Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(79,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 0, 0, 13]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.ci (of order \(18\), degree \(6\), 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: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{18})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 6 x^{17} - 3 x^{16} + 100 x^{15} - 171 x^{14} - 471 x^{13} + 1537 x^{12} + 321 x^{11} + \cdots + 1367631 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 223.2 | ||
Root | \(-2.61262 - 0.231530i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.223 |
Dual form | 912.2.ci.f.319.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{7}{18}\right)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.173648 | − | 0.984808i | 0.100256 | − | 0.568579i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.345737 | − | 0.290108i | −0.154618 | − | 0.129740i | 0.562197 | − | 0.827004i | \(-0.309956\pi\) |
−0.716815 | + | 0.697263i | \(0.754401\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.993418 | + | 0.573550i | −0.375477 | + | 0.216782i | −0.675848 | − | 0.737041i | \(-0.736223\pi\) |
0.300372 | + | 0.953822i | \(0.402889\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.939693 | − | 0.342020i | −0.313231 | − | 0.114007i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.09134 | + | 0.630083i | 0.329050 | + | 0.189977i | 0.655419 | − | 0.755265i | \(-0.272492\pi\) |
−0.326369 | + | 0.945242i | \(0.605825\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.39019 | + | 1.12676i | −1.77232 | + | 0.312508i | −0.961912 | − | 0.273358i | \(-0.911866\pi\) |
−0.810408 | + | 0.585866i | \(0.800754\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.345737 | + | 0.290108i | −0.0892689 | + | 0.0749055i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.00915 | + | 1.45921i | −0.972362 | + | 0.353911i | −0.778866 | − | 0.627190i | \(-0.784205\pi\) |
−0.193496 | + | 0.981101i | \(0.561983\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.14602 | − | 3.79402i | 0.492331 | − | 0.870408i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.392332 | + | 1.07792i | 0.0856138 | + | 0.235222i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.76755 | − | 6.87349i | −1.20262 | − | 1.43322i | −0.872034 | − | 0.489445i | \(-0.837199\pi\) |
−0.330583 | − | 0.943777i | \(-0.607245\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.832869 | − | 4.72344i | −0.166574 | − | 0.944687i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.500000 | + | 0.866025i | −0.0962250 | + | 0.166667i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.29392 | + | 6.30249i | −0.425970 | + | 1.17034i | 0.522268 | + | 0.852781i | \(0.325086\pi\) |
−0.948238 | + | 0.317561i | \(0.897136\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.64248 | + | 4.57690i | 0.474603 | + | 0.822036i | 0.999577 | − | 0.0290819i | \(-0.00925835\pi\) |
−0.524974 | + | 0.851118i | \(0.675925\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.810019 | − | 0.965343i | 0.141006 | − | 0.168045i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.509853 | + | 0.0899008i | 0.0861809 | + | 0.0151960i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.13949i | 0.516130i | 0.966128 | + | 0.258065i | \(0.0830848\pi\) | ||||
−0.966128 | + | 0.258065i | \(0.916915\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.48877i | 1.03903i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.40942 | − | 0.601174i | −0.532463 | − | 0.0938875i | −0.0990489 | − | 0.995083i | \(-0.531580\pi\) |
−0.433414 | + | 0.901195i | \(0.642691\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.46550 | + | 7.70528i | −0.985979 | + | 1.17504i | −0.00141867 | + | 0.999999i | \(0.500452\pi\) |
−0.984560 | + | 0.175045i | \(0.943993\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.225664 | + | 0.390861i | 0.0336400 | + | 0.0582662i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.37128 | − | 9.26251i | 0.491751 | − | 1.35108i | −0.407325 | − | 0.913283i | \(-0.633538\pi\) |
0.899076 | − | 0.437792i | \(-0.144239\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.84208 | + | 4.92263i | −0.406011 | + | 0.703232i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.740861 | + | 4.20163i | 0.103741 | + | 0.588346i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.68029 | − | 9.15302i | −1.05497 | − | 1.25726i | −0.965259 | − | 0.261296i | \(-0.915850\pi\) |
−0.0897105 | − | 0.995968i | \(-0.528594\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.194523 | − | 0.534448i | −0.0262295 | − | 0.0720650i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.36373 | − | 2.77224i | −0.445537 | − | 0.367192i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.0337 | − | 3.65196i | 1.30627 | − | 0.475445i | 0.407239 | − | 0.913322i | \(-0.366492\pi\) |
0.899035 | + | 0.437877i | \(0.144269\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.87608 | + | 4.93062i | −0.752355 | + | 0.631301i | −0.936125 | − | 0.351669i | \(-0.885614\pi\) |
0.183770 | + | 0.982969i | \(0.441170\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.12967 | − | 0.199192i | 0.142325 | − | 0.0250958i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.53621 | + | 1.46428i | 0.314578 | + | 0.181622i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.07297 | + | 2.21038i | 0.741931 | + | 0.270041i | 0.685206 | − | 0.728349i | \(-0.259712\pi\) |
0.0567248 | + | 0.998390i | \(0.481934\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.77059 | + | 4.48635i | −0.935470 | + | 0.540094i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.08682 | − | 5.10745i | −0.722373 | − | 0.606143i | 0.205668 | − | 0.978622i | \(-0.434063\pi\) |
−0.928041 | + | 0.372479i | \(0.878508\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.463830 | − | 2.63051i | 0.0542872 | − | 0.307878i | −0.945558 | − | 0.325453i | \(-0.894483\pi\) |
0.999846 | + | 0.0175745i | \(0.00559443\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.79630 | −0.553829 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.44554 | −0.164734 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.29356 | + | 13.0074i | −0.258046 | + | 1.46345i | 0.530086 | + | 0.847944i | \(0.322160\pi\) |
−0.788132 | + | 0.615506i | \(0.788951\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.766044 | + | 0.642788i | 0.0851160 | + | 0.0714208i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.21005 | + | 1.85332i | −0.352348 | + | 0.203428i | −0.665719 | − | 0.746202i | \(-0.731875\pi\) |
0.313371 | + | 0.949631i | \(0.398542\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.80944 | + | 0.658583i | 0.196261 | + | 0.0714333i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.80840 | + | 3.35348i | 0.622726 | + | 0.359531i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.48811 | − | 1.67301i | 1.00574 | − | 0.177339i | 0.353566 | − | 0.935410i | \(-0.384969\pi\) |
0.652172 | + | 0.758071i | \(0.273858\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.70188 | − | 4.78444i | 0.597719 | − | 0.501546i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.96623 | − | 1.80756i | 0.514974 | − | 0.187435i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.84263 | + | 0.689157i | −0.189050 | + | 0.0707060i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.447536 | − | 1.22960i | −0.0454404 | − | 0.124847i | 0.914897 | − | 0.403688i | \(-0.132272\pi\) |
−0.960337 | + | 0.278841i | \(0.910050\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.810019 | − | 0.965343i | −0.0814100 | − | 0.0970206i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.08089 | + | 11.8013i | 0.207056 | + | 1.17427i | 0.894171 | + | 0.447725i | \(0.147766\pi\) |
−0.687115 | + | 0.726549i | \(0.741123\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.863454 | + | 1.49555i | −0.0850786 | + | 0.147361i | −0.905425 | − | 0.424507i | \(-0.860447\pi\) |
0.820346 | + | 0.571867i | \(0.193781\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.177070 | − | 0.486496i | 0.0172803 | − | 0.0474772i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.29100 | − | 3.96813i | −0.221479 | − | 0.383614i | 0.733778 | − | 0.679389i | \(-0.237755\pi\) |
