Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(311,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.311");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.t (of order \(6\), 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: | \(5.03057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 311.13 | ||
Character | \(\chi\) | \(=\) | 630.311 |
Dual form | 630.2.t.b.551.13 |
$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | 1.11018 | + | 1.32948i | 0.640960 | + | 0.767574i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.296702 | + | 1.70645i | 0.121128 | + | 0.696655i | ||||
\(7\) | −0.142082 | − | 2.64193i | −0.0537021 | − | 0.998557i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −0.535019 | + | 2.95191i | −0.178340 | + | 0.983969i | ||||
\(10\) | −0.866025 | − | 0.500000i | −0.273861 | − | 0.158114i | ||||
\(11\) | 4.86026i | 1.46542i | 0.680539 | + | 0.732712i | \(0.261746\pi\) | ||||
−0.680539 | + | 0.732712i | \(0.738254\pi\) | |||||||
\(12\) | −0.596273 | + | 1.62618i | −0.172129 | + | 0.469437i | ||||
\(13\) | 3.42136 | + | 1.97532i | 0.948914 | + | 0.547856i | 0.892743 | − | 0.450566i | \(-0.148778\pi\) |
0.0561705 | + | 0.998421i | \(0.482111\pi\) | |||||||
\(14\) | 1.19792 | − | 2.35902i | 0.320158 | − | 0.630475i | ||||
\(15\) | −1.11018 | − | 1.32948i | −0.286646 | − | 0.343270i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.25228 | + | 2.16902i | −0.303723 | + | 0.526064i | −0.976976 | − | 0.213348i | \(-0.931563\pi\) |
0.673253 | + | 0.739412i | \(0.264896\pi\) | |||||||
\(18\) | −1.93929 | + | 2.28892i | −0.457096 | + | 0.539503i | ||||
\(19\) | −0.962409 | + | 0.555647i | −0.220792 | + | 0.127474i | −0.606317 | − | 0.795223i | \(-0.707354\pi\) |
0.385525 | + | 0.922697i | \(0.374020\pi\) | |||||||
\(20\) | −0.500000 | − | 0.866025i | −0.111803 | − | 0.193649i | ||||
\(21\) | 3.35465 | − | 3.12191i | 0.732045 | − | 0.681256i | ||||
\(22\) | −2.43013 | + | 4.20911i | −0.518106 | + | 0.897385i | ||||
\(23\) | 3.30404i | 0.688941i | 0.938797 | + | 0.344470i | \(0.111941\pi\) | ||||
−0.938797 | + | 0.344470i | \(0.888059\pi\) | |||||||
\(24\) | −1.32948 | + | 1.11018i | −0.271378 | + | 0.226614i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.97532 | + | 3.42136i | 0.387392 | + | 0.670983i | ||||
\(27\) | −4.51846 | + | 2.56584i | −0.869578 | + | 0.493796i | ||||
\(28\) | 2.21694 | − | 1.44401i | 0.418962 | − | 0.272893i | ||||
\(29\) | 3.70789 | − | 2.14075i | 0.688537 | − | 0.397527i | −0.114527 | − | 0.993420i | \(-0.536535\pi\) |
0.803064 | + | 0.595893i | \(0.203202\pi\) | |||||||
\(30\) | −0.296702 | − | 1.70645i | −0.0541701 | − | 0.311554i | ||||
\(31\) | 6.40644 | − | 3.69876i | 1.15063 | − | 0.664317i | 0.201590 | − | 0.979470i | \(-0.435389\pi\) |
0.949041 | + | 0.315153i | \(0.102056\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | −6.46161 | + | 5.39575i | −1.12482 | + | 0.939279i | ||||
\(34\) | −2.16902 | + | 1.25228i | −0.371983 | + | 0.214765i | ||||
\(35\) | 0.142082 | + | 2.64193i | 0.0240163 | + | 0.446568i | ||||
\(36\) | −2.82394 | + | 1.01261i | −0.470656 | + | 0.168769i | ||||
\(37\) | −1.82085 | − | 3.15380i | −0.299345 | − | 0.518482i | 0.676641 | − | 0.736313i | \(-0.263435\pi\) |
−0.975986 | + | 0.217832i | \(0.930102\pi\) | |||||||
\(38\) | −1.11129 | −0.180276 | ||||||||
\(39\) | 1.17216 | + | 6.74157i | 0.187696 | + | 1.07952i | ||||
\(40\) | − | 1.00000i | − | 0.158114i | ||||||
\(41\) | 3.91000 | − | 6.77231i | 0.610639 | − | 1.05766i | −0.380494 | − | 0.924783i | \(-0.624246\pi\) |
0.991133 | − | 0.132874i | \(-0.0424206\pi\) | |||||||
\(42\) | 4.46617 | − | 1.02632i | 0.689145 | − | 0.158365i | ||||
\(43\) | −3.62690 | − | 6.28198i | −0.553098 | − | 0.957993i | −0.998049 | − | 0.0624384i | \(-0.980112\pi\) |
0.444951 | − | 0.895555i | \(-0.353221\pi\) | |||||||
\(44\) | −4.20911 | + | 2.43013i | −0.634547 | + | 0.366356i | ||||
\(45\) | 0.535019 | − | 2.95191i | 0.0797559 | − | 0.440044i | ||||
\(46\) | −1.65202 | + | 2.86139i | −0.243577 | + | 0.421888i | ||||
\(47\) | 5.84258 | − | 10.1196i | 0.852227 | − | 1.47610i | −0.0269662 | − | 0.999636i | \(-0.508585\pi\) |
0.879194 | − | 0.476465i | \(-0.158082\pi\) | |||||||
\(48\) | −1.70645 | + | 0.296702i | −0.246305 | + | 0.0428252i | ||||
\(49\) | −6.95963 | + | 0.750744i | −0.994232 | + | 0.107249i | ||||
\(50\) | 0.866025 | + | 0.500000i | 0.122474 | + | 0.0707107i | ||||
\(51\) | −4.27391 | + | 0.743110i | −0.598468 | + | 0.104056i | ||||
\(52\) | 3.95064i | 0.547856i | ||||||||
\(53\) | −4.92292 | − | 2.84225i | −0.676216 | − | 0.390413i | 0.122212 | − | 0.992504i | \(-0.461001\pi\) |
−0.798428 | + | 0.602091i | \(0.794335\pi\) | |||||||
\(54\) | −5.19602 | − | 0.0371456i | −0.707089 | − | 0.00505487i | ||||
\(55\) | − | 4.86026i | − | 0.655358i | ||||||
\(56\) | 2.64193 | − | 0.142082i | 0.353043 | − | 0.0189866i | ||||
\(57\) | −1.80716 | − | 0.662634i | −0.239365 | − | 0.0877681i | ||||
\(58\) | 4.28150 | 0.562188 | ||||||||
\(59\) | −0.696461 | − | 1.20631i | −0.0906716 | − | 0.157048i | 0.817122 | − | 0.576464i | \(-0.195568\pi\) |
−0.907794 | + | 0.419417i | \(0.862235\pi\) | |||||||
\(60\) | 0.596273 | − | 1.62618i | 0.0769785 | − | 0.209939i | ||||
\(61\) | −7.97067 | − | 4.60187i | −1.02054 | − | 0.589209i | −0.106280 | − | 0.994336i | \(-0.533894\pi\) |
−0.914260 | + | 0.405127i | \(0.867227\pi\) | |||||||
\(62\) | 7.39752 | 0.939486 | ||||||||
\(63\) | 7.87476 | + | 0.994070i | 0.992126 | + | 0.125241i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −3.42136 | − | 1.97532i | −0.424367 | − | 0.245008i | ||||
\(66\) | −8.29379 | + | 1.44205i | −1.02090 | + | 0.177504i | ||||
\(67\) | −3.00724 | − | 5.20869i | −0.367393 | − | 0.636343i | 0.621764 | − | 0.783204i | \(-0.286416\pi\) |
−0.989157 | + | 0.146861i | \(0.953083\pi\) | |||||||
\(68\) | −2.50457 | −0.303723 | ||||||||
\(69\) | −4.39265 | + | 3.66807i | −0.528813 | + | 0.441584i | ||||
\(70\) | −1.19792 | + | 2.35902i | −0.143179 | + | 0.281957i | ||||
\(71\) | 9.66386i | 1.14689i | 0.819244 | + | 0.573445i | \(0.194393\pi\) | ||||
−0.819244 | + | 0.573445i | \(0.805607\pi\) | |||||||
\(72\) | −2.95191 | − | 0.535019i | −0.347886 | − | 0.0630526i | ||||
\(73\) | 12.0570 | + | 6.96114i | 1.41117 | + | 0.814739i | 0.995499 | − | 0.0947757i | \(-0.0302134\pi\) |
0.415671 | + | 0.909515i | \(0.363547\pi\) | |||||||
\(74\) | − | 3.64170i | − | 0.423338i | ||||||
\(75\) | 1.11018 | + | 1.32948i | 0.128192 | + | 0.153515i | ||||
\(76\) | −0.962409 | − | 0.555647i | −0.110396 | − | 0.0637371i | ||||
\(77\) | 12.8405 | − | 0.690557i | 1.46331 | − | 0.0786963i | ||||
\(78\) | −2.35566 | + | 6.42445i | −0.266726 | + | 0.727426i | ||||
\(79\) | 3.91911 | − | 6.78809i | 0.440934 | − | 0.763720i | −0.556825 | − | 0.830630i | \(-0.687981\pi\) |
0.997759 | + | 0.0669097i | \(0.0213140\pi\) | |||||||
\(80\) | 0.500000 | − | 0.866025i | 0.0559017 | − | 0.0968246i | ||||
\(81\) | −8.42751 | − | 3.15865i | −0.936390 | − | 0.350961i | ||||
\(82\) | 6.77231 | − | 3.91000i | 0.747877 | − | 0.431787i | ||||
\(83\) | −0.393868 | − | 0.682199i | −0.0432326 | − | 0.0748811i | 0.843599 | − | 0.536973i | \(-0.180432\pi\) |
−0.886832 | + | 0.462092i | \(0.847099\pi\) | |||||||
\(84\) | 4.38098 | + | 1.34426i | 0.478004 | + | 0.146671i | ||||
\(85\) | 1.25228 | − | 2.16902i | 0.135829 | − | 0.235263i | ||||
\(86\) | − | 7.25381i | − | 0.782198i | ||||||
\(87\) | 6.96248 | + | 2.55294i | 0.746456 | + | 0.273704i | ||||
\(88\) | −4.86026 | −0.518106 | ||||||||
\(89\) | 7.49361 | + | 12.9793i | 0.794321 | + | 1.37580i | 0.923270 | + | 0.384153i | \(0.125506\pi\) |
