Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(151,525)]
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, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.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: | \(4.19214610612\) |
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: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 226.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.226 |
Dual form | 525.2.i.f.151.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.366025 | − | 0.633975i | 0.258819 | − | 0.448288i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0.732051 | + | 1.26795i | 0.366025 | + | 0.633975i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −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 | 0 | ||||||||
\(11\) | 1.36603 | + | 2.36603i | 0.411872 | + | 0.713384i | 0.995094 | − | 0.0989291i | \(-0.0315417\pi\) |
−0.583222 | + | 0.812313i | \(0.698208\pi\) | |||||||
\(12\) | 0.732051 | − | 1.26795i | 0.211325 | − | 0.366025i | ||||
\(13\) | −5.73205 | −1.58978 | −0.794892 | − | 0.606750i | \(-0.792473\pi\) | ||||
−0.794892 | + | 0.606750i | \(0.792473\pi\) | |||||||
\(14\) | 1.90192 | + | 0.366025i | 0.508311 | + | 0.0978244i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.535898 | + | 0.928203i | −0.133975 | + | 0.232051i | ||||
\(17\) | 3.36603 | + | 5.83013i | 0.816381 | + | 1.41401i | 0.908332 | + | 0.418250i | \(0.137356\pi\) |
−0.0919509 | + | 0.995764i | \(0.529310\pi\) | |||||||
\(18\) | 0.366025 | + | 0.633975i | 0.0862730 | + | 0.149429i | ||||
\(19\) | 1.23205 | − | 2.13397i | 0.282652 | − | 0.489567i | −0.689385 | − | 0.724395i | \(-0.742119\pi\) |
0.972037 | + | 0.234828i | \(0.0754526\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 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 | \(-0.875535\pi\) |
0.792329 | + | 0.610094i | \(0.208868\pi\) | |||||||
\(24\) | −1.26795 | − | 2.19615i | −0.258819 | − | 0.448288i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −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 | 0 | ||||||||
\(31\) | −3.23205 | − | 5.59808i | −0.580493 | − | 1.00544i | −0.995421 | − | 0.0955896i | \(-0.969526\pi\) |
0.414927 | − | 0.909855i | \(-0.363807\pi\) | |||||||
\(32\) | 2.92820 | + | 5.07180i | 0.517638 | + | 0.896575i | ||||
\(33\) | 1.36603 | − | 2.36603i | 0.237795 | − | 0.411872i | ||||
\(34\) | 4.92820 | 0.845180 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.46410 | −0.244017 | ||||||||
\(37\) | 3.59808 | − | 6.23205i | 0.591520 | − | 1.02454i | −0.402508 | − | 0.915417i | \(-0.631861\pi\) |
0.994028 | − | 0.109126i | \(-0.0348053\pi\) | |||||||
\(38\) | −0.901924 | − | 1.56218i | −0.146311 | − | 0.253419i | ||||
\(39\) | 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 | \(0.431567\pi\) | |||||||
\(42\) | −0.633975 | − | 1.83013i | −0.0978244 | − | 0.282395i | ||||
\(43\) | 7.19615 | 1.09740 | 0.548701 | − | 0.836018i | \(-0.315122\pi\) | ||||
0.548701 | + | 0.836018i | \(0.315122\pi\) | |||||||
\(44\) | −2.00000 | + | 3.46410i | −0.301511 | + | 0.522233i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.464102 | + | 0.803848i | 0.0684280 | + | 0.118521i | ||||
\(47\) | 1.00000 | − | 1.73205i | 0.145865 | − | 0.252646i | −0.783830 | − | 0.620975i | \(-0.786737\pi\) |
0.929695 | + | 0.368329i | \(0.120070\pi\) | |||||||
\(48\) | 1.07180 | 0.154701 | ||||||||
\(49\) | −5.50000 | + | 4.33013i | −0.785714 | + | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 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 | −0.995890 | − | 0.0905760i | \(-0.971129\pi\) |
0.419504 | − | 0.907754i | \(-0.362204\pi\) | |||||||
\(54\) | 0.366025 | − | 0.633975i | 0.0498097 | − | 0.0862730i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 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 | −0.979633 | − | 0.200799i | \(-0.935646\pi\) |
0.315920 | − | 0.948786i | \(-0.397687\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | + | 3.46410i | −0.256074 | + | 0.443533i | −0.965187 | − | 0.261562i | \(-0.915762\pi\) |
0.709113 | + | 0.705095i | \(0.249096\pi\) | |||||||
\(62\) | −4.73205 | −0.600971 | ||||||||
\(63\) | −2.59808 | − | 0.500000i | −0.327327 | − | 0.0629941i | ||||
\(64\) | 2.14359 | 0.267949 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.00000 | − | 1.73205i | −0.123091 | − | 0.213201i | ||||
\(67\) | 1.33013 | + | 2.30385i | 0.162501 | + | 0.281460i | 0.935765 | − | 0.352624i | \(-0.114711\pi\) |
−0.773264 | + | 0.634084i | \(0.781377\pi\) | |||||||
\(68\) | −4.92820 | + | 8.53590i | −0.597632 | + | 1.03513i | ||||
\(69\) | 1.26795 | 0.152643 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.19615 | −0.497992 | −0.248996 | − | 0.968505i | \(-0.580101\pi\) | ||||
−0.248996 | + | 0.968505i | \(0.580101\pi\) | |||||||
\(72\) | −1.26795 | + | 2.19615i | −0.149429 | + | 0.258819i | ||||
\(73\) | −2.33013 | − | 4.03590i | −0.272721 | − | 0.472366i | 0.696837 | − | 0.717230i | \(-0.254590\pi\) |
−0.969558 | + | 0.244864i | \(0.921257\pi\) | |||||||
\(74\) | −2.63397 | − | 4.56218i | −0.306193 | − | 0.530342i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 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 | 0.192802 | + | 0.981238i | \(0.438243\pi\) |
−0.946178 | + | 0.323648i | \(0.895091\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −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 | \(-0.333052\pi\) | ||||
0.500764 | + | 0.865584i | \(0.333052\pi\) | |||||||
\(84\) | 3.80385 | + | 0.732051i | 0.415034 | + | 0.0798733i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 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 | −0.516233 | − | 0.856448i | \(-0.672666\pi\) |
0.999822 | + | 0.0188462i | \(0.00599930\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −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 | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.92820 | − | 5.07180i | 0.298858 | − | 0.517638i | ||||
\(97\) | −1.07180 | −0.108824 | −0.0544122 | − | 0.998519i | \(-0.517329\pi\) | ||||
−0.0544122 | + | 0.998519i | \(0.517329\pi\) | |||||||
\(98\) | 0.732051 | + | 5.07180i | 0.0739483 | + | 0.512329i | ||||
\(99\) | −2.73205 | −0.274581 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.36603 | + | 9.29423i | 0.533939 | + | 0.924810i | 0.999214 | + | 0.0396438i | \(0.0126223\pi\) |
−0.465274 | + | 0.885167i | \(0.654044\pi\) | |||||||
