Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,2,Mod(16,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.16");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.i (of order \(3\), degree \(2\), 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: | \(0.838429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 46.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.46 |
Dual form | 105.2.i.d.16.1 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.366025 | − | 0.633975i | −0.258819 | − | 0.448288i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0.732051 | − | 1.26795i | 0.366025 | − | 0.633975i | ||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | −0.732051 | −0.298858 | ||||||||
\(7\) | −0.866025 | + | 2.50000i | −0.327327 | + | 0.944911i | ||||
\(8\) | −2.53590 | −0.896575 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −0.366025 | + | 0.633975i | −0.115747 | + | 0.200480i | ||||
\(11\) | 1.36603 | − | 2.36603i | 0.411872 | − | 0.713384i | −0.583222 | − | 0.812313i | \(-0.698208\pi\) |
0.995094 | + | 0.0989291i | \(0.0315417\pi\) | |||||||
\(12\) | −0.732051 | − | 1.26795i | −0.211325 | − | 0.366025i | ||||
\(13\) | 5.73205 | 1.58978 | 0.794892 | − | 0.606750i | \(-0.207527\pi\) | ||||
0.794892 | + | 0.606750i | \(0.207527\pi\) | |||||||
\(14\) | 1.90192 | − | 0.366025i | 0.508311 | − | 0.0978244i | ||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | −0.535898 | − | 0.928203i | −0.133975 | − | 0.232051i | ||||
\(17\) | −3.36603 | + | 5.83013i | −0.816381 | + | 1.41401i | 0.0919509 | + | 0.995764i | \(0.470690\pi\) |
−0.908332 | + | 0.418250i | \(0.862644\pi\) | |||||||
\(18\) | −0.366025 | + | 0.633975i | −0.0862730 | + | 0.149429i | ||||
\(19\) | 1.23205 | + | 2.13397i | 0.282652 | + | 0.489567i | 0.972037 | − | 0.234828i | \(-0.0754526\pi\) |
−0.689385 | + | 0.724395i | \(0.742119\pi\) | |||||||
\(20\) | −1.46410 | −0.327383 | ||||||||
\(21\) | 1.73205 | + | 2.00000i | 0.377964 | + | 0.436436i | ||||
\(22\) | −2.00000 | −0.426401 | ||||||||
\(23\) | 0.633975 | + | 1.09808i | 0.132193 | + | 0.228965i | 0.924522 | − | 0.381130i | \(-0.124465\pi\) |
−0.792329 | + | 0.610094i | \(0.791132\pi\) | |||||||
\(24\) | −1.26795 | + | 2.19615i | −0.258819 | + | 0.448288i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | −2.09808 | − | 3.63397i | −0.411467 | − | 0.712681i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.53590 | + | 2.92820i | 0.479240 | + | 0.553378i | ||||
\(29\) | 6.19615 | 1.15060 | 0.575298 | − | 0.817944i | \(-0.304886\pi\) | ||||
0.575298 | + | 0.817944i | \(0.304886\pi\) | |||||||
\(30\) | 0.366025 | + | 0.633975i | 0.0668268 | + | 0.115747i | ||||
\(31\) | −3.23205 | + | 5.59808i | −0.580493 | + | 1.00544i | 0.414927 | + | 0.909855i | \(0.363807\pi\) |
−0.995421 | + | 0.0955896i | \(0.969526\pi\) | |||||||
\(32\) | −2.92820 | + | 5.07180i | −0.517638 | + | 0.896575i | ||||
\(33\) | −1.36603 | − | 2.36603i | −0.237795 | − | 0.411872i | ||||
\(34\) | 4.92820 | 0.845180 | ||||||||
\(35\) | 2.59808 | − | 0.500000i | 0.439155 | − | 0.0845154i | ||||
\(36\) | −1.46410 | −0.244017 | ||||||||
\(37\) | −3.59808 | − | 6.23205i | −0.591520 | − | 1.02454i | −0.994028 | − | 0.109126i | \(-0.965195\pi\) |
0.402508 | − | 0.915417i | \(-0.368139\pi\) | |||||||
\(38\) | 0.901924 | − | 1.56218i | 0.146311 | − | 0.253419i | ||||
\(39\) | 2.86603 | − | 4.96410i | 0.458931 | − | 0.794892i | ||||
\(40\) | 1.26795 | + | 2.19615i | 0.200480 | + | 0.347242i | ||||
\(41\) | 2.73205 | 0.426675 | 0.213337 | − | 0.976979i | \(-0.431567\pi\) | ||||
0.213337 | + | 0.976979i | \(0.431567\pi\) | |||||||
\(42\) | 0.633975 | − | 1.83013i | 0.0978244 | − | 0.282395i | ||||
\(43\) | −7.19615 | −1.09740 | −0.548701 | − | 0.836018i | \(-0.684878\pi\) | ||||
−0.548701 | + | 0.836018i | \(0.684878\pi\) | |||||||
\(44\) | −2.00000 | − | 3.46410i | −0.301511 | − | 0.522233i | ||||
\(45\) | −0.500000 | + | 0.866025i | −0.0745356 | + | 0.129099i | ||||
\(46\) | 0.464102 | − | 0.803848i | 0.0684280 | − | 0.118521i | ||||
\(47\) | −1.00000 | − | 1.73205i | −0.145865 | − | 0.252646i | 0.783830 | − | 0.620975i | \(-0.213263\pi\) |
−0.929695 | + | 0.368329i | \(0.879930\pi\) | |||||||
\(48\) | −1.07180 | −0.154701 | ||||||||
\(49\) | −5.50000 | − | 4.33013i | −0.785714 | − | 0.618590i | ||||
\(50\) | 0.732051 | 0.103528 | ||||||||
\(51\) | 3.36603 | + | 5.83013i | 0.471338 | + | 0.816381i | ||||
\(52\) | 4.19615 | − | 7.26795i | 0.581902 | − | 1.00788i | ||||
\(53\) | 4.19615 | − | 7.26795i | 0.576386 | − | 0.998330i | −0.419504 | − | 0.907754i | \(-0.637796\pi\) |
0.995890 | − | 0.0905760i | \(-0.0288708\pi\) | |||||||
\(54\) | 0.366025 | + | 0.633975i | 0.0498097 | + | 0.0862730i | ||||
\(55\) | −2.73205 | −0.368390 | ||||||||
\(56\) | 2.19615 | − | 6.33975i | 0.293473 | − | 0.847184i | ||||
\(57\) | 2.46410 | 0.326378 | ||||||||
\(58\) | −2.26795 | − | 3.92820i | −0.297796 | − | 0.515798i | ||||
\(59\) | −5.09808 | + | 8.83013i | −0.663713 | + | 1.14958i | 0.315920 | + | 0.948786i | \(0.397687\pi\) |
−0.979633 | + | 0.200799i | \(0.935646\pi\) | |||||||
\(60\) | −0.732051 | + | 1.26795i | −0.0945074 | + | 0.163692i | ||||
\(61\) | −2.00000 | − | 3.46410i | −0.256074 | − | 0.443533i | 0.709113 | − | 0.705095i | \(-0.249096\pi\) |
−0.965187 | + | 0.261562i | \(0.915762\pi\) | |||||||
\(62\) | 4.73205 | 0.600971 | ||||||||
\(63\) | 2.59808 | − | 0.500000i | 0.327327 | − | 0.0629941i | ||||
\(64\) | 2.14359 | 0.267949 | ||||||||
\(65\) | −2.86603 | − | 4.96410i | −0.355487 | − | 0.615721i | ||||
\(66\) | −1.00000 | + | 1.73205i | −0.123091 | + | 0.213201i | ||||
\(67\) | −1.33013 | + | 2.30385i | −0.162501 | + | 0.281460i | −0.935765 | − | 0.352624i | \(-0.885289\pi\) |
0.773264 | + | 0.634084i | \(0.218623\pi\) | |||||||
\(68\) | 4.92820 | + | 8.53590i | 0.597632 | + | 1.03513i | ||||
\(69\) | 1.26795 | 0.152643 | ||||||||
\(70\) | −1.26795 | − | 1.46410i | −0.151549 | − | 0.174994i | ||||
\(71\) | −4.19615 | −0.497992 | −0.248996 | − | 0.968505i | \(-0.580101\pi\) | ||||
−0.248996 | + | 0.968505i | \(0.580101\pi\) | |||||||
\(72\) | 1.26795 | + | 2.19615i | 0.149429 | + | 0.258819i | ||||
\(73\) | 2.33013 | − | 4.03590i | 0.272721 | − | 0.472366i | −0.696837 | − | 0.717230i | \(-0.745410\pi\) |
0.969558 | + | 0.244864i | \(0.0787432\pi\) | |||||||
\(74\) | −2.63397 | + | 4.56218i | −0.306193 | + | 0.530342i | ||||
\(75\) | 0.500000 | + | 0.866025i | 0.0577350 | + | 0.100000i | ||||
\(76\) | 3.60770 | 0.413831 | ||||||||
\(77\) | 4.73205 | + | 5.46410i | 0.539267 | + | 0.622692i | ||||
\(78\) | −4.19615 | −0.475121 | ||||||||
\(79\) | −6.69615 | − | 11.5981i | −0.753376 | − | 1.30489i | −0.946178 | − | 0.323648i | \(-0.895091\pi\) |
0.192802 | − | 0.981238i | \(-0.438243\pi\) | |||||||
\(80\) | −0.535898 | + | 0.928203i | −0.0599153 | + | 0.103776i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −1.00000 | − | 1.73205i | −0.110432 | − | 0.191273i | ||||
\(83\) | −9.12436 | −1.00153 | −0.500764 | − | 0.865584i | \(-0.666948\pi\) | ||||
−0.500764 | + | 0.865584i | \(0.666948\pi\) | |||||||
\(84\) | 3.80385 | − | 0.732051i | 0.415034 | − | 0.0798733i | ||||
\(85\) | 6.73205 | 0.730193 | ||||||||
\(86\) | 2.63397 | + | 4.56218i | 0.284029 | + | 0.491952i | ||||
\(87\) | 3.09808 | − | 5.36603i | 0.332149 | − | 0.575298i | ||||
\(88\) | −3.46410 | + | 6.00000i | −0.369274 | + | 0.639602i | ||||
\(89\) | 4.56218 | + | 7.90192i | 0.483590 | + | 0.837602i | 0.999822 | − | 0.0188462i | \(-0.00599930\pi\) |
−0.516233 | + | 0.856448i | \(0.672666\pi\) | |||||||
\(90\) | 0.732051 | 0.0771649 | ||||||||
\(91\) | −4.96410 | + | 14.3301i | −0.520379 | + | 1.50221i | ||||
\(92\) | 1.85641 | 0.193544 | ||||||||
\(93\) | 3.23205 | + | 5.59808i | 0.335148 | + | 0.580493i | ||||
\(94\) | −0.732051 | + | 1.26795i | −0.0755053 | + | 0.130779i | ||||
\(95\) | 1.23205 | − | 2.13397i | 0.126406 | − | 0.218941i | ||||
\(96\) | 2.92820 | + | 5.07180i | 0.298858 | + | 0.517638i | ||||
\(97\) | 1.07180 | 0.108824 | 0.0544122 | − | 0.998519i | \(-0.482671\pi\) | ||||
0.0544122 | + | 0.998519i | \(0.482671\pi\) | |||||||
\(98\) | −0.732051 | + | 5.07180i | −0.0739483 | + | 0.512329i | ||||
\(99\) | −2.73205 | −0.274581 | ||||||||
\(100\) | 0.732051 | + | 1.26795i | 0.0732051 | + | 0.126795i | ||||
\(101\) | 5.36603 | − | 9.29423i | 0.533939 | − | 0.924810i | −0.465274 | − | 0.885167i | \(-0.654044\pi\) |
0.999214 | − | 0.0396438i | \(-0.0126223\pi\) | |||||||
\(102\) | 2.46410 | − | 4.26795i | 0.243982 | − | 0.422590i | ||||
\(103\) | −0.598076 | − | 1.03590i | −0.0589302 | − | 0.102070i | 0.835055 | − | 0.550166i | \(-0.185436\pi\) |
−0.893985 | + | 0.448096i | \(0.852102\pi\) | |||||||
\(104\) | −14.5359 | −1.42536 | ||||||||
\(105\) | 0.866025 | − | 2.50000i | 0.0845154 | − | 0.243975i | ||||
\(106\) | −6.14359 | −0.596719 | ||||||||
\(107\) | 4.09808 | + | 7.09808i | 0.396176 | + | 0.686197i | 0.993251 | − | 0.115989i | \(-0.0370037\pi\) |
−0.597075 | + | 0.802186i | \(0.703670\pi\) | |||||||
\(108\) | −0.732051 | + | 1.26795i | −0.0704416 | + | 0.122008i | ||||
\(109\) | −5.50000 | + | 9.52628i | −0.526804 | + | 0.912452i | 0.472708 | + | 0.881219i | \(0.343277\pi\) |
−0.999512 | + | 0.0312328i | \(0.990057\pi\) | |||||||
\(110\) | 1.00000 | + | 1.73205i | 0.0953463 | + | 0.165145i | ||||
\(111\) | −7.19615 | −0.683029 | ||||||||
\(112\) | 2.78461 | − | 0.535898i | 0.263121 | − | 0.0506376i | ||||
\(113\) | −4.92820 | −0.463606 | −0.231803 | − | 0.972763i | \(-0.574463\pi\) | ||||
−0.231803 | + | 0.972763i | \(0.574463\pi\) | |||||||
\(114\) | −0.901924 | − | 1.56218i | −0.0844729 | − | 0.146311i | ||||
\(115\) | 0.633975 | − | 1.09808i | 0.0591184 | − | 0.102396i | ||||
\(116\) | 4.53590 | − | 7.85641i | 0.421148 | − | 0.729449i | ||||
\(117\) | −2.86603 | − | 4.96410i | −0.264964 | − | 0.458931i | ||||