−0.955257 | + | 0.295776i | \(0.904422\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.13325 | − | 4.92582i | 0.395894 | − | 0.471808i | −0.530870 | − | 0.847453i | \(-0.678135\pi\) |
0.926763 | + | 0.375646i | \(0.122579\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.09180 | + | 0.545167i | 0.293460 | + | 0.0517450i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 14.5994i | − | 1.37340i | −0.726942 | − | 0.686698i | \(-0.759059\pi\) | ||
0.726942 | − | 0.686698i | \(-0.240941\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.04963i | 0.377630i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.39019 | + | 1.12676i | 0.590773 | + | 0.104169i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.14583 | − | 3.74906i | 0.288378 | − | 0.343676i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.70599 | − | 8.15102i | −0.427817 | − | 0.741001i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.18408 | + | 3.25324i | −0.106765 | + | 0.293334i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.21067 | + | 3.82900i | −0.197728 | + | 0.342476i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.08507 | − | 17.4963i | −0.273755 | − | 1.55254i | −0.742888 | − | 0.669416i | \(-0.766544\pi\) |
0.469133 | − | 0.883128i | \(-0.344567\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.46550 | + | 7.70528i | 0.569255 | + | 0.678412i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.49975 | − | 6.86800i | −0.218404 | − | 0.600060i | 0.781306 | − | 0.624148i | \(-0.214554\pi\) |
−0.999710 | + | 0.0240885i | \(0.992332\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.0441677 | + | 4.99990i | 0.00382983 | + | 0.433546i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.424109 | − | 0.154363i | 0.0365015 | − | 0.0132855i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.23744 | − | 6.91203i | 0.703772 | − | 0.590535i | −0.219072 | − | 0.975709i | \(-0.570303\pi\) |
0.922844 | + | 0.385174i | \(0.125859\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.9469 | + | 3.34084i | −1.60705 | + | 0.283367i | −0.903923 | − | 0.427696i | \(-0.859326\pi\) |
−0.703129 | + | 0.711062i | \(0.748214\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.53637 | − | 4.92848i | −0.718892 | − | 0.415053i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.68380 | − | 2.79667i | −0.642551 | − | 0.233870i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.62149 | − | 1.51352i | 0.217703 | − | 0.125691i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.35432 | + | 3.65371i | 0.359138 | + | 0.301353i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.86619 | + | 16.2549i | −0.234807 | + | 1.33166i | 0.608213 | + | 0.793774i | \(0.291887\pi\) |
−0.843020 | + | 0.537883i | \(0.819224\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.24853 | 0.182983 | 0.0914916 | − | 0.995806i | \(-0.470837\pi\) | ||||
0.0914916 | + | 0.995806i | \(0.470837\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.26645 | 0.344922 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.414194 | − | 2.34901i | 0.0332688 | − | 0.188677i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.97845 | + | 4.17742i | 0.397324 | + | 0.333394i | 0.819458 | − | 0.573139i | \(-0.194275\pi\) |
−0.422134 | + | 0.906533i | \(0.638719\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.3476 | + | 5.97421i | −0.820620 | + | 0.473785i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.67188 | + | 3.52028i | 0.762251 | + | 0.277437i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.7890 | + | 7.96109i | 1.08004 | + | 0.623561i | 0.930907 | − | 0.365257i | \(-0.119019\pi\) |
0.149132 | + | 0.988817i | \(0.452352\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.560107 | + | 0.0987620i | −0.0436043 | + | 0.00768861i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.57630 | − | 6.35727i | 0.586272 | − | 0.491941i | −0.300728 | − | 0.953710i | \(-0.597230\pi\) |
0.887000 | + | 0.461769i | \(0.152785\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27.3489 | − | 9.95420i | 2.10376 | − | 0.765708i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.31423 | + | 2.83123i | −0.253446 | + | 0.216510i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.19786 | − | 19.7760i | −0.547244 | − | 1.50354i | −0.837417 | − | 0.546565i | \(-0.815935\pi\) |
0.290173 | − | 0.956974i | \(-0.406287\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.53652 | + | 4.21466i | 0.267335 | + | 0.318598i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.85415 | − | 10.5154i | −0.139366 | − | 0.790386i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.1500 | − | 17.5802i | 0.758644 | − | 1.31401i | −0.184899 | − | 0.982758i | \(-0.559196\pi\) |
0.943542 | − | 0.331252i | \(-0.107471\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.32528 | + | 6.38864i | −0.172836 | + | 0.474864i | −0.995620 | − | 0.0934904i | \(-0.970198\pi\) |
0.822784 | + | 0.568355i | \(0.192420\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.83534 | + | 6.64300i | 0.283516 | + | 0.491065i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.910792 | − | 1.08544i | 0.0669628 | − | 0.0798031i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.29476 | − | 0.933608i | −0.387191 | − | 0.0682722i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 1.14710i | − | 0.0834393i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 12.4753i | − | 0.902681i | −0.892352 | − | 0.451341i | \(-0.850946\pi\) | ||
0.892352 | − | 0.451341i | \(-0.149054\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.0298 | + | 2.65017i | 1.08187 | + | 0.190763i | 0.686043 | − | 0.727561i | \(-0.259346\pi\) |
0.395829 | + | 0.918324i | \(0.370457\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.88244 | − | 2.24341i | 0.134805 | − | 0.160654i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.19899 | + | 15.9331i | 0.655401 | + | 1.13519i | 0.981793 | + | 0.189953i | \(0.0608336\pi\) |
−0.326392 | + | 0.945234i | \(0.605833\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.670160 | − | 1.84125i | 0.0475064 | − | 0.130523i | −0.913671 | − | 0.406456i | \(-0.866765\pi\) |
0.961177 | + | 0.275933i | \(0.0889868\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.23136 | − | 5.59688i | 0.227922 | − | 0.394773i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.33597 | − | 7.57668i | −0.0937670 | − | 0.531779i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.00436 | + | 1.19695i | 0.0701475 | + | 0.0835985i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.06885 | + | 8.43159i | 0.213300 | + | 0.586036i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.73258 | − | 2.78838i | 0.327359 | − | 0.192876i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.44093 | + | 0.524454i | −0.0991975 | + | 0.0361049i | −0.391142 | − | 0.920330i | \(-0.627920\pi\) |
0.291945 | + | 0.956435i | \(0.405698\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.08682 | + | 5.10745i | −0.417062 | + | 0.349957i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.47072 | − | 0.788309i | 0.304901 | − | 0.0537623i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.25017 | − | 3.03119i | −0.356405 | − | 0.205770i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.51001 | − | 0.913567i | −0.169610 | − | 0.0617332i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 23.9751 | − | 13.8420i | 1.61274 | − | 0.931114i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.5124 | + | 13.0165i | 1.03879 | + | 0.871647i | 0.991870 | − | 0.127252i | \(-0.0406158\pi\) |
0.0469175 | + | 0.998899i | \(0.485060\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.832869 | + | 4.72344i | −0.0555246 | + | 0.314896i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −25.6706 | −1.70382 | −0.851908 | − | 0.523691i | \(-0.824555\pi\) | ||||
−0.851908 | + | 0.523691i | \(0.824555\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.90313 | −0.191844 | −0.0959221 | − | 0.995389i | \(-0.530580\pi\) | ||||
−0.0959221 | + | 0.995389i | \(0.530580\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.251015 | + | 1.42358i | −0.0165156 | + | 0.0936644i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.20495 | + | 6.04567i | 0.472012 | + | 0.396065i | 0.847528 | − | 0.530751i | \(-0.178090\pi\) |