\(102\) | −2.46410 | − | 4.26795i | −0.243982 | − | 0.422590i | ||||
\(103\) | 0.598076 | − | 1.03590i | 0.0589302 | − | 0.102070i | −0.835055 | − | 0.550166i | \(-0.814564\pi\) |
0.893985 | + | 0.448096i | \(0.147898\pi\) | |||||||
\(104\) | −14.5359 | −1.42536 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.14359 | −0.596719 | ||||||||
\(107\) | −4.09808 | + | 7.09808i | −0.396176 | + | 0.686197i | −0.993251 | − | 0.115989i | \(-0.962996\pi\) |
0.597075 | + | 0.802186i | \(0.296330\pi\) | |||||||
\(108\) | 0.732051 | + | 1.26795i | 0.0704416 | + | 0.122008i | ||||
\(109\) | −5.50000 | − | 9.52628i | −0.526804 | − | 0.912452i | −0.999512 | − | 0.0312328i | \(-0.990057\pi\) |
0.472708 | − | 0.881219i | \(-0.343277\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.19615 | −0.683029 | ||||||||
\(112\) | −2.78461 | − | 0.535898i | −0.263121 | − | 0.0506376i | ||||
\(113\) | 4.92820 | 0.463606 | 0.231803 | − | 0.972763i | \(-0.425537\pi\) | ||||
0.231803 | + | 0.972763i | \(0.425537\pi\) | |||||||
\(114\) | −0.901924 | + | 1.56218i | −0.0844729 | + | 0.146311i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 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 | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 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 | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.26795 | + | 1.46410i | −0.112958 | + | 0.130433i | ||||
\(127\) | −15.1962 | −1.34844 | −0.674220 | − | 0.738530i | \(-0.735520\pi\) | ||||
−0.674220 | + | 0.738530i | \(0.735520\pi\) | |||||||
\(128\) | −5.07180 | + | 8.78461i | −0.448288 | + | 0.776457i | ||||
\(129\) | −3.59808 | − | 6.23205i | −0.316793 | − | 0.548701i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.26795 | + | 7.39230i | −0.372892 | + | 0.645869i | −0.990009 | − | 0.141003i | \(-0.954967\pi\) |
0.617117 | + | 0.786872i | \(0.288301\pi\) | |||||||
\(132\) | 4.00000 | 0.348155 | ||||||||
\(133\) | 6.40192 | + | 1.23205i | 0.555117 | + | 0.106832i | ||||
\(134\) | 1.94744 | 0.168233 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.53590 | + | 14.7846i | 0.731947 | + | 1.26777i | ||||
\(137\) | −4.09808 | − | 7.09808i | −0.350122 | − | 0.606430i | 0.636148 | − | 0.771567i | \(-0.280527\pi\) |
−0.986271 | + | 0.165137i | \(0.947193\pi\) | |||||||
\(138\) | 0.464102 | − | 0.803848i | 0.0395070 | − | 0.0684280i | ||||
\(139\) | −7.92820 | −0.672461 | −0.336231 | − | 0.941780i | \(-0.609152\pi\) | ||||
−0.336231 | + | 0.941780i | \(0.609152\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −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 | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −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 | 0.0618073 | − | 0.998088i | \(-0.480314\pi\) |
0.833466 | − | 0.552571i | \(-0.186353\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.46410 | − | 4.26795i | −0.200526 | − | 0.347321i | 0.748172 | − | 0.663505i | \(-0.230932\pi\) |
−0.948698 | + | 0.316184i | \(0.897598\pi\) | |||||||
\(152\) | 3.12436 | − | 5.41154i | 0.253419 | − | 0.438934i | ||||
\(153\) | −6.73205 | −0.544254 | ||||||||
\(154\) | 1.73205 | + | 5.00000i | 0.139573 | + | 0.402911i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.19615 | + | 7.26795i | −0.335961 | + | 0.581902i | ||||
\(157\) | −7.19615 | − | 12.4641i | −0.574315 | − | 0.994744i | −0.996116 | − | 0.0880548i | \(-0.971935\pi\) |
0.421800 | − | 0.906689i | \(-0.361398\pi\) | |||||||
\(158\) | 4.90192 | + | 8.49038i | 0.389976 | + | 0.675458i | ||||
\(159\) | −4.19615 | + | 7.26795i | −0.332777 | + | 0.576386i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −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 | \(-0.906995\pi\) |
0.728262 | + | 0.685298i | \(0.240328\pi\) | |||||||
\(164\) | 2.00000 | + | 3.46410i | 0.156174 | + | 0.270501i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.33975 | − | 5.78461i | 0.259215 | − | 0.448973i | ||||
\(167\) | 0.339746 | 0.0262903 | 0.0131452 | − | 0.999914i | \(-0.495816\pi\) | ||||
0.0131452 | + | 0.999914i | \(0.495816\pi\) | |||||||
\(168\) | 4.39230 | − | 5.07180i | 0.338874 | − | 0.391298i | ||||
\(169\) | 19.8564 | 1.52742 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 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 | −0.0927063 | − | 0.995693i | \(-0.529552\pi\) |
0.908649 | − | 0.417561i | \(-0.137115\pi\) | |||||||
\(174\) | −4.53590 | −0.343866 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −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 | 0.990134 | − | 0.140122i | \(-0.0447496\pi\) |
−0.616417 | + | 0.787420i | \(0.711416\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 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 | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 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 | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.46410 | + | 4.26795i | −0.178296 | + | 0.308818i | −0.941297 | − | 0.337579i | \(-0.890392\pi\) |
0.763001 | + | 0.646397i | \(0.223725\pi\) | |||||||
\(192\) | −1.07180 | − | 1.85641i | −0.0773503 | − | 0.133975i | ||||
\(193\) | −4.59808 | − | 7.96410i | −0.330977 | − | 0.573269i | 0.651727 | − | 0.758454i | \(-0.274045\pi\) |
−0.982704 | + | 0.185185i | \(0.940712\pi\) | |||||||
\(194\) | −0.392305 | + | 0.679492i | −0.0281658 | + | 0.0487847i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.51666 | − | 3.80385i | −0.679761 | − | 0.271703i | ||||
\(197\) | 17.6603 | 1.25824 | 0.629121 | − | 0.777308i | \(-0.283415\pi\) | ||||
0.629121 | + | 0.777308i | \(0.283415\pi\) | |||||||
\(198\) | −1.00000 | + | 1.73205i | −0.0710669 | + | 0.123091i | ||||
\(199\) | −11.0000 | − | 19.0526i | −0.779769 | − | 1.35060i | −0.932075 | − | 0.362267i | \(-0.882003\pi\) |
0.152305 | − | 0.988334i | \(-0.451330\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 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 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −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 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 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 | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 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 | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −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 | \(-0.504181\pi\) | ||||
−0.0131353 | + | 0.999914i | \(0.504181\pi\) | |||||||
