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 | 424.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.424 |
Dual form | 525.2.r.f.499.1 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.633975 | − | 0.366025i | 0.448288 | − | 0.258819i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(3\) | −0.866025 | − | 0.500000i | −0.500000 | − | 0.288675i | ||||
\(4\) | −0.732051 | + | 1.26795i | −0.366025 | + | 0.633975i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.732051 | −0.298858 | ||||||||
\(7\) | −2.50000 | − | 0.866025i | −0.944911 | − | 0.327327i | ||||
\(8\) | 2.53590i | 0.896575i | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.36603 | − | 2.36603i | 0.411872 | − | 0.713384i | −0.583222 | − | 0.812313i | \(-0.698208\pi\) |
0.995094 | + | 0.0989291i | \(0.0315417\pi\) | |||||||
\(12\) | 1.26795 | − | 0.732051i | 0.366025 | − | 0.211325i | ||||
\(13\) | − | 5.73205i | − | 1.58978i | −0.606750 | − | 0.794892i | \(-0.707527\pi\) | ||
0.606750 | − | 0.794892i | \(-0.292473\pi\) | |||||||
\(14\) | −1.90192 | + | 0.366025i | −0.508311 | + | 0.0978244i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.535898 | − | 0.928203i | −0.133975 | − | 0.232051i | ||||
\(17\) | −5.83013 | − | 3.36603i | −1.41401 | − | 0.816381i | −0.418250 | − | 0.908332i | \(-0.637356\pi\) |
−0.995764 | + | 0.0919509i | \(0.970690\pi\) | |||||||
\(18\) | 0.633975 | + | 0.366025i | 0.149429 | + | 0.0862730i | ||||
\(19\) | −1.23205 | − | 2.13397i | −0.282652 | − | 0.489567i | 0.689385 | − | 0.724395i | \(-0.257881\pi\) |
−0.972037 | + | 0.234828i | \(0.924547\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.73205 | + | 2.00000i | 0.377964 | + | 0.436436i | ||||
\(22\) | − | 2.00000i | − | 0.426401i | ||||||
\(23\) | 1.09808 | − | 0.633975i | 0.228965 | − | 0.132193i | −0.381130 | − | 0.924522i | \(-0.624465\pi\) |
0.610094 | + | 0.792329i | \(0.291132\pi\) | |||||||
\(24\) | 1.26795 | − | 2.19615i | 0.258819 | − | 0.448288i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.09808 | − | 3.63397i | −0.411467 | − | 0.712681i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 2.92820 | − | 2.53590i | 0.553378 | − | 0.479240i | ||||
\(29\) | −6.19615 | −1.15060 | −0.575298 | − | 0.817944i | \(-0.695114\pi\) | ||||
−0.575298 | + | 0.817944i | \(0.695114\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.23205 | + | 5.59808i | −0.580493 | + | 1.00544i | 0.414927 | + | 0.909855i | \(0.363807\pi\) |
−0.995421 | + | 0.0955896i | \(0.969526\pi\) | |||||||
\(32\) | −5.07180 | − | 2.92820i | −0.896575 | − | 0.517638i | ||||
\(33\) | −2.36603 | + | 1.36603i | −0.411872 | + | 0.237795i | ||||
\(34\) | −4.92820 | −0.845180 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.46410 | −0.244017 | ||||||||
\(37\) | 6.23205 | − | 3.59808i | 1.02454 | − | 0.591520i | 0.109126 | − | 0.994028i | \(-0.465195\pi\) |
0.915417 | + | 0.402508i | \(0.131861\pi\) | |||||||
\(38\) | −1.56218 | − | 0.901924i | −0.253419 | − | 0.146311i | ||||
\(39\) | −2.86603 | + | 4.96410i | −0.458931 | + | 0.794892i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.73205 | 0.426675 | 0.213337 | − | 0.976979i | \(-0.431567\pi\) | ||||
0.213337 | + | 0.976979i | \(0.431567\pi\) | |||||||
\(42\) | 1.83013 | + | 0.633975i | 0.282395 | + | 0.0978244i | ||||
\(43\) | 7.19615i | 1.09740i | 0.836018 | + | 0.548701i | \(0.184878\pi\) | ||||
−0.836018 | + | 0.548701i | \(0.815122\pi\) | |||||||
\(44\) | 2.00000 | + | 3.46410i | 0.301511 | + | 0.522233i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.464102 | − | 0.803848i | 0.0684280 | − | 0.118521i | ||||
\(47\) | 1.73205 | − | 1.00000i | 0.252646 | − | 0.145865i | −0.368329 | − | 0.929695i | \(-0.620070\pi\) |
0.620975 | + | 0.783830i | \(0.286737\pi\) | |||||||
\(48\) | 1.07180i | 0.154701i | ||||||||
\(49\) | 5.50000 | + | 4.33013i | 0.785714 | + | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.36603 | + | 5.83013i | 0.471338 | + | 0.816381i | ||||
\(52\) | 7.26795 | + | 4.19615i | 1.00788 | + | 0.581902i | ||||
\(53\) | −7.26795 | − | 4.19615i | −0.998330 | − | 0.576386i | −0.0905760 | − | 0.995890i | \(-0.528871\pi\) |
−0.907754 | + | 0.419504i | \(0.862204\pi\) | |||||||
\(54\) | −0.366025 | − | 0.633975i | −0.0498097 | − | 0.0862730i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.19615 | − | 6.33975i | 0.293473 | − | 0.847184i | ||||
\(57\) | 2.46410i | 0.326378i | ||||||||
\(58\) | −3.92820 | + | 2.26795i | −0.515798 | + | 0.297796i | ||||
\(59\) | 5.09808 | − | 8.83013i | 0.663713 | − | 1.14958i | −0.315920 | − | 0.948786i | \(-0.602313\pi\) |
0.979633 | − | 0.200799i | \(-0.0643537\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | − | 3.46410i | −0.256074 | − | 0.443533i | 0.709113 | − | 0.705095i | \(-0.249096\pi\) |
−0.965187 | + | 0.261562i | \(0.915762\pi\) | |||||||
\(62\) | 4.73205i | 0.600971i | ||||||||
\(63\) | −0.500000 | − | 2.59808i | −0.0629941 | − | 0.327327i | ||||
\(64\) | −2.14359 | −0.267949 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.00000 | + | 1.73205i | −0.123091 | + | 0.213201i | ||||
\(67\) | −2.30385 | − | 1.33013i | −0.281460 | − | 0.162501i | 0.352624 | − | 0.935765i | \(-0.385289\pi\) |
−0.634084 | + | 0.773264i | \(0.718623\pi\) | |||||||
\(68\) | 8.53590 | − | 4.92820i | 1.03513 | − | 0.597632i | ||||
\(69\) | −1.26795 | −0.152643 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.19615 | −0.497992 | −0.248996 | − | 0.968505i | \(-0.580101\pi\) | ||||
−0.248996 | + | 0.968505i | \(0.580101\pi\) | |||||||
\(72\) | −2.19615 | + | 1.26795i | −0.258819 | + | 0.149429i | ||||
\(73\) | −4.03590 | − | 2.33013i | −0.472366 | − | 0.272721i | 0.244864 | − | 0.969558i | \(-0.421257\pi\) |
−0.717230 | + | 0.696837i | \(0.754590\pi\) | |||||||
\(74\) | 2.63397 | − | 4.56218i | 0.306193 | − | 0.530342i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.60770 | 0.413831 | ||||||||
\(77\) | −5.46410 | + | 4.73205i | −0.622692 | + | 0.539267i | ||||
\(78\) | 4.19615i | 0.475121i | ||||||||
\(79\) | 6.69615 | + | 11.5981i | 0.753376 | + | 1.30489i | 0.946178 | + | 0.323648i | \(0.104909\pi\) |
−0.192802 | + | 0.981238i | \(0.561757\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 1.73205 | − | 1.00000i | 0.191273 | − | 0.110432i | ||||
\(83\) | 9.12436i | 1.00153i | 0.865584 | + | 0.500764i | \(0.166948\pi\) | ||||
−0.865584 | + | 0.500764i | \(0.833052\pi\) | |||||||
\(84\) | −3.80385 | + | 0.732051i | −0.415034 | + | 0.0798733i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.63397 | + | 4.56218i | 0.284029 | + | 0.491952i | ||||
\(87\) | 5.36603 | + | 3.09808i | 0.575298 | + | 0.332149i | ||||
\(88\) | 6.00000 | + | 3.46410i | 0.639602 | + | 0.369274i | ||||
\(89\) | −4.56218 | − | 7.90192i | −0.483590 | − | 0.837602i | 0.516233 | − | 0.856448i | \(-0.327334\pi\) |
−0.999822 | + | 0.0188462i | \(0.994001\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.96410 | + | 14.3301i | −0.520379 | + | 1.50221i | ||||
\(92\) | 1.85641i | 0.193544i | ||||||||
\(93\) | 5.59808 | − | 3.23205i | 0.580493 | − | 0.335148i | ||||
\(94\) | 0.732051 | − | 1.26795i | 0.0755053 | − | 0.130779i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.92820 | + | 5.07180i | 0.298858 | + | 0.517638i | ||||
\(97\) | 1.07180i | 0.108824i | 0.998519 | + | 0.0544122i | \(0.0173285\pi\) | ||||
−0.998519 | + | 0.0544122i | \(0.982671\pi\) | |||||||
\(98\) | 5.07180 | + | 0.732051i | 0.512329 | + | 0.0739483i | ||||
\(99\) | 2.73205 | 0.274581 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.36603 | − | 9.29423i | 0.533939 | − | 0.924810i | −0.465274 | − | 0.885167i | \(-0.654044\pi\) |
0.999214 | − | 0.0396438i | \(-0.0126223\pi\) | |||||||
\(102\) | 4.26795 | + | 2.46410i | 0.422590 | + | 0.243982i | ||||
\(103\) | −1.03590 | + | 0.598076i | −0.102070 | + | 0.0589302i | −0.550166 | − | 0.835055i | \(-0.685436\pi\) |
0.448096 | + | 0.893985i | \(0.352102\pi\) | |||||||
\(104\) | 14.5359 | 1.42536 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.14359 | −0.596719 | ||||||||
\(107\) | −7.09808 | + | 4.09808i | −0.686197 | + | 0.396176i | −0.802186 | − | 0.597075i | \(-0.796330\pi\) |
0.115989 | + | 0.993251i | \(0.462996\pi\) | |||||||
\(108\) | 1.26795 | + | 0.732051i | 0.122008 | + | 0.0704416i | ||||
\(109\) | 5.50000 | − | 9.52628i | 0.526804 | − | 0.912452i | −0.472708 | − | 0.881219i | \(-0.656723\pi\) |
0.999512 | − | 0.0312328i | \(-0.00994332\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.19615 | −0.683029 | ||||||||
\(112\) | 0.535898 | + | 2.78461i | 0.0506376 | + | 0.263121i | ||||
\(113\) | 4.92820i | 0.463606i | 0.972763 | + | 0.231803i | \(0.0744625\pi\) | ||||
−0.972763 | + | 0.231803i | \(0.925537\pi\) | |||||||
\(114\) | 0.901924 | + | 1.56218i | 0.0844729 | + | 0.146311i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.53590 | − | 7.85641i | 0.421148 | − | 0.729449i | ||||
\(117\) | 4.96410 | − | 2.86603i | 0.458931 | − | 0.264964i | ||||
\(118\) | − | 7.46410i | − | 0.687126i | ||||||
\(119\) | 11.6603 | + | 13.4641i | 1.06889 | + | 1.23425i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.76795 | + | 3.06218i | 0.160723 | + | 0.278380i | ||||