\(118\) | 7.46410 | 0.687126 | ||||||||
\(119\) | −11.6603 | − | 13.4641i | −1.06889 | − | 1.23425i | ||||
\(120\) | 2.53590 | 0.231495 | ||||||||
\(121\) | 1.76795 | + | 3.06218i | 0.160723 | + | 0.278380i | ||||
\(122\) | −1.46410 | + | 2.53590i | −0.132554 | + | 0.229589i | ||||
\(123\) | 1.36603 | − | 2.36603i | 0.123170 | − | 0.213337i | ||||
\(124\) | 4.73205 | + | 8.19615i | 0.424951 | + | 0.736036i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.26795 | − | 1.46410i | −0.112958 | − | 0.130433i | ||||
\(127\) | 15.1962 | 1.34844 | 0.674220 | − | 0.738530i | \(-0.264480\pi\) | ||||
0.674220 | + | 0.738530i | \(0.264480\pi\) | |||||||
\(128\) | 5.07180 | + | 8.78461i | 0.448288 | + | 0.776457i | ||||
\(129\) | −3.59808 | + | 6.23205i | −0.316793 | + | 0.548701i | ||||
\(130\) | −2.09808 | + | 3.63397i | −0.184013 | + | 0.318721i | ||||
\(131\) | −4.26795 | − | 7.39230i | −0.372892 | − | 0.645869i | 0.617117 | − | 0.786872i | \(-0.288301\pi\) |
−0.990009 | + | 0.141003i | \(0.954967\pi\) | |||||||
\(132\) | −4.00000 | −0.348155 | ||||||||
\(133\) | −6.40192 | + | 1.23205i | −0.555117 | + | 0.106832i | ||||
\(134\) | 1.94744 | 0.168233 | ||||||||
\(135\) | 0.500000 | + | 0.866025i | 0.0430331 | + | 0.0745356i | ||||
\(136\) | 8.53590 | − | 14.7846i | 0.731947 | − | 1.26777i | ||||
\(137\) | 4.09808 | − | 7.09808i | 0.350122 | − | 0.606430i | −0.636148 | − | 0.771567i | \(-0.719473\pi\) |
0.986271 | + | 0.165137i | \(0.0528067\pi\) | |||||||
\(138\) | −0.464102 | − | 0.803848i | −0.0395070 | − | 0.0684280i | ||||
\(139\) | −7.92820 | −0.672461 | −0.336231 | − | 0.941780i | \(-0.609152\pi\) | ||||
−0.336231 | + | 0.941780i | \(0.609152\pi\) | |||||||
\(140\) | 1.26795 | − | 3.66025i | 0.107161 | − | 0.309348i | ||||
\(141\) | −2.00000 | −0.168430 | ||||||||
\(142\) | 1.53590 | + | 2.66025i | 0.128890 | + | 0.223244i | ||||
\(143\) | 7.83013 | − | 13.5622i | 0.654788 | − | 1.13413i | ||||
\(144\) | −0.535898 | + | 0.928203i | −0.0446582 | + | 0.0773503i | ||||
\(145\) | −3.09808 | − | 5.36603i | −0.257281 | − | 0.445624i | ||||
\(146\) | −3.41154 | −0.282341 | ||||||||
\(147\) | −6.50000 | + | 2.59808i | −0.536111 | + | 0.214286i | ||||
\(148\) | −10.5359 | −0.866046 | ||||||||
\(149\) | 10.9282 | + | 18.9282i | 0.895273 | + | 1.55066i | 0.833466 | + | 0.552571i | \(0.186353\pi\) |
0.0618073 | + | 0.998088i | \(0.480314\pi\) | |||||||
\(150\) | 0.366025 | − | 0.633975i | 0.0298858 | − | 0.0517638i | ||||
\(151\) | −2.46410 | + | 4.26795i | −0.200526 | + | 0.347321i | −0.948698 | − | 0.316184i | \(-0.897598\pi\) |
0.748172 | + | 0.663505i | \(0.230932\pi\) | |||||||
\(152\) | −3.12436 | − | 5.41154i | −0.253419 | − | 0.438934i | ||||
\(153\) | 6.73205 | 0.544254 | ||||||||
\(154\) | 1.73205 | − | 5.00000i | 0.139573 | − | 0.402911i | ||||
\(155\) | 6.46410 | 0.519209 | ||||||||
\(156\) | −4.19615 | − | 7.26795i | −0.335961 | − | 0.581902i | ||||
\(157\) | 7.19615 | − | 12.4641i | 0.574315 | − | 0.994744i | −0.421800 | − | 0.906689i | \(-0.638602\pi\) |
0.996116 | − | 0.0880548i | \(-0.0280651\pi\) | |||||||
\(158\) | −4.90192 | + | 8.49038i | −0.389976 | + | 0.675458i | ||||
\(159\) | −4.19615 | − | 7.26795i | −0.332777 | − | 0.576386i | ||||
\(160\) | 5.85641 | 0.462990 | ||||||||
\(161\) | −3.29423 | + | 0.633975i | −0.259622 | + | 0.0499642i | ||||
\(162\) | 0.732051 | 0.0575153 | ||||||||
\(163\) | 2.92820 | + | 5.07180i | 0.229355 | + | 0.397254i | 0.957617 | − | 0.288045i | \(-0.0930051\pi\) |
−0.728262 | + | 0.685298i | \(0.759672\pi\) | |||||||
\(164\) | 2.00000 | − | 3.46410i | 0.156174 | − | 0.270501i | ||||
\(165\) | −1.36603 | + | 2.36603i | −0.106345 | + | 0.184195i | ||||
\(166\) | 3.33975 | + | 5.78461i | 0.259215 | + | 0.448973i | ||||
\(167\) | −0.339746 | −0.0262903 | −0.0131452 | − | 0.999914i | \(-0.504184\pi\) | ||||
−0.0131452 | + | 0.999914i | \(0.504184\pi\) | |||||||
\(168\) | −4.39230 | − | 5.07180i | −0.338874 | − | 0.391298i | ||||
\(169\) | 19.8564 | 1.52742 | ||||||||
\(170\) | −2.46410 | − | 4.26795i | −0.188988 | − | 0.327337i | ||||
\(171\) | 1.23205 | − | 2.13397i | 0.0942173 | − | 0.163189i | ||||
\(172\) | −5.26795 | + | 9.12436i | −0.401677 | + | 0.695726i | ||||
\(173\) | −10.7321 | − | 18.5885i | −0.815943 | − | 1.41325i | −0.908649 | − | 0.417561i | \(-0.862885\pi\) |
0.0927063 | − | 0.995693i | \(-0.470448\pi\) | |||||||
\(174\) | −4.53590 | −0.343866 | ||||||||
\(175\) | −1.73205 | − | 2.00000i | −0.130931 | − | 0.151186i | ||||
\(176\) | −2.92820 | −0.220722 | ||||||||
\(177\) | 5.09808 | + | 8.83013i | 0.383195 | + | 0.663713i | ||||
\(178\) | 3.33975 | − | 5.78461i | 0.250325 | − | 0.433575i | ||||
\(179\) | 5.00000 | − | 8.66025i | 0.373718 | − | 0.647298i | −0.616417 | − | 0.787420i | \(-0.711416\pi\) |
0.990134 | + | 0.140122i | \(0.0447496\pi\) | |||||||
\(180\) | 0.732051 | + | 1.26795i | 0.0545638 | + | 0.0945074i | ||||
\(181\) | 10.3205 | 0.767117 | 0.383559 | − | 0.923517i | \(-0.374698\pi\) | ||||
0.383559 | + | 0.923517i | \(0.374698\pi\) | |||||||
\(182\) | 10.9019 | − | 2.09808i | 0.808104 | − | 0.155520i | ||||
\(183\) | −4.00000 | −0.295689 | ||||||||
\(184\) | −1.60770 | − | 2.78461i | −0.118521 | − | 0.205284i | ||||
\(185\) | −3.59808 | + | 6.23205i | −0.264536 | + | 0.458189i | ||||
\(186\) | 2.36603 | − | 4.09808i | 0.173485 | − | 0.300486i | ||||
\(187\) | 9.19615 | + | 15.9282i | 0.672489 | + | 1.16479i | ||||
\(188\) | −2.92820 | −0.213561 | ||||||||
\(189\) | 0.866025 | − | 2.50000i | 0.0629941 | − | 0.181848i | ||||
\(190\) | −1.80385 | −0.130865 | ||||||||
\(191\) | −2.46410 | − | 4.26795i | −0.178296 | − | 0.308818i | 0.763001 | − | 0.646397i | \(-0.223725\pi\) |
−0.941297 | + | 0.337579i | \(0.890392\pi\) | |||||||
\(192\) | 1.07180 | − | 1.85641i | 0.0773503 | − | 0.133975i | ||||
\(193\) | 4.59808 | − | 7.96410i | 0.330977 | − | 0.573269i | −0.651727 | − | 0.758454i | \(-0.725955\pi\) |
0.982704 | + | 0.185185i | \(0.0592885\pi\) | |||||||
\(194\) | −0.392305 | − | 0.679492i | −0.0281658 | − | 0.0487847i | ||||
\(195\) | −5.73205 | −0.410481 | ||||||||
\(196\) | −9.51666 | + | 3.80385i | −0.679761 | + | 0.271703i | ||||
\(197\) | −17.6603 | −1.25824 | −0.629121 | − | 0.777308i | \(-0.716585\pi\) | ||||
−0.629121 | + | 0.777308i | \(0.716585\pi\) | |||||||
\(198\) | 1.00000 | + | 1.73205i | 0.0710669 | + | 0.123091i | ||||
\(199\) | −11.0000 | + | 19.0526i | −0.779769 | + | 1.35060i | 0.152305 | + | 0.988334i | \(0.451330\pi\) |
−0.932075 | + | 0.362267i | \(0.882003\pi\) | |||||||
\(200\) | 1.26795 | − | 2.19615i | 0.0896575 | − | 0.155291i | ||||
\(201\) | 1.33013 | + | 2.30385i | 0.0938199 | + | 0.162501i | ||||
\(202\) | −7.85641 | −0.552775 | ||||||||
\(203\) | −5.36603 | + | 15.4904i | −0.376621 | + | 1.08721i | ||||
\(204\) | 9.85641 | 0.690086 | ||||||||
\(205\) | −1.36603 | − | 2.36603i | −0.0954074 | − | 0.165250i | ||||
\(206\) | −0.437822 | + | 0.758330i | −0.0305045 | + | 0.0528354i | ||||
\(207\) | 0.633975 | − | 1.09808i | 0.0440643 | − | 0.0763216i | ||||
\(208\) | −3.07180 | − | 5.32051i | −0.212991 | − | 0.368911i | ||||
\(209\) | 6.73205 | 0.465666 | ||||||||
\(210\) | −1.90192 | + | 0.366025i | −0.131245 | + | 0.0252582i | ||||
\(211\) | 20.9282 | 1.44076 | 0.720378 | − | 0.693581i | \(-0.243968\pi\) | ||||
0.720378 | + | 0.693581i | \(0.243968\pi\) | |||||||
\(212\) | −6.14359 | − | 10.6410i | −0.421944 | − | 0.730828i | ||||
\(213\) | −2.09808 | + | 3.63397i | −0.143758 | + | 0.248996i | ||||
\(214\) | 3.00000 | − | 5.19615i | 0.205076 | − | 0.355202i | ||||
\(215\) | 3.59808 | + | 6.23205i | 0.245387 | + | 0.425022i | ||||
\(216\) | 2.53590 | 0.172546 | ||||||||
\(217\) | −11.1962 | − | 12.9282i | −0.760044 | − | 0.877624i | ||||
\(218\) | 8.05256 | 0.545388 | ||||||||
\(219\) | −2.33013 | − | 4.03590i | −0.157455 | − | 0.272721i | ||||
\(220\) | −2.00000 | + | 3.46410i | −0.134840 | + | 0.233550i | ||||
\(221\) | −19.2942 | + | 33.4186i | −1.29787 | + | 2.24798i | ||||
\(222\) | 2.63397 | + | 4.56218i | 0.176781 | + | 0.306193i | ||||
\(223\) | 0.392305 | 0.0262707 | 0.0131353 | − | 0.999914i | \(-0.495819\pi\) | ||||
0.0131353 | + | 0.999914i | \(0.495819\pi\) | |||||||
\(224\) | −10.1436 | − | 11.7128i | −0.677747 | − | 0.782595i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 1.80385 | + | 3.12436i | 0.119990 | + | 0.207829i | ||||
\(227\) | −7.83013 | + | 13.5622i | −0.519704 | + | 0.900153i | 0.480034 | + | 0.877250i | \(0.340624\pi\) |
−0.999738 | + | 0.0229034i | \(0.992709\pi\) | |||||||
\(228\) | 1.80385 | − | 3.12436i | 0.119463 | − | 0.206916i | ||||
\(229\) | 1.50000 | + | 2.59808i | 0.0991228 | + | 0.171686i | 0.911322 | − | 0.411695i | \(-0.135063\pi\) |
−0.812199 | + | 0.583380i | \(0.801730\pi\) | |||||||
\(230\) | −0.928203 | −0.0612039 | ||||||||
\(231\) | 7.09808 | − | 1.36603i | 0.467019 | − | 0.0898779i | ||||
\(232\) | −15.7128 | −1.03160 | ||||||||
\(233\) | 8.66025 | + | 15.0000i | 0.567352 | + | 0.982683i | 0.996827 | + | 0.0796037i | \(0.0253655\pi\) |
−0.429474 | + | 0.903079i | \(0.641301\pi\) | |||||||
\(234\) | −2.09808 | + | 3.63397i | −0.137156 | + | 0.237560i | ||||
\(235\) | −1.00000 | + | 1.73205i | −0.0652328 | + | 0.112987i | ||||
\(236\) | 7.46410 | + | 12.9282i | 0.485872 | + | 0.841554i | ||||
\(237\) | −13.3923 | −0.869924 | ||||||||
\(238\) | −4.26795 | + | 12.3205i | −0.276650 | + | 0.798620i | ||||
\(239\) | 20.9282 | 1.35373 | 0.676866 | − | 0.736106i | \(-0.263337\pi\) | ||||
0.676866 | + | 0.736106i | \(0.263337\pi\) | |||||||
\(240\) | 0.535898 | + | 0.928203i | 0.0345921 | + | 0.0599153i | ||||
\(241\) | −3.26795 | + | 5.66025i | −0.210507 | + | 0.364609i | −0.951873 | − | 0.306492i | \(-0.900845\pi\) |
0.741366 | + | 0.671101i | \(0.234178\pi\) | |||||||
\(242\) | 1.29423 | − | 2.24167i | 0.0831962 | − | 0.144100i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −5.85641 | −0.374918 | ||||||||
