Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [750,2,Mod(107,750)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(750, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([10, 13]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("750.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 750 = 2 \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 750.l (of order \(20\), degree \(8\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.98878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{20})\) |
Twist minimal: | no (minimal twist has level 150) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{20}]$ |
Embedding invariants
Embedding label | 143.6 | ||
Character | \(\chi\) | \(=\) | 750.143 |
Dual form | 750.2.l.a.257.6 |
$q$-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 \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{3}{20}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.453990 | − | 0.891007i | 0.321020 | − | 0.630037i | ||||
\(3\) | −1.70181 | + | 0.322239i | −0.982541 | + | 0.186045i | ||||
\(4\) | −0.587785 | − | 0.809017i | −0.293893 | − | 0.404508i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.485490 | + | 1.66262i | −0.198200 | + | 0.678761i | ||||
\(7\) | −0.0556476 | + | 0.0556476i | −0.0210328 | + | 0.0210328i | −0.717545 | − | 0.696512i | \(-0.754734\pi\) |
0.696512 | + | 0.717545i | \(0.254734\pi\) | |||||||
\(8\) | −0.987688 | + | 0.156434i | −0.349201 | + | 0.0553079i | ||||
\(9\) | 2.79232 | − | 1.09678i | 0.930775 | − | 0.365593i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.04749 | + | 0.340351i | −0.315831 | + | 0.102620i | −0.462643 | − | 0.886545i | \(-0.653099\pi\) |
0.146812 | + | 0.989164i | \(0.453099\pi\) | |||||||
\(12\) | 1.26100 | + | 1.18739i | 0.364018 | + | 0.342769i | ||||
\(13\) | −4.54086 | + | 2.31368i | −1.25941 | + | 0.641700i | −0.950893 | − | 0.309520i | \(-0.899832\pi\) |
−0.308514 | + | 0.951220i | \(0.599832\pi\) | |||||||
\(14\) | 0.0243189 | + | 0.0748459i | 0.00649950 | + | 0.0200034i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.309017 | + | 0.951057i | −0.0772542 | + | 0.237764i | ||||
\(17\) | 0.491350 | + | 3.10226i | 0.119170 | + | 0.752408i | 0.972820 | + | 0.231562i | \(0.0743836\pi\) |
−0.853650 | + | 0.520846i | \(0.825616\pi\) | |||||||
\(18\) | 0.290452 | − | 2.98591i | 0.0684602 | − | 0.703785i | ||||
\(19\) | 0.824223 | − | 1.13445i | 0.189090 | − | 0.260260i | −0.703938 | − | 0.710262i | \(-0.748577\pi\) |
0.893028 | + | 0.450002i | \(0.148577\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.0767699 | − | 0.112634i | 0.0167526 | − | 0.0245787i | ||||
\(22\) | −0.172297 | + | 1.08784i | −0.0367338 | + | 0.231928i | ||||
\(23\) | −2.22575 | − | 1.13408i | −0.464102 | − | 0.236472i | 0.206273 | − | 0.978495i | \(-0.433867\pi\) |
−0.670375 | + | 0.742023i | \(0.733867\pi\) | |||||||
\(24\) | 1.63045 | − | 0.584493i | 0.332814 | − | 0.119309i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.09632i | 0.999471i | ||||||||
\(27\) | −4.39859 | + | 2.76630i | −0.846508 | + | 0.532376i | ||||
\(28\) | 0.0777287 | + | 0.0123110i | 0.0146893 | + | 0.00232656i | ||||
\(29\) | −5.66803 | + | 4.11807i | −1.05253 | + | 0.764705i | −0.972691 | − | 0.232103i | \(-0.925440\pi\) |
−0.0798355 | + | 0.996808i | \(0.525440\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.72991 | + | 5.61611i | 1.38833 | + | 1.00868i | 0.996046 | + | 0.0888399i | \(0.0283160\pi\) |
0.392287 | + | 0.919843i | \(0.371684\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | 1.67296 | − | 0.916756i | 0.291225 | − | 0.159587i | ||||
\(34\) | 2.98720 | + | 0.970601i | 0.512301 | + | 0.166457i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.52860 | − | 1.61437i | −0.421433 | − | 0.269061i | ||||
\(37\) | 4.70325 | + | 9.23065i | 0.773210 | + | 1.51751i | 0.853706 | + | 0.520755i | \(0.174350\pi\) |
−0.0804961 | + | 0.996755i | \(0.525650\pi\) | |||||||
\(38\) | −0.636609 | − | 1.24942i | −0.103272 | − | 0.202682i | ||||
\(39\) | 6.98213 | − | 5.40069i | 1.11803 | − | 0.864803i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.55210 | + | 1.15415i | 0.554745 | + | 0.180248i | 0.572956 | − | 0.819586i | \(-0.305797\pi\) |
−0.0182101 | + | 0.999834i | \(0.505797\pi\) | |||||||
\(42\) | −0.0655044 | − | 0.119537i | −0.0101075 | − | 0.0184450i | ||||
\(43\) | 1.00563 | + | 1.00563i | 0.153357 | + | 0.153357i | 0.779616 | − | 0.626258i | \(-0.215414\pi\) |
−0.626258 | + | 0.779616i | \(0.715414\pi\) | |||||||
\(44\) | 0.891050 | + | 0.647386i | 0.134331 | + | 0.0975971i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.02094 | + | 1.46830i | −0.297972 | + | 0.216489i | ||||
\(47\) | −12.5515 | − | 1.98797i | −1.83083 | − | 0.289975i | −0.856674 | − | 0.515858i | \(-0.827473\pi\) |
−0.974154 | + | 0.225883i | \(0.927473\pi\) | |||||||
\(48\) | 0.219422 | − | 1.71810i | 0.0316708 | − | 0.247986i | ||||
\(49\) | 6.99381i | 0.999115i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.83585 | − | 5.12113i | −0.257071 | − | 0.717101i | ||||
\(52\) | 4.54086 | + | 2.31368i | 0.629704 | + | 0.320850i | ||||
\(53\) | −1.06206 | + | 6.70559i | −0.145885 | + | 0.921083i | 0.800802 | + | 0.598929i | \(0.204407\pi\) |
−0.946687 | + | 0.322154i | \(0.895593\pi\) | |||||||
\(54\) | 0.467880 | + | 5.17504i | 0.0636704 | + | 0.704234i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.0462573 | − | 0.0636677i | 0.00618139 | − | 0.00850795i | ||||
\(57\) | −1.03711 | + | 2.19621i | −0.137369 | + | 0.290895i | ||||
\(58\) | 1.09599 | + | 6.91981i | 0.143911 | + | 0.908616i | ||||
\(59\) | −2.03647 | + | 6.26761i | −0.265126 | + | 0.815974i | 0.726538 | + | 0.687126i | \(0.241128\pi\) |
−0.991664 | + | 0.128848i | \(0.958872\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.23324 | + | 3.79553i | 0.157901 | + | 0.485968i | 0.998443 | − | 0.0557774i | \(-0.0177637\pi\) |
−0.840543 | + | 0.541745i | \(0.817764\pi\) | |||||||
\(62\) | 8.51329 | − | 4.33774i | 1.08119 | − | 0.550894i | ||||
\(63\) | −0.0943531 | + | 0.216419i | −0.0118874 | + | 0.0272663i | ||||
\(64\) | 0.951057 | − | 0.309017i | 0.118882 | − | 0.0386271i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.0573270 | − | 1.90682i | −0.00705647 | − | 0.234713i | ||||
\(67\) | 6.57696 | − | 1.04169i | 0.803504 | − | 0.127263i | 0.258844 | − | 0.965919i | \(-0.416659\pi\) |
0.544660 | + | 0.838657i | \(0.316659\pi\) | |||||||
\(68\) | 2.22097 | − | 2.22097i | 0.269332 | − | 0.269332i | ||||
\(69\) | 4.15326 | + | 1.21276i | 0.499993 | + | 0.146000i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.51096 | − | 10.3379i | −0.891387 | − | 1.22689i | −0.973135 | − | 0.230236i | \(-0.926050\pi\) |
0.0817481 | − | 0.996653i | \(-0.473950\pi\) | |||||||
\(72\) | −2.58637 | + | 1.52009i | −0.304807 | + | 0.179144i | ||||
\(73\) | 0.602914 | − | 1.18329i | 0.0705658 | − | 0.138493i | −0.853029 | − | 0.521864i | \(-0.825237\pi\) |
0.923595 | + | 0.383371i | \(0.125237\pi\) | |||||||
\(74\) | 10.3598 | 1.20430 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.40225 | −0.160849 | ||||||||
\(77\) | 0.0393507 | − | 0.0772302i | 0.00448443 | − | 0.00880119i | ||||
\(78\) | −1.64223 | − | 8.67298i | −0.185946 | − | 0.982022i | ||||
\(79\) | −5.85354 | − | 8.05671i | −0.658575 | − | 0.906451i | 0.340858 | − | 0.940115i | \(-0.389282\pi\) |
−0.999433 | + | 0.0336639i | \(0.989282\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.59415 | − | 6.12512i | 0.732684 | − | 0.680569i | ||||
\(82\) | 2.64098 | − | 2.64098i | 0.291647 | − | 0.291647i | ||||
\(83\) | −0.871279 | + | 0.137997i | −0.0956353 | + | 0.0151471i | −0.204069 | − | 0.978957i | \(-0.565417\pi\) |
0.108433 | + | 0.994104i | \(0.465417\pi\) | |||||||
\(84\) | −0.136247 | + | 0.00409615i | −0.0148657 | + | 0.000446927i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.35257 | − | 0.439477i | 0.145851 | − | 0.0473900i | ||||
\(87\) | 8.31892 | − | 8.83463i | 0.891882 | − | 0.947172i | ||||
\(88\) | 0.981353 | − | 0.500025i | 0.104613 | − | 0.0533028i | ||||
\(89\) | −1.01326 | − | 3.11850i | −0.107406 | − | 0.330560i | 0.882882 | − | 0.469595i | \(-0.155600\pi\) |
−0.990288 | + | 0.139035i | \(0.955600\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.123937 | − | 0.381439i | 0.0129921 | − | 0.0399856i | ||||
\(92\) | 0.390777 | + | 2.46727i | 0.0407413 | + | 0.257230i | ||||
\(93\) | −14.9646 | − | 7.06668i | −1.55175 | − | 0.732781i | ||||
\(94\) | −7.46957 | + | 10.2810i | −0.770427 | + | 1.06040i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.43122 | − | 0.975505i | −0.146073 | − | 0.0995621i | ||||
\(97\) | 1.62393 | − | 10.2531i | 0.164885 | − | 1.04104i | −0.756953 | − | 0.653469i | \(-0.773313\pi\) |
0.921838 | − | 0.387575i | \(-0.126687\pi\) | |||||||
\(98\) | 6.23153 | + | 3.17512i | 0.629479 | + | 0.320736i | ||||
\(99\) | −2.55165 | + | 2.09924i | −0.256450 | + | 0.210981i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.0377i | 1.39680i | 0.715708 | + | 0.698399i | \(0.246104\pi\) | ||||
−0.715708 | + | 0.698399i | \(0.753896\pi\) | |||||||
\(102\) | −5.39642 | − | 0.689188i | −0.534325 | − | 0.0682398i | ||||
\(103\) | 13.0416 | + | 2.06559i | 1.28503 | + | 0.203529i | 0.761324 | − | 0.648371i | \(-0.224549\pi\) |
0.523705 | + | 0.851900i | \(0.324549\pi\) | |||||||
\(104\) | 4.12301 | − | 2.99554i | 0.404295 | − | 0.293737i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.49256 | + | 3.99058i | 0.533484 | + | 0.387599i | ||||
\(107\) | −13.7619 | − | 13.7619i | −1.33041 | − | 1.33041i | −0.904999 | − | 0.425413i | \(-0.860129\pi\) |
−0.425413 | − | 0.904999i | \(-0.639871\pi\) | |||||||
\(108\) | 4.82341 | + | 1.93254i | 0.464133 | + | 0.185958i | ||||
\(109\) | −11.7044 | − | 3.80299i | −1.12108 | − | 0.364260i | −0.310898 | − | 0.950443i | \(-0.600630\pi\) |