−0.375516 | + | 0.926816i | \(0.622534\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.85270 | + | 2.22436i | −0.251323 | + | 0.145101i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.4115 | + | 4.51743i | 0.806217 | + | 0.293439i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.53002 | + | 3.19276i | 0.357707 | + | 0.206522i | 0.668075 | − | 0.744094i | \(-0.267119\pi\) |
−0.310367 | + | 0.950617i | \(0.600452\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.91521 | − | 0.514030i | 0.187785 | − | 0.0331116i | −0.0789646 | − | 0.996877i | \(-0.525161\pi\) |
0.266750 | + | 0.963766i | \(0.414050\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.766044 | − | 0.642788i | 0.0491418 | − | 0.0412348i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.41071 | − | 0.877425i | 0.154014 | − | 0.0560566i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.43851 | + | 26.6626i | −0.600558 | + | 1.69650i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.26775 | + | 3.48310i | 0.0803402 | + | 0.220733i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.50822 | + | 6.56444i | 0.347676 | + | 0.414344i | 0.911336 | − | 0.411663i | \(-0.135052\pi\) |
−0.563661 | + | 0.826007i | \(0.690607\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.96346 | − | 11.1353i | −0.123442 | − | 0.700072i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.962784 | − | 1.66759i | 0.0602919 | − | 0.104429i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.52809 | + | 6.94588i | −0.157698 | + | 0.433272i | −0.993229 | − | 0.116171i | \(-0.962938\pi\) |
0.835531 | + | 0.549443i | \(0.185160\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.80066 | − | 3.11883i | −0.111887 | − | 0.193795i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.31115 | − | 5.13783i | 0.266854 | − | 0.318024i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.2693 | − | 2.86872i | −1.00321 | − | 0.176893i | −0.352169 | − | 0.935936i | \(-0.614556\pi\) |
−0.651040 | + | 0.759043i | \(0.725667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.39265i | 0.331268i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 9.63448i | − | 0.589621i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.7156 | − | 2.41842i | −0.836252 | − | 0.147454i | −0.260906 | − | 0.965364i | \(-0.584021\pi\) |
−0.575346 | + | 0.817910i | \(0.695132\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.90186 | − | 7.03357i | 0.358513 | − | 0.427259i | −0.556397 | − | 0.830916i | \(-0.687817\pi\) |
0.914910 | + | 0.403657i | \(0.132261\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.72164 | − | 6.44606i | −0.225244 | − | 0.390133i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.06722 | − | 5.67963i | 0.124658 | − | 0.342495i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.27533 | − | 3.94099i | 0.136712 | − | 0.236791i | −0.789538 | − | 0.613701i | \(-0.789680\pi\) |
0.926250 | + | 0.376910i | \(0.123013\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.917723 | − | 5.20466i | −0.0549426 | − | 0.311595i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.4117 | − | 17.1751i | −0.859727 | − | 1.02458i | −0.999409 | − | 0.0343866i | \(-0.989052\pi\) |
0.139681 | − | 0.990197i | \(-0.455392\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.87946 | − | 5.16379i | −0.111723 | − | 0.306955i | 0.871213 | − | 0.490905i | \(-0.163334\pi\) |
−0.982936 | + | 0.183950i | \(0.941112\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.358717 | + | 1.93431i | 0.0212486 | + | 0.114579i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.73179 | − | 1.35826i | 0.220280 | − | 0.0801755i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.921241 | − | 0.773013i | 0.0541907 | − | 0.0454714i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.28863 | + | 0.227220i | −0.0755408 | + | 0.0133199i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.15482 | + | 4.70819i | 0.476410 | + | 0.275055i | 0.718919 | − | 0.695094i | \(-0.244637\pi\) |
−0.242509 | + | 0.970149i | \(0.577971\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.52848 | − | 1.64823i | −0.263658 | − | 0.0959637i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.09134 | + | 0.630083i | −0.0633257 | + | 0.0365611i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 44.6005 | + | 37.4243i | 2.57931 | + | 2.16430i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.00358 | − | 11.3629i | 0.115484 | − | 0.654944i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.9834 | 0.688426 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.46199 | 0.198233 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.946832 | − | 5.36975i | 0.0540385 | − | 0.306468i | −0.945794 | − | 0.324767i | \(-0.894714\pi\) |
0.999833 | + | 0.0182993i | \(0.00582518\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.32289 | + | 1.11003i | 0.0752565 | + | 0.0631477i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.7417 | + | 9.66584i | −0.949336 | + | 0.548099i | −0.892875 | − | 0.450306i | \(-0.851315\pi\) |
−0.0564612 | + | 0.998405i | \(0.517982\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.98062 | − | 1.44883i | −0.224998 | − | 0.0818926i | 0.227061 | − | 0.973880i | \(-0.427088\pi\) |
−0.452059 | + | 0.891988i | \(0.649310\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.448357 | − | 0.258859i | −0.0252621 | − | 0.0145851i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.68959 | + | 1.35588i | −0.431890 | + | 0.0761539i | −0.385367 | − | 0.922763i | \(-0.625925\pi\) |
−0.0465231 | + | 0.998917i | \(0.514814\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.47452 | + | 5.43277i | −0.362504 | + | 0.304177i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.30567 | + | 1.56714i | −0.240319 | + | 0.0874690i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.06743 | + | 18.3423i | −0.170677 | + | 1.02059i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.6444 | + | 29.2452i | 0.590444 | + | 1.62223i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.13325 | − | 4.92582i | −0.228569 | − | 0.272398i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.96343 | + | 11.1351i | 0.108247 | + | 0.613900i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.4730 | − | 21.6039i | 0.685578 | − | 1.18746i | −0.287677 | − | 0.957728i | \(-0.592883\pi\) |
0.973255 | − | 0.229728i | \(-0.0737838\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.07377 | − | 2.95016i | 0.0588422 | − | 0.161668i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.45840 | − | 2.52603i | −0.0796810 | − | 0.138012i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.59966 | − | 3.09815i | 0.141612 | − | 0.168767i | −0.690576 | − | 0.723259i | \(-0.742643\pi\) |
0.832189 | + | 0.554492i | \(0.187088\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.3776 | − | 2.53516i | −0.780885 | − | 0.137691i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.65992i | 0.360655i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 14.5500i | − | 0.785627i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.98811 | + | 0.703211i | 0.214713 | + | 0.0378596i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.0011 | + | 19.0694i | −0.858984 | + | 1.02370i | 0.140451 | + | 0.990088i | \(0.455145\pi\) |
−0.999435 | + | 0.0336098i | \(0.989300\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.667220 | + | 1.15566i | 0.0357155 | + | 0.0618610i | 0.883331 | − | 0.468750i | \(-0.155296\pi\) |
−0.847615 | + | 0.530612i | \(0.821962\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.21929 | − | 6.09745i | 0.118457 | − | 0.325458i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.57112 | + | 14.8456i | −0.456195 | + | 0.790153i | −0.998756 | − | 0.0498637i | \(-0.984121\pi\) |
0.542561 | + | 0.840016i | \(0.317455\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.622729 | + | 3.53167i | 0.0330510 | + | 0.187442i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.14583 | − | 3.74906i | −0.166495 | − | 0.198421i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.88443 | − | 21.6623i | −0.416124 | − | 1.14329i | −0.953879 | − | 0.300191i | \(-0.902950\pi\) |
