Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [560,2,Mod(141,560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(560, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("560.141");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.bd (of order \(4\), 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: | \(4.47162251319\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 141.2 | ||
Character | \(\chi\) | \(=\) | 560.141 |
Dual form | 560.2.bd.a.421.2 |
$q$-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 \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(351\) | \(421\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.40016 | − | 0.198865i | −0.990064 | − | 0.140619i | ||||
\(3\) | 1.92081 | + | 1.92081i | 1.10898 | + | 1.10898i | 0.993285 | + | 0.115692i | \(0.0369087\pi\) |
0.115692 | + | 0.993285i | \(0.463091\pi\) | |||||||
\(4\) | 1.92091 | + | 0.556887i | 0.960453 | + | 0.278443i | ||||
\(5\) | 0.707107 | − | 0.707107i | 0.316228 | − | 0.316228i | ||||
\(6\) | −2.30746 | − | 3.07142i | −0.942015 | − | 1.25390i | ||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | −2.57883 | − | 1.16173i | −0.911755 | − | 0.410734i | ||||
\(9\) | 4.37899i | 1.45966i | ||||||||
\(10\) | −1.13068 | + | 0.849445i | −0.357553 | + | 0.268618i | ||||
\(11\) | 2.40494 | − | 2.40494i | 0.725116 | − | 0.725116i | −0.244526 | − | 0.969643i | \(-0.578632\pi\) |
0.969643 | + | 0.244526i | \(0.0786325\pi\) | |||||||
\(12\) | 2.62001 | + | 4.75936i | 0.756333 | + | 1.37391i | ||||
\(13\) | −0.230047 | − | 0.230047i | −0.0638036 | − | 0.0638036i | 0.674485 | − | 0.738289i | \(-0.264366\pi\) |
−0.738289 | + | 0.674485i | \(0.764366\pi\) | |||||||
\(14\) | −0.198865 | + | 1.40016i | −0.0531489 | + | 0.374209i | ||||
\(15\) | 2.71643 | 0.701379 | ||||||||
\(16\) | 3.37975 | + | 2.13945i | 0.844939 | + | 0.534863i | ||||
\(17\) | 3.07426 | 0.745617 | 0.372809 | − | 0.927908i | \(-0.378395\pi\) | ||||
0.372809 | + | 0.927908i | \(0.378395\pi\) | |||||||
\(18\) | 0.870827 | − | 6.13129i | 0.205256 | − | 1.44516i | ||||
\(19\) | 4.98381 | + | 4.98381i | 1.14336 | + | 1.14336i | 0.987831 | + | 0.155534i | \(0.0497098\pi\) |
0.155534 | + | 0.987831i | \(0.450290\pi\) | |||||||
\(20\) | 1.75206 | − | 0.964507i | 0.391773 | − | 0.215670i | ||||
\(21\) | 1.92081 | − | 1.92081i | 0.419154 | − | 0.419154i | ||||
\(22\) | −3.84556 | + | 2.88904i | −0.819876 | + | 0.615946i | ||||
\(23\) | − | 2.85562i | − | 0.595438i | −0.954654 | − | 0.297719i | \(-0.903774\pi\) | ||
0.954654 | − | 0.297719i | \(-0.0962258\pi\) | |||||||
\(24\) | −2.72197 | − | 7.18490i | −0.555621 | − | 1.46661i | ||||
\(25\) | − | 1.00000i | − | 0.200000i | ||||||
\(26\) | 0.276355 | + | 0.367851i | 0.0541976 | + | 0.0721416i | ||||
\(27\) | −2.64876 | + | 2.64876i | −0.509755 | + | 0.509755i | ||||
\(28\) | 0.556887 | − | 1.92091i | 0.105242 | − | 0.363017i | ||||
\(29\) | 3.04810 | + | 3.04810i | 0.566018 | + | 0.566018i | 0.931011 | − | 0.364992i | \(-0.118928\pi\) |
−0.364992 | + | 0.931011i | \(0.618928\pi\) | |||||||
\(30\) | −3.80344 | − | 0.540203i | −0.694410 | − | 0.0986271i | ||||
\(31\) | −5.50995 | −0.989616 | −0.494808 | − | 0.869002i | \(-0.664762\pi\) | ||||
−0.494808 | + | 0.869002i | \(0.664762\pi\) | |||||||
\(32\) | −4.30674 | − | 3.66769i | −0.761331 | − | 0.648363i | ||||
\(33\) | 9.23884 | 1.60828 | ||||||||
\(34\) | −4.30446 | − | 0.611363i | −0.738209 | − | 0.104848i | ||||
\(35\) | −0.707107 | − | 0.707107i | −0.119523 | − | 0.119523i | ||||
\(36\) | −2.43860 | + | 8.41162i | −0.406433 | + | 1.40194i | ||||
\(37\) | −5.74684 | + | 5.74684i | −0.944774 | + | 0.944774i | −0.998553 | − | 0.0537789i | \(-0.982873\pi\) |
0.0537789 | + | 0.998553i | \(0.482873\pi\) | |||||||
\(38\) | −5.98703 | − | 7.96925i | −0.971225 | − | 1.29278i | ||||
\(39\) | − | 0.883751i | − | 0.141513i | ||||||
\(40\) | −2.64498 | + | 1.00204i | −0.418208 | + | 0.158437i | ||||
\(41\) | 2.73725i | 0.427487i | 0.976890 | + | 0.213744i | \(0.0685657\pi\) | ||||
−0.976890 | + | 0.213744i | \(0.931434\pi\) | |||||||
\(42\) | −3.07142 | + | 2.30746i | −0.473930 | + | 0.356048i | ||||
\(43\) | −1.65787 | + | 1.65787i | −0.252822 | + | 0.252822i | −0.822127 | − | 0.569304i | \(-0.807213\pi\) |
0.569304 | + | 0.822127i | \(0.307213\pi\) | |||||||
\(44\) | 5.95894 | − | 3.28038i | 0.898344 | − | 0.494536i | ||||
\(45\) | 3.09641 | + | 3.09641i | 0.461586 | + | 0.461586i | ||||
\(46\) | −0.567883 | + | 3.99833i | −0.0837298 | + | 0.589521i | ||||
\(47\) | −12.0114 | −1.75204 | −0.876019 | − | 0.482276i | \(-0.839810\pi\) | ||||
−0.876019 | + | 0.482276i | \(0.839810\pi\) | |||||||
\(48\) | 2.38238 | + | 10.6013i | 0.343867 | + | 1.53017i | ||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −0.198865 | + | 1.40016i | −0.0281238 | + | 0.198013i | ||||
\(51\) | 5.90505 | + | 5.90505i | 0.826873 | + | 0.826873i | ||||
\(52\) | −0.313789 | − | 0.570009i | −0.0435146 | − | 0.0790460i | ||||
\(53\) | 9.26864 | − | 9.26864i | 1.27315 | − | 1.27315i | 0.328717 | − | 0.944428i | \(-0.393384\pi\) |
0.944428 | − | 0.328717i | \(-0.106616\pi\) | |||||||
\(54\) | 4.23544 | − | 3.18195i | 0.576371 | − | 0.433008i | ||||
\(55\) | − | 3.40110i | − | 0.458604i | ||||||
\(56\) | −1.16173 | + | 2.57883i | −0.155243 | + | 0.344611i | ||||
\(57\) | 19.1459i | 2.53593i | ||||||||
\(58\) | −3.66167 | − | 4.87400i | −0.480801 | − | 0.639987i | ||||
\(59\) | −1.23554 | + | 1.23554i | −0.160854 | + | 0.160854i | −0.782945 | − | 0.622091i | \(-0.786283\pi\) |
0.622091 | + | 0.782945i | \(0.286283\pi\) | |||||||
\(60\) | 5.21800 | + | 1.51274i | 0.673641 | + | 0.195294i | ||||
\(61\) | 0.354752 | + | 0.354752i | 0.0454213 | + | 0.0454213i | 0.729453 | − | 0.684031i | \(-0.239775\pi\) |
−0.684031 | + | 0.729453i | \(0.739775\pi\) | |||||||
\(62\) | 7.71482 | + | 1.09574i | 0.979783 | + | 0.139159i | ||||
\(63\) | 4.37899 | 0.551700 | ||||||||
\(64\) | 5.30076 | + | 5.99183i | 0.662595 | + | 0.748978i | ||||
\(65\) | −0.325336 | −0.0403529 | ||||||||
\(66\) | −12.9359 | − | 1.83728i | −1.59230 | − | 0.226154i | ||||
\(67\) | −10.8475 | − | 10.8475i | −1.32524 | − | 1.32524i | −0.909474 | − | 0.415761i | \(-0.863515\pi\) |
−0.415761 | − | 0.909474i | \(-0.636485\pi\) | |||||||
\(68\) | 5.90536 | + | 1.71201i | 0.716130 | + | 0.207612i | ||||
\(69\) | 5.48509 | − | 5.48509i | 0.660327 | − | 0.660327i | ||||
\(70\) | 0.849445 | + | 1.13068i | 0.101528 | + | 0.135142i | ||||
\(71\) | − | 1.43189i | − | 0.169934i | −0.996384 | − | 0.0849671i | \(-0.972921\pi\) | ||
0.996384 | − | 0.0849671i | \(-0.0270785\pi\) | |||||||
\(72\) | 5.08721 | − | 11.2927i | 0.599533 | − | 1.33085i | ||||
\(73\) | 11.5526i | 1.35213i | 0.736844 | + | 0.676063i | \(0.236315\pi\) | ||||
−0.736844 | + | 0.676063i | \(0.763685\pi\) | |||||||
\(74\) | 9.18934 | − | 6.90365i | 1.06824 | − | 0.802534i | ||||
\(75\) | 1.92081 | − | 1.92081i | 0.221795 | − | 0.221795i | ||||
\(76\) | 6.79801 | + | 12.3488i | 0.779785 | + | 1.41651i | ||||
\(77\) | −2.40494 | − | 2.40494i | −0.274068 | − | 0.274068i | ||||
\(78\) | −0.175747 | + | 1.23739i | −0.0198995 | + | 0.140107i | ||||
\(79\) | 8.10993 | 0.912439 | 0.456219 | − | 0.889867i | \(-0.349203\pi\) | ||||
0.456219 | + | 0.889867i | \(0.349203\pi\) | |||||||
\(80\) | 3.90267 | − | 0.877026i | 0.436332 | − | 0.0980545i | ||||
\(81\) | 2.96144 | 0.329049 | ||||||||
\(82\) | 0.544344 | − | 3.83260i | 0.0601127 | − | 0.423239i | ||||
\(83\) | −0.0148642 | − | 0.0148642i | −0.00163155 | − | 0.00163155i | 0.706291 | − | 0.707922i | \(-0.250367\pi\) |
−0.707922 | + | 0.706291i | \(0.750367\pi\) | |||||||
\(84\) | 4.75936 | − | 2.62001i | 0.519288 | − | 0.285867i | ||||
\(85\) | 2.17383 | − | 2.17383i | 0.235785 | − | 0.235785i | ||||
\(86\) | 2.65097 | − | 1.99159i | 0.285862 | − | 0.214759i | ||||
\(87\) | 11.7096i | 1.25540i | ||||||||
\(88\) | −8.99583 | + | 3.40804i | −0.958959 | + | 0.363298i | ||||
\(89\) | − | 11.4609i | − | 1.21486i | −0.794375 | − | 0.607428i | \(-0.792201\pi\) | ||
0.794375 | − | 0.607428i | \(-0.207799\pi\) | |||||||
\(90\) | −3.71971 | − | 4.95124i | −0.392092 | − | 0.521907i | ||||
\(91\) | −0.230047 | + | 0.230047i | −0.0241155 | + | 0.0241155i | ||||
\(92\) | 1.59026 | − | 5.48537i | 0.165796 | − | 0.571890i | ||||
\(93\) | −10.5835 | − | 10.5835i | −1.09746 | − | 1.09746i | ||||
\(94\) | 16.8179 | + | 2.38864i | 1.73463 | + | 0.246370i | ||||
\(95\) | 7.04817 | 0.723127 | ||||||||
\(96\) | −1.22748 | − | 15.3173i | −0.125279 | − | 1.56332i | ||||
\(97\) | 7.61510 | 0.773197 | 0.386598 | − | 0.922248i | \(-0.373650\pi\) | ||||
0.386598 | + | 0.922248i | \(0.373650\pi\) | |||||||
\(98\) | 1.40016 | + | 0.198865i | 0.141438 | + | 0.0200884i | ||||
\(99\) | 10.5312 | + | 10.5312i | 1.05842 | + | 1.05842i | ||||
\(100\) | 0.556887 | − | 1.92091i | 0.0556887 | − | 0.192091i | ||||
\(101\) | 6.10829 | − | 6.10829i | 0.607797 | − | 0.607797i | −0.334573 | − | 0.942370i | \(-0.608592\pi\) |
0.942370 | + | 0.334573i | \(0.108592\pi\) | |||||||
\(102\) | −7.09372 | − | 9.44234i | −0.702383 | − | 0.934931i | ||||
\(103\) | 9.38744i | 0.924972i | 0.886627 | + | 0.462486i | \(0.153042\pi\) | ||||
−0.886627 | + | 0.462486i | \(0.846958\pi\) | |||||||
\(104\) | 0.326000 | + | 0.860506i | 0.0319669 | + | 0.0843796i | ||||
\(105\) | − | 2.71643i | − | 0.265096i | ||||||
\(106\) | −14.8208 | + | 11.1344i | −1.43952 | + | 1.08147i | ||||
\(107\) | −4.06190 | + | 4.06190i | −0.392679 | + | 0.392679i | −0.875641 | − | 0.482962i | \(-0.839561\pi\) |
0.482962 | + | 0.875641i | \(0.339561\pi\) | |||||||
\(108\) | −6.56308 | + | 3.61296i | −0.631533 | + | 0.347657i | ||||
\(109\) | −11.6383 | − | 11.6383i | −1.11475 | − | 1.11475i | −0.992499 | − | 0.122252i | \(-0.960988\pi\) |
−0.122252 | − | 0.992499i | \(-0.539012\pi\) | |||||||
\(110\) | −0.676359 | + | 4.76209i | −0.0644883 | + | 0.454047i | ||||