\(245\) | −1.00000 | + | 6.92820i | −0.0638877 | + | 0.442627i | ||||
\(246\) | −2.00000 | −0.127515 | ||||||||
\(247\) | 7.06218 | + | 12.2321i | 0.449356 | + | 0.778307i | ||||
\(248\) | 8.19615 | − | 14.1962i | 0.520456 | − | 0.901457i | ||||
\(249\) | −4.56218 | + | 7.90192i | −0.289116 | + | 0.500764i | ||||
\(250\) | −0.366025 | − | 0.633975i | −0.0231495 | − | 0.0400961i | ||||
\(251\) | 6.58846 | 0.415860 | 0.207930 | − | 0.978144i | \(-0.433327\pi\) | ||||
0.207930 | + | 0.978144i | \(0.433327\pi\) | |||||||
\(252\) | 1.26795 | − | 3.66025i | 0.0798733 | − | 0.230574i | ||||
\(253\) | 3.46410 | 0.217786 | ||||||||
\(254\) | −5.56218 | − | 9.63397i | −0.349002 | − | 0.604489i | ||||
\(255\) | 3.36603 | − | 5.83013i | 0.210789 | − | 0.365097i | ||||
\(256\) | 5.85641 | − | 10.1436i | 0.366025 | − | 0.633975i | ||||
\(257\) | −5.83013 | − | 10.0981i | −0.363673 | − | 0.629901i | 0.624889 | − | 0.780714i | \(-0.285144\pi\) |
−0.988562 | + | 0.150813i | \(0.951811\pi\) | |||||||
\(258\) | 5.26795 | 0.327968 | ||||||||
\(259\) | 18.6962 | − | 3.59808i | 1.16172 | − | 0.223574i | ||||
\(260\) | −8.39230 | −0.520469 | ||||||||
\(261\) | −3.09808 | − | 5.36603i | −0.191766 | − | 0.332149i | ||||
\(262\) | −3.12436 | + | 5.41154i | −0.193023 | + | 0.334326i | ||||
\(263\) | 6.19615 | − | 10.7321i | 0.382071 | − | 0.661767i | −0.609287 | − | 0.792950i | \(-0.708544\pi\) |
0.991358 | + | 0.131183i | \(0.0418776\pi\) | |||||||
\(264\) | 3.46410 | + | 6.00000i | 0.213201 | + | 0.369274i | ||||
\(265\) | −8.39230 | −0.515535 | ||||||||
\(266\) | 3.12436 | + | 3.60770i | 0.191567 | + | 0.221202i | ||||
\(267\) | 9.12436 | 0.558401 | ||||||||
\(268\) | 1.94744 | + | 3.37307i | 0.118959 | + | 0.206043i | ||||
\(269\) | 9.73205 | − | 16.8564i | 0.593374 | − | 1.02775i | −0.400401 | − | 0.916340i | \(-0.631129\pi\) |
0.993774 | − | 0.111413i | \(-0.0355377\pi\) | |||||||
\(270\) | 0.366025 | − | 0.633975i | 0.0222756 | − | 0.0385825i | ||||
\(271\) | −8.46410 | − | 14.6603i | −0.514158 | − | 0.890547i | −0.999865 | − | 0.0164256i | \(-0.994771\pi\) |
0.485708 | − | 0.874121i | \(-0.338562\pi\) | |||||||
\(272\) | 7.21539 | 0.437497 | ||||||||
\(273\) | 9.92820 | + | 11.4641i | 0.600882 | + | 0.693839i | ||||
\(274\) | −6.00000 | −0.362473 | ||||||||
\(275\) | 1.36603 | + | 2.36603i | 0.0823744 | + | 0.142677i | ||||
\(276\) | 0.928203 | − | 1.60770i | 0.0558713 | − | 0.0967719i | ||||
\(277\) | −1.33013 | + | 2.30385i | −0.0799196 | + | 0.138425i | −0.903215 | − | 0.429188i | \(-0.858800\pi\) |
0.823295 | + | 0.567613i | \(0.192133\pi\) | |||||||
\(278\) | 2.90192 | + | 5.02628i | 0.174046 | + | 0.301456i | ||||
\(279\) | 6.46410 | 0.386996 | ||||||||
\(280\) | −6.58846 | + | 1.26795i | −0.393736 | + | 0.0757745i | ||||
\(281\) | −13.8564 | −0.826604 | −0.413302 | − | 0.910594i | \(-0.635625\pi\) | ||||
−0.413302 | + | 0.910594i | \(0.635625\pi\) | |||||||
\(282\) | 0.732051 | + | 1.26795i | 0.0435930 | + | 0.0755053i | ||||
\(283\) | −0.0621778 | + | 0.107695i | −0.00369609 | + | 0.00640181i | −0.867868 | − | 0.496796i | \(-0.834510\pi\) |
0.864171 | + | 0.503197i | \(0.167843\pi\) | |||||||
\(284\) | −3.07180 | + | 5.32051i | −0.182278 | + | 0.315714i | ||||
\(285\) | −1.23205 | − | 2.13397i | −0.0729804 | − | 0.126406i | ||||
\(286\) | −11.4641 | −0.677887 | ||||||||
\(287\) | −2.36603 | + | 6.83013i | −0.139662 | + | 0.403170i | ||||
\(288\) | 5.85641 | 0.345092 | ||||||||
\(289\) | −14.1603 | − | 24.5263i | −0.832956 | − | 1.44272i | ||||
\(290\) | −2.26795 | + | 3.92820i | −0.133179 | + | 0.230672i | ||||
\(291\) | 0.535898 | − | 0.928203i | 0.0314149 | − | 0.0544122i | ||||
\(292\) | −3.41154 | − | 5.90897i | −0.199645 | − | 0.345796i | ||||
\(293\) | 5.07180 | 0.296298 | 0.148149 | − | 0.988965i | \(-0.452669\pi\) | ||||
0.148149 | + | 0.988965i | \(0.452669\pi\) | |||||||
\(294\) | 4.02628 | + | 3.16987i | 0.234817 | + | 0.184871i | ||||
\(295\) | 10.1962 | 0.593643 | ||||||||
\(296\) | 9.12436 | + | 15.8038i | 0.530342 | + | 0.918580i | ||||
\(297\) | −1.36603 | + | 2.36603i | −0.0792648 | + | 0.137291i | ||||
\(298\) | 8.00000 | − | 13.8564i | 0.463428 | − | 0.802680i | ||||
\(299\) | 3.63397 | + | 6.29423i | 0.210158 | + | 0.364005i | ||||
\(300\) | 1.46410 | 0.0845299 | ||||||||
\(301\) | 6.23205 | − | 17.9904i | 0.359209 | − | 1.03695i | ||||
\(302\) | 3.60770 | 0.207600 | ||||||||
\(303\) | −5.36603 | − | 9.29423i | −0.308270 | − | 0.533939i | ||||
\(304\) | 1.32051 | − | 2.28719i | 0.0757363 | − | 0.131179i | ||||
\(305\) | −2.00000 | + | 3.46410i | −0.114520 | + | 0.198354i | ||||
\(306\) | −2.46410 | − | 4.26795i | −0.140863 | − | 0.243982i | ||||
\(307\) | −7.87564 | −0.449487 | −0.224743 | − | 0.974418i | \(-0.572154\pi\) | ||||
−0.224743 | + | 0.974418i | \(0.572154\pi\) | |||||||
\(308\) | 10.3923 | − | 2.00000i | 0.592157 | − | 0.113961i | ||||
\(309\) | −1.19615 | −0.0680467 | ||||||||
\(310\) | −2.36603 | − | 4.09808i | −0.134381 | − | 0.232755i | ||||
\(311\) | 7.56218 | − | 13.0981i | 0.428812 | − | 0.742724i | −0.567956 | − | 0.823059i | \(-0.692266\pi\) |
0.996768 | + | 0.0803351i | \(0.0255990\pi\) | |||||||
\(312\) | −7.26795 | + | 12.5885i | −0.411467 | + | 0.712681i | ||||
\(313\) | −2.33013 | − | 4.03590i | −0.131707 | − | 0.228122i | 0.792628 | − | 0.609706i | \(-0.208712\pi\) |
−0.924335 | + | 0.381583i | \(0.875379\pi\) | |||||||
\(314\) | −10.5359 | −0.594575 | ||||||||
\(315\) | −1.73205 | − | 2.00000i | −0.0975900 | − | 0.112687i | ||||
\(316\) | −19.6077 | −1.10302 | ||||||||
\(317\) | −15.2224 | − | 26.3660i | −0.854977 | − | 1.48086i | −0.876666 | − | 0.481099i | \(-0.840238\pi\) |
0.0216894 | − | 0.999765i | \(-0.493095\pi\) | |||||||
\(318\) | −3.07180 | + | 5.32051i | −0.172258 | + | 0.298359i | ||||
\(319\) | 8.46410 | − | 14.6603i | 0.473899 | − | 0.820817i | ||||
\(320\) | −1.07180 | − | 1.85641i | −0.0599153 | − | 0.103776i | ||||
\(321\) | 8.19615 | 0.457465 | ||||||||
\(322\) | 1.60770 | + | 1.85641i | 0.0895933 | + | 0.103453i | ||||
\(323\) | −16.5885 | −0.923006 | ||||||||
\(324\) | 0.732051 | + | 1.26795i | 0.0406695 | + | 0.0704416i | ||||
\(325\) | −2.86603 | + | 4.96410i | −0.158978 | + | 0.275359i | ||||
\(326\) | 2.14359 | − | 3.71281i | 0.118723 | − | 0.205634i | ||||
\(327\) | 5.50000 | + | 9.52628i | 0.304151 | + | 0.526804i | ||||
\(328\) | −6.92820 | −0.382546 | ||||||||
\(329\) | 5.19615 | − | 1.00000i | 0.286473 | − | 0.0551318i | ||||
\(330\) | 2.00000 | 0.110096 | ||||||||
\(331\) | −10.9641 | − | 18.9904i | −0.602642 | − | 1.04381i | −0.992419 | − | 0.122897i | \(-0.960782\pi\) |
0.389778 | − | 0.920909i | \(-0.372552\pi\) | |||||||
\(332\) | −6.67949 | + | 11.5692i | −0.366585 | + | 0.634943i | ||||
\(333\) | −3.59808 | + | 6.23205i | −0.197173 | + | 0.341514i | ||||
\(334\) | 0.124356 | + | 0.215390i | 0.00680444 | + | 0.0117856i | ||||
\(335\) | 2.66025 | 0.145345 | ||||||||
\(336\) | 0.928203 | − | 2.67949i | 0.0506376 | − | 0.146178i | ||||
\(337\) | −33.9808 | −1.85105 | −0.925525 | − | 0.378686i | \(-0.876376\pi\) | ||||
−0.925525 | + | 0.378686i | \(0.876376\pi\) | |||||||
\(338\) | −7.26795 | − | 12.5885i | −0.395324 | − | 0.684722i | ||||
\(339\) | −2.46410 | + | 4.26795i | −0.133832 | + | 0.231803i | ||||
\(340\) | 4.92820 | − | 8.53590i | 0.267269 | − | 0.462924i | ||||
\(341\) | 8.83013 | + | 15.2942i | 0.478178 | + | 0.828229i | ||||
\(342\) | −1.80385 | −0.0975409 | ||||||||
\(343\) | 15.5885 | − | 10.0000i | 0.841698 | − | 0.539949i | ||||
\(344\) | 18.2487 | 0.983905 | ||||||||
\(345\) | −0.633975 | − | 1.09808i | −0.0341320 | − | 0.0591184i | ||||
\(346\) | −7.85641 | + | 13.6077i | −0.422363 | + | 0.731554i | ||||
\(347\) | 17.4641 | − | 30.2487i | 0.937522 | − | 1.62384i | 0.167449 | − | 0.985881i | \(-0.446447\pi\) |
0.770074 | − | 0.637955i | \(-0.220219\pi\) | |||||||
\(348\) | −4.53590 | − | 7.85641i | −0.243150 | − | 0.421148i | ||||
\(349\) | 22.0000 | 1.17763 | 0.588817 | − | 0.808267i | \(-0.299594\pi\) | ||||
0.588817 | + | 0.808267i | \(0.299594\pi\) | |||||||
\(350\) | −0.633975 | + | 1.83013i | −0.0338874 | + | 0.0978244i | ||||
\(351\) | −5.73205 | −0.305954 | ||||||||
\(352\) | 8.00000 | + | 13.8564i | 0.426401 | + | 0.738549i | ||||
\(353\) | −10.5622 | + | 18.2942i | −0.562168 | + | 0.973704i | 0.435139 | + | 0.900363i | \(0.356699\pi\) |
−0.997307 | + | 0.0733402i | \(0.976634\pi\) | |||||||
\(354\) | 3.73205 | − | 6.46410i | 0.198356 | − | 0.343563i | ||||
\(355\) | 2.09808 | + | 3.63397i | 0.111354 | + | 0.192871i | ||||
\(356\) | 13.3590 | 0.708025 | ||||||||
\(357\) | −17.4904 | + | 3.36603i | −0.925689 | + | 0.178149i | ||||
\(358\) | −7.32051 | −0.386901 | ||||||||
\(359\) | 2.36603 | + | 4.09808i | 0.124874 | + | 0.216288i | 0.921684 | − | 0.387942i | \(-0.126814\pi\) |
−0.796810 | + | 0.604230i | \(0.793481\pi\) | |||||||
\(360\) | 1.26795 | − | 2.19615i | 0.0668268 | − | 0.115747i | ||||
\(361\) | 6.46410 | − | 11.1962i | 0.340216 | − | 0.589271i | ||||
\(362\) | −3.77757 | − | 6.54294i | −0.198545 | − | 0.343889i | ||||
\(363\) | 3.53590 | 0.185587 | ||||||||
\(364\) | 14.5359 | + | 16.7846i | 0.761888 | + | 0.879753i | ||||
\(365\) | −4.66025 | −0.243929 | ||||||||
\(366\) | 1.46410 | + | 2.53590i | 0.0765298 | + | 0.132554i | ||||
\(367\) | −0.401924 | + | 0.696152i | −0.0209803 | + | 0.0363389i | −0.876325 | − | 0.481721i | \(-0.840012\pi\) |
0.855345 | + | 0.518059i | \(0.173345\pi\) | |||||||
\(368\) | 0.679492 | − | 1.17691i | 0.0354210 | − | 0.0613509i | ||||
\(369\) | −1.36603 | − | 2.36603i | −0.0711124 | − | 0.123170i | ||||
\(370\) | 5.26795 | 0.273868 | ||||||||
\(371\) | 14.5359 | + | 16.7846i | 0.754666 | + | 0.871414i | ||||
\(372\) | 9.46410 | 0.490691 | ||||||||
