Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(424,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.424");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.r (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 499.2 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.499 |
Dual form | 525.2.r.f.424.2 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.36603 | + | 1.36603i | 1.67303 | + | 0.965926i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | 2.73205 | + | 4.73205i | 1.36603 | + | 2.36603i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.73205 | 1.11536 | ||||||||
\(7\) | −2.50000 | + | 0.866025i | −0.944911 | + | 0.327327i | ||||
\(8\) | 9.46410i | 3.34607i | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.366025 | − | 0.633975i | −0.110361 | − | 0.191151i | 0.805555 | − | 0.592521i | \(-0.201867\pi\) |
−0.915916 | + | 0.401371i | \(0.868534\pi\) | |||||||
\(12\) | 4.73205 | + | 2.73205i | 1.36603 | + | 0.788675i | ||||
\(13\) | − | 2.26795i | − | 0.629016i | −0.949255 | − | 0.314508i | \(-0.898160\pi\) | ||
0.949255 | − | 0.314508i | \(-0.101840\pi\) | |||||||
\(14\) | −7.09808 | − | 1.36603i | −1.89704 | − | 0.365086i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −7.46410 | + | 12.9282i | −1.86603 | + | 3.23205i | ||||
\(17\) | 2.83013 | − | 1.63397i | 0.686407 | − | 0.396297i | −0.115858 | − | 0.993266i | \(-0.536962\pi\) |
0.802264 | + | 0.596969i | \(0.203628\pi\) | |||||||
\(18\) | 2.36603 | − | 1.36603i | 0.557678 | − | 0.321975i | ||||
\(19\) | 2.23205 | − | 3.86603i | 0.512068 | − | 0.886927i | −0.487835 | − | 0.872936i | \(-0.662213\pi\) |
0.999902 | − | 0.0139909i | \(-0.00445360\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.73205 | + | 2.00000i | −0.377964 | + | 0.436436i | ||||
\(22\) | − | 2.00000i | − | 0.426401i | ||||||
\(23\) | −4.09808 | − | 2.36603i | −0.854508 | − | 0.493350i | 0.00766135 | − | 0.999971i | \(-0.497561\pi\) |
−0.862169 | + | 0.506620i | \(0.830895\pi\) | |||||||
\(24\) | 4.73205 | + | 8.19615i | 0.965926 | + | 1.67303i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.09808 | − | 5.36603i | 0.607583 | − | 1.05236i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −10.9282 | − | 9.46410i | −2.06524 | − | 1.78855i | ||||
\(29\) | 4.19615 | 0.779206 | 0.389603 | − | 0.920983i | \(-0.372612\pi\) | ||||
0.389603 | + | 0.920983i | \(0.372612\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.232051 | + | 0.401924i | 0.0416776 | + | 0.0721876i | 0.886112 | − | 0.463472i | \(-0.153396\pi\) |
−0.844434 | + | 0.535659i | \(0.820063\pi\) | |||||||
\(32\) | −18.9282 | + | 10.9282i | −3.34607 | + | 1.93185i | ||||
\(33\) | −0.633975 | − | 0.366025i | −0.110361 | − | 0.0637168i | ||||
\(34\) | 8.92820 | 1.53117 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.46410 | 0.910684 | ||||||||
\(37\) | 2.76795 | + | 1.59808i | 0.455048 | + | 0.262722i | 0.709960 | − | 0.704242i | \(-0.248713\pi\) |
−0.254912 | + | 0.966964i | \(0.582046\pi\) | |||||||
\(38\) | 10.5622 | − | 6.09808i | 1.71341 | − | 0.989239i | ||||
\(39\) | −1.13397 | − | 1.96410i | −0.181581 | − | 0.314508i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.732051 | −0.114327 | −0.0571636 | − | 0.998365i | \(-0.518206\pi\) | ||||
−0.0571636 | + | 0.998365i | \(0.518206\pi\) | |||||||
\(42\) | −6.83013 | + | 2.36603i | −1.05391 | + | 0.365086i | ||||
\(43\) | − | 3.19615i | − | 0.487409i | −0.969850 | − | 0.243704i | \(-0.921637\pi\) | ||
0.969850 | − | 0.243704i | \(-0.0783627\pi\) | |||||||
\(44\) | 2.00000 | − | 3.46410i | 0.301511 | − | 0.522233i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.46410 | − | 11.1962i | −0.953080 | − | 1.65078i | ||||
\(47\) | −1.73205 | − | 1.00000i | −0.252646 | − | 0.145865i | 0.368329 | − | 0.929695i | \(-0.379930\pi\) |
−0.620975 | + | 0.783830i | \(0.713263\pi\) | |||||||
\(48\) | 14.9282i | 2.15470i | ||||||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.63397 | − | 2.83013i | 0.228802 | − | 0.396297i | ||||
\(52\) | 10.7321 | − | 6.19615i | 1.48827 | − | 0.859252i | ||||
\(53\) | −10.7321 | + | 6.19615i | −1.47416 | + | 0.851107i | −0.999576 | − | 0.0291032i | \(-0.990735\pi\) |
−0.474584 | + | 0.880210i | \(0.657402\pi\) | |||||||
\(54\) | 1.36603 | − | 2.36603i | 0.185893 | − | 0.321975i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −8.19615 | − | 23.6603i | −1.09526 | − | 3.16173i | ||||
\(57\) | − | 4.46410i | − | 0.591285i | ||||||
\(58\) | 9.92820 | + | 5.73205i | 1.30364 | + | 0.752655i | ||||
\(59\) | −0.0980762 | − | 0.169873i | −0.0127684 | − | 0.0221156i | 0.859571 | − | 0.511017i | \(-0.170731\pi\) |
−0.872339 | + | 0.488901i | \(0.837398\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | + | 3.46410i | −0.256074 | + | 0.443533i | −0.965187 | − | 0.261562i | \(-0.915762\pi\) |
0.709113 | + | 0.705095i | \(0.249096\pi\) | |||||||
\(62\) | 1.26795i | 0.161030i | ||||||||
\(63\) | −0.500000 | + | 2.59808i | −0.0629941 | + | 0.327327i | ||||
\(64\) | −29.8564 | −3.73205 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.00000 | − | 1.73205i | −0.123091 | − | 0.213201i | ||||
\(67\) | −12.6962 | + | 7.33013i | −1.55108 | + | 0.895518i | −0.553028 | + | 0.833163i | \(0.686528\pi\) |
−0.998054 | + | 0.0623548i | \(0.980139\pi\) | |||||||
\(68\) | 15.4641 | + | 8.92820i | 1.87530 | + | 1.08270i | ||||
\(69\) | −4.73205 | −0.569672 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.19615 | 0.735348 | 0.367674 | − | 0.929955i | \(-0.380154\pi\) | ||||
0.367674 | + | 0.929955i | \(0.380154\pi\) | |||||||
\(72\) | 8.19615 | + | 4.73205i | 0.965926 | + | 0.557678i | ||||
\(73\) | −10.9641 | + | 6.33013i | −1.28325 | + | 0.740885i | −0.977441 | − | 0.211207i | \(-0.932260\pi\) |
−0.305810 | + | 0.952093i | \(0.598927\pi\) | |||||||
\(74\) | 4.36603 | + | 7.56218i | 0.507540 | + | 0.879085i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 24.3923 | 2.79799 | ||||||||
\(77\) | 1.46410 | + | 1.26795i | 0.166850 | + | 0.144496i | ||||
\(78\) | − | 6.19615i | − | 0.701576i | ||||||
\(79\) | −3.69615 | + | 6.40192i | −0.415850 | + | 0.720273i | −0.995517 | − | 0.0945803i | \(-0.969849\pi\) |
0.579668 | + | 0.814853i | \(0.303182\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −1.73205 | − | 1.00000i | −0.191273 | − | 0.110432i | ||||
\(83\) | − | 15.1244i | − | 1.66011i | −0.557679 | − | 0.830057i | \(-0.688308\pi\) | ||
0.557679 | − | 0.830057i | \(-0.311692\pi\) | |||||||
\(84\) | −14.1962 | − | 2.73205i | −1.54893 | − | 0.298091i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.36603 | − | 7.56218i | 0.470801 | − | 0.815451i | ||||
\(87\) | 3.63397 | − | 2.09808i | 0.389603 | − | 0.224937i | ||||
\(88\) | 6.00000 | − | 3.46410i | 0.639602 | − | 0.369274i | ||||
\(89\) | 7.56218 | − | 13.0981i | 0.801589 | − | 1.38839i | −0.116980 | − | 0.993134i | \(-0.537321\pi\) |
0.918570 | − | 0.395259i | \(-0.129345\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.96410 | + | 5.66987i | 0.205894 | + | 0.594364i | ||||
\(92\) | − | 25.8564i | − | 2.69572i | ||||||
\(93\) | 0.401924 | + | 0.232051i | 0.0416776 | + | 0.0240625i | ||||
\(94\) | −2.73205 | − | 4.73205i | −0.281790 | − | 0.488074i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −10.9282 | + | 18.9282i | −1.11536 | + | 1.93185i | ||||
\(97\) | 14.9282i | 1.51573i | 0.652412 | + | 0.757865i | \(0.273757\pi\) | ||||
−0.652412 | + | 0.757865i | \(0.726243\pi\) | |||||||
\(98\) | 18.9282 | − | 2.73205i | 1.91204 | − | 0.275979i | ||||
\(99\) | −0.732051 | −0.0735739 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.63397 | + | 6.29423i | 0.361594 | + | 0.626299i | 0.988223 | − | 0.153018i | \(-0.0488993\pi\) |
−0.626629 | + | 0.779317i | \(0.715566\pi\) | |||||||
\(102\) | 7.73205 | − | 4.46410i | 0.765587 | − | 0.442012i | ||||
\(103\) | −7.96410 | − | 4.59808i | −0.784726 | − | 0.453062i | 0.0533764 | − | 0.998574i | \(-0.483002\pi\) |
−0.838103 | + | 0.545513i | \(0.816335\pi\) | |||||||
\(104\) | 21.4641 | 2.10473 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −33.8564 | −3.28842 | ||||||||
\(107\) | −1.90192 | − | 1.09808i | −0.183866 | − | 0.106155i | 0.405242 | − | 0.914210i | \(-0.367187\pi\) |
−0.589108 | + | 0.808054i | \(0.700521\pi\) | |||||||
\(108\) | 4.73205 | − | 2.73205i | 0.455342 | − | 0.262892i | ||||
\(109\) | 5.50000 | + | 9.52628i | 0.526804 | + | 0.912452i | 0.999512 | + | 0.0312328i | \(0.00994332\pi\) |
−0.472708 | + | 0.881219i | \(0.656723\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.19615 | 0.303365 | ||||||||
\(112\) | 7.46410 | − | 38.7846i | 0.705291 | − | 3.66480i | ||||
\(113\) | − | 8.92820i | − | 0.839895i | −0.907548 | − | 0.419947i | \(-0.862049\pi\) | ||
0.907548 | − | 0.419947i | \(-0.137951\pi\) | |||||||
\(114\) | 6.09808 | − | 10.5622i | 0.571137 | − | 0.989239i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 11.4641 | + | 19.8564i | 1.06442 | + | 1.84362i | ||||
\(117\) | −1.96410 | − | 1.13397i | −0.181581 | − | 0.104836i | ||||
\(118\) | − | 0.535898i | − | 0.0493334i | ||||||