\(111\) | −22.0771 | −2.09547 | ||||||||
\(112\) | 2.13945 | − | 3.37975i | 0.202159 | − | 0.319357i | ||||
\(113\) | −14.3735 | −1.35215 | −0.676074 | − | 0.736833i | \(-0.736320\pi\) | ||||
−0.676074 | + | 0.736833i | \(0.736320\pi\) | |||||||
\(114\) | 3.80744 | − | 26.8073i | 0.356600 | − | 2.51073i | ||||
\(115\) | −2.01923 | − | 2.01923i | −0.188294 | − | 0.188294i | ||||
\(116\) | 4.15767 | + | 7.55256i | 0.386030 | + | 0.701238i | ||||
\(117\) | 1.00737 | − | 1.00737i | 0.0931316 | − | 0.0931316i | ||||
\(118\) | 1.97567 | − | 1.48426i | 0.181875 | − | 0.136637i | ||||
\(119\) | − | 3.07426i | − | 0.281817i | ||||||
\(120\) | −7.00522 | − | 3.15576i | −0.639486 | − | 0.288080i | ||||
\(121\) | − | 0.567460i | − | 0.0515873i | ||||||
\(122\) | −0.426162 | − | 0.567258i | −0.0385829 | − | 0.0513571i | ||||
\(123\) | −5.25773 | + | 5.25773i | −0.474074 | + | 0.474074i | ||||
\(124\) | −10.5841 | − | 3.06842i | −0.950479 | − | 0.275552i | ||||
\(125\) | −0.707107 | − | 0.707107i | −0.0632456 | − | 0.0632456i | ||||
\(126\) | −6.13129 | − | 0.870827i | −0.546219 | − | 0.0775795i | ||||
\(127\) | −16.3150 | −1.44772 | −0.723860 | − | 0.689947i | \(-0.757634\pi\) | ||||
−0.723860 | + | 0.689947i | \(0.757634\pi\) | |||||||
\(128\) | −6.23035 | − | 9.44366i | −0.550690 | − | 0.834710i | ||||
\(129\) | −6.36888 | −0.560748 | ||||||||
\(130\) | 0.455523 | + | 0.0646979i | 0.0399520 | + | 0.00567438i | ||||
\(131\) | 1.51297 | + | 1.51297i | 0.132189 | + | 0.132189i | 0.770105 | − | 0.637917i | \(-0.220204\pi\) |
−0.637917 | + | 0.770105i | \(0.720204\pi\) | |||||||
\(132\) | 17.7469 | + | 5.14498i | 1.54467 | + | 0.447813i | ||||
\(133\) | 4.98381 | − | 4.98381i | 0.432151 | − | 0.432151i | ||||
\(134\) | 13.0311 | + | 17.3455i | 1.12571 | + | 1.49842i | ||||
\(135\) | 3.74592i | 0.322397i | ||||||||
\(136\) | −7.92800 | − | 3.57147i | −0.679820 | − | 0.306251i | ||||
\(137\) | − | 5.04227i | − | 0.430790i | −0.976527 | − | 0.215395i | \(-0.930896\pi\) | ||
0.976527 | − | 0.215395i | \(-0.0691040\pi\) | |||||||
\(138\) | −8.77080 | + | 6.58922i | −0.746620 | + | 0.560912i | ||||
\(139\) | −13.0200 | + | 13.0200i | −1.10434 | + | 1.10434i | −0.110465 | + | 0.993880i | \(0.535234\pi\) |
−0.993880 | + | 0.110465i | \(0.964766\pi\) | |||||||
\(140\) | −0.964507 | − | 1.75206i | −0.0815157 | − | 0.148076i | ||||
\(141\) | −23.0715 | − | 23.0715i | −1.94297 | − | 1.94297i | ||||
\(142\) | −0.284753 | + | 2.00488i | −0.0238959 | + | 0.168246i | ||||
\(143\) | −1.10650 | −0.0925300 | ||||||||
\(144\) | −9.36863 | + | 14.7999i | −0.780719 | + | 1.23332i | ||||
\(145\) | 4.31067 | 0.357981 | ||||||||
\(146\) | 2.29740 | − | 16.1755i | 0.190134 | − | 1.33869i | ||||
\(147\) | −1.92081 | − | 1.92081i | −0.158425 | − | 0.158425i | ||||
\(148\) | −14.2395 | + | 7.83879i | −1.17048 | + | 0.644345i | ||||
\(149\) | 2.92851 | − | 2.92851i | 0.239913 | − | 0.239913i | −0.576901 | − | 0.816814i | \(-0.695738\pi\) |
0.816814 | + | 0.576901i | \(0.195738\pi\) | |||||||
\(150\) | −3.07142 | + | 2.30746i | −0.250780 | + | 0.188403i | ||||
\(151\) | 10.4902i | 0.853682i | 0.904327 | + | 0.426841i | \(0.140374\pi\) | ||||
−0.904327 | + | 0.426841i | \(0.859626\pi\) | |||||||
\(152\) | −7.06256 | − | 18.6423i | −0.572849 | − | 1.51209i | ||||
\(153\) | 13.4621i | 1.08835i | ||||||||
\(154\) | 2.88904 | + | 3.84556i | 0.232806 | + | 0.309884i | ||||
\(155\) | −3.89612 | + | 3.89612i | −0.312944 | + | 0.312944i | ||||
\(156\) | 0.492149 | − | 1.69760i | 0.0394035 | − | 0.135917i | ||||
\(157\) | 11.3888 | + | 11.3888i | 0.908924 | + | 0.908924i | 0.996185 | − | 0.0872612i | \(-0.0278115\pi\) |
−0.0872612 | + | 0.996185i | \(0.527811\pi\) | |||||||
\(158\) | −11.3552 | − | 1.61278i | −0.903373 | − | 0.128306i | ||||
\(159\) | 35.6065 | 2.82378 | ||||||||
\(160\) | −5.63878 | + | 0.451874i | −0.445784 | + | 0.0357238i | ||||
\(161\) | −2.85562 | −0.225054 | ||||||||
\(162\) | −4.14650 | − | 0.588927i | −0.325780 | − | 0.0462705i | ||||
\(163\) | −6.58819 | − | 6.58819i | −0.516027 | − | 0.516027i | 0.400340 | − | 0.916367i | \(-0.368892\pi\) |
−0.916367 | + | 0.400340i | \(0.868892\pi\) | |||||||
\(164\) | −1.52434 | + | 5.25800i | −0.119031 | + | 0.410581i | ||||
\(165\) | 6.53284 | − | 6.53284i | 0.508581 | − | 0.508581i | ||||
\(166\) | 0.0178563 | + | 0.0237682i | 0.00138591 | + | 0.00184477i | ||||
\(167\) | − | 16.1238i | − | 1.24770i | −0.781544 | − | 0.623850i | \(-0.785568\pi\) | ||
0.781544 | − | 0.623850i | \(-0.214432\pi\) | |||||||
\(168\) | −7.18490 | + | 2.72197i | −0.554327 | + | 0.210005i | ||||
\(169\) | − | 12.8942i | − | 0.991858i | ||||||
\(170\) | −3.47601 | + | 2.61141i | −0.266598 | + | 0.200286i | ||||
\(171\) | −21.8240 | + | 21.8240i | −1.66893 | + | 1.66893i | ||||
\(172\) | −4.10785 | + | 2.26136i | −0.313221 | + | 0.172427i | ||||
\(173\) | −9.13304 | − | 9.13304i | −0.694372 | − | 0.694372i | 0.268818 | − | 0.963191i | \(-0.413367\pi\) |
−0.963191 | + | 0.268818i | \(0.913367\pi\) | |||||||
\(174\) | 2.32863 | − | 16.3954i | 0.176533 | − | 1.24293i | ||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 13.2734 | − | 2.98285i | 1.00052 | − | 0.224841i | ||||
\(177\) | −4.74648 | −0.356767 | ||||||||
\(178\) | −2.27918 | + | 16.0471i | −0.170832 | + | 1.20278i | ||||
\(179\) | −10.1552 | − | 10.1552i | −0.759035 | − | 0.759035i | 0.217112 | − | 0.976147i | \(-0.430336\pi\) |
−0.976147 | + | 0.217112i | \(0.930336\pi\) | |||||||
\(180\) | 4.22356 | + | 7.67226i | 0.314806 | + | 0.571857i | ||||
\(181\) | 9.05901 | − | 9.05901i | 0.673351 | − | 0.673351i | −0.285136 | − | 0.958487i | \(-0.592039\pi\) |
0.958487 | + | 0.285136i | \(0.0920388\pi\) | |||||||
\(182\) | 0.367851 | − | 0.276355i | 0.0272670 | − | 0.0204848i | ||||
\(183\) | 1.36282i | 0.100742i | ||||||||
\(184\) | −3.31746 | + | 7.36417i | −0.244567 | + | 0.542893i | ||||
\(185\) | 8.12725i | 0.597528i | ||||||||
\(186\) | 12.7140 | + | 16.9234i | 0.932233 | + | 1.24088i | ||||
\(187\) | 7.39340 | − | 7.39340i | 0.540659 | − | 0.540659i | ||||
\(188\) | −23.0727 | − | 6.68897i | −1.68275 | − | 0.487843i | ||||
\(189\) | 2.64876 | + | 2.64876i | 0.192669 | + | 0.192669i | ||||
\(190\) | −9.86858 | − | 1.40164i | −0.715942 | − | 0.101685i | ||||
\(191\) | 22.0651 | 1.59657 | 0.798286 | − | 0.602279i | \(-0.205741\pi\) | ||||
0.798286 | + | 0.602279i | \(0.205741\pi\) | |||||||
\(192\) | −1.32741 | + | 21.6909i | −0.0957975 | + | 1.56540i | ||||
\(193\) | 23.6088 | 1.69940 | 0.849700 | − | 0.527267i | \(-0.176783\pi\) | ||||
0.849700 | + | 0.527267i | \(0.176783\pi\) | |||||||
\(194\) | −10.6624 | − | 1.51438i | −0.765514 | − | 0.108726i | ||||
\(195\) | −0.624906 | − | 0.624906i | −0.0447505 | − | 0.0447505i | ||||
\(196\) | −1.92091 | − | 0.556887i | −0.137208 | − | 0.0397776i | ||||
\(197\) | −1.33955 | + | 1.33955i | −0.0954387 | + | 0.0954387i | −0.753214 | − | 0.657775i | \(-0.771498\pi\) |
0.657775 | + | 0.753214i | \(0.271498\pi\) | |||||||
\(198\) | −12.6511 | − | 16.8397i | −0.899073 | − | 1.19674i | ||||
\(199\) | − | 17.9500i | − | 1.27244i | −0.771508 | − | 0.636220i | \(-0.780497\pi\) | ||
0.771508 | − | 0.636220i | \(-0.219503\pi\) | |||||||
\(200\) | −1.16173 | + | 2.57883i | −0.0821469 | + | 0.182351i | ||||
\(201\) | − | 41.6719i | − | 2.93931i | ||||||
\(202\) | −9.76731 | + | 7.33786i | −0.687226 | + | 0.516290i | ||||
\(203\) | 3.04810 | − | 3.04810i | 0.213935 | − | 0.213935i | ||||
\(204\) | 8.05460 | + | 14.6315i | 0.563935 | + | 1.02441i | ||||
\(205\) | 1.93553 | + | 1.93553i | 0.135183 | + | 0.135183i | ||||
\(206\) | 1.86683 | − | 13.1439i | 0.130068 | − | 0.915781i | ||||
\(207\) | 12.5047 | 0.869138 | ||||||||
\(208\) | −0.285328 | − | 1.26968i | −0.0197839 | − | 0.0880363i | ||||
\(209\) | 23.9715 | 1.65814 | ||||||||
\(210\) | −0.540203 | + | 3.80344i | −0.0372775 | + | 0.262462i | ||||
\(211\) | −10.8590 | − | 10.8590i | −0.747567 | − | 0.747567i | 0.226455 | − | 0.974022i | \(-0.427286\pi\) |
−0.974022 | + | 0.226455i | \(0.927286\pi\) | |||||||
\(212\) | 22.9658 | − | 12.6426i | 1.57729 | − | 0.868297i | ||||
\(213\) | 2.75038 | − | 2.75038i | 0.188453 | − | 0.188453i | ||||
\(214\) | 6.49509 | − | 4.87955i | 0.443995 | − | 0.333559i | ||||
\(215\) | 2.34458i | 0.159899i | ||||||||
\(216\) | 9.90787 | − | 3.75356i | 0.674145 | − | 0.255398i | ||||
\(217\) | 5.50995i | 0.374040i | ||||||||
\(218\) | 13.9811 | + | 18.6100i | 0.946920 | + | 1.26043i | ||||
\(219\) | −22.1902 | + | 22.1902i | −1.49948 | + | 1.49948i | ||||
\(220\) | 1.89402 | − | 6.53319i | 0.127695 | − | 0.440467i | ||||
\(221\) | −0.707224 | − | 0.707224i | −0.0475731 | − | 0.0475731i | ||||
\(222\) | 30.9115 | + | 4.39037i | 2.07465 | + | 0.294662i | ||||
\(223\) | −1.51828 | −0.101671 | −0.0508357 | − | 0.998707i | \(-0.516188\pi\) | ||||
−0.0508357 | + | 0.998707i | \(0.516188\pi\) | |||||||
\(224\) | −3.66769 | + | 4.30674i | −0.245058 | + | 0.287756i | ||||
\(225\) | 4.37899 | 0.291932 | ||||||||
\(226\) | 20.1253 | + | 2.85839i | 1.33871 | + | 0.190138i | ||||
\(227\) | −6.58491 | − | 6.58491i | −0.437056 | − | 0.437056i | 0.453964 | − | 0.891020i | \(-0.350009\pi\) |
−0.891020 | + | 0.453964i | \(0.850009\pi\) | |||||||
\(228\) | −10.6621 | + | 36.7774i | −0.706113 | + | 2.43564i | ||||
\(229\) | −6.51956 | + | 6.51956i | −0.430825 | + | 0.430825i | −0.888909 | − | 0.458084i | \(-0.848536\pi\) |
0.458084 | + | 0.888909i | \(0.348536\pi\) | |||||||
\(230\) | 2.42569 | + | 3.22880i | 0.159945 | + | 0.212901i | ||||
\(231\) | − | 9.23884i | − | 0.607871i | ||||||
\(232\) | −4.31947 | − | 11.4016i | −0.283587 | − | 0.748553i | ||||
\(233\) | 18.0402i | 1.18185i | 0.806725 | + | 0.590927i | \(0.201238\pi\) | ||||
−0.806725 | + | 0.590927i | \(0.798762\pi\) | |||||||
\(234\) | −1.61082 | + | 1.21015i | −0.105302 | + | 0.0791102i | ||||
\(235\) | −8.49332 | + | 8.49332i | −0.554043 | + | 0.554043i | ||||