\(122\) | −2.53590 | − | 1.46410i | −0.229589 | − | 0.132554i | ||||
\(123\) | −2.36603 | − | 1.36603i | −0.213337 | − | 0.123170i | ||||
\(124\) | −4.73205 | − | 8.19615i | −0.424951 | − | 0.736036i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.26795 | − | 1.46410i | −0.112958 | − | 0.130433i | ||||
\(127\) | 15.1962i | 1.34844i | 0.738530 | + | 0.674220i | \(0.235520\pi\) | ||||
−0.738530 | + | 0.674220i | \(0.764480\pi\) | |||||||
\(128\) | 8.78461 | − | 5.07180i | 0.776457 | − | 0.448288i | ||||
\(129\) | 3.59808 | − | 6.23205i | 0.316793 | − | 0.548701i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.26795 | − | 7.39230i | −0.372892 | − | 0.645869i | 0.617117 | − | 0.786872i | \(-0.288301\pi\) |
−0.990009 | + | 0.141003i | \(0.954967\pi\) | |||||||
\(132\) | − | 4.00000i | − | 0.348155i | ||||||
\(133\) | 1.23205 | + | 6.40192i | 0.106832 | + | 0.555117i | ||||
\(134\) | −1.94744 | −0.168233 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.53590 | − | 14.7846i | 0.731947 | − | 1.26777i | ||||
\(137\) | 7.09808 | + | 4.09808i | 0.606430 | + | 0.350122i | 0.771567 | − | 0.636148i | \(-0.219473\pi\) |
−0.165137 | + | 0.986271i | \(0.552807\pi\) | |||||||
\(138\) | −0.803848 | + | 0.464102i | −0.0684280 | + | 0.0395070i | ||||
\(139\) | 7.92820 | 0.672461 | 0.336231 | − | 0.941780i | \(-0.390848\pi\) | ||||
0.336231 | + | 0.941780i | \(0.390848\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.00000 | −0.168430 | ||||||||
\(142\) | −2.66025 | + | 1.53590i | −0.223244 | + | 0.128890i | ||||
\(143\) | −13.5622 | − | 7.83013i | −1.13413 | − | 0.654788i | ||||
\(144\) | 0.535898 | − | 0.928203i | 0.0446582 | − | 0.0773503i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.41154 | −0.282341 | ||||||||
\(147\) | −2.59808 | − | 6.50000i | −0.214286 | − | 0.536111i | ||||
\(148\) | 10.5359i | 0.866046i | ||||||||
\(149\) | −10.9282 | − | 18.9282i | −0.895273 | − | 1.55066i | −0.833466 | − | 0.552571i | \(-0.813647\pi\) |
−0.0618073 | − | 0.998088i | \(-0.519686\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.46410 | + | 4.26795i | −0.200526 | + | 0.347321i | −0.948698 | − | 0.316184i | \(-0.897598\pi\) |
0.748172 | + | 0.663505i | \(0.230932\pi\) | |||||||
\(152\) | 5.41154 | − | 3.12436i | 0.438934 | − | 0.253419i | ||||
\(153\) | − | 6.73205i | − | 0.544254i | ||||||
\(154\) | −1.73205 | + | 5.00000i | −0.139573 | + | 0.402911i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.19615 | − | 7.26795i | −0.335961 | − | 0.581902i | ||||
\(157\) | 12.4641 | + | 7.19615i | 0.994744 | + | 0.574315i | 0.906689 | − | 0.421800i | \(-0.138602\pi\) |
0.0880548 | + | 0.996116i | \(0.471935\pi\) | |||||||
\(158\) | 8.49038 | + | 4.90192i | 0.675458 | + | 0.389976i | ||||
\(159\) | 4.19615 | + | 7.26795i | 0.332777 | + | 0.576386i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.29423 | + | 0.633975i | −0.259622 | + | 0.0499642i | ||||
\(162\) | 0.732051i | 0.0575153i | ||||||||
\(163\) | 5.07180 | − | 2.92820i | 0.397254 | − | 0.229355i | −0.288045 | − | 0.957617i | \(-0.593005\pi\) |
0.685298 | + | 0.728262i | \(0.259672\pi\) | |||||||
\(164\) | −2.00000 | + | 3.46410i | −0.156174 | + | 0.270501i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.33975 | + | 5.78461i | 0.259215 | + | 0.448973i | ||||
\(167\) | − | 0.339746i | − | 0.0262903i | −0.999914 | − | 0.0131452i | \(-0.995816\pi\) | ||
0.999914 | − | 0.0131452i | \(-0.00418436\pi\) | |||||||
\(168\) | −5.07180 | + | 4.39230i | −0.391298 | + | 0.338874i | ||||
\(169\) | −19.8564 | −1.52742 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.23205 | − | 2.13397i | 0.0942173 | − | 0.163189i | ||||
\(172\) | −9.12436 | − | 5.26795i | −0.695726 | − | 0.401677i | ||||
\(173\) | −18.5885 | + | 10.7321i | −1.41325 | + | 0.815943i | −0.995693 | − | 0.0927063i | \(-0.970448\pi\) |
−0.417561 | + | 0.908649i | \(0.637115\pi\) | |||||||
\(174\) | 4.53590 | 0.343866 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.92820 | −0.220722 | ||||||||
\(177\) | −8.83013 | + | 5.09808i | −0.663713 | + | 0.383195i | ||||
\(178\) | −5.78461 | − | 3.33975i | −0.433575 | − | 0.250325i | ||||
\(179\) | −5.00000 | + | 8.66025i | −0.373718 | + | 0.647298i | −0.990134 | − | 0.140122i | \(-0.955250\pi\) |
0.616417 | + | 0.787420i | \(0.288584\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.3205 | 0.767117 | 0.383559 | − | 0.923517i | \(-0.374698\pi\) | ||||
0.383559 | + | 0.923517i | \(0.374698\pi\) | |||||||
\(182\) | 2.09808 | + | 10.9019i | 0.155520 | + | 0.808104i | ||||
\(183\) | 4.00000i | 0.295689i | ||||||||
\(184\) | 1.60770 | + | 2.78461i | 0.118521 | + | 0.205284i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.36603 | − | 4.09808i | 0.173485 | − | 0.300486i | ||||
\(187\) | −15.9282 | + | 9.19615i | −1.16479 | + | 0.672489i | ||||
\(188\) | 2.92820i | 0.213561i | ||||||||
\(189\) | −0.866025 | + | 2.50000i | −0.0629941 | + | 0.181848i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.46410 | − | 4.26795i | −0.178296 | − | 0.308818i | 0.763001 | − | 0.646397i | \(-0.223725\pi\) |
−0.941297 | + | 0.337579i | \(0.890392\pi\) | |||||||
\(192\) | 1.85641 | + | 1.07180i | 0.133975 | + | 0.0773503i | ||||
\(193\) | −7.96410 | − | 4.59808i | −0.573269 | − | 0.330977i | 0.185185 | − | 0.982704i | \(-0.440712\pi\) |
−0.758454 | + | 0.651727i | \(0.774045\pi\) | |||||||
\(194\) | 0.392305 | + | 0.679492i | 0.0281658 | + | 0.0487847i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.51666 | + | 3.80385i | −0.679761 | + | 0.271703i | ||||
\(197\) | − | 17.6603i | − | 1.25824i | −0.777308 | − | 0.629121i | \(-0.783415\pi\) | ||
0.777308 | − | 0.629121i | \(-0.216585\pi\) | |||||||
\(198\) | 1.73205 | − | 1.00000i | 0.123091 | − | 0.0710669i | ||||
\(199\) | 11.0000 | − | 19.0526i | 0.779769 | − | 1.35060i | −0.152305 | − | 0.988334i | \(-0.548670\pi\) |
0.932075 | − | 0.362267i | \(-0.117997\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.33013 | + | 2.30385i | 0.0938199 | + | 0.162501i | ||||
\(202\) | − | 7.85641i | − | 0.552775i | ||||||
\(203\) | 15.4904 | + | 5.36603i | 1.08721 | + | 0.376621i | ||||
\(204\) | −9.85641 | −0.690086 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.437822 | + | 0.758330i | −0.0305045 | + | 0.0528354i | ||||
\(207\) | 1.09808 | + | 0.633975i | 0.0763216 | + | 0.0440643i | ||||
\(208\) | −5.32051 | + | 3.07180i | −0.368911 | + | 0.212991i | ||||
\(209\) | −6.73205 | −0.465666 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.9282 | 1.44076 | 0.720378 | − | 0.693581i | \(-0.243968\pi\) | ||||
0.720378 | + | 0.693581i | \(0.243968\pi\) | |||||||
\(212\) | 10.6410 | − | 6.14359i | 0.730828 | − | 0.421944i | ||||
\(213\) | 3.63397 | + | 2.09808i | 0.248996 | + | 0.143758i | ||||
\(214\) | −3.00000 | + | 5.19615i | −0.205076 | + | 0.355202i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.53590 | 0.172546 | ||||||||
\(217\) | 12.9282 | − | 11.1962i | 0.877624 | − | 0.760044i | ||||
\(218\) | − | 8.05256i | − | 0.545388i | ||||||
\(219\) | 2.33013 | + | 4.03590i | 0.157455 | + | 0.272721i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.2942 | + | 33.4186i | −1.29787 | + | 2.24798i | ||||
\(222\) | −4.56218 | + | 2.63397i | −0.306193 | + | 0.176781i | ||||
\(223\) | − | 0.392305i | − | 0.0262707i | −0.999914 | − | 0.0131353i | \(-0.995819\pi\) | ||
0.999914 | − | 0.0131353i | \(-0.00418123\pi\) | |||||||
\(224\) | 10.1436 | + | 11.7128i | 0.677747 | + | 0.782595i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.80385 | + | 3.12436i | 0.119990 | + | 0.207829i | ||||
\(227\) | −13.5622 | − | 7.83013i | −0.900153 | − | 0.519704i | −0.0229034 | − | 0.999738i | \(-0.507291\pi\) |
−0.877250 | + | 0.480034i | \(0.840624\pi\) | |||||||
\(228\) | −3.12436 | − | 1.80385i | −0.206916 | − | 0.119463i | ||||
\(229\) | −1.50000 | − | 2.59808i | −0.0991228 | − | 0.171686i | 0.812199 | − | 0.583380i | \(-0.198270\pi\) |
−0.911322 | + | 0.411695i | \(0.864937\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.09808 | − | 1.36603i | 0.467019 | − | 0.0898779i | ||||
\(232\) | − | 15.7128i | − | 1.03160i | ||||||
\(233\) | 15.0000 | − | 8.66025i | 0.982683 | − | 0.567352i | 0.0796037 | − | 0.996827i | \(-0.474635\pi\) |
0.903079 | + | 0.429474i | \(0.141301\pi\) | |||||||
\(234\) | 2.09808 | − | 3.63397i | 0.137156 | − | 0.237560i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.46410 | + | 12.9282i | 0.485872 | + | 0.841554i | ||||
\(237\) | − | 13.3923i | − | 0.869924i | ||||||
\(238\) | 12.3205 | + | 4.26795i | 0.798620 | + | 0.276650i | ||||
\(239\) | −20.9282 | −1.35373 | −0.676866 | − | 0.736106i | \(-0.736663\pi\) | ||||
−0.676866 | + | 0.736106i | \(0.736663\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.26795 | + | 5.66025i | −0.210507 | + | 0.364609i | −0.951873 | − | 0.306492i | \(-0.900845\pi\) |
0.741366 | + | 0.671101i | \(0.234178\pi\) | |||||||
\(242\) | 2.24167 | + | 1.29423i | 0.144100 | + | 0.0831962i | ||||
\(243\) | 0.866025 | − | 0.500000i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | 5.85641 | 0.374918 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.00000 | −0.127515 | ||||||||
