Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,4,Mod(107,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.107");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.b (of order \(2\), degree \(1\), 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: | \(6.37220628062\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 12x^{10} + 112x^{8} - 368x^{6} + 928x^{4} - 256x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{18}\cdot 3^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 107.9 | ||
Root | \(-0.456937 - 0.263813i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.107 |
Dual form | 108.4.b.a.107.10 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.51859 | − | 2.38619i | 0.536901 | − | 0.843645i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.38780 | − | 7.24726i | −0.423474 | − | 0.905908i | ||||
\(5\) | − | 13.1987i | − | 1.18052i | −0.807212 | − | 0.590262i | \(-0.799024\pi\) | ||
0.807212 | − | 0.590262i | \(-0.200976\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.49091i | 0.242486i | 0.992623 | + | 0.121243i | \(0.0386881\pi\) | ||||
−0.992623 | + | 0.121243i | \(0.961312\pi\) | |||||||
\(8\) | −22.4380 | − | 2.92167i | −0.991629 | − | 0.129121i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −31.4945 | − | 20.0433i | −0.995944 | − | 0.633825i | ||||
\(11\) | 22.3519 | 0.612669 | 0.306335 | − | 0.951924i | \(-0.400897\pi\) | ||||
0.306335 | + | 0.951924i | \(0.400897\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −73.5402 | −1.56895 | −0.784476 | − | 0.620159i | \(-0.787068\pi\) | ||||
−0.784476 | + | 0.620159i | \(0.787068\pi\) | |||||||
\(14\) | 10.7162 | + | 6.81984i | 0.204573 | + | 0.130191i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −41.0457 | + | 49.1045i | −0.641339 | + | 0.767258i | ||||
\(17\) | − | 42.6199i | − | 0.608050i | −0.952664 | − | 0.304025i | \(-0.901669\pi\) | ||
0.952664 | − | 0.304025i | \(-0.0983307\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 122.563i | − | 1.47989i | −0.672669 | − | 0.739943i | \(-0.734852\pi\) | ||
0.672669 | − | 0.739943i | \(-0.265148\pi\) | |||||||
\(20\) | −95.6542 | + | 44.7144i | −1.06945 | + | 0.499922i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 33.9433 | − | 53.3359i | 0.328943 | − | 0.516875i | ||||
\(23\) | 197.965 | 1.79472 | 0.897360 | − | 0.441299i | \(-0.145482\pi\) | ||||
0.897360 | + | 0.441299i | \(0.145482\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −49.2047 | −0.393638 | ||||||||
\(26\) | −111.677 | + | 175.481i | −0.842372 | + | 1.32364i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 32.5468 | − | 15.2143i | 0.219670 | − | 0.102687i | ||||
\(29\) | 14.6816i | 0.0940102i | 0.998895 | + | 0.0470051i | \(0.0149677\pi\) | ||||
−0.998895 | + | 0.0470051i | \(0.985032\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 147.133i | 0.852448i | 0.904618 | + | 0.426224i | \(0.140156\pi\) | ||||
−0.904618 | + | 0.426224i | \(0.859844\pi\) | |||||||
\(32\) | 54.8412 | + | 172.512i | 0.302958 | + | 0.953004i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −101.699 | − | 64.7220i | −0.512979 | − | 0.326463i | ||||
\(35\) | 59.2740 | 0.286261 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 234.154 | 1.04040 | 0.520199 | − | 0.854045i | \(-0.325858\pi\) | ||||
0.520199 | + | 0.854045i | \(0.325858\pi\) | |||||||
\(38\) | −292.458 | − | 186.122i | −1.24850 | − | 0.794553i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −38.5622 | + | 296.152i | −0.152430 | + | 1.17064i | ||||
\(41\) | − | 396.340i | − | 1.50970i | −0.655895 | − | 0.754852i | \(-0.727708\pi\) | ||
0.655895 | − | 0.754852i | \(-0.272292\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 280.764i | 0.995725i | 0.867256 | + | 0.497863i | \(0.165882\pi\) | ||||
−0.867256 | + | 0.497863i | \(0.834118\pi\) | |||||||
\(44\) | −75.7238 | − | 161.990i | −0.259450 | − | 0.555022i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 300.627 | − | 472.382i | 0.963587 | − | 1.51411i | ||||
\(47\) | 534.237 | 1.65801 | 0.829006 | − | 0.559240i | \(-0.188907\pi\) | ||||
0.829006 | + | 0.559240i | \(0.188907\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 322.832 | 0.941200 | ||||||||
\(50\) | −74.7216 | + | 117.412i | −0.211345 | + | 0.332091i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 249.139 | + | 532.965i | 0.664411 | + | 1.42133i | ||||
\(53\) | − | 337.497i | − | 0.874695i | −0.899293 | − | 0.437347i | \(-0.855918\pi\) | ||
0.899293 | − | 0.437347i | \(-0.144082\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 295.016i | − | 0.723271i | ||||||
\(56\) | 13.1210 | − | 100.767i | 0.0313101 | − | 0.240457i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 35.0330 | + | 22.2952i | 0.0793113 | + | 0.0504742i | ||||
\(59\) | −672.928 | −1.48488 | −0.742439 | − | 0.669914i | \(-0.766331\pi\) | ||||
−0.742439 | + | 0.669914i | \(0.766331\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −80.8693 | −0.169742 | −0.0848709 | − | 0.996392i | \(-0.527048\pi\) | ||||
−0.0848709 | + | 0.996392i | \(0.527048\pi\) | |||||||
\(62\) | 351.087 | + | 223.434i | 0.719164 | + | 0.457680i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 494.928 | + | 131.113i | 0.966656 | + | 0.256080i | ||||
\(65\) | 970.632i | 1.85219i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 251.791i | − | 0.459121i | −0.973294 | − | 0.229560i | \(-0.926271\pi\) | ||
0.973294 | − | 0.229560i | \(-0.0737289\pi\) | |||||||
\(68\) | −308.878 | + | 144.388i | −0.550838 | + | 0.257494i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 90.0127 | − | 141.439i | 0.153694 | − | 0.241503i | ||||
\(71\) | −95.8124 | −0.160153 | −0.0800763 | − | 0.996789i | \(-0.525516\pi\) | ||||
−0.0800763 | + | 0.996789i | \(0.525516\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −251.422 | −0.403106 | −0.201553 | − | 0.979478i | \(-0.564599\pi\) | ||||
−0.201553 | + | 0.979478i | \(0.564599\pi\) | |||||||
\(74\) | 355.583 | − | 558.737i | 0.558591 | − | 0.877727i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −888.245 | + | 415.218i | −1.34064 | + | 0.626694i | ||||
\(77\) | 100.381i | 0.148564i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 499.839i | 0.711852i | 0.934514 | + | 0.355926i | \(0.115835\pi\) | ||||
−0.934514 | + | 0.355926i | \(0.884165\pi\) | |||||||
\(80\) | 648.114 | + | 541.748i | 0.905766 | + | 0.757116i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −945.742 | − | 601.876i | −1.27366 | − | 0.810562i | ||||
\(83\) | 16.1731 | 0.0213882 | 0.0106941 | − | 0.999943i | \(-0.496596\pi\) | ||||
0.0106941 | + | 0.999943i | \(0.496596\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −562.526 | −0.717818 | ||||||||
\(86\) | 669.957 | + | 426.365i | 0.840039 | + | 0.534606i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −501.533 | − | 65.3050i | −0.607540 | − | 0.0791084i | ||||
\(89\) | 321.011i | 0.382327i | 0.981558 | + | 0.191164i | \(0.0612261\pi\) | ||||
−0.981558 | + | 0.191164i | \(0.938774\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 330.263i | − | 0.380450i | ||||||
\(92\) | −670.665 | − | 1434.71i | −0.760018 | − | 1.62585i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 811.285 | − | 1274.79i | 0.890188 | − | 1.39877i | ||||
\(95\) | −1617.67 | −1.74704 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −210.036 | −0.219855 | −0.109928 | − | 0.993940i | \(-0.535062\pi\) | ||||
−0.109928 | + | 0.993940i | \(0.535062\pi\) | |||||||
\(98\) | 490.248 | − | 770.337i | 0.505331 | − | 0.794039i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 166.696 | + | 356.600i | 0.166696 | + | 0.356600i | ||||
\(101\) | 1568.74i | 1.54550i | 0.634713 | + | 0.772748i | \(0.281118\pi\) | ||||
−0.634713 | + | 0.772748i | \(0.718882\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 544.057i | 0.520462i | 0.965546 | + | 0.260231i | \(0.0837987\pi\) | ||||
−0.965546 | + | 0.260231i | \(0.916201\pi\) | |||||||
\(104\) | 1650.09 | + | 214.860i | 1.55582 | + | 0.202585i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −805.333 | − | 512.519i | −0.737932 | − | 0.469625i | ||||
\(107\) | −1105.78 | −0.999064 | −0.499532 | − | 0.866295i | \(-0.666495\pi\) | ||||