\(224\) | −10.1436 | + | 11.7128i | −0.677747 | + | 0.782595i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.80385 | − | 3.12436i | 0.119990 | − | 0.207829i | ||||
\(227\) | 7.83013 | + | 13.5622i | 0.519704 | + | 0.900153i | 0.999738 | + | 0.0229034i | \(0.00729102\pi\) |
−0.480034 | + | 0.877250i | \(0.659376\pi\) | |||||||
\(228\) | −1.80385 | − | 3.12436i | −0.119463 | − | 0.206916i | ||||
\(229\) | 1.50000 | − | 2.59808i | 0.0991228 | − | 0.171686i | −0.812199 | − | 0.583380i | \(-0.801730\pi\) |
0.911322 | + | 0.411695i | \(0.135063\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.09808 | + | 1.36603i | 0.467019 | + | 0.0898779i | ||||
\(232\) | 15.7128 | 1.03160 | ||||||||
\(233\) | −8.66025 | + | 15.0000i | −0.567352 | + | 0.982683i | 0.429474 | + | 0.903079i | \(0.358699\pi\) |
−0.996827 | + | 0.0796037i | \(0.974635\pi\) | |||||||
\(234\) | −2.09808 | − | 3.63397i | −0.137156 | − | 0.237560i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 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 | 0 | ||||||||
\(241\) | −3.26795 | − | 5.66025i | −0.210507 | − | 0.364609i | 0.741366 | − | 0.671101i | \(-0.234178\pi\) |
−0.951873 | + | 0.306492i | \(0.900845\pi\) | |||||||
\(242\) | −1.29423 | − | 2.24167i | −0.0831962 | − | 0.144100i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −5.85641 | −0.374918 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −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 | 0 | ||||||||
\(251\) | 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 | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.85641 | + | 10.1436i | 0.366025 | + | 0.633975i | ||||
\(257\) | 5.83013 | − | 10.0981i | 0.363673 | − | 0.629901i | −0.624889 | − | 0.780714i | \(-0.714856\pi\) |
0.988562 | + | 0.150813i | \(0.0481891\pi\) | |||||||
\(258\) | −5.26795 | −0.327968 | ||||||||
\(259\) | 18.6962 | + | 3.59808i | 1.16172 | + | 0.223574i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −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 | \(-0.291456\pi\) |
−0.991358 | + | 0.131183i | \(0.958122\pi\) | |||||||
\(264\) | 3.46410 | − | 6.00000i | 0.213201 | − | 0.369274i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 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 | 0.993774 | + | 0.111413i | \(0.0355377\pi\) |
−0.400401 | + | 0.916340i | \(0.631129\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.46410 | + | 14.6603i | −0.514158 | + | 0.890547i | 0.485708 | + | 0.874121i | \(0.338562\pi\) |
−0.999865 | + | 0.0164256i | \(0.994771\pi\) | |||||||
\(272\) | −7.21539 | −0.437497 | ||||||||
\(273\) | −9.92820 | + | 11.4641i | −0.600882 | + | 0.693839i | ||||
\(274\) | −6.00000 | −0.362473 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.928203 | + | 1.60770i | 0.0558713 | + | 0.0967719i | ||||
\(277\) | 1.33013 | + | 2.30385i | 0.0799196 | + | 0.138425i | 0.903215 | − | 0.429188i | \(-0.141200\pi\) |
−0.823295 | + | 0.567613i | \(0.807867\pi\) | |||||||
\(278\) | −2.90192 | + | 5.02628i | −0.174046 | + | 0.301456i | ||||
\(279\) | 6.46410 | 0.386996 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.8564 | −0.826604 | −0.413302 | − | 0.910594i | \(-0.635625\pi\) | ||||
−0.413302 | + | 0.910594i | \(0.635625\pi\) | |||||||
\(282\) | −0.732051 | + | 1.26795i | −0.0435930 | + | 0.0755053i | ||||
\(283\) | 0.0621778 | + | 0.107695i | 0.00369609 | + | 0.00640181i | 0.867868 | − | 0.496796i | \(-0.165490\pi\) |
−0.864171 | + | 0.503197i | \(0.832157\pi\) | |||||||
\(284\) | −3.07180 | − | 5.32051i | −0.182278 | − | 0.315714i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −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 | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 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 | \(-0.547331\pi\) | ||||
−0.148149 | + | 0.988965i | \(0.547331\pi\) | |||||||
\(294\) | 4.02628 | − | 3.16987i | 0.234817 | − | 0.184871i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 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 | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 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 | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.46410 | + | 4.26795i | −0.140863 | + | 0.243982i | ||||
\(307\) | 7.87564 | 0.449487 | 0.224743 | − | 0.974418i | \(-0.427846\pi\) | ||||
0.224743 | + | 0.974418i | \(0.427846\pi\) | |||||||
\(308\) | −10.3923 | − | 2.00000i | −0.592157 | − | 0.113961i | ||||
\(309\) | −1.19615 | −0.0680467 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.56218 | + | 13.0981i | 0.428812 | + | 0.742724i | 0.996768 | − | 0.0803351i | \(-0.0255990\pi\) |
−0.567956 | + | 0.823059i | \(0.692266\pi\) | |||||||
\(312\) | 7.26795 | + | 12.5885i | 0.411467 | + | 0.712681i | ||||
\(313\) | 2.33013 | − | 4.03590i | 0.131707 | − | 0.228122i | −0.792628 | − | 0.609706i | \(-0.791288\pi\) |
0.924335 | + | 0.381583i | \(0.124621\pi\) | |||||||
\(314\) | −10.5359 | −0.594575 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −19.6077 | −1.10302 | ||||||||
\(317\) | 15.2224 | − | 26.3660i | 0.854977 | − | 1.48086i | −0.0216894 | − | 0.999765i | \(-0.506905\pi\) |
0.876666 | − | 0.481099i | \(-0.159762\pi\) | |||||||
\(318\) | 3.07180 | + | 5.32051i | 0.172258 | + | 0.298359i | ||||
\(319\) | 8.46410 | + | 14.6603i | 0.473899 | + | 0.820817i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 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 | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 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 | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.9641 | + | 18.9904i | −0.602642 | + | 1.04381i | 0.389778 | + | 0.920909i | \(0.372552\pi\) |
−0.992419 | + | 0.122897i | \(0.960782\pi\) | |||||||
\(332\) | 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 | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.928203 | + | 2.67949i | 0.0506376 | + | 0.146178i | ||||
\(337\) | 33.9808 | 1.85105 | 0.925525 | − | 0.378686i | \(-0.123624\pi\) | ||||
0.925525 | + | 0.378686i | \(0.123624\pi\) | |||||||
\(338\) | 7.26795 | − | 12.5885i | 0.395324 | − | 0.684722i | ||||
\(339\) | −2.46410 | − | 4.26795i | −0.133832 | − | 0.231803i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 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 | 0 | ||||||||
\(346\) | −7.85641 | − | 13.6077i | −0.422363 | − | 0.731554i | ||||