\(119\) | −5.66025 | + | 6.53590i | −0.518875 | + | 0.599145i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.23205 | − | 9.06218i | 0.475641 | − | 0.823834i | ||||
\(122\) | −9.46410 | + | 5.46410i | −0.856840 | + | 0.494697i | ||||
\(123\) | −0.633975 | + | 0.366025i | −0.0571636 | + | 0.0330034i | ||||
\(124\) | −1.26795 | + | 2.19615i | −0.113865 | + | 0.197220i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.73205 | + | 5.46410i | −0.421565 | + | 0.486781i | ||||
\(127\) | 4.80385i | 0.426273i | 0.977022 | + | 0.213136i | \(0.0683678\pi\) | ||||
−0.977022 | + | 0.213136i | \(0.931632\pi\) | |||||||
\(128\) | −32.7846 | − | 18.9282i | −2.89778 | − | 1.67303i | ||||
\(129\) | −1.59808 | − | 2.76795i | −0.140703 | − | 0.243704i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.73205 | + | 13.3923i | −0.675552 | + | 1.17009i | 0.300755 | + | 0.953702i | \(0.402761\pi\) |
−0.976307 | + | 0.216390i | \(0.930572\pi\) | |||||||
\(132\) | − | 4.00000i | − | 0.348155i | ||||||
\(133\) | −2.23205 | + | 11.5981i | −0.193543 | + | 1.00568i | ||||
\(134\) | −40.0526 | −3.46001 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 15.4641 | + | 26.7846i | 1.32604 | + | 2.29676i | ||||
\(137\) | 1.90192 | − | 1.09808i | 0.162492 | − | 0.0938150i | −0.416549 | − | 0.909113i | \(-0.636760\pi\) |
0.579041 | + | 0.815298i | \(0.303427\pi\) | |||||||
\(138\) | −11.1962 | − | 6.46410i | −0.953080 | − | 0.550261i | ||||
\(139\) | −5.92820 | −0.502824 | −0.251412 | − | 0.967880i | \(-0.580895\pi\) | ||||
−0.251412 | + | 0.967880i | \(0.580895\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.00000 | −0.168430 | ||||||||
\(142\) | 14.6603 | + | 8.46410i | 1.23026 | + | 0.710292i | ||||
\(143\) | −1.43782 | + | 0.830127i | −0.120237 | + | 0.0694187i | ||||
\(144\) | 7.46410 | + | 12.9282i | 0.622008 | + | 1.07735i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −34.5885 | −2.86256 | ||||||||
\(147\) | 2.59808 | − | 6.50000i | 0.214286 | − | 0.536111i | ||||
\(148\) | 17.4641i | 1.43554i | ||||||||
\(149\) | 2.92820 | − | 5.07180i | 0.239888 | − | 0.415498i | −0.720794 | − | 0.693149i | \(-0.756223\pi\) |
0.960682 | + | 0.277651i | \(0.0895560\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.46410 | + | 7.73205i | 0.363283 | + | 0.629225i | 0.988499 | − | 0.151227i | \(-0.0483223\pi\) |
−0.625216 | + | 0.780452i | \(0.714989\pi\) | |||||||
\(152\) | 36.5885 | + | 21.1244i | 2.96772 | + | 1.71341i | ||||
\(153\) | − | 3.26795i | − | 0.264198i | ||||||
\(154\) | 1.73205 | + | 5.00000i | 0.139573 | + | 0.402911i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.19615 | − | 10.7321i | 0.496089 | − | 0.859252i | ||||
\(157\) | 5.53590 | − | 3.19615i | 0.441813 | − | 0.255081i | −0.262553 | − | 0.964917i | \(-0.584565\pi\) |
0.704366 | + | 0.709837i | \(0.251231\pi\) | |||||||
\(158\) | −17.4904 | + | 10.0981i | −1.39146 | + | 0.803360i | ||||
\(159\) | −6.19615 | + | 10.7321i | −0.491387 | + | 0.851107i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.2942 | + | 2.36603i | 0.968921 | + | 0.186469i | ||||
\(162\) | − | 2.73205i | − | 0.214650i | ||||||
\(163\) | 18.9282 | + | 10.9282i | 1.48257 | + | 0.855963i | 0.999804 | − | 0.0197859i | \(-0.00629845\pi\) |
0.482767 | + | 0.875749i | \(0.339632\pi\) | |||||||
\(164\) | −2.00000 | − | 3.46410i | −0.156174 | − | 0.270501i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 20.6603 | − | 35.7846i | 1.60355 | − | 2.77742i | ||||
\(167\) | − | 17.6603i | − | 1.36659i | −0.730142 | − | 0.683296i | \(-0.760546\pi\) | ||
0.730142 | − | 0.683296i | \(-0.239454\pi\) | |||||||
\(168\) | −18.9282 | − | 16.3923i | −1.46034 | − | 1.26469i | ||||
\(169\) | 7.85641 | 0.604339 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.23205 | − | 3.86603i | −0.170689 | − | 0.295642i | ||||
\(172\) | 15.1244 | − | 8.73205i | 1.15322 | − | 0.665813i | ||||
\(173\) | 12.5885 | + | 7.26795i | 0.957083 | + | 0.552572i | 0.895274 | − | 0.445516i | \(-0.146980\pi\) |
0.0618087 | + | 0.998088i | \(0.480313\pi\) | |||||||
\(174\) | 11.4641 | 0.869091 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 10.9282 | 0.823744 | ||||||||
\(177\) | −0.169873 | − | 0.0980762i | −0.0127684 | − | 0.00737186i | ||||
\(178\) | 35.7846 | − | 20.6603i | 2.68217 | − | 1.54855i | ||||
\(179\) | −5.00000 | − | 8.66025i | −0.373718 | − | 0.647298i | 0.616417 | − | 0.787420i | \(-0.288584\pi\) |
−0.990134 | + | 0.140122i | \(0.955250\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.3205 | −1.80773 | −0.903865 | − | 0.427819i | \(-0.859282\pi\) | ||||
−0.903865 | + | 0.427819i | \(0.859282\pi\) | |||||||
\(182\) | −3.09808 | + | 16.0981i | −0.229645 | + | 1.19327i | ||||
\(183\) | 4.00000i | 0.295689i | ||||||||
\(184\) | 22.3923 | − | 38.7846i | 1.65078 | − | 2.85924i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.633975 | + | 1.09808i | 0.0464853 | + | 0.0805149i | ||||
\(187\) | −2.07180 | − | 1.19615i | −0.151505 | − | 0.0874713i | ||||
\(188\) | − | 10.9282i | − | 0.797021i | ||||||
\(189\) | 0.866025 | + | 2.50000i | 0.0629941 | + | 0.181848i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.46410 | − | 7.73205i | 0.323011 | − | 0.559472i | −0.658097 | − | 0.752933i | \(-0.728638\pi\) |
0.981108 | + | 0.193462i | \(0.0619716\pi\) | |||||||
\(192\) | −25.8564 | + | 14.9282i | −1.86603 | + | 1.07735i | ||||
\(193\) | −1.03590 | + | 0.598076i | −0.0745656 | + | 0.0430505i | −0.536819 | − | 0.843697i | \(-0.680374\pi\) |
0.462254 | + | 0.886748i | \(0.347041\pi\) | |||||||
\(194\) | −20.3923 | + | 35.3205i | −1.46408 | + | 2.53586i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 35.5167 | + | 14.1962i | 2.53690 | + | 1.01401i | ||||
\(197\) | − | 0.339746i | − | 0.0242059i | −0.999927 | − | 0.0121029i | \(-0.996147\pi\) | ||
0.999927 | − | 0.0121029i | \(-0.00385258\pi\) | |||||||
\(198\) | −1.73205 | − | 1.00000i | −0.123091 | − | 0.0710669i | ||||
\(199\) | 11.0000 | + | 19.0526i | 0.779769 | + | 1.35060i | 0.932075 | + | 0.362267i | \(0.117997\pi\) |
−0.152305 | + | 0.988334i | \(0.548670\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.33013 | + | 12.6962i | −0.517027 | + | 0.895518i | ||||
\(202\) | 19.8564i | 1.39709i | ||||||||
\(203\) | −10.4904 | + | 3.63397i | −0.736280 | + | 0.255055i | ||||
\(204\) | 17.8564 | 1.25020 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −12.5622 | − | 21.7583i | −0.875248 | − | 1.51597i | ||||
\(207\) | −4.09808 | + | 2.36603i | −0.284836 | + | 0.164450i | ||||
\(208\) | 29.3205 | + | 16.9282i | 2.03301 | + | 1.17376i | ||||
\(209\) | −3.26795 | −0.226049 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.07180 | 0.486843 | 0.243421 | − | 0.969921i | \(-0.421730\pi\) | ||||
0.243421 | + | 0.969921i | \(0.421730\pi\) | |||||||
\(212\) | −58.6410 | − | 33.8564i | −4.02748 | − | 2.32527i | ||||
\(213\) | 5.36603 | − | 3.09808i | 0.367674 | − | 0.212277i | ||||
\(214\) | −3.00000 | − | 5.19615i | −0.205076 | − | 0.355202i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 9.46410 | 0.643951 | ||||||||
\(217\) | −0.928203 | − | 0.803848i | −0.0630105 | − | 0.0545687i | ||||
\(218\) | 30.0526i | 2.03542i | ||||||||
\(219\) | −6.33013 | + | 10.9641i | −0.427750 | + | 0.740885i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.70577 | − | 6.41858i | −0.249277 | − | 0.431761i | ||||
\(222\) | 7.56218 | + | 4.36603i | 0.507540 | + | 0.293028i | ||||
\(223\) | 20.3923i | 1.36557i | 0.730619 | + | 0.682785i | \(0.239231\pi\) | ||||
−0.730619 | + | 0.682785i | \(0.760769\pi\) | |||||||
\(224\) | 37.8564 | − | 43.7128i | 2.52939 | − | 2.92069i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.1962 | − | 21.1244i | 0.811276 | − | 1.40517i | ||||
\(227\) | −1.43782 | + | 0.830127i | −0.0954316 | + | 0.0550975i | −0.546956 | − | 0.837161i | \(-0.684214\pi\) |
0.451525 | + | 0.892259i | \(0.350880\pi\) | |||||||
\(228\) | 21.1244 | − | 12.1962i | 1.39899 | − | 0.807710i | ||||
\(229\) | −1.50000 | + | 2.59808i | −0.0991228 | + | 0.171686i | −0.911322 | − | 0.411695i | \(-0.864937\pi\) |
0.812199 | + | 0.583380i | \(0.198270\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.90192 | + | 0.366025i | 0.125137 | + | 0.0240827i | ||||
\(232\) | 39.7128i | 2.60727i | ||||||||
\(233\) | 15.0000 | + | 8.66025i | 0.982683 | + | 0.567352i | 0.903079 | − | 0.429474i | \(-0.141301\pi\) |
0.0796037 | + | 0.996827i | \(0.474635\pi\) | |||||||
\(234\) | −3.09808 | − | 5.36603i | −0.202528 | − | 0.350788i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.535898 | − | 0.928203i | 0.0348840 | − | 0.0604209i | ||||
\(237\) | 7.39230i | 0.480182i | ||||||||
\(238\) | −22.3205 | + | 7.73205i | −1.44682 | + | 0.501194i | ||||
\(239\) | −7.07180 | −0.457437 | −0.228718 | − | 0.973493i | \(-0.573453\pi\) | ||||
−0.228718 | + | 0.973493i | \(0.573453\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.73205 | − | 11.6603i | −0.433650 | − | 0.751103i | 0.563535 | − | 0.826092i | \(-0.309441\pi\) |
−0.997184 | + | 0.0749893i | \(0.976108\pi\) | |||||||
\(242\) | 24.7583 | − | 14.2942i | 1.59153 | − | 0.918868i | ||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | −21.8564 | −1.39921 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.00000 | −0.127515 | ||||||||