−0.810178 | + | 0.586183i | \(0.800630\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.9785 | − | 14.1933i | −1.04204 | − | 1.34716i | ||||
\(112\) | −0.0357280 | − | 0.0701201i | −0.00337598 | − | 0.00662572i | ||||
\(113\) | −3.46581 | − | 6.80204i | −0.326036 | − | 0.639882i | 0.668565 | − | 0.743654i | \(-0.266909\pi\) |
−0.994601 | + | 0.103771i | \(0.966909\pi\) | |||||||
\(114\) | 1.48600 | + | 1.92113i | 0.139177 | + | 0.179930i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.66317 | + | 2.16499i | 0.618660 | + | 0.201015i | ||||
\(117\) | −10.1420 | + | 11.4409i | −0.937624 | + | 1.05771i | ||||
\(118\) | 4.65995 | + | 4.65995i | 0.428983 | + | 0.428983i | ||||
\(119\) | −0.199976 | − | 0.145291i | −0.0183317 | − | 0.0133188i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.91779 | + | 5.75261i | −0.719799 | + | 0.522964i | ||||
\(122\) | 3.94172 | + | 0.624308i | 0.356867 | + | 0.0565222i | ||||
\(123\) | −6.41692 | − | 0.819518i | −0.578594 | − | 0.0738935i | ||||
\(124\) | − | 9.55469i | − | 0.858037i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.149996 | + | 0.182322i | 0.0133627 | + | 0.0162425i | ||||
\(127\) | −2.87091 | − | 1.46280i | −0.254752 | − | 0.129803i | 0.321952 | − | 0.946756i | \(-0.395661\pi\) |
−0.576703 | + | 0.816954i | \(0.695661\pi\) | |||||||
\(128\) | 0.156434 | − | 0.987688i | 0.0138270 | − | 0.0873001i | ||||
\(129\) | −2.03545 | − | 1.38734i | −0.179211 | − | 0.122149i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.12598 | − | 4.30255i | 0.273118 | − | 0.375915i | −0.650321 | − | 0.759660i | \(-0.725366\pi\) |
0.923439 | + | 0.383744i | \(0.125366\pi\) | |||||||
\(132\) | −1.72501 | − | 0.814598i | −0.150143 | − | 0.0709017i | ||||
\(133\) | 0.0172632 | + | 0.108995i | 0.00149690 | + | 0.00945109i | ||||
\(134\) | 2.05773 | − | 6.33303i | 0.177761 | − | 0.547091i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.970601 | − | 2.98720i | −0.0832283 | − | 0.256150i | ||||
\(137\) | 10.2341 | − | 5.21451i | 0.874354 | − | 0.445506i | 0.0415907 | − | 0.999135i | \(-0.486757\pi\) |
0.832763 | + | 0.553629i | \(0.186757\pi\) | |||||||
\(138\) | 2.96612 | − | 3.15000i | 0.252493 | − | 0.268146i | ||||
\(139\) | −10.3684 | + | 3.36891i | −0.879440 | + | 0.285747i | −0.713725 | − | 0.700426i | \(-0.752993\pi\) |
−0.165715 | + | 0.986174i | \(0.552993\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 22.0009 | − | 0.661442i | 1.85281 | − | 0.0557034i | ||||
\(142\) | −12.6211 | + | 1.99898i | −1.05914 | + | 0.167751i | ||||
\(143\) | 3.96905 | − | 3.96905i | 0.331909 | − | 0.331909i | ||||
\(144\) | 0.180223 | + | 2.99458i | 0.0150186 | + | 0.249548i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.780598 | − | 1.07440i | −0.0646028 | − | 0.0889181i | ||||
\(147\) | −2.25367 | − | 11.9021i | −0.185880 | − | 0.981672i | ||||
\(148\) | 4.70325 | − | 9.23065i | 0.386605 | − | 0.758755i | ||||
\(149\) | −14.3679 | −1.17707 | −0.588534 | − | 0.808472i | \(-0.700295\pi\) | ||||
−0.588534 | + | 0.808472i | \(0.700295\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.326435 | −0.0265649 | −0.0132824 | − | 0.999912i | \(-0.504228\pi\) | ||||
−0.0132824 | + | 0.999912i | \(0.504228\pi\) | |||||||
\(152\) | −0.636609 | + | 1.24942i | −0.0516358 | + | 0.101341i | ||||
\(153\) | 4.77450 | + | 8.12361i | 0.385995 | + | 0.656755i | ||||
\(154\) | −0.0509477 | − | 0.0701235i | −0.00410548 | − | 0.00565071i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −8.47324 | − | 2.47421i | −0.678402 | − | 0.198096i | ||||
\(157\) | 3.47556 | − | 3.47556i | 0.277380 | − | 0.277380i | −0.554682 | − | 0.832062i | \(-0.687160\pi\) |
0.832062 | + | 0.554682i | \(0.187160\pi\) | |||||||
\(158\) | −9.83604 | + | 1.55788i | −0.782513 | + | 0.123938i | ||||
\(159\) | −0.353372 | − | 11.7539i | −0.0280242 | − | 0.932144i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.186967 | − | 0.0607491i | 0.0147350 | − | 0.00478770i | ||||
\(162\) | −2.46384 | − | 8.65618i | −0.193578 | − | 0.680094i | ||||
\(163\) | −1.36590 | + | 0.695961i | −0.106986 | + | 0.0545119i | −0.506664 | − | 0.862143i | \(-0.669122\pi\) |
0.399679 | + | 0.916655i | \(0.369122\pi\) | |||||||
\(164\) | −1.15415 | − | 3.55210i | −0.0901239 | − | 0.277373i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.272596 | + | 0.838964i | −0.0211576 | + | 0.0651163i | ||||
\(167\) | 3.50144 | + | 22.1072i | 0.270949 | + | 1.71071i | 0.629336 | + | 0.777133i | \(0.283327\pi\) |
−0.358387 | + | 0.933573i | \(0.616673\pi\) | |||||||
\(168\) | −0.0582050 | + | 0.123256i | −0.00449061 | + | 0.00950943i | ||||
\(169\) | 7.62505 | − | 10.4950i | 0.586542 | − | 0.807306i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.05726 | − | 4.07173i | 0.0808509 | − | 0.311373i | ||||
\(172\) | 0.222477 | − | 1.40467i | 0.0169637 | − | 0.107105i | ||||
\(173\) | 12.6292 | + | 6.43491i | 0.960182 | + | 0.489237i | 0.862542 | − | 0.505985i | \(-0.168871\pi\) |
0.0976395 | + | 0.995222i | \(0.468871\pi\) | |||||||
\(174\) | −4.09500 | − | 11.4230i | −0.310441 | − | 0.865979i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 1.10140i | − | 0.0830211i | ||||||
\(177\) | 1.44602 | − | 11.3225i | 0.108690 | − | 0.851053i | ||||
\(178\) | −3.23861 | − | 0.512946i | −0.242744 | − | 0.0384469i | ||||
\(179\) | 12.2896 | − | 8.92889i | 0.918565 | − | 0.667377i | −0.0246011 | − | 0.999697i | \(-0.507832\pi\) |
0.943167 | + | 0.332320i | \(0.107832\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.30933 | − | 6.03708i | −0.617627 | − | 0.448733i | 0.234465 | − | 0.972125i | \(-0.424666\pi\) |
−0.852092 | + | 0.523392i | \(0.824666\pi\) | |||||||
\(182\) | −0.283598 | − | 0.283598i | −0.0210217 | − | 0.0210217i | ||||
\(183\) | −3.32181 | − | 6.06188i | −0.245556 | − | 0.448107i | ||||
\(184\) | 2.37576 | + | 0.771931i | 0.175143 | + | 0.0569075i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −13.0902 | + | 10.1253i | −0.959823 | + | 0.742425i | ||||
\(187\) | −1.57054 | − | 3.08236i | −0.114849 | − | 0.225405i | ||||
\(188\) | 5.76930 | + | 11.3229i | 0.420770 | + | 0.825807i | ||||
\(189\) | 0.0908325 | − | 0.398709i | 0.00660709 | − | 0.0290018i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.3303 | − | 3.35652i | −0.747475 | − | 0.242869i | −0.0895805 | − | 0.995980i | \(-0.528553\pi\) |
−0.657894 | + | 0.753110i | \(0.728553\pi\) | |||||||
\(192\) | −1.51894 | + | 0.832356i | −0.109620 | + | 0.0600701i | ||||
\(193\) | 13.7241 | + | 13.7241i | 0.987880 | + | 0.987880i | 0.999927 | − | 0.0120476i | \(-0.00383498\pi\) |
−0.0120476 | + | 0.999927i | \(0.503835\pi\) | |||||||
\(194\) | −8.39833 | − | 6.10174i | −0.602965 | − | 0.438080i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.65811 | − | 4.11086i | 0.404151 | − | 0.293633i | ||||
\(197\) | 12.0795 | + | 1.91320i | 0.860625 | + | 0.136310i | 0.571120 | − | 0.820867i | \(-0.306509\pi\) |
0.289506 | + | 0.957176i | \(0.406509\pi\) | |||||||
\(198\) | 0.712010 | + | 3.22657i | 0.0506003 | + | 0.229302i | ||||
\(199\) | 15.9356i | 1.12965i | 0.825212 | + | 0.564823i | \(0.191056\pi\) | ||||
−0.825212 | + | 0.564823i | \(0.808944\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.8571 | + | 3.89211i | −0.765799 | + | 0.274528i | ||||
\(202\) | 12.5076 | + | 6.37296i | 0.880034 | + | 0.448400i | ||||
\(203\) | 0.0862519 | − | 0.544573i | 0.00605369 | − | 0.0382215i | ||||
\(204\) | −3.06399 | + | 4.49536i | −0.214522 | + | 0.314738i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.76123 | − | 10.6824i | 0.540750 | − | 0.744279i | ||||
\(207\) | −7.45886 | − | 0.725556i | −0.518427 | − | 0.0504296i | ||||
\(208\) | −0.797241 | − | 5.03358i | −0.0552787 | − | 0.349016i | ||||
\(209\) | −0.477258 | + | 1.46885i | −0.0330126 | + | 0.101602i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.41758 | − | 10.5182i | −0.235276 | − | 0.724104i | −0.997085 | − | 0.0763026i | \(-0.975689\pi\) |
0.761809 | − | 0.647802i | \(-0.224311\pi\) | |||||||
\(212\) | 6.04920 | − | 3.08222i | 0.415461 | − | 0.211688i | ||||
\(213\) | 16.1135 | + | 15.1729i | 1.10408 | + | 1.03963i | ||||
\(214\) | −18.5097 | + | 6.01417i | −1.26530 | + | 0.411120i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.91169 | − | 3.42034i | 0.266157 | − | 0.232724i | ||||
\(217\) | −0.742674 | + | 0.117628i | −0.0504160 | + | 0.00798511i | ||||
\(218\) | −8.70216 | + | 8.70216i | −0.589385 | + | 0.589385i | ||||
\(219\) | −0.644746 | + | 2.20801i | −0.0435679 | + | 0.149204i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.40879 | − | 12.9501i | −0.632904 | − | 0.871117i | ||||
\(222\) | −17.6304 | + | 3.33833i | −1.18328 | + | 0.224054i | ||||
\(223\) | 2.49393 | − | 4.89460i | 0.167006 | − | 0.327767i | −0.792302 | − | 0.610129i | \(-0.791118\pi\) |
0.959308 | + | 0.282362i | \(0.0911178\pi\) | |||||||
\(224\) | −0.0786976 | −0.00525820 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.63411 | −0.507814 | ||||||||
\(227\) | −3.07043 | + | 6.02606i | −0.203792 | + | 0.399964i | −0.970170 | − | 0.242426i | \(-0.922057\pi\) |
0.766378 | + | 0.642390i | \(0.222057\pi\) | |||||||
\(228\) | 2.38637 | − | 0.451860i | 0.158041 | − | 0.0299251i | ||||
\(229\) | 1.78525 | + | 2.45719i | 0.117973 | + | 0.162376i | 0.863919 | − | 0.503630i | \(-0.168003\pi\) |
−0.745947 | + | 0.666006i | \(0.768003\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.0420810 | + | 0.144111i | −0.00276873 | + | 0.00948184i | ||||
\(232\) | 4.95404 | − | 4.95404i | 0.325249 | − | 0.325249i | ||||
\(233\) | −1.36565 | + | 0.216297i | −0.0894666 | + | 0.0141701i | −0.201007 | − | 0.979590i | \(-0.564421\pi\) |
0.111541 | + | 0.993760i | \(0.464421\pi\) | |||||||
\(234\) | 5.58954 | + | 14.2306i | 0.365400 | + | 0.930283i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.26761 | − | 2.03647i | 0.407987 | − | 0.132563i | ||||