\(347\) | −17.4641 | − | 30.2487i | −0.937522 | − | 1.62384i | −0.770074 | − | 0.637955i | \(-0.779781\pi\) |
−0.167449 | − | 0.985881i | \(-0.553553\pi\) | |||||||
\(348\) | 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 | 0 | ||||||||
\(351\) | −5.73205 | −0.305954 | ||||||||
\(352\) | −8.00000 | + | 13.8564i | −0.426401 | + | 0.738549i | ||||
\(353\) | 10.5622 | + | 18.2942i | 0.562168 | + | 0.973704i | 0.997307 | + | 0.0733402i | \(0.0233659\pi\) |
−0.435139 | + | 0.900363i | \(0.643301\pi\) | |||||||
\(354\) | 3.73205 | + | 6.46410i | 0.198356 | + | 0.343563i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 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 | −0.796810 | − | 0.604230i | \(-0.793481\pi\) |
0.921684 | + | 0.387942i | \(0.126814\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 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 | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.46410 | − | 2.53590i | 0.0765298 | − | 0.132554i | ||||
\(367\) | 0.401924 | + | 0.696152i | 0.0209803 | + | 0.0363389i | 0.876325 | − | 0.481721i | \(-0.159988\pi\) |
−0.855345 | + | 0.518059i | \(0.826655\pi\) | |||||||
\(368\) | −0.679492 | − | 1.17691i | −0.0354210 | − | 0.0613509i | ||||
\(369\) | −1.36603 | + | 2.36603i | −0.0711124 | + | 0.123170i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 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 | \(-0.992471\pi\) |
0.520342 | + | 0.853958i | \(0.325804\pi\) | |||||||
\(374\) | 6.73205 | + | 11.6603i | 0.348106 | + | 0.602937i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 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 | \(0.759255\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 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 | \(-0.739936\pi\) |
0.973625 | + | 0.228154i | \(0.0732689\pi\) | |||||||
\(384\) | 10.1436 | 0.517638 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −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 | −0.787401 | − | 0.616441i | \(-0.788574\pi\) |
−0.140153 | − | 0.990130i | \(-0.544760\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −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 | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.00000 | − | 3.46410i | −0.100504 | − | 0.174078i | ||||
\(397\) | −10.4019 | + | 18.0167i | −0.522058 | + | 0.904230i | 0.477613 | + | 0.878570i | \(0.341502\pi\) |
−0.999671 | + | 0.0256600i | \(0.991831\pi\) | |||||||
\(398\) | −16.1051 | −0.807277 | ||||||||
\(399\) | −2.13397 | − | 6.16025i | −0.106832 | − | 0.308398i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.19615 | + | 3.80385i | −0.109671 | + | 0.189955i | −0.915637 | − | 0.402006i | \(-0.868313\pi\) |
0.805966 | + | 0.591962i | \(0.201646\pi\) | |||||||
\(402\) | −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 | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 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 | −0.941362 | − | 0.337397i | \(-0.890454\pi\) |
0.178487 | − | 0.983942i | \(-0.442880\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −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 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −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 | \(0.745498\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 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 | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 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 | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.66025 | + | 15.0000i | 0.417150 | + | 0.722525i | 0.995651 | − | 0.0931566i | \(-0.0296957\pi\) |
−0.578502 | + | 0.815681i | \(0.696362\pi\) | |||||||
\(432\) | −0.535898 | + | 0.928203i | −0.0257834 | + | 0.0446582i | ||||
\(433\) | −4.80385 | −0.230858 | −0.115429 | − | 0.993316i | \(-0.536824\pi\) | ||||
−0.115429 | + | 0.993316i | \(0.536824\pi\) | |||||||
\(434\) | −4.09808 | − | 11.8301i | −0.196714 | − | 0.567864i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 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 | −0.941237 | − | 0.337747i | \(-0.890335\pi\) |
0.763116 | + | 0.646262i | \(0.223669\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −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 | \(-0.814146\pi\) |
0.894574 | + | 0.446921i | \(0.147479\pi\) | |||||||
\(444\) | −5.26795 | − | 9.12436i | −0.250006 | − | 0.433023i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −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 | 0 | ||||||||
\(451\) | 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 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.24871 | −0.292623 | ||||||||
\(457\) | 0.330127 | − | 0.571797i | 0.0154427 | − | 0.0267475i | −0.858201 | − | 0.513314i | \(-0.828418\pi\) |
0.873643 | + | 0.486567i | \(0.161751\pi\) | |||||||
\(458\) | −1.09808 | − | 1.90192i | −0.0513097 | − | 0.0888711i | ||||
\(459\) | 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 | \(0.803048\pi\) | |||||||
\(462\) | 3.46410 | − | 4.00000i | 0.161165 | − | 0.186097i | ||||
\(463\) | −22.2679 | −1.03488 | −0.517440 | − | 0.855720i | \(-0.673115\pi\) | ||||
−0.517440 | + | 0.855720i | \(0.673115\pi\) | |||||||
\(464\) | −3.32051 | + | 5.75129i | −0.154151 | + | 0.266997i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.33975 | + | 10.9808i | 0.293683 | + | 0.508674i | ||||
\(467\) | −13.9282 | + | 24.1244i | −0.644520 | + | 1.11634i | 0.339892 | + | 0.940465i | \(0.389610\pi\) |
−0.984412 | + | 0.175877i | \(0.943724\pi\) | |||||||
\(468\) | 8.39230 | 0.387934 | ||||||||
\(469\) | −4.60770 | + | 5.32051i | −0.212764 | + | 0.245678i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −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 | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −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 | 0.948310 | + | 0.317344i | \(0.102791\pi\) |
−0.199327 | + | 0.979933i | \(0.563876\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −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 | 0 | ||||||||
\(486\) | 0.366025 | + | 0.633975i | 0.0166032 | + | 0.0287577i | ||||
\(487\) | −15.7942 | − | 27.3564i | −0.715705 | − | 1.23964i | −0.962687 | − | 0.270617i | \(-0.912772\pi\) |
0.246982 | − | 0.969020i | \(-0.420561\pi\) | |||||||
\(488\) | −5.07180 | + | 8.78461i | −0.229589 | + | 0.397661i | ||||