\(236\) | −3.06142 | + | 1.68531i | −0.199282 | + | 0.109704i | ||||
\(237\) | 15.5776 | + | 15.5776i | 1.01187 | + | 1.01187i | ||||
\(238\) | −0.611363 | + | 4.30446i | −0.0396288 | + | 0.279017i | ||||
\(239\) | −14.0959 | −0.911785 | −0.455892 | − | 0.890035i | \(-0.650680\pi\) | ||||
−0.455892 | + | 0.890035i | \(0.650680\pi\) | |||||||
\(240\) | 9.18086 | + | 5.81167i | 0.592622 | + | 0.375142i | ||||
\(241\) | 11.0900 | 0.714370 | 0.357185 | − | 0.934034i | \(-0.383737\pi\) | ||||
0.357185 | + | 0.934034i | \(0.383737\pi\) | |||||||
\(242\) | −0.112848 | + | 0.794536i | −0.00725414 | + | 0.0510747i | ||||
\(243\) | 13.6346 | + | 13.6346i | 0.874663 | + | 0.874663i | ||||
\(244\) | 0.483888 | + | 0.879001i | 0.0309778 | + | 0.0562723i | ||||
\(245\) | −0.707107 | + | 0.707107i | −0.0451754 | + | 0.0451754i | ||||
\(246\) | 8.40725 | − | 6.31609i | 0.536027 | − | 0.402699i | ||||
\(247\) | − | 2.29302i | − | 0.145901i | ||||||
\(248\) | 14.2092 | + | 6.40108i | 0.902287 | + | 0.406469i | ||||
\(249\) | − | 0.0571023i | − | 0.00361871i | ||||||
\(250\) | 0.849445 | + | 1.13068i | 0.0537236 | + | 0.0715106i | ||||
\(251\) | −6.24897 | + | 6.24897i | −0.394432 | + | 0.394432i | −0.876264 | − | 0.481832i | \(-0.839972\pi\) |
0.481832 | + | 0.876264i | \(0.339972\pi\) | |||||||
\(252\) | 8.41162 | + | 2.43860i | 0.529882 | + | 0.153617i | ||||
\(253\) | −6.86759 | − | 6.86759i | −0.431762 | − | 0.431762i | ||||
\(254\) | 22.8436 | + | 3.24448i | 1.43334 | + | 0.203577i | ||||
\(255\) | 8.35101 | 0.522960 | ||||||||
\(256\) | 6.84549 | + | 14.4617i | 0.427843 | + | 0.903853i | ||||
\(257\) | −16.6585 | −1.03913 | −0.519564 | − | 0.854431i | \(-0.673906\pi\) | ||||
−0.519564 | + | 0.854431i | \(0.673906\pi\) | |||||||
\(258\) | 8.91746 | + | 1.26655i | 0.555177 | + | 0.0788518i | ||||
\(259\) | 5.74684 | + | 5.74684i | 0.357091 | + | 0.357091i | ||||
\(260\) | −0.624939 | − | 0.181175i | −0.0387571 | − | 0.0112360i | ||||
\(261\) | −13.3476 | + | 13.3476i | −0.826195 | + | 0.826195i | ||||
\(262\) | −1.81752 | − | 2.41928i | −0.112287 | − | 0.149463i | ||||
\(263\) | 14.5446i | 0.896860i | 0.893818 | + | 0.448430i | \(0.148017\pi\) | ||||
−0.893818 | + | 0.448430i | \(0.851983\pi\) | |||||||
\(264\) | −23.8254 | − | 10.7331i | −1.46635 | − | 0.660574i | ||||
\(265\) | − | 13.1078i | − | 0.805208i | ||||||
\(266\) | −7.96925 | + | 5.98703i | −0.488626 | + | 0.367089i | ||||
\(267\) | 22.0142 | − | 22.0142i | 1.34725 | − | 1.34725i | ||||
\(268\) | −14.7962 | − | 26.8779i | −0.903823 | − | 1.64183i | ||||
\(269\) | −2.07516 | − | 2.07516i | −0.126525 | − | 0.126525i | 0.641009 | − | 0.767534i | \(-0.278516\pi\) |
−0.767534 | + | 0.641009i | \(0.778516\pi\) | |||||||
\(270\) | 0.744932 | − | 5.24489i | 0.0453351 | − | 0.319194i | ||||
\(271\) | −7.78531 | −0.472924 | −0.236462 | − | 0.971641i | \(-0.575988\pi\) | ||||
−0.236462 | + | 0.971641i | \(0.575988\pi\) | |||||||
\(272\) | 10.3902 | + | 6.57723i | 0.630001 | + | 0.398803i | ||||
\(273\) | −0.883751 | −0.0534871 | ||||||||
\(274\) | −1.00273 | + | 7.06000i | −0.0605772 | + | 0.426510i | ||||
\(275\) | −2.40494 | − | 2.40494i | −0.145023 | − | 0.145023i | ||||
\(276\) | 13.5909 | − | 7.48176i | 0.818077 | − | 0.450349i | ||||
\(277\) | −4.89400 | + | 4.89400i | −0.294052 | + | 0.294052i | −0.838679 | − | 0.544626i | \(-0.816671\pi\) |
0.544626 | + | 0.838679i | \(0.316671\pi\) | |||||||
\(278\) | 20.8194 | − | 15.6409i | 1.24866 | − | 0.938080i | ||||
\(279\) | − | 24.1280i | − | 1.44450i | ||||||
\(280\) | 1.00204 | + | 2.64498i | 0.0598834 | + | 0.158068i | ||||
\(281\) | 8.10490i | 0.483498i | 0.970339 | + | 0.241749i | \(0.0777210\pi\) | ||||
−0.970339 | + | 0.241749i | \(0.922279\pi\) | |||||||
\(282\) | 27.7157 | + | 36.8920i | 1.65045 | + | 2.19688i | ||||
\(283\) | 14.8117 | − | 14.8117i | 0.880467 | − | 0.880467i | −0.113115 | − | 0.993582i | \(-0.536083\pi\) |
0.993582 | + | 0.113115i | \(0.0360828\pi\) | |||||||
\(284\) | 0.797401 | − | 2.75053i | 0.0473170 | − | 0.163214i | ||||
\(285\) | 13.5382 | + | 13.5382i | 0.801932 | + | 0.801932i | ||||
\(286\) | 1.54928 | + | 0.220044i | 0.0916106 | + | 0.0130115i | ||||
\(287\) | 2.73725 | 0.161575 | ||||||||
\(288\) | 16.0608 | − | 18.8592i | 0.946391 | − | 1.11129i | ||||
\(289\) | −7.54893 | −0.444055 | ||||||||
\(290\) | −6.03563 | − | 0.857241i | −0.354424 | − | 0.0503389i | ||||
\(291\) | 14.6271 | + | 14.6271i | 0.857458 | + | 0.857458i | ||||
\(292\) | −6.43347 | + | 22.1914i | −0.376490 | + | 1.29865i | ||||
\(293\) | −5.07959 | + | 5.07959i | −0.296753 | + | 0.296753i | −0.839741 | − | 0.542988i | \(-0.817293\pi\) |
0.542988 | + | 0.839741i | \(0.317293\pi\) | |||||||
\(294\) | 2.30746 | + | 3.07142i | 0.134574 | + | 0.179129i | ||||
\(295\) | 1.74732i | 0.101733i | ||||||||
\(296\) | 21.4964 | − | 8.14384i | 1.24945 | − | 0.473351i | ||||
\(297\) | 12.7402i | 0.739263i | ||||||||
\(298\) | −4.68277 | + | 3.51801i | −0.271266 | + | 0.203793i | ||||
\(299\) | −0.656927 | + | 0.656927i | −0.0379911 | + | 0.0379911i | ||||
\(300\) | 4.75936 | − | 2.62001i | 0.274782 | − | 0.151267i | ||||
\(301\) | 1.65787 | + | 1.65787i | 0.0955578 | + | 0.0955578i | ||||
\(302\) | 2.08614 | − | 14.6880i | 0.120044 | − | 0.845200i | ||||
\(303\) | 23.4657 | 1.34807 | ||||||||
\(304\) | 6.18143 | + | 27.5067i | 0.354529 | + | 1.57762i | ||||
\(305\) | 0.501695 | 0.0287270 | ||||||||
\(306\) | 2.67715 | − | 18.8492i | 0.153042 | − | 1.07754i | ||||
\(307\) | −24.6662 | − | 24.6662i | −1.40778 | − | 1.40778i | −0.771275 | − | 0.636502i | \(-0.780381\pi\) |
−0.636502 | − | 0.771275i | \(-0.719619\pi\) | |||||||
\(308\) | −3.28038 | − | 5.95894i | −0.186917 | − | 0.339542i | ||||
\(309\) | −18.0314 | + | 18.0314i | −1.02577 | + | 1.02577i | ||||
\(310\) | 6.23000 | − | 4.68040i | 0.353840 | − | 0.265829i | ||||
\(311\) | 18.5460i | 1.05165i | 0.850594 | + | 0.525823i | \(0.176243\pi\) | ||||
−0.850594 | + | 0.525823i | \(0.823757\pi\) | |||||||
\(312\) | −1.02668 | + | 2.27905i | −0.0581244 | + | 0.129026i | ||||
\(313\) | − | 10.3997i | − | 0.587825i | −0.955832 | − | 0.293913i | \(-0.905043\pi\) | ||
0.955832 | − | 0.293913i | \(-0.0949575\pi\) | |||||||
\(314\) | −13.6813 | − | 18.2110i | −0.772081 | − | 1.02770i | ||||
\(315\) | 3.09641 | − | 3.09641i | 0.174463 | − | 0.174463i | ||||
\(316\) | 15.5784 | + | 4.51631i | 0.876354 | + | 0.254062i | ||||
\(317\) | −12.3716 | − | 12.3716i | −0.694857 | − | 0.694857i | 0.268439 | − | 0.963297i | \(-0.413492\pi\) |
−0.963297 | + | 0.268439i | \(0.913492\pi\) | |||||||
\(318\) | −49.8549 | − | 7.08089i | −2.79572 | − | 0.397077i | ||||
\(319\) | 14.6610 | 0.820858 | ||||||||
\(320\) | 7.98506 | + | 0.488660i | 0.446379 | + | 0.0273169i | ||||
\(321\) | −15.6042 | −0.870944 | ||||||||
\(322\) | 3.99833 | + | 0.567883i | 0.222818 | + | 0.0316469i | ||||
\(323\) | 15.3215 | + | 15.3215i | 0.852512 | + | 0.852512i | ||||
\(324\) | 5.68865 | + | 1.64919i | 0.316036 | + | 0.0916215i | ||||
\(325\) | −0.230047 | + | 0.230047i | −0.0127607 | + | 0.0127607i | ||||
\(326\) | 7.91437 | + | 10.5347i | 0.438336 | + | 0.583462i | ||||
\(327\) | − | 44.7100i | − | 2.47247i | ||||||
\(328\) | 3.17995 | − | 7.05892i | 0.175584 | − | 0.389763i | ||||
\(329\) | 12.0114i | 0.662208i | ||||||||
\(330\) | −10.4462 | + | 7.84788i | −0.575044 | + | 0.432012i | ||||
\(331\) | −17.6765 | + | 17.6765i | −0.971590 | + | 0.971590i | −0.999607 | − | 0.0280173i | \(-0.991081\pi\) |
0.0280173 | + | 0.999607i | \(0.491081\pi\) | |||||||
\(332\) | −0.0202750 | − | 0.0368303i | −0.00111273 | − | 0.00202132i | ||||
\(333\) | −25.1653 | − | 25.1653i | −1.37905 | − | 1.37905i | ||||
\(334\) | −3.20647 | + | 22.5760i | −0.175450 | + | 1.23530i | ||||
\(335\) | −15.3407 | −0.838152 | ||||||||
\(336\) | 10.6013 | − | 2.38238i | 0.578350 | − | 0.129969i | ||||
\(337\) | 18.6279 | 1.01473 | 0.507364 | − | 0.861732i | \(-0.330620\pi\) | ||||
0.507364 | + | 0.861732i | \(0.330620\pi\) | |||||||
\(338\) | −2.56420 | + | 18.0539i | −0.139474 | + | 0.982003i | ||||
\(339\) | −27.6088 | − | 27.6088i | −1.49950 | − | 1.49950i | ||||
\(340\) | 5.38630 | − | 2.96514i | 0.292113 | − | 0.160808i | ||||
\(341\) | −13.2511 | + | 13.2511i | −0.717587 | + | 0.717587i | ||||
\(342\) | 34.8972 | − | 26.2171i | 1.88703 | − | 1.41766i | ||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 6.20136 | − | 2.34936i | 0.334355 | − | 0.126669i | ||||
\(345\) | − | 7.75709i | − | 0.417628i | ||||||
\(346\) | 10.9715 | + | 14.6040i | 0.589831 | + | 0.785115i | ||||
\(347\) | 7.00942 | − | 7.00942i | 0.376286 | − | 0.376286i | −0.493475 | − | 0.869760i | \(-0.664273\pi\) |
0.869760 | + | 0.493475i | \(0.164273\pi\) | |||||||
\(348\) | −6.52093 | + | 22.4931i | −0.349559 | + | 1.20576i | ||||
\(349\) | 21.6394 | + | 21.6394i | 1.15833 | + | 1.15833i | 0.984835 | + | 0.173495i | \(0.0555061\pi\) |
0.173495 | + | 0.984835i | \(0.444494\pi\) | |||||||
\(350\) | 1.40016 | + | 0.198865i | 0.0748418 | + | 0.0106298i | ||||
\(351\) | 1.21868 | 0.0650483 | ||||||||
\(352\) | −19.1780 | + | 1.53687i | −1.02219 | + | 0.0819153i | ||||
\(353\) | 29.6199 | 1.57651 | 0.788253 | − | 0.615351i | \(-0.210986\pi\) | ||||
0.788253 | + | 0.615351i | \(0.210986\pi\) | |||||||
\(354\) | 6.64584 | + | 0.943910i | 0.353223 | + | 0.0501682i | ||||
\(355\) | −1.01250 | − | 1.01250i | −0.0537379 | − | 0.0537379i | ||||
\(356\) | 6.38243 | − | 22.0153i | 0.338268 | − | 1.16681i | ||||
\(357\) | 5.90505 | − | 5.90505i | 0.312529 | − | 0.312529i | ||||
\(358\) | 12.1994 | + | 16.2384i | 0.644758 | + | 0.858227i | ||||
\(359\) | 25.4894i | 1.34528i | 0.739971 | + | 0.672638i | \(0.234839\pi\) | ||||
−0.739971 | + | 0.672638i | \(0.765161\pi\) | |||||||
\(360\) | −4.38793 | − | 11.5823i | −0.231264 | − | 0.610442i | ||||
\(361\) | 30.6767i | 1.61456i | ||||||||
\(362\) | −14.4856 | + | 10.8826i | −0.761346 | + | 0.571975i | ||||