\(247\) | −8.76795 | − | 5.06218i | −0.557891 | − | 0.322099i | ||||
\(248\) | −3.80385 | + | 2.19615i | −0.241545 | + | 0.139456i | ||||
\(249\) | −7.56218 | − | 13.0981i | −0.479234 | − | 0.830057i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.5885 | −1.55201 | −0.776005 | − | 0.630727i | \(-0.782757\pi\) | ||||
−0.776005 | + | 0.630727i | \(0.782757\pi\) | |||||||
\(252\) | −13.6603 | + | 4.73205i | −0.860515 | + | 0.298091i | ||||
\(253\) | 3.46410i | 0.217786i | ||||||||
\(254\) | −6.56218 | + | 11.3660i | −0.411748 | + | 0.713168i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −21.8564 | − | 37.8564i | −1.36603 | − | 2.36603i | ||||
\(257\) | 4.90192 | + | 2.83013i | 0.305774 | + | 0.176538i | 0.645034 | − | 0.764154i | \(-0.276843\pi\) |
−0.339260 | + | 0.940693i | \(0.610177\pi\) | |||||||
\(258\) | − | 8.73205i | − | 0.543634i | ||||||
\(259\) | −8.30385 | − | 1.59808i | −0.515976 | − | 0.0992996i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.09808 | − | 3.63397i | 0.129868 | − | 0.224937i | ||||
\(262\) | −36.5885 | + | 21.1244i | −2.26044 | + | 1.30507i | ||||
\(263\) | −7.26795 | + | 4.19615i | −0.448161 | + | 0.258746i | −0.707053 | − | 0.707160i | \(-0.749976\pi\) |
0.258892 | + | 0.965906i | \(0.416643\pi\) | |||||||
\(264\) | 3.46410 | − | 6.00000i | 0.213201 | − | 0.369274i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −21.1244 | + | 24.3923i | −1.29522 | + | 1.49559i | ||||
\(267\) | − | 15.1244i | − | 0.925596i | ||||||
\(268\) | −69.3731 | − | 40.0526i | −4.23763 | − | 2.44660i | ||||
\(269\) | −6.26795 | − | 10.8564i | −0.382164 | − | 0.661927i | 0.609208 | − | 0.793011i | \(-0.291488\pi\) |
−0.991371 | + | 0.131084i | \(0.958154\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.53590 | + | 2.66025i | −0.0932992 | + | 0.161599i | −0.908897 | − | 0.417020i | \(-0.863075\pi\) |
0.815598 | + | 0.578619i | \(0.196408\pi\) | |||||||
\(272\) | 48.7846i | 2.95800i | ||||||||
\(273\) | 4.53590 | + | 3.92820i | 0.274525 | + | 0.237746i | ||||
\(274\) | 6.00000 | 0.362473 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −12.9282 | − | 22.3923i | −0.778186 | − | 1.34786i | ||||
\(277\) | −12.6962 | + | 7.33013i | −0.762838 | + | 0.440425i | −0.830314 | − | 0.557296i | \(-0.811839\pi\) |
0.0674759 | + | 0.997721i | \(0.478505\pi\) | |||||||
\(278\) | −14.0263 | − | 8.09808i | −0.841240 | − | 0.485690i | ||||
\(279\) | 0.464102 | 0.0277850 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.8564 | 0.826604 | 0.413302 | − | 0.910594i | \(-0.364375\pi\) | ||||
0.413302 | + | 0.910594i | \(0.364375\pi\) | |||||||
\(282\) | −4.73205 | − | 2.73205i | −0.281790 | − | 0.162691i | ||||
\(283\) | 20.8923 | − | 12.0622i | 1.24192 | − | 0.717022i | 0.272434 | − | 0.962174i | \(-0.412171\pi\) |
0.969485 | + | 0.245152i | \(0.0788380\pi\) | |||||||
\(284\) | 16.9282 | + | 29.3205i | 1.00450 | + | 1.73985i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.53590 | −0.268213 | ||||||||
\(287\) | 1.83013 | − | 0.633975i | 0.108029 | − | 0.0374223i | ||||
\(288\) | 21.8564i | 1.28790i | ||||||||
\(289\) | −3.16025 | + | 5.47372i | −0.185897 | + | 0.321984i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.46410 | + | 12.9282i | 0.437553 | + | 0.757865i | ||||
\(292\) | −59.9090 | − | 34.5885i | −3.50591 | − | 2.02414i | ||||
\(293\) | − | 18.9282i | − | 1.10580i | −0.833248 | − | 0.552899i | \(-0.813522\pi\) | ||
0.833248 | − | 0.552899i | \(-0.186478\pi\) | |||||||
\(294\) | 15.0263 | − | 11.8301i | 0.876350 | − | 0.689947i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −15.1244 | + | 26.1962i | −0.879085 | + | 1.52262i | ||||
\(297\) | −0.633975 | + | 0.366025i | −0.0367869 | + | 0.0212389i | ||||
\(298\) | 13.8564 | − | 8.00000i | 0.802680 | − | 0.463428i | ||||
\(299\) | −5.36603 | + | 9.29423i | −0.310325 | + | 0.537499i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.76795 | + | 7.99038i | 0.159542 | + | 0.460558i | ||||
\(302\) | 24.3923i | 1.40362i | ||||||||
\(303\) | 6.29423 | + | 3.63397i | 0.361594 | + | 0.208766i | ||||
\(304\) | 33.3205 | + | 57.7128i | 1.91106 | + | 3.31006i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4.46410 | − | 7.73205i | 0.255196 | − | 0.442012i | ||||
\(307\) | − | 32.1244i | − | 1.83343i | −0.399537 | − | 0.916717i | \(-0.630829\pi\) | ||
0.399537 | − | 0.916717i | \(-0.369171\pi\) | |||||||
\(308\) | −2.00000 | + | 10.3923i | −0.113961 | + | 0.592157i | ||||
\(309\) | −9.19615 | −0.523151 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.56218 | − | 7.90192i | −0.258697 | − | 0.448077i | 0.707196 | − | 0.707018i | \(-0.249960\pi\) |
−0.965893 | + | 0.258941i | \(0.916627\pi\) | |||||||
\(312\) | 18.5885 | − | 10.7321i | 1.05236 | − | 0.607583i | ||||
\(313\) | −10.9641 | − | 6.33013i | −0.619728 | − | 0.357800i | 0.157035 | − | 0.987593i | \(-0.449806\pi\) |
−0.776763 | + | 0.629793i | \(0.783140\pi\) | |||||||
\(314\) | 17.4641 | 0.985556 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −40.3923 | −2.27224 | ||||||||
\(317\) | 24.6340 | + | 14.2224i | 1.38358 | + | 0.798811i | 0.992582 | − | 0.121579i | \(-0.0387959\pi\) |
0.391000 | + | 0.920391i | \(0.372129\pi\) | |||||||
\(318\) | −29.3205 | + | 16.9282i | −1.64421 | + | 0.949286i | ||||
\(319\) | −1.53590 | − | 2.66025i | −0.0859938 | − | 0.148946i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.19615 | −0.122577 | ||||||||
\(322\) | 25.8564 | + | 22.3923i | 1.44092 | + | 1.24787i | ||||
\(323\) | − | 14.5885i | − | 0.811723i | ||||||
\(324\) | 2.73205 | − | 4.73205i | 0.151781 | − | 0.262892i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 29.8564 | + | 51.7128i | 1.65359 | + | 2.86411i | ||||
\(327\) | 9.52628 | + | 5.50000i | 0.526804 | + | 0.304151i | ||||
\(328\) | − | 6.92820i | − | 0.382546i | ||||||
\(329\) | 5.19615 | + | 1.00000i | 0.286473 | + | 0.0551318i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.03590 | + | 6.99038i | −0.221833 | + | 0.384226i | −0.955365 | − | 0.295429i | \(-0.904537\pi\) |
0.733532 | + | 0.679655i | \(0.237871\pi\) | |||||||
\(332\) | 71.5692 | − | 41.3205i | 3.92787 | − | 2.26776i | ||||
\(333\) | 2.76795 | − | 1.59808i | 0.151683 | − | 0.0875740i | ||||
\(334\) | 24.1244 | − | 41.7846i | 1.32003 | − | 2.28635i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −12.9282 | − | 37.3205i | −0.705291 | − | 2.03600i | ||||
\(337\) | 17.9808i | 0.979475i | 0.871870 | + | 0.489737i | \(0.162907\pi\) | ||||
−0.871870 | + | 0.489737i | \(0.837093\pi\) | |||||||
\(338\) | 18.5885 | + | 10.7321i | 1.01108 | + | 0.583747i | ||||
\(339\) | −4.46410 | − | 7.73205i | −0.242457 | − | 0.419947i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.169873 | − | 0.294229i | 0.00919914 | − | 0.0159334i | ||||
\(342\) | − | 12.1962i | − | 0.659492i | ||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 30.2487 | 1.63090 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 19.8564 | + | 34.3923i | 1.06749 | + | 1.84894i | ||||
\(347\) | −18.2487 | + | 10.5359i | −0.979642 | + | 0.565597i | −0.902162 | − | 0.431397i | \(-0.858021\pi\) |
−0.0774801 | + | 0.996994i | \(0.524687\pi\) | |||||||
\(348\) | 19.8564 | + | 11.4641i | 1.06442 | + | 0.614540i | ||||
\(349\) | −22.0000 | −1.17763 | −0.588817 | − | 0.808267i | \(-0.700406\pi\) | ||||
−0.588817 | + | 0.808267i | \(0.700406\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.26795 | −0.121054 | ||||||||
\(352\) | 13.8564 | + | 8.00000i | 0.738549 | + | 0.426401i | ||||
\(353\) | 2.70577 | − | 1.56218i | 0.144014 | − | 0.0831463i | −0.426262 | − | 0.904600i | \(-0.640170\pi\) |
0.570276 | + | 0.821453i | \(0.306836\pi\) | |||||||
\(354\) | −0.267949 | − | 0.464102i | −0.0142413 | − | 0.0246667i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 82.6410 | 4.37997 | ||||||||
\(357\) | −1.63397 | + | 8.49038i | −0.0864791 | + | 0.449359i | ||||
\(358\) | − | 27.3205i | − | 1.44393i | ||||||
\(359\) | −0.633975 | + | 1.09808i | −0.0334599 | + | 0.0579542i | −0.882270 | − | 0.470743i | \(-0.843986\pi\) |
0.848811 | + | 0.528697i | \(0.177319\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.464102 | − | 0.803848i | −0.0244264 | − | 0.0423078i | ||||
\(362\) | −57.5429 | − | 33.2224i | −3.02439 | − | 1.74613i | ||||
\(363\) | − | 10.4641i | − | 0.549223i | ||||||
\(364\) | −21.4641 | + | 24.7846i | −1.12502 | + | 1.29907i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5.46410 | + | 9.46410i | −0.285613 | + | 0.494697i | ||||
\(367\) | 9.69615 | − | 5.59808i | 0.506135 | − | 0.292217i | −0.225108 | − | 0.974334i | \(-0.572274\pi\) |
0.731244 | + | 0.682117i | \(0.238940\pi\) | |||||||
\(368\) | 61.1769 | − | 35.3205i | 3.18907 | − | 1.84121i | ||||
\(369\) | −0.366025 | + | 0.633975i | −0.0190545 | + | 0.0330034i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21.4641 | − | 24.7846i | 1.11436 | − | 1.28675i | ||||
\(372\) | 2.53590i | 0.131480i | ||||||||
\(373\) | 22.9641 | + | 13.2583i | 1.18904 | + | 0.686490i | 0.958088 | − | 0.286476i | \(-0.0924837\pi\) |
0.230949 | + | 0.972966i | \(0.425817\pi\) | |||||||