−0.128949 | + | 0.991651i | \(0.541160\pi\) | |||||||
\(90\) | 1.93929 | − | 2.28892i | 0.204419 | − | 0.241273i | ||||
\(91\) | 4.73255 | − | 9.31966i | 0.496106 | − | 0.976966i | ||||
\(92\) | −2.86139 | + | 1.65202i | −0.298320 | + | 0.172235i | ||||
\(93\) | 12.0297 | + | 4.41094i | 1.24742 | + | 0.457393i | ||||
\(94\) | 10.1196 | − | 5.84258i | 1.04376 | − | 0.602616i | ||||
\(95\) | 0.962409 | − | 0.555647i | 0.0987410 | − | 0.0570082i | ||||
\(96\) | −1.62618 | − | 0.596273i | −0.165971 | − | 0.0608569i | ||||
\(97\) | 14.9781 | − | 8.64760i | 1.52079 | − | 0.878031i | 0.521095 | − | 0.853499i | \(-0.325524\pi\) |
0.999699 | − | 0.0245323i | \(-0.00780966\pi\) | |||||||
\(98\) | −6.40258 | − | 2.82965i | −0.646759 | − | 0.285838i | ||||
\(99\) | −14.3470 | − | 2.60033i | −1.44193 | − | 0.261343i | ||||
\(100\) | 0.500000 | + | 0.866025i | 0.0500000 | + | 0.0866025i | ||||
\(101\) | 2.93286 | 0.291831 | 0.145915 | − | 0.989297i | \(-0.453387\pi\) | ||||
0.145915 | + | 0.989297i | \(0.453387\pi\) | |||||||
\(102\) | −4.07287 | − | 1.49340i | −0.403274 | − | 0.147869i | ||||
\(103\) | − | 2.58519i | − | 0.254727i | −0.991856 | − | 0.127363i | \(-0.959349\pi\) | ||
0.991856 | − | 0.127363i | \(-0.0406514\pi\) | |||||||
\(104\) | −1.97532 | + | 3.42136i | −0.193696 | + | 0.335492i | ||||
\(105\) | −3.35465 | + | 3.12191i | −0.327381 | + | 0.304667i | ||||
\(106\) | −2.84225 | − | 4.92292i | −0.276064 | − | 0.478157i | ||||
\(107\) | −6.46896 | + | 3.73486i | −0.625378 | + | 0.361062i | −0.778960 | − | 0.627074i | \(-0.784252\pi\) |
0.153582 | + | 0.988136i | \(0.450919\pi\) | |||||||
\(108\) | −4.48131 | − | 2.63018i | −0.431214 | − | 0.253089i | ||||
\(109\) | −8.23189 | + | 14.2581i | −0.788472 | + | 1.36567i | 0.138430 | + | 0.990372i | \(0.455794\pi\) |
−0.926903 | + | 0.375302i | \(0.877539\pi\) | |||||||
\(110\) | 2.43013 | − | 4.20911i | 0.231704 | − | 0.401323i | ||||
\(111\) | 2.17144 | − | 5.92205i | 0.206104 | − | 0.562096i | ||||
\(112\) | 2.35902 | + | 1.19792i | 0.222907 | + | 0.113193i | ||||
\(113\) | 2.91952 | + | 1.68559i | 0.274646 | + | 0.158567i | 0.630997 | − | 0.775785i | \(-0.282646\pi\) |
−0.356351 | + | 0.934352i | \(0.615979\pi\) | |||||||
\(114\) | −1.23373 | − | 1.47744i | −0.115550 | − | 0.138375i | ||||
\(115\) | − | 3.30404i | − | 0.308104i | ||||||
\(116\) | 3.70789 | + | 2.14075i | 0.344269 | + | 0.198764i | ||||
\(117\) | −7.66146 | + | 9.04269i | −0.708302 | + | 0.835997i | ||||
\(118\) | − | 1.39292i | − | 0.128229i | ||||||
\(119\) | 5.90833 | + | 3.00027i | 0.541615 | + | 0.275034i | ||||
\(120\) | 1.32948 | − | 1.11018i | 0.121364 | − | 0.101345i | ||||
\(121\) | −12.6222 | −1.14747 | ||||||||
\(122\) | −4.60187 | − | 7.97067i | −0.416634 | − | 0.721631i | ||||
\(123\) | 13.3444 | − | 2.32021i | 1.20323 | − | 0.209206i | ||||
\(124\) | 6.40644 | + | 3.69876i | 0.575315 | + | 0.332158i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 6.32271 | + | 4.79827i | 0.563271 | + | 0.427464i | ||||
\(127\) | 14.4595 | 1.28307 | 0.641535 | − | 0.767093i | \(-0.278298\pi\) | ||||
0.641535 | + | 0.767093i | \(0.278298\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 4.32525 | − | 11.7960i | 0.380817 | − | 1.03858i | ||||
\(130\) | −1.97532 | − | 3.42136i | −0.173247 | − | 0.300073i | ||||
\(131\) | −13.1850 | −1.15198 | −0.575988 | − | 0.817458i | \(-0.695382\pi\) | ||||
−0.575988 | + | 0.817458i | \(0.695382\pi\) | |||||||
\(132\) | −7.90366 | − | 2.89804i | −0.687925 | − | 0.252242i | ||||
\(133\) | 1.60472 | + | 2.46367i | 0.139147 | + | 0.213627i | ||||
\(134\) | − | 6.01448i | − | 0.519572i | ||||||
\(135\) | 4.51846 | − | 2.56584i | 0.388887 | − | 0.220832i | ||||
\(136\) | −2.16902 | − | 1.25228i | −0.185992 | − | 0.107382i | ||||
\(137\) | − | 10.3775i | − | 0.886614i | −0.896370 | − | 0.443307i | \(-0.853805\pi\) | ||
0.896370 | − | 0.443307i | \(-0.146195\pi\) | |||||||
\(138\) | −5.63818 | + | 0.980316i | −0.479954 | + | 0.0834501i | ||||
\(139\) | −7.92494 | − | 4.57547i | −0.672185 | − | 0.388086i | 0.124719 | − | 0.992192i | \(-0.460197\pi\) |
−0.796904 | + | 0.604106i | \(0.793530\pi\) | |||||||
\(140\) | −2.21694 | + | 1.44401i | −0.187366 | + | 0.122041i | ||||
\(141\) | 19.9401 | − | 3.46701i | 1.67926 | − | 0.291975i | ||||
\(142\) | −4.83193 | + | 8.36915i | −0.405487 | + | 0.702324i | ||||
\(143\) | −9.60058 | + | 16.6287i | −0.802841 | + | 1.39056i | ||||
\(144\) | −2.28892 | − | 1.93929i | −0.190743 | − | 0.161608i | ||||
\(145\) | −3.70789 | + | 2.14075i | −0.307923 | + | 0.177780i | ||||
\(146\) | 6.96114 | + | 12.0570i | 0.576108 | + | 0.997848i | ||||
\(147\) | −8.72451 | − | 8.41920i | −0.719585 | − | 0.694404i | ||||
\(148\) | 1.82085 | − | 3.15380i | 0.149673 | − | 0.259241i | ||||
\(149\) | 24.1838i | 1.98121i | 0.136746 | + | 0.990606i | \(0.456336\pi\) | ||||
−0.136746 | + | 0.990606i | \(0.543664\pi\) | |||||||
\(150\) | 0.296702 | + | 1.70645i | 0.0242256 | + | 0.139331i | ||||
\(151\) | −22.9956 | −1.87136 | −0.935679 | − | 0.352851i | \(-0.885212\pi\) | ||||
−0.935679 | + | 0.352851i | \(0.885212\pi\) | |||||||
\(152\) | −0.555647 | − | 0.962409i | −0.0450689 | − | 0.0780617i | ||||
\(153\) | −5.73274 | − | 4.85709i | −0.463465 | − | 0.392672i | ||||
\(154\) | 11.4655 | + | 5.82221i | 0.923914 | + | 0.469167i | ||||
\(155\) | −6.40644 | + | 3.69876i | −0.514578 | + | 0.297091i | ||||
\(156\) | −5.25229 | + | 4.38591i | −0.420520 | + | 0.351154i | ||||
\(157\) | 7.00637 | − | 4.04513i | 0.559169 | − | 0.322836i | −0.193643 | − | 0.981072i | \(-0.562030\pi\) |
0.752812 | + | 0.658236i | \(0.228697\pi\) | |||||||
\(158\) | 6.78809 | − | 3.91911i | 0.540032 | − | 0.311787i | ||||
\(159\) | −1.68660 | − | 9.70031i | −0.133756 | − | 0.769285i | ||||
\(160\) | 0.866025 | − | 0.500000i | 0.0684653 | − | 0.0395285i | ||||
\(161\) | 8.72906 | − | 0.469446i | 0.687947 | − | 0.0369975i | ||||
\(162\) | −5.71911 | − | 6.94923i | −0.449336 | − | 0.545983i | ||||
\(163\) | −0.616736 | − | 1.06822i | −0.0483065 | − | 0.0836693i | 0.840861 | − | 0.541251i | \(-0.182049\pi\) |
−0.889168 | + | 0.457582i | \(0.848716\pi\) | |||||||
\(164\) | 7.81999 | 0.610639 | ||||||||
\(165\) | 6.46161 | − | 5.39575i | 0.503036 | − | 0.420058i | ||||
\(166\) | − | 0.787736i | − | 0.0611401i | ||||||
\(167\) | 5.43643 | − | 9.41617i | 0.420683 | − | 0.728645i | −0.575323 | − | 0.817926i | \(-0.695124\pi\) |
0.996006 | + | 0.0892813i | \(0.0284570\pi\) | |||||||
\(168\) | 3.12191 | + | 3.35465i | 0.240860 | + | 0.258817i | ||||
\(169\) | 1.30379 | + | 2.25823i | 0.100292 | + | 0.173710i | ||||
\(170\) | 2.16902 | − | 1.25228i | 0.166356 | − | 0.0960457i | ||||
\(171\) | −1.12531 | − | 3.13822i | −0.0860547 | − | 0.239986i | ||||
\(172\) | 3.62690 | − | 6.28198i | 0.276549 | − | 0.478997i | ||||
\(173\) | 2.88695 | − | 5.00034i | 0.219491 | − | 0.380169i | −0.735162 | − | 0.677892i | \(-0.762894\pi\) |
0.954652 | + | 0.297723i | \(0.0962271\pi\) | |||||||
\(174\) | 4.75322 | + | 5.69215i | 0.360340 | + | 0.431521i | ||||
\(175\) | −0.142082 | − | 2.64193i | −0.0107404 | − | 0.199711i | ||||
\(176\) | −4.20911 | − | 2.43013i | −0.317274 | − | 0.183178i | ||||
\(177\) | 0.830562 | − | 2.26514i | 0.0624289 | − | 0.170259i | ||||
\(178\) | 14.9872i | 1.12334i | ||||||||
\(179\) | −4.85812 | − | 2.80484i | −0.363113 | − | 0.209643i | 0.307332 | − | 0.951602i | \(-0.400564\pi\) |
−0.670445 | + | 0.741959i | \(0.733897\pi\) | |||||||
\(180\) | 2.82394 | − | 1.01261i | 0.210484 | − | 0.0754758i | ||||
\(181\) | − | 24.0589i | − | 1.78828i | −0.447784 | − | 0.894142i | \(-0.647787\pi\) | ||
0.447784 | − | 0.894142i | \(-0.352213\pi\) | |||||||