\(373\) | 9.25833 | + | 16.0359i | 0.479378 | + | 0.830307i | 0.999720 | − | 0.0236505i | \(-0.00752890\pi\) |
−0.520342 | + | 0.853958i | \(0.674196\pi\) | |||||||
\(374\) | 6.73205 | − | 11.6603i | 0.348106 | − | 0.602937i | ||||
\(375\) | 0.500000 | − | 0.866025i | 0.0258199 | − | 0.0447214i | ||||
\(376\) | 2.53590 | + | 4.39230i | 0.130779 | + | 0.226516i | ||||
\(377\) | 35.5167 | 1.82920 | ||||||||
\(378\) | −1.90192 | + | 0.366025i | −0.0978244 | + | 0.0188263i | ||||
\(379\) | −28.3205 | −1.45473 | −0.727363 | − | 0.686253i | \(-0.759255\pi\) | ||||
−0.727363 | + | 0.686253i | \(0.759255\pi\) | |||||||
\(380\) | −1.80385 | − | 3.12436i | −0.0925354 | − | 0.160276i | ||||
\(381\) | 7.59808 | − | 13.1603i | 0.389261 | − | 0.674220i | ||||
\(382\) | −1.80385 | + | 3.12436i | −0.0922929 | + | 0.159856i | ||||
\(383\) | −5.66025 | − | 9.80385i | −0.289225 | − | 0.500953i | 0.684400 | − | 0.729107i | \(-0.260064\pi\) |
−0.973625 | + | 0.228154i | \(0.926731\pi\) | |||||||
\(384\) | 10.1436 | 0.517638 | ||||||||
\(385\) | 2.36603 | − | 6.83013i | 0.120584 | − | 0.348096i | ||||
\(386\) | −6.73205 | −0.342652 | ||||||||
\(387\) | 3.59808 | + | 6.23205i | 0.182900 | + | 0.316793i | ||||
\(388\) | 0.784610 | − | 1.35898i | 0.0398325 | − | 0.0689920i | ||||
\(389\) | −18.2942 | + | 31.6865i | −0.927554 | + | 1.60657i | −0.140153 | + | 0.990130i | \(0.544760\pi\) |
−0.787401 | + | 0.616441i | \(0.788574\pi\) | |||||||
\(390\) | 2.09808 | + | 3.63397i | 0.106240 | + | 0.184013i | ||||
\(391\) | −8.53590 | −0.431679 | ||||||||
\(392\) | 13.9474 | + | 10.9808i | 0.704452 | + | 0.554612i | ||||
\(393\) | −8.53590 | −0.430579 | ||||||||
\(394\) | 6.46410 | + | 11.1962i | 0.325657 | + | 0.564054i | ||||
\(395\) | −6.69615 | + | 11.5981i | −0.336920 | + | 0.583563i | ||||
\(396\) | −2.00000 | + | 3.46410i | −0.100504 | + | 0.174078i | ||||
\(397\) | 10.4019 | + | 18.0167i | 0.522058 | + | 0.904230i | 0.999671 | + | 0.0256600i | \(0.00816873\pi\) |
−0.477613 | + | 0.878570i | \(0.658498\pi\) | |||||||
\(398\) | 16.1051 | 0.807277 | ||||||||
\(399\) | −2.13397 | + | 6.16025i | −0.106832 | + | 0.308398i | ||||
\(400\) | 1.07180 | 0.0535898 | ||||||||
\(401\) | −2.19615 | − | 3.80385i | −0.109671 | − | 0.189955i | 0.805966 | − | 0.591962i | \(-0.201646\pi\) |
−0.915637 | + | 0.402006i | \(0.868313\pi\) | |||||||
\(402\) | 0.973721 | − | 1.68653i | 0.0485648 | − | 0.0841166i | ||||
\(403\) | −18.5263 | + | 32.0885i | −0.922860 | + | 1.59844i | ||||
\(404\) | −7.85641 | − | 13.6077i | −0.390871 | − | 0.677008i | ||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 11.7846 | − | 2.26795i | 0.584860 | − | 0.112556i | ||||
\(407\) | −19.6603 | −0.974523 | ||||||||
\(408\) | −8.53590 | − | 14.7846i | −0.422590 | − | 0.731947i | ||||
\(409\) | −15.4282 | + | 26.7224i | −0.762876 | + | 1.32134i | 0.178487 | + | 0.983942i | \(0.442880\pi\) |
−0.941362 | + | 0.337397i | \(0.890454\pi\) | |||||||
\(410\) | −1.00000 | + | 1.73205i | −0.0493865 | + | 0.0855399i | ||||
\(411\) | −4.09808 | − | 7.09808i | −0.202143 | − | 0.350122i | ||||
\(412\) | −1.75129 | −0.0862798 | ||||||||
\(413\) | −17.6603 | − | 20.3923i | −0.869004 | − | 1.00344i | ||||
\(414\) | −0.928203 | −0.0456187 | ||||||||
\(415\) | 4.56218 | + | 7.90192i | 0.223949 | + | 0.387890i | ||||
\(416\) | −16.7846 | + | 29.0718i | −0.822933 | + | 1.42536i | ||||
\(417\) | −3.96410 | + | 6.86603i | −0.194123 | + | 0.336231i | ||||
\(418\) | −2.46410 | − | 4.26795i | −0.120523 | − | 0.208752i | ||||
\(419\) | −28.5359 | −1.39407 | −0.697035 | − | 0.717037i | \(-0.745498\pi\) | ||||
−0.697035 | + | 0.717037i | \(0.745498\pi\) | |||||||
\(420\) | −2.53590 | − | 2.92820i | −0.123739 | − | 0.142882i | ||||
\(421\) | 13.9282 | 0.678819 | 0.339410 | − | 0.940639i | \(-0.389773\pi\) | ||||
0.339410 | + | 0.940639i | \(0.389773\pi\) | |||||||
\(422\) | −7.66025 | − | 13.2679i | −0.372895 | − | 0.645874i | ||||
\(423\) | −1.00000 | + | 1.73205i | −0.0486217 | + | 0.0842152i | ||||
\(424\) | −10.6410 | + | 18.4308i | −0.516773 | + | 0.895078i | ||||
\(425\) | −3.36603 | − | 5.83013i | −0.163276 | − | 0.282803i | ||||
\(426\) | 3.07180 | 0.148829 | ||||||||
\(427\) | 10.3923 | − | 2.00000i | 0.502919 | − | 0.0967868i | ||||
\(428\) | 12.0000 | 0.580042 | ||||||||
\(429\) | −7.83013 | − | 13.5622i | −0.378042 | − | 0.654788i | ||||
\(430\) | 2.63397 | − | 4.56218i | 0.127022 | − | 0.220008i | ||||
\(431\) | 8.66025 | − | 15.0000i | 0.417150 | − | 0.722525i | −0.578502 | − | 0.815681i | \(-0.696362\pi\) |
0.995651 | + | 0.0931566i | \(0.0296957\pi\) | |||||||
\(432\) | 0.535898 | + | 0.928203i | 0.0257834 | + | 0.0446582i | ||||
\(433\) | 4.80385 | 0.230858 | 0.115429 | − | 0.993316i | \(-0.463176\pi\) | ||||
0.115429 | + | 0.993316i | \(0.463176\pi\) | |||||||
\(434\) | −4.09808 | + | 11.8301i | −0.196714 | + | 0.567864i | ||||
\(435\) | −6.19615 | −0.297083 | ||||||||
\(436\) | 8.05256 | + | 13.9474i | 0.385648 | + | 0.667961i | ||||
\(437\) | −1.56218 | + | 2.70577i | −0.0747291 | + | 0.129435i | ||||
\(438\) | −1.70577 | + | 2.95448i | −0.0815049 | + | 0.141171i | ||||
\(439\) | −3.73205 | − | 6.46410i | −0.178121 | − | 0.308515i | 0.763116 | − | 0.646262i | \(-0.223669\pi\) |
−0.941237 | + | 0.337747i | \(0.890335\pi\) | |||||||
\(440\) | 6.92820 | 0.330289 | ||||||||
\(441\) | −1.00000 | + | 6.92820i | −0.0476190 | + | 0.329914i | ||||
\(442\) | 28.2487 | 1.34365 | ||||||||
\(443\) | −1.26795 | − | 2.19615i | −0.0602421 | − | 0.104342i | 0.834331 | − | 0.551263i | \(-0.185854\pi\) |
−0.894574 | + | 0.446921i | \(0.852521\pi\) | |||||||
\(444\) | −5.26795 | + | 9.12436i | −0.250006 | + | 0.433023i | ||||
\(445\) | 4.56218 | − | 7.90192i | 0.216268 | − | 0.374587i | ||||
\(446\) | −0.143594 | − | 0.248711i | −0.00679935 | − | 0.0117768i | ||||
\(447\) | 21.8564 | 1.03377 | ||||||||
\(448\) | −1.85641 | + | 5.35898i | −0.0877070 | + | 0.253188i | ||||
\(449\) | −8.14359 | −0.384320 | −0.192160 | − | 0.981364i | \(-0.561549\pi\) | ||||
−0.192160 | + | 0.981364i | \(0.561549\pi\) | |||||||
\(450\) | −0.366025 | − | 0.633975i | −0.0172546 | − | 0.0298858i | ||||
\(451\) | 3.73205 | − | 6.46410i | 0.175735 | − | 0.304383i | ||||
\(452\) | −3.60770 | + | 6.24871i | −0.169692 | + | 0.293915i | ||||
\(453\) | 2.46410 | + | 4.26795i | 0.115774 | + | 0.200526i | ||||
\(454\) | 11.4641 | 0.538037 | ||||||||
\(455\) | 14.8923 | − | 2.86603i | 0.698162 | − | 0.134361i | ||||
\(456\) | −6.24871 | −0.292623 | ||||||||
\(457\) | −0.330127 | − | 0.571797i | −0.0154427 | − | 0.0267475i | 0.858201 | − | 0.513314i | \(-0.171582\pi\) |
−0.873643 | + | 0.486567i | \(0.838249\pi\) | |||||||
\(458\) | 1.09808 | − | 1.90192i | 0.0513097 | − | 0.0888711i | ||||
\(459\) | 3.36603 | − | 5.83013i | 0.157113 | − | 0.272127i | ||||
\(460\) | −0.928203 | − | 1.60770i | −0.0432777 | − | 0.0749592i | ||||
\(461\) | −34.9808 | −1.62922 | −0.814608 | − | 0.580012i | \(-0.803048\pi\) | ||||
−0.814608 | + | 0.580012i | \(0.803048\pi\) | |||||||
\(462\) | −3.46410 | − | 4.00000i | −0.161165 | − | 0.186097i | ||||
\(463\) | 22.2679 | 1.03488 | 0.517440 | − | 0.855720i | \(-0.326885\pi\) | ||||
0.517440 | + | 0.855720i | \(0.326885\pi\) | |||||||
\(464\) | −3.32051 | − | 5.75129i | −0.154151 | − | 0.266997i | ||||
\(465\) | 3.23205 | − | 5.59808i | 0.149883 | − | 0.259605i | ||||
\(466\) | 6.33975 | − | 10.9808i | 0.293683 | − | 0.508674i | ||||
\(467\) | 13.9282 | + | 24.1244i | 0.644520 | + | 1.11634i | 0.984412 | + | 0.175877i | \(0.0562762\pi\) |
−0.339892 | + | 0.940465i | \(0.610390\pi\) | |||||||
\(468\) | −8.39230 | −0.387934 | ||||||||
\(469\) | −4.60770 | − | 5.32051i | −0.212764 | − | 0.245678i | ||||
\(470\) | 1.46410 | 0.0675340 | ||||||||
\(471\) | −7.19615 | − | 12.4641i | −0.331581 | − | 0.574315i | ||||
\(472\) | 12.9282 | − | 22.3923i | 0.595069 | − | 1.03069i | ||||
\(473\) | −9.83013 | + | 17.0263i | −0.451990 | + | 0.782869i | ||||
\(474\) | 4.90192 | + | 8.49038i | 0.225153 | + | 0.389976i | ||||
\(475\) | −2.46410 | −0.113061 | ||||||||
\(476\) | −25.6077 | + | 4.92820i | −1.17373 | + | 0.225884i | ||||
\(477\) | −8.39230 | −0.384257 | ||||||||
\(478\) | −7.66025 | − | 13.2679i | −0.350372 | − | 0.606862i | ||||
\(479\) | 16.3923 | − | 28.3923i | 0.748984 | − | 1.29728i | −0.199327 | − | 0.979933i | \(-0.563876\pi\) |
0.948310 | − | 0.317344i | \(-0.102791\pi\) | |||||||
\(480\) | 2.92820 | − | 5.07180i | 0.133654 | − | 0.231495i | ||||
\(481\) | −20.6244 | − | 35.7224i | −0.940390 | − | 1.62880i | ||||
\(482\) | 4.78461 | 0.217933 | ||||||||
\(483\) | −1.09808 | + | 3.16987i | −0.0499642 | + | 0.144234i | ||||
\(484\) | 5.17691 | 0.235314 | ||||||||
\(485\) | −0.535898 | − | 0.928203i | −0.0243339 | − | 0.0421475i | ||||
\(486\) | 0.366025 | − | 0.633975i | 0.0166032 | − | 0.0287577i | ||||
\(487\) | 15.7942 | − | 27.3564i | 0.715705 | − | 1.23964i | −0.246982 | − | 0.969020i | \(-0.579439\pi\) |
0.962687 | − | 0.270617i | \(-0.0872277\pi\) | |||||||
\(488\) | 5.07180 | + | 8.78461i | 0.229589 | + | 0.397661i | ||||
\(489\) | 5.85641 | 0.264836 | ||||||||
\(490\) | 4.75833 | − | 1.90192i | 0.214959 | − | 0.0859202i | ||||
\(491\) | 10.2487 | 0.462518 | 0.231259 | − | 0.972892i | \(-0.425716\pi\) | ||||
0.231259 | + | 0.972892i | \(0.425716\pi\) | |||||||
\(492\) | −2.00000 | − | 3.46410i | −0.0901670 | − | 0.156174i | ||||
\(493\) | −20.8564 | + | 36.1244i | −0.939325 | + | 1.62696i | ||||
\(494\) | 5.16987 | − | 8.95448i | 0.232604 | − | 0.402881i | ||||
\(495\) | 1.36603 | + | 2.36603i | 0.0613983 | + | 0.106345i | ||||
\(496\) | 6.92820 | 0.311086 | ||||||||
\(497\) | 3.63397 | − | 10.4904i | 0.163006 | − | 0.470558i | ||||
\(498\) | 6.67949 | 0.299315 | ||||||||
\(499\) | 10.2321 | + | 17.7224i | 0.458050 | + | 0.793365i | 0.998858 | − | 0.0477808i | \(-0.0152149\pi\) |
−0.540808 | + | 0.841146i | \(0.681882\pi\) | |||||||