−0.499532 | + | 0.866295i | \(0.666495\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.6601 | 0.0155186 | 0.00775932 | − | 0.999970i | \(-0.497530\pi\) | ||||
0.00775932 | + | 0.999970i | \(0.497530\pi\) | |||||||
\(110\) | −703.963 | − | 448.007i | −0.610184 | − | 0.388325i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −220.524 | − | 184.333i | −0.186050 | − | 0.155516i | ||||
\(113\) | − | 1603.29i | − | 1.33473i | −0.744729 | − | 0.667367i | \(-0.767421\pi\) | ||
0.744729 | − | 0.667367i | \(-0.232579\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 2612.87i | − | 2.11871i | ||||||
\(116\) | 106.401 | − | 49.7381i | 0.0851646 | − | 0.0398109i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1021.90 | + | 1605.73i | −0.797233 | + | 1.25271i | ||||
\(119\) | 191.402 | 0.147444 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −831.391 | −0.624636 | ||||||||
\(122\) | −122.807 | + | 192.969i | −0.0911345 | + | 0.143202i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1066.31 | − | 498.457i | 0.772240 | − | 0.360990i | ||||
\(125\) | − | 1000.40i | − | 0.715825i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2080.04i | 1.45334i | 0.686988 | + | 0.726669i | \(0.258932\pi\) | ||||
−0.686988 | + | 0.726669i | \(0.741068\pi\) | |||||||
\(128\) | 1064.45 | − | 981.885i | 0.735039 | − | 0.678025i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2316.11 | + | 1473.99i | 1.56259 | + | 0.994441i | ||||
\(131\) | 1093.35 | 0.729213 | 0.364606 | − | 0.931162i | \(-0.381204\pi\) | ||||
0.364606 | + | 0.931162i | \(0.381204\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 550.419 | 0.358853 | ||||||||
\(134\) | −600.820 | − | 382.365i | −0.387335 | − | 0.246503i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −124.521 | + | 956.306i | −0.0785120 | + | 0.602960i | ||||
\(137\) | 1344.61i | 0.838522i | 0.907866 | + | 0.419261i | \(0.137711\pi\) | ||||
−0.907866 | + | 0.419261i | \(0.862289\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 805.378i | − | 0.491448i | −0.969340 | − | 0.245724i | \(-0.920974\pi\) | ||
0.969340 | − | 0.245724i | \(-0.0790257\pi\) | |||||||
\(140\) | −200.808 | − | 429.575i | −0.121224 | − | 0.259326i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −145.499 | + | 228.627i | −0.0859862 | + | 0.135112i | ||||
\(143\) | −1643.77 | −0.961249 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 193.777 | 0.110981 | ||||||||
\(146\) | −381.806 | + | 599.941i | −0.216428 | + | 0.340079i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −793.267 | − | 1696.98i | −0.440582 | − | 0.942505i | ||||
\(149\) | 879.365i | 0.483493i | 0.970339 | + | 0.241746i | \(0.0777202\pi\) | ||||
−0.970339 | + | 0.241746i | \(0.922280\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1826.20i | 0.984197i | 0.870540 | + | 0.492098i | \(0.163770\pi\) | ||||
−0.870540 | + | 0.492098i | \(0.836230\pi\) | |||||||
\(152\) | −358.089 | + | 2750.07i | −0.191084 | + | 1.46750i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 239.527 | + | 152.437i | 0.125335 | + | 0.0797642i | ||||
\(155\) | 1941.96 | 1.00634 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3417.81 | 1.73740 | 0.868698 | − | 0.495342i | \(-0.164957\pi\) | ||||
0.868698 | + | 0.495342i | \(0.164957\pi\) | |||||||
\(158\) | 1192.71 | + | 759.049i | 0.600551 | + | 0.382194i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2276.93 | − | 723.831i | 1.12504 | − | 0.357649i | ||||
\(161\) | 889.044i | 0.435195i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1190.78i | 0.572204i | 0.958199 | + | 0.286102i | \(0.0923596\pi\) | ||||
−0.958199 | + | 0.286102i | \(0.907640\pi\) | |||||||
\(164\) | −2872.38 | + | 1342.72i | −1.36765 | + | 0.639321i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 24.5602 | − | 38.5920i | 0.0114834 | − | 0.0180441i | ||||
\(167\) | 2123.75 | 0.984077 | 0.492039 | − | 0.870573i | \(-0.336252\pi\) | ||||
0.492039 | + | 0.870573i | \(0.336252\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3211.16 | 1.46161 | ||||||||
\(170\) | −854.244 | + | 1342.29i | −0.385397 | + | 0.605584i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2034.77 | − | 951.173i | 0.902035 | − | 0.421664i | ||||
\(173\) | − | 1769.12i | − | 0.777477i | −0.921348 | − | 0.388738i | \(-0.872911\pi\) | ||
0.921348 | − | 0.388738i | \(-0.127089\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 220.974i | − | 0.0954519i | ||||||
\(176\) | −917.450 | + | 1097.58i | −0.392929 | + | 0.470075i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 765.993 | + | 487.483i | 0.322548 | + | 0.205272i | ||||
\(179\) | 3685.89 | 1.53909 | 0.769543 | − | 0.638595i | \(-0.220484\pi\) | ||||
0.769543 | + | 0.638595i | \(0.220484\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2425.51 | −0.996059 | −0.498030 | − | 0.867160i | \(-0.665943\pi\) | ||||
−0.498030 | + | 0.867160i | \(0.665943\pi\) | |||||||
\(182\) | −788.069 | − | 501.532i | −0.320965 | − | 0.204264i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4441.94 | − | 578.389i | −1.77970 | − | 0.231736i | ||||
\(185\) | − | 3090.52i | − | 1.22822i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 952.638i | − | 0.372534i | ||||||
\(188\) | −1809.89 | − | 3871.76i | −0.702125 | − | 1.50201i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2456.56 | + | 3860.06i | −0.937989 | + | 1.47388i | ||||
\(191\) | −1367.60 | −0.518096 | −0.259048 | − | 0.965865i | \(-0.583409\pi\) | ||||
−0.259048 | + | 0.965865i | \(0.583409\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1240.32 | −0.462591 | −0.231296 | − | 0.972883i | \(-0.574296\pi\) | ||||
−0.231296 | + | 0.972883i | \(0.574296\pi\) | |||||||
\(194\) | −318.958 | + | 501.187i | −0.118041 | + | 0.185480i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1093.69 | − | 2339.65i | −0.398574 | − | 0.852641i | ||||
\(197\) | − | 2889.56i | − | 1.04504i | −0.852628 | − | 0.522519i | \(-0.824992\pi\) | ||
0.852628 | − | 0.522519i | \(-0.175008\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1851.53i | 0.659555i | 0.944059 | + | 0.329777i | \(0.106974\pi\) | ||||
−0.944059 | + | 0.329777i | \(0.893026\pi\) | |||||||
\(200\) | 1104.06 | + | 143.760i | 0.390343 | + | 0.0508269i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3743.30 | + | 2382.26i | 1.30385 | + | 0.829778i | ||||
\(203\) | −65.9336 | −0.0227962 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5231.16 | −1.78224 | ||||||||
\(206\) | 1298.22 | + | 826.198i | 0.439085 | + | 0.279437i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3018.51 | − | 3611.15i | 1.00623 | − | 1.20379i | ||||
\(209\) | − | 2739.52i | − | 0.906681i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 4177.37i | − | 1.36295i | −0.731843 | − | 0.681474i | \(-0.761339\pi\) | ||
0.731843 | − | 0.681474i | \(-0.238661\pi\) | |||||||
\(212\) | −2445.93 | + | 1143.37i | −0.792393 | + | 0.370411i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1679.22 | + | 2638.60i | −0.536399 | + | 0.842856i | ||||
\(215\) | 3705.72 | 1.17548 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −660.762 | −0.206707 | ||||||||
\(218\) | 26.8184 | − | 42.1404i | 0.00833198 | − | 0.0130922i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2138.06 | + | 999.453i | −0.655217 | + | 0.306287i | ||||
\(221\) | 3134.28i | 0.954002i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1155.67i | − | 0.347039i | −0.984830 | − | 0.173519i | \(-0.944486\pi\) | ||
0.984830 | − | 0.173519i | \(-0.0555139\pi\) | |||||||
\(224\) | −774.737 | + | 246.287i | −0.231091 | + | 0.0734632i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3825.76 | − | 2434.74i | −1.12604 | − | 0.716620i | ||||
\(227\) | 1499.50 | 0.438437 | 0.219218 | − | 0.975676i | \(-0.429649\pi\) | ||||
0.219218 | + | 0.975676i | \(0.429649\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −320.011 | −0.0923445 | −0.0461723 | − | 0.998933i | \(-0.514702\pi\) | ||||
−0.0461723 | + | 0.998933i | \(0.514702\pi\) | |||||||
\(230\) | −6234.81 | − | 3967.87i | −1.78744 | − | 1.13754i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 42.8947 | − | 329.425i | 0.0121387 | − | 0.0932233i | ||||