\(374\) | −3.26795 | − | 5.66025i | −0.168982 | − | 0.292685i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.46410 | − | 16.3923i | 0.488074 | − | 0.845369i | ||||
\(377\) | − | 9.51666i | − | 0.490133i | ||||||
\(378\) | −1.36603 | + | 7.09808i | −0.0702608 | + | 0.365086i | ||||
\(379\) | −6.32051 | −0.324663 | −0.162331 | − | 0.986736i | \(-0.551901\pi\) | ||||
−0.162331 | + | 0.986736i | \(0.551901\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.40192 | + | 4.16025i | 0.123054 | + | 0.213136i | ||||
\(382\) | 21.1244 | − | 12.1962i | 1.08082 | − | 0.624009i | ||||
\(383\) | −20.1962 | − | 11.6603i | −1.03198 | − | 0.595811i | −0.114425 | − | 0.993432i | \(-0.536503\pi\) |
−0.917550 | + | 0.397621i | \(0.869836\pi\) | |||||||
\(384\) | −37.8564 | −1.93185 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.26795 | −0.166334 | ||||||||
\(387\) | −2.76795 | − | 1.59808i | −0.140703 | − | 0.0812348i | ||||
\(388\) | −70.6410 | + | 40.7846i | −3.58625 | + | 2.07052i | ||||
\(389\) | 2.70577 | + | 4.68653i | 0.137188 | + | 0.237617i | 0.926431 | − | 0.376464i | \(-0.122860\pi\) |
−0.789243 | + | 0.614081i | \(0.789527\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15.4641 | −0.782053 | ||||||||
\(392\) | 40.9808 | + | 52.0526i | 2.06984 | + | 2.62905i | ||||
\(393\) | 15.4641i | 0.780061i | ||||||||
\(394\) | 0.464102 | − | 0.803848i | 0.0233811 | − | 0.0404973i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.00000 | − | 3.46410i | −0.100504 | − | 0.174078i | ||||
\(397\) | 27.0167 | + | 15.5981i | 1.35593 | + | 0.782845i | 0.989072 | − | 0.147433i | \(-0.0471011\pi\) |
0.366855 | + | 0.930278i | \(0.380434\pi\) | |||||||
\(398\) | 60.1051i | 3.01280i | ||||||||
\(399\) | 3.86603 | + | 11.1603i | 0.193543 | + | 0.558712i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.19615 | − | 14.1962i | 0.409296 | − | 0.708922i | −0.585515 | − | 0.810662i | \(-0.699108\pi\) |
0.994811 | + | 0.101740i | \(0.0324409\pi\) | |||||||
\(402\) | −34.6865 | + | 20.0263i | −1.73001 | + | 0.998820i | ||||
\(403\) | 0.911543 | − | 0.526279i | 0.0454072 | − | 0.0262158i | ||||
\(404\) | −19.8564 | + | 34.3923i | −0.987893 | + | 1.71108i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −29.7846 | − | 5.73205i | −1.47819 | − | 0.284477i | ||||
\(407\) | − | 2.33975i | − | 0.115977i | ||||||
\(408\) | 26.7846 | + | 15.4641i | 1.32604 | + | 0.765587i | ||||
\(409\) | 1.57180 | + | 2.72243i | 0.0777203 | + | 0.134616i | 0.902266 | − | 0.431180i | \(-0.141903\pi\) |
−0.824546 | + | 0.565795i | \(0.808569\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.09808 | − | 1.90192i | 0.0541641 | − | 0.0938150i | ||||
\(412\) | − | 50.2487i | − | 2.47558i | ||||||
\(413\) | 0.392305 | + | 0.339746i | 0.0193041 | + | 0.0167178i | ||||
\(414\) | −12.9282 | −0.635387 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 24.7846 | + | 42.9282i | 1.21517 | + | 2.10473i | ||||
\(417\) | −5.13397 | + | 2.96410i | −0.251412 | + | 0.145153i | ||||
\(418\) | −7.73205 | − | 4.46410i | −0.378187 | − | 0.218346i | ||||
\(419\) | 35.4641 | 1.73253 | 0.866267 | − | 0.499581i | \(-0.166513\pi\) | ||||
0.866267 | + | 0.499581i | \(0.166513\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.0717968 | 0.00349916 | 0.00174958 | − | 0.999998i | \(-0.499443\pi\) | ||||
0.00174958 | + | 0.999998i | \(0.499443\pi\) | |||||||
\(422\) | 16.7321 | + | 9.66025i | 0.814503 | + | 0.470254i | ||||
\(423\) | −1.73205 | + | 1.00000i | −0.0842152 | + | 0.0486217i | ||||
\(424\) | −58.6410 | − | 101.569i | −2.84786 | − | 4.93264i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 16.9282 | 0.820174 | ||||||||
\(427\) | 2.00000 | − | 10.3923i | 0.0967868 | − | 0.502919i | ||||
\(428\) | − | 12.0000i | − | 0.580042i | ||||||
\(429\) | −0.830127 | + | 1.43782i | −0.0400789 | + | 0.0694187i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.66025 | − | 15.0000i | −0.417150 | − | 0.722525i | 0.578502 | − | 0.815681i | \(-0.303638\pi\) |
−0.995651 | + | 0.0931566i | \(0.970304\pi\) | |||||||
\(432\) | 12.9282 | + | 7.46410i | 0.622008 | + | 0.359117i | ||||
\(433\) | − | 15.1962i | − | 0.730280i | −0.930953 | − | 0.365140i | \(-0.881021\pi\) | ||
0.930953 | − | 0.365140i | \(-0.118979\pi\) | |||||||
\(434\) | −1.09808 | − | 3.16987i | −0.0527093 | − | 0.152159i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −30.0526 | + | 52.0526i | −1.43926 | + | 2.49287i | ||||
\(437\) | −18.2942 | + | 10.5622i | −0.875132 | + | 0.505257i | ||||
\(438\) | −29.9545 | + | 17.2942i | −1.43128 | + | 0.826350i | ||||
\(439\) | 0.267949 | − | 0.464102i | 0.0127885 | − | 0.0221504i | −0.859560 | − | 0.511034i | \(-0.829263\pi\) |
0.872349 | + | 0.488884i | \(0.162596\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00000 | − | 6.92820i | −0.0476190 | − | 0.329914i | ||||
\(442\) | − | 20.2487i | − | 0.963133i | ||||||
\(443\) | 8.19615 | + | 4.73205i | 0.389411 | + | 0.224827i | 0.681905 | − | 0.731441i | \(-0.261152\pi\) |
−0.292494 | + | 0.956267i | \(0.594485\pi\) | |||||||
\(444\) | 8.73205 | + | 15.1244i | 0.414405 | + | 0.717770i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −27.8564 | + | 48.2487i | −1.31904 | + | 2.28464i | ||||
\(447\) | − | 5.85641i | − | 0.276999i | ||||||
\(448\) | 74.6410 | − | 25.8564i | 3.52646 | − | 1.22160i | ||||
\(449\) | 35.8564 | 1.69217 | 0.846084 | − | 0.533049i | \(-0.178954\pi\) | ||||
0.846084 | + | 0.533049i | \(0.178954\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.267949 | + | 0.464102i | 0.0126172 | + | 0.0218537i | ||||
\(452\) | 42.2487 | − | 24.3923i | 1.98721 | − | 1.14732i | ||||
\(453\) | 7.73205 | + | 4.46410i | 0.363283 | + | 0.209742i | ||||
\(454\) | −4.53590 | −0.212880 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 42.2487 | 1.97848 | ||||||||
\(457\) | 14.4282 | + | 8.33013i | 0.674923 | + | 0.389667i | 0.797939 | − | 0.602738i | \(-0.205923\pi\) |
−0.123016 | + | 0.992405i | \(0.539257\pi\) | |||||||
\(458\) | −7.09808 | + | 4.09808i | −0.331671 | + | 0.191491i | ||||
\(459\) | −1.63397 | − | 2.83013i | −0.0762674 | − | 0.132099i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.9808 | 0.790873 | 0.395436 | − | 0.918493i | \(-0.370593\pi\) | ||||
0.395436 | + | 0.918493i | \(0.370593\pi\) | |||||||
\(462\) | 4.00000 | + | 3.46410i | 0.186097 | + | 0.161165i | ||||
\(463\) | − | 25.7321i | − | 1.19587i | −0.801545 | − | 0.597935i | \(-0.795988\pi\) | ||
0.801545 | − | 0.597935i | \(-0.204012\pi\) | |||||||
\(464\) | −31.3205 | + | 54.2487i | −1.45402 | + | 2.51843i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 23.6603 | + | 40.9808i | 1.09604 | + | 1.89840i | ||||
\(467\) | 0.124356 | + | 0.0717968i | 0.00575449 | + | 0.00332236i | 0.502874 | − | 0.864359i | \(-0.332276\pi\) |
−0.497120 | + | 0.867682i | \(0.665609\pi\) | |||||||
\(468\) | − | 12.3923i | − | 0.572834i | ||||||
\(469\) | 25.3923 | − | 29.3205i | 1.17251 | − | 1.35390i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.19615 | − | 5.53590i | 0.147271 | − | 0.255081i | ||||
\(472\) | 1.60770 | − | 0.928203i | 0.0740002 | − | 0.0427240i | ||||
\(473\) | −2.02628 | + | 1.16987i | −0.0931684 | + | 0.0537908i | ||||
\(474\) | −10.0981 | + | 17.4904i | −0.463820 | + | 0.803360i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −46.3923 | − | 8.92820i | −2.12639 | − | 0.409224i | ||||
\(477\) | 12.3923i | 0.567405i | ||||||||
\(478\) | −16.7321 | − | 9.66025i | −0.765306 | − | 0.441850i | ||||
\(479\) | 4.39230 | + | 7.60770i | 0.200690 | + | 0.347604i | 0.948751 | − | 0.316025i | \(-0.102348\pi\) |
−0.748061 | + | 0.663630i | \(0.769015\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.62436 | − | 6.27757i | 0.165256 | − | 0.286232i | ||||
\(482\) | − | 36.7846i | − | 1.67549i | ||||||
\(483\) | 11.8301 | − | 4.09808i | 0.538289 | − | 0.186469i | ||||
\(484\) | 57.1769 | 2.59895 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.36603 | − | 2.36603i | −0.0619642 | − | 0.107325i | ||||
\(487\) | −0.356406 | + | 0.205771i | −0.0161503 | + | 0.00932439i | −0.508053 | − | 0.861326i | \(-0.669635\pi\) |
0.491903 | + | 0.870650i | \(0.336301\pi\) | |||||||
\(488\) | −32.7846 | − | 18.9282i | −1.48409 | − | 0.856840i | ||||
\(489\) | 21.8564 | 0.988381 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −38.2487 | −1.72614 | −0.863070 | − | 0.505084i | \(-0.831461\pi\) | ||||
−0.863070 | + | 0.505084i | \(0.831461\pi\) | |||||||
\(492\) | −3.46410 | − | 2.00000i | −0.156174 | − | 0.0901670i | ||||
\(493\) | 11.8756 | − | 6.85641i | 0.534852 | − | 0.308797i | ||||
\(494\) | −13.8301 | − | 23.9545i | −0.622247 | − | 1.07776i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.92820 | −0.311086 | ||||||||
\(497\) | −15.4904 | + | 5.36603i | −0.694839 | + | 0.240699i | ||||
\(498\) | − | 41.3205i | − | 1.85162i | ||||||
\(499\) | −6.76795 | + | 11.7224i | −0.302975 | + | 0.524768i | −0.976808 | − | 0.214115i | \(-0.931313\pi\) |
0.673833 | + | 0.738883i | \(0.264647\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.83013 | − | 15.2942i | −0.394501 | − | 0.683296i | ||||