\(500\) | 0.732051 | − | 1.26795i | 0.0327383 | − | 0.0567044i | ||||
\(501\) | −0.169873 | + | 0.294229i | −0.00758937 | + | 0.0131452i | ||||
\(502\) | −2.41154 | − | 4.17691i | −0.107632 | − | 0.186425i | ||||
\(503\) | −6.39230 | −0.285019 | −0.142509 | − | 0.989793i | \(-0.545517\pi\) | ||||
−0.142509 | + | 0.989793i | \(0.545517\pi\) | |||||||
\(504\) | −6.58846 | + | 1.26795i | −0.293473 | + | 0.0564789i | ||||
\(505\) | −10.7321 | −0.477570 | ||||||||
\(506\) | −1.26795 | − | 2.19615i | −0.0563672 | − | 0.0976309i | ||||
\(507\) | 9.92820 | − | 17.1962i | 0.440927 | − | 0.763708i | ||||
\(508\) | 11.1244 | − | 19.2679i | 0.493563 | − | 0.854877i | ||||
\(509\) | −5.73205 | − | 9.92820i | −0.254069 | − | 0.440060i | 0.710573 | − | 0.703623i | \(-0.248436\pi\) |
−0.964642 | + | 0.263563i | \(0.915102\pi\) | |||||||
\(510\) | −4.92820 | −0.218225 | ||||||||
\(511\) | 8.07180 | + | 9.32051i | 0.357075 | + | 0.412315i | ||||
\(512\) | 11.7128 | 0.517638 | ||||||||
\(513\) | −1.23205 | − | 2.13397i | −0.0543964 | − | 0.0942173i | ||||
\(514\) | −4.26795 | + | 7.39230i | −0.188251 | + | 0.326061i | ||||
\(515\) | −0.598076 | + | 1.03590i | −0.0263544 | + | 0.0456471i | ||||
\(516\) | 5.26795 | + | 9.12436i | 0.231909 | + | 0.401677i | ||||
\(517\) | −5.46410 | −0.240311 | ||||||||
\(518\) | −9.12436 | − | 10.5359i | −0.400901 | − | 0.462921i | ||||
\(519\) | −21.4641 | −0.942169 | ||||||||
\(520\) | 7.26795 | + | 12.5885i | 0.318721 | + | 0.552040i | ||||
\(521\) | −0.732051 | + | 1.26795i | −0.0320717 | + | 0.0555499i | −0.881616 | − | 0.471968i | \(-0.843544\pi\) |
0.849544 | + | 0.527518i | \(0.176877\pi\) | |||||||
\(522\) | −2.26795 | + | 3.92820i | −0.0992654 | + | 0.171933i | ||||
\(523\) | 12.1340 | + | 21.0167i | 0.530582 | + | 0.918994i | 0.999363 | + | 0.0356803i | \(0.0113598\pi\) |
−0.468782 | + | 0.883314i | \(0.655307\pi\) | |||||||
\(524\) | −12.4974 | −0.545952 | ||||||||
\(525\) | −2.59808 | + | 0.500000i | −0.113389 | + | 0.0218218i | ||||
\(526\) | −9.07180 | −0.395549 | ||||||||
\(527\) | −21.7583 | − | 37.6865i | −0.947808 | − | 1.64165i | ||||
\(528\) | −1.46410 | + | 2.53590i | −0.0637168 | + | 0.110361i | ||||
\(529\) | 10.6962 | − | 18.5263i | 0.465050 | − | 0.805490i | ||||
\(530\) | 3.07180 | + | 5.32051i | 0.133430 | + | 0.231108i | ||||
\(531\) | 10.1962 | 0.442475 | ||||||||
\(532\) | −3.12436 | + | 9.01924i | −0.135458 | + | 0.391034i | ||||
\(533\) | 15.6603 | 0.678321 | ||||||||
\(534\) | −3.33975 | − | 5.78461i | −0.144525 | − | 0.250325i | ||||
\(535\) | 4.09808 | − | 7.09808i | 0.177175 | − | 0.306877i | ||||
\(536\) | 3.37307 | − | 5.84232i | 0.145694 | − | 0.252350i | ||||
\(537\) | −5.00000 | − | 8.66025i | −0.215766 | − | 0.373718i | ||||
\(538\) | −14.2487 | −0.614306 | ||||||||
\(539\) | −17.7583 | + | 7.09808i | −0.764905 | + | 0.305736i | ||||
\(540\) | 1.46410 | 0.0630049 | ||||||||
\(541\) | 17.8923 | + | 30.9904i | 0.769250 | + | 1.33238i | 0.937970 | + | 0.346716i | \(0.112703\pi\) |
−0.168720 | + | 0.985664i | \(0.553963\pi\) | |||||||
\(542\) | −6.19615 | + | 10.7321i | −0.266148 | + | 0.460981i | ||||
\(543\) | 5.16025 | − | 8.93782i | 0.221448 | − | 0.383559i | ||||
\(544\) | −19.7128 | − | 34.1436i | −0.845180 | − | 1.46389i | ||||
\(545\) | 11.0000 | 0.471188 | ||||||||
\(546\) | 3.63397 | − | 10.4904i | 0.155520 | − | 0.448947i | ||||
\(547\) | 22.2487 | 0.951286 | 0.475643 | − | 0.879638i | \(-0.342215\pi\) | ||||
0.475643 | + | 0.879638i | \(0.342215\pi\) | |||||||
\(548\) | −6.00000 | − | 10.3923i | −0.256307 | − | 0.443937i | ||||
\(549\) | −2.00000 | + | 3.46410i | −0.0853579 | + | 0.147844i | ||||
\(550\) | 1.00000 | − | 1.73205i | 0.0426401 | − | 0.0738549i | ||||
\(551\) | 7.63397 | + | 13.2224i | 0.325218 | + | 0.563295i | ||||
\(552\) | −3.21539 | −0.136856 | ||||||||
\(553\) | 34.7942 | − | 6.69615i | 1.47960 | − | 0.284749i | ||||
\(554\) | 1.94744 | 0.0827388 | ||||||||
\(555\) | 3.59808 | + | 6.23205i | 0.152730 | + | 0.264536i | ||||
\(556\) | −5.80385 | + | 10.0526i | −0.246138 | + | 0.426323i | ||||
\(557\) | 13.3923 | − | 23.1962i | 0.567450 | − | 0.982853i | −0.429367 | − | 0.903130i | \(-0.641263\pi\) |
0.996817 | − | 0.0797224i | \(-0.0254034\pi\) | |||||||
\(558\) | −2.36603 | − | 4.09808i | −0.100162 | − | 0.173485i | ||||
\(559\) | −41.2487 | −1.74463 | ||||||||
\(560\) | −1.85641 | − | 2.14359i | −0.0784475 | − | 0.0905834i | ||||
\(561\) | 18.3923 | 0.776524 | ||||||||
\(562\) | 5.07180 | + | 8.78461i | 0.213941 | + | 0.370556i | ||||
\(563\) | 9.00000 | − | 15.5885i | 0.379305 | − | 0.656975i | −0.611656 | − | 0.791123i | \(-0.709497\pi\) |
0.990961 | + | 0.134148i | \(0.0428299\pi\) | |||||||
\(564\) | −1.46410 | + | 2.53590i | −0.0616498 | + | 0.106781i | ||||
\(565\) | 2.46410 | + | 4.26795i | 0.103666 | + | 0.179554i | ||||
\(566\) | 0.0910347 | 0.00382647 | ||||||||
\(567\) | −1.73205 | − | 2.00000i | −0.0727393 | − | 0.0839921i | ||||
\(568\) | 10.6410 | 0.446487 | ||||||||
\(569\) | 13.2224 | + | 22.9019i | 0.554313 | + | 0.960099i | 0.997957 | + | 0.0638952i | \(0.0203523\pi\) |
−0.443643 | + | 0.896203i | \(0.646314\pi\) | |||||||
\(570\) | −0.901924 | + | 1.56218i | −0.0377774 | + | 0.0654324i | ||||
\(571\) | −19.6962 | + | 34.1147i | −0.824258 | + | 1.42766i | 0.0782265 | + | 0.996936i | \(0.475074\pi\) |
−0.902485 | + | 0.430722i | \(0.858259\pi\) | |||||||
\(572\) | −11.4641 | − | 19.8564i | −0.479338 | − | 0.830238i | ||||
\(573\) | −4.92820 | −0.205879 | ||||||||
\(574\) | 5.19615 | − | 1.00000i | 0.216883 | − | 0.0417392i | ||||
\(575\) | −1.26795 | −0.0528771 | ||||||||
\(576\) | −1.07180 | − | 1.85641i | −0.0446582 | − | 0.0773503i | ||||
\(577\) | −5.66987 | + | 9.82051i | −0.236040 | + | 0.408833i | −0.959574 | − | 0.281455i | \(-0.909183\pi\) |
0.723534 | + | 0.690288i | \(0.242516\pi\) | |||||||
\(578\) | −10.3660 | + | 17.9545i | −0.431170 | + | 0.746808i | ||||
\(579\) | −4.59808 | − | 7.96410i | −0.191090 | − | 0.330977i | ||||
\(580\) | −9.07180 | −0.376686 | ||||||||
\(581\) | 7.90192 | − | 22.8109i | 0.327827 | − | 0.946355i | ||||
\(582\) | −0.784610 | −0.0325231 | ||||||||
\(583\) | −11.4641 | − | 19.8564i | −0.474795 | − | 0.822368i | ||||
\(584\) | −5.90897 | + | 10.2346i | −0.244515 | + | 0.423512i | ||||
\(585\) | −2.86603 | + | 4.96410i | −0.118496 | + | 0.205240i | ||||
\(586\) | −1.85641 | − | 3.21539i | −0.0766874 | − | 0.132827i | ||||
\(587\) | 37.2679 | 1.53821 | 0.769106 | − | 0.639121i | \(-0.220702\pi\) | ||||
0.769106 | + | 0.639121i | \(0.220702\pi\) | |||||||
\(588\) | −1.46410 | + | 10.1436i | −0.0603785 | + | 0.418315i | ||||
\(589\) | −15.9282 | −0.656310 | ||||||||
\(590\) | −3.73205 | − | 6.46410i | −0.153646 | − | 0.266123i | ||||
\(591\) | −8.83013 | + | 15.2942i | −0.363223 | + | 0.629121i | ||||
\(592\) | −3.85641 | + | 6.67949i | −0.158497 | + | 0.274525i | ||||
\(593\) | 18.9545 | + | 32.8301i | 0.778367 | + | 1.34817i | 0.932882 | + | 0.360181i | \(0.117285\pi\) |
−0.154515 | + | 0.987990i | \(0.549381\pi\) | |||||||
\(594\) | 2.00000 | 0.0820610 | ||||||||
\(595\) | −5.83013 | + | 16.8301i | −0.239012 | + | 0.689968i | ||||
\(596\) | 32.0000 | 1.31077 | ||||||||
\(597\) | 11.0000 | + | 19.0526i | 0.450200 | + | 0.779769i | ||||
\(598\) | 2.66025 | − | 4.60770i | 0.108786 | − | 0.188423i | ||||
\(599\) | −5.12436 | + | 8.87564i | −0.209375 | + | 0.362649i | −0.951518 | − | 0.307593i | \(-0.900476\pi\) |
0.742142 | + | 0.670242i | \(0.233810\pi\) | |||||||
\(600\) | −1.26795 | − | 2.19615i | −0.0517638 | − | 0.0896575i | ||||
\(601\) | −13.9282 | −0.568143 | −0.284072 | − | 0.958803i | \(-0.591685\pi\) | ||||
−0.284072 | + | 0.958803i | \(0.591685\pi\) | |||||||
\(602\) | −13.6865 | + | 2.63397i | −0.557821 | + | 0.107353i | ||||
\(603\) | 2.66025 | 0.108334 | ||||||||
\(604\) | 3.60770 | + | 6.24871i | 0.146795 | + | 0.254256i | ||||
\(605\) | 1.76795 | − | 3.06218i | 0.0718774 | − | 0.124495i | ||||
\(606\) | −3.92820 | + | 6.80385i | −0.159572 | + | 0.276387i | ||||
\(607\) | 3.59808 | + | 6.23205i | 0.146041 | + | 0.252951i | 0.929761 | − | 0.368164i | \(-0.120013\pi\) |
−0.783720 | + | 0.621115i | \(0.786680\pi\) | |||||||
\(608\) | −14.4308 | −0.585245 | ||||||||
\(609\) | 10.7321 | + | 12.3923i | 0.434885 | + | 0.502162i | ||||
\(610\) | 2.92820 | 0.118559 | ||||||||
\(611\) | −5.73205 | − | 9.92820i | −0.231894 | − | 0.401652i | ||||
\(612\) | 4.92820 | − | 8.53590i | 0.199211 | − | 0.345043i | ||||
\(613\) | 6.53590 | − | 11.3205i | 0.263982 | − | 0.457231i | −0.703314 | − | 0.710879i | \(-0.748297\pi\) |
0.967297 | + | 0.253648i | \(0.0816306\pi\) | |||||||
\(614\) | 2.88269 | + | 4.99296i | 0.116336 | + | 0.201499i | ||||
\(615\) | −2.73205 | −0.110167 | ||||||||
\(616\) | −12.0000 | − | 13.8564i | −0.483494 | − | 0.558291i | ||||
\(617\) | 12.2487 | 0.493115 | 0.246557 | − | 0.969128i | \(-0.420701\pi\) | ||||
0.246557 | + | 0.969128i | \(0.420701\pi\) | |||||||
\(618\) | 0.437822 | + | 0.758330i | 0.0176118 | + | 0.0305045i | ||||
\(619\) | 21.9641 | − | 38.0429i | 0.882812 | − | 1.52907i | 0.0346105 | − | 0.999401i | \(-0.488981\pi\) |
0.848201 | − | 0.529674i | \(-0.177686\pi\) | |||||||
\(620\) | 4.73205 | − | 8.19615i | 0.190044 | − | 0.329165i | ||||
\(621\) | −0.633975 | − | 1.09808i | −0.0254405 | − | 0.0440643i | ||||
\(622\) | −11.0718 | −0.443939 | ||||||||
\(623\) | −23.7058 | + | 4.56218i | −0.949752 | + | 0.182780i | ||||
\(624\) | −6.14359 | −0.245941 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −1.70577 | + | 2.95448i | −0.0681763 | + | 0.118085i | ||||
\(627\) | 3.36603 | − | 5.83013i | 0.134426 | − | 0.232833i | ||||
\(628\) | −10.5359 | − | 18.2487i | −0.420428 | − | 0.728203i | ||||
\(629\) | 48.4449 | 1.93162 | ||||||||
\(630\) | −0.633975 | + | 1.83013i | −0.0252582 | + | 0.0729140i | ||||