\(247\) | −12.2321 | + | 7.06218i | −0.778307 | + | 0.449356i | ||||
\(248\) | −14.1962 | − | 8.19615i | −0.901457 | − | 0.520456i | ||||
\(249\) | 4.56218 | − | 7.90192i | 0.289116 | − | 0.500764i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.58846 | 0.415860 | 0.207930 | − | 0.978144i | \(-0.433327\pi\) | ||||
0.207930 | + | 0.978144i | \(0.433327\pi\) | |||||||
\(252\) | 3.66025 | + | 1.26795i | 0.230574 | + | 0.0798733i | ||||
\(253\) | − | 3.46410i | − | 0.217786i | ||||||
\(254\) | 5.56218 | + | 9.63397i | 0.349002 | + | 0.604489i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.85641 | − | 10.1436i | 0.366025 | − | 0.633975i | ||||
\(257\) | 10.0981 | − | 5.83013i | 0.629901 | − | 0.363673i | −0.150813 | − | 0.988562i | \(-0.548189\pi\) |
0.780714 | + | 0.624889i | \(0.214856\pi\) | |||||||
\(258\) | − | 5.26795i | − | 0.327968i | ||||||
\(259\) | −18.6962 | + | 3.59808i | −1.16172 | + | 0.223574i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.09808 | − | 5.36603i | −0.191766 | − | 0.332149i | ||||
\(262\) | −5.41154 | − | 3.12436i | −0.334326 | − | 0.193023i | ||||
\(263\) | −10.7321 | − | 6.19615i | −0.661767 | − | 0.382071i | 0.131183 | − | 0.991358i | \(-0.458122\pi\) |
−0.792950 | + | 0.609287i | \(0.791456\pi\) | |||||||
\(264\) | −3.46410 | − | 6.00000i | −0.213201 | − | 0.369274i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.12436 | + | 3.60770i | 0.191567 | + | 0.221202i | ||||
\(267\) | 9.12436i | 0.558401i | ||||||||
\(268\) | 3.37307 | − | 1.94744i | 0.206043 | − | 0.118959i | ||||
\(269\) | −9.73205 | + | 16.8564i | −0.593374 | + | 1.02775i | 0.400401 | + | 0.916340i | \(0.368871\pi\) |
−0.993774 | + | 0.111413i | \(0.964462\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.46410 | − | 14.6603i | −0.514158 | − | 0.890547i | −0.999865 | − | 0.0164256i | \(-0.994771\pi\) |
0.485708 | − | 0.874121i | \(-0.338562\pi\) | |||||||
\(272\) | 7.21539i | 0.437497i | ||||||||
\(273\) | 11.4641 | − | 9.92820i | 0.693839 | − | 0.600882i | ||||
\(274\) | 6.00000 | 0.362473 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.928203 | − | 1.60770i | 0.0558713 | − | 0.0967719i | ||||
\(277\) | −2.30385 | − | 1.33013i | −0.138425 | − | 0.0799196i | 0.429188 | − | 0.903215i | \(-0.358800\pi\) |
−0.567613 | + | 0.823295i | \(0.692133\pi\) | |||||||
\(278\) | 5.02628 | − | 2.90192i | 0.301456 | − | 0.174046i | ||||
\(279\) | −6.46410 | −0.386996 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.8564 | −0.826604 | −0.413302 | − | 0.910594i | \(-0.635625\pi\) | ||||
−0.413302 | + | 0.910594i | \(0.635625\pi\) | |||||||
\(282\) | −1.26795 | + | 0.732051i | −0.0755053 | + | 0.0435930i | ||||
\(283\) | 0.107695 | + | 0.0621778i | 0.00640181 | + | 0.00369609i | 0.503197 | − | 0.864171i | \(-0.332157\pi\) |
−0.496796 | + | 0.867868i | \(0.665490\pi\) | |||||||
\(284\) | 3.07180 | − | 5.32051i | 0.182278 | − | 0.315714i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −11.4641 | −0.677887 | ||||||||
\(287\) | −6.83013 | − | 2.36603i | −0.403170 | − | 0.139662i | ||||
\(288\) | − | 5.85641i | − | 0.345092i | ||||||
\(289\) | 14.1603 | + | 24.5263i | 0.832956 | + | 1.44272i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.535898 | − | 0.928203i | 0.0314149 | − | 0.0544122i | ||||
\(292\) | 5.90897 | − | 3.41154i | 0.345796 | − | 0.199645i | ||||
\(293\) | − | 5.07180i | − | 0.296298i | −0.988965 | − | 0.148149i | \(-0.952669\pi\) | ||
0.988965 | − | 0.148149i | \(-0.0473314\pi\) | |||||||
\(294\) | −4.02628 | − | 3.16987i | −0.234817 | − | 0.184871i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 9.12436 | + | 15.8038i | 0.530342 | + | 0.918580i | ||||
\(297\) | −2.36603 | − | 1.36603i | −0.137291 | − | 0.0792648i | ||||
\(298\) | −13.8564 | − | 8.00000i | −0.802680 | − | 0.463428i | ||||
\(299\) | −3.63397 | − | 6.29423i | −0.210158 | − | 0.364005i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.23205 | − | 17.9904i | 0.359209 | − | 1.03695i | ||||
\(302\) | 3.60770i | 0.207600i | ||||||||
\(303\) | −9.29423 | + | 5.36603i | −0.533939 | + | 0.308270i | ||||
\(304\) | −1.32051 | + | 2.28719i | −0.0757363 | + | 0.131179i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.46410 | − | 4.26795i | −0.140863 | − | 0.243982i | ||||
\(307\) | − | 7.87564i | − | 0.449487i | −0.974418 | − | 0.224743i | \(-0.927846\pi\) | ||
0.974418 | − | 0.224743i | \(-0.0721544\pi\) | |||||||
\(308\) | −2.00000 | − | 10.3923i | −0.113961 | − | 0.592157i | ||||
\(309\) | 1.19615 | 0.0680467 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.56218 | − | 13.0981i | 0.428812 | − | 0.742724i | −0.567956 | − | 0.823059i | \(-0.692266\pi\) |
0.996768 | + | 0.0803351i | \(0.0255990\pi\) | |||||||
\(312\) | −12.5885 | − | 7.26795i | −0.712681 | − | 0.411467i | ||||
\(313\) | −4.03590 | + | 2.33013i | −0.228122 | + | 0.131707i | −0.609706 | − | 0.792628i | \(-0.708712\pi\) |
0.381583 | + | 0.924335i | \(0.375379\pi\) | |||||||
\(314\) | 10.5359 | 0.594575 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −19.6077 | −1.10302 | ||||||||
\(317\) | 26.3660 | − | 15.2224i | 1.48086 | − | 0.854977i | 0.481099 | − | 0.876666i | \(-0.340238\pi\) |
0.999765 | + | 0.0216894i | \(0.00690451\pi\) | |||||||
\(318\) | 5.32051 | + | 3.07180i | 0.298359 | + | 0.172258i | ||||
\(319\) | −8.46410 | + | 14.6603i | −0.473899 | + | 0.820817i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.19615 | 0.457465 | ||||||||
\(322\) | −1.85641 | + | 1.60770i | −0.103453 | + | 0.0895933i | ||||
\(323\) | 16.5885i | 0.923006i | ||||||||
\(324\) | −0.732051 | − | 1.26795i | −0.0406695 | − | 0.0704416i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.14359 | − | 3.71281i | 0.118723 | − | 0.205634i | ||||
\(327\) | −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 | ||||||||
\(331\) | −10.9641 | − | 18.9904i | −0.602642 | − | 1.04381i | −0.992419 | − | 0.122897i | \(-0.960782\pi\) |
0.389778 | − | 0.920909i | \(-0.372552\pi\) | |||||||
\(332\) | −11.5692 | − | 6.67949i | −0.634943 | − | 0.366585i | ||||
\(333\) | 6.23205 | + | 3.59808i | 0.341514 | + | 0.197173i | ||||
\(334\) | −0.124356 | − | 0.215390i | −0.00680444 | − | 0.0117856i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.928203 | − | 2.67949i | 0.0506376 | − | 0.146178i | ||||
\(337\) | − | 33.9808i | − | 1.85105i | −0.378686 | − | 0.925525i | \(-0.623624\pi\) | ||
0.378686 | − | 0.925525i | \(-0.376376\pi\) | |||||||
\(338\) | −12.5885 | + | 7.26795i | −0.684722 | + | 0.395324i | ||||
\(339\) | 2.46410 | − | 4.26795i | 0.133832 | − | 0.231803i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.83013 | + | 15.2942i | 0.478178 | + | 0.828229i | ||||
\(342\) | − | 1.80385i | − | 0.0975409i | ||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | −18.2487 | −0.983905 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.85641 | + | 13.6077i | −0.422363 | + | 0.731554i | ||||
\(347\) | 30.2487 | + | 17.4641i | 1.62384 | + | 0.937522i | 0.985881 | + | 0.167449i | \(0.0535528\pi\) |
0.637955 | + | 0.770074i | \(0.279781\pi\) | |||||||
\(348\) | −7.85641 | + | 4.53590i | −0.421148 | + | 0.243150i | ||||
\(349\) | −22.0000 | −1.17763 | −0.588817 | − | 0.808267i | \(-0.700406\pi\) | ||||
−0.588817 | + | 0.808267i | \(0.700406\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.73205 | −0.305954 | ||||||||
\(352\) | −13.8564 | + | 8.00000i | −0.738549 | + | 0.426401i | ||||
\(353\) | 18.2942 | + | 10.5622i | 0.973704 | + | 0.562168i | 0.900363 | − | 0.435139i | \(-0.143301\pi\) |
0.0733402 | + | 0.997307i | \(0.476634\pi\) | |||||||
\(354\) | −3.73205 | + | 6.46410i | −0.198356 | + | 0.343563i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 13.3590 | 0.708025 | ||||||||
\(357\) | −3.36603 | − | 17.4904i | −0.178149 | − | 0.925689i | ||||
\(358\) | 7.32051i | 0.386901i | ||||||||
\(359\) | −2.36603 | − | 4.09808i | −0.124874 | − | 0.216288i | 0.796810 | − | 0.604230i | \(-0.206519\pi\) |
−0.921684 | + | 0.387942i | \(0.873186\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.46410 | − | 11.1962i | 0.340216 | − | 0.589271i | ||||
\(362\) | 6.54294 | − | 3.77757i | 0.343889 | − | 0.198545i | ||||
\(363\) | − | 3.53590i | − | 0.185587i | ||||||
\(364\) | −14.5359 | − | 16.7846i | −0.761888 | − | 0.879753i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.46410 | + | 2.53590i | 0.0765298 | + | 0.132554i | ||||
\(367\) | −0.696152 | − | 0.401924i | −0.0363389 | − | 0.0209803i | 0.481721 | − | 0.876325i | \(-0.340012\pi\) |
−0.518059 | + | 0.855345i | \(0.673345\pi\) | |||||||
\(368\) | −1.17691 | − | 0.679492i | −0.0613509 | − | 0.0354210i | ||||
\(369\) | 1.36603 | + | 2.36603i | 0.0711124 | + | 0.123170i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.5359 | + | 16.7846i | 0.754666 | + | 0.871414i | ||||
\(372\) | 9.46410i | 0.490691i | ||||||||
\(373\) | 16.0359 | − | 9.25833i | 0.830307 | − | 0.479378i | −0.0236505 | − | 0.999720i | \(-0.507529\pi\) |
0.853958 | + | 0.520342i | \(0.174196\pi\) | |||||||