0.537755 | − | 0.843101i | \(-0.319273\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.78920 | − | 16.2841i | −0.515221 | − | 0.857057i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.84437 | + | 3.21909i | −0.464209 | + | 0.168958i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.923496 | + | 0.774905i | −0.0483380 | + | 0.0405604i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.1452 | − | 3.37582i | 0.999372 | − | 0.176216i | 0.350051 | − | 0.936731i | \(-0.386164\pi\) |
0.649321 | + | 0.760514i | \(0.275053\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.99820 | + | 1.73101i | 0.156080 | + | 0.0901128i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.8795 | + | 4.68774i | 0.668668 | + | 0.243375i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.5154 | + | 6.07109i | −0.544468 | + | 0.314349i | −0.746888 | − | 0.664950i | \(-0.768453\pi\) |
0.202420 | + | 0.979299i | \(0.435120\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.38695 | + | 2.84198i | 0.174901 | + | 0.146759i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.55716 | − | 42.8588i | 0.389214 | − | 2.20734i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.1216 | −1.03358 | −0.516788 | − | 0.856114i | \(-0.672872\pi\) | ||||
−0.516788 | + | 0.856114i | \(0.672872\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.7662 | −0.910189 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.10309 | + | 17.5985i | −0.158560 | + | 0.899241i | 0.796898 | + | 0.604114i | \(0.206473\pi\) |
−0.955458 | + | 0.295127i | \(0.904638\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.499776 | + | 0.419362i | 0.0254709 | + | 0.0213727i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.71094 | − | 5.02926i | 0.442802 | − | 0.255652i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.36299 | − | 0.860058i | −0.119808 | − | 0.0436067i | 0.281420 | − | 0.959585i | \(-0.409195\pi\) |
−0.401229 | + | 0.915978i | \(0.631417\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 33.1528 | + | 19.1408i | 1.67661 | + | 0.967992i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.19773 | + | 1.26915i | −0.363078 | + | 0.0640204i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.56653 | − | 3.83177i | 0.229767 | − | 0.192797i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.0849 | + | 7.31032i | −1.00803 | + | 0.366895i | −0.792678 | − | 0.609641i | \(-0.791314\pi\) |
−0.215357 | + | 0.976535i | \(0.569091\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.93161 | + | 0.824727i | 0.246889 | + | 0.0412880i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.61950 | − | 12.6920i | −0.230687 | − | 0.633807i | 0.769300 | − | 0.638888i | \(-0.220605\pi\) |
−0.999987 | + | 0.00508032i | \(0.998383\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.0430 | − | 26.2698i | −1.09804 | − | 1.30859i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.0783722 | − | 0.444471i | −0.00389435 | − | 0.0220859i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.97814 | + | 3.42624i | −0.0980528 | + | 0.169833i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.3009 | + | 28.3014i | −0.509346 | + | 1.39942i | 0.372568 | + | 0.928005i | \(0.378477\pi\) |
−0.881914 | + | 0.471411i | \(0.843745\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.37661 | − | 9.31255i | −0.265208 | − | 0.459354i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.87306 | + | 9.38275i | −0.387408 | + | 0.461695i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.64750 | + | 0.290498i | 0.0808724 | + | 0.0142600i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 19.2391i | 0.942145i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.4841i | 0.512184i | 0.966652 | + | 0.256092i | \(0.0824350\pi\) | ||||
−0.966652 | + | 0.256092i | \(0.917565\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.8629 | − | 2.26807i | −0.626898 | − | 0.110539i | −0.148831 | − | 0.988863i | \(-0.547551\pi\) |
−0.478067 | + | 0.878324i | \(0.658662\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.33593 | + | 7.55086i | −0.308063 | + | 0.367136i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.2316 | + | 17.7216i | 0.496305 | + | 0.859626i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.00945 | − | 8.26839i | 0.145637 | − | 0.400135i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.08846 | + | 7.08143i | −0.197393 | + | 0.341895i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.85069 | − | 33.1809i | −0.281818 | − | 1.59827i | −0.716435 | − | 0.697654i | \(-0.754227\pi\) |
0.434617 | − | 0.900616i | \(-0.356884\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.21020 | − | 2.63401i | −0.106215 | − | 0.126583i | 0.710318 | − | 0.703881i | \(-0.248551\pi\) |
−0.816533 | + | 0.577299i | \(0.804107\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.03531 | − | 2.84449i | −0.0496393 | − | 0.136383i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −38.4555 | + | 7.13155i | −1.83957 | + | 0.341148i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.64682 | − | 1.32734i | 0.174053 | − | 0.0633503i | −0.253524 | − | 0.967329i | \(-0.581590\pi\) |
0.427577 | + | 0.903979i | \(0.359367\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.35432 | − | 3.65371i | 0.207349 | − | 0.173986i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.36498 | + | 1.29864i | −0.349921 | + | 0.0617005i | −0.345846 | − | 0.938291i | \(-0.612408\pi\) |
−0.00407456 | + | 0.999992i | \(0.501297\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.76575 | − | 2.17415i | −0.178514 | − | 0.103065i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 15.5103 | + | 5.64528i | 0.733612 | + | 0.267013i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13.8206 | + | 7.97934i | −0.652235 | + | 0.376568i | −0.789312 | − | 0.613992i | \(-0.789563\pi\) |
0.137077 | + | 0.990560i | \(0.456229\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.34204 | − | 2.80430i | −0.157370 | − | 0.132049i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.390454 | − | 2.21437i | 0.0183451 | − | 0.104040i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.35936 | −0.157489 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.2832 | −1.46337 | −0.731684 | − | 0.681645i | \(-0.761265\pi\) | ||||
−0.731684 | + | 0.681645i | \(0.761265\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.740861 | − | 4.20163i | 0.0345804 | − | 0.196115i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.97429 | − | 4.17392i | −0.231676 | − | 0.194399i | 0.519558 | − | 0.854435i | \(-0.326097\pi\) |
−0.751234 | + | 0.660036i | \(0.770541\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.7320 | + | 17.1658i | −1.38176 | + | 0.797761i | −0.992368 | − | 0.123310i | \(-0.960649\pi\) |
−0.389394 | + | 0.921071i | \(0.627316\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.24140 | − | 0.815802i | −0.103942 | − | 0.0378319i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 33.3097 | + | 19.2313i | 1.54139 | + | 0.889920i | 0.998752 | + | 0.0499518i | \(0.0159068\pi\) |
0.542635 | + | 0.839968i | \(0.317427\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.30076 | + | 1.28732i | −0.337118 | + | 0.0594430i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.97845 | − | 4.17742i | 0.229395 | − | 0.192485i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.9110 | + | 4.33525i | −0.547668 | + | 0.199335i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19.7082 | − | 6.97666i | −0.904273 | − | 0.320111i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.08660 | + | 11.2278i | 0.187112 | + | 0.514087i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.4800 | − | 14.8731i | −0.570225 | − | 0.679567i | 0.401453 | − | 0.915880i | \(-0.368505\pi\) |
−0.971677 | + | 0.236313i | \(0.924061\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.53747 | − | 20.0620i | −0.161295 | − | 0.914747i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.14630 | − | 8.91365i | 0.234165 | − | 0.405585i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.201985 | + | 0.554951i | −0.00917169 | + | 0.0251990i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.921131 | − | 1.59545i | −0.0417404 | − | 0.0722965i | 0.844400 | − | 0.535713i | \(-0.179957\pi\) |