\(233\) | 1446.64i | 0.406749i | 0.979101 | + | 0.203374i | \(0.0651909\pi\) | ||||
−0.979101 | + | 0.203374i | \(0.934809\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 7051.22i | − | 1.95732i | ||||||
\(236\) | 2279.74 | + | 4876.89i | 0.628808 | + | 1.34516i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 290.661 | − | 456.722i | 0.0791628 | − | 0.124390i | ||||
\(239\) | −1432.06 | −0.387582 | −0.193791 | − | 0.981043i | \(-0.562078\pi\) | ||||
−0.193791 | + | 0.981043i | \(0.562078\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1148.97 | −0.307102 | −0.153551 | − | 0.988141i | \(-0.549071\pi\) | ||||
−0.153551 | + | 0.988141i | \(0.549071\pi\) | |||||||
\(242\) | −1262.54 | + | 1983.86i | −0.335368 | + | 0.526972i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 273.968 | + | 586.081i | 0.0718813 | + | 0.153770i | ||||
\(245\) | − | 4260.95i | − | 1.11111i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9013.30i | 2.32187i | ||||||||
\(248\) | 429.875 | − | 3301.37i | 0.110069 | − | 0.845312i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2387.13 | − | 1519.19i | −0.603903 | − | 0.384327i | ||||
\(251\) | −3652.62 | −0.918531 | −0.459266 | − | 0.888299i | \(-0.651887\pi\) | ||||
−0.459266 | + | 0.888299i | \(0.651887\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4424.90 | 1.09957 | ||||||||
\(254\) | 4963.37 | + | 3158.72i | 1.22610 | + | 0.780298i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −726.503 | − | 4031.06i | −0.177369 | − | 0.984144i | ||||
\(257\) | 5362.37i | 1.30154i | 0.759275 | + | 0.650770i | \(0.225554\pi\) | ||||
−0.759275 | + | 0.650770i | \(0.774446\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1051.57i | 0.252283i | ||||||||
\(260\) | 7034.43 | − | 3288.30i | 1.67791 | − | 0.784354i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1660.35 | − | 2608.95i | 0.391515 | − | 0.615197i | ||||
\(263\) | −1096.98 | −0.257196 | −0.128598 | − | 0.991697i | \(-0.541048\pi\) | ||||
−0.128598 | + | 0.991697i | \(0.541048\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4454.51 | −1.03260 | ||||||||
\(266\) | 835.859 | − | 1313.40i | 0.192668 | − | 0.302744i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1824.79 | + | 853.015i | −0.415921 | + | 0.194426i | ||||
\(269\) | 5602.35i | 1.26982i | 0.772586 | + | 0.634910i | \(0.218963\pi\) | ||||
−0.772586 | + | 0.634910i | \(0.781037\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1051.62i | 0.235725i | 0.993030 | + | 0.117862i | \(0.0376041\pi\) | ||||
−0.993030 | + | 0.117862i | \(0.962396\pi\) | |||||||
\(272\) | 2092.83 | + | 1749.36i | 0.466531 | + | 0.389966i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3208.48 | + | 2041.90i | 0.707415 | + | 0.450203i | ||||
\(275\) | −1099.82 | −0.241170 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2739.10 | 0.594139 | 0.297069 | − | 0.954856i | \(-0.403991\pi\) | ||||
0.297069 | + | 0.954856i | \(0.403991\pi\) | |||||||
\(278\) | −1921.78 | − | 1223.04i | −0.414608 | − | 0.263859i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1329.99 | − | 173.179i | −0.283865 | − | 0.0369623i | ||||
\(281\) | 423.244i | 0.0898528i | 0.998990 | + | 0.0449264i | \(0.0143053\pi\) | ||||
−0.998990 | + | 0.0449264i | \(0.985695\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 1630.51i | − | 0.342486i | −0.985229 | − | 0.171243i | \(-0.945222\pi\) | ||
0.985229 | − | 0.171243i | \(-0.0547783\pi\) | |||||||
\(284\) | 324.593 | + | 694.378i | 0.0678206 | + | 0.145084i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2496.20 | + | 3922.33i | −0.516096 | + | 0.810953i | ||||
\(287\) | 1779.93 | 0.366083 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3096.54 | 0.630275 | ||||||||
\(290\) | 294.267 | − | 462.388i | 0.0595860 | − | 0.0936289i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 851.767 | + | 1822.12i | 0.170705 | + | 0.365177i | ||||
\(293\) | 2352.75i | 0.469109i | 0.972103 | + | 0.234554i | \(0.0753631\pi\) | ||||
−0.972103 | + | 0.234554i | \(0.924637\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8881.76i | 1.75293i | ||||||||
\(296\) | −5253.96 | − | 684.122i | −1.03169 | − | 0.134337i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2098.33 | + | 1335.39i | 0.407896 | + | 0.259588i | ||||
\(299\) | −14558.4 | −2.81583 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1260.89 | −0.241450 | ||||||||
\(302\) | 4357.65 | + | 2773.23i | 0.830313 | + | 0.528416i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6018.39 | + | 5030.68i | 1.13545 | + | 0.949109i | ||||
\(305\) | 1067.37i | 0.200384i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 10088.6i | − | 1.87554i | −0.347263 | − | 0.937768i | \(-0.612889\pi\) | ||
0.347263 | − | 0.937768i | \(-0.387111\pi\) | |||||||
\(308\) | 727.485 | − | 340.069i | 0.134585 | − | 0.0629131i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2949.03 | − | 4633.89i | 0.540303 | − | 0.848990i | ||||
\(311\) | 3970.97 | 0.724029 | 0.362015 | − | 0.932172i | \(-0.382089\pi\) | ||||
0.362015 | + | 0.932172i | \(0.382089\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4539.33 | 0.819738 | 0.409869 | − | 0.912144i | \(-0.365574\pi\) | ||||
0.409869 | + | 0.912144i | \(0.365574\pi\) | |||||||
\(314\) | 5190.24 | − | 8155.55i | 0.932810 | − | 1.46575i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3622.47 | − | 1693.35i | 0.644873 | − | 0.301451i | ||||
\(317\) | − | 4211.47i | − | 0.746181i | −0.927795 | − | 0.373091i | \(-0.878298\pi\) | ||
0.927795 | − | 0.373091i | \(-0.121702\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 328.161i | 0.0575972i | ||||||||
\(320\) | 1730.52 | − | 6532.38i | 0.302309 | − | 1.14116i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2121.43 | + | 1350.09i | 0.367151 | + | 0.233657i | ||||
\(323\) | −5223.62 | −0.899846 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3618.52 | 0.617599 | ||||||||
\(326\) | 2841.43 | + | 1808.30i | 0.482737 | + | 0.307217i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1157.98 | + | 8893.08i | −0.194934 | + | 1.49707i | ||||
\(329\) | 2399.21i | 0.402045i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 3143.43i | − | 0.521990i | −0.965340 | − | 0.260995i | \(-0.915949\pi\) | ||
0.965340 | − | 0.260995i | \(-0.0840506\pi\) | |||||||
\(332\) | −54.7910 | − | 117.210i | −0.00905738 | − | 0.0193758i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3225.10 | − | 5067.68i | 0.528352 | − | 0.830212i | ||||
\(335\) | −3323.30 | −0.542004 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7102.24 | 1.14802 | 0.574012 | − | 0.818847i | \(-0.305386\pi\) | ||||
0.574012 | + | 0.818847i | \(0.305386\pi\) | |||||||
\(338\) | 4876.42 | − | 7662.43i | 0.784741 | − | 1.23308i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1905.72 | + | 4076.78i | 0.303978 | + | 0.650277i | ||||
\(341\) | 3288.71i | 0.522269i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2990.19i | 0.470715i | ||||||||
\(344\) | 820.302 | − | 6299.79i | 0.128569 | − | 0.987390i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4221.45 | − | 2686.56i | −0.655915 | − | 0.417428i | ||||
\(347\) | 4871.70 | 0.753678 | 0.376839 | − | 0.926279i | \(-0.377011\pi\) | ||||
0.376839 | + | 0.926279i | \(0.377011\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7245.91 | −1.11136 | −0.555680 | − | 0.831396i | \(-0.687542\pi\) | ||||
−0.555680 | + | 0.831396i | \(0.687542\pi\) | |||||||
\(350\) | −527.286 | − | 335.568i | −0.0805275 | − | 0.0512482i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1225.81 | + | 3855.98i | 0.185613 | + | 0.583876i | ||||
\(353\) | − | 9352.32i | − | 1.41012i | −0.709146 | − | 0.705062i | \(-0.750919\pi\) | ||
0.709146 | − | 0.705062i | \(-0.249081\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1264.60i | 0.189064i | ||||||||
\(356\) | 2326.45 | − | 1087.52i | 0.346353 | − | 0.161906i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5597.34 | − | 8795.24i | 0.826337 | − | 1.29844i | ||||
\(359\) | −5162.08 | −0.758898 | −0.379449 | − | 0.925213i | \(-0.623886\pi\) | ||||