\(374\) | −6.73205 | + | 11.6603i | −0.348106 | + | 0.602937i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.53590 | + | 4.39230i | 0.130779 | + | 0.226516i | ||||
\(377\) | 35.5167i | 1.82920i | ||||||||
\(378\) | 0.366025 | + | 1.90192i | 0.0188263 | + | 0.0978244i | ||||
\(379\) | 28.3205 | 1.45473 | 0.727363 | − | 0.686253i | \(-0.240745\pi\) | ||||
0.727363 | + | 0.686253i | \(0.240745\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.59808 | − | 13.1603i | 0.389261 | − | 0.674220i | ||||
\(382\) | −3.12436 | − | 1.80385i | −0.159856 | − | 0.0922929i | ||||
\(383\) | −9.80385 | + | 5.66025i | −0.500953 | + | 0.289225i | −0.729107 | − | 0.684400i | \(-0.760064\pi\) |
0.228154 | + | 0.973625i | \(0.426731\pi\) | |||||||
\(384\) | −10.1436 | −0.517638 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.73205 | −0.342652 | ||||||||
\(387\) | −6.23205 | + | 3.59808i | −0.316793 | + | 0.182900i | ||||
\(388\) | −1.35898 | − | 0.784610i | −0.0689920 | − | 0.0398325i | ||||
\(389\) | 18.2942 | − | 31.6865i | 0.927554 | − | 1.60657i | 0.140153 | − | 0.990130i | \(-0.455240\pi\) |
0.787401 | − | 0.616441i | \(-0.211426\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.53590 | −0.431679 | ||||||||
\(392\) | −10.9808 | + | 13.9474i | −0.554612 | + | 0.704452i | ||||
\(393\) | 8.53590i | 0.430579i | ||||||||
\(394\) | −6.46410 | − | 11.1962i | −0.325657 | − | 0.564054i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.00000 | + | 3.46410i | −0.100504 | + | 0.174078i | ||||
\(397\) | −18.0167 | + | 10.4019i | −0.904230 | + | 0.522058i | −0.878570 | − | 0.477613i | \(-0.841502\pi\) |
−0.0256600 | + | 0.999671i | \(0.508169\pi\) | |||||||
\(398\) | − | 16.1051i | − | 0.807277i | ||||||
\(399\) | 2.13397 | − | 6.16025i | 0.106832 | − | 0.308398i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.19615 | − | 3.80385i | −0.109671 | − | 0.189955i | 0.805966 | − | 0.591962i | \(-0.201646\pi\) |
−0.915637 | + | 0.402006i | \(0.868313\pi\) | |||||||
\(402\) | 1.68653 | + | 0.973721i | 0.0841166 | + | 0.0485648i | ||||
\(403\) | 32.0885 | + | 18.5263i | 1.59844 | + | 0.922860i | ||||
\(404\) | 7.85641 | + | 13.6077i | 0.390871 | + | 0.677008i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 11.7846 | − | 2.26795i | 0.584860 | − | 0.112556i | ||||
\(407\) | − | 19.6603i | − | 0.974523i | ||||||
\(408\) | −14.7846 | + | 8.53590i | −0.731947 | + | 0.422590i | ||||
\(409\) | 15.4282 | − | 26.7224i | 0.762876 | − | 1.32134i | −0.178487 | − | 0.983942i | \(-0.557120\pi\) |
0.941362 | − | 0.337397i | \(-0.109546\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.09808 | − | 7.09808i | −0.202143 | − | 0.350122i | ||||
\(412\) | − | 1.75129i | − | 0.0862798i | ||||||
\(413\) | −20.3923 | + | 17.6603i | −1.00344 | + | 0.869004i | ||||
\(414\) | 0.928203 | 0.0456187 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −16.7846 | + | 29.0718i | −0.822933 | + | 1.42536i | ||||
\(417\) | −6.86603 | − | 3.96410i | −0.336231 | − | 0.194123i | ||||
\(418\) | −4.26795 | + | 2.46410i | −0.208752 | + | 0.120523i | ||||
\(419\) | 28.5359 | 1.39407 | 0.697035 | − | 0.717037i | \(-0.254502\pi\) | ||||
0.697035 | + | 0.717037i | \(0.254502\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.9282 | 0.678819 | 0.339410 | − | 0.940639i | \(-0.389773\pi\) | ||||
0.339410 | + | 0.940639i | \(0.389773\pi\) | |||||||
\(422\) | 13.2679 | − | 7.66025i | 0.645874 | − | 0.372895i | ||||
\(423\) | 1.73205 | + | 1.00000i | 0.0842152 | + | 0.0486217i | ||||
\(424\) | 10.6410 | − | 18.4308i | 0.516773 | − | 0.895078i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.07180 | 0.148829 | ||||||||
\(427\) | 2.00000 | + | 10.3923i | 0.0967868 | + | 0.502919i | ||||
\(428\) | − | 12.0000i | − | 0.580042i | ||||||
\(429\) | 7.83013 | + | 13.5622i | 0.378042 | + | 0.654788i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.66025 | − | 15.0000i | 0.417150 | − | 0.722525i | −0.578502 | − | 0.815681i | \(-0.696362\pi\) |
0.995651 | + | 0.0931566i | \(0.0296957\pi\) | |||||||
\(432\) | −0.928203 | + | 0.535898i | −0.0446582 | + | 0.0257834i | ||||
\(433\) | − | 4.80385i | − | 0.230858i | −0.993316 | − | 0.115429i | \(-0.963176\pi\) | ||
0.993316 | − | 0.115429i | \(-0.0368243\pi\) | |||||||
\(434\) | 4.09808 | − | 11.8301i | 0.196714 | − | 0.567864i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.05256 | + | 13.9474i | 0.385648 | + | 0.667961i | ||||
\(437\) | −2.70577 | − | 1.56218i | −0.129435 | − | 0.0747291i | ||||
\(438\) | 2.95448 | + | 1.70577i | 0.141171 | + | 0.0815049i | ||||
\(439\) | 3.73205 | + | 6.46410i | 0.178121 | + | 0.308515i | 0.941237 | − | 0.337747i | \(-0.109665\pi\) |
−0.763116 | + | 0.646262i | \(0.776331\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00000 | + | 6.92820i | −0.0476190 | + | 0.329914i | ||||
\(442\) | 28.2487i | 1.34365i | ||||||||
\(443\) | −2.19615 | + | 1.26795i | −0.104342 | + | 0.0602421i | −0.551263 | − | 0.834331i | \(-0.685854\pi\) |
0.446921 | + | 0.894574i | \(0.352521\pi\) | |||||||
\(444\) | 5.26795 | − | 9.12436i | 0.250006 | − | 0.433023i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.143594 | − | 0.248711i | −0.00679935 | − | 0.0117768i | ||||
\(447\) | 21.8564i | 1.03377i | ||||||||
\(448\) | 5.35898 | + | 1.85641i | 0.253188 | + | 0.0877070i | ||||
\(449\) | 8.14359 | 0.384320 | 0.192160 | − | 0.981364i | \(-0.438451\pi\) | ||||
0.192160 | + | 0.981364i | \(0.438451\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.73205 | − | 6.46410i | 0.175735 | − | 0.304383i | ||||
\(452\) | −6.24871 | − | 3.60770i | −0.293915 | − | 0.169692i | ||||
\(453\) | 4.26795 | − | 2.46410i | 0.200526 | − | 0.115774i | ||||
\(454\) | −11.4641 | −0.538037 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.24871 | −0.292623 | ||||||||
\(457\) | 0.571797 | − | 0.330127i | 0.0267475 | − | 0.0154427i | −0.486567 | − | 0.873643i | \(-0.661751\pi\) |
0.513314 | + | 0.858201i | \(0.328418\pi\) | |||||||
\(458\) | −1.90192 | − | 1.09808i | −0.0888711 | − | 0.0513097i | ||||
\(459\) | −3.36603 | + | 5.83013i | −0.157113 | + | 0.272127i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −34.9808 | −1.62922 | −0.814608 | − | 0.580012i | \(-0.803048\pi\) | ||||
−0.814608 | + | 0.580012i | \(0.803048\pi\) | |||||||
\(462\) | 4.00000 | − | 3.46410i | 0.186097 | − | 0.161165i | ||||
\(463\) | − | 22.2679i | − | 1.03488i | −0.855720 | − | 0.517440i | \(-0.826885\pi\) | ||
0.855720 | − | 0.517440i | \(-0.173115\pi\) | |||||||
\(464\) | 3.32051 | + | 5.75129i | 0.154151 | + | 0.266997i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.33975 | − | 10.9808i | 0.293683 | − | 0.508674i | ||||
\(467\) | −24.1244 | + | 13.9282i | −1.11634 | + | 0.644520i | −0.940465 | − | 0.339892i | \(-0.889610\pi\) |
−0.175877 | + | 0.984412i | \(0.556276\pi\) | |||||||
\(468\) | 8.39230i | 0.387934i | ||||||||
\(469\) | 4.60770 | + | 5.32051i | 0.212764 | + | 0.245678i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.19615 | − | 12.4641i | −0.331581 | − | 0.574315i | ||||
\(472\) | 22.3923 | + | 12.9282i | 1.03069 | + | 0.595069i | ||||
\(473\) | 17.0263 | + | 9.83013i | 0.782869 | + | 0.451990i | ||||
\(474\) | −4.90192 | − | 8.49038i | −0.225153 | − | 0.389976i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −25.6077 | + | 4.92820i | −1.17373 | + | 0.225884i | ||||
\(477\) | − | 8.39230i | − | 0.384257i | ||||||
\(478\) | −13.2679 | + | 7.66025i | −0.606862 | + | 0.350372i | ||||
\(479\) | −16.3923 | + | 28.3923i | −0.748984 | + | 1.29728i | 0.199327 | + | 0.979933i | \(0.436124\pi\) |
−0.948310 | + | 0.317344i | \(0.897209\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.6244 | − | 35.7224i | −0.940390 | − | 1.62880i | ||||
\(482\) | 4.78461i | 0.217933i | ||||||||
\(483\) | 3.16987 | + | 1.09808i | 0.144234 | + | 0.0499642i | ||||
\(484\) | −5.17691 | −0.235314 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.366025 | − | 0.633975i | 0.0166032 | − | 0.0287577i | ||||
\(487\) | 27.3564 | + | 15.7942i | 1.23964 | + | 0.715705i | 0.969020 | − | 0.246982i | \(-0.0794389\pi\) |
0.270617 | + | 0.962687i | \(0.412772\pi\) | |||||||
\(488\) | 8.78461 | − | 5.07180i | 0.397661 | − | 0.229589i | ||||
\(489\) | −5.85641 | −0.264836 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.2487 | 0.462518 | 0.231259 | − | 0.972892i | \(-0.425716\pi\) | ||||
0.231259 | + | 0.972892i | \(0.425716\pi\) | |||||||
\(492\) | 3.46410 | − | 2.00000i | 0.156174 | − | 0.0901670i | ||||
\(493\) | 36.1244 | + | 20.8564i | 1.62696 | + | 0.939325i | ||||
\(494\) | −5.16987 | + | 8.95448i | −0.232604 | + | 0.402881i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.92820 | 0.311086 | ||||||||
\(497\) | 10.4904 | + | 3.63397i | 0.470558 | + | 0.163006i | ||||
\(498\) | − | 6.67949i | − | 0.299315i | ||||||
\(499\) | −10.2321 | − | 17.7224i | −0.458050 | − | 0.793365i | 0.540808 | − | 0.841146i | \(-0.318118\pi\) |
−0.998858 | + | 0.0477808i | \(0.984785\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.169873 | + | 0.294229i | −0.00758937 | + | 0.0131452i | ||||
\(502\) | 4.17691 | − | 2.41154i | 0.186425 | − | 0.107632i | ||||
\(503\) | 6.39230i | 0.285019i | 0.989793 | + | 0.142509i | \(0.0455171\pi\) | ||||