\(237\) | 12.5578 | + | 11.8248i | 0.815717 | + | 0.768101i | ||||
\(238\) | −0.220242 | + | 0.112219i | −0.0142762 | + | 0.00727408i | ||||
\(239\) | 3.51376 | + | 10.8143i | 0.227287 | + | 0.699516i | 0.998051 | + | 0.0623963i | \(0.0198743\pi\) |
−0.770765 | + | 0.637120i | \(0.780126\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.72661 | + | 8.39163i | −0.175636 | + | 0.540552i | −0.999662 | − | 0.0259998i | \(-0.991723\pi\) |
0.824026 | + | 0.566552i | \(0.191723\pi\) | |||||||
\(242\) | 1.53101 | + | 9.66643i | 0.0984172 | + | 0.621382i | ||||
\(243\) | −9.24826 | + | 12.5487i | −0.593276 | + | 0.804999i | ||||
\(244\) | 2.34577 | − | 3.22867i | 0.150172 | − | 0.206695i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.64342 | + | 5.34547i | −0.232296 | + | 0.340814i | ||||
\(247\) | −1.11793 | + | 7.05835i | −0.0711323 | + | 0.449112i | ||||
\(248\) | −8.51329 | − | 4.33774i | −0.540595 | − | 0.275447i | ||||
\(249\) | 1.43828 | − | 0.515604i | 0.0911475 | − | 0.0326751i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.6104i | 0.922197i | 0.887349 | + | 0.461099i | \(0.152545\pi\) | ||||
−0.887349 | + | 0.461099i | \(0.847455\pi\) | |||||||
\(252\) | 0.230546 | − | 0.0508748i | 0.0145230 | − | 0.00320481i | ||||
\(253\) | 2.71745 | + | 0.430401i | 0.170844 | + | 0.0270591i | ||||
\(254\) | −2.60673 | + | 1.89390i | −0.163561 | + | 0.118834i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.809017 | − | 0.587785i | −0.0505636 | − | 0.0367366i | ||||
\(257\) | −1.57229 | − | 1.57229i | −0.0980767 | − | 0.0980767i | 0.656366 | − | 0.754443i | \(-0.272093\pi\) |
−0.754443 | + | 0.656366i | \(0.772093\pi\) | |||||||
\(258\) | −2.16020 | + | 1.18376i | −0.134488 | + | 0.0736975i | ||||
\(259\) | −0.775389 | − | 0.251939i | −0.0481803 | − | 0.0156547i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.3104 | + | 17.7155i | −0.700095 | + | 1.09656i | ||||
\(262\) | −2.41443 | − | 4.73859i | −0.149164 | − | 0.292751i | ||||
\(263\) | −8.79695 | − | 17.2650i | −0.542443 | − | 1.06460i | −0.985747 | − | 0.168233i | \(-0.946194\pi\) |
0.443304 | − | 0.896371i | \(-0.353806\pi\) | |||||||
\(264\) | −1.50895 | + | 1.16718i | −0.0928695 | + | 0.0718348i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.104953 | + | 0.0341012i | 0.00643507 | + | 0.00209088i | ||||
\(267\) | 2.72928 | + | 4.98058i | 0.167029 | + | 0.304807i | ||||
\(268\) | −4.70859 | − | 4.70859i | −0.287623 | − | 0.287623i | ||||
\(269\) | −4.44596 | − | 3.23018i | −0.271075 | − | 0.196948i | 0.443940 | − | 0.896056i | \(-0.353580\pi\) |
−0.715015 | + | 0.699109i | \(0.753580\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.02194 | − | 4.37520i | 0.365807 | − | 0.265774i | −0.389663 | − | 0.920957i | \(-0.627409\pi\) |
0.755470 | + | 0.655183i | \(0.227409\pi\) | |||||||
\(272\) | −3.10226 | − | 0.491350i | −0.188102 | − | 0.0297924i | ||||
\(273\) | −0.0880031 | + | 0.689074i | −0.00532619 | + | 0.0417047i | ||||
\(274\) | − | 11.4859i | − | 0.693891i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.46008 | − | 4.07290i | −0.0878863 | − | 0.245160i | ||||
\(277\) | −17.0144 | − | 8.66928i | −1.02230 | − | 0.520886i | −0.139293 | − | 0.990251i | \(-0.544483\pi\) |
−0.883004 | + | 0.469365i | \(0.844483\pi\) | |||||||
\(278\) | −1.70545 | + | 10.7678i | −0.102286 | + | 0.645810i | ||||
\(279\) | 27.7440 | + | 7.20400i | 1.66099 | + | 0.431292i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.827936 | − | 1.13956i | 0.0493905 | − | 0.0679802i | −0.783607 | − | 0.621256i | \(-0.786623\pi\) |
0.832998 | + | 0.553276i | \(0.186623\pi\) | |||||||
\(282\) | 9.39887 | − | 19.9033i | 0.559694 | − | 1.18522i | ||||
\(283\) | −1.49164 | − | 9.41786i | −0.0886689 | − | 0.559834i | −0.991528 | − | 0.129896i | \(-0.958536\pi\) |
0.902859 | − | 0.429937i | \(-0.141464\pi\) | |||||||
\(284\) | −3.94874 | + | 12.1530i | −0.234315 | + | 0.721147i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.73454 | − | 5.33836i | −0.102565 | − | 0.315664i | ||||
\(287\) | −0.261892 | + | 0.133440i | −0.0154590 | + | 0.00787674i | ||||
\(288\) | 2.75001 | + | 1.19893i | 0.162046 | + | 0.0706478i | ||||
\(289\) | 6.78537 | − | 2.20470i | 0.399139 | − | 0.129688i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.540319 | + | 17.9721i | 0.0316740 | + | 1.05355i | ||||
\(292\) | −1.31168 | + | 0.207750i | −0.0767604 | + | 0.0121577i | ||||
\(293\) | 22.0266 | − | 22.0266i | 1.28681 | − | 1.28681i | 0.350091 | − | 0.936716i | \(-0.386151\pi\) |
0.936716 | − | 0.350091i | \(-0.113849\pi\) | |||||||
\(294\) | −11.6280 | − | 3.39542i | −0.678161 | − | 0.198025i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.08934 | − | 8.38126i | −0.353936 | − | 0.487151i | ||||
\(297\) | 3.66597 | − | 4.39475i | 0.212721 | − | 0.255009i | ||||
\(298\) | −6.52291 | + | 12.8019i | −0.377862 | + | 0.741596i | ||||
\(299\) | 12.7307 | 0.736237 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.111922 | −0.00645107 | ||||||||
\(302\) | −0.148198 | + | 0.290856i | −0.00852785 | + | 0.0167369i | ||||
\(303\) | −4.52347 | − | 23.8894i | −0.259867 | − | 1.37241i | ||||
\(304\) | 0.824223 | + | 1.13445i | 0.0472724 | + | 0.0650649i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 9.40577 | − | 0.566067i | 0.537692 | − | 0.0323599i | ||||
\(307\) | −1.56450 | + | 1.56450i | −0.0892910 | + | 0.0892910i | −0.750341 | − | 0.661050i | \(-0.770111\pi\) |
0.661050 | + | 0.750341i | \(0.270111\pi\) | |||||||
\(308\) | −0.0856103 | + | 0.0135593i | −0.00487810 | + | 0.000772615i | ||||
\(309\) | −22.8600 | + | 0.687269i | −1.30046 | + | 0.0390974i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.9644 | − | 4.21240i | 0.735145 | − | 0.238863i | 0.0825681 | − | 0.996585i | \(-0.473688\pi\) |
0.652577 | + | 0.757722i | \(0.273688\pi\) | |||||||
\(312\) | −6.05131 | + | 6.42644i | −0.342588 | + | 0.363826i | ||||
\(313\) | −17.0167 | + | 8.67043i | −0.961839 | + | 0.490082i | −0.863101 | − | 0.505032i | \(-0.831481\pi\) |
−0.0987386 | + | 0.995113i | \(0.531481\pi\) | |||||||
\(314\) | −1.51888 | − | 4.67462i | −0.0857152 | − | 0.263804i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.07739 | + | 9.47123i | −0.173117 | + | 0.532798i | ||||
\(317\) | 1.42135 | + | 8.97408i | 0.0798312 | + | 0.504034i | 0.994911 | + | 0.100761i | \(0.0321277\pi\) |
−0.915079 | + | 0.403274i | \(0.867872\pi\) | |||||||
\(318\) | −10.6332 | − | 5.02130i | −0.596281 | − | 0.281580i | ||||
\(319\) | 4.53563 | − | 6.24276i | 0.253947 | − | 0.349528i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 27.8548 | + | 18.9855i | 1.55470 | + | 1.05967i | ||||
\(322\) | 0.0307532 | − | 0.194168i | 0.00171381 | − | 0.0108206i | ||||
\(323\) | 3.92433 | + | 1.99954i | 0.218355 | + | 0.111258i | ||||
\(324\) | −8.83128 | − | 1.73453i | −0.490626 | − | 0.0963625i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.53299i | 0.0849043i | ||||||||
\(327\) | 21.1441 | + | 2.70036i | 1.16927 | + | 0.149330i | ||||
\(328\) | −3.68892 | − | 0.584268i | −0.203687 | − | 0.0322608i | ||||
\(329\) | 0.809088 | − | 0.587837i | 0.0446065 | − | 0.0324085i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.94485 | + | 6.49882i | 0.491654 | + | 0.357207i | 0.805820 | − | 0.592161i | \(-0.201725\pi\) |
−0.314166 | + | 0.949368i | \(0.601725\pi\) | |||||||
\(332\) | 0.623767 | + | 0.623767i | 0.0342336 | + | 0.0342336i | ||||
\(333\) | 23.2570 | + | 20.6166i | 1.27448 | + | 1.12978i | ||||
\(334\) | 21.2873 | + | 6.91666i | 1.16479 | + | 0.378463i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.0833977 | + | 0.107818i | 0.00454971 | + | 0.00588197i | ||||
\(337\) | 7.85531 | + | 15.4169i | 0.427906 | + | 0.839813i | 0.999810 | + | 0.0194923i | \(0.00620499\pi\) |
−0.571904 | + | 0.820321i | \(0.693795\pi\) | |||||||
\(338\) | −5.88940 | − | 11.5586i | −0.320341 | − | 0.628705i | ||||
\(339\) | 8.09004 | + | 10.4590i | 0.439391 | + | 0.568054i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.0085 | − | 3.25195i | −0.541989 | − | 0.176103i | ||||
\(342\) | −3.14795 | − | 2.79056i | −0.170222 | − | 0.150896i | ||||
\(343\) | −0.778722 | − | 0.778722i | −0.0420470 | − | 0.0420470i | ||||
\(344\) | −1.15057 | − | 0.835934i | −0.0620343 | − | 0.0450706i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.4671 | − | 8.33133i | 0.616475 | − | 0.447895i | ||||
\(347\) | −14.7693 | − | 2.33923i | −0.792857 | − | 0.125576i | −0.253148 | − | 0.967428i | \(-0.581466\pi\) |
−0.539709 | + | 0.841851i | \(0.681466\pi\) | |||||||
\(348\) | −12.0371 | − | 1.53728i | −0.645256 | − | 0.0824070i | ||||
\(349\) | 0.345103i | 0.0184729i | 0.999957 | + | 0.00923647i | \(0.00294010\pi\) | ||||
−0.999957 | + | 0.00923647i | \(0.997060\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.5730 | − | 22.7383i | 0.724473 | − | 1.21368i | ||||
\(352\) | −0.981353 | − | 0.500025i | −0.0523063 | − | 0.0266514i | ||||
\(353\) | 3.13409 | − | 19.7879i | 0.166811 | − | 1.05320i | −0.752190 | − | 0.658947i | \(-0.771002\pi\) |
0.919001 | − | 0.394256i | \(-0.128998\pi\) | |||||||
\(354\) | −9.43196 | − | 6.42874i | −0.501303 | − | 0.341683i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.92734 | + | 2.65275i | −0.102149 | + | 0.140596i | ||||
\(357\) | 0.387139 | + | 0.182818i | 0.0204896 | + | 0.00967574i | ||||
\(358\) | −2.37636 | − | 15.0037i | −0.125594 | − | 0.792971i | ||||
\(359\) | 5.66877 | − | 17.4467i | 0.299186 | − | 0.920800i | −0.682597 | − | 0.730795i | \(-0.739150\pi\) |
0.981783 | − | 0.190005i | \(-0.0608505\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.26370 | + | 16.2000i | 0.277037 | + | 0.852632i | ||||
\(362\) | −9.15143 | + | 4.66289i | −0.480989 | + | 0.245076i | ||||
\(363\) | 11.6209 | − | 12.3413i | 0.609937 | − | 0.647749i | ||||
\(364\) | −0.381439 | + | 0.123937i | −0.0199928 | + | 0.00649606i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −6.90925 | + | 0.207721i | −0.361152 | + | 0.0108578i | ||||