−0.379449 | + | 0.925213i | \(0.623886\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8162.66 | −1.19006 | ||||||||
\(362\) | −3683.34 | + | 5787.73i | −0.534785 | + | 0.840321i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2393.50 | + | 1118.86i | −0.344652 | + | 0.161111i | ||||
\(365\) | 3318.44i | 0.475877i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3138.93i | 0.446460i | 0.974766 | + | 0.223230i | \(0.0716600\pi\) | ||||
−0.974766 | + | 0.223230i | \(0.928340\pi\) | |||||||
\(368\) | −8125.61 | + | 9720.97i | −1.15102 | + | 1.37701i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7374.58 | − | 4693.23i | −1.03618 | − | 0.659430i | ||||
\(371\) | 1515.67 | 0.212102 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3085.24 | 0.428278 | 0.214139 | − | 0.976803i | \(-0.431305\pi\) | ||||
0.214139 | + | 0.976803i | \(0.431305\pi\) | |||||||
\(374\) | −2273.17 | − | 1446.66i | −0.314286 | − | 0.200014i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11987.2 | − | 1560.87i | −1.64413 | − | 0.214084i | ||||
\(377\) | − | 1079.68i | − | 0.147498i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13468.6i | 1.82542i | 0.408611 | + | 0.912709i | \(0.366013\pi\) | ||||
−0.408611 | + | 0.912709i | \(0.633987\pi\) | |||||||
\(380\) | 5480.32 | + | 11723.7i | 0.739828 | + | 1.58266i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2076.82 | + | 3263.36i | −0.278166 | + | 0.437089i | ||||
\(383\) | 1100.69 | 0.146847 | 0.0734235 | − | 0.997301i | \(-0.476608\pi\) | ||||
0.0734235 | + | 0.997301i | \(0.476608\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1324.89 | 0.175383 | ||||||||
\(386\) | −1883.53 | + | 2959.64i | −0.248366 | + | 0.390263i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 711.560 | + | 1522.19i | 0.0931031 | + | 0.199169i | ||||
\(389\) | 10089.1i | 1.31501i | 0.753452 | + | 0.657503i | \(0.228387\pi\) | ||||
−0.753452 | + | 0.657503i | \(0.771613\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 8437.26i | − | 1.09128i | ||||||
\(392\) | −7243.70 | − | 943.208i | −0.933321 | − | 0.121529i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6895.03 | − | 4388.04i | −0.881641 | − | 0.561082i | ||||
\(395\) | 6597.21 | 0.840359 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1596.47 | 0.201825 | 0.100912 | − | 0.994895i | \(-0.467824\pi\) | ||||
0.100912 | + | 0.994895i | \(0.467824\pi\) | |||||||
\(398\) | 4418.10 | + | 2811.70i | 0.556430 | + | 0.354116i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2019.64 | − | 2416.17i | 0.252455 | − | 0.302022i | ||||
\(401\) | 4818.54i | 0.600066i | 0.953929 | + | 0.300033i | \(0.0969977\pi\) | ||||
−0.953929 | + | 0.300033i | \(0.903002\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 10820.2i | − | 1.33745i | ||||||
\(404\) | 11369.0 | − | 5314.56i | 1.40008 | − | 0.654478i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −100.126 | + | 157.330i | −0.0122393 | + | 0.0192319i | ||||
\(407\) | 5233.80 | 0.637420 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4223.57 | −0.510617 | −0.255308 | − | 0.966860i | \(-0.582177\pi\) | ||||
−0.255308 | + | 0.966860i | \(0.582177\pi\) | |||||||
\(410\) | −7943.96 | + | 12482.5i | −0.956888 | + | 1.50358i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3942.93 | − | 1843.16i | 0.471491 | − | 0.220402i | ||||
\(413\) | − | 3022.06i | − | 0.360063i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 213.463i | − | 0.0252493i | ||||||
\(416\) | −4033.03 | − | 12686.6i | −0.475326 | − | 1.49522i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6537.00 | − | 4160.19i | −0.764917 | − | 0.486798i | ||||
\(419\) | −1165.75 | −0.135921 | −0.0679604 | − | 0.997688i | \(-0.521649\pi\) | ||||
−0.0679604 | + | 0.997688i | \(0.521649\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9114.56 | −1.05515 | −0.527573 | − | 0.849510i | \(-0.676898\pi\) | ||||
−0.527573 | + | 0.849510i | \(0.676898\pi\) | |||||||
\(422\) | −9967.99 | − | 6343.69i | −1.14984 | − | 0.731768i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −986.057 | + | 7572.77i | −0.112941 | + | 0.867373i | ||||
\(425\) | 2097.10i | 0.239352i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 363.177i | − | 0.0411601i | ||||||
\(428\) | 3746.16 | + | 8013.88i | 0.423078 | + | 0.905060i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5627.45 | − | 8842.54i | 0.631115 | − | 0.991686i | ||||
\(431\) | 6631.38 | 0.741120 | 0.370560 | − | 0.928809i | \(-0.379166\pi\) | ||||
0.370560 | + | 0.928809i | \(0.379166\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15681.8 | −1.74046 | −0.870230 | − | 0.492646i | \(-0.836030\pi\) | ||||
−0.870230 | + | 0.492646i | \(0.836030\pi\) | |||||||
\(434\) | −1003.42 | + | 1576.70i | −0.110981 | + | 0.174388i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −59.8289 | − | 127.988i | −0.00657175 | − | 0.0140585i | ||||
\(437\) | − | 24263.2i | − | 2.65598i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 7923.17i | − | 0.861395i | −0.902496 | − | 0.430697i | \(-0.858268\pi\) | ||
0.902496 | − | 0.430697i | \(-0.141732\pi\) | |||||||
\(440\) | −861.939 | + | 6619.56i | −0.0933894 | + | 0.717216i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7478.98 | + | 4759.67i | 0.804839 | + | 0.512205i | ||||
\(443\) | 14013.0 | 1.50289 | 0.751445 | − | 0.659796i | \(-0.229357\pi\) | ||||
0.751445 | + | 0.659796i | \(0.229357\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4236.92 | 0.451346 | ||||||||
\(446\) | −2757.65 | − | 1754.99i | −0.292777 | − | 0.186325i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −588.817 | + | 2222.68i | −0.0620959 | + | 0.234401i | ||||
\(449\) | − | 5967.60i | − | 0.627235i | −0.949549 | − | 0.313617i | \(-0.898459\pi\) | ||
0.949549 | − | 0.313617i | \(-0.101541\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 8858.96i | − | 0.924950i | ||||||
\(452\) | −11619.5 | + | 5431.62i | −1.20915 | + | 0.565226i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2277.12 | − | 3578.09i | 0.235397 | − | 0.369885i | ||||
\(455\) | −4359.02 | −0.449130 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12901.4 | 1.32057 | 0.660285 | − | 0.751015i | \(-0.270435\pi\) | ||||
0.660285 | + | 0.751015i | \(0.270435\pi\) | |||||||
\(458\) | −485.963 | + | 763.606i | −0.0495799 | + | 0.0779060i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −18936.2 | + | 8851.88i | −1.91936 | + | 0.897220i | ||||
\(461\) | − | 9801.20i | − | 0.990212i | −0.868833 | − | 0.495106i | \(-0.835129\pi\) | ||
0.868833 | − | 0.495106i | \(-0.164871\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3427.68i | 0.344056i | 0.985092 | + | 0.172028i | \(0.0550320\pi\) | ||||
−0.985092 | + | 0.172028i | \(0.944968\pi\) | |||||||
\(464\) | −720.930 | − | 602.615i | −0.0721301 | − | 0.0602924i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3451.96 | + | 2196.85i | 0.343152 | + | 0.218384i | ||||
\(467\) | 13777.2 | 1.36517 | 0.682583 | − | 0.730808i | \(-0.260856\pi\) | ||||
0.682583 | + | 0.730808i | \(0.260856\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1130.77 | 0.111331 | ||||||||
\(470\) | −16825.5 | − | 10707.9i | −1.65129 | − | 1.05089i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 15099.2 | + | 1966.08i | 1.47245 | + | 0.191729i | ||||
\(473\) | 6275.63i | 0.610050i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6030.67i | 0.582539i | ||||||||
\(476\) | −648.432 | − | 1387.14i | −0.0624387 | − | 0.133571i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2174.70 | + | 3417.16i | −0.208093 | + | 0.326982i | ||||
\(479\) | 2793.91 | 0.266507 | 0.133254 | − | 0.991082i | \(-0.457458\pi\) | ||||
0.133254 | + | 0.991082i | \(0.457458\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17219.8 | −1.63234 | ||||||||
\(482\) | −1744.81 | + | 2741.66i | −0.164883 | + | 0.259085i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2816.58 | + | 6025.31i | 0.264518 | + | 0.565863i | ||||
\(485\) | 2772.20i | 0.259545i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17643.8i | 1.64172i | 0.571131 | + | 0.820859i | \(0.306505\pi\) | ||||
−0.571131 | + | 0.820859i | \(0.693495\pi\) | |||||||