−0.989793 | + | 0.142509i | \(0.954483\pi\) | |||||||
\(504\) | 6.58846 | − | 1.26795i | 0.293473 | − | 0.0564789i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.26795 | − | 2.19615i | −0.0563672 | − | 0.0976309i | ||||
\(507\) | 17.1962 | + | 9.92820i | 0.763708 | + | 0.440927i | ||||
\(508\) | −19.2679 | − | 11.1244i | −0.854877 | − | 0.493563i | ||||
\(509\) | 5.73205 | + | 9.92820i | 0.254069 | + | 0.440060i | 0.964642 | − | 0.263563i | \(-0.0848977\pi\) |
−0.710573 | + | 0.703623i | \(0.751564\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.07180 | + | 9.32051i | 0.357075 | + | 0.412315i | ||||
\(512\) | 11.7128i | 0.517638i | ||||||||
\(513\) | −2.13397 | + | 1.23205i | −0.0942173 | + | 0.0543964i | ||||
\(514\) | 4.26795 | − | 7.39230i | 0.188251 | − | 0.326061i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.26795 | + | 9.12436i | 0.231909 | + | 0.401677i | ||||
\(517\) | − | 5.46410i | − | 0.240311i | ||||||
\(518\) | −10.5359 | + | 9.12436i | −0.462921 | + | 0.400901i | ||||
\(519\) | 21.4641 | 0.942169 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.732051 | + | 1.26795i | −0.0320717 | + | 0.0555499i | −0.881616 | − | 0.471968i | \(-0.843544\pi\) |
0.849544 | + | 0.527518i | \(0.176877\pi\) | |||||||
\(522\) | −3.92820 | − | 2.26795i | −0.171933 | − | 0.0992654i | ||||
\(523\) | 21.0167 | − | 12.1340i | 0.918994 | − | 0.530582i | 0.0356803 | − | 0.999363i | \(-0.488640\pi\) |
0.883314 | + | 0.468782i | \(0.155307\pi\) | |||||||
\(524\) | 12.4974 | 0.545952 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.07180 | −0.395549 | ||||||||
\(527\) | 37.6865 | − | 21.7583i | 1.64165 | − | 0.947808i | ||||
\(528\) | 2.53590 | + | 1.46410i | 0.110361 | + | 0.0637168i | ||||
\(529\) | −10.6962 | + | 18.5263i | −0.465050 | + | 0.805490i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.1962 | 0.442475 | ||||||||
\(532\) | −9.01924 | − | 3.12436i | −0.391034 | − | 0.135458i | ||||
\(533\) | − | 15.6603i | − | 0.678321i | ||||||
\(534\) | 3.33975 | + | 5.78461i | 0.144525 | + | 0.250325i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.37307 | − | 5.84232i | 0.145694 | − | 0.252350i | ||||
\(537\) | 8.66025 | − | 5.00000i | 0.373718 | − | 0.215766i | ||||
\(538\) | 14.2487i | 0.614306i | ||||||||
\(539\) | 17.7583 | − | 7.09808i | 0.764905 | − | 0.305736i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.8923 | + | 30.9904i | 0.769250 | + | 1.33238i | 0.937970 | + | 0.346716i | \(0.112703\pi\) |
−0.168720 | + | 0.985664i | \(0.553963\pi\) | |||||||
\(542\) | −10.7321 | − | 6.19615i | −0.460981 | − | 0.266148i | ||||
\(543\) | −8.93782 | − | 5.16025i | −0.383559 | − | 0.221448i | ||||
\(544\) | 19.7128 | + | 34.1436i | 0.845180 | + | 1.46389i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.63397 | − | 10.4904i | 0.155520 | − | 0.448947i | ||||
\(547\) | 22.2487i | 0.951286i | 0.879638 | + | 0.475643i | \(0.157785\pi\) | ||||
−0.879638 | + | 0.475643i | \(0.842215\pi\) | |||||||
\(548\) | −10.3923 | + | 6.00000i | −0.443937 | + | 0.256307i | ||||
\(549\) | 2.00000 | − | 3.46410i | 0.0853579 | − | 0.147844i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.63397 | + | 13.2224i | 0.325218 | + | 0.563295i | ||||
\(552\) | − | 3.21539i | − | 0.136856i | ||||||
\(553\) | −6.69615 | − | 34.7942i | −0.284749 | − | 1.47960i | ||||
\(554\) | −1.94744 | −0.0827388 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.80385 | + | 10.0526i | −0.246138 | + | 0.426323i | ||||
\(557\) | 23.1962 | + | 13.3923i | 0.982853 | + | 0.567450i | 0.903130 | − | 0.429367i | \(-0.141263\pi\) |
0.0797224 | + | 0.996817i | \(0.474597\pi\) | |||||||
\(558\) | −4.09808 | + | 2.36603i | −0.173485 | + | 0.100162i | ||||
\(559\) | 41.2487 | 1.74463 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18.3923 | 0.776524 | ||||||||
\(562\) | −8.78461 | + | 5.07180i | −0.370556 | + | 0.213941i | ||||
\(563\) | −15.5885 | − | 9.00000i | −0.656975 | − | 0.379305i | 0.134148 | − | 0.990961i | \(-0.457170\pi\) |
−0.791123 | + | 0.611656i | \(0.790503\pi\) | |||||||
\(564\) | 1.46410 | − | 2.53590i | 0.0616498 | − | 0.106781i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.0910347 | 0.00382647 | ||||||||
\(567\) | 2.00000 | − | 1.73205i | 0.0839921 | − | 0.0727393i | ||||
\(568\) | − | 10.6410i | − | 0.446487i | ||||||
\(569\) | −13.2224 | − | 22.9019i | −0.554313 | − | 0.960099i | −0.997957 | − | 0.0638952i | \(-0.979648\pi\) |
0.443643 | − | 0.896203i | \(-0.353686\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.6962 | + | 34.1147i | −0.824258 | + | 1.42766i | 0.0782265 | + | 0.996936i | \(0.475074\pi\) |
−0.902485 | + | 0.430722i | \(0.858259\pi\) | |||||||
\(572\) | 19.8564 | − | 11.4641i | 0.830238 | − | 0.479338i | ||||
\(573\) | 4.92820i | 0.205879i | ||||||||
\(574\) | −5.19615 | + | 1.00000i | −0.216883 | + | 0.0417392i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.07180 | − | 1.85641i | −0.0446582 | − | 0.0773503i | ||||
\(577\) | −9.82051 | − | 5.66987i | −0.408833 | − | 0.236040i | 0.281455 | − | 0.959574i | \(-0.409183\pi\) |
−0.690288 | + | 0.723534i | \(0.742516\pi\) | |||||||
\(578\) | 17.9545 | + | 10.3660i | 0.746808 | + | 0.431170i | ||||
\(579\) | 4.59808 | + | 7.96410i | 0.191090 | + | 0.330977i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.90192 | − | 22.8109i | 0.327827 | − | 0.946355i | ||||
\(582\) | − | 0.784610i | − | 0.0325231i | ||||||
\(583\) | −19.8564 | + | 11.4641i | −0.822368 | + | 0.474795i | ||||
\(584\) | 5.90897 | − | 10.2346i | 0.244515 | − | 0.423512i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.85641 | − | 3.21539i | −0.0766874 | − | 0.132827i | ||||
\(587\) | 37.2679i | 1.53821i | 0.639121 | + | 0.769106i | \(0.279298\pi\) | ||||
−0.639121 | + | 0.769106i | \(0.720702\pi\) | |||||||
\(588\) | 10.1436 | + | 1.46410i | 0.418315 | + | 0.0603785i | ||||
\(589\) | 15.9282 | 0.656310 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.83013 | + | 15.2942i | −0.363223 | + | 0.629121i | ||||
\(592\) | −6.67949 | − | 3.85641i | −0.274525 | − | 0.158497i | ||||
\(593\) | 32.8301 | − | 18.9545i | 1.34817 | − | 0.778367i | 0.360181 | − | 0.932882i | \(-0.382715\pi\) |
0.987990 | + | 0.154515i | \(0.0493815\pi\) | |||||||
\(594\) | −2.00000 | −0.0820610 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 32.0000 | 1.31077 | ||||||||
\(597\) | −19.0526 | + | 11.0000i | −0.779769 | + | 0.450200i | ||||
\(598\) | −4.60770 | − | 2.66025i | −0.188423 | − | 0.108786i | ||||
\(599\) | 5.12436 | − | 8.87564i | 0.209375 | − | 0.362649i | −0.742142 | − | 0.670242i | \(-0.766190\pi\) |
0.951518 | + | 0.307593i | \(0.0995236\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.9282 | −0.568143 | −0.284072 | − | 0.958803i | \(-0.591685\pi\) | ||||
−0.284072 | + | 0.958803i | \(0.591685\pi\) | |||||||
\(602\) | −2.63397 | − | 13.6865i | −0.107353 | − | 0.557821i | ||||
\(603\) | − | 2.66025i | − | 0.108334i | ||||||
\(604\) | −3.60770 | − | 6.24871i | −0.146795 | − | 0.254256i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.92820 | + | 6.80385i | −0.159572 | + | 0.276387i | ||||
\(607\) | −6.23205 | + | 3.59808i | −0.252951 | + | 0.146041i | −0.621115 | − | 0.783720i | \(-0.713320\pi\) |
0.368164 | + | 0.929761i | \(0.379987\pi\) | |||||||
\(608\) | 14.4308i | 0.585245i | ||||||||
\(609\) | −10.7321 | − | 12.3923i | −0.434885 | − | 0.502162i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.73205 | − | 9.92820i | −0.231894 | − | 0.401652i | ||||
\(612\) | 8.53590 | + | 4.92820i | 0.345043 | + | 0.199211i | ||||
\(613\) | −11.3205 | − | 6.53590i | −0.457231 | − | 0.263982i | 0.253648 | − | 0.967297i | \(-0.418369\pi\) |
−0.710879 | + | 0.703314i | \(0.751703\pi\) | |||||||
\(614\) | −2.88269 | − | 4.99296i | −0.116336 | − | 0.201499i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.0000 | − | 13.8564i | −0.483494 | − | 0.558291i | ||||
\(617\) | 12.2487i | 0.493115i | 0.969128 | + | 0.246557i | \(0.0792993\pi\) | ||||
−0.969128 | + | 0.246557i | \(0.920701\pi\) | |||||||
\(618\) | 0.758330 | − | 0.437822i | 0.0305045 | − | 0.0176118i | ||||
\(619\) | −21.9641 | + | 38.0429i | −0.882812 | + | 1.52907i | −0.0346105 | + | 0.999401i | \(0.511019\pi\) |
−0.848201 | + | 0.529674i | \(0.822314\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.633975 | − | 1.09808i | −0.0254405 | − | 0.0440643i | ||||
\(622\) | − | 11.0718i | − | 0.443939i | ||||||
\(623\) | 4.56218 | + | 23.7058i | 0.182780 | + | 0.949752i | ||||
\(624\) | 6.14359 | 0.245941 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.70577 | + | 2.95448i | −0.0681763 | + | 0.118085i | ||||
\(627\) | 5.83013 | + | 3.36603i | 0.232833 | + | 0.134426i | ||||
\(628\) | −18.2487 | + | 10.5359i | −0.728203 | + | 0.420428i | ||||
\(629\) | −48.4449 | −1.93162 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.21539 | 0.287240 | 0.143620 | − | 0.989633i | \(-0.454126\pi\) | ||||
0.143620 | + | 0.989633i | \(0.454126\pi\) | |||||||
\(632\) | −29.4115 | + | 16.9808i | −1.16993 | + | 0.675458i | ||||
\(633\) | −18.1244 | − | 10.4641i | −0.720378 | − | 0.415911i | ||||