\(182\) | 8.75834 | − | 5.70478i | 0.649211 | − | 0.422867i | ||||
\(183\) | −2.73077 | − | 15.7057i | −0.201864 | − | 1.16100i | ||||
\(184\) | −3.30404 | −0.243577 | ||||||||
\(185\) | 1.82085 | + | 3.15380i | 0.133871 | + | 0.231872i | ||||
\(186\) | 8.21255 | + | 9.83483i | 0.602173 | + | 0.721125i | ||||
\(187\) | −10.5420 | − | 6.08642i | −0.770907 | − | 0.445083i | ||||
\(188\) | 11.6852 | 0.852227 | ||||||||
\(189\) | 7.42077 | + | 11.5729i | 0.539782 | + | 0.841805i | ||||
\(190\) | 1.11129 | 0.0806217 | ||||||||
\(191\) | 20.9885 | + | 12.1177i | 1.51867 | + | 0.876807i | 0.999758 | + | 0.0219813i | \(0.00699743\pi\) |
0.518916 | + | 0.854826i | \(0.326336\pi\) | |||||||
\(192\) | −1.11018 | − | 1.32948i | −0.0801200 | − | 0.0959467i | ||||
\(193\) | 0.308738 | + | 0.534750i | 0.0222235 | + | 0.0384921i | 0.876923 | − | 0.480630i | \(-0.159592\pi\) |
−0.854700 | + | 0.519123i | \(0.826259\pi\) | |||||||
\(194\) | 17.2952 | 1.24172 | ||||||||
\(195\) | −1.17216 | − | 6.74157i | −0.0839404 | − | 0.482774i | ||||
\(196\) | −4.12998 | − | 5.65184i | −0.294998 | − | 0.403703i | ||||
\(197\) | 2.28650i | 0.162906i | 0.996677 | + | 0.0814531i | \(0.0259561\pi\) | ||||
−0.996677 | + | 0.0814531i | \(0.974044\pi\) | |||||||
\(198\) | −11.1247 | − | 9.42548i | −0.790601 | − | 0.669839i | ||||
\(199\) | −3.60562 | − | 2.08171i | −0.255596 | − | 0.147568i | 0.366728 | − | 0.930328i | \(-0.380478\pi\) |
−0.622324 | + | 0.782760i | \(0.713811\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | 3.58627 | − | 9.78062i | 0.252956 | − | 0.689872i | ||||
\(202\) | 2.53993 | + | 1.46643i | 0.178709 | + | 0.103178i | ||||
\(203\) | −6.18254 | − | 9.49182i | −0.433929 | − | 0.666195i | ||||
\(204\) | −2.78051 | − | 3.32976i | −0.194675 | − | 0.233130i | ||||
\(205\) | −3.91000 | + | 6.77231i | −0.273086 | + | 0.472999i | ||||
\(206\) | 1.29260 | − | 2.23884i | 0.0900595 | − | 0.155988i | ||||
\(207\) | −9.75323 | − | 1.76773i | −0.677896 | − | 0.122865i | ||||
\(208\) | −3.42136 | + | 1.97532i | −0.237228 | + | 0.136964i | ||||
\(209\) | −2.70059 | − | 4.67756i | −0.186804 | − | 0.323554i | ||||
\(210\) | −4.46617 | + | 1.02632i | −0.308195 | + | 0.0708230i | ||||
\(211\) | 1.26573 | − | 2.19231i | 0.0871365 | − | 0.150925i | −0.819163 | − | 0.573561i | \(-0.805562\pi\) |
0.906300 | + | 0.422636i | \(0.138895\pi\) | |||||||
\(212\) | − | 5.68450i | − | 0.390413i | ||||||
\(213\) | −12.8479 | + | 10.7286i | −0.880323 | + | 0.735111i | ||||
\(214\) | −7.46971 | −0.510619 | ||||||||
\(215\) | 3.62690 | + | 6.28198i | 0.247353 | + | 0.428428i | ||||
\(216\) | −2.56584 | − | 4.51846i | −0.174583 | − | 0.307442i | ||||
\(217\) | −10.6821 | − | 16.3999i | −0.725149 | − | 1.11329i | ||||
\(218\) | −14.2581 | + | 8.23189i | −0.965677 | + | 0.557534i | ||||
\(219\) | 4.13077 | + | 23.7576i | 0.279131 | + | 1.60539i | ||||
\(220\) | 4.20911 | − | 2.43013i | 0.283778 | − | 0.163839i | ||||
\(221\) | −8.56901 | + | 4.94732i | −0.576414 | + | 0.332793i | ||||
\(222\) | 4.84155 | − | 4.04292i | 0.324944 | − | 0.271343i | ||||
\(223\) | −9.62445 | + | 5.55668i | −0.644501 | + | 0.372103i | −0.786346 | − | 0.617786i | \(-0.788030\pi\) |
0.141845 | + | 0.989889i | \(0.454696\pi\) | |||||||
\(224\) | 1.44401 | + | 2.21694i | 0.0964822 | + | 0.148126i | ||||
\(225\) | −0.535019 | + | 2.95191i | −0.0356679 | + | 0.196794i | ||||
\(226\) | 1.68559 | + | 2.91952i | 0.112124 | + | 0.194204i | ||||
\(227\) | −11.5284 | −0.765168 | −0.382584 | − | 0.923921i | \(-0.624966\pi\) | ||||
−0.382584 | + | 0.923921i | \(0.624966\pi\) | |||||||
\(228\) | −0.329723 | − | 1.89637i | −0.0218364 | − | 0.125590i | ||||
\(229\) | 26.2564i | 1.73507i | 0.497376 | + | 0.867535i | \(0.334297\pi\) | ||||
−0.497376 | + | 0.867535i | \(0.665703\pi\) | |||||||
\(230\) | 1.65202 | − | 2.86139i | 0.108931 | − | 0.188674i | ||||
\(231\) | 15.1733 | + | 16.3045i | 0.998329 | + | 1.07276i | ||||
\(232\) | 2.14075 | + | 3.70789i | 0.140547 | + | 0.243435i | ||||
\(233\) | −0.657636 | + | 0.379686i | −0.0430832 | + | 0.0248741i | −0.521387 | − | 0.853320i | \(-0.674585\pi\) |
0.478304 | + | 0.878194i | \(0.341252\pi\) | |||||||
\(234\) | −11.1564 | + | 4.00048i | −0.729314 | + | 0.261519i | ||||
\(235\) | −5.84258 | + | 10.1196i | −0.381128 | + | 0.660132i | ||||
\(236\) | 0.696461 | − | 1.20631i | 0.0453358 | − | 0.0785239i | ||||
\(237\) | 13.3755 | − | 2.32561i | 0.868833 | − | 0.151065i | ||||
\(238\) | 3.61663 | + | 5.55247i | 0.234431 | + | 0.359913i | ||||
\(239\) | −21.2951 | − | 12.2947i | −1.37746 | − | 0.795280i | −0.385611 | − | 0.922661i | \(-0.626009\pi\) |
−0.991854 | + | 0.127382i | \(0.959343\pi\) | |||||||
\(240\) | 1.70645 | − | 0.296702i | 0.110151 | − | 0.0191520i | ||||
\(241\) | − | 13.4712i | − | 0.867754i | −0.900972 | − | 0.433877i | \(-0.857145\pi\) | ||
0.900972 | − | 0.433877i | \(-0.142855\pi\) | |||||||
\(242\) | −10.9311 | − | 6.31108i | −0.702678 | − | 0.405691i | ||||
\(243\) | −5.15666 | − | 14.7108i | −0.330800 | − | 0.943701i | ||||
\(244\) | − | 9.20374i | − | 0.589209i | ||||||
\(245\) | 6.95963 | − | 0.750744i | 0.444634 | − | 0.0479633i | ||||
\(246\) | 12.7167 | + | 4.66285i | 0.810788 | + | 0.297292i | ||||
\(247\) | −4.39033 | −0.279350 | ||||||||
\(248\) | 3.69876 | + | 6.40644i | 0.234871 | + | 0.406809i | ||||
\(249\) | 0.469705 | − | 1.28100i | 0.0297664 | − | 0.0811800i | ||||
\(250\) | −0.866025 | − | 0.500000i | −0.0547723 | − | 0.0316228i | ||||
\(251\) | −1.02268 | −0.0645513 | −0.0322756 | − | 0.999479i | \(-0.510275\pi\) | ||||
−0.0322756 | + | 0.999479i | \(0.510275\pi\) | |||||||
\(252\) | 3.07649 | + | 7.31678i | 0.193801 | + | 0.460914i | ||||
\(253\) | −16.0585 | −1.00959 | ||||||||
\(254\) | 12.5223 | + | 7.22974i | 0.785717 | + | 0.453634i | ||||
\(255\) | 4.27391 | − | 0.743110i | 0.267643 | − | 0.0465353i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 23.8069 | 1.48503 | 0.742517 | − | 0.669827i | \(-0.233632\pi\) | ||||
0.742517 | + | 0.669827i | \(0.233632\pi\) | |||||||
\(258\) | 9.64377 | − | 8.05300i | 0.600395 | − | 0.501358i | ||||
\(259\) | −8.07342 | + | 5.25866i | −0.501658 | + | 0.326757i | ||||
\(260\) | − | 3.95064i | − | 0.245008i | ||||||
\(261\) | 4.33550 | + | 12.0907i | 0.268361 | + | 0.748394i | ||||
\(262\) | −11.4185 | − | 6.59248i | −0.705438 | − | 0.407285i | ||||
\(263\) | − | 7.59726i | − | 0.468467i | −0.972180 | − | 0.234234i | \(-0.924742\pi\) | ||
0.972180 | − | 0.234234i | \(-0.0752580\pi\) | |||||||
\(264\) | −5.39575 | − | 6.46161i | −0.332085 | − | 0.397684i | ||||
\(265\) | 4.92292 | + | 2.84225i | 0.302413 | + | 0.174598i | ||||
\(266\) | 0.157895 | + | 2.93596i | 0.00968118 | + | 0.180016i | ||||
\(267\) | −8.93647 | + | 24.3719i | −0.546903 | + | 1.49154i | ||||
\(268\) | 3.00724 | − | 5.20869i | 0.183696 | − | 0.318172i | ||||
\(269\) | −3.58635 | + | 6.21175i | −0.218664 | + | 0.378737i | −0.954400 | − | 0.298532i | \(-0.903503\pi\) |
0.735736 | + | 0.677269i | \(0.236836\pi\) | |||||||
\(270\) | 5.19602 | + | 0.0371456i | 0.316220 | + | 0.00226061i | ||||
\(271\) | −3.19806 | + | 1.84640i | −0.194268 | + | 0.112161i | −0.593979 | − | 0.804480i | \(-0.702444\pi\) |
0.399711 | + | 0.916641i | \(0.369111\pi\) | |||||||
\(272\) | −1.25228 | − | 2.16902i | −0.0759308 | − | 0.131516i | ||||
\(273\) | 17.6442 | − | 4.05464i | 1.06788 | − | 0.245398i | ||||
\(274\) | 5.18877 | − | 8.98722i | 0.313465 | − | 0.542938i | ||||
\(275\) | 4.86026i | 0.293085i | ||||||||
\(276\) | −5.37297 | − | 1.97011i | −0.323415 | − | 0.118587i | ||||
\(277\) | 24.9090 | 1.49663 | 0.748317 | − | 0.663341i | \(-0.230862\pi\) | ||||