\(502\) | −58.1769 | − | 33.5885i | −2.59656 | − | 1.49913i | ||||
\(503\) | − | 14.3923i | − | 0.641721i | −0.947126 | − | 0.320861i | \(-0.896028\pi\) | ||
0.947126 | − | 0.320861i | \(-0.103972\pi\) | |||||||
\(504\) | −24.5885 | − | 4.73205i | −1.09526 | − | 0.210782i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.73205 | + | 8.19615i | −0.210365 | + | 0.364363i | ||||
\(507\) | 6.80385 | − | 3.92820i | 0.302169 | − | 0.174458i | ||||
\(508\) | −22.7321 | + | 13.1244i | −1.00857 | + | 0.582299i | ||||
\(509\) | 2.26795 | − | 3.92820i | 0.100525 | − | 0.174115i | −0.811376 | − | 0.584525i | \(-0.801281\pi\) |
0.911901 | + | 0.410410i | \(0.134614\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.9282 | − | 25.3205i | 0.970047 | − | 1.12011i | ||||
\(512\) | − | 43.7128i | − | 1.93185i | ||||||
\(513\) | −3.86603 | − | 2.23205i | −0.170689 | − | 0.0985475i | ||||
\(514\) | 7.73205 | + | 13.3923i | 0.341046 | + | 0.590709i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 8.73205 | − | 15.1244i | 0.384407 | − | 0.665813i | ||||
\(517\) | 1.46410i | 0.0643911i | ||||||||
\(518\) | −17.4641 | − | 15.1244i | −0.767329 | − | 0.664526i | ||||
\(519\) | 14.5359 | 0.638055 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.73205 | + | 4.73205i | 0.119693 | + | 0.207315i | 0.919646 | − | 0.392748i | \(-0.128476\pi\) |
−0.799953 | + | 0.600063i | \(0.795142\pi\) | |||||||
\(522\) | 9.92820 | − | 5.73205i | 0.434546 | − | 0.250885i | ||||
\(523\) | −24.0167 | − | 13.8660i | −1.05018 | − | 0.606319i | −0.127477 | − | 0.991842i | \(-0.540688\pi\) |
−0.922698 | + | 0.385523i | \(0.874021\pi\) | |||||||
\(524\) | −84.4974 | −3.69129 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.9282 | −0.999717 | ||||||||
\(527\) | 1.31347 | + | 0.758330i | 0.0572155 | + | 0.0330334i | ||||
\(528\) | 9.46410 | − | 5.46410i | 0.411872 | − | 0.237795i | ||||
\(529\) | −0.303848 | − | 0.526279i | −0.0132108 | − | 0.0228817i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.196152 | −0.00851229 | ||||||||
\(532\) | −60.9808 | + | 21.1244i | −2.64385 | + | 0.915857i | ||||
\(533\) | 1.66025i | 0.0719136i | ||||||||
\(534\) | 20.6603 | − | 35.7846i | 0.894057 | − | 1.54855i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −69.3731 | − | 120.158i | −2.99646 | − | 5.19002i | ||||
\(537\) | −8.66025 | − | 5.00000i | −0.373718 | − | 0.215766i | ||||
\(538\) | − | 34.2487i | − | 1.47657i | ||||||
\(539\) | −4.75833 | − | 1.90192i | −0.204956 | − | 0.0819217i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.89230 | + | 5.00962i | −0.124350 | + | 0.215380i | −0.921479 | − | 0.388429i | \(-0.873018\pi\) |
0.797129 | + | 0.603809i | \(0.206351\pi\) | |||||||
\(542\) | −7.26795 | + | 4.19615i | −0.312185 | + | 0.180240i | ||||
\(543\) | −21.0622 | + | 12.1603i | −0.903865 | + | 0.521846i | ||||
\(544\) | −35.7128 | + | 61.8564i | −1.53117 | + | 2.65207i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 5.36603 | + | 15.4904i | 0.229645 | + | 0.662927i | ||||
\(547\) | − | 26.2487i | − | 1.12231i | −0.827709 | − | 0.561157i | \(-0.810356\pi\) | ||
0.827709 | − | 0.561157i | \(-0.189644\pi\) | |||||||
\(548\) | 10.3923 | + | 6.00000i | 0.443937 | + | 0.256307i | ||||
\(549\) | 2.00000 | + | 3.46410i | 0.0853579 | + | 0.147844i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.36603 | − | 16.2224i | 0.399006 | − | 0.691099i | ||||
\(552\) | − | 44.7846i | − | 1.90616i | ||||||
\(553\) | 3.69615 | − | 19.2058i | 0.157176 | − | 0.816712i | ||||
\(554\) | −40.0526 | −1.70167 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16.1962 | − | 28.0526i | −0.686870 | − | 1.18969i | ||||
\(557\) | 12.8038 | − | 7.39230i | 0.542516 | − | 0.313222i | −0.203582 | − | 0.979058i | \(-0.565258\pi\) |
0.746098 | + | 0.665836i | \(0.231925\pi\) | |||||||
\(558\) | 1.09808 | + | 0.633975i | 0.0464853 | + | 0.0268383i | ||||
\(559\) | −7.24871 | −0.306588 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.39230 | −0.101003 | ||||||||
\(562\) | 32.7846 | + | 18.9282i | 1.38294 | + | 0.798438i | ||||
\(563\) | 15.5885 | − | 9.00000i | 0.656975 | − | 0.379305i | −0.134148 | − | 0.990961i | \(-0.542830\pi\) |
0.791123 | + | 0.611656i | \(0.209497\pi\) | |||||||
\(564\) | −5.46410 | − | 9.46410i | −0.230080 | − | 0.398511i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 65.9090 | 2.77036 | ||||||||
\(567\) | 2.00000 | + | 1.73205i | 0.0839921 | + | 0.0727393i | ||||
\(568\) | 58.6410i | 2.46052i | ||||||||
\(569\) | 16.2224 | − | 28.0981i | 0.680080 | − | 1.17793i | −0.294876 | − | 0.955535i | \(-0.595278\pi\) |
0.974956 | − | 0.222397i | \(-0.0713882\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.30385 | − | 16.1147i | −0.389354 | − | 0.674381i | 0.603009 | − | 0.797734i | \(-0.293968\pi\) |
−0.992363 | + | 0.123354i | \(0.960635\pi\) | |||||||
\(572\) | −7.85641 | − | 4.53590i | −0.328493 | − | 0.189655i | ||||
\(573\) | − | 8.92820i | − | 0.372981i | ||||||
\(574\) | 5.19615 | + | 1.00000i | 0.216883 | + | 0.0417392i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −14.9282 | + | 25.8564i | −0.622008 | + | 1.07735i | ||||
\(577\) | 24.8205 | − | 14.3301i | 1.03329 | − | 0.596571i | 0.115365 | − | 0.993323i | \(-0.463196\pi\) |
0.917926 | + | 0.396752i | \(0.129863\pi\) | |||||||
\(578\) | −14.9545 | + | 8.63397i | −0.622024 | + | 0.359126i | ||||
\(579\) | −0.598076 | + | 1.03590i | −0.0248552 | + | 0.0430505i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.0981 | + | 37.8109i | 0.543400 | + | 1.56866i | ||||
\(582\) | 40.7846i | 1.69058i | ||||||||
\(583\) | 7.85641 | + | 4.53590i | 0.325379 | + | 0.187858i | ||||
\(584\) | −59.9090 | − | 103.765i | −2.47905 | − | 4.29384i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 25.8564 | − | 44.7846i | 1.06812 | − | 1.85004i | ||||
\(587\) | 40.7321i | 1.68119i | 0.541663 | + | 0.840596i | \(0.317795\pi\) | ||||
−0.541663 | + | 0.840596i | \(0.682205\pi\) | |||||||
\(588\) | 37.8564 | − | 5.46410i | 1.56117 | − | 0.225336i | ||||
\(589\) | 2.07180 | 0.0853669 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.169873 | − | 0.294229i | −0.00698764 | − | 0.0121029i | ||||
\(592\) | −41.3205 | + | 23.8564i | −1.69826 | + | 0.980492i | ||||
\(593\) | 24.1699 | + | 13.9545i | 0.992538 | + | 0.573042i | 0.906032 | − | 0.423209i | \(-0.139097\pi\) |
0.0865058 | + | 0.996251i | \(0.472430\pi\) | |||||||
\(594\) | −2.00000 | −0.0820610 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 32.0000 | 1.31077 | ||||||||
\(597\) | 19.0526 | + | 11.0000i | 0.779769 | + | 0.450200i | ||||
\(598\) | −25.3923 | + | 14.6603i | −1.03837 | + | 0.599502i | ||||
\(599\) | −19.1244 | − | 33.1244i | −0.781400 | − | 1.35342i | −0.931126 | − | 0.364697i | \(-0.881173\pi\) |
0.149726 | − | 0.988727i | \(-0.452161\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.0717968 | −0.00292865 | −0.00146433 | − | 0.999999i | \(-0.500466\pi\) | ||||
−0.00146433 | + | 0.999999i | \(0.500466\pi\) | |||||||
\(602\) | −4.36603 | + | 22.6865i | −0.177946 | + | 0.924634i | ||||
\(603\) | 14.6603i | 0.597012i | ||||||||
\(604\) | −24.3923 | + | 42.2487i | −0.992509 | + | 1.71908i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 9.92820 | + | 17.1962i | 0.403306 | + | 0.698546i | ||||
\(607\) | −2.76795 | − | 1.59808i | −0.112348 | − | 0.0648639i | 0.442773 | − | 0.896634i | \(-0.353995\pi\) |
−0.555121 | + | 0.831770i | \(0.687328\pi\) | |||||||
\(608\) | 97.5692i | 3.95695i | ||||||||
\(609\) | −7.26795 | + | 8.39230i | −0.294512 | + | 0.340073i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.26795 | + | 3.92820i | −0.0917514 | + | 0.158918i | ||||
\(612\) | 15.4641 | − | 8.92820i | 0.625099 | − | 0.360901i | ||||
\(613\) | 23.3205 | − | 13.4641i | 0.941906 | − | 0.543810i | 0.0513490 | − | 0.998681i | \(-0.483648\pi\) |
0.890557 | + | 0.454871i | \(0.150315\pi\) | |||||||
\(614\) | 43.8827 | − | 76.0070i | 1.77096 | − | 3.06739i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.0000 | + | 13.8564i | −0.483494 | + | 0.558291i | ||||
\(617\) | − | 36.2487i | − | 1.45932i | −0.683811 | − | 0.729659i | \(-0.739679\pi\) | ||
0.683811 | − | 0.729659i | \(-0.260321\pi\) | |||||||
\(618\) | −21.7583 | − | 12.5622i | −0.875248 | − | 0.505325i | ||||
\(619\) | −15.0359 | − | 26.0429i | −0.604344 | − | 1.04675i | −0.992155 | − | 0.125015i | \(-0.960102\pi\) |
0.387811 | − | 0.921739i | \(-0.373231\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.36603 | + | 4.09808i | −0.0949453 | + | 0.164450i | ||||
\(622\) | − | 24.9282i | − | 0.999530i | ||||||
\(623\) | −7.56218 | + | 39.2942i | −0.302972 | + | 1.57429i | ||||
\(624\) | 33.8564 | 1.35534 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −17.2942 | − | 29.9545i | −0.691216 | − | 1.19722i | ||||
\(627\) | −2.83013 | + | 1.63397i | −0.113024 | + | 0.0652547i | ||||
\(628\) | 30.2487 | + | 17.4641i | 1.20705 | + | 0.696894i | ||||
\(629\) | 10.4449 | 0.416464 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 48.7846 | 1.94208 | 0.971042 | − | 0.238908i | \(-0.0767893\pi\) | ||||
0.971042 | + | 0.238908i | \(0.0767893\pi\) | |||||||