\(489\) | 5.85641 | 0.264836 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.2487 | 0.462518 | 0.231259 | − | 0.972892i | \(-0.425716\pi\) | ||||
0.231259 | + | 0.972892i | \(0.425716\pi\) | |||||||
\(492\) | 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 | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 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 | −0.540808 | − | 0.841146i | \(-0.681882\pi\) |
0.998858 | + | 0.0477808i | \(0.0152149\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −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 | \(-0.454483\pi\) | ||||
0.142509 | + | 0.989793i | \(0.454483\pi\) | |||||||
\(504\) | −6.58846 | − | 1.26795i | −0.293473 | − | 0.0564789i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −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 | −0.964642 | − | 0.263563i | \(-0.915102\pi\) |
0.710573 | + | 0.703623i | \(0.248436\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 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 | 0 | ||||||||
\(516\) | 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 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.732051 | − | 1.26795i | −0.0320717 | − | 0.0555499i | 0.849544 | − | 0.527518i | \(-0.176877\pi\) |
−0.881616 | + | 0.471968i | \(0.843544\pi\) | |||||||
\(522\) | 2.26795 | + | 3.92820i | 0.0992654 | + | 0.171933i | ||||
\(523\) | −12.1340 | + | 21.0167i | −0.530582 | + | 0.918994i | 0.468782 | + | 0.883314i | \(0.344693\pi\) |
−0.999363 | + | 0.0356803i | \(0.988640\pi\) | |||||||
\(524\) | −12.4974 | −0.545952 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −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 | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 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 | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 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 | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.8923 | − | 30.9904i | 0.769250 | − | 1.33238i | −0.168720 | − | 0.985664i | \(-0.553963\pi\) |
0.937970 | − | 0.346716i | \(-0.112703\pi\) | |||||||
\(542\) | 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 | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.63397 | + | 10.4904i | 0.155520 | + | 0.448947i | ||||
\(547\) | −22.2487 | −0.951286 | −0.475643 | − | 0.879638i | \(-0.657785\pi\) | ||||
−0.475643 | + | 0.879638i | \(0.657785\pi\) | |||||||
\(548\) | 6.00000 | − | 10.3923i | 0.256307 | − | 0.443937i | ||||
\(549\) | −2.00000 | − | 3.46410i | −0.0853579 | − | 0.147844i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 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 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.80385 | − | 10.0526i | −0.246138 | − | 0.426323i | ||||
\(557\) | −13.3923 | − | 23.1962i | −0.567450 | − | 0.982853i | −0.996817 | − | 0.0797224i | \(-0.974597\pi\) |
0.429367 | − | 0.903130i | \(-0.358737\pi\) | |||||||
\(558\) | 2.36603 | − | 4.09808i | 0.100162 | − | 0.173485i | ||||
\(559\) | −41.2487 | −1.74463 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 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 | \(-0.290503\pi\) |
−0.990961 | + | 0.134148i | \(0.957170\pi\) | |||||||
\(564\) | −1.46410 | − | 2.53590i | −0.0616498 | − | 0.106781i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 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 | −0.443643 | − | 0.896203i | \(-0.646314\pi\) |
0.997957 | − | 0.0638952i | \(-0.0203523\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.6962 | − | 34.1147i | −0.824258 | − | 1.42766i | −0.902485 | − | 0.430722i | \(-0.858259\pi\) |
0.0782265 | − | 0.996936i | \(-0.475074\pi\) | |||||||
\(572\) | 11.4641 | − | 19.8564i | 0.479338 | − | 0.830238i | ||||
\(573\) | 4.92820 | 0.205879 | ||||||||
\(574\) | 5.19615 | + | 1.00000i | 0.216883 | + | 0.0417392i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.07180 | + | 1.85641i | −0.0446582 | + | 0.0773503i | ||||
\(577\) | 5.66987 | + | 9.82051i | 0.236040 | + | 0.408833i | 0.959574 | − | 0.281455i | \(-0.0908171\pi\) |
−0.723534 | + | 0.690288i | \(0.757484\pi\) | |||||||
\(578\) | 10.3660 | + | 17.9545i | 0.431170 | + | 0.746808i | ||||
\(579\) | −4.59808 | + | 7.96410i | −0.191090 | + | 0.330977i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 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 | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.85641 | + | 3.21539i | −0.0766874 | + | 0.132827i | ||||
\(587\) | −37.2679 | −1.53821 | −0.769106 | − | 0.639121i | \(-0.779298\pi\) | ||||
−0.769106 | + | 0.639121i | \(0.779298\pi\) | |||||||
\(588\) | 1.46410 | + | 10.1436i | 0.0603785 | + | 0.418315i | ||||
\(589\) | −15.9282 | −0.656310 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −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 | 0.154515 | + | 0.987990i | \(0.450619\pi\) |
−0.932882 | + | 0.360181i | \(0.882715\pi\) | |||||||
\(594\) | 2.00000 | 0.0820610 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 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 | 0.742142 | − | 0.670242i | \(-0.233810\pi\) |
−0.951518 | + | 0.307593i | \(0.900476\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −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 | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.92820 | − | 6.80385i | −0.159572 | − | 0.276387i | ||||
\(607\) | −3.59808 | + | 6.23205i | −0.146041 | + | 0.252951i | −0.929761 | − | 0.368164i | \(-0.879987\pi\) |
0.783720 | + | 0.621115i | \(0.213320\pi\) | |||||||
\(608\) | 14.4308 | 0.585245 | ||||||||
\(609\) | 10.7321 | − | 12.3923i | 0.434885 | − | 0.502162i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −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 | \(-0.251703\pi\) |
−0.967297 | + | 0.253648i | \(0.918369\pi\) | |||||||
\(614\) | 2.88269 | − | 4.99296i | 0.116336 | − | 0.201499i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.0000 | + | 13.8564i | −0.483494 | + | 0.558291i | ||||
\(617\) | −12.2487 | −0.493115 | −0.246557 | − | 0.969128i | \(-0.579299\pi\) | ||||
−0.246557 | + | 0.969128i | \(0.579299\pi\) | |||||||
\(618\) | −0.437822 | + | 0.758330i | −0.0176118 | + | 0.0305045i | ||||
\(619\) | 21.9641 | + | 38.0429i | 0.882812 | + | 1.52907i | 0.848201 | + | 0.529674i | \(0.177686\pi\) |