\(488\) | 1814.54 | + | 236.273i | 0.168321 | + | 0.0219172i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −10167.4 | − | 6470.61i | −0.937383 | − | 0.596556i | ||||
\(491\) | −4816.53 | −0.442703 | −0.221351 | − | 0.975194i | \(-0.571047\pi\) | ||||
−0.221351 | + | 0.975194i | \(0.571047\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 625.727 | 0.0571629 | ||||||||
\(494\) | 21507.4 | + | 13687.5i | 1.95884 | + | 1.24662i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7224.90 | − | 6039.18i | −0.654047 | − | 0.546708i | ||||
\(497\) | − | 430.285i | − | 0.0388349i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 9504.01i | − | 0.852621i | −0.904577 | − | 0.426311i | \(-0.859813\pi\) | ||
0.904577 | − | 0.426311i | \(-0.140187\pi\) | |||||||
\(500\) | −7250.14 | + | 3389.14i | −0.648472 | + | 0.303134i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5546.82 | + | 8715.84i | −0.493161 | + | 0.774915i | ||||
\(503\) | −13840.8 | −1.22690 | −0.613452 | − | 0.789732i | \(-0.710220\pi\) | ||||
−0.613452 | + | 0.789732i | \(0.710220\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20705.2 | 1.82450 | ||||||||
\(506\) | 6719.59 | − | 10558.7i | 0.590360 | − | 0.927647i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 15074.6 | − | 7046.75i | 1.31659 | − | 0.615451i | ||||
\(509\) | − | 8144.19i | − | 0.709204i | −0.935017 | − | 0.354602i | \(-0.884616\pi\) | ||
0.935017 | − | 0.354602i | \(-0.115384\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 1129.12i | − | 0.0977478i | ||||||
\(512\) | −10722.1 | − | 4387.93i | −0.925498 | − | 0.378752i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 12795.6 | + | 8143.22i | 1.09804 | + | 0.698798i | ||||
\(515\) | 7180.83 | 0.614418 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11941.2 | 1.01581 | ||||||||
\(518\) | 2509.24 | + | 1596.89i | 0.212837 | + | 0.135451i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2835.87 | − | 21779.0i | 0.239156 | − | 1.83668i | ||||
\(521\) | − | 21121.1i | − | 1.77607i | −0.459779 | − | 0.888034i | \(-0.652071\pi\) | ||
0.459779 | − | 0.888034i | \(-0.347929\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15414.6i | 1.28878i | 0.764696 | + | 0.644391i | \(0.222889\pi\) | ||||
−0.764696 | + | 0.644391i | \(0.777111\pi\) | |||||||
\(524\) | −3704.06 | − | 7923.83i | −0.308803 | − | 0.660600i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1665.85 | + | 2617.59i | −0.138089 | + | 0.216982i | ||||
\(527\) | 6270.81 | 0.518331 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27023.2 | 2.22102 | ||||||||
\(530\) | −6764.56 | + | 10629.3i | −0.554403 | + | 0.871147i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1864.71 | − | 3989.03i | −0.151965 | − | 0.325087i | ||||
\(533\) | 29146.9i | 2.36865i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14594.8i | 1.17942i | ||||||||
\(536\) | −735.649 | + | 5649.68i | −0.0592821 | + | 0.455278i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 13368.3 | + | 8507.65i | 1.07128 | + | 0.681767i | ||||
\(539\) | 7215.91 | 0.576644 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3269.66 | −0.259840 | −0.129920 | − | 0.991524i | \(-0.541472\pi\) | ||||
−0.129920 | + | 0.991524i | \(0.541472\pi\) | |||||||
\(542\) | 2509.36 | + | 1596.97i | 0.198868 | + | 0.126561i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7352.46 | − | 2337.33i | 0.579474 | − | 0.184214i | ||||
\(545\) | − | 233.090i | − | 0.0183201i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 2028.46i | − | 0.158557i | −0.996853 | − | 0.0792784i | \(-0.974738\pi\) | ||
0.996853 | − | 0.0792784i | \(-0.0252616\pi\) | |||||||
\(548\) | 9744.72 | − | 4555.25i | 0.759624 | − | 0.355092i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1670.17 | + | 2624.38i | −0.129484 | + | 0.203462i | ||||
\(551\) | 1799.41 | 0.139124 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2244.74 | −0.172615 | ||||||||
\(554\) | 4159.56 | − | 6536.01i | 0.318994 | − | 0.501242i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5836.79 | + | 2728.45i | −0.445207 | + | 0.208116i | ||||
\(557\) | 5968.99i | 0.454065i | 0.973887 | + | 0.227032i | \(0.0729023\pi\) | ||||
−0.973887 | + | 0.227032i | \(0.927098\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 20647.5i | − | 1.56225i | ||||||
\(560\) | −2432.94 | + | 2910.62i | −0.183590 | + | 0.219636i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1009.94 | + | 642.733i | 0.0758039 | + | 0.0482421i | ||||
\(563\) | −13107.0 | −0.981161 | −0.490581 | − | 0.871396i | \(-0.663215\pi\) | ||||
−0.490581 | + | 0.871396i | \(0.663215\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21161.3 | −1.57569 | ||||||||
\(566\) | −3890.70 | − | 2476.06i | −0.288937 | − | 0.183881i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2149.84 | + | 279.932i | 0.158812 | + | 0.0206791i | ||||
\(569\) | 20162.7i | 1.48553i | 0.669553 | + | 0.742764i | \(0.266486\pi\) | ||||
−0.669553 | + | 0.742764i | \(0.733514\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9396.23i | 0.688652i | 0.938850 | + | 0.344326i | \(0.111892\pi\) | ||||
−0.938850 | + | 0.344326i | \(0.888108\pi\) | |||||||
\(572\) | 5568.74 | + | 11912.8i | 0.407064 | + | 0.870803i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2702.97 | − | 4247.24i | 0.196550 | − | 0.308844i | ||||
\(575\) | −9740.82 | −0.706470 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3349.25 | −0.241648 | −0.120824 | − | 0.992674i | \(-0.538554\pi\) | ||||
−0.120824 | + | 0.992674i | \(0.538554\pi\) | |||||||
\(578\) | 4702.36 | − | 7388.93i | 0.338395 | − | 0.531728i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −656.477 | − | 1404.35i | −0.0469978 | − | 0.100539i | ||||
\(581\) | 72.6318i | 0.00518636i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 7543.72i | − | 0.535899i | ||||||
\(584\) | 5641.41 | + | 734.573i | 0.399732 | + | 0.0520494i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5614.10 | + | 3572.85i | 0.395762 | + | 0.251865i | ||||
\(587\) | 5156.24 | 0.362557 | 0.181278 | − | 0.983432i | \(-0.441977\pi\) | ||||
0.181278 | + | 0.983432i | \(0.441977\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18033.1 | 1.26153 | ||||||||
\(590\) | 21193.5 | + | 13487.7i | 1.47886 | + | 0.941153i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9611.03 | + | 11498.0i | −0.667248 | + | 0.798254i | ||||
\(593\) | 19449.0i | 1.34684i | 0.739261 | + | 0.673419i | \(0.235175\pi\) | ||||
−0.739261 | + | 0.673419i | \(0.764825\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 2526.26i | − | 0.174061i | ||||||
\(596\) | 6372.99 | − | 2979.11i | 0.438000 | − | 0.204747i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −22108.2 | + | 34739.1i | −1.51182 | + | 2.37556i | ||||
\(599\) | −25726.7 | −1.75486 | −0.877432 | − | 0.479701i | \(-0.840745\pi\) | ||||
−0.877432 | + | 0.479701i | \(0.840745\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11668.4 | −0.791952 | −0.395976 | − | 0.918261i | \(-0.629594\pi\) | ||||
−0.395976 | + | 0.918261i | \(0.629594\pi\) | |||||||
\(602\) | −1914.77 | + | 3008.72i | −0.129635 | + | 0.203698i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 13234.9 | − | 6186.78i | 0.891592 | − | 0.416782i | ||||
\(605\) | 10973.3i | 0.737399i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 26441.9i | − | 1.76811i | −0.467382 | − | 0.884055i | \(-0.654803\pi\) | ||
0.467382 | − | 0.884055i | \(-0.345197\pi\) | |||||||
\(608\) | 21143.6 | − | 6721.50i | 1.41034 | − | 0.448343i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2546.94 | + | 1620.89i | 0.169053 | + | 0.107587i | ||||
\(611\) | −39287.9 | −2.60134 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4001.56 | −0.263656 | −0.131828 | − | 0.991273i | \(-0.542085\pi\) | ||||
−0.131828 | + | 0.991273i | \(0.542085\pi\) | |||||||
\(614\) | −24073.4 | − | 15320.5i | −1.58229 | − | 1.00698i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 293.279 | − | 2252.34i | 0.0191827 | − | 0.147320i | ||||
\(617\) | − | 25511.2i | − | 1.66457i | −0.554347 | − | 0.832286i | \(-0.687032\pi\) | ||