\(367\) | −0.0192492 | + | 0.00304877i | −0.00100480 | + | 0.000159144i | −0.156937 | − | 0.987609i | \(-0.550162\pi\) |
0.155932 | + | 0.987768i | \(0.450162\pi\) | |||||||
\(368\) | 1.76637 | − | 1.76637i | 0.0920783 | − | 0.0920783i | ||||
\(369\) | 11.1845 | − | 0.673114i | 0.582240 | − | 0.0350409i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.314049 | − | 0.432251i | −0.0163046 | − | 0.0224414i | ||||
\(372\) | 3.07889 | + | 16.2603i | 0.159633 | + | 0.843057i | ||||
\(373\) | −3.17602 | + | 6.23329i | −0.164448 | + | 0.322748i | −0.958495 | − | 0.285109i | \(-0.907970\pi\) |
0.794047 | + | 0.607856i | \(0.207970\pi\) | |||||||
\(374\) | −3.45942 | −0.178882 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12.7080 | 0.655364 | ||||||||
\(377\) | 16.2098 | − | 31.8136i | 0.834848 | − | 1.63848i | ||||
\(378\) | −0.314015 | − | 0.261942i | −0.0161512 | − | 0.0134729i | ||||
\(379\) | 7.15293 | + | 9.84516i | 0.367421 | + | 0.505712i | 0.952198 | − | 0.305483i | \(-0.0988178\pi\) |
−0.584776 | + | 0.811194i | \(0.698818\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.35711 | + | 1.56429i | 0.274453 | + | 0.0801412i | ||||
\(382\) | −7.68054 | + | 7.68054i | −0.392971 | + | 0.392971i | ||||
\(383\) | −0.936062 | + | 0.148258i | −0.0478305 | + | 0.00757561i | −0.180304 | − | 0.983611i | \(-0.557708\pi\) |
0.132473 | + | 0.991187i | \(0.457708\pi\) | |||||||
\(384\) | 0.0520493 | + | 1.73127i | 0.00265613 | + | 0.0883484i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 18.4588 | − | 5.99764i | 0.939530 | − | 0.305272i | ||||
\(387\) | 3.91100 | + | 1.70509i | 0.198807 | + | 0.0866748i | ||||
\(388\) | −9.24945 | + | 4.71283i | −0.469570 | + | 0.239258i | ||||
\(389\) | 6.14102 | + | 18.9001i | 0.311362 | + | 0.958273i | 0.977226 | + | 0.212200i | \(0.0680630\pi\) |
−0.665864 | + | 0.746073i | \(0.731937\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.42458 | − | 7.46210i | 0.122616 | − | 0.377374i | ||||
\(392\) | −1.09407 | − | 6.90770i | −0.0552590 | − | 0.348892i | ||||
\(393\) | −3.93339 | + | 8.32944i | −0.198413 | + | 0.420164i | ||||
\(394\) | 7.18863 | − | 9.89430i | 0.362158 | − | 0.498468i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.19814 | + | 0.830427i | 0.160713 | + | 0.0417305i | ||||
\(397\) | −4.21926 | + | 26.6394i | −0.211759 | + | 1.33699i | 0.621198 | + | 0.783654i | \(0.286646\pi\) |
−0.832957 | + | 0.553338i | \(0.813354\pi\) | |||||||
\(398\) | 14.1987 | + | 7.23462i | 0.711719 | + | 0.362639i | ||||
\(399\) | −0.0645011 | − | 0.179927i | −0.00322909 | − | 0.00900759i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 33.9394i | 1.69485i | 0.530912 | + | 0.847427i | \(0.321849\pi\) | ||||
−0.530912 | + | 0.847427i | \(0.678151\pi\) | |||||||
\(402\) | −1.46112 | + | 11.4407i | −0.0728739 | + | 0.570611i | ||||
\(403\) | −48.0943 | − | 7.61739i | −2.39575 | − | 0.379449i | ||||
\(404\) | 11.3567 | − | 8.25112i | 0.565017 | − | 0.410509i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.446060 | − | 0.324082i | −0.0221376 | − | 0.0160839i | ||||
\(407\) | −8.06828 | − | 8.06828i | −0.399930 | − | 0.399930i | ||||
\(408\) | 2.61437 | + | 4.77089i | 0.129431 | + | 0.236194i | ||||
\(409\) | 15.1218 | + | 4.91338i | 0.747726 | + | 0.242951i | 0.658002 | − | 0.753016i | \(-0.271402\pi\) |
0.0897236 | + | 0.995967i | \(0.471402\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.7361 | + | 12.1719i | −0.776205 | + | 0.600396i | ||||
\(412\) | −5.99458 | − | 11.7650i | −0.295332 | − | 0.579621i | ||||
\(413\) | −0.235453 | − | 0.462102i | −0.0115859 | − | 0.0227386i | ||||
\(414\) | −4.03273 | + | 6.31650i | −0.198198 | + | 0.310439i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.84689 | − | 1.57485i | −0.237638 | − | 0.0772134i | ||||
\(417\) | 16.5595 | − | 9.07436i | 0.810924 | − | 0.444373i | ||||
\(418\) | 1.09208 | + | 1.09208i | 0.0534155 | + | 0.0534155i | ||||
\(419\) | 22.2455 | + | 16.1623i | 1.08677 | + | 0.789582i | 0.978850 | − | 0.204578i | \(-0.0655823\pi\) |
0.107916 | + | 0.994160i | \(0.465582\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.8507 | − | 18.7816i | 1.25988 | − | 0.915359i | 0.261132 | − | 0.965303i | \(-0.415904\pi\) |
0.998752 | + | 0.0499438i | \(0.0159042\pi\) | |||||||
\(422\) | −10.9234 | − | 1.73009i | −0.531741 | − | 0.0842194i | ||||
\(423\) | −37.2283 | + | 8.21520i | −1.81010 | + | 0.399437i | ||||
\(424\) | − | 6.78917i | − | 0.329711i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 20.8346 | − | 7.46889i | 1.00944 | − | 0.361869i | ||||
\(427\) | −0.279839 | − | 0.142585i | −0.0135424 | − | 0.00690018i | ||||
\(428\) | −3.04457 | + | 19.2226i | −0.147165 | + | 0.929162i | ||||
\(429\) | −5.47559 | + | 8.03356i | −0.264364 | + | 0.387864i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.09101 | + | 7.00718i | −0.245225 | + | 0.337524i | −0.913832 | − | 0.406093i | \(-0.866891\pi\) |
0.668607 | + | 0.743616i | \(0.266891\pi\) | |||||||
\(432\) | −1.27167 | − | 5.03814i | −0.0611835 | − | 0.242398i | ||||
\(433\) | −1.68664 | − | 10.6490i | −0.0810548 | − | 0.511760i | −0.994495 | − | 0.104786i | \(-0.966584\pi\) |
0.913440 | − | 0.406974i | \(-0.133416\pi\) | |||||||
\(434\) | −0.232360 | + | 0.715129i | −0.0111536 | + | 0.0343273i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.80299 | + | 11.7044i | 0.182130 | + | 0.560538i | ||||
\(437\) | −3.12107 | + | 1.59026i | −0.149301 | + | 0.0760726i | ||||
\(438\) | 1.67464 | + | 1.57689i | 0.0800176 | + | 0.0753467i | ||||
\(439\) | 32.6251 | − | 10.6006i | 1.55711 | − | 0.505937i | 0.601078 | − | 0.799190i | \(-0.294738\pi\) |
0.956035 | + | 0.293253i | \(0.0947379\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.67066 | + | 19.5290i | 0.365269 | + | 0.929951i | ||||
\(442\) | −15.8101 | + | 2.50408i | −0.752011 | + | 0.119107i | ||||
\(443\) | −4.58214 | + | 4.58214i | −0.217704 | + | 0.217704i | −0.807530 | − | 0.589826i | \(-0.799196\pi\) |
0.589826 | + | 0.807530i | \(0.299196\pi\) | |||||||
\(444\) | −5.02958 | + | 17.2244i | −0.238693 | + | 0.817434i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.22891 | − | 4.44421i | −0.152893 | − | 0.210439i | ||||
\(447\) | 24.4515 | − | 4.62991i | 1.15652 | − | 0.218987i | ||||
\(448\) | −0.0357280 | + | 0.0701201i | −0.00168799 | + | 0.00331286i | ||||
\(449\) | −22.7460 | −1.07345 | −0.536726 | − | 0.843756i | \(-0.680339\pi\) | ||||
−0.536726 | + | 0.843756i | \(0.680339\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.11362 | −0.193703 | ||||||||
\(452\) | −3.46581 | + | 6.80204i | −0.163018 | + | 0.319941i | ||||
\(453\) | 0.555530 | − | 0.105190i | 0.0261011 | − | 0.00494225i | ||||
\(454\) | 3.97531 | + | 5.47155i | 0.186571 | + | 0.256792i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.680779 | − | 2.33141i | 0.0318804 | − | 0.109178i | ||||
\(457\) | 6.28077 | − | 6.28077i | 0.293802 | − | 0.293802i | −0.544778 | − | 0.838580i | \(-0.683386\pi\) |
0.838580 | + | 0.544778i | \(0.183386\pi\) | |||||||
\(458\) | 2.99986 | − | 0.475131i | 0.140174 | − | 0.0222014i | ||||
\(459\) | −10.7430 | − | 12.2863i | −0.501442 | − | 0.573477i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.3397 | + | 6.93369i | −0.993889 | + | 0.322934i | −0.760421 | − | 0.649430i | \(-0.775007\pi\) |
−0.233468 | + | 0.972364i | \(0.575007\pi\) | |||||||
\(462\) | 0.109300 | + | 0.102920i | 0.00508509 | + | 0.00478826i | ||||
\(463\) | 21.5722 | − | 10.9916i | 1.00255 | − | 0.510823i | 0.125944 | − | 0.992037i | \(-0.459804\pi\) |
0.876603 | + | 0.481214i | \(0.159804\pi\) | |||||||
\(464\) | −2.16499 | − | 6.66317i | −0.100507 | − | 0.309330i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.427269 | + | 1.31500i | −0.0197929 | + | 0.0609161i | ||||
\(467\) | −2.10730 | − | 13.3049i | −0.0975140 | − | 0.615679i | −0.987247 | − | 0.159197i | \(-0.949109\pi\) |
0.889733 | − | 0.456482i | \(-0.150891\pi\) | |||||||
\(468\) | 15.2171 | + | 1.48024i | 0.703413 | + | 0.0684240i | ||||
\(469\) | −0.308025 | + | 0.423960i | −0.0142233 | + | 0.0195766i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.79479 | + | 7.03472i | −0.220932 | + | 0.324143i | ||||
\(472\) | 1.03093 | − | 6.50902i | 0.0474523 | − | 0.299602i | ||||
\(473\) | −1.39566 | − | 0.711123i | −0.0641724 | − | 0.0326975i | ||||
\(474\) | 16.2371 | − | 5.82076i | 0.745793 | − | 0.267356i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.247184i | 0.0113296i | ||||||||
\(477\) | 4.38893 | + | 19.8890i | 0.200955 | + | 0.910656i | ||||
\(478\) | 11.2308 | + | 1.77878i | 0.513684 | + | 0.0813596i | ||||
\(479\) | −13.9808 | + | 10.1576i | −0.638797 | + | 0.464113i | −0.859437 | − | 0.511242i | \(-0.829186\pi\) |
0.220639 | + | 0.975355i | \(0.429186\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −42.7136 | − | 31.0332i | −1.94757 | − | 1.41499i | ||||
\(482\) | 6.23914 | + | 6.23914i | 0.284185 | + | 0.284185i | ||||
\(483\) | −0.298606 | + | 0.163631i | −0.0135871 | + | 0.00744549i | ||||
\(484\) | 9.30791 | + | 3.02432i | 0.423087 | + | 0.137469i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 6.98235 | + | 13.9372i | 0.316726 | + | 0.632206i | ||||
\(487\) | 1.64469 | + | 3.22789i | 0.0745281 | + | 0.146270i | 0.925264 | − | 0.379324i | \(-0.123843\pi\) |
−0.850736 | + | 0.525593i | \(0.823843\pi\) | |||||||
\(488\) | −1.81181 | − | 3.55588i | −0.0820169 | − | 0.160967i | ||||
\(489\) | 2.10024 | − | 1.62454i | 0.0949761 | − | 0.0734643i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.48953 | − | 1.78366i | −0.247739 | − | 0.0804953i | 0.182515 | − | 0.983203i | \(-0.441576\pi\) |
−0.430254 | + | 0.902708i | \(0.641576\pi\) | |||||||
\(492\) | 3.10877 | + | 5.67310i | 0.140154 | + | 0.255763i | ||||
\(493\) | −15.5603 | − | 15.5603i | −0.700800 | − | 0.700800i | ||||