0.748317 | + | 0.663341i | \(0.230862\pi\) | |||||||
\(278\) | −4.57547 | − | 7.92494i | −0.274418 | − | 0.475306i | ||||
\(279\) | 7.49083 | + | 20.8901i | 0.448464 | + | 1.25066i | ||||
\(280\) | −2.64193 | + | 0.142082i | −0.157886 | + | 0.00849104i | ||||
\(281\) | −12.6865 | + | 7.32455i | −0.756813 | + | 0.436946i | −0.828150 | − | 0.560506i | \(-0.810607\pi\) |
0.0713375 | + | 0.997452i | \(0.477273\pi\) | |||||||
\(282\) | 19.0022 | + | 6.96754i | 1.13156 | + | 0.414911i | ||||
\(283\) | 5.49922 | − | 3.17497i | 0.326895 | − | 0.188733i | −0.327567 | − | 0.944828i | \(-0.606229\pi\) |
0.654462 | + | 0.756095i | \(0.272895\pi\) | |||||||
\(284\) | −8.36915 | + | 4.83193i | −0.496618 | + | 0.286722i | ||||
\(285\) | 1.80716 | + | 0.662634i | 0.107047 | + | 0.0392511i | ||||
\(286\) | −16.6287 | + | 9.60058i | −0.983275 | + | 0.567694i | ||||
\(287\) | −18.4475 | − | 9.36772i | −1.08892 | − | 0.552959i | ||||
\(288\) | −1.01261 | − | 2.82394i | −0.0596688 | − | 0.166402i | ||||
\(289\) | 5.36358 | + | 9.28999i | 0.315504 | + | 0.546470i | ||||
\(290\) | −4.28150 | −0.251418 | ||||||||
\(291\) | 28.1251 | + | 10.3127i | 1.64872 | + | 0.604539i | ||||
\(292\) | 13.9223i | 0.814739i | ||||||||
\(293\) | 1.79507 | − | 3.10915i | 0.104869 | − | 0.181638i | −0.808816 | − | 0.588062i | \(-0.799891\pi\) |
0.913685 | + | 0.406424i | \(0.133224\pi\) | |||||||
\(294\) | −3.34604 | − | 11.6535i | −0.195145 | − | 0.679646i | ||||
\(295\) | 0.696461 | + | 1.20631i | 0.0405496 | + | 0.0702339i | ||||
\(296\) | 3.15380 | − | 1.82085i | 0.183311 | − | 0.105835i | ||||
\(297\) | −12.4707 | − | 21.9609i | −0.723621 | − | 1.27430i | ||||
\(298\) | −12.0919 | + | 20.9438i | −0.700464 | + | 1.21324i | ||||
\(299\) | −6.52655 | + | 11.3043i | −0.377440 | + | 0.653745i | ||||
\(300\) | −0.596273 | + | 1.62618i | −0.0344258 | + | 0.0938875i | ||||
\(301\) | −16.0813 | + | 10.4746i | −0.926908 | + | 0.603746i | ||||
\(302\) | −19.9148 | − | 11.4978i | −1.14597 | − | 0.661625i | ||||
\(303\) | 3.25599 | + | 3.89917i | 0.187052 | + | 0.224001i | ||||
\(304\) | − | 1.11129i | − | 0.0637371i | ||||||
\(305\) | 7.97067 | + | 4.60187i | 0.456399 | + | 0.263502i | ||||
\(306\) | −2.53616 | − | 7.07273i | −0.144982 | − | 0.404321i | ||||
\(307\) | − | 11.0589i | − | 0.631166i | −0.948898 | − | 0.315583i | \(-0.897800\pi\) | ||
0.948898 | − | 0.315583i | \(-0.102200\pi\) | |||||||
\(308\) | 7.01829 | + | 10.7749i | 0.399904 | + | 0.613958i | ||||
\(309\) | 3.43696 | − | 2.87002i | 0.195522 | − | 0.163270i | ||||
\(310\) | −7.39752 | −0.420151 | ||||||||
\(311\) | −6.97233 | − | 12.0764i | −0.395364 | − | 0.684791i | 0.597783 | − | 0.801658i | \(-0.296048\pi\) |
−0.993148 | + | 0.116867i | \(0.962715\pi\) | |||||||
\(312\) | −6.74157 | + | 1.17216i | −0.381666 | + | 0.0663607i | ||||
\(313\) | 11.4932 | + | 6.63558i | 0.649632 | + | 0.375065i | 0.788315 | − | 0.615272i | \(-0.210954\pi\) |
−0.138683 | + | 0.990337i | \(0.544287\pi\) | |||||||
\(314\) | 8.09026 | 0.456560 | ||||||||
\(315\) | −7.87476 | − | 0.994070i | −0.443692 | − | 0.0560095i | ||||
\(316\) | 7.83821 | 0.440934 | ||||||||
\(317\) | 3.85429 | + | 2.22528i | 0.216478 | + | 0.124984i | 0.604319 | − | 0.796743i | \(-0.293445\pi\) |
−0.387840 | + | 0.921727i | \(0.626779\pi\) | |||||||
\(318\) | 3.38952 | − | 9.24402i | 0.190075 | − | 0.518379i | ||||
\(319\) | 10.4046 | + | 18.0213i | 0.582546 | + | 1.00900i | ||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −12.1471 | − | 4.45399i | −0.677984 | − | 0.248597i | ||||
\(322\) | 7.79431 | + | 3.95798i | 0.434360 | + | 0.220570i | ||||
\(323\) | − | 2.78331i | − | 0.154867i | ||||||
\(324\) | −1.47828 | − | 8.87776i | −0.0821268 | − | 0.493209i | ||||
\(325\) | 3.42136 | + | 1.97532i | 0.189783 | + | 0.109571i | ||||
\(326\) | − | 1.23347i | − | 0.0683157i | ||||||
\(327\) | −28.0946 | + | 4.88484i | −1.55364 | + | 0.270132i | ||||
\(328\) | 6.77231 | + | 3.91000i | 0.373938 | + | 0.215893i | ||||
\(329\) | −27.5655 | − | 13.9979i | −1.51974 | − | 0.771728i | ||||
\(330\) | 8.29379 | − | 1.44205i | 0.456558 | − | 0.0793822i | ||||
\(331\) | −3.91980 | + | 6.78928i | −0.215451 | + | 0.373173i | −0.953412 | − | 0.301671i | \(-0.902456\pi\) |
0.737961 | + | 0.674844i | \(0.235789\pi\) | |||||||
\(332\) | 0.393868 | − | 0.682199i | 0.0216163 | − | 0.0374405i | ||||
\(333\) | 10.2839 | − | 3.68763i | 0.563555 | − | 0.202081i | ||||
\(334\) | 9.41617 | − | 5.43643i | 0.515230 | − | 0.297468i | ||||
\(335\) | 3.00724 | + | 5.20869i | 0.164303 | + | 0.284581i | ||||
\(336\) | 1.02632 | + | 4.46617i | 0.0559905 | + | 0.243649i | ||||
\(337\) | −4.66042 | + | 8.07208i | −0.253869 | + | 0.439714i | −0.964588 | − | 0.263762i | \(-0.915037\pi\) |
0.710719 | + | 0.703476i | \(0.248370\pi\) | |||||||
\(338\) | 2.60758i | 0.141834i | ||||||||
\(339\) | 1.00023 | + | 5.75274i | 0.0543253 | + | 0.312446i | ||||
\(340\) | 2.50457 | 0.135829 | ||||||||
\(341\) | 17.9769 | + | 31.1370i | 0.973506 | + | 1.68616i | ||||
\(342\) | 0.594563 | − | 3.28044i | 0.0321503 | − | 0.177386i | ||||
\(343\) | 2.97226 | + | 18.2802i | 0.160487 | + | 0.987038i | ||||
\(344\) | 6.28198 | − | 3.62690i | 0.338702 | − | 0.195550i | ||||
\(345\) | 4.39265 | − | 3.66807i | 0.236492 | − | 0.197482i | ||||
\(346\) | 5.00034 | − | 2.88695i | 0.268820 | − | 0.155203i | ||||
\(347\) | −25.6810 | + | 14.8269i | −1.37863 | + | 0.795951i | −0.991994 | − | 0.126283i | \(-0.959695\pi\) |
−0.386633 | + | 0.922234i | \(0.626362\pi\) | |||||||
\(348\) | 1.27033 | + | 7.30616i | 0.0680968 | + | 0.391651i | ||||
\(349\) | 28.0322 | − | 16.1844i | 1.50053 | − | 0.866330i | 0.500528 | − | 0.865720i | \(-0.333139\pi\) |
1.00000 | 0.000609911i | \(-0.000194141\pi\) | ||||||||
\(350\) | 1.19792 | − | 2.35902i | 0.0640315 | − | 0.126095i | ||||
\(351\) | −20.5276 | − | 0.146749i | −1.09568 | − | 0.00783288i | ||||
\(352\) | −2.43013 | − | 4.20911i | −0.129526 | − | 0.224346i | ||||
\(353\) | 6.05699 | 0.322381 | 0.161191 | − | 0.986923i | \(-0.448467\pi\) | ||||
0.161191 | + | 0.986923i | \(0.448467\pi\) | |||||||
\(354\) | 1.85186 | − | 1.54639i | 0.0984252 | − | 0.0821897i | ||||
\(355\) | − | 9.66386i | − | 0.512905i | ||||||
\(356\) | −7.49361 | + | 12.9793i | −0.397160 | + | 0.687902i | ||||
\(357\) | 2.57049 | + | 11.1858i | 0.136045 | + | 0.592016i | ||||
\(358\) | −2.80484 | − | 4.85812i | −0.148240 | − | 0.256760i | ||||
\(359\) | 11.4661 | − | 6.61995i | 0.605157 | − | 0.349388i | −0.165911 | − | 0.986141i | \(-0.553056\pi\) |
0.771068 | + | 0.636753i | \(0.219723\pi\) | |||||||
\(360\) | 2.95191 | + | 0.535019i | 0.155579 | + | 0.0281980i | ||||
\(361\) | −8.88251 | + | 15.3850i | −0.467501 | + | 0.809735i | ||||
\(362\) | 12.0294 | − | 20.8356i | 0.632254 | − | 1.09510i | ||||
\(363\) | −14.0128 | − | 16.7809i | −0.735482 | − | 0.880767i | ||||
\(364\) | 10.4373 | − | 0.561317i | 0.547065 | − | 0.0294210i | ||||
\(365\) | −12.0570 | − | 6.96114i | −0.631094 | − | 0.364362i | ||||
\(366\) | 5.48794 | − | 14.9669i | 0.286859 | − | 0.782334i | ||||
\(367\) | 17.8999i | 0.934366i | 0.884161 | + | 0.467183i | \(0.154731\pi\) | ||||
−0.884161 | + | 0.467183i | \(0.845269\pi\) | |||||||
\(368\) | −2.86139 | − | 1.65202i | −0.149160 | − | 0.0861176i | ||||
\(369\) | 17.8993 | + | 15.1653i | 0.931801 | + | 0.789472i | ||||
\(370\) | 3.64170i | 0.189323i | ||||||||
\(371\) | −6.80958 | + | 13.4099i | −0.353536 | + | 0.696206i | ||||
\(372\) | 2.19486 | + | 12.6235i | 0.113798 | + | 0.654497i | ||||
\(373\) | −4.52467 | −0.234279 | −0.117139 | − | 0.993115i | \(-0.537372\pi\) | ||||