−0.886141 | + | 0.463416i | \(0.846624\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.2346 | − | 12.1971i | 0.462824 | − | 0.551572i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.1909 | + | 2.50225i | 0.640428 | + | 0.112925i | 0.484427 | − | 0.874832i | \(-0.339028\pi\) |
0.156002 | + | 0.987757i | \(0.450139\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 28.6149i | − | 1.28875i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.568748i | 0.0255633i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.97614 | + | 1.58273i | 0.402635 | + | 0.0709954i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.73938 | + | 8.03168i | −0.301696 | + | 0.359547i | −0.895499 | − | 0.445063i | \(-0.853181\pi\) |
0.593803 | + | 0.804610i | \(0.297626\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.94508 | − | 8.56513i | −0.220930 | − | 0.382662i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.14166 | + | 11.3791i | −0.184668 | + | 0.507370i | −0.997136 | − | 0.0756357i | \(-0.975901\pi\) |
0.812468 | + | 0.583006i | \(0.198124\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.70421 | − | 4.68383i | 0.120336 | − | 0.208428i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.05388 | − | 28.6620i | −0.224451 | − | 1.27292i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.30624 | + | 9.89899i | 0.368168 | + | 0.438765i | 0.918043 | − | 0.396482i | \(-0.129769\pi\) |
−0.549875 | + | 0.835247i | \(0.685325\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.04795 | + | 2.87923i | 0.0463587 | + | 0.127370i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.21271 | + | 3.75552i | 0.0976935 | + | 0.165810i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.732398 | − | 0.266571i | 0.0322733 | − | 0.0117465i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.51534 | − | 7.98432i | 0.418484 | − | 0.351150i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.7254 | + | 3.65445i | −0.909745 | + | 0.160413i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.9330 | − | 8.62156i | −0.654226 | − | 0.377717i | 0.135848 | − | 0.990730i | \(-0.456624\pi\) |
−0.790073 | + | 0.613012i | \(0.789958\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.8077 | − | 4.66163i | −0.560043 | − | 0.203839i | 0.0464600 | − | 0.998920i | \(-0.485206\pi\) |
−0.606503 | + | 0.795081i | \(0.707428\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.76474 | − | 2.75092i | 0.207950 | − | 0.120060i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17.2728 | − | 14.4936i | −0.752413 | − | 0.631350i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.98642 | + | 56.6358i | −0.434192 | + | 2.46243i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.6776 | −0.463369 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.4643 | 0.973035 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.359102 | + | 2.03657i | −0.0155253 | + | 0.0880485i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.5506 | − | 13.0485i | −0.671060 | − | 0.563086i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.20333 | + | 3.58149i | −0.267196 | + | 0.154266i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.2817 | + | 7.74590i | 0.914971 | + | 0.333022i | 0.756236 | − | 0.654299i | \(-0.227036\pi\) |
0.158735 | + | 0.987321i | \(0.449258\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.88781 | + | 3.39933i | 0.252670 | + | 0.145879i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.85804 | + | 0.503949i | −0.122425 | + | 0.0215868i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.2694 | − | 27.9163i | 1.42250 | − | 1.19362i | 0.472510 | − | 0.881325i | \(-0.343348\pi\) |
0.949987 | − | 0.312291i | \(-0.101096\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.20808 | − | 2.62353i | 0.307633 | − | 0.111969i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.9890 | + | 22.2284i | 0.808958 | + | 0.946963i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.18195 | − | 14.2373i | −0.220359 | − | 0.605431i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.910792 | − | 1.08544i | −0.0386610 | − | 0.0460743i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.73039 | − | 15.4848i | −0.115690 | − | 0.656112i | −0.986406 | − | 0.164325i | \(-0.947455\pi\) |
0.870716 | − | 0.491786i | \(-0.163656\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.6337 | − | 56.5233i | 1.38026 | − | 2.39068i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.83885 | + | 5.05220i | −0.0776363 | + | 0.213304i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.1940 | + | 21.1207i | 0.513917 | + | 0.890129i | 0.999870 | + | 0.0161446i | \(0.00513922\pi\) |
−0.485953 | + | 0.873985i | \(0.661527\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.23540 | + | 5.04756i | −0.178185 | + | 0.212352i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.12967 | − | 0.199192i | −0.0474418 | − | 0.00836527i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.40585i | 0.394314i | 0.980372 | + | 0.197157i | \(0.0631708\pi\) | ||||
−0.980372 | + | 0.197157i | \(0.936829\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.7817i | 1.16263i | 0.813679 | + | 0.581314i | \(0.197461\pi\) | ||||
−0.813679 | + | 0.581314i | \(0.802539\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.2858 | − | 2.16631i | −0.513246 | − | 0.0904990i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −27.6629 | + | 32.9674i | −1.15362 | + | 1.37483i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.2279 | + | 29.8396i | 0.717207 | + | 1.24224i | 0.962102 | + | 0.272690i | \(0.0879132\pi\) |
−0.244895 | + | 0.969550i | \(0.578753\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.21981 | − | 14.3413i | 0.216928 | − | 0.596005i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.12595 | − | 3.68225i | 0.0881991 | − | 0.152765i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.61462 | − | 14.8282i | −0.108286 | − | 0.614123i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.88244 | − | 2.24341i | −0.0778295 | − | 0.0927535i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.38030 | + | 23.0247i | 0.345892 | + | 0.950330i | 0.983650 | + | 0.180093i | \(0.0576399\pi\) |
−0.637758 | + | 0.770237i | \(0.720138\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.0357 | − | 0.203491i | 0.949169 | − | 0.00838469i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.2884 | − | 6.29248i | 0.711151 | − | 0.258838i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −32.9668 | + | 27.6624i | −1.35379 | + | 1.13596i | −0.375937 | + | 0.926645i | \(0.622679\pi\) |
−0.977848 | + | 0.209315i | \(0.932877\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.17526 | + | 0.383557i | −0.0891771 | + | 0.0157243i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.69690 | − | 0.979708i | −0.0694497 | − | 0.0400968i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.2010 | + | 7.71653i | 0.866249 | + | 0.315289i | 0.736647 | − | 0.676277i | \(-0.236408\pi\) |
0.129602 | + | 0.991566i | \(0.458630\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.197687 | + | 0.114135i | −0.00806382 | + | 0.00465565i | −0.504026 | − | 0.863688i | \(-0.668149\pi\) |
0.495963 | + | 0.868344i | \(0.334815\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.95073 | − | 4.15416i | −0.201609 | − | 0.169170i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.737638 | + | 4.18335i | −0.0299893 | + | 0.170078i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.5108 | −0.913684 | −0.456842 | − | 0.889548i | \(-0.651020\pi\) | ||||
−0.456842 | + | 0.889548i | \(0.651020\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.69356 | −0.311759 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.1065 | + | 62.9878i | −0.449319 | + | 2.54821i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.2545 | − | 22.8693i | −1.10080 | − | 0.923681i | −0.103321 | − | 0.994648i | \(-0.532947\pi\) |