\(634\) | 11.1436 | − | 19.3013i | 0.442569 | − | 0.766551i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −12.2872 | −0.487219 | ||||||||
\(637\) | 24.8205 | − | 31.5263i | 0.983424 | − | 1.24912i | ||||
\(638\) | 12.3923i | 0.490616i | ||||||||
\(639\) | −2.09808 | − | 3.63397i | −0.0829986 | − | 0.143758i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.09808 | + | 12.2942i | −0.280357 | + | 0.485593i | −0.971473 | − | 0.237151i | \(-0.923786\pi\) |
0.691116 | + | 0.722744i | \(0.257120\pi\) | |||||||
\(642\) | 5.19615 | − | 3.00000i | 0.205076 | − | 0.118401i | ||||
\(643\) | 40.5167i | 1.59782i | 0.601450 | + | 0.798911i | \(0.294590\pi\) | ||||
−0.601450 | + | 0.798911i | \(0.705410\pi\) | |||||||
\(644\) | 1.60770 | − | 4.64102i | 0.0633521 | − | 0.182882i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.07180 | + | 10.5167i | 0.238892 | + | 0.413772i | ||||
\(647\) | −32.8301 | − | 18.9545i | −1.29069 | − | 0.745178i | −0.311910 | − | 0.950112i | \(-0.600969\pi\) |
−0.978776 | + | 0.204934i | \(0.934302\pi\) | |||||||
\(648\) | −2.19615 | − | 1.26795i | −0.0862730 | − | 0.0498097i | ||||
\(649\) | −13.9282 | − | 24.1244i | −0.546730 | − | 0.946964i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.7942 | + | 3.23205i | −0.658218 | + | 0.126674i | ||||
\(652\) | 8.57437i | 0.335798i | ||||||||
\(653\) | 11.6147 | − | 6.70577i | 0.454520 | − | 0.262417i | −0.255217 | − | 0.966884i | \(-0.582147\pi\) |
0.709737 | + | 0.704467i | \(0.248814\pi\) | |||||||
\(654\) | −4.02628 | + | 6.97372i | −0.157440 | + | 0.272694i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.46410 | − | 2.53590i | −0.0571636 | − | 0.0990102i | ||||
\(657\) | − | 4.66025i | − | 0.181814i | ||||||
\(658\) | −2.92820 | + | 2.53590i | −0.114153 | + | 0.0988596i | ||||
\(659\) | 10.9282 | 0.425702 | 0.212851 | − | 0.977085i | \(-0.431725\pi\) | ||||
0.212851 | + | 0.977085i | \(0.431725\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.76795 | + | 3.06218i | −0.0687653 | + | 0.119105i | −0.898358 | − | 0.439264i | \(-0.855239\pi\) |
0.829593 | + | 0.558369i | \(0.188573\pi\) | |||||||
\(662\) | −13.9019 | − | 8.02628i | −0.540314 | − | 0.311950i | ||||
\(663\) | 33.4186 | − | 19.2942i | 1.29787 | − | 0.749326i | ||||
\(664\) | −23.1384 | −0.897946 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.26795 | 0.204129 | ||||||||
\(667\) | −6.80385 | + | 3.92820i | −0.263446 | + | 0.152101i | ||||
\(668\) | 0.430781 | + | 0.248711i | 0.0166674 | + | 0.00962293i | ||||
\(669\) | −0.196152 | + | 0.339746i | −0.00758369 | + | 0.0131353i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.9282 | −0.421879 | ||||||||
\(672\) | −2.92820 | − | 15.2154i | −0.112958 | − | 0.586946i | ||||
\(673\) | 44.6603i | 1.72153i | 0.509006 | + | 0.860763i | \(0.330013\pi\) | ||||
−0.509006 | + | 0.860763i | \(0.669987\pi\) | |||||||
\(674\) | −12.4378 | − | 21.5429i | −0.479087 | − | 0.829803i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 14.5359 | − | 25.1769i | 0.559073 | − | 0.968343i | ||||
\(677\) | −7.68653 | + | 4.43782i | −0.295417 | + | 0.170559i | −0.640382 | − | 0.768056i | \(-0.721224\pi\) |
0.344965 | + | 0.938616i | \(0.387891\pi\) | |||||||
\(678\) | − | 3.60770i | − | 0.138553i | ||||||
\(679\) | 0.928203 | − | 2.67949i | 0.0356212 | − | 0.102829i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.83013 | + | 13.5622i | 0.300051 | + | 0.519704i | ||||
\(682\) | 11.1962 | + | 6.46410i | 0.428723 | + | 0.247523i | ||||
\(683\) | 8.70577 | + | 5.02628i | 0.333117 | + | 0.192325i | 0.657224 | − | 0.753695i | \(-0.271730\pi\) |
−0.324107 | + | 0.946020i | \(0.605064\pi\) | |||||||
\(684\) | 1.80385 | + | 3.12436i | 0.0689718 | + | 0.119463i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −12.0455 | − | 6.22243i | −0.459900 | − | 0.237574i | ||||
\(687\) | 3.00000i | 0.114457i | ||||||||
\(688\) | 6.67949 | − | 3.85641i | 0.254653 | − | 0.147024i | ||||
\(689\) | −24.0526 | + | 41.6603i | −0.916330 | + | 1.58713i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.42820 | + | 16.3301i | 0.358666 | + | 0.621227i | 0.987738 | − | 0.156119i | \(-0.0498985\pi\) |
−0.629072 | + | 0.777347i | \(0.716565\pi\) | |||||||
\(692\) | − | 31.4256i | − | 1.19462i | ||||||
\(693\) | −6.83013 | − | 2.36603i | −0.259455 | − | 0.0898779i | ||||
\(694\) | 25.5692 | 0.970594 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7.85641 | + | 13.6077i | −0.297796 | + | 0.515798i | ||||
\(697\) | −15.9282 | − | 9.19615i | −0.603324 | − | 0.348329i | ||||
\(698\) | −13.9474 | + | 8.05256i | −0.527918 | + | 0.304794i | ||||
\(699\) | −17.3205 | −0.655122 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.5885 | 0.853154 | 0.426577 | − | 0.904451i | \(-0.359719\pi\) | ||||
0.426577 | + | 0.904451i | \(0.359719\pi\) | |||||||
\(702\) | −3.63397 | + | 2.09808i | −0.137156 | + | 0.0791868i | ||||
\(703\) | −15.3564 | − | 8.86603i | −0.579178 | − | 0.334388i | ||||
\(704\) | −2.92820 | + | 5.07180i | −0.110361 | + | 0.191151i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.4641 | 0.581999 | ||||||||
\(707\) | −21.4641 | + | 18.5885i | −0.807241 | + | 0.699091i | ||||
\(708\) | − | 14.9282i | − | 0.561036i | ||||||
\(709\) | −7.46410 | − | 12.9282i | −0.280320 | − | 0.485529i | 0.691143 | − | 0.722718i | \(-0.257107\pi\) |
−0.971464 | + | 0.237189i | \(0.923774\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.69615 | + | 11.5981i | −0.251125 | + | 0.434962i | ||||
\(712\) | 20.0385 | − | 11.5692i | 0.750974 | − | 0.433575i | ||||
\(713\) | 8.19615i | 0.306948i | ||||||||
\(714\) | −8.53590 | − | 9.85641i | −0.319448 | − | 0.368867i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.32051 | − | 12.6795i | −0.273580 | − | 0.473855i | ||||
\(717\) | 18.1244 | + | 10.4641i | 0.676866 | + | 0.390789i | ||||
\(718\) | −3.00000 | − | 1.73205i | −0.111959 | − | 0.0646396i | ||||
\(719\) | −13.7321 | − | 23.7846i | −0.512119 | − | 0.887016i | −0.999901 | − | 0.0140509i | \(-0.995527\pi\) |
0.487782 | − | 0.872965i | \(-0.337806\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.10770 | − | 0.598076i | 0.115737 | − | 0.0222735i | ||||
\(722\) | − | 9.46410i | − | 0.352217i | ||||||
\(723\) | 5.66025 | − | 3.26795i | 0.210507 | − | 0.121536i | ||||
\(724\) | −7.55514 | + | 13.0859i | −0.280784 | + | 0.486333i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.29423 | − | 2.24167i | −0.0480333 | − | 0.0831962i | ||||
\(727\) | − | 30.6603i | − | 1.13713i | −0.822640 | − | 0.568563i | \(-0.807500\pi\) | ||
0.822640 | − | 0.568563i | \(-0.192500\pi\) | |||||||
\(728\) | −36.3397 | − | 12.5885i | −1.34684 | − | 0.466559i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.2224 | − | 41.9545i | 0.895899 | − | 1.55174i | ||||
\(732\) | −5.07180 | − | 2.92820i | −0.187459 | − | 0.108230i | ||||
\(733\) | 16.1603 | − | 9.33013i | 0.596893 | − | 0.344616i | −0.170926 | − | 0.985284i | \(-0.554676\pi\) |
0.767818 | + | 0.640668i | \(0.221342\pi\) | |||||||
\(734\) | −0.588457 | −0.0217204 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.42563 | −0.273712 | ||||||||
\(737\) | −6.29423 | + | 3.63397i | −0.231851 | + | 0.133859i | ||||
\(738\) | 1.73205 | + | 1.00000i | 0.0637577 | + | 0.0368105i | ||||
\(739\) | −6.89230 | + | 11.9378i | −0.253538 | + | 0.439140i | −0.964497 | − | 0.264093i | \(-0.914927\pi\) |
0.710960 | + | 0.703233i | \(0.248261\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14.1244 | 0.518871 | ||||||||
\(742\) | 15.3590 | + | 5.32051i | 0.563846 | + | 0.195322i | ||||
\(743\) | − | 49.9090i | − | 1.83098i | −0.402338 | − | 0.915491i | \(-0.631802\pi\) | ||
0.402338 | − | 0.915491i | \(-0.368198\pi\) | |||||||
\(744\) | 8.19615 | + | 14.1962i | 0.300486 | + | 0.520456i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6.77757 | − | 11.7391i | 0.248144 | − | 0.429799i | ||||
\(747\) | −7.90192 | + | 4.56218i | −0.289116 | + | 0.166921i | ||||
\(748\) | − | 26.9282i | − | 0.984593i | ||||||
\(749\) | 21.2942 | − | 4.09808i | 0.778074 | − | 0.149740i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.9641 | − | 27.6506i | −0.582538 | − | 1.00899i | −0.995177 | − | 0.0980914i | \(-0.968726\pi\) |
0.412639 | − | 0.910895i | \(-0.364607\pi\) | |||||||
\(752\) | −1.85641 | − | 1.07180i | −0.0676962 | − | 0.0390844i | ||||
\(753\) | −5.70577 | − | 3.29423i | −0.207930 | − | 0.120048i | ||||
\(754\) | 13.0000 | + | 22.5167i | 0.473432 | + | 0.820008i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.53590 | − | 2.92820i | −0.0922297 | − | 0.106498i | ||||
\(757\) | − | 0.143594i | − | 0.00521900i | −0.999997 | − | 0.00260950i | \(-0.999169\pi\) | ||
0.999997 | − | 0.00260950i | \(-0.000830630\pi\) | |||||||
\(758\) | 17.9545 | − | 10.3660i | 0.652136 | − | 0.376511i | ||||
\(759\) | −1.73205 | + | 3.00000i | −0.0628695 | + | 0.108893i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.6340 | − | 37.4711i | −0.784231 | − | 1.35833i | −0.929457 | − | 0.368929i | \(-0.879724\pi\) |
0.145226 | − | 0.989398i | \(-0.453609\pi\) | |||||||
\(762\) | − | 11.1244i | − | 0.402993i | ||||||
