\pi\) |
−0.380190 | + | 0.924908i | \(0.624141\pi\) | |||||||
\(998\) | −7726.65 | + | 4460.98i | −0.245073 | + | 0.141493i | ||||
\(999\) | 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 | 441.4.p.d.215.16 | 48 | ||
3.2 | odd | 2 | inner | 441.4.p.d.215.9 | 48 | ||
7.2 | even | 3 | 441.4.c.b.440.15 | yes | 24 | ||
7.3 | odd | 6 | inner | 441.4.p.d.80.9 | 48 | ||
7.4 | even | 3 | inner | 441.4.p.d.80.10 | 48 | ||
7.5 | odd | 6 | 441.4.c.b.440.9 | ✓ | 24 | ||
7.6 | odd | 2 | inner | 441.4.p.d.215.15 | 48 | ||
21.2 | odd | 6 | 441.4.c.b.440.10 | yes | 24 | ||
21.5 | even | 6 | 441.4.c.b.440.16 | yes | 24 | ||
21.11 | odd | 6 | inner | 441.4.p.d.80.15 | 48 | ||
21.17 | even | 6 | inner | 441.4.p.d.80.16 | 48 | ||
21.20 | even | 2 | inner | 441.4.p.d.215.10 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.4.c.b.440.9 | ✓ | 24 | 7.5 | odd | 6 | ||
441.4.c.b.440.10 | yes | 24 | 21.2 | odd | 6 | ||
441.4.c.b.440.15 | yes | 24 | 7.2 | even | 3 | ||
441.4.c.b.440.16 | yes | 24 | 21.5 | even | 6 | ||
441.4.p.d.80.9 | 48 | 7.3 | odd | 6 | inner | ||
441.4.p.d.80.10 | 48 | 7.4 | even | 3 | inner | ||
441.4.p.d.80.15 | 48 | 21.11 | odd | 6 | inner | ||
441.4.p.d.80.16 | 48 | 21.17 | even | 6 | inner | ||
441.4.p.d.215.9 | 48 | 3.2 | odd | 2 | inner | ||
441.4.p.d.215.10 | 48 | 21.20 | even | 2 | inner | ||
441.4.p.d.215.15 | 48 | 7.6 | odd | 2 | inner | ||
441.4.p.d.215.16 | 48 | 1.1 | even | 1 | trivial |