\(494\) | 5.78150 | + | 4.20051i | 0.260122 | + | 0.188990i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.72991 | + | 5.61611i | −0.347083 | + | 0.252171i | ||||
\(497\) | 0.993249 | + | 0.157315i | 0.0445533 | + | 0.00705655i | ||||
\(498\) | 0.193560 | − | 1.51560i | 0.00867365 | − | 0.0679157i | ||||
\(499\) | 28.5582i | 1.27844i | 0.769024 | + | 0.639220i | \(0.220743\pi\) | ||||
−0.769024 | + | 0.639220i | \(0.779257\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.0826 | − | 36.4940i | −0.584486 | − | 1.63043i | ||||
\(502\) | 13.0179 | + | 6.63296i | 0.581018 | + | 0.296044i | ||||
\(503\) | −3.76856 | + | 23.7938i | −0.168032 | + | 1.06091i | 0.749138 | + | 0.662414i | \(0.230468\pi\) |
−0.917170 | + | 0.398497i | \(0.869532\pi\) | |||||||
\(504\) | 0.0593360 | − | 0.228515i | 0.00264304 | − | 0.0101789i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.61718 | − | 2.22586i | 0.0718926 | − | 0.0989517i | ||||
\(507\) | −9.59451 | + | 20.3176i | −0.426107 | + | 0.902335i | ||||
\(508\) | 0.504047 | + | 3.18243i | 0.0223635 | + | 0.141197i | ||||
\(509\) | 1.35722 | − | 4.17708i | 0.0601576 | − | 0.185146i | −0.916462 | − | 0.400123i | \(-0.868968\pi\) |
0.976619 | + | 0.214977i | \(0.0689675\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.0322963 | + | 0.0993978i | 0.00142870 | + | 0.00439710i | ||||
\(512\) | −0.891007 | + | 0.453990i | −0.0393773 | + | 0.0200637i | ||||
\(513\) | −0.487193 | + | 7.27001i | −0.0215101 | + | 0.320979i | ||||
\(514\) | −2.11472 | + | 0.687116i | −0.0932765 | + | 0.0303074i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.0740233 | + | 2.46217i | 0.00325869 | + | 0.108391i | ||||
\(517\) | 13.8242 | − | 2.18954i | 0.607989 | − | 0.0962960i | ||||
\(518\) | −0.576498 | + | 0.576498i | −0.0253299 | + | 0.0253299i | ||||
\(519\) | −23.5661 | − | 6.88138i | −1.03444 | − | 0.302059i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.85216 | + | 5.30205i | 0.168766 | + | 0.232287i | 0.885020 | − | 0.465553i | \(-0.154145\pi\) |
−0.716254 | + | 0.697840i | \(0.754145\pi\) | |||||||
\(522\) | 10.6499 | + | 18.1203i | 0.466132 | + | 0.793104i | ||||
\(523\) | 4.06078 | − | 7.96973i | 0.177566 | − | 0.348492i | −0.785020 | − | 0.619471i | \(-0.787347\pi\) |
0.962585 | + | 0.270979i | \(0.0873473\pi\) | |||||||
\(524\) | −5.31824 | −0.232328 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.3769 | −0.844875 | ||||||||
\(527\) | −13.6245 | + | 26.7397i | −0.593494 | + | 1.16480i | ||||
\(528\) | 0.354913 | + | 1.87437i | 0.0154456 | + | 0.0815716i | ||||
\(529\) | −9.85121 | − | 13.5590i | −0.428314 | − | 0.589523i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.18770 | + | 19.7348i | 0.0515416 | + | 0.856416i | ||||
\(532\) | 0.0780320 | − | 0.0780320i | 0.00338312 | − | 0.00338312i | ||||
\(533\) | −18.7999 | + | 2.97762i | −0.814315 | + | 0.128975i | ||||
\(534\) | 5.67680 | − | 0.170669i | 0.245659 | − | 0.00738556i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.33303 | + | 2.05773i | −0.273545 | + | 0.0888803i | ||||
\(537\) | −18.0373 | + | 19.1555i | −0.778367 | + | 0.826619i | ||||
\(538\) | −4.89653 | + | 2.49491i | −0.211105 | + | 0.107563i | ||||
\(539\) | −2.38035 | − | 7.32596i | −0.102529 | − | 0.315551i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.98127 | − | 15.3308i | 0.214161 | − | 0.659121i | −0.785051 | − | 0.619432i | \(-0.787363\pi\) |
0.999212 | − | 0.0396896i | \(-0.0126369\pi\) | |||||||
\(542\) | −1.16442 | − | 7.35189i | −0.0500163 | − | 0.315791i | ||||
\(543\) | 16.0863 | + | 7.59639i | 0.690329 | + | 0.325992i | ||||
\(544\) | −1.84619 | + | 2.54107i | −0.0791548 | + | 0.108947i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.574017 | + | 0.391244i | 0.0245657 | + | 0.0167437i | ||||
\(547\) | 3.70025 | − | 23.3625i | 0.158211 | − | 0.998907i | −0.772994 | − | 0.634413i | \(-0.781242\pi\) |
0.931206 | − | 0.364494i | \(-0.118758\pi\) | |||||||
\(548\) | −10.2341 | − | 5.21451i | −0.437177 | − | 0.222753i | ||||
\(549\) | 7.60647 | + | 9.24576i | 0.324636 | + | 0.394599i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.82428i | 0.418528i | ||||||||
\(552\) | −4.29184 | − | 0.548120i | −0.182673 | − | 0.0233295i | ||||
\(553\) | 0.774072 | + | 0.122601i | 0.0329169 | + | 0.00521353i | ||||
\(554\) | −15.4488 | + | 11.2242i | −0.656355 | + | 0.476870i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.81992 | + | 6.40805i | 0.374048 | + | 0.271762i | ||||
\(557\) | 27.5142 | + | 27.5142i | 1.16581 | + | 1.16581i | 0.983181 | + | 0.182634i | \(0.0584623\pi\) |
0.182634 | + | 0.983181i | \(0.441538\pi\) | |||||||
\(558\) | 19.0143 | − | 21.4496i | 0.804941 | − | 0.908033i | ||||
\(559\) | −6.89314 | − | 2.23972i | −0.291549 | − | 0.0947299i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.66602 | + | 4.73951i | 0.154780 | + | 0.200102i | ||||
\(562\) | −0.639477 | − | 1.25504i | −0.0269747 | − | 0.0529408i | ||||
\(563\) | 11.3007 | + | 22.1789i | 0.476267 | + | 0.934728i | 0.996727 | + | 0.0808412i | \(0.0257607\pi\) |
−0.520460 | + | 0.853886i | \(0.674239\pi\) | |||||||
\(564\) | −13.4669 | − | 17.4103i | −0.567061 | − | 0.733108i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −9.06857 | − | 2.94656i | −0.381180 | − | 0.123853i | ||||
\(567\) | −0.0261004 | + | 0.707797i | −0.00109611 | + | 0.0297247i | ||||
\(568\) | 9.03570 | + | 9.03570i | 0.379129 | + | 0.379129i | ||||
\(569\) | −25.9540 | − | 18.8567i | −1.08805 | − | 0.790515i | −0.108981 | − | 0.994044i | \(-0.534759\pi\) |
−0.979069 | + | 0.203529i | \(0.934759\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.1170 | + | 24.7874i | −1.42775 | + | 1.03732i | −0.437322 | + | 0.899305i | \(0.644073\pi\) |
−0.990430 | + | 0.138017i | \(0.955927\pi\) | |||||||
\(572\) | −5.54398 | − | 0.878080i | −0.231805 | − | 0.0367144i | ||||
\(573\) | 18.6618 | + | 2.38334i | 0.779609 | + | 0.0995655i | ||||
\(574\) | 0.293928i | 0.0122683i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.31674 | − | 1.90597i | 0.0965306 | − | 0.0794156i | ||||
\(577\) | −19.6556 | − | 10.0150i | −0.818274 | − | 0.416931i | −0.00583873 | − | 0.999983i | \(-0.501859\pi\) |
−0.812435 | + | 0.583052i | \(0.801859\pi\) | |||||||
\(578\) | 1.11609 | − | 7.04672i | 0.0464233 | − | 0.293105i | ||||
\(579\) | −27.7782 | − | 18.9333i | −1.15442 | − | 0.786843i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.0408054 | − | 0.0561638i | 0.00169289 | − | 0.00233007i | ||||
\(582\) | 16.2586 | + | 7.67775i | 0.673940 | + | 0.318253i | ||||
\(583\) | −1.16975 | − | 7.38553i | −0.0484462 | − | 0.305877i | ||||
\(584\) | −0.410385 | + | 1.26303i | −0.0169818 | + | 0.0522647i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.62597 | − | 29.6257i | −0.397645 | − | 1.22383i | ||||
\(587\) | −11.4960 | + | 5.85750i | −0.474490 | + | 0.241765i | −0.674846 | − | 0.737958i | \(-0.735790\pi\) |
0.200356 | + | 0.979723i | \(0.435790\pi\) | |||||||
\(588\) | −8.30436 | + | 8.81916i | −0.342466 | + | 0.363696i | ||||
\(589\) | 12.7423 | − | 4.14024i | 0.525039 | − | 0.170596i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −21.1735 | + | 0.636564i | −0.870960 | + | 0.0261848i | ||||
\(592\) | −10.2323 | + | 1.62063i | −0.420543 | + | 0.0666075i | ||||
\(593\) | −3.75033 | + | 3.75033i | −0.154007 | + | 0.154007i | −0.779905 | − | 0.625898i | \(-0.784733\pi\) |
0.625898 | + | 0.779905i | \(0.284733\pi\) | |||||||
\(594\) | −2.25143 | − | 5.26158i | −0.0923774 | − | 0.215885i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.44527 | + | 11.6239i | 0.345932 | + | 0.476134i | ||||
\(597\) | −5.13507 | − | 27.1194i | −0.210165 | − | 1.10992i | ||||
\(598\) | 5.77963 | − | 11.3432i | 0.236347 | − | 0.463856i | ||||
\(599\) | 29.8620 | 1.22013 | 0.610065 | − | 0.792352i | \(-0.291143\pi\) | ||||
0.610065 | + | 0.792352i | \(0.291143\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.0008 | 0.775058 | 0.387529 | − | 0.921858i | \(-0.373329\pi\) | ||||
0.387529 | + | 0.921858i | \(0.373329\pi\) | |||||||
\(602\) | −0.0508115 | + | 0.0997231i | −0.00207092 | + | 0.00406441i | ||||
\(603\) | 17.2225 | − | 10.1222i | 0.701355 | − | 0.412208i | ||||
\(604\) | 0.191874 | + | 0.264091i | 0.00780722 | + | 0.0107457i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −23.3393 | − | 6.81513i | −0.948092 | − | 0.276846i | ||||
\(607\) | −29.8007 | + | 29.8007i | −1.20957 | + | 1.20957i | −0.238406 | + | 0.971165i | \(0.576625\pi\) |
−0.971165 | + | 0.238406i | \(0.923375\pi\) | |||||||
\(608\) | 1.38499 | − | 0.219361i | 0.0561687 | − | 0.00889625i | ||||
\(609\) | 0.0286980 | + | 0.954554i | 0.00116290 | + | 0.0386805i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 61.5942 | − | 20.0132i | 2.49184 | − | 0.809646i | ||||
\(612\) | 3.76576 | − | 8.63759i | 0.152222 | − | 0.349154i | ||||
\(613\) | 1.17929 | − | 0.600877i | 0.0476310 | − | 0.0242692i | −0.430013 | − | 0.902823i | \(-0.641491\pi\) |
0.477644 | + | 0.878554i | \(0.341491\pi\) | |||||||
\(614\) | 0.683714 | + | 2.10425i | 0.0275924 | + | 0.0849208i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.0267848 | + | 0.0824351i | −0.00107919 | + | 0.00332141i | ||||
\(617\) | −6.57400 | − | 41.5066i | −0.264659 | − | 1.67099i | −0.659087 | − | 0.752067i | \(-0.729057\pi\) |
0.394428 | − | 0.918927i | \(-0.370943\pi\) | |||||||
\(618\) | −9.76586 | + | 20.6804i | −0.392841 | + | 0.831889i | ||||
\(619\) | 9.51877 | − | 13.1015i | 0.382592 | − | 0.526592i | −0.573677 | − | 0.819082i | \(-0.694484\pi\) |
0.956269 | + | 0.292489i | \(0.0944836\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.9274 | − | 1.16877i | 0.518758 | − | 0.0469013i | ||||
\(622\) | 2.13245 | − | 13.4638i | 0.0855036 | − | 0.539848i | ||||
\(623\) | 0.229923 | + | 0.117151i | 0.00921165 | + | 0.00469357i | ||||