\(763\) | −22.0000 | + | 19.0526i | −0.796453 | + | 0.689749i | ||||
\(764\) | 7.21539 | 0.261044 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.14359 | + | 7.17691i | −0.149714 | + | 0.259312i | ||||
\(767\) | −50.6147 | − | 29.2224i | −1.82759 | − | 1.05516i | ||||
\(768\) | −10.1436 | + | 5.85641i | −0.366025 | + | 0.211325i | ||||
\(769\) | −17.6795 | −0.637539 | −0.318769 | − | 0.947832i | \(-0.603270\pi\) | ||||
−0.318769 | + | 0.947832i | \(0.603270\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.6603 | −0.419934 | ||||||||
\(772\) | 11.6603 | − | 6.73205i | 0.419662 | − | 0.242292i | ||||
\(773\) | −1.31347 | − | 0.758330i | −0.0472421 | − | 0.0272752i | 0.476193 | − | 0.879341i | \(-0.342016\pi\) |
−0.523435 | + | 0.852066i | \(0.675350\pi\) | |||||||
\(774\) | −2.63397 | + | 4.56218i | −0.0946763 | + | 0.163984i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.71797 | −0.0975694 | ||||||||
\(777\) | 17.9904 | + | 6.23205i | 0.645401 | + | 0.223574i | ||||
\(778\) | − | 26.7846i | − | 0.960275i | ||||||
\(779\) | −3.36603 | − | 5.83013i | −0.120600 | − | 0.208886i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.73205 | + | 9.92820i | −0.205109 | + | 0.355259i | ||||
\(782\) | −5.41154 | + | 3.12436i | −0.193516 | + | 0.111727i | ||||
\(783\) | 6.19615i | 0.221432i | ||||||||
\(784\) | 1.07180 | − | 7.42563i | 0.0382785 | − | 0.265201i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.12436 | + | 5.41154i | 0.111442 | + | 0.193023i | ||||
\(787\) | −5.66025 | − | 3.26795i | −0.201766 | − | 0.116490i | 0.395713 | − | 0.918374i | \(-0.370498\pi\) |
−0.597479 | + | 0.801885i | \(0.703831\pi\) | |||||||
\(788\) | 22.3923 | + | 12.9282i | 0.797693 | + | 0.460548i | ||||
\(789\) | 6.19615 | + | 10.7321i | 0.220589 | + | 0.382071i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.26795 | − | 12.3205i | 0.151751 | − | 0.438067i | ||||
\(792\) | 6.92820i | 0.246183i | ||||||||
\(793\) | −19.8564 | + | 11.4641i | −0.705122 | + | 0.407102i | ||||
\(794\) | −7.61474 | + | 13.1891i | −0.270237 | + | 0.468064i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.1051 | + | 27.8949i | 0.570831 | + | 0.988708i | ||||
\(797\) | − | 42.0526i | − | 1.48958i | −0.667300 | − | 0.744789i | \(-0.732550\pi\) | ||
0.667300 | − | 0.744789i | \(-0.267450\pi\) | |||||||
\(798\) | −0.901924 | − | 4.68653i | −0.0319278 | − | 0.165901i | ||||
\(799\) | −13.4641 | −0.476326 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.56218 | − | 7.90192i | 0.161197 | − | 0.279201i | ||||
\(802\) | −2.78461 | − | 1.60770i | −0.0983280 | − | 0.0567697i | ||||
\(803\) | −11.0263 | + | 6.36603i | −0.389109 | + | 0.224652i | ||||
\(804\) | −3.89488 | −0.137362 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 27.1244 | 0.955415 | ||||||||
\(807\) | 16.8564 | − | 9.73205i | 0.593374 | − | 0.342584i | ||||
\(808\) | 23.5692 | + | 13.6077i | 0.829162 | + | 0.478717i | ||||
\(809\) | −14.8564 | + | 25.7321i | −0.522323 | + | 0.904691i | 0.477339 | + | 0.878719i | \(0.341601\pi\) |
−0.999663 | + | 0.0259716i | \(0.991732\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.46410 | 0.121641 | 0.0608205 | − | 0.998149i | \(-0.480628\pi\) | ||||
0.0608205 | + | 0.998149i | \(0.480628\pi\) | |||||||
\(812\) | −18.1436 | + | 15.7128i | −0.636715 | + | 0.551412i | ||||
\(813\) | 16.9282i | 0.593698i | ||||||||
\(814\) | −7.19615 | − | 12.4641i | −0.252225 | − | 0.436867i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.60770 | − | 6.24871i | 0.126295 | − | 0.218749i | ||||
\(817\) | 15.3564 | − | 8.86603i | 0.537253 | − | 0.310183i | ||||
\(818\) | − | 22.5885i | − | 0.789787i | ||||||
\(819\) | −14.8923 | + | 2.86603i | −0.520379 | + | 0.100147i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.75833 | − | 16.9019i | −0.340568 | − | 0.589881i | 0.643970 | − | 0.765051i | \(-0.277286\pi\) |
−0.984538 | + | 0.175169i | \(0.943953\pi\) | |||||||
\(822\) | −5.19615 | − | 3.00000i | −0.181237 | − | 0.104637i | ||||
\(823\) | −20.0718 | − | 11.5885i | −0.699659 | − | 0.403948i | 0.107561 | − | 0.994198i | \(-0.465696\pi\) |
−0.807220 | + | 0.590250i | \(0.799029\pi\) | |||||||
\(824\) | −1.51666 | − | 2.62693i | −0.0528354 | − | 0.0915135i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.46410 | + | 18.6603i | −0.224915 | + | 0.649273i | ||||
\(827\) | − | 52.2487i | − | 1.81687i | −0.418031 | − | 0.908433i | \(-0.637280\pi\) | ||
0.418031 | − | 0.908433i | \(-0.362720\pi\) | |||||||
\(828\) | −1.60770 | + | 0.928203i | −0.0558713 | + | 0.0322573i | ||||
\(829\) | −12.6962 | + | 21.9904i | −0.440956 | + | 0.763758i | −0.997761 | − | 0.0668857i | \(-0.978694\pi\) |
0.556805 | + | 0.830643i | \(0.312027\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.33013 | + | 2.30385i | 0.0461416 | + | 0.0799196i | ||||
\(832\) | 12.2872i | 0.425982i | ||||||||
\(833\) | −17.4904 | − | 43.7583i | −0.606006 | − | 1.51614i | ||||
\(834\) | −5.80385 | −0.200971 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.92820 | − | 8.53590i | 0.170445 | − | 0.295220i | ||||
\(837\) | 5.59808 | + | 3.23205i | 0.193498 | + | 0.111716i | ||||
\(838\) | 18.0910 | − | 10.4449i | 0.624944 | − | 0.360812i | ||||
\(839\) | 40.4449 | 1.39631 | 0.698156 | − | 0.715946i | \(-0.254004\pi\) | ||||
0.698156 | + | 0.715946i | \(0.254004\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.39230 | 0.323873 | ||||||||
\(842\) | 8.83013 | − | 5.09808i | 0.304306 | − | 0.175691i | ||||
\(843\) | 12.0000 | + | 6.92820i | 0.413302 | + | 0.238620i | ||||
\(844\) | −15.3205 | + | 26.5359i | −0.527354 | + | 0.913403i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.46410 | 0.0503369 | ||||||||
\(847\) | −1.76795 | − | 9.18653i | −0.0607475 | − | 0.315653i | ||||
\(848\) | 8.99485i | 0.308884i | ||||||||
\(849\) | −0.0621778 | − | 0.107695i | −0.00213394 | − | 0.00369609i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.56218 | − | 7.90192i | 0.156389 | − | 0.270874i | ||||
\(852\) | −5.32051 | + | 3.07180i | −0.182278 | + | 0.105238i | ||||
\(853\) | − | 19.9808i | − | 0.684128i | −0.939677 | − | 0.342064i | \(-0.888874\pi\) | ||
0.939677 | − | 0.342064i | \(-0.111126\pi\) | |||||||
\(854\) | 5.07180 | + | 5.85641i | 0.173553 | + | 0.200402i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.3923 | − | 18.0000i | −0.355202 | − | 0.615227i | ||||
\(857\) | −4.22243 | − | 2.43782i | −0.144236 | − | 0.0832744i | 0.426146 | − | 0.904655i | \(-0.359871\pi\) |
−0.570381 | + | 0.821380i | \(0.693204\pi\) | |||||||
\(858\) | 9.92820 | + | 5.73205i | 0.338943 | + | 0.195689i | ||||
\(859\) | 0.267949 | + | 0.464102i | 0.00914231 | + | 0.0158349i | 0.870560 | − | 0.492062i | \(-0.163757\pi\) |
−0.861418 | + | 0.507897i | \(0.830423\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.73205 | + | 5.46410i | 0.161268 | + | 0.186216i | ||||
\(862\) | − | 12.6795i | − | 0.431865i | ||||||
\(863\) | 5.53590 | − | 3.19615i | 0.188444 | − | 0.108798i | −0.402810 | − | 0.915284i | \(-0.631966\pi\) |
0.591254 | + | 0.806485i | \(0.298633\pi\) | |||||||
\(864\) | −2.92820 | + | 5.07180i | −0.0996195 | + | 0.172546i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.75833 | − | 3.04552i | −0.0597505 | − | 0.103491i | ||||
\(867\) | − | 28.3205i | − | 0.961815i | ||||||
\(868\) | 4.73205 | + | 24.5885i | 0.160616 | + | 0.834587i | ||||
\(869\) | 36.5885 | 1.24118 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.62436 | + | 13.2058i | −0.258341 | + | 0.447460i | ||||
\(872\) | 24.1577 | + | 13.9474i | 0.818082 | + | 0.472320i | ||||
\(873\) | −0.928203 | + | 0.535898i | −0.0314149 | + | 0.0181374i | ||||
\(874\) | −2.28719 | −0.0773653 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.82309 | −0.230531 | ||||||||
\(877\) | −27.5885 | + | 15.9282i | −0.931596 | + | 0.537857i | −0.887316 | − | 0.461162i | \(-0.847433\pi\) |
−0.0442800 | + | 0.999019i | \(0.514099\pi\) | |||||||
\(878\) | 4.73205 | + | 2.73205i | 0.159699 | + | 0.0922022i | ||||
\(879\) | −2.53590 | + | 4.39230i | −0.0855337 | + | 0.148149i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17.8564 | −0.601598 | −0.300799 | − | 0.953688i | \(-0.597253\pi\) | ||||
−0.300799 | + | 0.953688i | \(0.597253\pi\) | |||||||
\(882\) | 1.90192 | + | 4.75833i | 0.0640411 | + | 0.160221i | ||||
\(883\) | − | 22.4115i | − | 0.754208i | −0.926171 | − | 0.377104i | \(-0.876920\pi\) | ||
0.926171 | − | 0.377104i | \(-0.123080\pi\) | |||||||
\(884\) | −28.2487 | − | 48.9282i | −0.950107 | − | 1.64563i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.928203 | + | 1.60770i | −0.0311836 | + | 0.0540116i | ||||
\(887\) | −24.8827 | + | 14.3660i | −0.835479 | + | 0.482364i | −0.855725 | − | 0.517431i | \(-0.826888\pi\) |
0.0202460 | + | 0.999795i | \(0.493555\pi\) | |||||||
\(888\) | − | 18.2487i | − | 0.612387i | ||||||
\(889\) | 13.1603 | − | 37.9904i | 0.441381 | − | 1.27416i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.36603 | + | 2.36603i | 0.0457636 | + | 0.0792648i | ||||
\(892\) | 0.497423 | + | 0.287187i | 0.0166549 | + | 0.00961573i | ||||
\(893\) | −4.26795 | − | 2.46410i | −0.142821 | − | 0.0824580i | ||||