\(363\) | 1.08998 | − | 1.08998i | 0.0572091 | − | 0.0572091i | ||||
\(364\) | −0.570009 | + | 0.313789i | −0.0298766 | + | 0.0164470i | ||||
\(365\) | 8.16890 | + | 8.16890i | 0.427580 | + | 0.427580i | ||||
\(366\) | 0.271017 | − | 1.90817i | 0.0141663 | − | 0.0997414i | ||||
\(367\) | 25.4780 | 1.32994 | 0.664970 | − | 0.746870i | \(-0.268444\pi\) | ||||
0.664970 | + | 0.746870i | \(0.268444\pi\) | |||||||
\(368\) | 6.10946 | − | 9.65129i | 0.318478 | − | 0.503108i | ||||
\(369\) | −11.9864 | −0.623987 | ||||||||
\(370\) | 1.61623 | − | 11.3795i | 0.0840236 | − | 0.591590i | ||||
\(371\) | −9.26864 | − | 9.26864i | −0.481204 | − | 0.481204i | ||||
\(372\) | −14.4361 | − | 26.2238i | −0.748479 | − | 1.35964i | ||||
\(373\) | −9.10570 | + | 9.10570i | −0.471475 | + | 0.471475i | −0.902392 | − | 0.430917i | \(-0.858190\pi\) |
0.430917 | + | 0.902392i | \(0.358190\pi\) | |||||||
\(374\) | −11.8223 | + | 8.88167i | −0.611314 | + | 0.459260i | ||||
\(375\) | − | 2.71643i | − | 0.140276i | ||||||
\(376\) | 30.9753 | + | 13.9540i | 1.59743 | + | 0.719622i | ||||
\(377\) | − | 1.40241i | − | 0.0722280i | ||||||
\(378\) | −3.18195 | − | 4.23544i | −0.163662 | − | 0.217848i | ||||
\(379\) | −9.54063 | + | 9.54063i | −0.490069 | + | 0.490069i | −0.908328 | − | 0.418259i | \(-0.862641\pi\) |
0.418259 | + | 0.908328i | \(0.362641\pi\) | |||||||
\(380\) | 13.5389 | + | 3.92503i | 0.694529 | + | 0.201350i | ||||
\(381\) | −31.3379 | − | 31.3379i | −1.60549 | − | 1.60549i | ||||
\(382\) | −30.8946 | − | 4.38797i | −1.58071 | − | 0.224508i | ||||
\(383\) | −2.95979 | −0.151238 | −0.0756191 | − | 0.997137i | \(-0.524093\pi\) | ||||
−0.0756191 | + | 0.997137i | \(0.524093\pi\) | |||||||
\(384\) | 6.17214 | − | 30.1067i | 0.314971 | − | 1.53638i | ||||
\(385\) | −3.40110 | −0.173336 | ||||||||
\(386\) | −33.0562 | − | 4.69497i | −1.68251 | − | 0.238968i | ||||
\(387\) | −7.25977 | − | 7.25977i | −0.369035 | − | 0.369035i | ||||
\(388\) | 14.6279 | + | 4.24075i | 0.742619 | + | 0.215291i | ||||
\(389\) | −17.7128 | + | 17.7128i | −0.898077 | + | 0.898077i | −0.995266 | − | 0.0971889i | \(-0.969015\pi\) |
0.0971889 | + | 0.995266i | \(0.469015\pi\) | |||||||
\(390\) | 0.750698 | + | 0.999242i | 0.0380131 | + | 0.0505986i | ||||
\(391\) | − | 8.77891i | − | 0.443969i | ||||||
\(392\) | 2.57883 | + | 1.16173i | 0.130251 | + | 0.0586763i | ||||
\(393\) | 5.81224i | 0.293189i | ||||||||
\(394\) | 2.14197 | − | 1.60919i | 0.107911 | − | 0.0810699i | ||||
\(395\) | 5.73459 | − | 5.73459i | 0.288538 | − | 0.288538i | ||||
\(396\) | 14.3647 | + | 26.0941i | 0.721856 | + | 1.31128i | ||||
\(397\) | −3.14511 | − | 3.14511i | −0.157849 | − | 0.157849i | 0.623764 | − | 0.781613i | \(-0.285603\pi\) |
−0.781613 | + | 0.623764i | \(0.785603\pi\) | |||||||
\(398\) | −3.56962 | + | 25.1329i | −0.178929 | + | 1.25980i | ||||
\(399\) | 19.1459 | 0.958492 | ||||||||
\(400\) | 2.13945 | − | 3.37975i | 0.106973 | − | 0.168988i | ||||
\(401\) | −23.9530 | −1.19616 | −0.598078 | − | 0.801438i | \(-0.704069\pi\) | ||||
−0.598078 | + | 0.801438i | \(0.704069\pi\) | |||||||
\(402\) | −8.28709 | + | 58.3474i | −0.413323 | + | 2.91011i | ||||
\(403\) | 1.26755 | + | 1.26755i | 0.0631410 | + | 0.0631410i | ||||
\(404\) | 15.1351 | − | 8.33182i | 0.752997 | − | 0.414523i | ||||
\(405\) | 2.09406 | − | 2.09406i | 0.104054 | − | 0.104054i | ||||
\(406\) | −4.87400 | + | 3.66167i | −0.241892 | + | 0.181726i | ||||
\(407\) | 27.6416i | 1.37014i | ||||||||
\(408\) | −8.36805 | − | 22.0882i | −0.414280 | − | 1.09353i | ||||
\(409\) | − | 5.26405i | − | 0.260291i | −0.991495 | − | 0.130145i | \(-0.958456\pi\) | ||
0.991495 | − | 0.130145i | \(-0.0415444\pi\) | |||||||
\(410\) | −2.32515 | − | 3.09496i | −0.114831 | − | 0.152849i | ||||
\(411\) | 9.68522 | − | 9.68522i | 0.477737 | − | 0.477737i | ||||
\(412\) | −5.22774 | + | 18.0324i | −0.257552 | + | 0.888392i | ||||
\(413\) | 1.23554 | + | 1.23554i | 0.0607972 | + | 0.0607972i | ||||
\(414\) | −17.5086 | − | 2.48675i | −0.860502 | − | 0.122217i | ||||
\(415\) | −0.0210211 | −0.00103188 | ||||||||
\(416\) | 0.147011 | + | 1.83450i | 0.00720779 | + | 0.0899435i | ||||
\(417\) | −50.0179 | −2.44939 | ||||||||
\(418\) | −33.5640 | − | 4.76710i | −1.64167 | − | 0.233166i | ||||
\(419\) | −5.40200 | − | 5.40200i | −0.263905 | − | 0.263905i | 0.562733 | − | 0.826638i | \(-0.309750\pi\) |
−0.826638 | + | 0.562733i | \(0.809750\pi\) | |||||||
\(420\) | 1.51274 | − | 5.21800i | 0.0738143 | − | 0.254612i | ||||
\(421\) | −14.2595 | + | 14.2595i | −0.694963 | + | 0.694963i | −0.963320 | − | 0.268357i | \(-0.913519\pi\) |
0.268357 | + | 0.963320i | \(0.413519\pi\) | |||||||
\(422\) | 13.0449 | + | 17.3639i | 0.635017 | + | 0.845261i | ||||
\(423\) | − | 52.5976i | − | 2.55738i | ||||||
\(424\) | −34.6699 | + | 13.1346i | −1.68372 | + | 0.637872i | ||||
\(425\) | − | 3.07426i | − | 0.149123i | ||||||
\(426\) | −4.39794 | + | 3.30403i | −0.213081 | + | 0.160081i | ||||
\(427\) | 0.354752 | − | 0.354752i | 0.0171676 | − | 0.0171676i | ||||
\(428\) | −10.0645 | + | 5.54051i | −0.486488 | + | 0.267811i | ||||
\(429\) | −2.12537 | − | 2.12537i | −0.102614 | − | 0.102614i | ||||
\(430\) | 0.466255 | − | 3.28279i | 0.0224848 | − | 0.158310i | ||||
\(431\) | −5.88265 | −0.283357 | −0.141679 | − | 0.989913i | \(-0.545250\pi\) | ||||
−0.141679 | + | 0.989913i | \(0.545250\pi\) | |||||||
\(432\) | −14.6191 | + | 3.28527i | −0.703360 | + | 0.158062i | ||||
\(433\) | 34.1231 | 1.63985 | 0.819925 | − | 0.572471i | \(-0.194015\pi\) | ||||
0.819925 | + | 0.572471i | \(0.194015\pi\) | |||||||
\(434\) | 1.09574 | − | 7.71482i | 0.0525970 | − | 0.370323i | ||||
\(435\) | 8.27995 | + | 8.27995i | 0.396993 | + | 0.396993i | ||||
\(436\) | −15.8749 | − | 28.8374i | −0.760271 | − | 1.38106i | ||||
\(437\) | 14.2319 | − | 14.2319i | 0.680802 | − | 0.680802i | ||||
\(438\) | 35.4828 | − | 26.6571i | 1.69543 | − | 1.27372i | ||||
\(439\) | − | 30.0006i | − | 1.43185i | −0.698176 | − | 0.715926i | \(-0.746005\pi\) | ||
0.698176 | − | 0.715926i | \(-0.253995\pi\) | |||||||
\(440\) | −3.95116 | + | 8.77086i | −0.188364 | + | 0.418134i | ||||
\(441\) | − | 4.37899i | − | 0.208523i | ||||||
\(442\) | 0.849586 | + | 1.13087i | 0.0404107 | + | 0.0537900i | ||||
\(443\) | 21.0503 | − | 21.0503i | 1.00013 | − | 1.00013i | 0.000131473 | − | 1.00000i | \(-0.499958\pi\) |
1.00000 | 0.000131473i | \(-4.18492e-5\pi\) | ||||||||
\(444\) | −42.4080 | − | 12.2944i | −2.01260 | − | 0.583468i | ||||
\(445\) | −8.10410 | − | 8.10410i | −0.384171 | − | 0.384171i | ||||
\(446\) | 2.12583 | + | 0.301932i | 0.100661 | + | 0.0142969i | ||||
\(447\) | 11.2502 | 0.532116 | ||||||||
\(448\) | 5.99183 | − | 5.30076i | 0.283087 | − | 0.250437i | ||||
\(449\) | −13.0169 | −0.614305 | −0.307153 | − | 0.951660i | \(-0.599376\pi\) | ||||
−0.307153 | + | 0.951660i | \(0.599376\pi\) | |||||||
\(450\) | −6.13129 | − | 0.870827i | −0.289032 | − | 0.0410512i | ||||
\(451\) | 6.58293 | + | 6.58293i | 0.309978 | + | 0.309978i | ||||
\(452\) | −27.6102 | − | 8.00443i | −1.29867 | − | 0.376497i | ||||
\(453\) | −20.1497 | + | 20.1497i | −0.946715 | + | 0.946715i | ||||
\(454\) | 7.91042 | + | 10.5294i | 0.371255 | + | 0.494171i | ||||
\(455\) | 0.325336i | 0.0152520i | ||||||||
\(456\) | 22.2424 | − | 49.3740i | 1.04159 | − | 2.31215i | ||||
\(457\) | 27.5356i | 1.28806i | 0.764999 | + | 0.644031i | \(0.222739\pi\) | ||||
−0.764999 | + | 0.644031i | \(0.777261\pi\) | |||||||
\(458\) | 10.4250 | − | 7.83193i | 0.487126 | − | 0.365962i | ||||
\(459\) | −8.14298 | + | 8.14298i | −0.380082 | + | 0.380082i | ||||
\(460\) | −2.75426 | − | 5.00323i | −0.128418 | − | 0.233277i | ||||
\(461\) | −3.02388 | − | 3.02388i | −0.140836 | − | 0.140836i | 0.633174 | − | 0.774010i | \(-0.281752\pi\) |
−0.774010 | + | 0.633174i | \(0.781752\pi\) | |||||||
\(462\) | −1.83728 | + | 12.9359i | −0.0854781 | + | 0.601831i | ||||
\(463\) | −29.8214 | −1.38592 | −0.692958 | − | 0.720978i | \(-0.743693\pi\) | ||||
−0.692958 | + | 0.720978i | \(0.743693\pi\) | |||||||
\(464\) | 3.78057 | + | 16.8231i | 0.175508 | + | 0.780993i | ||||
\(465\) | −14.9674 | −0.694096 | ||||||||
\(466\) | 3.58757 | − | 25.2592i | 0.166191 | − | 1.17011i | ||||
\(467\) | −20.0298 | − | 20.0298i | −0.926870 | − | 0.926870i | 0.0706323 | − | 0.997502i | \(-0.477498\pi\) |
−0.997502 | + | 0.0706323i | \(0.977498\pi\) | |||||||
\(468\) | 2.49606 | − | 1.37408i | 0.115380 | − | 0.0635167i | ||||
\(469\) | −10.8475 | + | 10.8475i | −0.500892 | + | 0.500892i | ||||
\(470\) | 13.5811 | − | 10.2030i | 0.626447 | − | 0.470629i | ||||
\(471\) | 43.7513i | 2.01595i | ||||||||
\(472\) | 4.62164 | − | 1.75089i | 0.212728 | − | 0.0805913i | ||||
\(473\) | 7.97414i | 0.366651i | ||||||||
\(474\) | −18.7133 | − | 24.9090i | −0.859531 | − | 1.14411i | ||||
\(475\) | 4.98381 | − | 4.98381i | 0.228673 | − | 0.228673i | ||||
\(476\) | 1.71201 | − | 5.90536i | 0.0784700 | − | 0.270672i | ||||
\(477\) | 40.5872 | + | 40.5872i | 1.85836 | + | 1.85836i | ||||
\(478\) | 19.7365 | + | 2.80317i | 0.902725 | + | 0.128214i | ||||
\(479\) | 27.6154 | 1.26178 | 0.630889 | − | 0.775873i | \(-0.282690\pi\) | ||||
0.630889 | + | 0.775873i | \(0.282690\pi\) | |||||||
\(480\) | −11.6990 | − | 9.96303i | −0.533982 | − | 0.454748i | ||||
\(481\) | 2.64409 | 0.120560 | ||||||||
\(482\) | −15.5278 | − | 2.20541i | −0.707272 | − | 0.100454i | ||||
\(483\) | −5.48509 | − | 5.48509i | −0.249580 | − | 0.249580i | ||||
\(484\) | 0.316011 | − | 1.09004i | 0.0143641 | − | 0.0495471i | ||||
\(485\) | 5.38469 | − | 5.38469i | 0.244506 | − | 0.244506i | ||||
\(486\) | −16.3792 | − | 21.8022i | −0.742978 | − | 0.988966i | ||||
\(487\) | 26.5614i | 1.20361i | 0.798642 | + | 0.601807i | \(0.205552\pi\) | ||||
−0.798642 | + | 0.601807i | \(0.794448\pi\) | |||||||
\(488\) | −0.502719 | − | 1.32697i | −0.0227570 | − | 0.0600692i | ||||