0.554347 | − | 0.832286i | \(-0.312968\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25105.1i | 1.63014i | 0.579361 | + | 0.815071i | \(0.303302\pi\) | ||||
−0.579361 | + | 0.815071i | \(0.696698\pi\) | |||||||
\(620\) | −6578.97 | − | 14073.9i | −0.426157 | − | 0.911648i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6030.26 | − | 9475.48i | 0.388732 | − | 0.610824i | ||||
\(623\) | −1441.63 | −0.0927091 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19354.5 | −1.23869 | ||||||||
\(626\) | 6893.36 | − | 10831.7i | 0.440118 | − | 0.691568i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11578.8 | − | 24769.8i | −0.735743 | − | 1.57392i | ||||
\(629\) | − | 9979.65i | − | 0.632614i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 10090.6i | − | 0.636612i | −0.947988 | − | 0.318306i | \(-0.896886\pi\) | ||
0.947988 | − | 0.318306i | \(-0.103114\pi\) | |||||||
\(632\) | 1460.37 | − | 11215.4i | 0.0919150 | − | 0.705893i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10049.4 | − | 6395.47i | −0.629512 | − | 0.400626i | ||||
\(635\) | 27453.8 | 1.71570 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −23741.1 | −1.47670 | ||||||||
\(638\) | 783.055 | + | 498.341i | 0.0485916 | + | 0.0309240i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −12959.6 | − | 14049.3i | −0.800425 | − | 0.867732i | ||||
\(641\) | 155.209i | 0.00956376i | 0.999989 | + | 0.00478188i | \(0.00152213\pi\) | ||||
−0.999989 | + | 0.00478188i | \(0.998478\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8048.26i | 0.493612i | 0.969065 | + | 0.246806i | \(0.0793810\pi\) | ||||
−0.969065 | + | 0.246806i | \(0.920619\pi\) | |||||||
\(644\) | 6443.14 | − | 3011.90i | 0.394247 | − | 0.184294i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7932.52 | + | 12464.5i | −0.483128 | + | 0.759150i | ||||
\(647\) | 17128.5 | 1.04079 | 0.520394 | − | 0.853926i | \(-0.325785\pi\) | ||||
0.520394 | + | 0.853926i | \(0.325785\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15041.2 | −0.909739 | ||||||||
\(650\) | 5495.04 | − | 8634.48i | 0.331590 | − | 0.521034i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8629.91 | − | 4034.13i | 0.518364 | − | 0.242314i | ||||
\(653\) | 5854.10i | 0.350825i | 0.984495 | + | 0.175412i | \(0.0561259\pi\) | ||||
−0.984495 | + | 0.175412i | \(0.943874\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 14430.8i | − | 0.860853i | ||||||
\(656\) | 19462.1 | + | 16268.0i | 1.15833 | + | 0.968232i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5724.98 | + | 3643.41i | 0.339184 | + | 0.215859i | ||||
\(659\) | −22130.6 | −1.30817 | −0.654086 | − | 0.756420i | \(-0.726947\pi\) | ||||
−0.654086 | + | 0.756420i | \(0.726947\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19160.0 | 1.12744 | 0.563721 | − | 0.825965i | \(-0.309369\pi\) | ||||
0.563721 | + | 0.825965i | \(0.309369\pi\) | |||||||
\(662\) | −7500.82 | − | 4773.57i | −0.440374 | − | 0.280257i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −362.891 | − | 47.2524i | −0.0212092 | − | 0.00276167i | ||||
\(665\) | − | 7264.80i | − | 0.423634i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2906.44i | 0.168722i | ||||||||
\(668\) | −7194.84 | − | 15391.4i | −0.416732 | − | 0.891484i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5046.71 | + | 7930.02i | −0.291002 | + | 0.457259i | ||||
\(671\) | −1807.58 | −0.103996 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24302.6 | 1.39197 | 0.695984 | − | 0.718057i | \(-0.254968\pi\) | ||||
0.695984 | + | 0.718057i | \(0.254968\pi\) | |||||||
\(674\) | 10785.4 | − | 16947.3i | 0.616375 | − | 0.968524i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10878.8 | − | 23272.1i | −0.618955 | − | 1.32409i | ||||
\(677\) | − | 16656.4i | − | 0.945581i | −0.881175 | − | 0.472791i | \(-0.843247\pi\) | ||
0.881175 | − | 0.472791i | \(-0.156753\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 943.255i | − | 0.0533120i | ||||||
\(680\) | 12622.0 | + | 1643.52i | 0.711809 | + | 0.0926853i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7847.48 | + | 4994.19i | 0.440610 | + | 0.280407i | ||||
\(683\) | −24952.6 | −1.39793 | −0.698964 | − | 0.715157i | \(-0.746355\pi\) | ||||
−0.698964 | + | 0.715157i | \(0.746355\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17747.0 | 0.989895 | ||||||||
\(686\) | 7135.16 | + | 4540.86i | 0.397116 | + | 0.252727i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −13786.8 | − | 11524.2i | −0.763978 | − | 0.638597i | ||||
\(689\) | 24819.6i | 1.37235i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15536.7i | 0.855346i | 0.903934 | + | 0.427673i | \(0.140666\pi\) | ||||
−0.903934 | + | 0.427673i | \(0.859334\pi\) | |||||||
\(692\) | −12821.3 | + | 5993.41i | −0.704323 | + | 0.329242i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7398.09 | − | 11624.8i | 0.404651 | − | 0.635837i | ||||
\(695\) | −10629.9 | −0.580166 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16892.0 | −0.917976 | ||||||||
\(698\) | −11003.5 | + | 17290.1i | −0.596691 | + | 0.937594i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1601.46 | + | 748.615i | −0.0864706 | + | 0.0404214i | ||||
\(701\) | 9683.38i | 0.521735i | 0.965375 | + | 0.260868i | \(0.0840086\pi\) | ||||
−0.965375 | + | 0.260868i | \(0.915991\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 28698.6i | − | 1.53967i | ||||||
\(704\) | 11062.6 | + | 2930.63i | 0.592240 | + | 0.156892i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −22316.4 | − | 14202.3i | −1.18964 | − | 0.757097i | ||||
\(707\) | −7045.06 | −0.374762 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15665.5 | −0.829801 | −0.414901 | − | 0.909867i | \(-0.636184\pi\) | ||||
−0.414901 | + | 0.909867i | \(0.636184\pi\) | |||||||
\(710\) | 3017.56 | + | 1920.40i | 0.159503 | + | 0.101509i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 937.889 | − | 7202.85i | 0.0493664 | − | 0.379127i | ||||
\(713\) | 29127.2i | 1.52991i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 21695.5i | 1.13478i | ||||||||
\(716\) | −12487.0 | − | 26712.6i | −0.651764 | − | 1.39427i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7839.06 | + | 12317.7i | −0.407453 | + | 0.640240i | ||||
\(719\) | 15944.3 | 0.827015 | 0.413507 | − | 0.910501i | \(-0.364304\pi\) | ||||
0.413507 | + | 0.910501i | \(0.364304\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2443.31 | −0.126205 | ||||||||
\(722\) | −12395.7 | + | 19477.6i | −0.638947 | + | 1.00399i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8217.13 | + | 17578.3i | 0.421806 | + | 0.902338i | ||||
\(725\) | − | 722.402i | − | 0.0370060i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23773.6i | 1.21281i | 0.795156 | + | 0.606405i | \(0.207389\pi\) | ||||
−0.795156 | + | 0.606405i | \(0.792611\pi\) | |||||||
\(728\) | −964.919 | + | 7410.43i | −0.0491240 | + | 0.377265i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7918.42 | + | 5039.33i | 0.401471 | + | 0.255499i | ||||
\(731\) | 11966.2 | 0.605451 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16190.1 | −0.815818 | −0.407909 | − | 0.913023i | \(-0.633742\pi\) | ||||
−0.407909 | + | 0.913023i | \(0.633742\pi\) | |||||||
\(734\) | 7490.07 | + | 4766.73i | 0.376653 | + | 0.239705i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10856.6 | + | 34151.4i | 0.543724 | + | 1.71038i | ||||
\(737\) | − | 5628.00i | − | 0.281289i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 3013.13i | − | 0.149986i | −0.997184 | − | 0.0749930i | \(-0.976107\pi\) | ||
0.997184 | − | 0.0749930i | \(-0.0238934\pi\) | |||||||
\(740\) | −22397.9 | + | 10470.1i | −1.11265 | + | 0.520118i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2301.68 | − | 3616.68i | 0.113878 | − | 0.178939i | ||||
\(743\) | 14363.7 | 0.709225 | 0.354613 | − | 0.935013i | \(-0.384613\pi\) | ||||
0.354613 | + | 0.935013i | \(0.384613\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11606.4 | 0.570775 | ||||||||
\(746\) | 4685.20 | − | 7361.97i | 0.229943 | − | 0.361315i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6904.02 | + | 3227.34i | −0.337481 | + | 0.157758i | ||||