\(624\) | 2.97877 | + | 8.30930i | 0.119246 | + | 0.332638i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 19.0983i | 0.763320i | ||||||||
\(627\) | 0.338883 | − | 2.65349i | 0.0135337 | − | 0.105970i | ||||
\(628\) | −4.85468 | − | 0.768905i | −0.193723 | − | 0.0306827i | ||||
\(629\) | −26.3249 | + | 19.1262i | −1.04964 | + | 0.762611i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.33690 | − | 6.78365i | −0.371696 | − | 0.270053i | 0.386218 | − | 0.922408i | \(-0.373781\pi\) |
−0.757914 | + | 0.652355i | \(0.773781\pi\) | |||||||
\(632\) | 7.04182 | + | 7.04182i | 0.280109 | + | 0.280109i | ||||
\(633\) | 9.20545 | + | 16.7988i | 0.365884 | + | 0.667691i | ||||
\(634\) | 8.64124 | + | 2.80771i | 0.343188 | + | 0.111508i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −9.30139 | + | 7.19464i | −0.368824 | + | 0.285286i | ||||
\(637\) | −16.1814 | − | 31.7579i | −0.641132 | − | 1.25829i | ||||
\(638\) | −3.50321 | − | 6.87543i | −0.138693 | − | 0.272201i | ||||
\(639\) | −32.3115 | − | 20.6290i | −1.27822 | − | 0.816073i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.5088 | − | 5.03912i | −0.612561 | − | 0.199033i | −0.0137264 | − | 0.999906i | \(-0.504369\pi\) |
−0.598835 | + | 0.800873i | \(0.704369\pi\) | |||||||
\(642\) | 29.5620 | − | 16.1995i | 1.16672 | − | 0.639344i | ||||
\(643\) | 12.8296 | + | 12.8296i | 0.505952 | + | 0.505952i | 0.913281 | − | 0.407330i | \(-0.133540\pi\) |
−0.407330 | + | 0.913281i | \(0.633540\pi\) | |||||||
\(644\) | −0.159043 | − | 0.115552i | −0.00626719 | − | 0.00455338i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.56321 | − | 2.58883i | 0.140193 | − | 0.101856i | ||||
\(647\) | 25.1179 | + | 3.97829i | 0.987488 | + | 0.156403i | 0.629229 | − | 0.777220i | \(-0.283371\pi\) |
0.358259 | + | 0.933622i | \(0.383371\pi\) | |||||||
\(648\) | −5.55479 | + | 7.08127i | −0.218213 | + | 0.278178i | ||||
\(649\) | − | 7.25839i | − | 0.284917i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.22599 | − | 0.439499i | 0.0480502 | − | 0.0172253i | ||||
\(652\) | 1.36590 | + | 0.695961i | 0.0534928 | + | 0.0272559i | ||||
\(653\) | −4.76127 | + | 30.0615i | −0.186323 | + | 1.17640i | 0.700281 | + | 0.713867i | \(0.253058\pi\) |
−0.886604 | + | 0.462529i | \(0.846942\pi\) | |||||||
\(654\) | 12.0053 | − | 17.6136i | 0.469443 | − | 0.688747i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.19532 | + | 3.02160i | −0.0857129 | + | 0.117974i | ||||
\(657\) | 0.385730 | − | 3.96538i | 0.0150488 | − | 0.154704i | ||||
\(658\) | −0.156448 | − | 0.987775i | −0.00609899 | − | 0.0385075i | ||||
\(659\) | −3.19473 | + | 9.83236i | −0.124449 | + | 0.383014i | −0.993800 | − | 0.111180i | \(-0.964537\pi\) |
0.869351 | + | 0.494195i | \(0.164537\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.97825 | + | 12.2438i | 0.154736 | + | 0.476229i | 0.998134 | − | 0.0610606i | \(-0.0194483\pi\) |
−0.843398 | + | 0.537289i | \(0.819448\pi\) | |||||||
\(662\) | 9.85137 | − | 5.01952i | 0.382884 | − | 0.195089i | ||||
\(663\) | 20.1850 | + | 19.0067i | 0.783921 | + | 0.738161i | ||||
\(664\) | 0.838964 | − | 0.272596i | 0.0325581 | − | 0.0105788i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 28.9279 | − | 11.3624i | 1.12093 | − | 0.440284i | ||||
\(667\) | 17.2859 | − | 2.73781i | 0.669311 | − | 0.106008i | ||||
\(668\) | 15.8270 | − | 15.8270i | 0.612365 | − | 0.612365i | ||||
\(669\) | −2.66696 | + | 9.13333i | −0.103111 | + | 0.353115i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.58363 | − | 3.55605i | −0.0997397 | − | 0.137280i | ||||
\(672\) | 0.133928 | − | 0.0253594i | 0.00516640 | − | 0.000978260i | ||||
\(673\) | 15.3006 | − | 30.0291i | 0.589794 | − | 1.15754i | −0.382540 | − | 0.923939i | \(-0.624951\pi\) |
0.972334 | − | 0.233596i | \(-0.0750494\pi\) | |||||||
\(674\) | 17.3028 | 0.666479 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.9725 | −0.498943 | ||||||||
\(677\) | −7.07682 | + | 13.8891i | −0.271984 | + | 0.533800i | −0.986085 | − | 0.166244i | \(-0.946836\pi\) |
0.714100 | + | 0.700044i | \(0.246836\pi\) | |||||||
\(678\) | 12.9918 | − | 2.46001i | 0.498948 | − | 0.0944759i | ||||
\(679\) | 0.480192 | + | 0.660928i | 0.0184281 | + | 0.0253641i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.28346 | − | 11.2446i | 0.125823 | − | 0.430895i | ||||
\(682\) | −7.44126 | + | 7.44126i | −0.284940 | + | 0.284940i | ||||
\(683\) | −26.5524 | + | 4.20549i | −1.01600 | + | 0.160919i | −0.642157 | − | 0.766573i | \(-0.721960\pi\) |
−0.373844 | + | 0.927492i | \(0.621960\pi\) | |||||||
\(684\) | −3.91554 | + | 1.53796i | −0.149715 | + | 0.0588054i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.04738 | + | 0.340314i | −0.0399891 | + | 0.0129932i | ||||
\(687\) | −3.82996 | − | 3.60640i | −0.146122 | − | 0.137593i | ||||
\(688\) | −1.26717 | + | 0.645655i | −0.0483104 | + | 0.0246154i | ||||
\(689\) | −10.6919 | − | 32.9064i | −0.407330 | − | 1.25363i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.00128 | − | 21.5477i | 0.266341 | − | 0.819714i | −0.725040 | − | 0.688707i | \(-0.758179\pi\) |
0.991381 | − | 0.131007i | \(-0.0418212\pi\) | |||||||
\(692\) | −2.21732 | − | 13.9996i | −0.0842898 | − | 0.532185i | ||||
\(693\) | 0.0251756 | − | 0.258811i | 0.000956343 | − | 0.00983141i | ||||
\(694\) | −8.78938 | + | 12.0975i | −0.333640 | + | 0.459217i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −6.83446 | + | 10.0272i | −0.259060 | + | 0.380081i | ||||
\(697\) | −1.83514 | + | 11.5866i | −0.0695110 | + | 0.438875i | ||||
\(698\) | 0.307489 | + | 0.156673i | 0.0116386 | + | 0.00593018i | ||||
\(699\) | 2.25438 | − | 0.808162i | 0.0852684 | − | 0.0305675i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 37.8133i | − | 1.42819i | −0.700049 | − | 0.714095i | \(-0.746839\pi\) | ||
0.700049 | − | 0.714095i | \(-0.253161\pi\) | |||||||
\(702\) | −14.0980 | − | 22.4166i | −0.532094 | − | 0.846061i | ||||
\(703\) | 14.3482 | + | 2.27253i | 0.541153 | + | 0.0857102i | ||||
\(704\) | −0.891050 | + | 0.647386i | −0.0335827 | + | 0.0243993i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16.2083 | − | 11.7760i | −0.610007 | − | 0.443196i | ||||
\(707\) | −0.781162 | − | 0.781162i | −0.0293786 | − | 0.0293786i | ||||
\(708\) | −10.0101 | + | 5.48536i | −0.376201 | + | 0.206152i | ||||
\(709\) | −37.7779 | − | 12.2748i | −1.41878 | − | 0.460989i | −0.503565 | − | 0.863958i | \(-0.667978\pi\) |
−0.915214 | + | 0.402968i | \(0.867978\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −25.1814 | − | 16.0769i | −0.944377 | − | 0.602931i | ||||
\(712\) | 1.48863 | + | 2.92160i | 0.0557887 | + | 0.109491i | ||||
\(713\) | −10.8358 | − | 21.2664i | −0.405803 | − | 0.796433i | ||||
\(714\) | 0.338649 | − | 0.261946i | 0.0126736 | − | 0.00980309i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −14.4473 | − | 4.69420i | −0.539919 | − | 0.175430i | ||||
\(717\) | −9.46453 | − | 17.2716i | −0.353459 | − | 0.645018i | ||||
\(718\) | −12.9715 | − | 12.9715i | −0.484093 | − | 0.484093i | ||||
\(719\) | 25.6075 | + | 18.6049i | 0.954998 | + | 0.693847i | 0.951984 | − | 0.306149i | \(-0.0990405\pi\) |
0.00301445 | + | 0.999995i | \(0.499040\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.840680 | + | 0.610790i | −0.0313086 | + | 0.0227470i | ||||
\(722\) | 16.8240 | + | 2.66466i | 0.626124 | + | 0.0991682i | ||||
\(723\) | 1.93606 | − | 15.1596i | 0.0720029 | − | 0.563791i | ||||
\(724\) | 10.2709i | 0.381715i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.72039 | − | 15.9571i | −0.212304 | − | 0.592223i | ||||
\(727\) | −45.9671 | − | 23.4214i | −1.70483 | − | 0.868652i | −0.984580 | − | 0.174934i | \(-0.944029\pi\) |
−0.720246 | − | 0.693719i | \(-0.755971\pi\) | |||||||
\(728\) | −0.0627409 | + | 0.396131i | −0.00232533 | + | 0.0146816i | ||||
\(729\) | 11.6951 | − | 24.3357i | 0.433152 | − | 0.901321i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.62561 | + | 3.61384i | −0.0971117 | + | 0.133663i | ||||
\(732\) | −2.95165 | + | 6.25049i | −0.109096 | + | 0.231025i | ||||
\(733\) | 3.31036 | + | 20.9008i | 0.122271 | + | 0.771988i | 0.970276 | + | 0.242000i | \(0.0778035\pi\) |
−0.848005 | + | 0.529988i | \(0.822197\pi\) | |||||||
\(734\) | −0.00602247 | + | 0.0185352i | −0.000222293 | + | 0.000684148i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.771931 | − | 2.37576i | −0.0284538 | − | 0.0875717i | ||||
\(737\) | −6.53478 | + | 3.32964i | −0.240712 | + | 0.122649i | ||||
\(738\) | 4.47789 | − | 10.2710i | 0.164834 | − | 0.378082i | ||||
\(739\) | −11.8537 | + | 3.85150i | −0.436046 | + | 0.141680i | −0.518811 | − | 0.854889i | \(-0.673625\pi\) |
0.0827648 | + | 0.996569i | \(0.473625\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.371961 | − | 12.3722i | −0.0136643 | − | 0.454505i | ||||
\(742\) | −0.527714 | + | 0.0835816i | −0.0193730 | + | 0.00306838i | ||||
\(743\) | −2.30237 | + | 2.30237i | −0.0844658 | + | 0.0844658i | −0.748077 | − | 0.663612i | \(-0.769023\pi\) |
0.663612 | + | 0.748077i | \(0.269023\pi\) | |||||||
\(744\) | 15.8858 | + | 4.63870i | 0.582402 | + | 0.170063i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 4.11202 | + | 5.65971i | 0.150552 | + | 0.207217i | ||||
\(747\) | −2.28154 | + | 1.34093i | −0.0834772 | + | 0.0490621i | ||||
\(748\) | −1.57054 | + | 3.08236i | −0.0574247 | + | 0.112702i | ||||
\(749\) | 1.53163 | 0.0559646 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.7652 | 0.684751 | 0.342375 | − | 0.939563i | \(-0.388769\pi\) | ||||
0.342375 | + | 0.939563i | \(0.388769\pi\) | |||||||
\(752\) | 5.76930 | − | 11.3229i | 0.210385 | − | 0.412904i | ||||
\(753\) | −4.70802 | − | 24.8641i | −0.171570 | − | 0.906097i | ||||
\(754\) | −20.9870 | − | 28.8861i | −0.764301 | − | 1.05197i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.375952 | + | 0.160870i | −0.0136733 | + | 0.00585079i | ||||