\(894\) | 8.00000 | + | 13.8564i | 0.267560 | + | 0.463428i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −26.3538 | + | 5.07180i | −0.880420 | + | 0.169437i | ||||
\(897\) | 7.26795i | 0.242670i | ||||||||
\(898\) | 5.16283 | − | 2.98076i | 0.172286 | − | 0.0994693i | ||||
\(899\) | 20.0263 | − | 34.6865i | 0.667914 | − | 1.15686i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.2487 | + | 48.9282i | 0.941101 | + | 1.63003i | ||||
\(902\) | − | 5.46410i | − | 0.181935i | ||||||
\(903\) | −14.3923 | + | 12.4641i | −0.478946 | + | 0.414779i | ||||
\(904\) | −12.4974 | −0.415658 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.80385 | − | 3.12436i | 0.0599288 | − | 0.103800i | ||||
\(907\) | −2.08846 | − | 1.20577i | −0.0693461 | − | 0.0400370i | 0.464926 | − | 0.885350i | \(-0.346081\pi\) |
−0.534272 | + | 0.845313i | \(0.679414\pi\) | |||||||
\(908\) | 19.8564 | − | 11.4641i | 0.658958 | − | 0.380450i | ||||
\(909\) | 10.7321 | 0.355960 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.2679 | −0.373324 | −0.186662 | − | 0.982424i | \(-0.559767\pi\) | ||||
−0.186662 | + | 0.982424i | \(0.559767\pi\) | |||||||
\(912\) | 2.28719 | − | 1.32051i | 0.0757363 | − | 0.0437264i | ||||
\(913\) | 21.5885 | + | 12.4641i | 0.714474 | + | 0.412502i | ||||
\(914\) | 0.241670 | − | 0.418584i | 0.00799372 | − | 0.0138455i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.39230 | 0.145126 | ||||||||
\(917\) | 4.26795 | + | 22.1769i | 0.140940 | + | 0.732346i | ||||
\(918\) | 4.92820i | 0.162655i | ||||||||
\(919\) | −1.57180 | − | 2.72243i | −0.0518488 | − | 0.0898047i | 0.838936 | − | 0.544230i | \(-0.183178\pi\) |
−0.890785 | + | 0.454425i | \(0.849845\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.93782 | + | 6.82051i | −0.129756 | + | 0.224743i | ||||
\(922\) | −22.1769 | + | 12.8038i | −0.730358 | + | 0.421672i | ||||
\(923\) | 24.0526i | 0.791700i | ||||||||
\(924\) | −3.46410 | + | 10.0000i | −0.113961 | + | 0.328976i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −8.15064 | − | 14.1173i | −0.267846 | − | 0.463924i | ||||
\(927\) | −1.03590 | − | 0.598076i | −0.0340234 | − | 0.0196434i | ||||
\(928\) | 31.4256 | + | 18.1436i | 1.03160 | + | 0.595593i | ||||
\(929\) | 3.22243 | + | 5.58142i | 0.105725 | + | 0.183120i | 0.914034 | − | 0.405638i | \(-0.132950\pi\) |
−0.808309 | + | 0.588758i | \(0.799617\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.46410 | − | 17.0718i | 0.0807577 | − | 0.559506i | ||||
\(932\) | 25.3590i | 0.830661i | ||||||||
\(933\) | −13.0981 | + | 7.56218i | −0.428812 | + | 0.247575i | ||||
\(934\) | −10.1962 | + | 17.6603i | −0.333628 | + | 0.577861i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.26795 | + | 12.5885i | 0.237560 | + | 0.411467i | ||||
\(937\) | 28.2679i | 0.923474i | 0.887017 | + | 0.461737i | \(0.152774\pi\) | ||||
−0.887017 | + | 0.461737i | \(0.847226\pi\) | |||||||
\(938\) | 4.86860 | + | 1.68653i | 0.158966 | + | 0.0550673i | ||||
\(939\) | 4.66025 | 0.152082 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.02628 | + | 6.97372i | −0.131253 | + | 0.227337i | −0.924160 | − | 0.382006i | \(-0.875233\pi\) |
0.792907 | + | 0.609343i | \(0.208567\pi\) | |||||||
\(942\) | −9.12436 | − | 5.26795i | −0.297288 | − | 0.171639i | ||||
\(943\) | 3.00000 | − | 1.73205i | 0.0976934 | − | 0.0564033i | ||||
\(944\) | −10.9282 | −0.355683 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14.3923 | 0.467934 | ||||||||
\(947\) | 10.0981 | − | 5.83013i | 0.328143 | − | 0.189454i | −0.326873 | − | 0.945068i | \(-0.605995\pi\) |
0.655017 | + | 0.755615i | \(0.272662\pi\) | |||||||
\(948\) | 16.9808 | + | 9.80385i | 0.551510 | + | 0.318414i | ||||
\(949\) | −13.3564 | + | 23.1340i | −0.433567 | + | 0.750961i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −30.4449 | −0.987242 | ||||||||
\(952\) | −34.1436 | + | 29.5692i | −1.10660 | + | 0.958344i | ||||
\(953\) | − | 40.1051i | − | 1.29913i | −0.760305 | − | 0.649566i | \(-0.774951\pi\) | ||
0.760305 | − | 0.649566i | \(-0.225049\pi\) | |||||||
\(954\) | −3.07180 | − | 5.32051i | −0.0994531 | − | 0.172258i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 15.3205 | − | 26.5359i | 0.495501 | − | 0.858232i | ||||
\(957\) | 14.6603 | − | 8.46410i | 0.473899 | − | 0.273606i | ||||
\(958\) | 24.0000i | 0.775405i | ||||||||
\(959\) | −14.1962 | − | 16.3923i | −0.458418 | − | 0.529335i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.39230 | − | 9.33975i | −0.173945 | − | 0.301282i | ||||
\(962\) | −26.1506 | − | 15.0981i | −0.843130 | − | 0.486782i | ||||
\(963\) | −7.09808 | − | 4.09808i | −0.228732 | − | 0.132059i | ||||
\(964\) | −4.78461 | − | 8.28719i | −0.154102 | − | 0.266912i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.41154 | − | 0.464102i | 0.0775901 | − | 0.0149322i | ||||
\(967\) | 14.1244i | 0.454209i | 0.973870 | + | 0.227104i | \(0.0729258\pi\) | ||||
−0.973870 | + | 0.227104i | \(0.927074\pi\) | |||||||
\(968\) | −7.76537 | + | 4.48334i | −0.249589 | + | 0.144100i | ||||
\(969\) | 8.29423 | − | 14.3660i | 0.266449 | − | 0.461503i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.0000 | + | 20.7846i | 0.385098 | + | 0.667010i | 0.991783 | − | 0.127933i | \(-0.0408342\pi\) |
−0.606685 | + | 0.794943i | \(0.707501\pi\) | |||||||
\(972\) | 1.46410i | 0.0469611i | ||||||||
\(973\) | −19.8205 | − | 6.86603i | −0.635416 | − | 0.220115i | ||||
\(974\) | 23.1244 | 0.740952 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.14359 | + | 3.71281i | −0.0686148 | + | 0.118844i | ||||
\(977\) | −12.6340 | − | 7.29423i | −0.404197 | − | 0.233363i | 0.284097 | − | 0.958796i | \(-0.408306\pi\) |
−0.688293 | + | 0.725433i | \(0.741640\pi\) | |||||||
\(978\) | −3.71281 | + | 2.14359i | −0.118723 | + | 0.0685446i | ||||
\(979\) | −24.9282 | −0.796709 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.0000 | 0.351203 | ||||||||
\(982\) | 6.49742 | − | 3.75129i | 0.207341 | − | 0.119708i | ||||
\(983\) | 17.4904 | + | 10.0981i | 0.557857 | + | 0.322079i | 0.752285 | − | 0.658838i | \(-0.228952\pi\) |
−0.194428 | + | 0.980917i | \(0.562285\pi\) | |||||||
\(984\) | 3.46410 | − | 6.00000i | 0.110432 | − | 0.191273i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 30.5359 | 0.972461 | ||||||||
\(987\) | 5.00000 | + | 1.73205i | 0.159152 | + | 0.0551318i | ||||
\(988\) | − | 20.6795i | − | 0.657902i | ||||||
\(989\) | 4.56218 | + | 7.90192i | 0.145069 | + | 0.251267i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.5526 | + | 47.7224i | −0.875236 | + | 1.51595i | −0.0187246 | + | 0.999825i | \(0.505961\pi\) |
−0.856511 | + | 0.516128i | \(0.827373\pi\) | |||||||
\(992\) | 32.7846 | − | 18.9282i | 1.04091 | − | 0.600971i | ||||
\(993\) | 21.9282i | 0.695870i | ||||||||
\(994\) | 7.98076 | − | 1.53590i | 0.253134 | − | 0.0487157i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.67949 | + | 11.5692i | 0.211648 | + | 0.366585i | ||||
\(997\) | 3.48076 | + | 2.00962i | 0.110237 | + | 0.0636453i | 0.554105 | − | 0.832447i | \(-0.313061\pi\) |
−0.443868 | + | 0.896092i | \(0.646394\pi\) | |||||||
\(998\) | −12.9737 | − | 7.49038i | −0.410676 | − | 0.237104i | ||||
\(999\) | −3.59808 | − | 6.23205i | −0.113838 | − | 0.197173i |
(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.424.1 | 4 | ||
5.2 | odd | 4 | 525.2.i.f.151.2 | 4 | |||
5.3 | odd | 4 | 105.2.i.d.46.1 | yes | 4 | ||
5.4 | even | 2 | 525.2.r.a.424.2 | 4 | |||
7.2 | even | 3 | 525.2.r.a.499.2 | 4 | |||
15.8 | even | 4 | 315.2.j.c.46.2 | 4 | |||
20.3 | even | 4 | 1680.2.bg.o.1201.2 | 4 | |||
35.2 | odd | 12 | 525.2.i.f.226.2 | 4 | |||
35.3 | even | 12 | 735.2.a.h.1.2 | 2 | |||
35.9 | even | 6 | inner | 525.2.r.f.499.1 | 4 | ||
35.13 | even | 4 | 735.2.i.l.361.1 | 4 | |||
35.17 | even | 12 | 3675.2.a.be.1.1 | 2 | |||
35.18 | odd | 12 | 735.2.a.g.1.2 | 2 | |||
35.23 | odd | 12 | 105.2.i.d.16.1 | ✓ | 4 | ||
35.32 | odd | 12 | 3675.2.a.bg.1.1 | 2 | |||
35.33 | even | 12 | 735.2.i.l.226.1 | 4 | |||
105.23 | even | 12 | 315.2.j.c.226.2 | 4 | |||
105.38 | odd | 12 | 2205.2.a.ba.1.1 | 2 | |||
105.53 | even | 12 | 2205.2.a.z.1.1 | 2 | |||
140.23 | even | 12 | 1680.2.bg.o.961.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.i.d.16.1 | ✓ | 4 | 35.23 | odd | 12 | ||
105.2.i.d.46.1 | yes | 4 | 5.3 | odd | 4 | ||
315.2.j.c.46.2 | 4 | 15.8 | even | 4 | |||
315.2.j.c.226.2 | 4 | 105.23 | even | 12 | |||
525.2.i.f.151.2 | 4 | 5.2 | odd | 4 | |||
525.2.i.f.226.2 | 4 | 35.2 | odd | 12 | |||
525.2.r.a.424.2 | 4 | 5.4 | even | 2 | |||
525.2.r.a.499.2 | 4 | 7.2 | even | 3 | |||
525.2.r.f.424.1 | 4 | 1.1 | even | 1 | trivial | ||
525.2.r.f.499.1 | 4 | 35.9 | even | 6 | inner | ||
735.2.a.g.1.2 | 2 | 35.18 | odd | 12 | |||
735.2.a.h.1.2 | 2 | 35.3 | even | 12 | |||
735.2.i.l.226.1 | 4 | 35.33 | even | 12 | |||
735.2.i.l.361.1 | 4 | 35.13 | even | 4 | |||
1680.2.bg.o.961.2 | 4 | 140.23 | even | 12 | |||
1680.2.bg.o.1201.2 | 4 | 20.3 | even | 4 | |||
2205.2.a.z.1.1 | 2 | 105.53 | even | 12 | |||
2205.2.a.ba.1.1 | 2 | 105.38 | odd | 12 | |||
3675.2.a.be.1.1 | 2 | 35.17 | even | 12 | |||
3675.2.a.bg.1.1 | 2 | 35.32 | odd | 12 |