\(632\) | −60.5885 | − | 34.9808i | −2.41008 | − | 1.39146i | ||||
\(633\) | 6.12436 | − | 3.53590i | 0.243421 | − | 0.140539i | ||||
\(634\) | 38.8564 | + | 67.3013i | 1.54319 | + | 2.67287i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −67.7128 | −2.68499 | ||||||||
\(637\) | −9.82051 | − | 12.4737i | −0.389103 | − | 0.494227i | ||||
\(638\) | − | 8.39230i | − | 0.332255i | ||||||
\(639\) | 3.09808 | − | 5.36603i | 0.122558 | − | 0.212277i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.90192 | − | 3.29423i | −0.0751215 | − | 0.130114i | 0.826018 | − | 0.563644i | \(-0.190601\pi\) |
−0.901139 | + | 0.433530i | \(0.857268\pi\) | |||||||
\(642\) | −5.19615 | − | 3.00000i | −0.205076 | − | 0.118401i | ||||
\(643\) | − | 4.51666i | − | 0.178120i | −0.996026 | − | 0.0890599i | \(-0.971614\pi\) | ||
0.996026 | − | 0.0890599i | \(-0.0283862\pi\) | |||||||
\(644\) | 22.3923 | + | 64.6410i | 0.882380 | + | 2.54721i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 19.9282 | − | 34.5167i | 0.784065 | − | 1.35804i | ||||
\(647\) | −24.1699 | + | 13.9545i | −0.950216 | + | 0.548607i | −0.893148 | − | 0.449763i | \(-0.851508\pi\) |
−0.0570678 | + | 0.998370i | \(0.518175\pi\) | |||||||
\(648\) | 8.19615 | − | 4.73205i | 0.321975 | − | 0.185893i | ||||
\(649\) | −0.0717968 | + | 0.124356i | −0.00281827 | + | 0.00488139i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.20577 | − | 0.232051i | −0.0472579 | − | 0.00909479i | ||||
\(652\) | 119.426i | 4.67707i | ||||||||
\(653\) | −38.6147 | − | 22.2942i | −1.51111 | − | 0.872441i | −0.999916 | − | 0.0129762i | \(-0.995869\pi\) |
−0.511196 | − | 0.859464i | \(-0.670797\pi\) | |||||||
\(654\) | 15.0263 | + | 26.0263i | 0.587574 | + | 1.01771i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.46410 | − | 9.46410i | 0.213337 | − | 0.369511i | ||||
\(657\) | 12.6603i | 0.493924i | ||||||||
\(658\) | 10.9282 | + | 9.46410i | 0.426026 | + | 0.368949i | ||||
\(659\) | −2.92820 | −0.114067 | −0.0570333 | − | 0.998372i | \(-0.518164\pi\) | ||||
−0.0570333 | + | 0.998372i | \(0.518164\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.23205 | − | 9.06218i | −0.203503 | − | 0.352478i | 0.746152 | − | 0.665776i | \(-0.231899\pi\) |
−0.949655 | + | 0.313298i | \(0.898566\pi\) | |||||||
\(662\) | −19.0981 | + | 11.0263i | −0.742268 | + | 0.428549i | ||||
\(663\) | −6.41858 | − | 3.70577i | −0.249277 | − | 0.143920i | ||||
\(664\) | 143.138 | 5.55485 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.73205 | 0.338360 | ||||||||
\(667\) | −17.1962 | − | 9.92820i | −0.665838 | − | 0.384422i | ||||
\(668\) | 83.5692 | − | 48.2487i | 3.23339 | − | 1.86680i | ||||
\(669\) | 10.1962 | + | 17.6603i | 0.394206 | + | 0.682785i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.92820 | 0.113042 | ||||||||
\(672\) | 10.9282 | − | 56.7846i | 0.421565 | − | 2.19051i | ||||
\(673\) | 27.3397i | 1.05387i | 0.849906 | + | 0.526935i | \(0.176659\pi\) | ||||
−0.849906 | + | 0.526935i | \(0.823341\pi\) | |||||||
\(674\) | −24.5622 | + | 42.5429i | −0.946100 | + | 1.63869i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 21.4641 | + | 37.1769i | 0.825542 | + | 1.42988i | ||||
\(677\) | 28.6865 | + | 16.5622i | 1.10251 | + | 0.636536i | 0.936880 | − | 0.349651i | \(-0.113700\pi\) |
0.165633 | + | 0.986187i | \(0.447033\pi\) | |||||||
\(678\) | − | 24.3923i | − | 0.936781i | ||||||
\(679\) | −12.9282 | − | 37.3205i | −0.496139 | − | 1.43223i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.830127 | + | 1.43782i | −0.0318105 | + | 0.0550975i | ||||
\(682\) | 0.803848 | − | 0.464102i | 0.0307809 | − | 0.0177714i | ||||
\(683\) | 24.2942 | − | 14.0263i | 0.929593 | − | 0.536701i | 0.0429101 | − | 0.999079i | \(-0.486337\pi\) |
0.886683 | + | 0.462378i | \(0.153004\pi\) | |||||||
\(684\) | 12.1962 | − | 21.1244i | 0.466332 | − | 0.807710i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −44.9545 | + | 23.2224i | −1.71637 | + | 0.886637i | ||||
\(687\) | 3.00000i | 0.114457i | ||||||||
\(688\) | 41.3205 | + | 23.8564i | 1.57533 | + | 0.909517i | ||||
\(689\) | 14.0526 | + | 24.3397i | 0.535360 | + | 0.927270i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.42820 | + | 7.66987i | −0.168457 | + | 0.291776i | −0.937877 | − | 0.346967i | \(-0.887212\pi\) |
0.769421 | + | 0.638742i | \(0.220545\pi\) | |||||||
\(692\) | 79.4256i | 3.01931i | ||||||||
\(693\) | 1.83013 | − | 0.633975i | 0.0695208 | − | 0.0240827i | ||||
\(694\) | −57.5692 | −2.18530 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 19.8564 | + | 34.3923i | 0.752655 | + | 1.30364i | ||||
\(697\) | −2.07180 | + | 1.19615i | −0.0784749 | + | 0.0453075i | ||||
\(698\) | −52.0526 | − | 30.0526i | −1.97022 | − | 1.13751i | ||||
\(699\) | 17.3205 | 0.655122 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.58846 | −0.324382 | −0.162191 | − | 0.986759i | \(-0.551856\pi\) | ||||
−0.162191 | + | 0.986759i | \(0.551856\pi\) | |||||||
\(702\) | −5.36603 | − | 3.09808i | −0.202528 | − | 0.116929i | ||||
\(703\) | 12.3564 | − | 7.13397i | 0.466031 | − | 0.269063i | ||||
\(704\) | 10.9282 | + | 18.9282i | 0.411872 | + | 0.713384i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.53590 | 0.321253 | ||||||||
\(707\) | −14.5359 | − | 12.5885i | −0.546679 | − | 0.473438i | ||||
\(708\) | − | 1.07180i | − | 0.0402806i | ||||||
\(709\) | −0.535898 | + | 0.928203i | −0.0201261 | + | 0.0348594i | −0.875913 | − | 0.482469i | \(-0.839740\pi\) |
0.855787 | + | 0.517328i | \(0.173073\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.69615 | + | 6.40192i | 0.138617 | + | 0.240091i | ||||
\(712\) | 123.962 | + | 71.5692i | 4.64565 | + | 2.68217i | ||||
\(713\) | − | 2.19615i | − | 0.0822466i | ||||||
\(714\) | −15.4641 | + | 17.8564i | −0.578729 | + | 0.668259i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 27.3205 | − | 47.3205i | 1.02102 | − | 1.76845i | ||||
\(717\) | −6.12436 | + | 3.53590i | −0.228718 | + | 0.132051i | ||||
\(718\) | −3.00000 | + | 1.73205i | −0.111959 | + | 0.0646396i | ||||
\(719\) | −10.2679 | + | 17.7846i | −0.382930 | + | 0.663254i | −0.991480 | − | 0.130262i | \(-0.958418\pi\) |
0.608550 | + | 0.793516i | \(0.291752\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.8923 | + | 4.59808i | 0.889796 | + | 0.171241i | ||||
\(722\) | − | 2.53590i | − | 0.0943764i | ||||||
\(723\) | −11.6603 | − | 6.73205i | −0.433650 | − | 0.250368i | ||||
\(724\) | −66.4449 | − | 115.086i | −2.46940 | − | 4.27713i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 14.2942 | − | 24.7583i | 0.530509 | − | 0.918868i | ||||
\(727\) | − | 13.3397i | − | 0.494744i | −0.968921 | − | 0.247372i | \(-0.920433\pi\) | ||
0.968921 | − | 0.247372i | \(-0.0795669\pi\) | |||||||
\(728\) | −53.6603 | + | 18.5885i | −1.98878 | + | 0.688934i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.22243 | − | 9.04552i | −0.193159 | − | 0.334561i | ||||
\(732\) | −18.9282 | + | 10.9282i | −0.699607 | + | 0.403918i | ||||
\(733\) | −1.16025 | − | 0.669873i | −0.0428550 | − | 0.0247423i | 0.478419 | − | 0.878131i | \(-0.341210\pi\) |
−0.521274 | + | 0.853389i | \(0.674543\pi\) | |||||||
\(734\) | 30.5885 | 1.12904 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 103.426 | 3.81232 | ||||||||
\(737\) | 9.29423 | + | 5.36603i | 0.342357 | + | 0.197660i | ||||
\(738\) | −1.73205 | + | 1.00000i | −0.0637577 | + | 0.0368105i | ||||
\(739\) | 13.8923 | + | 24.0622i | 0.511037 | + | 0.885142i | 0.999918 | + | 0.0127913i | \(0.00407171\pi\) |
−0.488881 | + | 0.872350i | \(0.662595\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.1244 | −0.371927 | ||||||||
\(742\) | 84.6410 | − | 29.3205i | 3.10727 | − | 1.07639i | ||||
\(743\) | 15.9090i | 0.583643i | 0.956473 | + | 0.291822i | \(0.0942614\pi\) | ||||
−0.956473 | + | 0.291822i | \(0.905739\pi\) | |||||||
\(744\) | −2.19615 | + | 3.80385i | −0.0805149 | + | 0.139456i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 36.2224 | + | 62.7391i | 1.32620 | + | 2.29704i | ||||
\(747\) | −13.0981 | − | 7.56218i | −0.479234 | − | 0.276686i | ||||
\(748\) | − | 13.0718i | − | 0.477952i | ||||||
\(749\) | 5.70577 | + | 1.09808i | 0.208484 | + | 0.0401228i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.03590 | + | 15.6506i | −0.329725 | + | 0.571100i | −0.982457 | − | 0.186489i | \(-0.940289\pi\) |
0.652732 | + | 0.757588i | \(0.273623\pi\) | |||||||
\(752\) | 25.8564 | − | 14.9282i | 0.942886 | − | 0.544376i | ||||
\(753\) | −21.2942 | + | 12.2942i | −0.776005 | + | 0.448027i | ||||
\(754\) | 13.0000 | − | 22.5167i | 0.473432 | − | 0.820008i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −9.46410 | + | 10.9282i | −0.344206 | + | 0.397455i | ||||
\(757\) | − | 27.8564i | − | 1.01246i | −0.862399 | − | 0.506229i | \(-0.831039\pi\) | ||
0.862399 | − | 0.506229i | \(-0.168961\pi\) | |||||||
\(758\) | −14.9545 | − | 8.63397i | −0.543171 | − | 0.313600i | ||||
\(759\) | 1.73205 | + | 3.00000i | 0.0628695 | + | 0.108893i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.3660 | + | 40.4711i | −0.847018 | + | 1.46708i | 0.0368396 | + | 0.999321i | \(0.488271\pi\) |
−0.883857 | + | 0.467757i | \(0.845062\pi\) | |||||||