0.0346105 | + | 0.999401i | \(0.488981\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −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 | 0 | ||||||||
\(626\) | −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 | 0 | ||||||||
\(631\) | 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 | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −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 | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.09808 | − | 12.2942i | −0.280357 | − | 0.485593i | 0.691116 | − | 0.722744i | \(-0.257120\pi\) |
−0.971473 | + | 0.237151i | \(0.923786\pi\) | |||||||
\(642\) | 3.00000 | − | 5.19615i | 0.118401 | − | 0.205076i | ||||
\(643\) | 40.5167 | 1.59782 | 0.798911 | − | 0.601450i | \(-0.205410\pi\) | ||||
0.798911 | + | 0.601450i | \(0.205410\pi\) | |||||||
\(644\) | −1.60770 | − | 4.64102i | −0.0633521 | − | 0.182882i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.07180 | − | 10.5167i | 0.238892 | − | 0.413772i | ||||
\(647\) | 18.9545 | + | 32.8301i | 0.745178 | + | 1.29069i | 0.950112 | + | 0.311910i | \(0.100969\pi\) |
−0.204934 | + | 0.978776i | \(0.565698\pi\) | |||||||
\(648\) | −1.26795 | − | 2.19615i | −0.0498097 | − | 0.0862730i | ||||
\(649\) | 13.9282 | − | 24.1244i | 0.546730 | − | 0.946964i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −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 | \(-0.917853\pi\) |
0.704467 | + | 0.709737i | \(0.251186\pi\) | |||||||
\(654\) | 4.02628 | + | 6.97372i | 0.157440 | + | 0.272694i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −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 | \(0.568275\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.76795 | − | 3.06218i | −0.0687653 | − | 0.119105i | 0.829593 | − | 0.558369i | \(-0.188573\pi\) |
−0.898358 | + | 0.439264i | \(0.855239\pi\) | |||||||
\(662\) | 8.02628 | + | 13.9019i | 0.311950 | + | 0.540314i | ||||
\(663\) | −19.2942 | + | 33.4186i | −0.749326 | + | 1.29787i | ||||
\(664\) | 23.1384 | 0.897946 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 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 | 0 | ||||||||
\(671\) | −10.9282 | −0.421879 | ||||||||
\(672\) | 15.2154 | + | 2.92820i | 0.586946 | + | 0.112958i | ||||
\(673\) | 44.6603 | 1.72153 | 0.860763 | − | 0.509006i | \(-0.169987\pi\) | ||||
0.860763 | + | 0.509006i | \(0.169987\pi\) | |||||||
\(674\) | 12.4378 | − | 21.5429i | 0.479087 | − | 0.829803i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 14.5359 | + | 25.1769i | 0.559073 | + | 0.968343i | ||||
\(677\) | −4.43782 | + | 7.68653i | −0.170559 | + | 0.295417i | −0.938616 | − | 0.344965i | \(-0.887891\pi\) |
0.768056 | + | 0.640382i | \(0.221224\pi\) | |||||||
\(678\) | −3.60770 | −0.138553 | ||||||||
\(679\) | −0.928203 | − | 2.67949i | −0.0356212 | − | 0.102829i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 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 | \(-0.105064\pi\) |
−0.753695 | + | 0.657224i | \(0.771730\pi\) | |||||||
\(684\) | −1.80385 | + | 3.12436i | −0.0689718 | + | 0.119463i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −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 | 0 | ||||||||
\(691\) | 9.42820 | − | 16.3301i | 0.358666 | − | 0.621227i | −0.629072 | − | 0.777347i | \(-0.716565\pi\) |
0.987738 | + | 0.156119i | \(0.0498985\pi\) | |||||||
\(692\) | 31.4256 | 1.19462 | ||||||||
\(693\) | −2.36603 | − | 6.83013i | −0.0898779 | − | 0.259455i | ||||
\(694\) | −25.5692 | −0.970594 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −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 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 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 | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 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 | −0.691143 | − | 0.722718i | \(-0.742893\pi\) |
0.971464 | + | 0.237189i | \(0.0762260\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −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 | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −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 | −0.487782 | − | 0.872965i | \(-0.662194\pi\) |
0.999901 | − | 0.0140509i | \(-0.00447269\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 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 | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.29423 | + | 2.24167i | −0.0480333 | + | 0.0831962i | ||||
\(727\) | 30.6603 | 1.13713 | 0.568563 | − | 0.822640i | \(-0.307500\pi\) | ||||
0.568563 | + | 0.822640i | \(0.307500\pi\) | |||||||
\(728\) | −12.5885 | − | 36.3397i | −0.466559 | − | 1.34684i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 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 | \(-0.945324\pi\) |
0.640668 | + | 0.767818i | \(0.278658\pi\) | |||||||
\(734\) | 0.588457 | 0.0217204 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −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 | 0.964497 | − | 0.264093i | \(-0.0850725\pi\) |
−0.710960 | + | 0.703233i | \(0.751739\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14.1244 | 0.518871 | ||||||||
\(742\) | −5.32051 | − | 15.3590i | −0.195322 | − | 0.563846i | ||||
\(743\) | −49.9090 | −1.83098 | −0.915491 | − | 0.402338i | \(-0.868198\pi\) | ||||
−0.915491 | + | 0.402338i | \(0.868198\pi\) | |||||||
\(744\) | −8.19615 | + | 14.1962i | −0.300486 | + | 0.520456i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 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 | 0 | ||||||||
\(751\) | −15.9641 | + | 27.6506i | −0.582538 | + | 1.00899i | 0.412639 | + | 0.910895i | \(0.364607\pi\) |
−0.995177 | + | 0.0980914i | \(0.968726\pi\) | |||||||
\(752\) | 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 | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.53590 | + | 2.92820i | −0.0922297 | + | 0.106498i | ||||
\(757\) | 0.143594 | 0.00521900 | 0.00260950 | − | 0.999997i | \(-0.499169\pi\) | ||||
0.00260950 | + | 0.999997i | \(0.499169\pi\) | |||||||
\(758\) | −10.3660 | + | 17.9545i | −0.376511 | + | 0.652136i | ||||
\(759\) | 1.73205 | + | 3.00000i | 0.0628695 | + | 0.108893i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.6340 | + | 37.4711i | −0.784231 | + | 1.35833i | 0.145226 | + | 0.989398i | \(0.453609\pi\) |
−0.929457 | + | 0.368929i | \(0.879724\pi\) | |||||||
\(762\) | 11.1244 | 0.402993 | ||||||||
\(763\) | 19.0526 | − | 22.0000i | 0.689749 | − | 0.796453i | ||||