−0.997479 | + | 0.0709674i | \(0.977391\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.35317 | − | 0.781253i | 0.0545651 | − | 0.0315032i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −33.0077 | − | 12.0138i | −1.32884 | − | 0.483658i | −0.422560 | − | 0.906335i | \(-0.638868\pi\) |
−0.906280 | + | 0.422677i | \(0.861090\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.19055 | + | 5.30616i | 0.369399 | + | 0.213273i | 0.673196 | − | 0.739464i | \(-0.264921\pi\) |
−0.303797 | + | 0.952737i | \(0.598254\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.83639 | − | 1.55809i | 0.354592 | − | 0.0625242i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.46611 | + | 7.10391i | −0.339188 | + | 0.284612i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.6601 | + | 7.51967i | −0.826405 | + | 0.300787i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.92422 | − | 5.14488i | −0.0768458 | − | 0.205467i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.58119 | − | 12.5867i | −0.182664 | − | 0.501865i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.2744 | − | 27.7373i | −0.926538 | − | 1.10421i | −0.994312 | − | 0.106504i | \(-0.966034\pi\) |
0.0677741 | − | 0.997701i | \(-0.478410\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.266272 | + | 1.51011i | 0.0105834 | + | 0.0600213i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.00919 | + | 6.94411i | −0.159100 | + | 0.275569i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.6148 | − | 34.6589i | 0.499817 | − | 1.37323i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.97289 | + | 6.88125i | 0.157165 | + | 0.272218i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.4346 | + | 37.4623i | −1.24159 | + | 1.47967i | −0.422137 | + | 0.906532i | \(0.638720\pi\) |
−0.819456 | + | 0.573142i | \(0.805725\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.69253 | + | 1.00375i | 0.224491 | + | 0.0395839i | 0.284762 | − | 0.958598i | \(-0.408085\pi\) |
−0.0602709 | + | 0.998182i | \(0.519196\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 4.53969i | − | 0.178750i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.6857i | 0.813240i | 0.913597 | + | 0.406620i | \(0.133293\pi\) | ||||
−0.913597 | + | 0.406620i | \(0.866707\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.2512 | + | 2.33654i | 0.520153 | + | 0.0917171i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.89682 | + | 4.64405i | −0.152728 | + | 0.182015i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.0648 | − | 27.8250i | −0.628663 | − | 1.08888i | −0.987820 | − | 0.155600i | \(-0.950269\pi\) |
0.359157 | − | 0.933277i | \(-0.383064\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.12821 | + | 3.09972i | −0.0440826 | + | 0.121116i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.33555 | + | 2.31323i | −0.0521046 | + | 0.0902478i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.89652 | + | 10.7557i | 0.0738780 | + | 0.418983i | 0.999207 | + | 0.0398176i | \(0.0126777\pi\) |
−0.925329 | + | 0.379165i | \(0.876211\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.14723 | + | 3.75072i | 0.122413 | + | 0.145886i | 0.823770 | − | 0.566924i | \(-0.191867\pi\) |
−0.701357 | + | 0.712810i | \(0.747422\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.46849 | − | 26.0145i | −0.367726 | − | 1.01032i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.43524 | − | 1.74146i | 0.0556562 | − | 0.0675311i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 56.5504 | − | 20.5827i | 2.18964 | − | 0.796964i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15.5124 | − | 13.0165i | 0.599744 | − | 0.503245i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.51947 | + | 1.67854i | −0.367495 | + | 0.0647993i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.8068 | − | 12.0128i | −0.802042 | − | 0.463059i | 0.0421428 | − | 0.999112i | \(-0.486582\pi\) |
−0.844185 | + | 0.536053i | \(0.819915\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.50705 | + | 1.64043i | 0.173476 | + | 0.0631403i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.6225 | − | 14.2158i | 0.946319 | − | 0.546357i | 0.0543833 | − | 0.998520i | \(-0.482681\pi\) |
0.891935 | + | 0.452163i | \(0.149347\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.14983 | + | 0.964818i | 0.0441263 | + | 0.0370263i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.45765 | + | 25.2806i | −0.170818 | + | 0.968754i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.9631 | 0.534282 | 0.267141 | − | 0.963657i | \(-0.413921\pi\) | ||||
0.267141 | + | 0.963657i | \(0.413921\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.85322 | −0.185432 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.504123 | + | 2.85902i | −0.0192335 | + | 0.109079i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 59.3918 | + | 49.8357i | 2.26265 | + | 1.89859i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.6029 | + | 20.5553i | −1.35440 | + | 0.781962i | −0.988862 | − | 0.148835i | \(-0.952448\pi\) |
−0.365536 | + | 0.930797i | \(0.619114\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.35836 | + | 0.494403i | 0.0515999 | + | 0.0187808i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.51984 | + | 4.34158i | 0.285244 | + | 0.164686i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.5461 | − | 2.56488i | 0.550974 | − | 0.0971516i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.20495 | − | 6.04567i | 0.272516 | − | 0.228668i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.5935 | − | 11.1351i | 1.15550 | − | 0.420568i | 0.308013 | − | 0.951382i | \(-0.400336\pi\) |
0.847488 | + | 0.530814i | \(0.178114\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.9113 | + | 6.73741i | 0.449243 | + | 0.254106i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.52155 | + | 4.18043i | 0.0573049 | + | 0.157444i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.83584 | − | 10.5301i | −0.332306 | − | 0.396027i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.88409 | + | 44.7129i | 0.296093 | + | 1.67923i | 0.662725 | + | 0.748863i | \(0.269400\pi\) |
−0.366632 | + | 0.930366i | \(0.619489\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.60405 | − | 11.4385i | 0.247671 | − | 0.428979i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.2187 | − | 44.5606i | 0.607396 | − | 1.66881i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.84524 | + | 3.19604i | 0.0690080 | + | 0.119525i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.10453 | − | 4.89159i | 0.153287 | − | 0.182680i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.27096 | + | 0.753085i | 0.159280 | + | 0.0280853i | 0.252719 | − | 0.967540i | \(-0.418675\pi\) |
−0.0934395 | + | 0.995625i | \(0.529786\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 1.98094i | − | 0.0737739i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 2.96018i | − | 0.110090i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 31.6799 | + | 5.58603i | 1.17656 | + | 0.207460i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.9656 | + | 16.6436i | −0.517956 | + | 0.617276i | −0.960096 | − | 0.279670i | \(-0.909775\pi\) |
0.442140 | + | 0.896946i | \(0.354219\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.500000 | − | 0.866025i | −0.0185185 | − | 0.0320750i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.6775 | − | 40.3262i | 0.542868 | − | 1.49152i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.286737 | + | 0.496644i | −0.0105909 | + | 0.0183439i | −0.871272 | − | 0.490800i | \(-0.836705\pi\) |
0.860681 | + | 0.509144i | \(0.170038\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.445480 | − | 2.52644i | −0.0164318 | − | 0.0931893i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.23493 | + | 6.23874i | 0.192831 | + | 0.229807i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.67878 | − | 26.5922i | −0.356040 | − | 0.978211i | −0.980390 | − | 0.197066i | \(-0.936859\pi\) |
0.624351 | − | 0.781144i | \(-0.285364\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 24.6185 | + | 13.9250i | 0.904384 | + | 0.511549i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37.7541 | − | 13.7414i | 1.38507 | − | 0.504122i | 0.461355 | − | 0.887215i | \(-0.347363\pi\) |