\(489\) | − | 25.3092i | − | 1.14452i | ||||||
\(490\) | 1.13068 | − | 0.849445i | 0.0510790 | − | 0.0383740i | ||||
\(491\) | −1.69651 | + | 1.69651i | −0.0765626 | + | 0.0765626i | −0.744351 | − | 0.667789i | \(-0.767241\pi\) |
0.667789 | + | 0.744351i | \(0.267241\pi\) | |||||||
\(492\) | −13.0276 | + | 7.17164i | −0.587328 | + | 0.323323i | ||||
\(493\) | 9.37066 | + | 9.37066i | 0.422033 | + | 0.422033i | ||||
\(494\) | −0.456002 | + | 3.21060i | −0.0205165 | + | 0.144452i | ||||
\(495\) | 14.8934 | 0.669406 | ||||||||
\(496\) | −18.6223 | − | 11.7883i | −0.836165 | − | 0.529309i | ||||
\(497\) | −1.43189 | −0.0642291 | ||||||||
\(498\) | −0.0113557 | + | 0.0799524i | −0.000508859 | + | 0.00358275i | ||||
\(499\) | −18.0448 | − | 18.0448i | −0.807795 | − | 0.807795i | 0.176505 | − | 0.984300i | \(-0.443521\pi\) |
−0.984300 | + | 0.176505i | \(0.943521\pi\) | |||||||
\(500\) | −0.964507 | − | 1.75206i | −0.0431341 | − | 0.0783547i | ||||
\(501\) | 30.9707 | − | 30.9707i | 1.38367 | − | 1.38367i | ||||
\(502\) | 9.99227 | − | 7.50687i | 0.445977 | − | 0.335048i | ||||
\(503\) | 28.8592i | 1.28677i | 0.765544 | + | 0.643383i | \(0.222470\pi\) | ||||
−0.765544 | + | 0.643383i | \(0.777530\pi\) | |||||||
\(504\) | −11.2927 | − | 5.08721i | −0.503016 | − | 0.226602i | ||||
\(505\) | − | 8.63842i | − | 0.384405i | ||||||
\(506\) | 8.25001 | + | 10.9815i | 0.366758 | + | 0.488185i | ||||
\(507\) | 24.7672 | − | 24.7672i | 1.09995 | − | 1.09995i | ||||
\(508\) | −31.3395 | − | 9.08559i | −1.39047 | − | 0.403108i | ||||
\(509\) | 12.7993 | + | 12.7993i | 0.567318 | + | 0.567318i | 0.931376 | − | 0.364058i | \(-0.118609\pi\) |
−0.364058 | + | 0.931376i | \(0.618609\pi\) | |||||||
\(510\) | −11.6928 | − | 1.66072i | −0.517764 | − | 0.0735381i | ||||
\(511\) | 11.5526 | 0.511056 | ||||||||
\(512\) | −6.70887 | − | 21.6100i | −0.296493 | − | 0.955035i | ||||
\(513\) | −26.4019 | −1.16567 | ||||||||
\(514\) | 23.3246 | + | 3.31279i | 1.02880 | + | 0.146121i | ||||
\(515\) | 6.63792 | + | 6.63792i | 0.292502 | + | 0.292502i | ||||
\(516\) | −12.2340 | − | 3.54674i | −0.538572 | − | 0.156137i | ||||
\(517\) | −28.8866 | + | 28.8866i | −1.27043 | + | 1.27043i | ||||
\(518\) | −6.90365 | − | 9.18934i | −0.303329 | − | 0.403757i | ||||
\(519\) | − | 35.0856i | − | 1.54009i | ||||||
\(520\) | 0.838986 | + | 0.377953i | 0.0367920 | + | 0.0165743i | ||||
\(521\) | 35.5497i | 1.55746i | 0.627358 | + | 0.778731i | \(0.284136\pi\) | ||||
−0.627358 | + | 0.778731i | \(0.715864\pi\) | |||||||
\(522\) | 21.3432 | − | 16.0344i | 0.934165 | − | 0.701807i | ||||
\(523\) | 2.94875 | − | 2.94875i | 0.128940 | − | 0.128940i | −0.639692 | − | 0.768632i | \(-0.720938\pi\) |
0.768632 | + | 0.639692i | \(0.220938\pi\) | |||||||
\(524\) | 2.06372 | + | 3.74882i | 0.0901539 | + | 0.163768i | ||||
\(525\) | −1.92081 | − | 1.92081i | −0.0838308 | − | 0.0838308i | ||||
\(526\) | 2.89242 | − | 20.3648i | 0.126115 | − | 0.887949i | ||||
\(527\) | −16.9390 | −0.737875 | ||||||||
\(528\) | 31.2250 | + | 19.7661i | 1.35889 | + | 0.860207i | ||||
\(529\) | 14.8454 | 0.645454 | ||||||||
\(530\) | −2.60669 | + | 18.3531i | −0.113227 | + | 0.797207i | ||||
\(531\) | −5.41043 | − | 5.41043i | −0.234793 | − | 0.234793i | ||||
\(532\) | 12.3488 | − | 6.79801i | 0.535390 | − | 0.294731i | ||||
\(533\) | 0.629697 | − | 0.629697i | 0.0272752 | − | 0.0272752i | ||||
\(534\) | −35.2013 | + | 26.4456i | −1.52331 | + | 1.14441i | ||||
\(535\) | 5.74439i | 0.248352i | ||||||||
\(536\) | 15.3720 | + | 40.5758i | 0.663970 | + | 1.75261i | ||||
\(537\) | − | 39.0123i | − | 1.68350i | ||||||
\(538\) | 2.49288 | + | 3.31824i | 0.107476 | + | 0.143059i | ||||
\(539\) | −2.40494 | + | 2.40494i | −0.103588 | + | 0.103588i | ||||
\(540\) | −2.08605 | + | 7.19555i | −0.0897693 | + | 0.309647i | ||||
\(541\) | −0.870655 | − | 0.870655i | −0.0374324 | − | 0.0374324i | 0.688143 | − | 0.725575i | \(-0.258426\pi\) |
−0.725575 | + | 0.688143i | \(0.758426\pi\) | |||||||
\(542\) | 10.9007 | + | 1.54823i | 0.468225 | + | 0.0665021i | ||||
\(543\) | 34.8012 | 1.49346 | ||||||||
\(544\) | −13.2400 | − | 11.2754i | −0.567662 | − | 0.483431i | ||||
\(545\) | −16.4591 | −0.705030 | ||||||||
\(546\) | 1.23739 | + | 0.175747i | 0.0529556 | + | 0.00752129i | ||||
\(547\) | 27.4186 | + | 27.4186i | 1.17233 | + | 1.17233i | 0.981652 | + | 0.190681i | \(0.0610695\pi\) |
0.190681 | + | 0.981652i | \(0.438930\pi\) | |||||||
\(548\) | 2.80797 | − | 9.68573i | 0.119951 | − | 0.413754i | ||||
\(549\) | −1.55345 | + | 1.55345i | −0.0662998 | + | 0.0662998i | ||||
\(550\) | 2.88904 | + | 3.84556i | 0.123189 | + | 0.163975i | ||||
\(551\) | 30.3823i | 1.29433i | ||||||||
\(552\) | −20.5173 | + | 7.77292i | −0.873276 | + | 0.330838i | ||||
\(553\) | − | 8.10993i | − | 0.344869i | ||||||
\(554\) | 7.82564 | − | 5.87915i | 0.332480 | − | 0.249781i | ||||
\(555\) | −15.6109 | + | 15.6109i | −0.662645 | + | 0.662645i | ||||
\(556\) | −32.2609 | + | 17.7596i | −1.36817 | + | 0.753174i | ||||
\(557\) | 9.50051 | + | 9.50051i | 0.402550 | + | 0.402550i | 0.879131 | − | 0.476581i | \(-0.158124\pi\) |
−0.476581 | + | 0.879131i | \(0.658124\pi\) | |||||||
\(558\) | −4.79821 | + | 33.7831i | −0.203125 | + | 1.43015i | ||||
\(559\) | 0.762775 | 0.0322619 | ||||||||
\(560\) | −0.877026 | − | 3.90267i | −0.0370611 | − | 0.164918i | ||||
\(561\) | 28.4026 | 1.19916 | ||||||||
\(562\) | 1.61178 | − | 11.3482i | 0.0679889 | − | 0.478694i | ||||
\(563\) | −23.3659 | − | 23.3659i | −0.984754 | − | 0.984754i | 0.0151319 | − | 0.999886i | \(-0.495183\pi\) |
−0.999886 | + | 0.0151319i | \(0.995183\pi\) | |||||||
\(564\) | −31.4700 | − | 57.1664i | −1.32512 | − | 2.40714i | ||||
\(565\) | −10.1636 | + | 10.1636i | −0.427587 | + | 0.427587i | ||||
\(566\) | −23.6844 | + | 17.7933i | −0.995529 | + | 0.747908i | ||||
\(567\) | − | 2.96144i | − | 0.124369i | ||||||
\(568\) | −1.66347 | + | 3.69261i | −0.0697978 | + | 0.154938i | ||||
\(569\) | 3.93387i | 0.164917i | 0.996595 | + | 0.0824583i | \(0.0262771\pi\) | ||||
−0.996595 | + | 0.0824583i | \(0.973723\pi\) | |||||||
\(570\) | −16.2634 | − | 21.6479i | −0.681197 | − | 0.906730i | ||||
\(571\) | 13.0268 | − | 13.0268i | 0.545157 | − | 0.545157i | −0.379879 | − | 0.925036i | \(-0.624035\pi\) |
0.925036 | + | 0.379879i | \(0.124035\pi\) | |||||||
\(572\) | −2.12548 | − | 0.616194i | −0.0888707 | − | 0.0257644i | ||||
\(573\) | 42.3827 | + | 42.3827i | 1.77056 | + | 1.77056i | ||||
\(574\) | −3.83260 | − | 0.544344i | −0.159969 | − | 0.0227205i | ||||
\(575\) | −2.85562 | −0.119088 | ||||||||
\(576\) | −26.2381 | + | 23.2119i | −1.09325 | + | 0.967164i | ||||
\(577\) | 18.7292 | 0.779709 | 0.389854 | − | 0.920877i | \(-0.372525\pi\) | ||||
0.389854 | + | 0.920877i | \(0.372525\pi\) | |||||||
\(578\) | 10.5697 | + | 1.50122i | 0.439643 | + | 0.0624425i | ||||
\(579\) | 45.3479 | + | 45.3479i | 1.88460 | + | 1.88460i | ||||
\(580\) | 8.28038 | + | 2.40055i | 0.343824 | + | 0.0996775i | ||||
\(581\) | −0.0148642 | + | 0.0148642i | −0.000616669 | + | 0.000616669i | ||||
\(582\) | −17.5715 | − | 23.3892i | −0.728363 | − | 0.969513i | ||||
\(583\) | − | 44.5810i | − | 1.84636i | ||||||
\(584\) | 13.4210 | − | 29.7921i | 0.555365 | − | 1.23281i | ||||
\(585\) | − | 1.42464i | − | 0.0589016i | ||||||
\(586\) | 8.12240 | − | 6.10209i | 0.335533 | − | 0.252075i | ||||
\(587\) | −2.58925 | + | 2.58925i | −0.106870 | + | 0.106870i | −0.758520 | − | 0.651650i | \(-0.774077\pi\) |
0.651650 | + | 0.758520i | \(0.274077\pi\) | |||||||
\(588\) | −2.62001 | − | 4.75936i | −0.108048 | − | 0.196273i | ||||
\(589\) | −27.4605 | − | 27.4605i | −1.13149 | − | 1.13149i | ||||
\(590\) | 0.347482 | − | 2.44654i | 0.0143056 | − | 0.100722i | ||||
\(591\) | −5.14601 | −0.211679 | ||||||||
\(592\) | −31.7180 | + | 7.12781i | −1.30360 | + | 0.292951i | ||||
\(593\) | 35.5707 | 1.46072 | 0.730358 | − | 0.683065i | \(-0.239353\pi\) | ||||
0.730358 | + | 0.683065i | \(0.239353\pi\) | |||||||
\(594\) | 2.53359 | − | 17.8384i | 0.103954 | − | 0.731917i | ||||
\(595\) | −2.17383 | − | 2.17383i | −0.0891183 | − | 0.0891183i | ||||
\(596\) | 7.25624 | − | 3.99455i | 0.297227 | − | 0.163623i | ||||
\(597\) | 34.4784 | − | 34.4784i | 1.41111 | − | 1.41111i | ||||
\(598\) | 1.05044 | − | 0.789164i | 0.0429558 | − | 0.0322713i | ||||
\(599\) | − | 16.7637i | − | 0.684945i | −0.939528 | − | 0.342473i | \(-0.888736\pi\) | ||
0.939528 | − | 0.342473i | \(-0.111264\pi\) | |||||||
\(600\) | −7.18490 | + | 2.72197i | −0.293322 | + | 0.111124i | ||||
\(601\) | 31.5684i | 1.28770i | 0.765151 | + | 0.643850i | \(0.222664\pi\) | ||||
−0.765151 | + | 0.643850i | \(0.777336\pi\) | |||||||
\(602\) | −1.99159 | − | 2.65097i | −0.0811711 | − | 0.108046i | ||||
\(603\) | 47.5011 | − | 47.5011i | 1.93440 | − | 1.93440i | ||||
\(604\) | −5.84187 | + | 20.1507i | −0.237702 | + | 0.819922i | ||||
\(605\) | −0.401255 | − | 0.401255i | −0.0163133 | − | 0.0163133i | ||||
\(606\) | −32.8557 | − | 4.66650i | −1.33467 | − | 0.189564i | ||||
\(607\) | −5.46877 | −0.221970 | −0.110985 | − | 0.993822i | \(-0.535401\pi\) | ||||
−0.110985 | + | 0.993822i | \(0.535401\pi\) | |||||||
\(608\) | −3.18488 | − | 39.7431i | −0.129164 | − | 1.61179i | ||||
\(609\) | 11.7096 | 0.474498 | ||||||||
\(610\) | −0.702454 | − | 0.0997696i | −0.0284415 | − | 0.00403955i | ||||
\(611\) | 2.76318 | + | 2.76318i | 0.111786 | + | 0.111786i | ||||
\(612\) | −7.49688 | + | 25.8595i | −0.303044 | + | 1.04531i | ||||
\(613\) | 26.1963 | − | 26.1963i | 1.05806 | − | 1.05806i | 0.0598509 | − | 0.998207i | \(-0.480937\pi\) |
0.998207 | − | 0.0598509i | \(-0.0190625\pi\) | |||||||
\(614\) | 29.6315 | + | 39.4420i | 1.19583 | + | 1.59175i | ||||
\(615\) | 7.43555i | 0.299830i | ||||||||
\(616\) | 3.40804 | + | 8.99583i | 0.137314 | + | 0.362452i | ||||
\(617\) | 26.9821i | 1.08626i | 0.839649 | + | 0.543129i | \(0.182761\pi\) | ||||