\(757\) | 7.02667 | − | 7.02667i | 0.255389 | − | 0.255389i | −0.567787 | − | 0.823176i | \(-0.692200\pi\) |
0.823176 | + | 0.567787i | \(0.192200\pi\) | |||||||
\(758\) | 12.0195 | − | 1.90370i | 0.436567 | − | 0.0691453i | ||||
\(759\) | −4.76327 | + | 0.143204i | −0.172896 | + | 0.00519798i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 48.1462 | − | 15.6436i | 1.74530 | − | 0.567081i | 0.749782 | − | 0.661685i | \(-0.230158\pi\) |
0.995515 | + | 0.0946038i | \(0.0301584\pi\) | |||||||
\(762\) | 3.82587 | − | 4.06305i | 0.138597 | − | 0.147189i | ||||
\(763\) | 0.862948 | − | 0.439694i | 0.0312408 | − | 0.0159180i | ||||
\(764\) | 3.35652 | + | 10.3303i | 0.121435 | + | 0.373737i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.292865 | + | 0.901344i | −0.0105816 | + | 0.0325669i | ||||
\(767\) | −5.25394 | − | 33.1721i | −0.189709 | − | 1.19777i | ||||
\(768\) | 1.56620 | + | 0.739603i | 0.0565154 | + | 0.0266881i | ||||
\(769\) | −21.2813 | + | 29.2912i | −0.767422 | + | 1.05627i | 0.229138 | + | 0.973394i | \(0.426409\pi\) |
−0.996560 | + | 0.0828721i | \(0.973591\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.18239 | + | 2.16909i | 0.114611 | + | 0.0781178i | ||||
\(772\) | 3.03620 | − | 19.1698i | 0.109275 | − | 0.689936i | ||||
\(773\) | 20.9544 | + | 10.6768i | 0.753679 | + | 0.384019i | 0.788227 | − | 0.615384i | \(-0.210999\pi\) |
−0.0345481 | + | 0.999403i | \(0.510999\pi\) | |||||||
\(774\) | 3.29481 | − | 2.71063i | 0.118429 | − | 0.0974317i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 10.3809i | 0.372653i | ||||||||
\(777\) | 1.40075 | + | 0.178893i | 0.0502516 | + | 0.00641774i | ||||
\(778\) | 19.6281 | + | 3.10878i | 0.703701 | + | 0.111455i | ||||
\(779\) | 4.23704 | − | 3.07839i | 0.151808 | − | 0.110295i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.3862 | + | 8.27256i | 0.407430 | + | 0.296015i | ||||
\(782\) | −5.54804 | − | 5.54804i | −0.198397 | − | 0.198397i | ||||
\(783\) | 13.5395 | − | 33.7932i | 0.483862 | − | 1.20767i | ||||
\(784\) | −6.65151 | − | 2.16121i | −0.237554 | − | 0.0771859i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 5.63586 | + | 7.28616i | 0.201025 | + | 0.259889i | ||||
\(787\) | −14.2872 | − | 28.0403i | −0.509285 | − | 0.999529i | −0.992293 | − | 0.123913i | \(-0.960456\pi\) |
0.483008 | − | 0.875616i | \(-0.339544\pi\) | |||||||
\(788\) | −5.55232 | − | 10.8970i | −0.197793 | − | 0.388191i | ||||
\(789\) | 20.5342 | + | 26.5470i | 0.731036 | + | 0.945099i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.571382 | + | 0.185653i | 0.0203160 | + | 0.00660107i | ||||
\(792\) | 2.19184 | − | 2.47256i | 0.0778837 | − | 0.0878585i | ||||
\(793\) | −14.3816 | − | 14.3816i | −0.510707 | − | 0.510707i | ||||
\(794\) | 21.8203 | + | 15.8534i | 0.774375 | + | 0.562616i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.8922 | − | 9.36672i | 0.456952 | − | 0.331995i | ||||
\(797\) | 6.24831 | + | 0.989635i | 0.221326 | + | 0.0350547i | 0.266113 | − | 0.963942i | \(-0.414261\pi\) |
−0.0447862 | + | 0.998997i | \(0.514261\pi\) | |||||||
\(798\) | −0.189599 | − | 0.0242140i | −0.00671172 | − | 0.000857167i | ||||
\(799\) | − | 39.9149i | − | 1.41209i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.24966 | − | 7.59654i | −0.220821 | − | 0.268410i | ||||
\(802\) | 30.2402 | + | 15.4082i | 1.06782 | + | 0.544081i | ||||
\(803\) | −0.228816 | + | 1.44469i | −0.00807473 | + | 0.0509818i | ||||
\(804\) | 9.53041 | + | 6.49584i | 0.336112 | + | 0.229091i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −28.6215 | + | 39.3941i | −1.00815 | + | 1.38760i | ||||
\(807\) | 8.60707 | + | 4.06450i | 0.302983 | + | 0.143077i | ||||
\(808\) | −2.19597 | − | 13.8648i | −0.0772540 | − | 0.487763i | ||||
\(809\) | 10.4456 | − | 32.1483i | 0.367249 | − | 1.13028i | −0.581312 | − | 0.813681i | \(-0.697461\pi\) |
0.948561 | − | 0.316595i | \(-0.102539\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.3720 | − | 34.9993i | −0.399324 | − | 1.22899i | −0.925543 | − | 0.378643i | \(-0.876391\pi\) |
0.526219 | − | 0.850349i | \(-0.323609\pi\) | |||||||
\(812\) | −0.491266 | + | 0.250313i | −0.0172401 | + | 0.00878425i | ||||
\(813\) | −8.83835 | + | 9.38626i | −0.309975 | + | 0.329191i | ||||
\(814\) | −10.8518 | + | 3.52597i | −0.380356 | + | 0.123585i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5.43779 | − | 0.163483i | 0.190361 | − | 0.00572306i | ||||
\(817\) | 1.96970 | − | 0.311969i | 0.0689110 | − | 0.0109144i | ||||
\(818\) | 11.2430 | − | 11.2430i | 0.393103 | − | 0.393103i | ||||
\(819\) | −0.0722816 | − | 1.20103i | −0.00252572 | − | 0.0419675i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.94467 | − | 2.67661i | −0.0678695 | − | 0.0934144i | 0.773733 | − | 0.633512i | \(-0.218387\pi\) |
−0.841602 | + | 0.540098i | \(0.818387\pi\) | |||||||
\(822\) | 3.70121 | + | 19.5469i | 0.129095 | + | 0.681777i | ||||
\(823\) | −16.1380 | + | 31.6727i | −0.562537 | + | 1.10404i | 0.418136 | + | 0.908385i | \(0.362684\pi\) |
−0.980673 | + | 0.195656i | \(0.937316\pi\) | |||||||
\(824\) | −13.2042 | −0.459990 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.518630 | −0.0180454 | ||||||||
\(827\) | 4.05871 | − | 7.96567i | 0.141135 | − | 0.276993i | −0.809609 | − | 0.586969i | \(-0.800321\pi\) |
0.950744 | + | 0.309976i | \(0.100321\pi\) | |||||||
\(828\) | 3.79722 | + | 6.46082i | 0.131963 | + | 0.224529i | ||||
\(829\) | 6.82593 | + | 9.39508i | 0.237074 | + | 0.326305i | 0.910932 | − | 0.412556i | \(-0.135364\pi\) |
−0.673858 | + | 0.738861i | \(0.735364\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 31.7489 | + | 9.27078i | 1.10136 | + | 0.321600i | ||||
\(832\) | −3.60364 | + | 3.60364i | −0.124934 | + | 0.124934i | ||||
\(833\) | −21.6966 | + | 3.43640i | −0.751743 | + | 0.119064i | ||||
\(834\) | −0.567443 | − | 18.8743i | −0.0196489 | − | 0.653565i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.46885 | − | 0.477258i | 0.0508012 | − | 0.0165063i | ||||
\(837\) | −49.5365 | − | 3.31965i | −1.71223 | − | 0.114744i | ||||
\(838\) | 24.5000 | − | 12.4834i | 0.846339 | − | 0.431231i | ||||
\(839\) | 1.99464 | + | 6.13888i | 0.0688628 | + | 0.211938i | 0.979566 | − | 0.201124i | \(-0.0644594\pi\) |
−0.910703 | + | 0.413062i | \(0.864459\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.20662 | − | 19.1020i | 0.214021 | − | 0.658690i | ||||
\(842\) | −4.99858 | − | 31.5598i | −0.172262 | − | 1.08762i | ||||
\(843\) | −1.04178 | + | 2.20610i | −0.0358809 | + | 0.0759822i | ||||
\(844\) | −6.50062 | + | 8.94734i | −0.223761 | + | 0.307980i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9.58150 | + | 36.9003i | −0.329419 | + | 1.26866i | ||||
\(847\) | 0.120487 | − | 0.760725i | 0.00413998 | − | 0.0261388i | ||||
\(848\) | −6.04920 | − | 3.08222i | −0.207730 | − | 0.105844i | ||||
\(849\) | 5.57329 | + | 15.5468i | 0.191275 | + | 0.533563i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 25.8790i | − | 0.887121i | ||||||
\(852\) | 2.80386 | − | 21.9545i | 0.0960586 | − | 0.752150i | ||||
\(853\) | 26.0890 | + | 4.13209i | 0.893271 | + | 0.141480i | 0.586162 | − | 0.810194i | \(-0.300638\pi\) |
0.307109 | + | 0.951674i | \(0.400638\pi\) | |||||||
\(854\) | −0.254089 | + | 0.184606i | −0.00869474 | + | 0.00631710i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.7453 | + | 11.4396i | 0.538163 | + | 0.390998i | ||||
\(857\) | 21.7170 | + | 21.7170i | 0.741840 | + | 0.741840i | 0.972932 | − | 0.231092i | \(-0.0742298\pi\) |
−0.231092 | + | 0.972932i | \(0.574230\pi\) | |||||||
\(858\) | 4.67208 | + | 8.52595i | 0.159502 | + | 0.291071i | ||||
\(859\) | 2.16755 | + | 0.704281i | 0.0739560 | + | 0.0240298i | 0.345761 | − | 0.938322i | \(-0.387621\pi\) |
−0.271805 | + | 0.962352i | \(0.587621\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.402691 | − | 0.311482i | 0.0137237 | − | 0.0106153i | ||||
\(862\) | 3.93217 | + | 7.71732i | 0.133930 | + | 0.262853i | ||||
\(863\) | −0.924026 | − | 1.81350i | −0.0314542 | − | 0.0617324i | 0.874745 | − | 0.484584i | \(-0.161029\pi\) |
−0.906199 | + | 0.422852i | \(0.861029\pi\) | |||||||
\(864\) | −5.06634 | − | 1.15420i | −0.172360 | − | 0.0392666i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −10.2541 | − | 3.33175i | −0.348448 | − | 0.113218i | ||||
\(867\) | −10.8370 | + | 5.93849i | −0.368043 | + | 0.201682i | ||||
\(868\) | 0.531696 | + | 0.531696i | 0.0180469 | + | 0.0180469i | ||||
\(869\) | 8.87365 | + | 6.44709i | 0.301018 | + | 0.218702i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27.4549 | + | 19.9472i | −0.930274 | + | 0.675884i | ||||
\(872\) | 12.1552 | + | 1.92520i | 0.411627 | + | 0.0651953i | ||||
\(873\) | −6.71083 | − | 30.4111i | −0.227127 | − | 1.02926i | ||||
\(874\) | 3.50286i | 0.118486i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.16529 | − | 0.776226i | 0.0731584 | − | 0.0262263i | ||||
\(877\) | −5.66858 | − | 2.88829i | −0.191414 | − | 0.0975305i | 0.355657 | − | 0.934617i | \(-0.384257\pi\) |
−0.547071 | + | 0.837086i | \(0.684257\pi\) | |||||||
\(878\) | 5.36634 | − | 33.8818i | 0.181105 | − | 1.14345i | ||||
\(879\) | −30.3873 | + | 44.5829i | −1.02494 | + | 1.50374i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.61099 | + | 4.97010i | −0.121657 | + | 0.167447i | −0.865502 | − | 0.500906i | \(-0.833000\pi\) |
0.743844 | + | 0.668353i | \(0.233000\pi\) | |||||||
\(882\) | 20.8829 | + | 2.03137i | 0.703162 | + | 0.0683996i | ||||
\(883\) | 6.19390 | + | 39.1067i | 0.208441 | + | 1.31605i | 0.840789 | + | 0.541362i | \(0.182091\pi\) |
−0.632348 | + | 0.774684i | \(0.717909\pi\) | |||||||
\(884\) | −4.94649 | + | 15.2237i | −0.166369 | + | 0.512030i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.00247 | + | 6.16296i | 0.0672742 | + | 0.207049i | ||||
\(887\) | −43.0525 | + | 21.9363i | −1.44556 | + | 0.736550i | −0.988263 | − | 0.152763i | \(-0.951183\pi\) |