−0.117139 | + | 0.993115i | \(0.537372\pi\) | |||||||
\(374\) | −6.08642 | − | 10.5420i | −0.314721 | − | 0.545114i | ||||
\(375\) | −1.11018 | − | 1.32948i | −0.0573292 | − | 0.0686539i | ||||
\(376\) | 10.1196 | + | 5.84258i | 0.521881 | + | 0.301308i | ||||
\(377\) | 16.9147 | 0.871150 | ||||||||
\(378\) | 0.640127 | + | 13.7328i | 0.0329246 | + | 0.706340i | ||||
\(379\) | −7.47021 | −0.383719 | −0.191860 | − | 0.981422i | \(-0.561452\pi\) | ||||
−0.191860 | + | 0.981422i | \(0.561452\pi\) | |||||||
\(380\) | 0.962409 | + | 0.555647i | 0.0493705 | + | 0.0285041i | ||||
\(381\) | 16.0526 | + | 19.2235i | 0.822398 | + | 0.984852i | ||||
\(382\) | 12.1177 | + | 20.9885i | 0.619996 | + | 1.07386i | ||||
\(383\) | −33.0831 | −1.69047 | −0.845234 | − | 0.534396i | \(-0.820539\pi\) | ||||
−0.845234 | + | 0.534396i | \(0.820539\pi\) | |||||||
\(384\) | −0.296702 | − | 1.70645i | −0.0151410 | − | 0.0870819i | ||||
\(385\) | −12.8405 | + | 0.690557i | −0.654412 | + | 0.0351941i | ||||
\(386\) | 0.617476i | 0.0314287i | ||||||||
\(387\) | 20.4843 | − | 7.34530i | 1.04127 | − | 0.373383i | ||||
\(388\) | 14.9781 | + | 8.64760i | 0.760397 | + | 0.439015i | ||||
\(389\) | − | 36.4482i | − | 1.84800i | −0.382395 | − | 0.923999i | \(-0.624901\pi\) | ||
0.382395 | − | 0.923999i | \(-0.375099\pi\) | |||||||
\(390\) | 2.35566 | − | 6.42445i | 0.119284 | − | 0.325315i | ||||
\(391\) | −7.16653 | − | 4.13760i | −0.362427 | − | 0.209247i | ||||
\(392\) | −0.750744 | − | 6.95963i | −0.0379183 | − | 0.351514i | ||||
\(393\) | −14.6376 | − | 17.5291i | −0.738370 | − | 0.884226i | ||||
\(394\) | −1.14325 | + | 1.98016i | −0.0575960 | + | 0.0997593i | ||||
\(395\) | −3.91911 | + | 6.78809i | −0.197192 | + | 0.341546i | ||||
\(396\) | −4.92157 | − | 13.7251i | −0.247318 | − | 0.689711i | ||||
\(397\) | −13.3331 | + | 7.69789i | −0.669171 | + | 0.386346i | −0.795762 | − | 0.605609i | \(-0.792930\pi\) |
0.126592 | + | 0.991955i | \(0.459596\pi\) | |||||||
\(398\) | −2.08171 | − | 3.60562i | −0.104346 | − | 0.180733i | ||||
\(399\) | −1.49387 | + | 4.86855i | −0.0747871 | + | 0.243732i | ||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | 16.4073i | 0.819341i | 0.912234 | + | 0.409670i | \(0.134356\pi\) | ||||
−0.912234 | + | 0.409670i | \(0.865644\pi\) | |||||||
\(402\) | 7.99611 | − | 6.67713i | 0.398810 | − | 0.333025i | ||||
\(403\) | 29.2250 | 1.45580 | ||||||||
\(404\) | 1.46643 | + | 2.53993i | 0.0729576 | + | 0.126366i | ||||
\(405\) | 8.42751 | + | 3.15865i | 0.418766 | + | 0.156955i | ||||
\(406\) | −0.608325 | − | 11.3114i | −0.0301907 | − | 0.561377i | ||||
\(407\) | 15.3283 | − | 8.84980i | 0.759796 | − | 0.438668i | ||||
\(408\) | −0.743110 | − | 4.27391i | −0.0367894 | − | 0.211590i | ||||
\(409\) | −18.3018 | + | 10.5665i | −0.904964 | + | 0.522481i | −0.878807 | − | 0.477177i | \(-0.841660\pi\) |
−0.0261565 | + | 0.999658i | \(0.508327\pi\) | |||||||
\(410\) | −6.77231 | + | 3.91000i | −0.334461 | + | 0.193101i | ||||
\(411\) | 13.7967 | − | 11.5209i | 0.680541 | − | 0.568284i | ||||
\(412\) | 2.23884 | − | 1.29260i | 0.110300 | − | 0.0636817i | ||||
\(413\) | −3.08803 | + | 2.01140i | −0.151952 | + | 0.0989745i | ||||
\(414\) | −7.56268 | − | 6.40751i | −0.371686 | − | 0.314912i | ||||
\(415\) | 0.393868 | + | 0.682199i | 0.0193342 | + | 0.0334878i | ||||
\(416\) | −3.95064 | −0.193696 | ||||||||
\(417\) | −2.71510 | − | 15.6156i | −0.132959 | − | 0.764699i | ||||
\(418\) | − | 5.40118i | − | 0.264180i | ||||||
\(419\) | 2.31087 | − | 4.00254i | 0.112893 | − | 0.195537i | −0.804042 | − | 0.594572i | \(-0.797322\pi\) |
0.916936 | + | 0.399035i | \(0.130655\pi\) | |||||||
\(420\) | −4.38098 | − | 1.34426i | −0.213770 | − | 0.0655933i | ||||
\(421\) | 1.15555 | + | 2.00148i | 0.0563183 | + | 0.0975461i | 0.892810 | − | 0.450433i | \(-0.148731\pi\) |
−0.836492 | + | 0.547979i | \(0.815397\pi\) | |||||||
\(422\) | 2.19231 | − | 1.26573i | 0.106720 | − | 0.0616148i | ||||
\(423\) | 26.7463 | + | 22.6609i | 1.30045 | + | 1.10181i | ||||
\(424\) | 2.84225 | − | 4.92292i | 0.138032 | − | 0.239078i | ||||
\(425\) | −1.25228 | + | 2.16902i | −0.0607446 | + | 0.105213i | ||||
\(426\) | −16.4909 | + | 2.86729i | −0.798986 | + | 0.138921i | ||||
\(427\) | −11.0253 | + | 21.7118i | −0.533554 | + | 1.05071i | ||||
\(428\) | −6.46896 | − | 3.73486i | −0.312689 | − | 0.180531i | ||||
\(429\) | −32.7658 | + | 5.69702i | −1.58195 | + | 0.275055i | ||||
\(430\) | 7.25381i | 0.349810i | ||||||||
\(431\) | −21.3345 | − | 12.3175i | −1.02765 | − | 0.593313i | −0.111338 | − | 0.993783i | \(-0.535514\pi\) |
−0.916310 | + | 0.400469i | \(0.868847\pi\) | |||||||
\(432\) | 0.0371456 | − | 5.19602i | 0.00178717 | − | 0.249994i | ||||
\(433\) | − | 6.55773i | − | 0.315144i | −0.987507 | − | 0.157572i | \(-0.949633\pi\) | ||
0.987507 | − | 0.157572i | \(-0.0503667\pi\) | |||||||
\(434\) | −1.05106 | − | 19.5438i | −0.0504523 | − | 0.938130i | ||||
\(435\) | −6.96248 | − | 2.55294i | −0.333825 | − | 0.122404i | ||||
\(436\) | −16.4638 | −0.788472 | ||||||||
\(437\) | −1.83588 | − | 3.17984i | −0.0878221 | − | 0.152112i | ||||
\(438\) | −8.30147 | + | 22.6401i | −0.396660 | + | 1.08179i | ||||
\(439\) | 28.0844 | + | 16.2145i | 1.34040 | + | 0.773878i | 0.986865 | − | 0.161545i | \(-0.0516477\pi\) |
0.353531 | + | 0.935423i | \(0.384981\pi\) | |||||||
\(440\) | 4.86026 | 0.231704 | ||||||||
\(441\) | 1.50740 | − | 20.9458i | 0.0717811 | − | 0.997420i | ||||
\(442\) | −9.89465 | −0.470640 | ||||||||
\(443\) | 0.204110 | + | 0.117843i | 0.00969755 | + | 0.00559888i | 0.504841 | − | 0.863212i | \(-0.331551\pi\) |
−0.495143 | + | 0.868811i | \(0.664884\pi\) | |||||||
\(444\) | 6.21437 | − | 1.08050i | 0.294921 | − | 0.0512782i | ||||
\(445\) | −7.49361 | − | 12.9793i | −0.355231 | − | 0.615278i | ||||
\(446\) | −11.1134 | −0.526233 | ||||||||
\(447\) | −32.1518 | + | 26.8482i | −1.52073 | + | 1.26988i | ||||
\(448\) | 0.142082 | + | 2.64193i | 0.00671276 | + | 0.124820i | ||||
\(449\) | − | 18.8068i | − | 0.887549i | −0.896139 | − | 0.443774i | \(-0.853639\pi\) | ||
0.896139 | − | 0.443774i | \(-0.146361\pi\) | |||||||
\(450\) | −1.93929 | + | 2.28892i | −0.0914192 | + | 0.107901i | ||||
\(451\) | 32.9152 | + | 19.0036i | 1.54992 | + | 0.894845i | ||||
\(452\) | 3.37117i | 0.158567i | ||||||||
\(453\) | −25.5292 | − | 30.5722i | −1.19947 | − | 1.43641i | ||||
\(454\) | −9.98390 | − | 5.76421i | −0.468568 | − | 0.270528i | ||||
\(455\) | −4.73255 | + | 9.31966i | −0.221866 | + | 0.436912i | ||||
\(456\) | 0.662634 | − | 1.80716i | 0.0310307 | − | 0.0846282i | ||||
\(457\) | 9.30583 | − | 16.1182i | 0.435308 | − | 0.753976i | −0.562012 | − | 0.827129i | \(-0.689973\pi\) |
0.997321 | + | 0.0731525i | \(0.0233060\pi\) | |||||||
\(458\) | −13.1282 | + | 22.7387i | −0.613440 | + | 1.06251i | ||||
\(459\) | 0.0930335 | − | 13.0138i | 0.00434243 | − | 0.607431i | ||||
\(460\) | 2.86139 | − | 1.65202i | 0.133413 | − | 0.0770259i | ||||
\(461\) | 13.7720 | + | 23.8538i | 0.641426 | + | 1.11098i | 0.985115 | + | 0.171898i | \(0.0549901\pi\) |
−0.343689 | + | 0.939084i | \(0.611677\pi\) | |||||||
\(462\) | 4.98820 | + | 21.7068i | 0.232072 | + | 1.00989i | ||||
\(463\) | 0.239162 | − | 0.414241i | 0.0111148 | − | 0.0192514i | −0.860415 | − | 0.509595i | \(-0.829795\pi\) |
0.871529 | + | 0.490343i | \(0.163129\pi\) | |||||||
\(464\) | 4.28150i | 0.198764i | ||||||||
\(465\) | −12.0297 | − | 4.41094i | −0.557863 | − | 0.204552i | ||||
\(466\) | −0.759373 | −0.0351773 | ||||||||
\(467\) | −6.08486 | − | 10.5393i | −0.281574 | − | 0.487700i | 0.690199 | − | 0.723620i | \(-0.257523\pi\) |
−0.971773 | + | 0.235920i | \(0.924190\pi\) | |||||||