−0.839649 | + | 0.543129i | \(0.817239\pi\) | |||||||
\(618\) | 28.8328 | − | 21.6611i | 1.15982 | − | 0.871338i | ||||
\(619\) | 27.0870 | − | 27.0870i | 1.08872 | − | 1.08872i | 0.0930566 | − | 0.995661i | \(-0.470336\pi\) |
0.995661 | − | 0.0930566i | \(-0.0296637\pi\) | |||||||
\(620\) | −9.65378 | + | 5.31438i | −0.387705 | + | 0.213431i | ||||
\(621\) | 7.56386 | + | 7.56386i | 0.303527 | + | 0.303527i | ||||
\(622\) | 3.68815 | − | 25.9674i | 0.147881 | − | 1.04120i | ||||
\(623\) | −11.4609 | −0.459172 | ||||||||
\(624\) | 1.89074 | − | 2.98686i | 0.0756903 | − | 0.119570i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | −2.06814 | + | 14.5612i | −0.0826593 | + | 0.581985i | ||||
\(627\) | 46.0446 | + | 46.0446i | 1.83884 | + | 1.83884i | ||||
\(628\) | 15.5345 | + | 28.2190i | 0.619895 | + | 1.12606i | ||||
\(629\) | −17.6673 | + | 17.6673i | −0.704440 | + | 0.704440i | ||||
\(630\) | −4.95124 | + | 3.71971i | −0.197262 | + | 0.148197i | ||||
\(631\) | − | 30.8360i | − | 1.22756i | −0.789476 | − | 0.613781i | \(-0.789648\pi\) | ||
0.789476 | − | 0.613781i | \(-0.210352\pi\) | |||||||
\(632\) | −20.9142 | − | 9.42157i | −0.831921 | − | 0.374770i | ||||
\(633\) | − | 41.7162i | − | 1.65807i | ||||||
\(634\) | 14.8619 | + | 19.7825i | 0.590243 | + | 0.785663i | ||||
\(635\) | −11.5364 | + | 11.5364i | −0.457809 | + | 0.457809i | ||||
\(636\) | 68.3967 | + | 19.8288i | 2.71211 | + | 0.786262i | ||||
\(637\) | 0.230047 | + | 0.230047i | 0.00911480 | + | 0.00911480i | ||||
\(638\) | −20.5278 | − | 2.91556i | −0.812702 | − | 0.115428i | ||||
\(639\) | 6.27023 | 0.248046 | ||||||||
\(640\) | −11.0832 | − | 2.27215i | −0.438102 | − | 0.0898147i | ||||
\(641\) | −21.0782 | −0.832540 | −0.416270 | − | 0.909241i | \(-0.636663\pi\) | ||||
−0.416270 | + | 0.909241i | \(0.636663\pi\) | |||||||
\(642\) | 21.8485 | + | 3.10314i | 0.862290 | + | 0.122471i | ||||
\(643\) | 25.6837 | + | 25.6837i | 1.01286 | + | 1.01286i | 0.999916 | + | 0.0129487i | \(0.00412181\pi\) |
0.0129487 | + | 0.999916i | \(0.495878\pi\) | |||||||
\(644\) | −5.48537 | − | 1.59026i | −0.216154 | − | 0.0626649i | ||||
\(645\) | −4.50348 | + | 4.50348i | −0.177324 | + | 0.177324i | ||||
\(646\) | −18.4057 | − | 24.4995i | −0.724162 | − | 0.963921i | ||||
\(647\) | − | 4.30694i | − | 0.169323i | −0.996410 | − | 0.0846616i | \(-0.973019\pi\) | ||
0.996410 | − | 0.0846616i | \(-0.0269809\pi\) | |||||||
\(648\) | −7.63706 | − | 3.44040i | −0.300012 | − | 0.135152i | ||||
\(649\) | 5.94282i | 0.233276i | ||||||||
\(650\) | 0.367851 | − | 0.276355i | 0.0144283 | − | 0.0108395i | ||||
\(651\) | −10.5835 | + | 10.5835i | −0.414802 | + | 0.414802i | ||||
\(652\) | −8.98641 | − | 16.3242i | −0.351935 | − | 0.639303i | ||||
\(653\) | 7.40886 | + | 7.40886i | 0.289931 | + | 0.289931i | 0.837053 | − | 0.547122i | \(-0.184277\pi\) |
−0.547122 | + | 0.837053i | \(0.684277\pi\) | |||||||
\(654\) | −8.89125 | + | 62.6012i | −0.347675 | + | 2.44790i | ||||
\(655\) | 2.13966 | 0.0836035 | ||||||||
\(656\) | −5.85622 | + | 9.25124i | −0.228647 | + | 0.361200i | ||||
\(657\) | −50.5885 | −1.97365 | ||||||||
\(658\) | 2.38864 | − | 16.8179i | 0.0931190 | − | 0.655629i | ||||
\(659\) | 5.83069 | + | 5.83069i | 0.227132 | + | 0.227132i | 0.811493 | − | 0.584362i | \(-0.198655\pi\) |
−0.584362 | + | 0.811493i | \(0.698655\pi\) | |||||||
\(660\) | 16.1870 | − | 8.91092i | 0.630079 | − | 0.346857i | ||||
\(661\) | 21.9055 | − | 21.9055i | 0.852026 | − | 0.852026i | −0.138357 | − | 0.990382i | \(-0.544182\pi\) |
0.990382 | + | 0.138357i | \(0.0441821\pi\) | |||||||
\(662\) | 28.2652 | − | 21.2348i | 1.09856 | − | 0.825312i | ||||
\(663\) | − | 2.71688i | − | 0.105515i | ||||||
\(664\) | 0.0210640 | + | 0.0556003i | 0.000817442 | + | 0.00215771i | ||||
\(665\) | − | 7.04817i | − | 0.273316i | ||||||
\(666\) | 30.2310 | + | 40.2400i | 1.17143 | + | 1.55927i | ||||
\(667\) | 8.70422 | − | 8.70422i | 0.337029 | − | 0.337029i | ||||
\(668\) | 8.97914 | − | 30.9723i | 0.347413 | − | 1.19836i | ||||
\(669\) | −2.91631 | − | 2.91631i | −0.112751 | − | 0.112751i | ||||
\(670\) | 21.4795 | + | 3.05073i | 0.829824 | + | 0.117860i | ||||
\(671\) | 1.70631 | 0.0658715 | ||||||||
\(672\) | −15.3173 | + | 1.22748i | −0.590879 | + | 0.0473512i | ||||
\(673\) | 22.3632 | 0.862038 | 0.431019 | − | 0.902343i | \(-0.358154\pi\) | ||||
0.431019 | + | 0.902343i | \(0.358154\pi\) | |||||||
\(674\) | −26.0821 | − | 3.70445i | −1.00465 | − | 0.142690i | ||||
\(675\) | 2.64876 | + | 2.64876i | 0.101951 | + | 0.101951i | ||||
\(676\) | 7.18058 | − | 24.7685i | 0.276176 | − | 0.952633i | ||||
\(677\) | 8.00808 | − | 8.00808i | 0.307775 | − | 0.307775i | −0.536271 | − | 0.844046i | \(-0.680167\pi\) |
0.844046 | + | 0.536271i | \(0.180167\pi\) | |||||||
\(678\) | 33.1663 | + | 44.1472i | 1.27374 | + | 1.69546i | ||||
\(679\) | − | 7.61510i | − | 0.292241i | ||||||
\(680\) | −8.13135 | + | 3.08054i | −0.311823 | + | 0.118133i | ||||
\(681\) | − | 25.2966i | − | 0.969369i | ||||||
\(682\) | 21.1888 | − | 15.9185i | 0.811363 | − | 0.609550i | ||||
\(683\) | −31.7140 | + | 31.7140i | −1.21350 | + | 1.21350i | −0.243636 | + | 0.969867i | \(0.578340\pi\) |
−0.969867 | + | 0.243636i | \(0.921660\pi\) | |||||||
\(684\) | −54.0754 | + | 29.7684i | −2.06763 | + | 1.13822i | ||||
\(685\) | −3.56542 | − | 3.56542i | −0.136228 | − | 0.136228i | ||||
\(686\) | 0.198865 | − | 1.40016i | 0.00759270 | − | 0.0534584i | ||||
\(687\) | −25.0456 | −0.955550 | ||||||||
\(688\) | −9.15011 | + | 2.05626i | −0.348845 | + | 0.0783940i | ||||
\(689\) | −4.26445 | −0.162462 | ||||||||
\(690\) | −1.54261 | + | 10.8612i | −0.0587263 | + | 0.413478i | ||||
\(691\) | 33.6095 | + | 33.6095i | 1.27857 | + | 1.27857i | 0.941471 | + | 0.337095i | \(0.109444\pi\) |
0.337095 | + | 0.941471i | \(0.390556\pi\) | |||||||
\(692\) | −12.4576 | − | 22.6298i | −0.473569 | − | 0.860255i | ||||
\(693\) | 10.5312 | − | 10.5312i | 0.400047 | − | 0.400047i | ||||
\(694\) | −11.2083 | + | 8.42040i | −0.425460 | + | 0.319634i | ||||
\(695\) | 18.4131i | 0.698449i | ||||||||
\(696\) | 13.6034 | − | 30.1972i | 0.515637 | − | 1.14462i | ||||
\(697\) | 8.41502i | 0.318742i | ||||||||
\(698\) | −25.9953 | − | 34.6020i | −0.983938 | − | 1.30970i | ||||
\(699\) | −34.6518 | + | 34.6518i | −1.31065 | + | 1.31065i | ||||
\(700\) | −1.92091 | − | 0.556887i | −0.0726034 | − | 0.0210483i | ||||
\(701\) | −12.7954 | − | 12.7954i | −0.483277 | − | 0.483277i | 0.422900 | − | 0.906176i | \(-0.361012\pi\) |
−0.906176 | + | 0.422900i | \(0.861012\pi\) | |||||||
\(702\) | −1.70635 | − | 0.242353i | −0.0644020 | − | 0.00914702i | ||||
\(703\) | −57.2823 | −2.16044 | ||||||||
\(704\) | 27.1580 | + | 1.66198i | 1.02355 | + | 0.0626382i | ||||
\(705\) | −32.6280 | −1.22884 | ||||||||
\(706\) | −41.4726 | − | 5.89036i | −1.56084 | − | 0.221687i | ||||
\(707\) | −6.10829 | − | 6.10829i | −0.229726 | − | 0.229726i | ||||
\(708\) | −9.11754 | − | 2.64325i | −0.342658 | − | 0.0993395i | ||||
\(709\) | 16.8053 | − | 16.8053i | 0.631135 | − | 0.631135i | −0.317218 | − | 0.948353i | \(-0.602749\pi\) |
0.948353 | + | 0.317218i | \(0.102749\pi\) | |||||||
\(710\) | 1.21631 | + | 1.61901i | 0.0456474 | + | 0.0607605i | ||||
\(711\) | 35.5133i | 1.33185i | ||||||||
\(712\) | −13.3145 | + | 29.5558i | −0.498983 | + | 1.10765i | ||||
\(713\) | 15.7343i | 0.589255i | ||||||||
\(714\) | −9.44234 | + | 7.09372i | −0.353371 | + | 0.265476i | ||||
\(715\) | −0.782412 | + | 0.782412i | −0.0292606 | + | 0.0292606i | ||||
\(716\) | −13.8519 | − | 25.1625i | −0.517669 | − | 0.940365i | ||||
\(717\) | −27.0754 | − | 27.0754i | −1.01115 | − | 1.01115i | ||||
\(718\) | 5.06894 | − | 35.6892i | 0.189171 | − | 1.33191i | ||||
\(719\) | −33.0315 | −1.23187 | −0.615934 | − | 0.787798i | \(-0.711221\pi\) | ||||
−0.615934 | + | 0.787798i | \(0.711221\pi\) | |||||||
\(720\) | 3.84048 | + | 17.0897i | 0.143126 | + | 0.636897i | ||||
\(721\) | 9.38744 | 0.349606 | ||||||||
\(722\) | 6.10053 | − | 42.9524i | 0.227038 | − | 1.59852i | ||||
\(723\) | 21.3017 | + | 21.3017i | 0.792220 | + | 0.792220i | ||||
\(724\) | 22.4463 | − | 12.3567i | 0.834212 | − | 0.459232i | ||||
\(725\) | 3.04810 | − | 3.04810i | 0.113204 | − | 0.113204i | ||||
\(726\) | −1.74291 | + | 1.30939i | −0.0646854 | + | 0.0485960i | ||||
\(727\) | 41.3991i | 1.53541i | 0.640805 | + | 0.767704i | \(0.278601\pi\) | ||||
−0.640805 | + | 0.767704i | \(0.721399\pi\) | |||||||
\(728\) | 0.860506 | − | 0.326000i | 0.0318925 | − | 0.0120824i | ||||
\(729\) | 43.4947i | 1.61091i | ||||||||
\(730\) | −9.81327 | − | 13.0623i | −0.363206 | − | 0.483457i | ||||
\(731\) | −5.09671 | + | 5.09671i | −0.188509 | + | 0.188509i | ||||
\(732\) | −0.758935 | + | 2.61785i | −0.0280511 | + | 0.0967583i | ||||
\(733\) | 19.7963 | + | 19.7963i | 0.731195 | + | 0.731195i | 0.970856 | − | 0.239662i | \(-0.0770366\pi\) |
−0.239662 | + | 0.970856i | \(0.577037\pi\) | |||||||
\(734\) | −35.6733 | − | 5.06669i | −1.31673 | − | 0.187015i | ||||
\(735\) | −2.71643 | −0.100197 | ||||||||
\(736\) | −10.4735 | + | 12.2984i | −0.386060 | + | 0.453326i | ||||
\(737\) | −52.1752 | −1.92190 | ||||||||
\(738\) | 16.7829 | + | 2.38367i | 0.617787 | + | 0.0877443i | ||||
\(739\) | 0.304171 | + | 0.304171i | 0.0111891 | + | 0.0111891i | 0.712679 | − | 0.701490i | \(-0.247482\pi\) |
−0.701490 | + | 0.712679i | \(0.747482\pi\) | |||||||
\(740\) | −4.52596 | + | 15.6117i | −0.166378 | + | 0.573897i | ||||
\(741\) | 4.40445 | − | 4.40445i | 0.161801 | − | 0.161801i | ||||
\(742\) | 11.1344 | + | 14.8208i | 0.408756 | + | 0.544089i | ||||
\(743\) | 47.0701i | 1.72684i | 0.504490 | + | 0.863418i | \(0.331681\pi\) | ||||
−0.504490 | + | 0.863418i | \(0.668319\pi\) | |||||||
\(744\) | 14.9979 | + | 39.5884i | 0.549851 | + | 1.45138i | ||||
\(745\) | − | 4.14154i | − | 0.151734i | ||||||