0.923710 | + | 0.383093i | \(0.125141\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.70663 | − | 4.78844i | 0.209075 | − | 0.175435i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.65033 | − | 0.643652i | 0.133559 | − | 0.0235500i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.55184 | + | 2.62801i | 0.166321 | + | 0.0960253i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.3464 | + | 5.22168i | 0.523509 | + | 0.190542i | 0.590238 | − | 0.807230i | \(-0.299034\pi\) |
−0.0667288 | + | 0.997771i | \(0.521256\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.42120 | − | 4.28463i | 0.270444 | − | 0.156141i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.777402 | − | 0.652317i | −0.0282925 | − | 0.0237403i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.95117 | − | 33.7507i | 0.216299 | − | 1.22669i | −0.662339 | − | 0.749204i | \(-0.730436\pi\) |
0.878638 | − | 0.477488i | \(-0.158453\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11.3071 | −0.410422 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.4377 | 0.559615 | 0.279808 | − | 0.960056i | \(-0.409729\pi\) | ||||
0.279808 | + | 0.960056i | \(0.409729\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.28084 | + | 7.26402i | −0.0463696 | + | 0.262975i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.47507 | − | 1.23773i | −0.0533313 | − | 0.0447503i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −60.0022 | + | 34.6423i | −2.16656 | + | 1.25086i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.42227 | + | 0.881633i | 0.0873492 | + | 0.0317925i | 0.385325 | − | 0.922781i | \(-0.374089\pi\) |
−0.297976 | + | 0.954573i | \(0.596312\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.40136 | + | 3.69583i | 0.230539 | + | 0.133102i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28.2934 | − | 4.98889i | 1.01764 | − | 0.179438i | 0.360146 | − | 0.932896i | \(-0.382727\pi\) |
0.657496 | + | 0.753458i | \(0.271616\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 19.4179 | − | 16.2935i | 0.697511 | − | 0.585281i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.38413 | + | 1.23172i | −0.121405 | + | 0.0441878i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.59756 | + | 11.6453i | −0.343868 | + | 0.417236i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.42465 | − | 9.40914i | −0.122544 | − | 0.336686i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.31115 | − | 5.13783i | −0.154068 | − | 0.183611i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.509334 | − | 2.88858i | −0.0181789 | − | 0.103098i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.5771 | + | 37.3726i | −0.769140 | + | 1.33219i | 0.168890 | + | 0.985635i | \(0.445982\pi\) |
−0.938030 | + | 0.346554i | \(0.887352\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.65028 | + | 15.5240i | −0.201155 | + | 0.552669i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.37350 | + | 14.5033i | 0.297727 | + | 0.515679i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31.9936 | − | 38.1285i | 1.13613 | − | 1.35398i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.31072 | + | 0.936424i | 0.188352 | + | 0.0332115i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 13.8710i | − | 0.491337i | −0.969354 | − | 0.245669i | \(-0.920993\pi\) | ||
0.969354 | − | 0.245669i | \(-0.0790075\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 42.0542i | 1.48777i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.48811 | − | 1.67301i | −0.335246 | − | 0.0591129i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.16364 | − | 2.57852i | 0.0763530 | − | 0.0909940i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.32267 | − | 4.02298i | −0.0818633 | − | 0.141791i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.76336 | + | 13.0872i | −0.167678 | + | 0.460692i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.180910 | + | 0.313345i | −0.00636045 | + | 0.0110166i | −0.869188 | − | 0.494482i | \(-0.835358\pi\) |
0.862828 | + | 0.505498i | \(0.168691\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.82369 | − | 38.6991i | −0.239612 | − | 1.35891i | −0.832680 | − | 0.553755i | \(-0.813194\pi\) |
0.593067 | − | 0.805153i | \(-0.297917\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.90186 | − | 7.03357i | −0.206987 | − | 0.246678i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.45780 | − | 6.75275i | −0.0860929 | − | 0.236538i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.3589 | + | 41.0659i | 0.537341 | + | 1.43671i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.99439 | + | 2.54575i | −0.244404 | + | 0.0889557i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.5564 | + | 15.5707i | −0.647624 | + | 0.543421i | −0.906349 | − | 0.422530i | \(-0.861142\pi\) |
0.258725 | + | 0.965951i | \(0.416698\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.68599 | + | 0.826267i | −0.163343 | + | 0.0288019i | −0.254722 | − | 0.967014i | \(-0.581984\pi\) |
0.0913783 | + | 0.995816i | \(0.470873\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.23438 | − | 3.02207i | −0.182238 | − | 0.105215i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.4868 | − | 4.18086i | −0.399436 | − | 0.145383i | 0.134488 | − | 0.990915i | \(-0.457061\pi\) |
−0.533924 | + | 0.845532i | \(0.679283\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.7311 | + | 9.08236i | −0.546364 | + | 0.315443i | −0.747654 | − | 0.664088i | \(-0.768820\pi\) |
0.201290 | + | 0.979532i | \(0.435487\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.48601 | − | 2.92511i | −0.120928 | − | 0.101471i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.21117 | − | 23.8828i | 0.145909 | − | 0.827488i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.46370 | −0.154473 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.28495 | −0.182675 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.02590 | − | 34.1746i | 0.208037 | − | 1.17984i | −0.684551 | − | 0.728965i | \(-0.740002\pi\) |
0.892588 | − | 0.450872i | \(-0.148887\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.2440 | − | 10.2739i | −0.422207 | − | 0.354273i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19.4168 | + | 11.2103i | −0.668749 | + | 0.386103i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.3433 | − | 4.49261i | −0.424624 | − | 0.154550i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.35003 | + | 5.39824i | 0.321271 | + | 0.185486i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.41170 | + | 0.954229i | −0.185729 | + | 0.0327491i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21.5793 | − | 18.1072i | 0.739729 | − | 0.620706i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 48.5240 | − | 17.6613i | 1.66143 | − | 0.604711i | 0.670844 | − | 0.741599i | \(-0.265932\pi\) |
0.990587 | + | 0.136887i | \(0.0437098\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.96722 | − | 0.0173778i | 0.0672773 | − | 0.000594309i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.79546 | + | 15.9229i | 0.197969 | + | 0.543916i | 0.998463 | − | 0.0554253i | \(-0.0176515\pi\) |
−0.800494 | + | 0.599341i | \(0.795429\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.19470 | − | 10.9578i | −0.313719 | − | 0.373876i | 0.586026 | − | 0.810293i | \(-0.300692\pi\) |
−0.899745 | + | 0.436417i | \(0.856247\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.689607 | − | 3.91095i | −0.0235017 | − | 0.133285i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.6380 | − | 42.6743i | 0.838688 | − | 1.45265i | −0.0523045 | − | 0.998631i | \(-0.516657\pi\) |
0.890992 | − | 0.454019i | \(-0.150010\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.24860 | + | 8.92544i | −0.110456 | + | 0.303474i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.601298 | − | 1.04148i | −0.0204211 | − | 0.0353704i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.6988 | + | 12.7503i | −0.362932 | + | 0.432526i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −41.2980 | − | 7.28195i | −1.39933 | − | 0.246740i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.30851i | 0.0442863i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 5.07173i | − | 0.171456i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.53804 | + | 0.271199i | 0.0519361 | + | 0.00915773i | 0.199556 | − | 0.979886i | \(-0.436050\pi\) |