\(468\) | −11.6619 | − | 2.11367i | −0.539073 | − | 0.0977044i | ||||
\(469\) | −13.3337 | + | 8.68499i | −0.615695 | + | 0.401036i | ||||
\(470\) | −10.1196 | + | 5.84258i | −0.466784 | + | 0.269498i | ||||
\(471\) | 13.1562 | + | 4.82400i | 0.606206 | + | 0.222278i | ||||
\(472\) | 1.20631 | − | 0.696461i | 0.0555248 | − | 0.0320572i | ||||
\(473\) | 30.5321 | − | 17.6277i | 1.40387 | − | 0.810523i | ||||
\(474\) | 12.7463 | + | 4.67372i | 0.585459 | + | 0.214671i | ||||
\(475\) | −0.962409 | + | 0.555647i | −0.0441583 | + | 0.0254948i | ||||
\(476\) | 0.355855 | + | 6.61690i | 0.0163106 | + | 0.303285i | ||||
\(477\) | 11.0239 | − | 13.0114i | 0.504751 | − | 0.595749i | ||||
\(478\) | −12.2947 | − | 21.2951i | −0.562348 | − | 0.974015i | ||||
\(479\) | −40.3538 | −1.84381 | −0.921906 | − | 0.387413i | \(-0.873369\pi\) | ||||
−0.921906 | + | 0.387413i | \(0.873369\pi\) | |||||||
\(480\) | 1.62618 | + | 0.596273i | 0.0742246 | + | 0.0272160i | ||||
\(481\) | − | 14.3870i | − | 0.655992i | ||||||
\(482\) | 6.73558 | − | 11.6664i | 0.306797 | − | 0.531389i | ||||
\(483\) | 10.3149 | + | 11.0839i | 0.469345 | + | 0.504336i | ||||
\(484\) | −6.31108 | − | 10.9311i | −0.286867 | − | 0.496868i | ||||
\(485\) | −14.9781 | + | 8.64760i | −0.680120 | + | 0.392667i | ||||
\(486\) | 2.88962 | − | 15.3183i | 0.131076 | − | 0.694852i | ||||
\(487\) | −4.11277 | + | 7.12353i | −0.186367 | + | 0.322798i | −0.944036 | − | 0.329841i | \(-0.893005\pi\) |
0.757669 | + | 0.652639i | \(0.226338\pi\) | |||||||
\(488\) | 4.60187 | − | 7.97067i | 0.208317 | − | 0.360815i | ||||
\(489\) | 0.735486 | − | 2.00585i | 0.0332598 | − | 0.0907075i | ||||
\(490\) | 6.40258 | + | 2.82965i | 0.289239 | + | 0.127831i | ||||
\(491\) | 9.11388 | + | 5.26190i | 0.411303 | + | 0.237466i | 0.691350 | − | 0.722520i | \(-0.257016\pi\) |
−0.280046 | + | 0.959987i | \(0.590350\pi\) | |||||||
\(492\) | 8.68157 | + | 10.3965i | 0.391395 | + | 0.468710i | ||||
\(493\) | 10.7233i | 0.482953i | ||||||||
\(494\) | −3.80213 | − | 2.19516i | −0.171066 | − | 0.0987650i | ||||
\(495\) | 14.3470 | + | 2.60033i | 0.644852 | + | 0.116876i | ||||
\(496\) | 7.39752i | 0.332158i | ||||||||
\(497\) | 25.5313 | − | 1.37306i | 1.14523 | − | 0.0615904i | ||||
\(498\) | 1.04728 | − | 0.874525i | 0.0469296 | − | 0.0391884i | ||||
\(499\) | 0.850484 | 0.0380729 | 0.0190364 | − | 0.999819i | \(-0.493940\pi\) | ||||
0.0190364 | + | 0.999819i | \(0.493940\pi\) | |||||||
\(500\) | −0.500000 | − | 0.866025i | −0.0223607 | − | 0.0387298i | ||||
\(501\) | 18.5540 | − | 3.22600i | 0.828930 | − | 0.144127i | ||||
\(502\) | −0.885671 | − | 0.511342i | −0.0395294 | − | 0.0228223i | ||||
\(503\) | −21.5476 | −0.960759 | −0.480380 | − | 0.877061i | \(-0.659501\pi\) | ||||
−0.480380 | + | 0.877061i | \(0.659501\pi\) | |||||||
\(504\) | −0.994070 | + | 7.87476i | −0.0442794 | + | 0.350770i | ||||
\(505\) | −2.93286 | −0.130511 | ||||||||
\(506\) | −13.9071 | − | 8.02926i | −0.618245 | − | 0.356944i | ||||
\(507\) | −1.55483 | + | 4.24039i | −0.0690524 | + | 0.188323i | ||||
\(508\) | 7.22974 | + | 12.5223i | 0.320768 | + | 0.555586i | ||||
\(509\) | −2.20898 | −0.0979113 | −0.0489556 | − | 0.998801i | \(-0.515589\pi\) | ||||
−0.0489556 | + | 0.998801i | \(0.515589\pi\) | |||||||
\(510\) | 4.07287 | + | 1.49340i | 0.180350 | + | 0.0661291i | ||||
\(511\) | 16.6778 | − | 32.8430i | 0.737781 | − | 1.45289i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 2.92290 | − | 4.98005i | 0.129049 | − | 0.219875i | ||||
\(514\) | 20.6174 | + | 11.9035i | 0.909394 | + | 0.525039i | ||||
\(515\) | 2.58519i | 0.113917i | ||||||||
\(516\) | 12.3783 | − | 2.15222i | 0.544922 | − | 0.0947462i | ||||
\(517\) | 49.1841 | + | 28.3965i | 2.16311 | + | 1.24887i | ||||
\(518\) | −9.62112 | + | 0.517421i | −0.422728 | + | 0.0227342i | ||||
\(519\) | 9.85286 | − | 1.71313i | 0.432493 | − | 0.0751979i | ||||
\(520\) | 1.97532 | − | 3.42136i | 0.0866236 | − | 0.150036i | ||||
\(521\) | −12.0872 | + | 20.9356i | −0.529548 | + | 0.917204i | 0.469858 | + | 0.882742i | \(0.344305\pi\) |
−0.999406 | + | 0.0344623i | \(0.989028\pi\) | |||||||
\(522\) | −2.29068 | + | 12.6386i | −0.100260 | + | 0.553176i | ||||
\(523\) | −10.3393 | + | 5.96937i | −0.452104 | + | 0.261022i | −0.708718 | − | 0.705492i | \(-0.750726\pi\) |
0.256614 | + | 0.966514i | \(0.417393\pi\) | |||||||
\(524\) | −6.59248 | − | 11.4185i | −0.287994 | − | 0.498820i | ||||
\(525\) | 3.35465 | − | 3.12191i | 0.146409 | − | 0.136251i | ||||
\(526\) | 3.79863 | − | 6.57942i | 0.165628 | − | 0.286876i | ||||
\(527\) | 18.5276i | 0.807074i | ||||||||
\(528\) | −1.44205 | − | 8.29379i | −0.0627572 | − | 0.360941i | ||||
\(529\) | 12.0833 | 0.525361 | ||||||||
\(530\) | 2.84225 | + | 4.92292i | 0.123460 | + | 0.213838i | ||||
\(531\) | 3.93352 | − | 1.41049i | 0.170700 | − | 0.0612102i | ||||
\(532\) | −1.33124 | + | 2.62157i | −0.0577166 | + | 0.113659i | ||||
\(533\) | 26.7550 | − | 15.4470i | 1.15889 | − | 0.669084i | ||||
\(534\) | −19.9252 | + | 16.6384i | −0.862246 | + | 0.720016i | ||||
\(535\) | 6.46896 | − | 3.73486i | 0.279678 | − | 0.161472i | ||||
\(536\) | 5.20869 | − | 3.00724i | 0.224981 | − | 0.129893i | ||||
\(537\) | −1.66440 | − | 9.57262i | −0.0718242 | − | 0.413089i | ||||
\(538\) | −6.21175 | + | 3.58635i | −0.267807 | + | 0.154619i | ||||
\(539\) | −3.64881 | − | 33.8256i | −0.157166 | − | 1.45697i | ||||
\(540\) | 4.48131 | + | 2.63018i | 0.192845 | + | 0.113185i | ||||
\(541\) | 7.35700 | + | 12.7427i | 0.316302 | + | 0.547852i | 0.979713 | − | 0.200403i | \(-0.0642253\pi\) |
−0.663411 | + | 0.748255i | \(0.730892\pi\) | |||||||
\(542\) | −3.69280 | −0.158620 | ||||||||
\(543\) | 31.9857 | − | 26.7096i | 1.37264 | − | 1.14622i | ||||
\(544\) | − | 2.50457i | − | 0.107382i | ||||||
\(545\) | 8.23189 | − | 14.2581i | 0.352616 | − | 0.610748i | ||||
\(546\) | 17.3077 | + | 5.31070i | 0.740700 | + | 0.227277i | ||||
\(547\) | 8.78526 | + | 15.2165i | 0.375631 | + | 0.650611i | 0.990421 | − | 0.138079i | \(-0.0440928\pi\) |
−0.614791 | + | 0.788690i | \(0.710759\pi\) | |||||||
\(548\) | 8.98722 | − | 5.18877i | 0.383915 | − | 0.221653i | ||||
\(549\) | 17.8488 | − | 21.0666i | 0.761766 | − | 0.899100i | ||||
\(550\) | −2.43013 | + | 4.20911i | −0.103621 | + | 0.179477i | ||||
\(551\) | −2.37900 | + | 4.12055i | −0.101349 | + | 0.175541i | ||||
\(552\) | −3.66807 | − | 4.39265i | −0.156123 | − | 0.186964i | ||||
\(553\) | −18.4905 | − | 9.38955i | −0.786297 | − | 0.399284i | ||||
\(554\) | 21.5718 | + | 12.4545i | 0.916498 | + | 0.529140i | ||||
\(555\) | −2.17144 | + | 5.92205i | −0.0921727 | + | 0.251377i | ||||
\(556\) | − | 9.15093i | − | 0.388086i | ||||||
\(557\) | −16.7457 | − | 9.66812i | −0.709537 | − | 0.409652i | 0.101352 | − | 0.994851i | \(-0.467683\pi\) |
−0.810890 | + | 0.585199i | \(0.801016\pi\) | |||||||
\(558\) | −3.95781 | + | 21.8368i | −0.167548 | + | 0.924425i | ||||
\(559\) | − | 28.6572i | − | 1.21207i | ||||||
\(560\) | −2.35902 | − | 1.19792i | −0.0996869 | − | 0.0506214i | ||||
\(561\) | −3.61171 | − | 20.7723i | −0.152486 | − | 0.877009i | ||||
\(562\) | −14.6491 | −0.617935 | ||||||||
\(563\) | −12.0323 | − | 20.8406i | −0.507103 | − | 0.878327i | −0.999966 | − | 0.00822091i | \(-0.997383\pi\) |
0.492864 | − | 0.870107i | \(-0.335950\pi\) | |||||||
\(564\) | 12.9726 | + | 15.5351i | 0.546244 | + | 0.654148i | ||||
\(565\) | −2.91952 | − | 1.68559i | −0.122825 | − | 0.0709132i | ||||
\(566\) | 6.34995 | 0.266908 | ||||||||
\(567\) | −7.14755 | + | 22.7137i | −0.300169 | + | 0.953886i | ||||
\(568\) | −9.66386 | −0.405487 | ||||||||