\(749\) | − | 4965.96i | − | 0.242260i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 21754.9i | − | 1.05705i | −0.848917 | − | 0.528526i | \(-0.822745\pi\) | ||
0.848917 | − | 0.528526i | \(-0.177255\pi\) | |||||||
\(752\) | −21928.1 | + | 26233.5i | −1.06335 | + | 1.27212i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2576.33 | − | 1639.59i | −0.124436 | − | 0.0791916i | ||||
\(755\) | 24103.3 | 1.16187 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25070.4 | 1.20370 | 0.601848 | − | 0.798611i | \(-0.294431\pi\) | ||||
0.601848 | + | 0.798611i | \(0.294431\pi\) | |||||||
\(758\) | 32138.5 | + | 20453.2i | 1.54000 | + | 0.980069i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 36297.2 | + | 4726.29i | 1.73242 | + | 0.225580i | ||||
\(761\) | − | 20326.9i | − | 0.968263i | −0.874995 | − | 0.484132i | \(-0.839136\pi\) | ||
0.874995 | − | 0.484132i | \(-0.160864\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 79.3101i | 0.00376306i | ||||||||
\(764\) | 4633.16 | + | 9911.38i | 0.219400 | + | 0.469347i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1671.48 | − | 2626.44i | 0.0788423 | − | 0.123887i | ||||
\(767\) | 49487.3 | 2.32970 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4680.89 | −0.219502 | −0.109751 | − | 0.993959i | \(-0.535005\pi\) | ||||
−0.109751 | + | 0.993959i | \(0.535005\pi\) | |||||||
\(770\) | 2011.96 | − | 3161.44i | 0.0941636 | − | 0.147961i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4201.95 | + | 8988.92i | 0.195896 | + | 0.419065i | ||||
\(773\) | − | 2385.68i | − | 0.111005i | −0.998459 | − | 0.0555025i | \(-0.982324\pi\) | ||
0.998459 | − | 0.0555025i | \(-0.0176761\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 7239.65i | − | 0.335556i | ||||||
\(776\) | 4712.80 | + | 613.658i | 0.218015 | + | 0.0283879i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 24074.5 | + | 15321.2i | 1.10940 | + | 0.706028i | ||||
\(779\) | −48576.6 | −2.23419 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2141.59 | −0.0981206 | ||||||||
\(782\) | −20132.9 | − | 12812.7i | −0.920653 | − | 0.585909i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −13250.8 | + | 15852.5i | −0.603628 | + | 0.722143i | ||||
\(785\) | − | 45110.6i | − | 2.05104i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8714.78i | 0.394725i | 0.980331 | + | 0.197362i | \(0.0632375\pi\) | ||||
−0.980331 | + | 0.197362i | \(0.936762\pi\) | |||||||
\(788\) | −20941.4 | + | 9789.23i | −0.946708 | + | 0.442547i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 10018.4 | − | 15742.2i | 0.451190 | − | 0.708965i | ||||
\(791\) | 7200.24 | 0.323655 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5947.14 | 0.266317 | ||||||||
\(794\) | 2424.37 | − | 3809.48i | 0.108360 | − | 0.170269i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13418.5 | − | 6272.60i | 0.597496 | − | 0.279304i | ||||
\(797\) | 15364.9i | 0.682876i | 0.939904 | + | 0.341438i | \(0.110914\pi\) | ||||
−0.939904 | + | 0.341438i | \(0.889086\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 22769.2i | − | 1.00815i | ||||||
\(800\) | −2698.45 | − | 8488.41i | −0.119256 | − | 0.375138i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 11497.9 | + | 7317.37i | 0.506243 | + | 0.322176i | ||||
\(803\) | −5619.77 | −0.246971 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11734.2 | 0.513759 | ||||||||
\(806\) | −25819.0 | − | 16431.4i | −1.12833 | − | 0.718079i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4583.33 | − | 35199.3i | 0.199556 | − | 1.53256i | ||||
\(809\) | 25153.9i | 1.09316i | 0.837408 | + | 0.546578i | \(0.184070\pi\) | ||||
−0.837408 | + | 0.546578i | \(0.815930\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20366.0i | 0.881807i | 0.897554 | + | 0.440904i | \(0.145342\pi\) | ||||
−0.897554 | + | 0.440904i | \(0.854658\pi\) | |||||||
\(812\) | 223.370 | + | 477.838i | 0.00965361 | + | 0.0206513i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7947.98 | − | 12488.8i | 0.342232 | − | 0.537756i | ||||
\(815\) | 15716.7 | 0.675501 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34411.3 | 1.47356 | ||||||||
\(818\) | −6413.86 | + | 10078.2i | −0.274151 | + | 0.430779i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 17722.1 | + | 37911.6i | 0.754734 | + | 1.61455i | ||||
\(821\) | − | 781.431i | − | 0.0332182i | −0.999862 | − | 0.0166091i | \(-0.994713\pi\) | ||
0.999862 | − | 0.0166091i | \(-0.00528708\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32821.3i | 1.39013i | 0.718945 | + | 0.695067i | \(0.244625\pi\) | ||||
−0.718945 | + | 0.695067i | \(0.755375\pi\) | |||||||
\(824\) | 1589.56 | − | 12207.6i | 0.0672025 | − | 0.516105i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7211.21 | − | 4589.26i | −0.303765 | − | 0.193318i | ||||
\(827\) | 43717.4 | 1.83821 | 0.919106 | − | 0.394010i | \(-0.128913\pi\) | ||||
0.919106 | + | 0.394010i | \(0.128913\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13211.9 | 0.553521 | 0.276761 | − | 0.960939i | \(-0.410739\pi\) | ||||
0.276761 | + | 0.960939i | \(0.410739\pi\) | |||||||
\(830\) | −509.363 | − | 324.162i | −0.0213015 | − | 0.0135564i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −36397.1 | − | 9642.07i | −1.51664 | − | 0.401777i | ||||
\(833\) | − | 13759.1i | − | 0.572297i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 28030.7i | − | 1.16173i | ||||||
\(836\) | −19854.0 | + | 9280.92i | −0.821370 | + | 0.383956i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1770.30 | + | 2781.71i | −0.0729760 | + | 0.114669i | ||||
\(839\) | −33876.0 | −1.39396 | −0.696978 | − | 0.717092i | \(-0.745473\pi\) | ||||
−0.696978 | + | 0.717092i | \(0.745473\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24173.5 | 0.991162 | ||||||||
\(842\) | −13841.2 | + | 21749.1i | −0.566509 | + | 0.890169i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −30274.5 | + | 14152.1i | −1.23471 | + | 0.577173i | ||||
\(845\) | − | 42383.0i | − | 1.72547i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 3733.70i | − | 0.151466i | ||||||
\(848\) | 16572.6 | + | 13852.8i | 0.671116 | + | 0.560976i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5004.08 | + | 3184.63i | 0.201928 | + | 0.128508i | ||||
\(851\) | 46354.4 | 1.86722 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14748.5 | −0.592005 | −0.296002 | − | 0.955187i | \(-0.595654\pi\) | ||||
−0.296002 | + | 0.955187i | \(0.595654\pi\) | |||||||
\(854\) | −866.608 | − | 551.515i | −0.0347245 | − | 0.0220989i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 24811.5 | + | 3230.73i | 0.990701 | + | 0.129000i | ||||
\(857\) | − | 24382.3i | − | 0.971859i | −0.873998 | − | 0.485929i | \(-0.838481\pi\) | ||
0.873998 | − | 0.485929i | \(-0.161519\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21247.2i | 0.843942i | 0.906609 | + | 0.421971i | \(0.138662\pi\) | ||||
−0.906609 | + | 0.421971i | \(0.861338\pi\) | |||||||
\(860\) | −12554.2 | − | 26856.3i | −0.497785 | − | 1.06487i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10070.3 | − | 15823.7i | 0.397908 | − | 0.625242i | ||||
\(863\) | −4434.51 | −0.174916 | −0.0874581 | − | 0.996168i | \(-0.527874\pi\) | ||||
−0.0874581 | + | 0.996168i | \(0.527874\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23350.0 | −0.917830 | ||||||||
\(866\) | −23814.2 | + | 37419.7i | −0.934455 | + | 1.46833i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2238.53 | + | 4788.72i | 0.0875352 | + | 0.187258i | ||||
\(869\) | 11172.4i | 0.436130i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18516.7i | 0.720339i | ||||||||
\(872\) | −396.258 | − | 51.5971i | −0.0153887 | − | 0.00200378i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −57896.5 | − | 36845.7i | −2.24071 | − | 1.42600i | ||||
\(875\) | 4492.69 | 0.173578 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13985.9 | −0.538507 | −0.269253 | − | 0.963069i | \(-0.586777\pi\) | ||||
−0.269253 | + | 0.963069i | \(0.586777\pi\) | |||||||
\(878\) | −18906.2 | − | 12032.0i | −0.726711 | − | 0.462484i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 14486.6 | + | 12109.1i | 0.554935 | + | 0.463862i | ||||