\(631\) | 7.21539 | 0.287240 | 0.143620 | − | 0.989633i | \(-0.454126\pi\) | ||||
0.143620 | + | 0.989633i | \(0.454126\pi\) | |||||||
\(632\) | 16.9808 | + | 29.4115i | 0.675458 | + | 1.16993i | ||||
\(633\) | 10.4641 | − | 18.1244i | 0.415911 | − | 0.720378i | ||||
\(634\) | −11.1436 | + | 19.3013i | −0.442569 | + | 0.766551i | ||||
\(635\) | −7.59808 | − | 13.1603i | −0.301520 | − | 0.522249i | ||||
\(636\) | −12.2872 | −0.487219 | ||||||||
\(637\) | −31.5263 | − | 24.8205i | −1.24912 | − | 0.983424i | ||||
\(638\) | −12.3923 | −0.490616 | ||||||||
\(639\) | 2.09808 | + | 3.63397i | 0.0829986 | + | 0.143758i | ||||
\(640\) | 5.07180 | − | 8.78461i | 0.200480 | − | 0.347242i | ||||
\(641\) | −7.09808 | + | 12.2942i | −0.280357 | + | 0.485593i | −0.971473 | − | 0.237151i | \(-0.923786\pi\) |
0.691116 | + | 0.722744i | \(0.257120\pi\) | |||||||
\(642\) | −3.00000 | − | 5.19615i | −0.118401 | − | 0.205076i | ||||
\(643\) | −40.5167 | −1.59782 | −0.798911 | − | 0.601450i | \(-0.794590\pi\) | ||||
−0.798911 | + | 0.601450i | \(0.794590\pi\) | |||||||
\(644\) | −1.60770 | + | 4.64102i | −0.0633521 | + | 0.182882i | ||||
\(645\) | 7.19615 | 0.283348 | ||||||||
\(646\) | 6.07180 | + | 10.5167i | 0.238892 | + | 0.413772i | ||||
\(647\) | −18.9545 | + | 32.8301i | −0.745178 | + | 1.29069i | 0.204934 | + | 0.978776i | \(0.434302\pi\) |
−0.950112 | + | 0.311910i | \(0.899031\pi\) | |||||||
\(648\) | 1.26795 | − | 2.19615i | 0.0498097 | − | 0.0862730i | ||||
\(649\) | 13.9282 | + | 24.1244i | 0.546730 | + | 0.946964i | ||||
\(650\) | 4.19615 | 0.164587 | ||||||||
\(651\) | −16.7942 | + | 3.23205i | −0.658218 | + | 0.126674i | ||||
\(652\) | 8.57437 | 0.335798 | ||||||||
\(653\) | 6.70577 | + | 11.6147i | 0.262417 | + | 0.454520i | 0.966884 | − | 0.255217i | \(-0.0821470\pi\) |
−0.704467 | + | 0.709737i | \(0.748814\pi\) | |||||||
\(654\) | 4.02628 | − | 6.97372i | 0.157440 | − | 0.272694i | ||||
\(655\) | −4.26795 | + | 7.39230i | −0.166763 | + | 0.288841i | ||||
\(656\) | −1.46410 | − | 2.53590i | −0.0571636 | − | 0.0990102i | ||||
\(657\) | −4.66025 | −0.181814 | ||||||||
\(658\) | −2.53590 | − | 2.92820i | −0.0988596 | − | 0.114153i | ||||
\(659\) | −10.9282 | −0.425702 | −0.212851 | − | 0.977085i | \(-0.568275\pi\) | ||||
−0.212851 | + | 0.977085i | \(0.568275\pi\) | |||||||
\(660\) | 2.00000 | + | 3.46410i | 0.0778499 | + | 0.134840i | ||||
\(661\) | −1.76795 | + | 3.06218i | −0.0687653 | + | 0.119105i | −0.898358 | − | 0.439264i | \(-0.855239\pi\) |
0.829593 | + | 0.558369i | \(0.188573\pi\) | |||||||
\(662\) | −8.02628 | + | 13.9019i | −0.311950 | + | 0.540314i | ||||
\(663\) | 19.2942 | + | 33.4186i | 0.749326 | + | 1.29787i | ||||
\(664\) | 23.1384 | 0.897946 | ||||||||
\(665\) | 4.26795 | + | 4.92820i | 0.165504 | + | 0.191108i | ||||
\(666\) | 5.26795 | 0.204129 | ||||||||
\(667\) | 3.92820 | + | 6.80385i | 0.152101 | + | 0.263446i | ||||
\(668\) | −0.248711 | + | 0.430781i | −0.00962293 | + | 0.0166674i | ||||
\(669\) | 0.196152 | − | 0.339746i | 0.00758369 | − | 0.0131353i | ||||
\(670\) | −0.973721 | − | 1.68653i | −0.0376181 | − | 0.0651565i | ||||
\(671\) | −10.9282 | −0.421879 | ||||||||
\(672\) | −15.2154 | + | 2.92820i | −0.586946 | + | 0.112958i | ||||
\(673\) | −44.6603 | −1.72153 | −0.860763 | − | 0.509006i | \(-0.830013\pi\) | ||||
−0.860763 | + | 0.509006i | \(0.830013\pi\) | |||||||
\(674\) | 12.4378 | + | 21.5429i | 0.479087 | + | 0.829803i | ||||
\(675\) | 0.500000 | − | 0.866025i | 0.0192450 | − | 0.0333333i | ||||
\(676\) | 14.5359 | − | 25.1769i | 0.559073 | − | 0.968343i | ||||
\(677\) | 4.43782 | + | 7.68653i | 0.170559 | + | 0.295417i | 0.938616 | − | 0.344965i | \(-0.112109\pi\) |
−0.768056 | + | 0.640382i | \(0.778776\pi\) | |||||||
\(678\) | 3.60770 | 0.138553 | ||||||||
\(679\) | −0.928203 | + | 2.67949i | −0.0356212 | + | 0.102829i | ||||
\(680\) | −17.0718 | −0.654674 | ||||||||
\(681\) | 7.83013 | + | 13.5622i | 0.300051 | + | 0.519704i | ||||
\(682\) | 6.46410 | − | 11.1962i | 0.247523 | − | 0.428723i | ||||
\(683\) | −5.02628 | + | 8.70577i | −0.192325 | + | 0.333117i | −0.946020 | − | 0.324107i | \(-0.894936\pi\) |
0.753695 | + | 0.657224i | \(0.228270\pi\) | |||||||
\(684\) | −1.80385 | − | 3.12436i | −0.0689718 | − | 0.119463i | ||||
\(685\) | −8.19615 | −0.313159 | ||||||||
\(686\) | −12.0455 | − | 6.22243i | −0.459900 | − | 0.237574i | ||||
\(687\) | 3.00000 | 0.114457 | ||||||||
\(688\) | 3.85641 | + | 6.67949i | 0.147024 | + | 0.254653i | ||||
\(689\) | 24.0526 | − | 41.6603i | 0.916330 | − | 1.58713i | ||||
\(690\) | −0.464102 | + | 0.803848i | −0.0176680 | + | 0.0306020i | ||||
\(691\) | 9.42820 | + | 16.3301i | 0.358666 | + | 0.621227i | 0.987738 | − | 0.156119i | \(-0.0498985\pi\) |
−0.629072 | + | 0.777347i | \(0.716565\pi\) | |||||||
\(692\) | −31.4256 | −1.19462 | ||||||||
\(693\) | 2.36603 | − | 6.83013i | 0.0898779 | − | 0.259455i | ||||
\(694\) | −25.5692 | −0.970594 | ||||||||
\(695\) | 3.96410 | + | 6.86603i | 0.150367 | + | 0.260443i | ||||
\(696\) | −7.85641 | + | 13.6077i | −0.297796 | + | 0.515798i | ||||
\(697\) | −9.19615 | + | 15.9282i | −0.348329 | + | 0.603324i | ||||
\(698\) | −8.05256 | − | 13.9474i | −0.304794 | − | 0.527918i | ||||
\(699\) | 17.3205 | 0.655122 | ||||||||
\(700\) | −3.80385 | + | 0.732051i | −0.143772 | + | 0.0276689i | ||||
\(701\) | 22.5885 | 0.853154 | 0.426577 | − | 0.904451i | \(-0.359719\pi\) | ||||
0.426577 | + | 0.904451i | \(0.359719\pi\) | |||||||
\(702\) | 2.09808 | + | 3.63397i | 0.0791868 | + | 0.137156i | ||||
\(703\) | 8.86603 | − | 15.3564i | 0.334388 | − | 0.579178i | ||||
\(704\) | 2.92820 | − | 5.07180i | 0.110361 | − | 0.191151i | ||||
\(705\) | 1.00000 | + | 1.73205i | 0.0376622 | + | 0.0652328i | ||||
\(706\) | 15.4641 | 0.581999 | ||||||||
\(707\) | 18.5885 | + | 21.4641i | 0.699091 | + | 0.807241i | ||||
\(708\) | 14.9282 | 0.561036 | ||||||||
\(709\) | 7.46410 | + | 12.9282i | 0.280320 | + | 0.485529i | 0.971464 | − | 0.237189i | \(-0.0762260\pi\) |
−0.691143 | + | 0.722718i | \(0.742893\pi\) | |||||||
\(710\) | 1.53590 | − | 2.66025i | 0.0576412 | − | 0.0998376i | ||||
\(711\) | −6.69615 | + | 11.5981i | −0.251125 | + | 0.434962i | ||||
\(712\) | −11.5692 | − | 20.0385i | −0.433575 | − | 0.750974i | ||||
\(713\) | −8.19615 | −0.306948 | ||||||||
\(714\) | 8.53590 | + | 9.85641i | 0.319448 | + | 0.368867i | ||||
\(715\) | −15.6603 | −0.585660 | ||||||||
\(716\) | −7.32051 | − | 12.6795i | −0.273580 | − | 0.473855i | ||||
\(717\) | 10.4641 | − | 18.1244i | 0.390789 | − | 0.676866i | ||||
\(718\) | 1.73205 | − | 3.00000i | 0.0646396 | − | 0.111959i | ||||
\(719\) | 13.7321 | + | 23.7846i | 0.512119 | + | 0.887016i | 0.999901 | + | 0.0140509i | \(0.00447269\pi\) |
−0.487782 | + | 0.872965i | \(0.662194\pi\) | |||||||
\(720\) | 1.07180 | 0.0399435 | ||||||||
\(721\) | 3.10770 | − | 0.598076i | 0.115737 | − | 0.0222735i | ||||
\(722\) | −9.46410 | −0.352217 | ||||||||
\(723\) | 3.26795 | + | 5.66025i | 0.121536 | + | 0.210507i | ||||
\(724\) | 7.55514 | − | 13.0859i | 0.280784 | − | 0.486333i | ||||
\(725\) | −3.09808 | + | 5.36603i | −0.115060 | + | 0.199289i | ||||
\(726\) | −1.29423 | − | 2.24167i | −0.0480333 | − | 0.0831962i | ||||
\(727\) | −30.6603 | −1.13713 | −0.568563 | − | 0.822640i | \(-0.692500\pi\) | ||||
−0.568563 | + | 0.822640i | \(0.692500\pi\) | |||||||
\(728\) | 12.5885 | − | 36.3397i | 0.466559 | − | 1.34684i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.70577 | + | 2.95448i | 0.0631334 | + | 0.109350i | ||||
\(731\) | 24.2224 | − | 41.9545i | 0.895899 | − | 1.55174i | ||||
\(732\) | −2.92820 | + | 5.07180i | −0.108230 | + | 0.187459i | ||||
\(733\) | 9.33013 | + | 16.1603i | 0.344616 | + | 0.596893i | 0.985284 | − | 0.170926i | \(-0.0546758\pi\) |
−0.640668 | + | 0.767818i | \(0.721342\pi\) | |||||||
\(734\) | 0.588457 | 0.0217204 | ||||||||
\(735\) | 5.50000 | + | 4.33013i | 0.202871 | + | 0.159719i | ||||
\(736\) | −7.42563 | −0.273712 | ||||||||
\(737\) | 3.63397 | + | 6.29423i | 0.133859 | + | 0.231851i | ||||
\(738\) | −1.00000 | + | 1.73205i | −0.0368105 | + | 0.0637577i | ||||
\(739\) | 6.89230 | − | 11.9378i | 0.253538 | − | 0.439140i | −0.710960 | − | 0.703233i | \(-0.751739\pi\) |
0.964497 | + | 0.264093i | \(0.0850725\pi\) | |||||||
\(740\) | 5.26795 | + | 9.12436i | 0.193654 | + | 0.335418i | ||||
\(741\) | 14.1244 | 0.518871 | ||||||||
\(742\) | 5.32051 | − | 15.3590i | 0.195322 | − | 0.563846i | ||||
\(743\) | 49.9090 | 1.83098 | 0.915491 | − | 0.402338i | \(-0.131802\pi\) | ||||
0.915491 | + | 0.402338i | \(0.131802\pi\) | |||||||
\(744\) | −8.19615 | − | 14.1962i | −0.300486 | − | 0.520456i | ||||
\(745\) | 10.9282 | − | 18.9282i | 0.400378 | − | 0.693476i | ||||
\(746\) | 6.77757 | − | 11.7391i | 0.248144 | − | 0.429799i | ||||
\(747\) | 4.56218 | + | 7.90192i | 0.166921 | + | 0.289116i | ||||
\(748\) | 26.9282 | 0.984593 | ||||||||
\(749\) | −21.2942 | + | 4.09808i | −0.778074 | + | 0.149740i | ||||
\(750\) | −0.732051 | −0.0267307 | ||||||||
\(751\) | −15.9641 | − | 27.6506i | −0.582538 | − | 1.00899i | −0.995177 | − | 0.0980914i | \(-0.968726\pi\) |
0.412639 | − | 0.910895i | \(-0.364607\pi\) | |||||||
\(752\) | −1.07180 | + | 1.85641i | −0.0390844 | + | 0.0676962i | ||||
\(753\) | 3.29423 | − | 5.70577i | 0.120048 | − | 0.207930i | ||||
\(754\) | −13.0000 | − | 22.5167i | −0.473432 | − | 0.820008i | ||||
\(755\) | 4.92820 | 0.179356 | ||||||||
\(756\) | −2.53590 | − | 2.92820i | −0.0922297 | − | 0.106498i | ||||
\(757\) | −0.143594 | −0.00521900 | −0.00260950 | − | 0.999997i | \(-0.500831\pi\) | ||||
−0.00260950 | + | 0.999997i | \(0.500831\pi\) | |||||||
\(758\) | 10.3660 | + | 17.9545i | 0.376511 | + | 0.652136i | ||||
\(759\) | 1.73205 | − | 3.00000i | 0.0628695 | − | 0.108893i | ||||
\(760\) | −3.12436 | + | 5.41154i | −0.113332 | + | 0.196297i | ||||