\(569\) | −32.2967 | − | 18.6465i | −1.35395 | − | 0.781703i | −0.365149 | − | 0.930949i | \(-0.618982\pi\) |
−0.988800 | + | 0.149246i | \(0.952315\pi\) | |||||||
\(570\) | 1.23373 | + | 1.47744i | 0.0516753 | + | 0.0618831i | ||||
\(571\) | −3.82570 | − | 6.62630i | −0.160100 | − | 0.277302i | 0.774804 | − | 0.632201i | \(-0.217848\pi\) |
−0.934905 | + | 0.354899i | \(0.884515\pi\) | |||||||
\(572\) | −19.2012 | −0.802841 | ||||||||
\(573\) | 7.19070 | + | 41.3565i | 0.300396 | + | 1.72769i | ||||
\(574\) | −11.2922 | − | 17.3365i | −0.471326 | − | 0.723610i | ||||
\(575\) | 3.30404i | 0.137788i | ||||||||
\(576\) | 0.535019 | − | 2.95191i | 0.0222925 | − | 0.122996i | ||||
\(577\) | 34.5692 | + | 19.9585i | 1.43913 | + | 0.830884i | 0.997789 | − | 0.0664543i | \(-0.0211687\pi\) |
0.441344 | + | 0.897338i | \(0.354502\pi\) | |||||||
\(578\) | 10.7272i | 0.446191i | ||||||||
\(579\) | −0.368184 | + | 1.00413i | −0.0153012 | + | 0.0417301i | ||||
\(580\) | −3.70789 | − | 2.14075i | −0.153962 | − | 0.0888898i | ||||
\(581\) | −1.74636 | + | 1.13750i | −0.0724513 | + | 0.0471915i | ||||
\(582\) | 19.2007 | + | 22.9936i | 0.795895 | + | 0.953114i | ||||
\(583\) | 13.8141 | − | 23.9267i | 0.572121 | − | 0.990943i | ||||
\(584\) | −6.96114 | + | 12.0570i | −0.288054 | + | 0.498924i | ||||
\(585\) | 7.66146 | − | 9.04269i | 0.316762 | − | 0.373869i | ||||
\(586\) | 3.10915 | − | 1.79507i | 0.128438 | − | 0.0741535i | ||||
\(587\) | −12.0540 | − | 20.8782i | −0.497523 | − | 0.861734i | 0.502473 | − | 0.864593i | \(-0.332423\pi\) |
−0.999996 | + | 0.00285838i | \(0.999090\pi\) | |||||||
\(588\) | 2.92899 | − | 11.7652i | 0.120790 | − | 0.485191i | ||||
\(589\) | −4.11041 | + | 7.11944i | −0.169366 | + | 0.293351i | ||||
\(590\) | 1.39292i | 0.0573457i | ||||||||
\(591\) | −3.03985 | + | 2.53841i | −0.125043 | + | 0.104416i | ||||
\(592\) | 3.64170 | 0.149673 | ||||||||
\(593\) | −7.23840 | − | 12.5373i | −0.297246 | − | 0.514844i | 0.678259 | − | 0.734823i | \(-0.262735\pi\) |
−0.975505 | + | 0.219978i | \(0.929401\pi\) | |||||||
\(594\) | 0.180537 | − | 25.2540i | 0.00740753 | − | 1.03619i | ||||
\(595\) | −5.90833 | − | 3.00027i | −0.242218 | − | 0.122999i | ||||
\(596\) | −20.9438 | + | 12.0919i | −0.857890 | + | 0.495303i | ||||
\(597\) | −1.23529 | − | 7.10465i | −0.0505571 | − | 0.290774i | ||||
\(598\) | −11.3043 | + | 6.52655i | −0.462268 | + | 0.266890i | ||||
\(599\) | 14.7387 | − | 8.50937i | 0.602205 | − | 0.347683i | −0.167703 | − | 0.985838i | \(-0.553635\pi\) |
0.769909 | + | 0.638154i | \(0.220302\pi\) | |||||||
\(600\) | −1.32948 | + | 1.11018i | −0.0542757 | + | 0.0453227i | ||||
\(601\) | −23.0713 | + | 13.3202i | −0.941099 | + | 0.543344i | −0.890305 | − | 0.455365i | \(-0.849509\pi\) |
−0.0507942 | + | 0.998709i | \(0.516175\pi\) | |||||||
\(602\) | −19.1641 | + | 1.03064i | −0.781070 | + | 0.0420057i | ||||
\(603\) | 16.9845 | − | 6.09035i | 0.691663 | − | 0.248018i | ||||
\(604\) | −11.4978 | − | 19.9148i | −0.467840 | − | 0.810322i | ||||
\(605\) | 12.6222 | 0.513164 | ||||||||
\(606\) | 0.870185 | + | 5.00478i | 0.0353489 | + | 0.203305i | ||||
\(607\) | − | 30.2436i | − | 1.22755i | −0.789482 | − | 0.613774i | \(-0.789651\pi\) | ||
0.789482 | − | 0.613774i | \(-0.210349\pi\) | |||||||
\(608\) | 0.555647 | − | 0.962409i | 0.0225345 | − | 0.0390308i | ||||
\(609\) | 5.75546 | − | 18.7571i | 0.233223 | − | 0.760078i | ||||
\(610\) | 4.60187 | + | 7.97067i | 0.186324 | + | 0.322723i | ||||
\(611\) | 39.9791 | − | 23.0819i | 1.61738 | − | 0.933795i | ||||
\(612\) | 1.33999 | − | 7.39324i | 0.0541659 | − | 0.298854i | ||||
\(613\) | −10.5704 | + | 18.3085i | −0.426934 | + | 0.739472i | −0.996599 | − | 0.0824054i | \(-0.973740\pi\) |
0.569665 | + | 0.821877i | \(0.307073\pi\) | |||||||
\(614\) | 5.52946 | − | 9.57730i | 0.223151 | − | 0.386508i | ||||
\(615\) | −13.3444 | + | 2.32021i | −0.538099 | + | 0.0935598i | ||||
\(616\) | 0.690557 | + | 12.8405i | 0.0278234 | + | 0.517358i | ||||
\(617\) | 27.0032 | + | 15.5903i | 1.08711 | + | 0.627641i | 0.932805 | − | 0.360382i | \(-0.117354\pi\) |
0.154302 | + | 0.988024i | \(0.450687\pi\) | |||||||
\(618\) | 4.41150 | − | 0.767032i | 0.177457 | − | 0.0308546i | ||||
\(619\) | − | 17.3939i | − | 0.699119i | −0.936914 | − | 0.349559i | \(-0.886331\pi\) | ||
0.936914 | − | 0.349559i | \(-0.113669\pi\) | |||||||
\(620\) | −6.40644 | − | 3.69876i | −0.257289 | − | 0.148546i | ||||
\(621\) | −8.47765 | − | 14.9292i | −0.340196 | − | 0.599087i | ||||
\(622\) | − | 13.9447i | − | 0.559130i | ||||||
\(623\) | 33.2258 | − | 21.6417i | 1.33116 | − | 0.867058i | ||||
\(624\) | −6.42445 | − | 2.35566i | −0.257184 | − | 0.0943019i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 6.63558 | + | 11.4932i | 0.265211 | + | 0.459359i | ||||
\(627\) | 3.22058 | − | 8.78329i | 0.128617 | − | 0.350771i | ||||
\(628\) | 7.00637 | + | 4.04513i | 0.279584 | + | 0.161418i | ||||
\(629\) | 9.12086 | 0.363673 | ||||||||
\(630\) | −6.32271 | − | 4.79827i | −0.251903 | − | 0.191168i | ||||
\(631\) | −2.59501 | −0.103306 | −0.0516529 | − | 0.998665i | \(-0.516449\pi\) | ||||
−0.0516529 | + | 0.998665i | \(0.516449\pi\) | |||||||
\(632\) | 6.78809 | + | 3.91911i | 0.270016 | + | 0.155894i | ||||
\(633\) | 4.31981 | − | 0.751089i | 0.171697 | − | 0.0298531i | ||||
\(634\) | 2.22528 | + | 3.85429i | 0.0883770 | + | 0.153073i | ||||
\(635\) | −14.4595 | −0.573807 | ||||||||
\(636\) | 7.55742 | − | 6.31080i | 0.299671 | − | 0.250239i | ||||
\(637\) | −25.2943 | − | 11.1789i | −1.00220 | − | 0.442925i | ||||
\(638\) | 20.8092i | 0.823844i | ||||||||
\(639\) | −28.5268 | − | 5.17035i | −1.12850 | − | 0.204536i | ||||
\(640\) | 0.866025 | + | 0.500000i | 0.0342327 | + | 0.0197642i | ||||
\(641\) | 5.38544i | 0.212712i | 0.994328 | + | 0.106356i | \(0.0339183\pi\) | ||||
−0.994328 | + | 0.106356i | \(0.966082\pi\) | |||||||
\(642\) | −8.29269 | − | 9.93081i | −0.327287 | − | 0.391938i | ||||
\(643\) | −16.1682 | − | 9.33469i | −0.637610 | − | 0.368124i | 0.146083 | − | 0.989272i | \(-0.453333\pi\) |
−0.783693 | + | 0.621148i | \(0.786667\pi\) | |||||||
\(644\) | 4.77108 | + | 7.32487i | 0.188007 | + | 0.288640i | ||||
\(645\) | −4.32525 | + | 11.7960i | −0.170307 | + | 0.464467i | ||||
\(646\) | 1.39165 | − | 2.41042i | 0.0547539 | − | 0.0948365i | ||||
\(647\) | −2.10117 | + | 3.63934i | −0.0826056 | + | 0.143077i | −0.904368 | − | 0.426753i | \(-0.859658\pi\) |
0.821763 | + | 0.569830i | \(0.192991\pi\) | |||||||
\(648\) | 3.15865 | − | 8.42751i | 0.124084 | − | 0.331064i | ||||
\(649\) | 5.86297 | − | 3.38499i | 0.230142 | − | 0.132872i | ||||
\(650\) | 1.97532 | + | 3.42136i | 0.0774785 | + | 0.134197i | ||||
\(651\) | 9.94420 | − | 32.4084i | 0.389744 | − | 1.27018i | ||||
\(652\) | 0.616736 | − | 1.06822i | 0.0241532 | − | 0.0418346i | ||||
\(653\) | − | 26.6081i | − | 1.04126i | −0.853783 | − | 0.520628i | \(-0.825698\pi\) | ||
0.853783 | − | 0.520628i | \(-0.174302\pi\) | |||||||
\(654\) | −26.7731 | − | 9.81691i | −1.04691 | − | 0.383872i | ||||
\(655\) | 13.1850 | 0.515179 | ||||||||
\(656\) | 3.91000 | + | 6.77231i | 0.152660 | + | 0.264414i | ||||
\(657\) | −26.9994 | + | 31.8669i | −1.05335 | + | 1.24325i | ||||
\(658\) | −16.8735 | − | 25.9053i | −0.657798 | − | 1.00989i | ||||
\(659\) | 35.1130 | − | 20.2725i | 1.36781 | − | 0.789704i | 0.377160 | − | 0.926148i | \(-0.376901\pi\) |
0.990648 | + | 0.136444i | \(0.0435674\pi\) | |||||||
\(660\) | 7.90366 | + | 2.89804i | 0.307649 | + | 0.112806i | ||||
\(661\) | −24.0371 | + | 13.8778i | −0.934936 | + | 0.539785i | −0.888369 | − | 0.459130i | \(-0.848161\pi\) |