\(764\) | −7.21539 | −0.261044 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −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 | \(0.396730\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −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 | \(-0.175350\pi\) |
−0.879341 | + | 0.476193i | \(0.842016\pi\) | |||||||
\(774\) | 2.63397 | + | 4.56218i | 0.0946763 | + | 0.163984i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −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 | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −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 | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.12436 | − | 5.41154i | 0.111442 | − | 0.193023i | ||||
\(787\) | 3.26795 | + | 5.66025i | 0.116490 | + | 0.201766i | 0.918374 | − | 0.395713i | \(-0.129502\pi\) |
−0.801885 | + | 0.597479i | \(0.796169\pi\) | |||||||
\(788\) | 12.9282 | + | 22.3923i | 0.460548 | + | 0.797693i | ||||
\(789\) | −6.19615 | + | 10.7321i | −0.220589 | + | 0.382071i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 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 | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.1051 | − | 27.8949i | 0.570831 | − | 0.988708i | ||||
\(797\) | 42.0526 | 1.48958 | 0.744789 | − | 0.667300i | \(-0.232550\pi\) | ||||
0.744789 | + | 0.667300i | \(0.232550\pi\) | |||||||
\(798\) | −4.68653 | − | 0.901924i | −0.165901 | − | 0.0319278i | ||||
\(799\) | 13.4641 | 0.476326 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 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 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 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 | 0.999663 | + | 0.0259716i | \(0.00826796\pi\) |
−0.477339 | + | 0.878719i | \(0.658399\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 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 | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 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 | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.75833 | + | 16.9019i | −0.340568 | + | 0.589881i | −0.984538 | − | 0.175169i | \(-0.943953\pi\) |
0.643970 | + | 0.765051i | \(0.277286\pi\) | |||||||
\(822\) | 3.00000 | + | 5.19615i | 0.104637 | + | 0.181237i | ||||
\(823\) | −11.5885 | − | 20.0718i | −0.403948 | − | 0.699659i | 0.590250 | − | 0.807220i | \(-0.299029\pi\) |
−0.994198 | + | 0.107561i | \(0.965696\pi\) | |||||||
\(824\) | 1.51666 | − | 2.62693i | 0.0528354 | − | 0.0915135i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.46410 | − | 18.6603i | −0.224915 | − | 0.649273i | ||||
\(827\) | 52.2487 | 1.81687 | 0.908433 | − | 0.418031i | \(-0.137280\pi\) | ||||
0.908433 | + | 0.418031i | \(0.137280\pi\) | |||||||
\(828\) | 0.928203 | − | 1.60770i | 0.0322573 | − | 0.0558713i | ||||
\(829\) | 12.6962 | + | 21.9904i | 0.440956 | + | 0.763758i | 0.997761 | − | 0.0668857i | \(-0.0213063\pi\) |
−0.556805 | + | 0.830643i | \(0.687973\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 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 | 0 | ||||||||
\(836\) | 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 | \(0.745996\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 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 | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 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 | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 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 | \(-0.611126\pi\) | ||||
−0.342064 | + | 0.939677i | \(0.611126\pi\) | |||||||
\(854\) | −5.07180 | + | 5.85641i | −0.173553 | + | 0.200402i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.3923 | + | 18.0000i | −0.355202 | + | 0.615227i | ||||
\(857\) | 2.43782 | + | 4.22243i | 0.0832744 | + | 0.144236i | 0.904655 | − | 0.426146i | \(-0.140129\pi\) |
−0.821380 | + | 0.570381i | \(0.806796\pi\) | |||||||
\(858\) | 5.73205 | + | 9.92820i | 0.195689 | + | 0.338943i | ||||
\(859\) | −0.267949 | + | 0.464102i | −0.00914231 | + | 0.0158349i | −0.870560 | − | 0.492062i | \(-0.836243\pi\) |
0.861418 | + | 0.507897i | \(0.169577\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 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 | \(-0.868034\pi\) |
0.806485 | + | 0.591254i | \(0.201367\pi\) | |||||||
\(864\) | 2.92820 | + | 5.07180i | 0.0996195 | + | 0.172546i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −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 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −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 | 0 | ||||||||
\(876\) | −6.82309 | −0.230531 | ||||||||
\(877\) | −15.9282 | + | 27.5885i | −0.537857 | + | 0.931596i | 0.461162 | + | 0.887316i | \(0.347433\pi\) |
−0.999019 | + | 0.0442800i | \(0.985901\pi\) | |||||||
\(878\) | 2.73205 | + | 4.73205i | 0.0922022 | + | 0.159699i | ||||
\(879\) | 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 | \(0.597253\pi\) | |||||||
\(882\) | −4.75833 | − | 1.90192i | −0.160221 | − | 0.0640411i | ||||
\(883\) | −22.4115 | −0.754208 | −0.377104 | − | 0.926171i | \(-0.623080\pi\) | ||||
−0.377104 | + | 0.926171i | \(0.623080\pi\) | |||||||
\(884\) | 28.2487 | − | 48.9282i | 0.950107 | − | 1.64563i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.928203 | − | 1.60770i | −0.0311836 | − | 0.0540116i | ||||
\(887\) | −14.3660 | + | 24.8827i | −0.482364 | + | 0.835479i | −0.999795 | − | 0.0202460i | \(-0.993555\pi\) |
0.517431 | + | 0.855725i | \(0.326888\pi\) | |||||||
\(888\) | −18.2487 | −0.612387 | ||||||||
\(889\) | −13.1603 | − | 37.9904i | −0.441381 | − | 1.27416i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 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 | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −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 | 0 | ||||||||
\(901\) | 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 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.80385 | + | 3.12436i | 0.0599288 | + | 0.103800i | ||||
\(907\) | 1.20577 | + | 2.08846i | 0.0400370 | + | 0.0693461i | 0.885350 | − | 0.464926i | \(-0.153919\pi\) |
−0.845313 | + | 0.534272i | \(0.820586\pi\) | |||||||
\(908\) | −11.4641 | + | 19.8564i | −0.380450 | + | 0.658958i | ||||
\(909\) | −10.7321 | −0.355960 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.2679 | −0.373324 | −0.186662 | − | 0.982424i | \(-0.559767\pi\) | ||||