−0.147620 | + | 0.989044i | \(0.547161\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.05273 | − | 7.21336i | 0.204153 | − | 0.243301i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.22902 | + | 2.12873i | 0.0414069 | + | 0.0717188i | 0.885986 | − | 0.463712i | \(-0.153483\pi\) |
−0.844579 | + | 0.535431i | \(0.820149\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.9395 | − | 52.0359i | 0.637365 | − | 1.75115i | −0.0224821 | − | 0.999747i | \(-0.507157\pi\) |
0.659847 | − | 0.751400i | \(-0.270621\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.40955 | + | 4.17347i | −0.0809962 | + | 0.140290i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.67671 | − | 20.8517i | −0.123452 | − | 0.700130i | −0.982215 | − | 0.187758i | \(-0.939878\pi\) |
0.858763 | − | 0.512372i | \(-0.171233\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.0998 | + | 15.6117i | 0.439352 | + | 0.523599i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.431002 | + | 1.18417i | 0.0144391 | + | 0.0396711i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −27.9073 | − | 32.6682i | −0.933883 | − | 1.09320i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.60939 | + | 3.13356i | −0.287780 | + | 0.104743i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 44.6005 | − | 37.4243i | 1.48917 | − | 1.24956i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −34.9075 | + | 6.15513i | −1.16423 | + | 0.205285i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 44.1476 | + | 25.4887i | 1.47077 | + | 0.849150i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.8423 | − | 3.94628i | −0.360809 | − | 0.131324i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.65733 | − | 1.53421i | 0.0883326 | − | 0.0509989i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.0549 | + | 26.8973i | 1.06437 | + | 0.893109i | 0.994530 | − | 0.104449i | \(-0.0333079\pi\) |
0.0698362 | + | 0.997558i | \(0.477752\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.08089 | − | 11.8013i | 0.0690187 | − | 0.391425i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.0644 | −0.731027 | −0.365513 | − | 0.930806i | \(-0.619107\pi\) | ||||
−0.365513 | + | 0.930806i | \(0.619107\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.67098 | −0.154587 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.601168 | − | 3.40939i | 0.0198740 | − | 0.112711i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.42244 | + | 5.38906i | 0.212088 | + | 0.177963i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.25325 | − | 4.18767i | 0.239263 | − | 0.138138i | −0.375575 | − | 0.926792i | \(-0.622555\pi\) |
0.614838 | + | 0.788654i | \(0.289221\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.12376 | − | 1.86489i | −0.168833 | − | 0.0614504i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 44.6508 | + | 25.7792i | 1.46970 | + | 0.848532i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.8292 | − | 2.61479i | 0.487581 | − | 0.0859737i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.32289 | − | 1.11003i | 0.0434493 | − | 0.0364583i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.94216 | − | 2.52674i | 0.227765 | − | 0.0828996i | −0.225617 | − | 0.974216i | \(-0.572440\pi\) |
0.453382 | + | 0.891317i | \(0.350217\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.5774 | + | 21.3470i | 0.412208 | + | 0.699619i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.61182 | + | 18.1658i | 0.216461 | + | 0.594723i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.55975 | + | 1.85883i | 0.0510092 | + | 0.0607903i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.270086 | + | 1.53173i | 0.00882332 | + | 0.0500395i | 0.988902 | − | 0.148572i | \(-0.0474678\pi\) |
−0.980078 | + | 0.198612i | \(0.936357\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.11804 | + | 3.66856i | −0.0691198 | + | 0.119719i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.9064 | − | 32.7127i | 0.388139 | − | 1.06640i | −0.579699 | − | 0.814830i | \(-0.696830\pi\) |
0.967838 | − | 0.251573i | \(-0.0809477\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.5319 | + | 26.9020i | 0.505787 | + | 0.876048i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.332783 | + | 0.396595i | −0.0108254 | + | 0.0129012i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −39.1043 | − | 6.89514i | −1.27072 | − | 0.224062i | −0.502684 | − | 0.864471i | \(-0.667654\pi\) |
−0.768034 | + | 0.640409i | \(0.778765\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.3321i | 0.562624i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.80821i | 0.253199i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.11544 | − | 0.373010i | −0.0685259 | − | 0.0120830i | 0.139280 | − | 0.990253i | \(-0.455521\pi\) |
−0.207806 | + | 0.978170i | \(0.566632\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.61918 | + | 4.31318i | −0.117114 | + | 0.139571i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.22595 | + | 7.31955i | 0.136605 | + | 0.236608i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.21882 | + | 11.5911i | −0.136233 | + | 0.374297i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.53463 | − | 2.65806i | 0.0495042 | − | 0.0857438i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.795656 | + | 4.51239i | 0.0256397 | + | 0.145410i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.42754 | − | 5.27654i | −0.142528 | − | 0.169858i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.78041 | − | 10.3866i | −0.121570 | − | 0.334011i | 0.863948 | − | 0.503581i | \(-0.167984\pi\) |
−0.985518 | + | 0.169570i | \(0.945762\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 17.5310 | + | 6.20594i | 0.563177 | + | 0.199364i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.94831 | − | 3.62089i | 0.319256 | − | 0.116200i | −0.177421 | − | 0.984135i | \(-0.556775\pi\) |
0.496677 | + | 0.867935i | \(0.334553\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.9060 | − | 14.1858i | 0.541982 | − | 0.454777i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 30.6493 | − | 5.40430i | 0.981563 | − | 0.173076i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.1721 | + | 17.4198i | 0.965290 | + | 0.557310i | 0.897797 | − | 0.440410i | \(-0.145167\pi\) |
0.0674927 | + | 0.997720i | \(0.478500\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.4089 | + | 4.15248i | 0.364629 | + | 0.132714i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.56871 | + | 3.21510i | −0.177795 | + | 0.102650i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.4994 | + | 25.5921i | 0.972781 | + | 0.816260i | 0.982985 | − | 0.183688i | \(-0.0588036\pi\) |
−0.0102039 | + | 0.999948i | \(0.503248\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.44189 | − | 8.17737i | 0.0459425 | − | 0.260553i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.3069 | 0.359903 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 90.2522 | 2.86985 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.24648 | − | 41.0968i | 0.230192 | − | 1.30548i | −0.622315 | − | 0.782767i | \(-0.713808\pi\) |
0.852507 | − | 0.522716i | \(-0.175081\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −19.1097 | − | 16.0350i | −0.606429 | − | 0.508855i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.765860 | + | 0.442169i | −0.0242794 | + | 0.0140177i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.37230 | + | 1.95536i | 0.170142 | + | 0.0619267i | 0.425687 | − | 0.904871i | \(-0.360033\pi\) |
−0.255545 | + | 0.966797i | \(0.582255\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.71888 | − | 1.56975i | −0.0860216 | − | 0.0496646i |
(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 | 912.2.ci.f.223.2 | yes | 18 | |
4.3 | odd | 2 | 912.2.ci.e.223.2 | ✓ | 18 | ||
19.15 | odd | 18 | 912.2.ci.e.319.2 | yes | 18 | ||
76.15 | even | 18 | inner | 912.2.ci.f.319.2 | yes | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
912.2.ci.e.223.2 | ✓ | 18 | 4.3 | odd | 2 | ||
912.2.ci.e.319.2 | yes | 18 | 19.15 | odd | 18 | ||
912.2.ci.f.223.2 | yes | 18 | 1.1 | even | 1 | trivial | |
912.2.ci.f.319.2 | yes | 18 | 76.15 | even | 18 | inner |