\(881\) | 4428.74i | 0.169362i | 0.996408 | + | 0.0846812i | \(0.0269872\pi\) | ||||
−0.996408 | + | 0.0846812i | \(0.973013\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40519.1i | 1.54426i | 0.635467 | + | 0.772128i | \(0.280808\pi\) | ||||
−0.635467 | + | 0.772128i | \(0.719192\pi\) | |||||||
\(884\) | 22714.9 | − | 10618.3i | 0.864238 | − | 0.403995i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 21280.0 | − | 33437.8i | 0.806903 | − | 1.26791i | ||||
\(887\) | 31161.7 | 1.17960 | 0.589802 | − | 0.807548i | \(-0.299206\pi\) | ||||
0.589802 | + | 0.807548i | \(0.299206\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9341.29 | −0.352415 | ||||||||
\(890\) | 6434.12 | − | 10110.1i | 0.242328 | − | 0.380776i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8375.47 | + | 3915.18i | −0.314385 | + | 0.146962i | ||||
\(893\) | − | 65477.7i | − | 2.45367i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 48648.9i | − | 1.81693i | ||||||
\(896\) | 4409.56 | + | 4780.35i | 0.164412 | + | 0.178237i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −14239.8 | − | 9062.31i | −0.529164 | − | 0.336763i | ||||
\(899\) | −2160.14 | −0.0801388 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14384.1 | −0.531858 | ||||||||
\(902\) | −21139.2 | − | 13453.1i | −0.780329 | − | 0.496607i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4684.29 | + | 35974.7i | −0.172342 | + | 1.32356i | ||||
\(905\) | 32013.5i | 1.17587i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24021.4i | 0.879402i | 0.898144 | + | 0.439701i | \(0.144916\pi\) | ||||
−0.898144 | + | 0.439701i | \(0.855084\pi\) | |||||||
\(908\) | −5079.99 | − | 10867.3i | −0.185667 | − | 0.397184i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −6619.55 | + | 10401.5i | −0.241138 | + | 0.378907i | ||||
\(911\) | −33057.5 | −1.20225 | −0.601123 | − | 0.799157i | \(-0.705280\pi\) | ||||
−0.601123 | + | 0.799157i | \(0.705280\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 361.499 | 0.0131039 | ||||||||
\(914\) | 19591.8 | − | 30785.1i | 0.709016 | − | 1.11409i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1084.13 | + | 2319.20i | 0.0391055 | + | 0.0836556i | ||||
\(917\) | 4910.16i | 0.176824i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10303.3i | 0.369831i | 0.982754 | + | 0.184915i | \(0.0592011\pi\) | ||||
−0.982754 | + | 0.184915i | \(0.940799\pi\) | |||||||
\(920\) | −7633.96 | + | 58627.7i | −0.273570 | + | 2.10098i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −23387.5 | − | 14884.0i | −0.835387 | − | 0.531646i | ||||
\(923\) | 7046.06 | 0.251272 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11521.5 | −0.409540 | ||||||||
\(926\) | 8179.10 | + | 5205.23i | 0.290261 | + | 0.184724i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2532.75 | + | 805.154i | −0.0895921 | + | 0.0284811i | ||||
\(929\) | 7704.91i | 0.272110i | 0.990701 | + | 0.136055i | \(0.0434424\pi\) | ||||
−0.990701 | + | 0.136055i | \(0.956558\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 39567.2i | − | 1.39287i | ||||||
\(932\) | 10484.2 | − | 4900.92i | 0.368477 | − | 0.172248i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 20921.9 | − | 32875.0i | 0.732959 | − | 1.15172i | ||||
\(935\) | −12573.5 | −0.439785 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −44189.8 | −1.54068 | −0.770340 | − | 0.637633i | \(-0.779914\pi\) | ||||
−0.770340 | + | 0.637633i | \(0.779914\pi\) | |||||||
\(938\) | 1717.17 | − | 2698.23i | 0.0597735 | − | 0.0939236i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −51102.1 | + | 23888.1i | −1.77315 | + | 0.828876i | ||||
\(941\) | 51448.1i | 1.78232i | 0.453691 | + | 0.891159i | \(0.350107\pi\) | ||||
−0.453691 | + | 0.891159i | \(0.649893\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 78461.5i | − | 2.70950i | ||||||
\(944\) | 27620.8 | − | 33043.8i | 0.952310 | − | 1.13928i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14974.8 | + | 9530.08i | 0.514666 | + | 0.327537i | ||||
\(947\) | −17691.3 | −0.607066 | −0.303533 | − | 0.952821i | \(-0.598166\pi\) | ||||
−0.303533 | + | 0.952821i | \(0.598166\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18489.6 | 0.632454 | ||||||||
\(950\) | 14390.3 | + | 9158.09i | 0.491457 | + | 0.312766i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4294.69 | − | 559.215i | −0.146210 | − | 0.0190381i | ||||
\(953\) | 27331.2i | 0.929007i | 0.885571 | + | 0.464504i | \(0.153767\pi\) | ||||
−0.885571 | + | 0.464504i | \(0.846233\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18050.5i | 0.611624i | ||||||||
\(956\) | 4851.52 | + | 10378.5i | 0.164131 | + | 0.351114i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4242.79 | − | 6666.79i | 0.143088 | − | 0.224837i | ||||
\(959\) | −6038.51 | −0.203330 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8142.84 | 0.273332 | ||||||||
\(962\) | −26149.7 | + | 41089.6i | −0.876403 | + | 1.37711i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3892.47 | + | 8326.88i | 0.130050 | + | 0.278206i | ||||
\(965\) | 16370.6i | 0.546101i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 48045.3i | − | 1.59776i | −0.601492 | − | 0.798879i | \(-0.705427\pi\) | ||
0.601492 | − | 0.798879i | \(-0.294573\pi\) | |||||||
\(968\) | 18654.8 | + | 2429.05i | 0.619408 | + | 0.0806536i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6614.99 | + | 4209.82i | 0.218964 | + | 0.139350i | ||||
\(971\) | −6999.70 | −0.231340 | −0.115670 | − | 0.993288i | \(-0.536901\pi\) | ||||
−0.115670 | + | 0.993288i | \(0.536901\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3616.88 | 0.119169 | ||||||||
\(974\) | 42101.4 | + | 26793.6i | 1.38503 | + | 0.881440i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3319.33 | − | 3971.04i | 0.108862 | − | 0.130236i | ||||
\(977\) | − | 42914.1i | − | 1.40527i | −0.711552 | − | 0.702633i | \(-0.752008\pi\) | ||
0.711552 | − | 0.702633i | \(-0.247992\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7175.22i | 0.234240i | ||||||||
\(980\) | −30880.2 | + | 14435.2i | −1.00656 | + | 0.470527i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7314.31 | + | 11493.2i | −0.237688 | + | 0.373484i | ||||
\(983\) | 1615.78 | 0.0524266 | 0.0262133 | − | 0.999656i | \(-0.491655\pi\) | ||||
0.0262133 | + | 0.999656i | \(0.491655\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −38138.3 | −1.23369 | ||||||||
\(986\) | 950.220 | − | 1493.10i | 0.0306908 | − | 0.0482252i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 65321.7 | − | 30535.2i | 2.10340 | − | 0.983253i | ||||
\(989\) | 55581.6i | 1.78705i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15725.6i | 0.504076i | 0.967717 | + | 0.252038i | \(0.0811008\pi\) | ||||
−0.967717 | + | 0.252038i | \(0.918899\pi\) | |||||||
\(992\) | −25382.3 | + | 8068.96i | −0.812386 | + | 0.258256i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1026.74 | − | 653.425i | −0.0327628 | − | 0.0208505i | ||||
\(995\) | 24437.7 | 0.778620 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22555.5 | −0.716489 | −0.358244 | − | 0.933628i | \(-0.616625\pi\) | ||||
−0.358244 | + | 0.933628i | \(0.616625\pi\) | |||||||
\(998\) | −22678.4 | − | 14432.7i | −0.719310 | − | 0.457773i | ||||
\(999\) | 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 | 108.4.b.a.107.9 | yes | 12 | |
3.2 | odd | 2 | inner | 108.4.b.a.107.4 | yes | 12 | |
4.3 | odd | 2 | inner | 108.4.b.a.107.3 | ✓ | 12 | |
8.3 | odd | 2 | 1728.4.c.i.1727.9 | 12 | |||
8.5 | even | 2 | 1728.4.c.i.1727.10 | 12 | |||
12.11 | even | 2 | inner | 108.4.b.a.107.10 | yes | 12 | |
24.5 | odd | 2 | 1728.4.c.i.1727.4 | 12 | |||
24.11 | even | 2 | 1728.4.c.i.1727.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.4.b.a.107.3 | ✓ | 12 | 4.3 | odd | 2 | inner | |
108.4.b.a.107.4 | yes | 12 | 3.2 | odd | 2 | inner | |
108.4.b.a.107.9 | yes | 12 | 1.1 | even | 1 | trivial | |
108.4.b.a.107.10 | yes | 12 | 12.11 | even | 2 | inner | |
1728.4.c.i.1727.3 | 12 | 24.11 | even | 2 | |||
1728.4.c.i.1727.4 | 12 | 24.5 | odd | 2 | |||
1728.4.c.i.1727.9 | 12 | 8.3 | odd | 2 | |||
1728.4.c.i.1727.10 | 12 | 8.5 | even | 2 |