\(762\) | 13.1244i | 0.475445i | ||||||||
\(763\) | −22.0000 | − | 19.0526i | −0.796453 | − | 0.689749i | ||||
\(764\) | 48.7846 | 1.76497 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −31.8564 | − | 55.1769i | −1.15102 | − | 1.99362i | ||||
\(767\) | −0.385263 | + | 0.222432i | −0.0139111 | + | 0.00803155i | ||||
\(768\) | −37.8564 | − | 21.8564i | −1.36603 | − | 0.788675i | ||||
\(769\) | −52.3205 | −1.88673 | −0.943363 | − | 0.331763i | \(-0.892357\pi\) | ||||
−0.943363 | + | 0.331763i | \(0.892357\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.66025 | 0.203849 | ||||||||
\(772\) | −5.66025 | − | 3.26795i | −0.203717 | − | 0.117616i | ||||
\(773\) | −37.6865 | + | 21.7583i | −1.35549 | + | 0.782593i | −0.989012 | − | 0.147834i | \(-0.952770\pi\) |
−0.366478 | + | 0.930427i | \(0.619437\pi\) | |||||||
\(774\) | −4.36603 | − | 7.56218i | −0.156934 | − | 0.271817i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −141.282 | −5.07173 | ||||||||
\(777\) | −7.99038 | + | 2.76795i | −0.286653 | + | 0.0992996i | ||||
\(778\) | 14.7846i | 0.530054i | ||||||||
\(779\) | −1.63397 | + | 2.83013i | −0.0585432 | + | 0.101400i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.26795 | − | 3.92820i | −0.0811536 | − | 0.140562i | ||||
\(782\) | −36.5885 | − | 21.1244i | −1.30840 | − | 0.755405i | ||||
\(783\) | − | 4.19615i | − | 0.149958i | ||||||
\(784\) | 14.9282 | + | 103.426i | 0.533150 | + | 3.69377i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −21.1244 | + | 36.5885i | −0.753481 | + | 1.30507i | ||||
\(787\) | 11.6603 | − | 6.73205i | 0.415643 | − | 0.239972i | −0.277568 | − | 0.960706i | \(-0.589529\pi\) |
0.693212 | + | 0.720734i | \(0.256195\pi\) | |||||||
\(788\) | 1.60770 | − | 0.928203i | 0.0572718 | − | 0.0330659i | ||||
\(789\) | −4.19615 | + | 7.26795i | −0.149387 | + | 0.258746i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.73205 | + | 22.3205i | 0.274920 | + | 0.793626i | ||||
\(792\) | − | 6.92820i | − | 0.246183i | ||||||
\(793\) | 7.85641 | + | 4.53590i | 0.278989 | + | 0.161074i | ||||
\(794\) | 42.6147 | + | 73.8109i | 1.51234 | + | 2.61945i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −60.1051 | + | 104.105i | −2.13037 | + | 3.68991i | ||||
\(797\) | − | 3.94744i | − | 0.139826i | −0.997553 | − | 0.0699128i | \(-0.977728\pi\) | ||
0.997553 | − | 0.0699128i | \(-0.0222721\pi\) | |||||||
\(798\) | −6.09808 | + | 31.6865i | −0.215870 | + | 1.12169i | ||||
\(799\) | −6.53590 | −0.231223 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.56218 | − | 13.0981i | −0.267196 | − | 0.462798i | ||||
\(802\) | 38.7846 | − | 22.3923i | 1.36953 | − | 0.790700i | ||||
\(803\) | 8.02628 | + | 4.63397i | 0.283241 | + | 0.163529i | ||||
\(804\) | −80.1051 | −2.82509 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.87564 | 0.101290 | ||||||||
\(807\) | −10.8564 | − | 6.26795i | −0.382164 | − | 0.220642i | ||||
\(808\) | −59.5692 | + | 34.3923i | −2.09564 | + | 1.20992i | ||||
\(809\) | 12.8564 | + | 22.2679i | 0.452007 | + | 0.782899i | 0.998511 | − | 0.0545574i | \(-0.0173748\pi\) |
−0.546503 | + | 0.837457i | \(0.684041\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.46410 | −0.121641 | −0.0608205 | − | 0.998149i | \(-0.519372\pi\) | ||||
−0.0608205 | + | 0.998149i | \(0.519372\pi\) | |||||||
\(812\) | −45.8564 | − | 39.7128i | −1.60924 | − | 1.39365i | ||||
\(813\) | 3.07180i | 0.107733i | ||||||||
\(814\) | 3.19615 | − | 5.53590i | 0.112025 | − | 0.194033i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 24.3923 | + | 42.2487i | 0.853901 | + | 1.47900i | ||||
\(817\) | −12.3564 | − | 7.13397i | −0.432296 | − | 0.249586i | ||||
\(818\) | 8.58846i | 0.300288i | ||||||||
\(819\) | 5.89230 | + | 1.13397i | 0.205894 | + | 0.0396243i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.7583 | − | 22.0981i | 0.445269 | − | 0.771228i | −0.552802 | − | 0.833313i | \(-0.686441\pi\) |
0.998071 | + | 0.0620844i | \(0.0197748\pi\) | |||||||
\(822\) | 5.19615 | − | 3.00000i | 0.181237 | − | 0.104637i | ||||
\(823\) | −33.9282 | + | 19.5885i | −1.18266 | + | 0.682811i | −0.956629 | − | 0.291309i | \(-0.905909\pi\) |
−0.226034 | + | 0.974119i | \(0.572576\pi\) | |||||||
\(824\) | 43.5167 | − | 75.3731i | 1.51597 | − | 2.62575i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.464102 | + | 1.33975i | 0.0161482 | + | 0.0466157i | ||||
\(827\) | − | 3.75129i | − | 0.130445i | −0.997871 | − | 0.0652225i | \(-0.979224\pi\) | ||
0.997871 | − | 0.0652225i | \(-0.0207757\pi\) | |||||||
\(828\) | −22.3923 | − | 12.9282i | −0.778186 | − | 0.449286i | ||||
\(829\) | −2.30385 | − | 3.99038i | −0.0800159 | − | 0.138592i | 0.823241 | − | 0.567693i | \(-0.192164\pi\) |
−0.903257 | + | 0.429101i | \(0.858830\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.33013 | + | 12.6962i | −0.254279 | + | 0.440425i | ||||
\(832\) | 67.7128i | 2.34752i | ||||||||
\(833\) | 8.49038 | − | 21.2417i | 0.294174 | − | 0.735980i | ||||
\(834\) | −16.1962 | −0.560827 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −8.92820 | − | 15.4641i | −0.308788 | − | 0.534837i | ||||
\(837\) | 0.401924 | − | 0.232051i | 0.0138925 | − | 0.00802085i | ||||
\(838\) | 83.9090 | + | 48.4449i | 2.89859 | + | 1.67350i | ||||
\(839\) | −18.4449 | −0.636787 | −0.318394 | − | 0.947959i | \(-0.603143\pi\) | ||||
−0.318394 | + | 0.947959i | \(0.603143\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.3923 | −0.392838 | ||||||||
\(842\) | 0.169873 | + | 0.0980762i | 0.00585421 | + | 0.00337993i | ||||
\(843\) | 12.0000 | − | 6.92820i | 0.413302 | − | 0.238620i | ||||
\(844\) | 19.3205 | + | 33.4641i | 0.665039 | + | 1.15188i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5.46410 | −0.187860 | ||||||||
\(847\) | −5.23205 | + | 27.1865i | −0.179775 | + | 0.934140i | ||||
\(848\) | − | 184.995i | − | 6.35275i | ||||||
\(849\) | 12.0622 | − | 20.8923i | 0.413973 | − | 0.717022i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.56218 | − | 13.0981i | −0.259228 | − | 0.448996i | ||||
\(852\) | 29.3205 | + | 16.9282i | 1.00450 | + | 0.579951i | ||||
\(853\) | 31.9808i | 1.09500i | 0.836806 | + | 0.547500i | \(0.184420\pi\) | ||||
−0.836806 | + | 0.547500i | \(0.815580\pi\) | |||||||
\(854\) | 18.9282 | − | 21.8564i | 0.647710 | − | 0.747911i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.3923 | − | 18.0000i | 0.355202 | − | 0.615227i | ||||
\(857\) | 25.2224 | − | 14.5622i | 0.861582 | − | 0.497435i | −0.00295983 | − | 0.999996i | \(-0.500942\pi\) |
0.864542 | + | 0.502561i | \(0.167609\pi\) | |||||||
\(858\) | −3.92820 | + | 2.26795i | −0.134107 | + | 0.0774265i | ||||
\(859\) | 3.73205 | − | 6.46410i | 0.127336 | − | 0.220552i | −0.795308 | − | 0.606206i | \(-0.792691\pi\) |
0.922644 | + | 0.385654i | \(0.126024\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.26795 | − | 1.46410i | 0.0432116 | − | 0.0498964i | ||||
\(862\) | − | 47.3205i | − | 1.61174i | ||||||
\(863\) | 12.4641 | + | 7.19615i | 0.424283 | + | 0.244960i | 0.696908 | − | 0.717160i | \(-0.254559\pi\) |
−0.272625 | + | 0.962120i | \(0.587892\pi\) | |||||||
\(864\) | 10.9282 | + | 18.9282i | 0.371785 | + | 0.643951i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 20.7583 | − | 35.9545i | 0.705397 | − | 1.22178i | ||||
\(867\) | 6.32051i | 0.214656i | ||||||||
\(868\) | 1.26795 | − | 6.58846i | 0.0430370 | − | 0.223627i | ||||
\(869\) | 5.41154 | 0.183574 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.6244 | + | 28.7942i | 0.563295 | + | 0.975655i | ||||
\(872\) | −90.1577 | + | 52.0526i | −3.05312 | + | 1.76272i | ||||
\(873\) | 12.9282 | + | 7.46410i | 0.437553 | + | 0.252622i | ||||
\(874\) | −57.7128 | −1.95217 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −69.1769 | −2.33727 | ||||||||
\(877\) | 3.58846 | + | 2.07180i | 0.121174 | + | 0.0699596i | 0.559362 | − | 0.828924i | \(-0.311046\pi\) |
−0.438188 | + | 0.898883i | \(0.644380\pi\) | |||||||
\(878\) | 1.26795 | − | 0.732051i | 0.0427912 | − | 0.0247055i | ||||
\(879\) | −9.46410 | − | 16.3923i | −0.319216 | − | 0.552899i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.85641 | 0.332071 | 0.166035 | − | 0.986120i | \(-0.446903\pi\) | ||||
0.166035 | + | 0.986120i | \(0.446903\pi\) | |||||||
\(882\) | 7.09808 | − | 17.7583i | 0.239005 | − | 0.597954i | ||||
\(883\) | − | 53.5885i | − | 1.80340i | −0.432367 | − | 0.901698i | \(-0.642322\pi\) | ||
0.432367 | − | 0.901698i | \(-0.357678\pi\) | |||||||
\(884\) | 20.2487 | − | 35.0718i | 0.681038 | − | 1.17959i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.9282 | + | 22.3923i | 0.434331 | + | 0.752284i | ||||
\(887\) | 21.8827 | + | 12.6340i | 0.734749 | + | 0.424207i | 0.820157 | − | 0.572139i | \(-0.193886\pi\) |
−0.0854082 | + | 0.996346i | \(0.527219\pi\) | |||||||
\(888\) | 30.2487i | 1.01508i | ||||||||
\(889\) | −4.16025 | − | 12.0096i | −0.139530 | − | 0.402790i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.366025 | + | 0.633975i | −0.0122623 | + | 0.0212389i | ||||
\(892\) | −96.4974 | + | 55.7128i | −3.23097 | + | 1.86540i | ||||
\(893\) | −7.73205 | + | 4.46410i | −0.258743 | + | 0.149385i | ||||