\(761\) | −21.6340 | − | 37.4711i | −0.784231 | − | 1.35833i | −0.929457 | − | 0.368929i | \(-0.879724\pi\) |
0.145226 | − | 0.989398i | \(-0.453609\pi\) | |||||||
\(762\) | −11.1244 | −0.402993 | ||||||||
\(763\) | −19.0526 | − | 22.0000i | −0.689749 | − | 0.796453i | ||||
\(764\) | −7.21539 | −0.261044 | ||||||||
\(765\) | −3.36603 | − | 5.83013i | −0.121699 | − | 0.210789i | ||||
\(766\) | −4.14359 | + | 7.17691i | −0.149714 | + | 0.259312i | ||||
\(767\) | −29.2224 | + | 50.6147i | −1.05516 | + | 1.82759i | ||||
\(768\) | −5.85641 | − | 10.1436i | −0.211325 | − | 0.366025i | ||||
\(769\) | 17.6795 | 0.637539 | 0.318769 | − | 0.947832i | \(-0.396730\pi\) | ||||
0.318769 | + | 0.947832i | \(0.396730\pi\) | |||||||
\(770\) | −5.19615 | + | 1.00000i | −0.187256 | + | 0.0360375i | ||||
\(771\) | −11.6603 | −0.419934 | ||||||||
\(772\) | −6.73205 | − | 11.6603i | −0.242292 | − | 0.419662i | ||||
\(773\) | 0.758330 | − | 1.31347i | 0.0272752 | − | 0.0472421i | −0.852066 | − | 0.523435i | \(-0.824650\pi\) |
0.879341 | + | 0.476193i | \(0.157984\pi\) | |||||||
\(774\) | 2.63397 | − | 4.56218i | 0.0946763 | − | 0.163984i | ||||
\(775\) | −3.23205 | − | 5.59808i | −0.116099 | − | 0.201089i | ||||
\(776\) | −2.71797 | −0.0975694 | ||||||||
\(777\) | 6.23205 | − | 17.9904i | 0.223574 | − | 0.645401i | ||||
\(778\) | 26.7846 | 0.960275 | ||||||||
\(779\) | 3.36603 | + | 5.83013i | 0.120600 | + | 0.208886i | ||||
\(780\) | −4.19615 | + | 7.26795i | −0.150246 | + | 0.260234i | ||||
\(781\) | −5.73205 | + | 9.92820i | −0.205109 | + | 0.355259i | ||||
\(782\) | 3.12436 | + | 5.41154i | 0.111727 | + | 0.193516i | ||||
\(783\) | −6.19615 | −0.221432 | ||||||||
\(784\) | −1.07180 | + | 7.42563i | −0.0382785 | + | 0.265201i | ||||
\(785\) | −14.3923 | −0.513683 | ||||||||
\(786\) | 3.12436 | + | 5.41154i | 0.111442 | + | 0.193023i | ||||
\(787\) | −3.26795 | + | 5.66025i | −0.116490 | + | 0.201766i | −0.918374 | − | 0.395713i | \(-0.870498\pi\) |
0.801885 | + | 0.597479i | \(0.203831\pi\) | |||||||
\(788\) | −12.9282 | + | 22.3923i | −0.460548 | + | 0.797693i | ||||
\(789\) | −6.19615 | − | 10.7321i | −0.220589 | − | 0.382071i | ||||
\(790\) | 9.80385 | 0.348805 | ||||||||
\(791\) | 4.26795 | − | 12.3205i | 0.151751 | − | 0.438067i | ||||
\(792\) | 6.92820 | 0.246183 | ||||||||
\(793\) | −11.4641 | − | 19.8564i | −0.407102 | − | 0.705122i | ||||
\(794\) | 7.61474 | − | 13.1891i | 0.270237 | − | 0.468064i | ||||
\(795\) | −4.19615 | + | 7.26795i | −0.148822 | + | 0.257768i | ||||
\(796\) | 16.1051 | + | 27.8949i | 0.570831 | + | 0.988708i | ||||
\(797\) | −42.0526 | −1.48958 | −0.744789 | − | 0.667300i | \(-0.767450\pi\) | ||||
−0.744789 | + | 0.667300i | \(0.767450\pi\) | |||||||
\(798\) | 4.68653 | − | 0.901924i | 0.165901 | − | 0.0319278i | ||||
\(799\) | 13.4641 | 0.476326 | ||||||||
\(800\) | −2.92820 | − | 5.07180i | −0.103528 | − | 0.179315i | ||||
\(801\) | 4.56218 | − | 7.90192i | 0.161197 | − | 0.279201i | ||||
\(802\) | −1.60770 | + | 2.78461i | −0.0567697 | + | 0.0983280i | ||||
\(803\) | −6.36603 | − | 11.0263i | −0.224652 | − | 0.389109i | ||||
\(804\) | 3.89488 | 0.137362 | ||||||||
\(805\) | 2.19615 | + | 2.53590i | 0.0774042 | + | 0.0893787i | ||||
\(806\) | 27.1244 | 0.955415 | ||||||||
\(807\) | −9.73205 | − | 16.8564i | −0.342584 | − | 0.593374i | ||||
\(808\) | −13.6077 | + | 23.5692i | −0.478717 | + | 0.829162i | ||||
\(809\) | 14.8564 | − | 25.7321i | 0.522323 | − | 0.904691i | −0.477339 | − | 0.878719i | \(-0.658399\pi\) |
0.999663 | − | 0.0259716i | \(-0.00826796\pi\) | |||||||
\(810\) | −0.366025 | − | 0.633975i | −0.0128608 | − | 0.0222756i | ||||
\(811\) | 3.46410 | 0.121641 | 0.0608205 | − | 0.998149i | \(-0.480628\pi\) | ||||
0.0608205 | + | 0.998149i | \(0.480628\pi\) | |||||||
\(812\) | 15.7128 | + | 18.1436i | 0.551412 | + | 0.636715i | ||||
\(813\) | −16.9282 | −0.593698 | ||||||||
\(814\) | 7.19615 | + | 12.4641i | 0.252225 | + | 0.436867i | ||||
\(815\) | 2.92820 | − | 5.07180i | 0.102570 | − | 0.177657i | ||||
\(816\) | 3.60770 | − | 6.24871i | 0.126295 | − | 0.218749i | ||||
\(817\) | −8.86603 | − | 15.3564i | −0.310183 | − | 0.537253i | ||||
\(818\) | 22.5885 | 0.789787 | ||||||||
\(819\) | 14.8923 | − | 2.86603i | 0.520379 | − | 0.100147i | ||||
\(820\) | −4.00000 | −0.139686 | ||||||||
\(821\) | −9.75833 | − | 16.9019i | −0.340568 | − | 0.589881i | 0.643970 | − | 0.765051i | \(-0.277286\pi\) |
−0.984538 | + | 0.175169i | \(0.943953\pi\) | |||||||
\(822\) | −3.00000 | + | 5.19615i | −0.104637 | + | 0.181237i | ||||
\(823\) | 11.5885 | − | 20.0718i | 0.403948 | − | 0.699659i | −0.590250 | − | 0.807220i | \(-0.700971\pi\) |
0.994198 | + | 0.107561i | \(0.0343043\pi\) | |||||||
\(824\) | 1.51666 | + | 2.62693i | 0.0528354 | + | 0.0915135i | ||||
\(825\) | 2.73205 | 0.0951178 | ||||||||
\(826\) | −6.46410 | + | 18.6603i | −0.224915 | + | 0.649273i | ||||
\(827\) | −52.2487 | −1.81687 | −0.908433 | − | 0.418031i | \(-0.862720\pi\) | ||||
−0.908433 | + | 0.418031i | \(0.862720\pi\) | |||||||
\(828\) | −0.928203 | − | 1.60770i | −0.0322573 | − | 0.0558713i | ||||
\(829\) | 12.6962 | − | 21.9904i | 0.440956 | − | 0.763758i | −0.556805 | − | 0.830643i | \(-0.687973\pi\) |
0.997761 | + | 0.0668857i | \(0.0213063\pi\) | |||||||
\(830\) | 3.33975 | − | 5.78461i | 0.115924 | − | 0.200787i | ||||
\(831\) | 1.33013 | + | 2.30385i | 0.0461416 | + | 0.0799196i | ||||
\(832\) | 12.2872 | 0.425982 | ||||||||
\(833\) | 43.7583 | − | 17.4904i | 1.51614 | − | 0.606006i | ||||
\(834\) | 5.80385 | 0.200971 | ||||||||
\(835\) | 0.169873 | + | 0.294229i | 0.00587870 | + | 0.0101822i | ||||
\(836\) | 4.92820 | − | 8.53590i | 0.170445 | − | 0.295220i | ||||
\(837\) | 3.23205 | − | 5.59808i | 0.111716 | − | 0.193498i | ||||
\(838\) | 10.4449 | + | 18.0910i | 0.360812 | + | 0.624944i | ||||
\(839\) | −40.4449 | −1.39631 | −0.698156 | − | 0.715946i | \(-0.745996\pi\) | ||||
−0.698156 | + | 0.715946i | \(0.745996\pi\) | |||||||
\(840\) | −2.19615 | + | 6.33975i | −0.0757745 | + | 0.218742i | ||||
\(841\) | 9.39230 | 0.323873 | ||||||||
\(842\) | −5.09808 | − | 8.83013i | −0.175691 | − | 0.304306i | ||||
\(843\) | −6.92820 | + | 12.0000i | −0.238620 | + | 0.413302i | ||||
\(844\) | 15.3205 | − | 26.5359i | 0.527354 | − | 0.913403i | ||||
\(845\) | −9.92820 | − | 17.1962i | −0.341541 | − | 0.591566i | ||||
\(846\) | 1.46410 | 0.0503369 | ||||||||
\(847\) | −9.18653 | + | 1.76795i | −0.315653 | + | 0.0607475i | ||||
\(848\) | −8.99485 | −0.308884 | ||||||||
\(849\) | 0.0621778 | + | 0.107695i | 0.00213394 | + | 0.00369609i | ||||
\(850\) | −2.46410 | + | 4.26795i | −0.0845180 | + | 0.146389i | ||||
\(851\) | 4.56218 | − | 7.90192i | 0.156389 | − | 0.270874i | ||||
\(852\) | 3.07180 | + | 5.32051i | 0.105238 | + | 0.182278i | ||||
\(853\) | 19.9808 | 0.684128 | 0.342064 | − | 0.939677i | \(-0.388874\pi\) | ||||
0.342064 | + | 0.939677i | \(0.388874\pi\) | |||||||
\(854\) | −5.07180 | − | 5.85641i | −0.173553 | − | 0.200402i | ||||
\(855\) | −2.46410 | −0.0842705 | ||||||||
\(856\) | −10.3923 | − | 18.0000i | −0.355202 | − | 0.615227i | ||||
\(857\) | −2.43782 | + | 4.22243i | −0.0832744 | + | 0.144236i | −0.904655 | − | 0.426146i | \(-0.859871\pi\) |
0.821380 | + | 0.570381i | \(0.193204\pi\) | |||||||
\(858\) | −5.73205 | + | 9.92820i | −0.195689 | + | 0.338943i | ||||
\(859\) | −0.267949 | − | 0.464102i | −0.00914231 | − | 0.0158349i | 0.861418 | − | 0.507897i | \(-0.169577\pi\) |
−0.870560 | + | 0.492062i | \(0.836243\pi\) | |||||||
\(860\) | 10.5359 | 0.359271 | ||||||||
\(861\) | 4.73205 | + | 5.46410i | 0.161268 | + | 0.186216i | ||||
\(862\) | −12.6795 | −0.431865 | ||||||||
\(863\) | 3.19615 | + | 5.53590i | 0.108798 | + | 0.188444i | 0.915284 | − | 0.402810i | \(-0.131966\pi\) |
−0.806485 | + | 0.591254i | \(0.798633\pi\) | |||||||
\(864\) | 2.92820 | − | 5.07180i | 0.0996195 | − | 0.172546i | ||||
\(865\) | −10.7321 | + | 18.5885i | −0.364901 | + | 0.632027i | ||||
\(866\) | −1.75833 | − | 3.04552i | −0.0597505 | − | 0.103491i | ||||
\(867\) | −28.3205 | −0.961815 | ||||||||
\(868\) | −24.5885 | + | 4.73205i | −0.834587 | + | 0.160616i | ||||
\(869\) | −36.5885 | −1.24118 | ||||||||
\(870\) | 2.26795 | + | 3.92820i | 0.0768907 | + | 0.133179i | ||||
\(871\) | −7.62436 | + | 13.2058i | −0.258341 | + | 0.447460i | ||||
\(872\) | 13.9474 | − | 24.1577i | 0.472320 | − | 0.818082i | ||||
\(873\) | −0.535898 | − | 0.928203i | −0.0181374 | − | 0.0314149i | ||||
\(874\) | 2.28719 | 0.0773653 | ||||||||
\(875\) | −0.866025 | + | 2.50000i | −0.0292770 | + | 0.0845154i | ||||
\(876\) | −6.82309 | −0.230531 | ||||||||
\(877\) | 15.9282 | + | 27.5885i | 0.537857 | + | 0.931596i | 0.999019 | + | 0.0442800i | \(0.0140994\pi\) |
−0.461162 | + | 0.887316i | \(0.652567\pi\) | |||||||
\(878\) | −2.73205 | + | 4.73205i | −0.0922022 | + | 0.159699i | ||||
\(879\) | 2.53590 | − | 4.39230i | 0.0855337 | − | 0.148149i | ||||
\(880\) | 1.46410 | + | 2.53590i | 0.0493549 | + | 0.0854851i | ||||
\(881\) | −17.8564 | −0.601598 | −0.300799 | − | 0.953688i | \(-0.597253\pi\) | ||||
−0.300799 | + | 0.953688i | \(0.597253\pi\) | |||||||
\(882\) | 4.75833 | − | 1.90192i | 0.160221 | − | 0.0640411i | ||||
\(883\) | 22.4115 | 0.754208 | 0.377104 | − | 0.926171i | \(-0.376920\pi\) | ||||
0.377104 | + | 0.926171i | \(0.376920\pi\) | |||||||
\(884\) | 28.2487 | + | 48.9282i | 0.950107 | + | 1.64563i | ||||
\(885\) | 5.09808 | − | 8.83013i | 0.171370 | − | 0.296821i | ||||
\(886\) | −0.928203 | + | 1.60770i | −0.0311836 | + | 0.0540116i | ||||
\(887\) | 14.3660 | + | 24.8827i | 0.482364 | + | 0.835479i | 0.999795 | − | 0.0202460i | \(-0.00644496\pi\) |
−0.517431 | + | 0.855725i | \(0.673112\pi\) | |||||||
\(888\) | 18.2487 | 0.612387 | ||||||||
\(889\) | −13.1603 | + | 37.9904i | −0.441381 | + | 1.27416i | ||||
\(890\) | −6.67949 | −0.223897 | ||||||||