\(746\) | 14.5603 | − | 10.9386i | 0.533089 | − | 0.400492i | ||||
\(747\) | 0.0650899 | − | 0.0650899i | 0.00238152 | − | 0.00238152i | ||||
\(748\) | 18.3193 | − | 10.0847i | 0.669821 | − | 0.368735i | ||||
\(749\) | 4.06190 | + | 4.06190i | 0.148419 | + | 0.148419i | ||||
\(750\) | −0.540203 | + | 3.80344i | −0.0197254 | + | 0.138882i | ||||
\(751\) | −17.5637 | −0.640910 | −0.320455 | − | 0.947264i | \(-0.603836\pi\) | ||||
−0.320455 | + | 0.947264i | \(0.603836\pi\) | |||||||
\(752\) | −40.5955 | − | 25.6978i | −1.48037 | − | 0.937101i | ||||
\(753\) | −24.0061 | −0.874831 | ||||||||
\(754\) | −0.278891 | + | 1.96361i | −0.0101566 | + | 0.0715103i | ||||
\(755\) | 7.41771 | + | 7.41771i | 0.269958 | + | 0.269958i | ||||
\(756\) | 3.61296 | + | 6.56308i | 0.131402 | + | 0.238697i | ||||
\(757\) | −7.56441 | + | 7.56441i | −0.274933 | + | 0.274933i | −0.831082 | − | 0.556149i | \(-0.812278\pi\) |
0.556149 | + | 0.831082i | \(0.312278\pi\) | |||||||
\(758\) | 15.2557 | − | 11.4611i | 0.554113 | − | 0.416287i | ||||
\(759\) | − | 26.3826i | − | 0.957628i | ||||||
\(760\) | −18.1761 | − | 8.18809i | −0.659315 | − | 0.297013i | ||||
\(761\) | − | 48.4501i | − | 1.75631i | −0.478372 | − | 0.878157i | \(-0.658773\pi\) | ||
0.478372 | − | 0.878157i | \(-0.341227\pi\) | |||||||
\(762\) | 37.6461 | + | 50.1101i | 1.36377 | + | 1.81530i | ||||
\(763\) | −11.6383 | + | 11.6383i | −0.421336 | + | 0.421336i | ||||
\(764\) | 42.3849 | + | 12.2877i | 1.53343 | + | 0.444554i | ||||
\(765\) | 9.51917 | + | 9.51917i | 0.344166 | + | 0.344166i | ||||
\(766\) | 4.14419 | + | 0.588599i | 0.149736 | + | 0.0212669i | ||||
\(767\) | 0.568467 | 0.0205262 | ||||||||
\(768\) | −14.6292 | + | 40.9269i | −0.527885 | + | 1.47682i | ||||
\(769\) | 1.55437 | 0.0560519 | 0.0280259 | − | 0.999607i | \(-0.491078\pi\) | ||||
0.0280259 | + | 0.999607i | \(0.491078\pi\) | |||||||
\(770\) | 4.76209 | + | 0.676359i | 0.171614 | + | 0.0243743i | ||||
\(771\) | −31.9977 | − | 31.9977i | −1.15237 | − | 1.15237i | ||||
\(772\) | 45.3503 | + | 13.1474i | 1.63219 | + | 0.473186i | ||||
\(773\) | −8.53373 | + | 8.53373i | −0.306937 | + | 0.306937i | −0.843720 | − | 0.536783i | \(-0.819639\pi\) |
0.536783 | + | 0.843720i | \(0.319639\pi\) | |||||||
\(774\) | 8.72114 | + | 11.6086i | 0.313475 | + | 0.417262i | ||||
\(775\) | 5.50995i | 0.197923i | ||||||||
\(776\) | −19.6381 | − | 8.84671i | −0.704966 | − | 0.317578i | ||||
\(777\) | 22.0771i | 0.792012i | ||||||||
\(778\) | 28.3233 | − | 21.2784i | 1.01544 | − | 0.762867i | ||||
\(779\) | −13.6419 | + | 13.6419i | −0.488774 | + | 0.488774i | ||||
\(780\) | −0.852384 | − | 1.54839i | −0.0305203 | − | 0.0554412i | ||||
\(781\) | −3.44361 | − | 3.44361i | −0.123222 | − | 0.123222i | ||||
\(782\) | −1.74582 | + | 12.2919i | −0.0624304 | + | 0.439557i | ||||
\(783\) | −16.1474 | −0.577061 | ||||||||
\(784\) | −3.37975 | − | 2.13945i | −0.120706 | − | 0.0764090i | ||||
\(785\) | 16.1062 | 0.574854 | ||||||||
\(786\) | 1.15585 | − | 8.13807i | 0.0412278 | − | 0.290275i | ||||
\(787\) | 0.786007 | + | 0.786007i | 0.0280181 | + | 0.0280181i | 0.720977 | − | 0.692959i | \(-0.243693\pi\) |
−0.692959 | + | 0.720977i | \(0.743693\pi\) | |||||||
\(788\) | −3.31911 | + | 1.82717i | −0.118239 | + | 0.0650901i | ||||
\(789\) | −27.9374 | + | 27.9374i | −0.994598 | + | 0.994598i | ||||
\(790\) | −9.16976 | + | 6.88894i | −0.326245 | + | 0.245098i | ||||
\(791\) | 14.3735i | 0.511064i | ||||||||
\(792\) | −14.9238 | − | 39.3926i | −0.530293 | − | 1.39976i | ||||
\(793\) | − | 0.163219i | − | 0.00579609i | ||||||
\(794\) | 3.77821 | + | 5.02912i | 0.134084 | + | 0.178477i | ||||
\(795\) | 25.1776 | − | 25.1776i | 0.892957 | − | 0.892957i | ||||
\(796\) | 9.99610 | − | 34.4802i | 0.354302 | − | 1.22212i | ||||
\(797\) | −22.3948 | − | 22.3948i | −0.793264 | − | 0.793264i | 0.188759 | − | 0.982023i | \(-0.439554\pi\) |
−0.982023 | + | 0.188759i | \(0.939554\pi\) | |||||||
\(798\) | −26.8073 | − | 3.80744i | −0.948968 | − | 0.134782i | ||||
\(799\) | −36.9261 | −1.30635 | ||||||||
\(800\) | −3.66769 | + | 4.30674i | −0.129673 | + | 0.152266i | ||||
\(801\) | 50.1872 | 1.77328 | ||||||||
\(802\) | 33.5381 | + | 4.76342i | 1.18427 | + | 0.168202i | ||||
\(803\) | 27.7832 | + | 27.7832i | 0.980449 | + | 0.980449i | ||||
\(804\) | 23.2065 | − | 80.0478i | 0.818432 | − | 2.82307i | ||||
\(805\) | −2.01923 | + | 2.01923i | −0.0711684 | + | 0.0711684i | ||||
\(806\) | −1.52270 | − | 2.02684i | −0.0536348 | − | 0.0713925i | ||||
\(807\) | − | 7.97196i | − | 0.280626i | ||||||
\(808\) | −22.8484 | + | 8.65606i | −0.803805 | + | 0.304519i | ||||
\(809\) | 4.46309i | 0.156914i | 0.996918 | + | 0.0784569i | \(0.0249993\pi\) | ||||
−0.996918 | + | 0.0784569i | \(0.975001\pi\) | |||||||
\(810\) | −3.34845 | + | 2.51558i | −0.117653 | + | 0.0883885i | ||||
\(811\) | 38.5046 | − | 38.5046i | 1.35208 | − | 1.35208i | 0.468750 | − | 0.883331i | \(-0.344704\pi\) |
0.883331 | − | 0.468750i | \(-0.155296\pi\) | |||||||
\(812\) | 7.55256 | − | 4.15767i | 0.265043 | − | 0.145906i | ||||
\(813\) | −14.9541 | − | 14.9541i | −0.524462 | − | 0.524462i | ||||
\(814\) | 5.49694 | − | 38.7027i | 0.192668 | − | 1.35653i | ||||
\(815\) | −9.31710 | −0.326364 | ||||||||
\(816\) | 7.32405 | + | 32.5912i | 0.256393 | + | 1.14092i | ||||
\(817\) | −16.5250 | −0.578136 | ||||||||
\(818\) | −1.04684 | + | 7.37052i | −0.0366018 | + | 0.257704i | ||||
\(819\) | −1.00737 | − | 1.00737i | −0.0352005 | − | 0.0352005i | ||||
\(820\) | 2.64010 | + | 4.79584i | 0.0921963 | + | 0.167478i | ||||
\(821\) | −9.18132 | + | 9.18132i | −0.320430 | + | 0.320430i | −0.848932 | − | 0.528502i | \(-0.822754\pi\) |
0.528502 | + | 0.848932i | \(0.322754\pi\) | |||||||
\(822\) | −15.4869 | + | 11.6348i | −0.540169 | + | 0.405811i | ||||
\(823\) | − | 42.0956i | − | 1.46736i | −0.679495 | − | 0.733680i | \(-0.737801\pi\) | ||
0.679495 | − | 0.733680i | \(-0.262199\pi\) | |||||||
\(824\) | 10.9057 | − | 24.2086i | 0.379918 | − | 0.843348i | ||||
\(825\) | − | 9.23884i | − | 0.321655i | ||||||
\(826\) | −1.48426 | − | 1.97567i | −0.0516439 | − | 0.0687423i | ||||
\(827\) | 34.6267 | − | 34.6267i | 1.20409 | − | 1.20409i | 0.231178 | − | 0.972912i | \(-0.425742\pi\) |
0.972912 | − | 0.231178i | \(-0.0742578\pi\) | |||||||
\(828\) | 24.0204 | + | 6.96371i | 0.834766 | + | 0.242006i | ||||
\(829\) | −4.45262 | − | 4.45262i | −0.154646 | − | 0.154646i | 0.625543 | − | 0.780189i | \(-0.284877\pi\) |
−0.780189 | + | 0.625543i | \(0.784877\pi\) | |||||||
\(830\) | 0.0294329 | + | 0.00418036i | 0.00102163 | + | 0.000145102i | ||||
\(831\) | −18.8009 | −0.652195 | ||||||||
\(832\) | 0.158978 | − | 2.59783i | 0.00551158 | − | 0.0900634i | ||||
\(833\) | −3.07426 | −0.106517 | ||||||||
\(834\) | 70.0331 | + | 9.94681i | 2.42505 | + | 0.344430i | ||||
\(835\) | −11.4013 | − | 11.4013i | −0.394557 | − | 0.394557i | ||||
\(836\) | 46.0470 | + | 13.3494i | 1.59257 | + | 0.461699i | ||||
\(837\) | 14.5945 | − | 14.5945i | 0.504461 | − | 0.504461i | ||||
\(838\) | 6.48941 | + | 8.63795i | 0.224173 | + | 0.298393i | ||||
\(839\) | − | 7.15578i | − | 0.247045i | −0.992342 | − | 0.123523i | \(-0.960581\pi\) | ||
0.992342 | − | 0.123523i | \(-0.0394191\pi\) | |||||||
\(840\) | −3.15576 | + | 7.00522i | −0.108884 | + | 0.241703i | ||||
\(841\) | − | 10.4181i | − | 0.359247i | ||||||
\(842\) | 22.8012 | − | 17.1298i | 0.785783 | − | 0.590333i | ||||
\(843\) | −15.5679 | + | 15.5679i | −0.536188 | + | 0.536188i | ||||
\(844\) | −14.8119 | − | 26.9064i | −0.509848 | − | 0.926157i | ||||
\(845\) | −9.11755 | − | 9.11755i | −0.313653 | − | 0.313653i | ||||
\(846\) | −10.4598 | + | 73.6452i | −0.359616 | + | 2.53197i | ||||
\(847\) | −0.567460 | −0.0194982 | ||||||||
\(848\) | 51.1555 | − | 11.4959i | 1.75669 | − | 0.394771i | ||||
\(849\) | 56.9010 | 1.95284 | ||||||||
\(850\) | −0.611363 | + | 4.30446i | −0.0209696 | + | 0.147642i | ||||
\(851\) | 16.4108 | + | 16.4108i | 0.562554 | + | 0.562554i | ||||
\(852\) | 6.81488 | − | 3.75157i | 0.233474 | − | 0.128527i | ||||
\(853\) | −17.4128 | + | 17.4128i | −0.596205 | + | 0.596205i | −0.939300 | − | 0.343096i | \(-0.888524\pi\) |
0.343096 | + | 0.939300i | \(0.388524\pi\) | |||||||
\(854\) | −0.567258 | + | 0.426162i | −0.0194112 | + | 0.0145830i | ||||
\(855\) | 30.8638i | 1.05552i | ||||||||
\(856\) | 15.1938 | − | 5.75612i | 0.519313 | − | 0.196740i | ||||
\(857\) | − | 33.3568i | − | 1.13945i | −0.821837 | − | 0.569723i | \(-0.807050\pi\) | ||
0.821837 | − | 0.569723i | \(-0.192950\pi\) | |||||||
\(858\) | 2.55320 | + | 3.39852i | 0.0871647 | + | 0.116024i | ||||
\(859\) | 2.96984 | − | 2.96984i | 0.101330 | − | 0.101330i | −0.654624 | − | 0.755954i | \(-0.727173\pi\) |
0.755954 | + | 0.654624i | \(0.227173\pi\) | |||||||
\(860\) | −1.30566 | + | 4.50371i | −0.0445228 | + | 0.153575i | ||||
\(861\) | 5.25773 | + | 5.25773i | 0.179183 | + | 0.179183i | ||||
\(862\) | 8.23666 | + | 1.16985i | 0.280542 | + | 0.0398453i | ||||
\(863\) | 30.1859 | 1.02754 | 0.513770 | − | 0.857928i | \(-0.328249\pi\) | ||||
0.513770 | + | 0.857928i | \(0.328249\pi\) | |||||||
\(864\) | 21.1224 | − | 1.69268i | 0.718598 | − | 0.0575862i | ||||
\(865\) | −12.9161 | −0.439160 | ||||||||
\(866\) | −47.7778 | − | 6.78589i | −1.62356 | − | 0.230594i | ||||
\(867\) | −14.5000 | − | 14.5000i | −0.492447 | − | 0.492447i | ||||
\(868\) | −3.06842 | + | 10.5841i | −0.104149 | + | 0.359247i | ||||
\(869\) | 19.5039 | − | 19.5039i | 0.661624 | − | 0.661624i | ||||
\(870\) | −9.94668 | − | 13.2399i | −0.337224 | − | 0.448873i | ||||
\(871\) | 4.99088i | 0.169109i | ||||||||
\(872\) | 16.4927 | + | 43.5340i | 0.558513 | + | 1.47425i | ||||
\(873\) | 33.3464i | 1.12861i | ||||||||
\(874\) | −22.7571 | + | 17.0967i | −0.769772 | + | 0.578304i | ||||
\(875\) | −0.707107 | + | 0.707107i | −0.0239046 | + | 0.0239046i | ||||
\(876\) | −54.9828 | + | 30.2679i | −1.85770 | + | 1.02266i | ||||