\(894\) | 8.00000 | − | 13.8564i | 0.267560 | − | 0.463428i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 98.3538 | + | 18.9282i | 3.28577 | + | 0.632347i | ||||
\(897\) | 10.7321i | 0.358333i | ||||||||
\(898\) | 84.8372 | + | 48.9808i | 2.83105 | + | 1.63451i | ||||
\(899\) | 0.973721 | + | 1.68653i | 0.0324754 | + | 0.0562490i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.2487 | + | 35.0718i | −0.674582 | + | 1.16841i | ||||
\(902\) | 1.46410i | 0.0487493i | ||||||||
\(903\) | 6.39230 | + | 5.53590i | 0.212723 | + | 0.184223i | ||||
\(904\) | 84.4974 | 2.81034 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 12.1962 | + | 21.1244i | 0.405190 | + | 0.701810i | ||||
\(907\) | 29.0885 | − | 16.7942i | 0.965866 | − | 0.557643i | 0.0678928 | − | 0.997693i | \(-0.478372\pi\) |
0.897974 | + | 0.440049i | \(0.145039\pi\) | |||||||
\(908\) | −7.85641 | − | 4.53590i | −0.260724 | − | 0.150529i | ||||
\(909\) | 7.26795 | 0.241063 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.7321 | −0.488095 | −0.244047 | − | 0.969763i | \(-0.578475\pi\) | ||||
−0.244047 | + | 0.969763i | \(0.578475\pi\) | |||||||
\(912\) | 57.7128 | + | 33.3205i | 1.91106 | + | 1.10335i | ||||
\(913\) | −9.58846 | + | 5.53590i | −0.317332 | + | 0.183211i | ||||
\(914\) | 22.7583 | + | 39.4186i | 0.752779 | + | 1.30385i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.3923 | −0.541617 | ||||||||
\(917\) | 7.73205 | − | 40.1769i | 0.255335 | − | 1.32676i | ||||
\(918\) | − | 8.92820i | − | 0.294675i | ||||||
\(919\) | −15.4282 | + | 26.7224i | −0.508929 | + | 0.881492i | 0.491017 | + | 0.871150i | \(0.336625\pi\) |
−0.999947 | + | 0.0103417i | \(0.996708\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.0622 | − | 27.8205i | −0.529267 | − | 0.916717i | ||||
\(922\) | 40.1769 | + | 23.1962i | 1.32316 | + | 0.763925i | ||||
\(923\) | − | 14.0526i | − | 0.462546i | ||||||
\(924\) | 3.46410 | + | 10.0000i | 0.113961 | + | 0.328976i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 35.1506 | − | 60.8827i | 1.15512 | − | 2.00073i | ||||
\(927\) | −7.96410 | + | 4.59808i | −0.261575 | + | 0.151021i | ||||
\(928\) | −79.4256 | + | 45.8564i | −2.60727 | + | 1.50531i | ||||
\(929\) | −26.2224 | + | 45.4186i | −0.860330 | + | 1.49014i | 0.0112804 | + | 0.999936i | \(0.496409\pi\) |
−0.871611 | + | 0.490199i | \(0.836924\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.46410 | − | 30.9282i | −0.146305 | − | 1.01363i | ||||
\(932\) | 94.6410i | 3.10007i | ||||||||
\(933\) | −7.90192 | − | 4.56218i | −0.258697 | − | 0.149359i | ||||
\(934\) | 0.196152 | + | 0.339746i | 0.00641830 | + | 0.0111168i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 10.7321 | − | 18.5885i | 0.350788 | − | 0.607583i | ||||
\(937\) | 31.7321i | 1.03664i | 0.855186 | + | 0.518320i | \(0.173443\pi\) | ||||
−0.855186 | + | 0.518320i | \(0.826557\pi\) | |||||||
\(938\) | 100.131 | − | 34.6865i | 3.26941 | − | 1.13256i | ||||
\(939\) | −12.6603 | −0.413152 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.0263 | + | 26.0263i | 0.489843 | + | 0.848432i | 0.999932 | − | 0.0116892i | \(-0.00372087\pi\) |
−0.510089 | + | 0.860122i | \(0.670388\pi\) | |||||||
\(942\) | 15.1244 | − | 8.73205i | 0.492778 | − | 0.284506i | ||||
\(943\) | 3.00000 | + | 1.73205i | 0.0976934 | + | 0.0564033i | ||||
\(944\) | 2.92820 | 0.0953049 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.39230 | −0.207832 | ||||||||
\(947\) | 4.90192 | + | 2.83013i | 0.159291 | + | 0.0919668i | 0.577527 | − | 0.816372i | \(-0.304018\pi\) |
−0.418235 | + | 0.908339i | \(0.637351\pi\) | |||||||
\(948\) | −34.9808 | + | 20.1962i | −1.13612 | + | 0.655941i | ||||
\(949\) | 14.3564 | + | 24.8660i | 0.466029 | + | 0.807185i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28.4449 | 0.922388 | ||||||||
\(952\) | −61.8564 | − | 53.5692i | −2.00478 | − | 1.73619i | ||||
\(953\) | 36.1051i | 1.16956i | 0.811192 | + | 0.584780i | \(0.198819\pi\) | ||||
−0.811192 | + | 0.584780i | \(0.801181\pi\) | |||||||
\(954\) | −16.9282 | + | 29.3205i | −0.548071 | + | 0.949286i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −19.3205 | − | 33.4641i | −0.624870 | − | 1.08231i | ||||
\(957\) | −2.66025 | − | 1.53590i | −0.0859938 | − | 0.0496485i | ||||
\(958\) | 24.0000i | 0.775405i | ||||||||
\(959\) | −3.80385 | + | 4.39230i | −0.122833 | + | 0.141835i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.3923 | − | 26.6603i | 0.496526 | − | 0.860008i | ||||
\(962\) | 17.1506 | − | 9.90192i | 0.552959 | − | 0.319251i | ||||
\(963\) | −1.90192 | + | 1.09808i | −0.0612886 | + | 0.0353850i | ||||
\(964\) | 36.7846 | − | 63.7128i | 1.18475 | − | 2.05205i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 33.5885 | + | 6.46410i | 1.08069 | + | 0.207979i | ||||
\(967\) | − | 10.1244i | − | 0.325577i | −0.986661 | − | 0.162789i | \(-0.947951\pi\) | ||
0.986661 | − | 0.162789i | \(-0.0520489\pi\) | |||||||
\(968\) | 85.7654 | + | 49.5167i | 2.75660 | + | 1.59153i | ||||
\(969\) | −7.29423 | − | 12.6340i | −0.234324 | − | 0.405862i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.0000 | − | 20.7846i | 0.385098 | − | 0.667010i | −0.606685 | − | 0.794943i | \(-0.707501\pi\) |
0.991783 | + | 0.127933i | \(0.0408342\pi\) | |||||||
\(972\) | − | 5.46410i | − | 0.175261i | ||||||
\(973\) | 14.8205 | − | 5.13397i | 0.475124 | − | 0.164588i | ||||
\(974\) | −1.12436 | −0.0360267 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −29.8564 | − | 51.7128i | −0.955680 | − | 1.65529i | ||||
\(977\) | −14.3660 | + | 8.29423i | −0.459610 | + | 0.265356i | −0.711880 | − | 0.702301i | \(-0.752156\pi\) |
0.252270 | + | 0.967657i | \(0.418823\pi\) | |||||||
\(978\) | 51.7128 | + | 29.8564i | 1.65359 | + | 0.954703i | ||||
\(979\) | −11.0718 | −0.353856 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.0000 | 0.351203 | ||||||||
\(982\) | −90.4974 | − | 52.2487i | −2.88789 | − | 1.66732i | ||||
\(983\) | −8.49038 | + | 4.90192i | −0.270801 | + | 0.156347i | −0.629252 | − | 0.777202i | \(-0.716639\pi\) |
0.358451 | + | 0.933549i | \(0.383305\pi\) | |||||||
\(984\) | −3.46410 | − | 6.00000i | −0.110432 | − | 0.191273i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 37.4641 | 1.19310 | ||||||||
\(987\) | 5.00000 | − | 1.73205i | 0.159152 | − | 0.0551318i | ||||
\(988\) | − | 55.3205i | − | 1.75998i | ||||||
\(989\) | −7.56218 | + | 13.0981i | −0.240463 | + | 0.416495i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.5526 | + | 18.2776i | 0.335213 | + | 0.580606i | 0.983526 | − | 0.180768i | \(-0.0578584\pi\) |
−0.648313 | + | 0.761374i | \(0.724525\pi\) | |||||||
\(992\) | −8.78461 | − | 5.07180i | −0.278912 | − | 0.161030i | ||||
\(993\) | 8.07180i | 0.256151i | ||||||||
\(994\) | −43.9808 | − | 8.46410i | −1.39499 | − | 0.268465i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 41.3205 | − | 71.5692i | 1.30929 | − | 2.26776i | ||||
\(997\) | −48.4808 | + | 27.9904i | −1.53540 | + | 0.886464i | −0.536302 | + | 0.844026i | \(0.680179\pi\) |
−0.999099 | + | 0.0424381i | \(0.986487\pi\) | |||||||
\(998\) | −32.0263 | + | 18.4904i | −1.01377 | + | 0.585303i | ||||
\(999\) | 1.59808 | − | 2.76795i | 0.0505609 | − | 0.0875740i |
(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 | 525.2.r.f.499.2 | 4 | ||
5.2 | odd | 4 | 525.2.i.f.226.1 | 4 | |||
5.3 | odd | 4 | 105.2.i.d.16.2 | ✓ | 4 | ||
5.4 | even | 2 | 525.2.r.a.499.1 | 4 | |||
7.4 | even | 3 | 525.2.r.a.424.1 | 4 | |||
15.8 | even | 4 | 315.2.j.c.226.1 | 4 | |||
20.3 | even | 4 | 1680.2.bg.o.961.1 | 4 | |||
35.2 | odd | 12 | 3675.2.a.bg.1.2 | 2 | |||
35.3 | even | 12 | 735.2.i.l.361.2 | 4 | |||
35.4 | even | 6 | inner | 525.2.r.f.424.2 | 4 | ||
35.12 | even | 12 | 3675.2.a.be.1.2 | 2 | |||
35.13 | even | 4 | 735.2.i.l.226.2 | 4 | |||
35.18 | odd | 12 | 105.2.i.d.46.2 | yes | 4 | ||
35.23 | odd | 12 | 735.2.a.g.1.1 | 2 | |||
35.32 | odd | 12 | 525.2.i.f.151.1 | 4 | |||
35.33 | even | 12 | 735.2.a.h.1.1 | 2 | |||
105.23 | even | 12 | 2205.2.a.z.1.2 | 2 | |||
105.53 | even | 12 | 315.2.j.c.46.1 | 4 | |||
105.68 | odd | 12 | 2205.2.a.ba.1.2 | 2 | |||
140.123 | even | 12 | 1680.2.bg.o.1201.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.i.d.16.2 | ✓ | 4 | 5.3 | odd | 4 | ||
105.2.i.d.46.2 | yes | 4 | 35.18 | odd | 12 | ||
315.2.j.c.46.1 | 4 | 105.53 | even | 12 | |||
315.2.j.c.226.1 | 4 | 15.8 | even | 4 | |||
525.2.i.f.151.1 | 4 | 35.32 | odd | 12 | |||
525.2.i.f.226.1 | 4 | 5.2 | odd | 4 | |||
525.2.r.a.424.1 | 4 | 7.4 | even | 3 | |||
525.2.r.a.499.1 | 4 | 5.4 | even | 2 | |||
525.2.r.f.424.2 | 4 | 35.4 | even | 6 | inner | ||
525.2.r.f.499.2 | 4 | 1.1 | even | 1 | trivial | ||
735.2.a.g.1.1 | 2 | 35.23 | odd | 12 | |||
735.2.a.h.1.1 | 2 | 35.33 | even | 12 | |||
735.2.i.l.226.2 | 4 | 35.13 | even | 4 | |||
735.2.i.l.361.2 | 4 | 35.3 | even | 12 | |||
1680.2.bg.o.961.1 | 4 | 20.3 | even | 4 | |||
1680.2.bg.o.1201.1 | 4 | 140.123 | even | 12 | |||
2205.2.a.z.1.2 | 2 | 105.23 | even | 12 | |||
2205.2.a.ba.1.2 | 2 | 105.68 | odd | 12 | |||
3675.2.a.be.1.2 | 2 | 35.12 | even | 12 | |||
3675.2.a.bg.1.2 | 2 | 35.2 | odd | 12 |