\(891\) | 1.36603 | + | 2.36603i | 0.0457636 | + | 0.0792648i | ||||
\(892\) | 0.287187 | − | 0.497423i | 0.00961573 | − | 0.0166549i | ||||
\(893\) | 2.46410 | − | 4.26795i | 0.0824580 | − | 0.142821i | ||||
\(894\) | −8.00000 | − | 13.8564i | −0.267560 | − | 0.463428i | ||||
\(895\) | −10.0000 | −0.334263 | ||||||||
\(896\) | −26.3538 | + | 5.07180i | −0.880420 | + | 0.169437i | ||||
\(897\) | 7.26795 | 0.242670 | ||||||||
\(898\) | 2.98076 | + | 5.16283i | 0.0994693 | + | 0.172286i | ||||
\(899\) | −20.0263 | + | 34.6865i | −0.667914 | + | 1.15686i | ||||
\(900\) | 0.732051 | − | 1.26795i | 0.0244017 | − | 0.0422650i | ||||
\(901\) | 28.2487 | + | 48.9282i | 0.941101 | + | 1.63003i | ||||
\(902\) | −5.46410 | −0.181935 | ||||||||
\(903\) | −12.4641 | − | 14.3923i | −0.414779 | − | 0.478946i | ||||
\(904\) | 12.4974 | 0.415658 | ||||||||
\(905\) | −5.16025 | − | 8.93782i | −0.171533 | − | 0.297103i | ||||
\(906\) | 1.80385 | − | 3.12436i | 0.0599288 | − | 0.103800i | ||||
\(907\) | −1.20577 | + | 2.08846i | −0.0400370 | + | 0.0693461i | −0.885350 | − | 0.464926i | \(-0.846081\pi\) |
0.845313 | + | 0.534272i | \(0.179414\pi\) | |||||||
\(908\) | 11.4641 | + | 19.8564i | 0.380450 | + | 0.658958i | ||||
\(909\) | −10.7321 | −0.355960 | ||||||||
\(910\) | −7.26795 | − | 8.39230i | −0.240930 | − | 0.278202i | ||||
\(911\) | −11.2679 | −0.373324 | −0.186662 | − | 0.982424i | \(-0.559767\pi\) | ||||
−0.186662 | + | 0.982424i | \(0.559767\pi\) | |||||||
\(912\) | −1.32051 | − | 2.28719i | −0.0437264 | − | 0.0757363i | ||||
\(913\) | −12.4641 | + | 21.5885i | −0.412502 | + | 0.714474i | ||||
\(914\) | −0.241670 | + | 0.418584i | −0.00799372 | + | 0.0138455i | ||||
\(915\) | 2.00000 | + | 3.46410i | 0.0661180 | + | 0.114520i | ||||
\(916\) | 4.39230 | 0.145126 | ||||||||
\(917\) | 22.1769 | − | 4.26795i | 0.732346 | − | 0.140940i | ||||
\(918\) | −4.92820 | −0.162655 | ||||||||
\(919\) | 1.57180 | + | 2.72243i | 0.0518488 | + | 0.0898047i | 0.890785 | − | 0.454425i | \(-0.150155\pi\) |
−0.838936 | + | 0.544230i | \(0.816822\pi\) | |||||||
\(920\) | −1.60770 | + | 2.78461i | −0.0530041 | + | 0.0918059i | ||||
\(921\) | −3.93782 | + | 6.82051i | −0.129756 | + | 0.224743i | ||||
\(922\) | 12.8038 | + | 22.1769i | 0.421672 | + | 0.730358i | ||||
\(923\) | −24.0526 | −0.791700 | ||||||||
\(924\) | 3.46410 | − | 10.0000i | 0.113961 | − | 0.328976i | ||||
\(925\) | 7.19615 | 0.236608 | ||||||||
\(926\) | −8.15064 | − | 14.1173i | −0.267846 | − | 0.463924i | ||||
\(927\) | −0.598076 | + | 1.03590i | −0.0196434 | + | 0.0340234i | ||||
\(928\) | −18.1436 | + | 31.4256i | −0.595593 | + | 1.03160i | ||||
\(929\) | −3.22243 | − | 5.58142i | −0.105725 | − | 0.183120i | 0.808309 | − | 0.588758i | \(-0.200383\pi\) |
−0.914034 | + | 0.405638i | \(0.867050\pi\) | |||||||
\(930\) | −4.73205 | −0.155170 | ||||||||
\(931\) | 2.46410 | − | 17.0718i | 0.0807577 | − | 0.559506i | ||||
\(932\) | 25.3590 | 0.830661 | ||||||||
\(933\) | −7.56218 | − | 13.0981i | −0.247575 | − | 0.428812i | ||||
\(934\) | 10.1962 | − | 17.6603i | 0.333628 | − | 0.577861i | ||||
\(935\) | 9.19615 | − | 15.9282i | 0.300746 | − | 0.520908i | ||||
\(936\) | 7.26795 | + | 12.5885i | 0.237560 | + | 0.411467i | ||||
\(937\) | 28.2679 | 0.923474 | 0.461737 | − | 0.887017i | \(-0.347226\pi\) | ||||
0.461737 | + | 0.887017i | \(0.347226\pi\) | |||||||
\(938\) | −1.68653 | + | 4.86860i | −0.0550673 | + | 0.158966i | ||||
\(939\) | −4.66025 | −0.152082 | ||||||||
\(940\) | 1.46410 | + | 2.53590i | 0.0477537 | + | 0.0827119i | ||||
\(941\) | −4.02628 | + | 6.97372i | −0.131253 | + | 0.227337i | −0.924160 | − | 0.382006i | \(-0.875233\pi\) |
0.792907 | + | 0.609343i | \(0.208567\pi\) | |||||||
\(942\) | −5.26795 | + | 9.12436i | −0.171639 | + | 0.297288i | ||||
\(943\) | 1.73205 | + | 3.00000i | 0.0564033 | + | 0.0976934i | ||||
\(944\) | 10.9282 | 0.355683 | ||||||||
\(945\) | −2.59808 | + | 0.500000i | −0.0845154 | + | 0.0162650i | ||||
\(946\) | 14.3923 | 0.467934 | ||||||||
\(947\) | −5.83013 | − | 10.0981i | −0.189454 | − | 0.328143i | 0.755615 | − | 0.655017i | \(-0.227338\pi\) |
−0.945068 | + | 0.326873i | \(0.894005\pi\) | |||||||
\(948\) | −9.80385 | + | 16.9808i | −0.318414 | + | 0.551510i | ||||
\(949\) | 13.3564 | − | 23.1340i | 0.433567 | − | 0.750961i | ||||
\(950\) | 0.901924 | + | 1.56218i | 0.0292623 | + | 0.0506837i | ||||
\(951\) | −30.4449 | −0.987242 | ||||||||
\(952\) | 29.5692 | + | 34.1436i | 0.958344 | + | 1.10660i | ||||
\(953\) | 40.1051 | 1.29913 | 0.649566 | − | 0.760305i | \(-0.274951\pi\) | ||||
0.649566 | + | 0.760305i | \(0.274951\pi\) | |||||||
\(954\) | 3.07180 | + | 5.32051i | 0.0994531 | + | 0.172258i | ||||
\(955\) | −2.46410 | + | 4.26795i | −0.0797365 | + | 0.138108i | ||||
\(956\) | 15.3205 | − | 26.5359i | 0.495501 | − | 0.858232i | ||||
\(957\) | −8.46410 | − | 14.6603i | −0.273606 | − | 0.473899i | ||||
\(958\) | −24.0000 | −0.775405 | ||||||||
\(959\) | 14.1962 | + | 16.3923i | 0.458418 | + | 0.529335i | ||||
\(960\) | −2.14359 | −0.0691842 | ||||||||
\(961\) | −5.39230 | − | 9.33975i | −0.173945 | − | 0.301282i | ||||
\(962\) | −15.0981 | + | 26.1506i | −0.486782 | + | 0.843130i | ||||
\(963\) | 4.09808 | − | 7.09808i | 0.132059 | − | 0.228732i | ||||
\(964\) | 4.78461 | + | 8.28719i | 0.154102 | + | 0.266912i | ||||
\(965\) | −9.19615 | −0.296035 | ||||||||
\(966\) | 2.41154 | − | 0.464102i | 0.0775901 | − | 0.0149322i | ||||
\(967\) | 14.1244 | 0.454209 | 0.227104 | − | 0.973870i | \(-0.427074\pi\) | ||||
0.227104 | + | 0.973870i | \(0.427074\pi\) | |||||||
\(968\) | −4.48334 | − | 7.76537i | −0.144100 | − | 0.249589i | ||||
\(969\) | −8.29423 | + | 14.3660i | −0.266449 | + | 0.461503i | ||||
\(970\) | −0.392305 | + | 0.679492i | −0.0125961 | + | 0.0218172i | ||||
\(971\) | 12.0000 | + | 20.7846i | 0.385098 | + | 0.667010i | 0.991783 | − | 0.127933i | \(-0.0408342\pi\) |
−0.606685 | + | 0.794943i | \(0.707501\pi\) | |||||||
\(972\) | 1.46410 | 0.0469611 | ||||||||
\(973\) | 6.86603 | − | 19.8205i | 0.220115 | − | 0.635416i | ||||
\(974\) | −23.1244 | −0.740952 | ||||||||
\(975\) | 2.86603 | + | 4.96410i | 0.0917863 | + | 0.158978i | ||||
\(976\) | −2.14359 | + | 3.71281i | −0.0686148 | + | 0.118844i | ||||
\(977\) | −7.29423 | + | 12.6340i | −0.233363 | + | 0.404197i | −0.958796 | − | 0.284097i | \(-0.908306\pi\) |
0.725433 | + | 0.688293i | \(0.241640\pi\) | |||||||
\(978\) | −2.14359 | − | 3.71281i | −0.0685446 | − | 0.118723i | ||||
\(979\) | 24.9282 | 0.796709 | ||||||||
\(980\) | 8.05256 | + | 6.33975i | 0.257230 | + | 0.202516i | ||||
\(981\) | 11.0000 | 0.351203 | ||||||||
\(982\) | −3.75129 | − | 6.49742i | −0.119708 | − | 0.207341i | ||||
\(983\) | −10.0981 | + | 17.4904i | −0.322079 | + | 0.557857i | −0.980917 | − | 0.194428i | \(-0.937715\pi\) |
0.658838 | + | 0.752285i | \(0.271048\pi\) | |||||||
\(984\) | −3.46410 | + | 6.00000i | −0.110432 | + | 0.191273i | ||||
\(985\) | 8.83013 | + | 15.2942i | 0.281351 | + | 0.487315i | ||||
\(986\) | 30.5359 | 0.972461 | ||||||||
\(987\) | 1.73205 | − | 5.00000i | 0.0551318 | − | 0.159152i | ||||
\(988\) | 20.6795 | 0.657902 | ||||||||
\(989\) | −4.56218 | − | 7.90192i | −0.145069 | − | 0.251267i | ||||
\(990\) | 1.00000 | − | 1.73205i | 0.0317821 | − | 0.0550482i | ||||
\(991\) | −27.5526 | + | 47.7224i | −0.875236 | + | 1.51595i | −0.0187246 | + | 0.999825i | \(0.505961\pi\) |
−0.856511 | + | 0.516128i | \(0.827373\pi\) | |||||||
\(992\) | −18.9282 | − | 32.7846i | −0.600971 | − | 1.04091i | ||||
\(993\) | −21.9282 | −0.695870 | ||||||||
\(994\) | −7.98076 | + | 1.53590i | −0.253134 | + | 0.0487157i | ||||
\(995\) | 22.0000 | 0.697447 | ||||||||
\(996\) | 6.67949 | + | 11.5692i | 0.211648 | + | 0.366585i | ||||
\(997\) | 2.00962 | − | 3.48076i | 0.0636453 | − | 0.110237i | −0.832447 | − | 0.554105i | \(-0.813061\pi\) |
0.896092 | + | 0.443868i | \(0.146394\pi\) | |||||||
\(998\) | 7.49038 | − | 12.9737i | 0.237104 | − | 0.410676i | ||||
\(999\) | 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 | 105.2.i.d.46.1 | yes | 4 | |
3.2 | odd | 2 | 315.2.j.c.46.2 | 4 | |||
4.3 | odd | 2 | 1680.2.bg.o.1201.2 | 4 | |||
5.2 | odd | 4 | 525.2.r.f.424.1 | 4 | |||
5.3 | odd | 4 | 525.2.r.a.424.2 | 4 | |||
5.4 | even | 2 | 525.2.i.f.151.2 | 4 | |||
7.2 | even | 3 | inner | 105.2.i.d.16.1 | ✓ | 4 | |
7.3 | odd | 6 | 735.2.a.h.1.2 | 2 | |||
7.4 | even | 3 | 735.2.a.g.1.2 | 2 | |||
7.5 | odd | 6 | 735.2.i.l.226.1 | 4 | |||
7.6 | odd | 2 | 735.2.i.l.361.1 | 4 | |||
21.2 | odd | 6 | 315.2.j.c.226.2 | 4 | |||
21.11 | odd | 6 | 2205.2.a.z.1.1 | 2 | |||
21.17 | even | 6 | 2205.2.a.ba.1.1 | 2 | |||
28.23 | odd | 6 | 1680.2.bg.o.961.2 | 4 | |||
35.2 | odd | 12 | 525.2.r.a.499.2 | 4 | |||
35.4 | even | 6 | 3675.2.a.bg.1.1 | 2 | |||
35.9 | even | 6 | 525.2.i.f.226.2 | 4 | |||
35.23 | odd | 12 | 525.2.r.f.499.1 | 4 | |||
35.24 | odd | 6 | 3675.2.a.be.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.i.d.16.1 | ✓ | 4 | 7.2 | even | 3 | inner | |
105.2.i.d.46.1 | yes | 4 | 1.1 | even | 1 | trivial | |
315.2.j.c.46.2 | 4 | 3.2 | odd | 2 | |||
315.2.j.c.226.2 | 4 | 21.2 | odd | 6 | |||
525.2.i.f.151.2 | 4 | 5.4 | even | 2 | |||
525.2.i.f.226.2 | 4 | 35.9 | even | 6 | |||
525.2.r.a.424.2 | 4 | 5.3 | odd | 4 | |||
525.2.r.a.499.2 | 4 | 35.2 | odd | 12 | |||
525.2.r.f.424.1 | 4 | 5.2 | odd | 4 | |||
525.2.r.f.499.1 | 4 | 35.23 | odd | 12 | |||
735.2.a.g.1.2 | 2 | 7.4 | even | 3 | |||
735.2.a.h.1.2 | 2 | 7.3 | odd | 6 | |||
735.2.i.l.226.1 | 4 | 7.5 | odd | 6 | |||
735.2.i.l.361.1 | 4 | 7.6 | odd | 2 | |||
1680.2.bg.o.961.2 | 4 | 28.23 | odd | 6 | |||
1680.2.bg.o.1201.2 | 4 | 4.3 | odd | 2 | |||
2205.2.a.z.1.1 | 2 | 21.11 | odd | 6 | |||
2205.2.a.ba.1.1 | 2 | 21.17 | even | 6 | |||
3675.2.a.be.1.1 | 2 | 35.24 | odd | 6 | |||
3675.2.a.bg.1.1 | 2 | 35.4 | even | 6 |