\(877\) | 17.5002 | + | 17.5002i | 0.590941 | + | 0.590941i | 0.937886 | − | 0.346945i | \(-0.112781\pi\) |
−0.346945 | + | 0.937886i | \(0.612781\pi\) | |||||||
\(878\) | −5.96608 | + | 42.0057i | −0.201345 | + | 1.41762i | ||||
\(879\) | −19.5138 | −0.658184 | ||||||||
\(880\) | 7.27649 | − | 11.4949i | 0.245290 | − | 0.387492i | ||||
\(881\) | 27.1194 | 0.913677 | 0.456839 | − | 0.889550i | \(-0.348982\pi\) | ||||
0.456839 | + | 0.889550i | \(0.348982\pi\) | |||||||
\(882\) | −0.870827 | + | 6.13129i | −0.0293223 | + | 0.206451i | ||||
\(883\) | −26.3544 | − | 26.3544i | −0.886897 | − | 0.886897i | 0.107326 | − | 0.994224i | \(-0.465771\pi\) |
−0.994224 | + | 0.107326i | \(0.965771\pi\) | |||||||
\(884\) | −0.964667 | − | 1.75235i | −0.0324453 | − | 0.0589381i | ||||
\(885\) | −3.35627 | + | 3.35627i | −0.112820 | + | 0.112820i | ||||
\(886\) | −33.6600 | + | 25.2877i | −1.13083 | + | 0.849557i | ||||
\(887\) | 34.8464i | 1.17003i | 0.811024 | + | 0.585013i | \(0.198911\pi\) | ||||
−0.811024 | + | 0.585013i | \(0.801089\pi\) | |||||||
\(888\) | 56.9332 | + | 25.6477i | 1.91055 | + | 0.860680i | ||||
\(889\) | 16.3150i | 0.547187i | ||||||||
\(890\) | 9.73542 | + | 12.9587i | 0.326332 | + | 0.434375i | ||||
\(891\) | 7.12209 | − | 7.12209i | 0.238599 | − | 0.238599i | ||||
\(892\) | −2.91647 | − | 0.845508i | −0.0976505 | − | 0.0283097i | ||||
\(893\) | −59.8624 | − | 59.8624i | −2.00322 | − | 2.00322i | ||||
\(894\) | −15.7521 | − | 2.23727i | −0.526829 | − | 0.0748256i | ||||
\(895\) | −14.3616 | −0.480056 | ||||||||
\(896\) | −9.44366 | + | 6.23035i | −0.315491 | + | 0.208141i | ||||
\(897\) | −2.52366 | −0.0842625 | ||||||||
\(898\) | 18.2258 | + | 2.58861i | 0.608202 | + | 0.0863829i | ||||
\(899\) | −16.7949 | − | 16.7949i | −0.560141 | − | 0.560141i | ||||
\(900\) | 8.41162 | + | 2.43860i | 0.280387 | + | 0.0812866i | ||||
\(901\) | 28.4942 | − | 28.4942i | 0.949279 | − | 0.949279i | ||||
\(902\) | −7.90805 | − | 10.5263i | −0.263309 | − | 0.350487i | ||||
\(903\) | 6.36888i | 0.211943i | ||||||||
\(904\) | 37.0669 | + | 16.6982i | 1.23283 | + | 0.555374i | ||||
\(905\) | − | 12.8114i | − | 0.425865i | ||||||
\(906\) | 32.2199 | − | 24.2057i | 1.07043 | − | 0.804182i | ||||
\(907\) | 5.34624 | − | 5.34624i | 0.177519 | − | 0.177519i | −0.612754 | − | 0.790273i | \(-0.709938\pi\) |
0.790273 | + | 0.612754i | \(0.209938\pi\) | |||||||
\(908\) | −8.98193 | − | 16.3160i | −0.298076 | − | 0.541466i | ||||
\(909\) | 26.7481 | + | 26.7481i | 0.887178 | + | 0.887178i | ||||
\(910\) | 0.0646979 | − | 0.455523i | 0.00214471 | − | 0.0151004i | ||||
\(911\) | 14.0817 | 0.466546 | 0.233273 | − | 0.972411i | \(-0.425056\pi\) | ||||
0.233273 | + | 0.972411i | \(0.425056\pi\) | |||||||
\(912\) | −40.9617 | + | 64.7083i | −1.35638 | + | 2.14271i | ||||
\(913\) | −0.0714948 | −0.00236613 | ||||||||
\(914\) | 5.47588 | − | 38.5543i | 0.181126 | − | 1.27526i | ||||
\(915\) | 0.963658 | + | 0.963658i | 0.0318576 | + | 0.0318576i | ||||
\(916\) | −16.1541 | + | 8.89281i | −0.533747 | + | 0.293827i | ||||
\(917\) | 1.51297 | − | 1.51297i | 0.0499626 | − | 0.0499626i | ||||
\(918\) | 13.0208 | − | 9.78214i | 0.429752 | − | 0.322859i | ||||
\(919\) | 12.1569i | 0.401020i | 0.979692 | + | 0.200510i | \(0.0642599\pi\) | ||||
−0.979692 | + | 0.200510i | \(0.935740\pi\) | |||||||
\(920\) | 2.86145 | + | 7.55305i | 0.0943392 | + | 0.249017i | ||||
\(921\) | − | 94.7581i | − | 3.12239i | ||||||
\(922\) | 3.63258 | + | 4.83527i | 0.119633 | + | 0.159241i | ||||
\(923\) | −0.329402 | + | 0.329402i | −0.0108424 | + | 0.0108424i | ||||
\(924\) | 5.14498 | − | 17.7469i | 0.169258 | − | 0.583831i | ||||
\(925\) | 5.74684 | + | 5.74684i | 0.188955 | + | 0.188955i | ||||
\(926\) | 41.7547 | + | 5.93043i | 1.37215 | + | 0.194886i | ||||
\(927\) | −41.1075 | −1.35015 | ||||||||
\(928\) | −1.94788 | − | 24.3069i | −0.0639422 | − | 0.797913i | ||||
\(929\) | −38.5694 | −1.26542 | −0.632711 | − | 0.774388i | \(-0.718058\pi\) | ||||
−0.632711 | + | 0.774388i | \(0.718058\pi\) | |||||||
\(930\) | 20.9568 | + | 2.97649i | 0.687199 | + | 0.0976029i | ||||
\(931\) | −4.98381 | − | 4.98381i | −0.163338 | − | 0.163338i | ||||
\(932\) | −10.0464 | + | 34.6536i | −0.329080 | + | 1.13512i | ||||
\(933\) | −35.6232 | + | 35.6232i | −1.16625 | + | 1.16625i | ||||
\(934\) | 24.0618 | + | 32.0282i | 0.787325 | + | 1.04800i | ||||
\(935\) | − | 10.4559i | − | 0.341943i | ||||||
\(936\) | −3.76814 | + | 1.42755i | −0.123166 | + | 0.0466609i | ||||
\(937\) | − | 0.399807i | − | 0.0130611i | −0.999979 | − | 0.00653056i | \(-0.997921\pi\) | ||
0.999979 | − | 0.00653056i | \(-0.00207876\pi\) | |||||||
\(938\) | 17.3455 | − | 13.0311i | 0.566350 | − | 0.425480i | ||||
\(939\) | 19.9758 | − | 19.9758i | 0.651885 | − | 0.651885i | ||||
\(940\) | −21.0447 | + | 11.5851i | −0.686402 | + | 0.377863i | ||||
\(941\) | 35.2038 | + | 35.2038i | 1.14761 | + | 1.14761i | 0.987021 | + | 0.160589i | \(0.0513394\pi\) |
0.160589 | + | 0.987021i | \(0.448661\pi\) | |||||||
\(942\) | 8.70060 | − | 61.2589i | 0.283481 | − | 1.99592i | ||||
\(943\) | 7.81655 | 0.254542 | ||||||||
\(944\) | −6.81923 | + | 1.53245i | −0.221947 | + | 0.0498770i | ||||
\(945\) | 3.74592 | 0.121855 | ||||||||
\(946\) | 1.58578 | − | 11.1651i | 0.0515581 | − | 0.363008i | ||||
\(947\) | −16.0232 | − | 16.0232i | −0.520685 | − | 0.520685i | 0.397093 | − | 0.917778i | \(-0.370019\pi\) |
−0.917778 | + | 0.397093i | \(0.870019\pi\) | |||||||
\(948\) | 21.2481 | + | 38.5981i | 0.690108 | + | 1.25361i | ||||
\(949\) | 2.65764 | − | 2.65764i | 0.0862705 | − | 0.0862705i | ||||
\(950\) | −7.96925 | + | 5.98703i | −0.258556 | + | 0.194245i | ||||
\(951\) | − | 47.5268i | − | 1.54116i | ||||||
\(952\) | −3.57147 | + | 7.92800i | −0.115752 | + | 0.256948i | ||||
\(953\) | 29.2213i | 0.946572i | 0.880909 | + | 0.473286i | \(0.156932\pi\) | ||||
−0.880909 | + | 0.473286i | \(0.843068\pi\) | |||||||
\(954\) | −48.7573 | − | 64.9001i | −1.57858 | − | 2.10122i | ||||
\(955\) | 15.6023 | − | 15.6023i | 0.504880 | − | 0.504880i | ||||
\(956\) | −27.0768 | − | 7.84979i | −0.875726 | − | 0.253880i | ||||
\(957\) | 28.1609 | + | 28.1609i | 0.910313 | + | 0.910313i | ||||
\(958\) | −38.6660 | − | 5.49173i | −1.24924 | − | 0.177430i | ||||
\(959\) | −5.04227 | −0.162823 | ||||||||
\(960\) | 14.3991 | + | 16.2764i | 0.464730 | + | 0.525318i | ||||
\(961\) | −0.640466 | −0.0206602 | ||||||||
\(962\) | −3.70215 | − | 0.525816i | −0.119362 | − | 0.0169530i | ||||
\(963\) | −17.7870 | − | 17.7870i | −0.573178 | − | 0.573178i | ||||
\(964\) | 21.3028 | + | 6.17587i | 0.686119 | + | 0.198911i | ||||
\(965\) | 16.6940 | − | 16.6940i | 0.537397 | − | 0.537397i | ||||
\(966\) | 6.58922 | + | 8.77080i | 0.212005 | + | 0.282196i | ||||
\(967\) | 10.4230i | 0.335183i | 0.985857 | + | 0.167591i | \(0.0535989\pi\) | ||||
−0.985857 | + | 0.167591i | \(0.946401\pi\) | |||||||
\(968\) | −0.659236 | + | 1.46338i | −0.0211887 | + | 0.0470350i | ||||
\(969\) | 58.8593i | 1.89083i | ||||||||
\(970\) | −8.61027 | + | 6.46861i | −0.276459 | + | 0.207695i | ||||
\(971\) | −2.97442 | + | 2.97442i | −0.0954537 | + | 0.0954537i | −0.753221 | − | 0.657767i | \(-0.771501\pi\) |
0.657767 | + | 0.753221i | \(0.271501\pi\) | |||||||
\(972\) | 18.5979 | + | 33.7838i | 0.596528 | + | 1.08362i | ||||
\(973\) | 13.0200 | + | 13.0200i | 0.417403 | + | 0.417403i | ||||
\(974\) | 5.28214 | − | 37.1903i | 0.169251 | − | 1.19165i | ||||
\(975\) | −0.883751 | −0.0283027 | ||||||||
\(976\) | 0.440000 | + | 1.95795i | 0.0140840 | + | 0.0626724i | ||||
\(977\) | −12.4194 | −0.397331 | −0.198666 | − | 0.980067i | \(-0.563661\pi\) | ||||
−0.198666 | + | 0.980067i | \(0.563661\pi\) | |||||||
\(978\) | −5.03313 | + | 35.4370i | −0.160942 | + | 1.13315i | ||||
\(979\) | −27.5628 | − | 27.5628i | −0.880911 | − | 0.880911i | ||||
\(980\) | −1.75206 | + | 0.964507i | −0.0559676 | + | 0.0308100i | ||||
\(981\) | 50.9641 | − | 50.9641i | 1.62716 | − | 1.62716i | ||||
\(982\) | 2.71277 | − | 2.03802i | 0.0865680 | − | 0.0650357i | ||||
\(983\) | 44.7477i | 1.42723i | 0.700538 | + | 0.713615i | \(0.252943\pi\) | ||||
−0.700538 | + | 0.713615i | \(0.747057\pi\) | |||||||
\(984\) | 19.6669 | − | 7.45073i | 0.626957 | − | 0.237521i | ||||
\(985\) | 1.89440i | 0.0603607i | ||||||||
\(986\) | −11.2569 | − | 14.9839i | −0.358494 | − | 0.477185i | ||||
\(987\) | −23.0715 | + | 23.0715i | −0.734374 | + | 0.734374i | ||||
\(988\) | 1.27695 | − | 4.40468i | 0.0406253 | − | 0.140131i | ||||
\(989\) | 4.73424 | + | 4.73424i | 0.150540 | + | 0.150540i | ||||
\(990\) | −20.8531 | − | 2.96177i | −0.662755 | − | 0.0941312i | ||||
\(991\) | −16.8014 | −0.533714 | −0.266857 | − | 0.963736i | \(-0.585985\pi\) | ||||
−0.266857 | + | 0.963736i | \(0.585985\pi\) | |||||||
\(992\) | 23.7299 | + | 20.2088i | 0.753426 | + | 0.641630i | ||||
\(993\) | −67.9064 | −2.15494 | ||||||||
\(994\) | 2.00488 | + | 0.284753i | 0.0635909 | + | 0.00903182i | ||||
\(995\) | −12.6925 | − | 12.6925i | −0.402381 | − | 0.402381i | ||||
\(996\) | 0.0317995 | − | 0.109688i | 0.00100761 | − | 0.00347560i | ||||
\(997\) | −8.71750 | + | 8.71750i | −0.276086 | + | 0.276086i | −0.831544 | − | 0.555458i | \(-0.812543\pi\) |
0.555458 | + | 0.831544i | \(0.312543\pi\) | |||||||
\(998\) | 21.6771 | + | 28.8541i | 0.686177 | + | 0.913360i | ||||
\(999\) | − | 30.4440i | − | 0.963206i |
(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 | 560.2.bd.a.141.2 | ✓ | 44 | |
4.3 | odd | 2 | 2240.2.bd.a.1681.3 | 44 | |||
16.5 | even | 4 | inner | 560.2.bd.a.421.2 | yes | 44 | |
16.11 | odd | 4 | 2240.2.bd.a.561.3 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
560.2.bd.a.141.2 | ✓ | 44 | 1.1 | even | 1 | trivial | |
560.2.bd.a.421.2 | yes | 44 | 16.5 | even | 4 | inner | |
2240.2.bd.a.561.3 | 44 | 16.11 | odd | 4 | |||
2240.2.bd.a.1681.3 | 44 | 4.3 | odd | 2 |