−0.186662 | + | 0.982424i | \(0.559767\pi\) | |||||||
\(912\) | 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 | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 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 | −0.838936 | − | 0.544230i | \(-0.816822\pi\) |
0.890785 | + | 0.454425i | \(0.150155\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −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 | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −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 | −0.914034 | − | 0.405638i | \(-0.867050\pi\) |
0.808309 | + | 0.588758i | \(0.200383\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 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 | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.26795 | − | 12.5885i | 0.237560 | − | 0.411467i | ||||
\(937\) | −28.2679 | −0.923474 | −0.461737 | − | 0.887017i | \(-0.652774\pi\) | ||||
−0.461737 | + | 0.887017i | \(0.652774\pi\) | |||||||
\(938\) | 1.68653 | + | 4.86860i | 0.0550673 | + | 0.158966i | ||||
\(939\) | −4.66025 | −0.152082 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.02628 | − | 6.97372i | −0.131253 | − | 0.227337i | 0.792907 | − | 0.609343i | \(-0.208567\pi\) |
−0.924160 | + | 0.382006i | \(0.875233\pi\) | |||||||
\(942\) | 5.26795 | + | 9.12436i | 0.171639 | + | 0.297288i | ||||
\(943\) | −1.73205 | + | 3.00000i | −0.0564033 | + | 0.0976934i | ||||
\(944\) | 10.9282 | 0.355683 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14.3923 | 0.467934 | ||||||||
\(947\) | 5.83013 | − | 10.0981i | 0.189454 | − | 0.328143i | −0.755615 | − | 0.655017i | \(-0.772662\pi\) |
0.945068 | + | 0.326873i | \(0.105995\pi\) | |||||||
\(948\) | 9.80385 | + | 16.9808i | 0.318414 | + | 0.551510i | ||||
\(949\) | 13.3564 | + | 23.1340i | 0.433567 | + | 0.750961i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −30.4449 | −0.987242 | ||||||||
\(952\) | −29.5692 | + | 34.1436i | −0.958344 | + | 1.10660i | ||||
\(953\) | −40.1051 | −1.29913 | −0.649566 | − | 0.760305i | \(-0.725049\pi\) | ||||
−0.649566 | + | 0.760305i | \(0.725049\pi\) | |||||||
\(954\) | 3.07180 | − | 5.32051i | 0.0994531 | − | 0.172258i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 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 | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −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 | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.41154 | + | 0.464102i | 0.0775901 | + | 0.0149322i | ||||
\(967\) | −14.1244 | −0.454209 | −0.227104 | − | 0.973870i | \(-0.572926\pi\) | ||||
−0.227104 | + | 0.973870i | \(0.572926\pi\) | |||||||
\(968\) | 4.48334 | − | 7.76537i | 0.144100 | − | 0.249589i | ||||
\(969\) | −8.29423 | − | 14.3660i | −0.266449 | − | 0.461503i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.0000 | − | 20.7846i | 0.385098 | − | 0.667010i | −0.606685 | − | 0.794943i | \(-0.707501\pi\) |
0.991783 | + | 0.127933i | \(0.0408342\pi\) | |||||||
\(972\) | −1.46410 | −0.0469611 | ||||||||
\(973\) | −6.86603 | − | 19.8205i | −0.220115 | − | 0.635416i | ||||
\(974\) | −23.1244 | −0.740952 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.14359 | − | 3.71281i | −0.0686148 | − | 0.118844i | ||||
\(977\) | 7.29423 | + | 12.6340i | 0.233363 | + | 0.404197i | 0.958796 | − | 0.284097i | \(-0.0916936\pi\) |
−0.725433 | + | 0.688293i | \(0.758360\pi\) | |||||||
\(978\) | 2.14359 | − | 3.71281i | 0.0685446 | − | 0.118723i | ||||
\(979\) | 24.9282 | 0.796709 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 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 | \(-0.0622851\pi\) |
−0.658838 | + | 0.752285i | \(0.728952\pi\) | |||||||
\(984\) | −3.46410 | − | 6.00000i | −0.110432 | − | 0.191273i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 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 | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.5526 | − | 47.7224i | −0.875236 | − | 1.51595i | −0.856511 | − | 0.516128i | \(-0.827373\pi\) |
−0.0187246 | − | 0.999825i | \(-0.505961\pi\) | |||||||
\(992\) | 18.9282 | − | 32.7846i | 0.600971 | − | 1.04091i | ||||
\(993\) | 21.9282 | 0.695870 | ||||||||
\(994\) | −7.98076 | − | 1.53590i | −0.253134 | − | 0.0487157i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.67949 | − | 11.5692i | 0.211648 | − | 0.366585i | ||||
\(997\) | −2.00962 | − | 3.48076i | −0.0636453 | − | 0.110237i | 0.832447 | − | 0.554105i | \(-0.186939\pi\) |
−0.896092 | + | 0.443868i | \(0.853606\pi\) | |||||||
\(998\) | −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 | 525.2.i.f.226.2 | 4 | ||
5.2 | odd | 4 | 525.2.r.f.499.1 | 4 | |||
5.3 | odd | 4 | 525.2.r.a.499.2 | 4 | |||
5.4 | even | 2 | 105.2.i.d.16.1 | ✓ | 4 | ||
7.2 | even | 3 | 3675.2.a.bg.1.1 | 2 | |||
7.4 | even | 3 | inner | 525.2.i.f.151.2 | 4 | ||
7.5 | odd | 6 | 3675.2.a.be.1.1 | 2 | |||
15.14 | odd | 2 | 315.2.j.c.226.2 | 4 | |||
20.19 | odd | 2 | 1680.2.bg.o.961.2 | 4 | |||
35.4 | even | 6 | 105.2.i.d.46.1 | yes | 4 | ||
35.9 | even | 6 | 735.2.a.g.1.2 | 2 | |||
35.18 | odd | 12 | 525.2.r.f.424.1 | 4 | |||
35.19 | odd | 6 | 735.2.a.h.1.2 | 2 | |||
35.24 | odd | 6 | 735.2.i.l.361.1 | 4 | |||
35.32 | odd | 12 | 525.2.r.a.424.2 | 4 | |||
35.34 | odd | 2 | 735.2.i.l.226.1 | 4 | |||
105.44 | odd | 6 | 2205.2.a.z.1.1 | 2 | |||
105.74 | odd | 6 | 315.2.j.c.46.2 | 4 | |||
105.89 | even | 6 | 2205.2.a.ba.1.1 | 2 | |||
140.39 | odd | 6 | 1680.2.bg.o.1201.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.i.d.16.1 | ✓ | 4 | 5.4 | even | 2 | ||
105.2.i.d.46.1 | yes | 4 | 35.4 | even | 6 | ||
315.2.j.c.46.2 | 4 | 105.74 | odd | 6 | |||
315.2.j.c.226.2 | 4 | 15.14 | odd | 2 | |||
525.2.i.f.151.2 | 4 | 7.4 | even | 3 | inner | ||
525.2.i.f.226.2 | 4 | 1.1 | even | 1 | trivial | ||
525.2.r.a.424.2 | 4 | 35.32 | odd | 12 | |||
525.2.r.a.499.2 | 4 | 5.3 | odd | 4 | |||
525.2.r.f.424.1 | 4 | 35.18 | odd | 12 | |||
525.2.r.f.499.1 | 4 | 5.2 | odd | 4 | |||
735.2.a.g.1.2 | 2 | 35.9 | even | 6 | |||
735.2.a.h.1.2 | 2 | 35.19 | odd | 6 | |||
735.2.i.l.226.1 | 4 | 35.34 | odd | 2 | |||
735.2.i.l.361.1 | 4 | 35.24 | odd | 6 | |||
1680.2.bg.o.961.2 | 4 | 20.19 | odd | 2 | |||
1680.2.bg.o.1201.2 | 4 | 140.39 | odd | 6 | |||
2205.2.a.z.1.1 | 2 | 105.44 | odd | 6 | |||
2205.2.a.ba.1.1 | 2 | 105.89 | even | 6 | |||
3675.2.a.be.1.1 | 2 | 7.5 | odd | 6 | |||
3675.2.a.bg.1.1 | 2 | 7.2 | even | 3 |