−0.457299 | + | 0.889313i | \(0.651183\pi\) | |||||||
\(888\) | 13.0637 | + | 12.3011i | 0.438388 | + | 0.412798i | ||||
\(889\) | 0.241160 | − | 0.0783578i | 0.00808826 | − | 0.00262804i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.82263 | + | 8.66035i | −0.161564 | + | 0.290133i | ||||
\(892\) | −5.42571 | + | 0.859348i | −0.181666 | + | 0.0287731i | ||||
\(893\) | −12.6005 | + | 12.6005i | −0.421660 | + | 0.421660i | ||||
\(894\) | 6.97549 | − | 23.8884i | 0.233295 | − | 0.798948i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.0462573 | + | 0.0636677i | 0.00154535 | + | 0.00212699i | ||||
\(897\) | −21.6653 | + | 4.10233i | −0.723383 | + | 0.136973i | ||||
\(898\) | −10.3265 | + | 20.2669i | −0.344599 | + | 0.676314i | ||||
\(899\) | −66.9409 | −2.23260 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.3243 | −0.710416 | ||||||||
\(902\) | −1.86754 | + | 3.66526i | −0.0621824 | + | 0.122040i | ||||
\(903\) | 0.190470 | − | 0.0360655i | 0.00633844 | − | 0.00120019i | ||||
\(904\) | 4.48722 | + | 6.17613i | 0.149243 | + | 0.205415i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.158481 | − | 0.542736i | 0.00526517 | − | 0.0180312i | ||||
\(907\) | 24.7561 | − | 24.7561i | 0.822014 | − | 0.822014i | −0.164383 | − | 0.986397i | \(-0.552563\pi\) |
0.986397 | + | 0.164383i | \(0.0525632\pi\) | |||||||
\(908\) | 6.67994 | − | 1.05800i | 0.221682 | − | 0.0351109i | ||||
\(909\) | 15.3962 | + | 39.1977i | 0.510660 | + | 1.30010i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.5335 | − | 15.7695i | 1.60799 | − | 0.522466i | 0.638921 | − | 0.769272i | \(-0.279381\pi\) |
0.969065 | + | 0.246806i | \(0.0793810\pi\) | |||||||
\(912\) | −1.76823 | − | 1.66502i | −0.0585521 | − | 0.0551342i | ||||
\(913\) | 0.865690 | − | 0.441091i | 0.0286502 | − | 0.0145980i | ||||
\(914\) | −2.74480 | − | 8.44762i | −0.0907898 | − | 0.279422i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.938563 | − | 2.88860i | 0.0310110 | − | 0.0954420i | ||||
\(917\) | 0.0654729 | + | 0.413380i | 0.00216211 | + | 0.0136510i | ||||
\(918\) | −15.8244 | + | 3.99424i | −0.522284 | + | 0.131830i | ||||
\(919\) | −6.34757 | + | 8.73668i | −0.209387 | + | 0.288196i | −0.900774 | − | 0.434288i | \(-0.857000\pi\) |
0.691387 | + | 0.722485i | \(0.257000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.15835 | − | 3.16664i | 0.0711200 | − | 0.104344i | ||||
\(922\) | −3.51006 | + | 22.1617i | −0.115598 | + | 0.729855i | ||||
\(923\) | 58.0249 | + | 29.5652i | 1.90991 | + | 0.973150i | ||||
\(924\) | 0.141323 | − | 0.0506624i | 0.00464919 | − | 0.00166667i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 24.2111i | − | 0.795626i | ||||||
\(927\) | 38.6819 | − | 8.53597i | 1.27048 | − | 0.280358i | ||||
\(928\) | −6.91981 | − | 1.09599i | −0.227154 | − | 0.0359777i | ||||
\(929\) | 38.0194 | − | 27.6227i | 1.24738 | − | 0.906272i | 0.249310 | − | 0.968424i | \(-0.419796\pi\) |
0.998067 | + | 0.0621513i | \(0.0197961\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.93409 | + | 5.76446i | 0.260029 | + | 0.188922i | ||||
\(932\) | 0.977696 | + | 0.977696i | 0.0320255 | + | 0.0320255i | ||||
\(933\) | −20.7056 | + | 11.3463i | −0.677871 | + | 0.371463i | ||||
\(934\) | −12.8115 | − | 4.16270i | −0.419204 | − | 0.136208i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 8.22734 | − | 12.8866i | 0.268919 | − | 0.421210i | ||||
\(937\) | 20.7717 | + | 40.7667i | 0.678581 | + | 1.33179i | 0.931301 | + | 0.364250i | \(0.118675\pi\) |
−0.252721 | + | 0.967539i | \(0.581325\pi\) | |||||||
\(938\) | 0.237911 | + | 0.466926i | 0.00776806 | + | 0.0152457i | ||||
\(939\) | 26.1652 | − | 20.2389i | 0.853870 | − | 0.660470i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.1364 | − | 9.46699i | −0.949820 | − | 0.308615i | −0.207177 | − | 0.978303i | \(-0.566428\pi\) |
−0.742642 | + | 0.669688i | \(0.766428\pi\) | |||||||
\(942\) | 4.09119 | + | 7.46589i | 0.133298 | + | 0.243252i | ||||
\(943\) | −6.59721 | − | 6.59721i | −0.214835 | − | 0.214835i | ||||
\(944\) | −5.33155 | − | 3.87360i | −0.173527 | − | 0.126075i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.26723 | + | 0.920697i | −0.0412012 | + | 0.0299344i | ||||
\(947\) | 14.2493 | + | 2.25687i | 0.463040 | + | 0.0733384i | 0.383596 | − | 0.923501i | \(-0.374685\pi\) |
0.0794442 | + | 0.996839i | \(0.474685\pi\) | |||||||
\(948\) | 2.18514 | − | 17.1099i | 0.0709701 | − | 0.555704i | ||||
\(949\) | 6.76809i | 0.219701i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.31067 | − | 14.8142i | −0.172210 | − | 0.480382i | ||||
\(952\) | 0.220242 | + | 0.112219i | 0.00713809 | + | 0.00363704i | ||||
\(953\) | 0.616563 | − | 3.89283i | 0.0199724 | − | 0.126101i | −0.975688 | − | 0.219166i | \(-0.929666\pi\) |
0.995660 | + | 0.0930649i | \(0.0296664\pi\) | |||||||
\(954\) | 19.7138 | + | 5.11887i | 0.638257 | + | 0.165729i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 6.68358 | − | 9.19915i | 0.216162 | − | 0.297522i | ||||
\(957\) | −5.70713 | + | 12.0856i | −0.184485 | + | 0.390671i | ||||
\(958\) | 2.70337 | + | 17.0684i | 0.0873420 | + | 0.551455i | ||||
\(959\) | −0.279326 | + | 0.859676i | −0.00901989 | + | 0.0277604i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.6313 | + | 57.3413i | 0.601010 | + | 1.84972i | ||||
\(962\) | −47.0424 | + | 23.9693i | −1.51671 | + | 0.772801i | ||||
\(963\) | −53.5214 | − | 23.3339i | −1.72470 | − | 0.751925i | ||||
\(964\) | 8.39163 | − | 2.72661i | 0.270276 | − | 0.0878181i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.0102323 | + | 0.340347i | 0.000329218 | + | 0.0109505i | ||||
\(967\) | 51.5598 | − | 8.16627i | 1.65805 | − | 0.262610i | 0.743992 | − | 0.668189i | \(-0.232930\pi\) |
0.914060 | + | 0.405579i | \(0.132930\pi\) | |||||||
\(968\) | 6.92040 | − | 6.92040i | 0.222430 | − | 0.222430i | ||||
\(969\) | −7.32280 | − | 2.13828i | −0.235242 | − | 0.0686914i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.69176 | + | 3.70489i | 0.0863828 | + | 0.118896i | 0.850021 | − | 0.526748i | \(-0.176589\pi\) |
−0.763638 | + | 0.645644i | \(0.776589\pi\) | |||||||
\(972\) | 15.5881 | + | 0.106057i | 0.499988 | + | 0.00340179i | ||||
\(973\) | 0.389507 | − | 0.764451i | 0.0124870 | − | 0.0245072i | ||||
\(974\) | 3.62274 | 0.116080 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.99086 | −0.127744 | ||||||||
\(977\) | −1.87651 | + | 3.68285i | −0.0600348 | + | 0.117825i | −0.919074 | − | 0.394085i | \(-0.871062\pi\) |
0.859039 | + | 0.511910i | \(0.171062\pi\) | |||||||
\(978\) | −0.493987 | − | 2.60885i | −0.0157960 | − | 0.0834219i | ||||
\(979\) | 2.12277 | + | 2.92174i | 0.0678439 | + | 0.0933792i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −36.8535 | + | 2.21795i | −1.17664 | + | 0.0708137i | ||||
\(982\) | −4.08144 | + | 4.08144i | −0.130244 | + | 0.130244i | ||||
\(983\) | 25.6200 | − | 4.05781i | 0.817151 | − | 0.129424i | 0.266153 | − | 0.963931i | \(-0.414247\pi\) |
0.550998 | + | 0.834507i | \(0.314247\pi\) | |||||||
\(984\) | 6.46612 | − | 0.194399i | 0.206132 | − | 0.00619722i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −20.9285 | + | 6.80010i | −0.666501 | + | 0.216559i | ||||
\(987\) | −1.18749 | + | 1.26111i | −0.0377983 | + | 0.0401415i | ||||
\(988\) | 6.36743 | − | 3.24437i | 0.202575 | − | 0.103217i | ||||
\(989\) | −1.09782 | − | 3.37875i | −0.0349087 | − | 0.107438i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.36863 | + | 22.6783i | −0.234072 | + | 0.720400i | 0.763171 | + | 0.646197i | \(0.223641\pi\) |
−0.997243 | + | 0.0742035i | \(0.976359\pi\) | |||||||
\(992\) | 1.49468 | + | 9.43706i | 0.0474562 | + | 0.299627i | ||||
\(993\) | −17.3166 | − | 8.17738i | −0.549526 | − | 0.259501i | ||||
\(994\) | 0.591094 | − | 0.813572i | 0.0187484 | − | 0.0258049i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.26253 | − | 0.860532i | −0.0400049 | − | 0.0272670i | ||||
\(997\) | −2.45546 | + | 15.5032i | −0.0777652 | + | 0.490990i | 0.917810 | + | 0.397020i | \(0.129956\pi\) |
−0.995575 | + | 0.0939699i | \(0.970044\pi\) | |||||||
\(998\) | 25.4455 | + | 12.9651i | 0.805464 | + | 0.410404i | ||||
\(999\) | −46.2225 | − | 27.5912i | −1.46241 | − | 0.872947i |
(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 | 750.2.l.a.143.6 | 80 | ||
3.2 | odd | 2 | inner | 750.2.l.a.143.1 | 80 | ||
5.2 | odd | 4 | 750.2.l.b.107.8 | 80 | |||
5.3 | odd | 4 | 150.2.l.a.17.3 | ✓ | 80 | ||
5.4 | even | 2 | 750.2.l.c.143.5 | 80 | |||
15.2 | even | 4 | 750.2.l.b.107.2 | 80 | |||
15.8 | even | 4 | 150.2.l.a.17.9 | yes | 80 | ||
15.14 | odd | 2 | 750.2.l.c.143.10 | 80 | |||
25.3 | odd | 20 | 750.2.l.c.257.10 | 80 | |||
25.4 | even | 10 | 150.2.l.a.53.9 | yes | 80 | ||
25.21 | even | 5 | 750.2.l.b.743.2 | 80 | |||
25.22 | odd | 20 | inner | 750.2.l.a.257.1 | 80 | ||
75.29 | odd | 10 | 150.2.l.a.53.3 | yes | 80 | ||
75.47 | even | 20 | inner | 750.2.l.a.257.6 | 80 | ||
75.53 | even | 20 | 750.2.l.c.257.5 | 80 | |||
75.71 | odd | 10 | 750.2.l.b.743.8 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.l.a.17.3 | ✓ | 80 | 5.3 | odd | 4 | ||
150.2.l.a.17.9 | yes | 80 | 15.8 | even | 4 | ||
150.2.l.a.53.3 | yes | 80 | 75.29 | odd | 10 | ||
150.2.l.a.53.9 | yes | 80 | 25.4 | even | 10 | ||
750.2.l.a.143.1 | 80 | 3.2 | odd | 2 | inner | ||
750.2.l.a.143.6 | 80 | 1.1 | even | 1 | trivial | ||
750.2.l.a.257.1 | 80 | 25.22 | odd | 20 | inner | ||
750.2.l.a.257.6 | 80 | 75.47 | even | 20 | inner | ||
750.2.l.b.107.2 | 80 | 15.2 | even | 4 | |||
750.2.l.b.107.8 | 80 | 5.2 | odd | 4 | |||
750.2.l.b.743.2 | 80 | 25.21 | even | 5 | |||
750.2.l.b.743.8 | 80 | 75.71 | odd | 10 | |||
750.2.l.c.143.5 | 80 | 5.4 | even | 2 | |||
750.2.l.c.143.10 | 80 | 15.14 | odd | 2 | |||
750.2.l.c.257.5 | 80 | 75.53 | even | 20 | |||
750.2.l.c.257.10 | 80 | 25.3 | odd | 20 |