−0.0465665 | + | 0.998915i | \(0.514828\pi\) | |||||||
\(662\) | −6.78928 | + | 3.91980i | −0.263873 | + | 0.152347i | ||||
\(663\) | −16.0905 | − | 5.89991i | −0.624902 | − | 0.229134i | ||||
\(664\) | 0.682199 | − | 0.393868i | 0.0264745 | − | 0.0152850i | ||||
\(665\) | −1.60472 | − | 2.46367i | −0.0622285 | − | 0.0955371i | ||||
\(666\) | 10.7499 | + | 1.94838i | 0.416552 | + | 0.0754980i | ||||
\(667\) | 7.07313 | + | 12.2510i | 0.273873 | + | 0.474361i | ||||
\(668\) | 10.8729 | 0.420683 | ||||||||
\(669\) | −18.0723 | − | 6.62659i | −0.698716 | − | 0.256199i | ||||
\(670\) | 6.01448i | 0.232360i | ||||||||
\(671\) | 22.3663 | − | 38.7396i | 0.863441 | − | 1.49552i | ||||
\(672\) | −1.34426 | + | 4.38098i | −0.0518560 | + | 0.169000i | ||||
\(673\) | 19.5469 | + | 33.8562i | 0.753477 | + | 1.30506i | 0.946128 | + | 0.323794i | \(0.104958\pi\) |
−0.192650 | + | 0.981267i | \(0.561708\pi\) | |||||||
\(674\) | −8.07208 | + | 4.66042i | −0.310925 | + | 0.179513i | ||||
\(675\) | −4.51846 | + | 2.56584i | −0.173916 | + | 0.0987593i | ||||
\(676\) | −1.30379 | + | 2.25823i | −0.0501458 | + | 0.0868551i | ||||
\(677\) | −19.0123 | + | 32.9302i | −0.730700 | + | 1.26561i | 0.225884 | + | 0.974154i | \(0.427473\pi\) |
−0.956584 | + | 0.291456i | \(0.905860\pi\) | |||||||
\(678\) | −2.01014 | + | 5.48213i | −0.0771990 | + | 0.210540i | ||||
\(679\) | −24.9745 | − | 38.3424i | −0.958434 | − | 1.47145i | ||||
\(680\) | 2.16902 | + | 1.25228i | 0.0831780 | + | 0.0480229i | ||||
\(681\) | −12.7986 | − | 15.3268i | −0.490442 | − | 0.587323i | ||||
\(682\) | 35.9539i | 1.37675i | ||||||||
\(683\) | −27.3258 | − | 15.7765i | −1.04559 | − | 0.603673i | −0.124180 | − | 0.992260i | \(-0.539630\pi\) |
−0.921412 | + | 0.388587i | \(0.872963\pi\) | |||||||
\(684\) | 2.15512 | − | 2.54366i | 0.0824033 | − | 0.0972592i | ||||
\(685\) | 10.3775i | 0.396506i | ||||||||
\(686\) | −6.56605 | + | 17.3172i | −0.250693 | + | 0.661175i | ||||
\(687\) | −34.9073 | + | 29.1492i | −1.33179 | + | 1.11211i | ||||
\(688\) | 7.25381 | 0.276549 | ||||||||
\(689\) | −11.2287 | − | 19.4487i | −0.427780 | − | 0.740937i | ||||
\(690\) | 5.63818 | − | 0.980316i | 0.214642 | − | 0.0373200i | ||||
\(691\) | −41.9888 | − | 24.2422i | −1.59733 | − | 0.922218i | −0.991999 | − | 0.126242i | \(-0.959708\pi\) |
−0.605329 | − | 0.795976i | \(-0.706958\pi\) | |||||||
\(692\) | 5.77390 | 0.219491 | ||||||||
\(693\) | −4.83144 | + | 38.2734i | −0.183531 | + | 1.45389i | ||||
\(694\) | −29.6538 | −1.12564 | ||||||||
\(695\) | 7.92494 | + | 4.57547i | 0.300610 | + | 0.173557i | ||||
\(696\) | −2.55294 | + | 6.96248i | −0.0967690 | + | 0.263912i | ||||
\(697\) | 9.79284 | + | 16.9617i | 0.370930 | + | 0.642470i | ||||
\(698\) | 32.3688 | 1.22518 | ||||||||
\(699\) | −1.23488 | − | 0.452793i | −0.0467073 | − | 0.0171262i | ||||
\(700\) | 2.21694 | − | 1.44401i | 0.0837925 | − | 0.0545786i | ||||
\(701\) | − | 48.2125i | − | 1.82096i | −0.413553 | − | 0.910480i | \(-0.635712\pi\) | ||
0.413553 | − | 0.910480i | \(-0.364288\pi\) | |||||||
\(702\) | −17.7041 | − | 10.3909i | −0.668197 | − | 0.392179i | ||||
\(703\) | 3.50480 | + | 2.02350i | 0.132186 | + | 0.0763176i | ||||
\(704\) | − | 4.86026i | − | 0.183178i | ||||||
\(705\) | −19.9401 | + | 3.46701i | −0.750988 | + | 0.130575i | ||||
\(706\) | 5.24551 | + | 3.02849i | 0.197417 | + | 0.113979i | ||||
\(707\) | −0.416708 | − | 7.74842i | −0.0156719 | − | 0.291409i | ||||
\(708\) | 2.37695 | − | 0.413283i | 0.0893313 | − | 0.0155321i | ||||
\(709\) | −19.3691 | + | 33.5483i | −0.727422 | + | 1.25993i | 0.230547 | + | 0.973061i | \(0.425948\pi\) |
−0.957969 | + | 0.286871i | \(0.907385\pi\) | |||||||
\(710\) | 4.83193 | − | 8.36915i | 0.181339 | − | 0.314089i | ||||
\(711\) | 17.9410 | + | 15.2006i | 0.672841 | + | 0.570067i | ||||
\(712\) | −12.9793 | + | 7.49361i | −0.486420 | + | 0.280835i | ||||
\(713\) | 12.2209 | + | 21.1672i | 0.457675 | + | 0.792716i | ||||
\(714\) | −3.36679 | + | 10.9724i | −0.125999 | + | 0.410633i | ||||
\(715\) | 9.60058 | − | 16.6287i | 0.359041 | − | 0.621878i | ||||
\(716\) | − | 5.60968i | − | 0.209643i | ||||||
\(717\) | −7.29574 | − | 41.9606i | −0.272464 | − | 1.56705i | ||||
\(718\) | 13.2399 | 0.494109 | ||||||||
\(719\) | 8.83033 | + | 15.2946i | 0.329316 | + | 0.570392i | 0.982376 | − | 0.186914i | \(-0.0598486\pi\) |
−0.653060 | + | 0.757306i | \(0.726515\pi\) | |||||||
\(720\) | 2.28892 | + | 1.93929i | 0.0853029 | + | 0.0722732i | ||||
\(721\) | −6.82991 | + | 0.367310i | −0.254359 | + | 0.0136794i | ||||
\(722\) | −15.3850 | + | 8.88251i | −0.572569 | + | 0.330573i | ||||
\(723\) | 17.9096 | − | 14.9554i | 0.666065 | − | 0.556196i | ||||
\(724\) | 20.8356 | − | 12.0294i | 0.774349 | − | 0.447071i | ||||
\(725\) | 3.70789 | − | 2.14075i | 0.137707 | − | 0.0795054i | ||||
\(726\) | −3.74502 | − | 21.5391i | −0.138991 | − | 0.799390i | ||||
\(727\) | 15.3445 | − | 8.85913i | 0.569094 | − | 0.328567i | −0.187693 | − | 0.982228i | \(-0.560101\pi\) |
0.756788 | + | 0.653661i | \(0.226768\pi\) | |||||||
\(728\) | 9.31966 | + | 4.73255i | 0.345409 | + | 0.175400i | ||||
\(729\) | 13.8329 | − | 23.1873i | 0.512330 | − | 0.858788i | ||||
\(730\) | −6.96114 | − | 12.0570i | −0.257643 | − | 0.446251i | ||||
\(731\) | 18.1676 | 0.671954 | ||||||||
\(732\) | 12.2362 | − | 10.2178i | 0.452262 | − | 0.377660i | ||||
\(733\) | − | 38.6147i | − | 1.42627i | −0.701028 | − | 0.713133i | \(-0.747275\pi\) | ||
0.701028 | − | 0.713133i | \(-0.252725\pi\) | |||||||
\(734\) | −8.94994 | + | 15.5018i | −0.330348 | + | 0.572180i | ||||
\(735\) | 8.72451 | + | 8.41920i | 0.321808 | + | 0.310547i | ||||
\(736\) | −1.65202 | − | 2.86139i | −0.0608943 | − | 0.105472i | ||||
\(737\) | 25.3156 | − | 14.6160i | 0.932513 | − | 0.538386i | ||||
\(738\) | 7.91863 | + | 22.0832i | 0.291489 | + | 0.812892i | ||||
\(739\) | 18.1858 | − | 31.4988i | 0.668976 | − | 1.15870i | −0.309215 | − | 0.950992i | \(-0.600066\pi\) |
0.978191 | − | 0.207708i | \(-0.0666004\pi\) | |||||||
\(740\) | −1.82085 | + | 3.15380i | −0.0669357 | + | 0.115936i | ||||
\(741\) | −4.87403 | − | 5.83684i | −0.179052 | − | 0.214422i | ||||
\(742\) | −12.6022 | + | 8.20850i | −0.462642 | + | 0.301344i | ||||
\(743\) | 28.2741 | + | 16.3241i | 1.03728 | + | 0.598872i | 0.919061 | − | 0.394116i | \(-0.128949\pi\) |
0.118216 | + | 0.992988i | \(0.462283\pi\) | |||||||
\(744\) | −4.41094 | + | 12.0297i | −0.161713 | + | 0.441030i | ||||
\(745\) | − | 24.1838i | − | 0.886025i | ||||||
\(746\) | −3.91848 | − | 2.26234i | −0.143466 | − | 0.0828300i | ||||
\(747\) | 2.22451 | − | 0.797672i | 0.0813907 | − | 0.0291853i | ||||
\(748\) | − | 12.1728i | − | 0.445083i | ||||||
\(749\) | 10.7864 | + | 16.5599i | 0.394125 | + | 0.605086i | ||||
\(750\) | −0.296702 | − | 1.70645i | −0.0108340 | − | 0.0623107i | ||||
\(751\) | 12.3870 | 0.452008 | 0.226004 | − | 0.974126i | \(-0.427434\pi\) | ||||
0.226004 | + | 0.974126i | \(0.427434\pi\) | |||||||
\(752\) | 5.84258 | + | 10.1196i | 0.213057 | + | 0.369025i | ||||
\(753\) | −1.13536 | − | 1.35964i | −0.0413748 | − | 0.0495479i | ||||
\(754\) | 14.6485 | + | 8.45733i | 0.533468 | + | 0.307998i | ||||
\(755\) | 22.9956 | 0.836897 | ||||||||
\(756\) | −6.31204 | + | 12.2130i | −0.229567 | + | 0.444184i | ||||
\(757\) | 39.2473 | 1.42647 | 0.713234 | − | 0.700926i | \(-0.247230\pi\) | ||||
0.713234 | + | 0.700926i | \(0.247230\pi\) | |||||||
\(758\) | −6.46940 | − | 3.73511i | −0.234979 | − | 0.135665i | ||||
\(759\) | −17.8278 | − | 21.3494i | −0.647108 | − | 0.774935i | ||||
\(760\) | 0.555647 | + | 0.962409i | 0.0201554 | + | 0.0349102i | ||||
\(761\) | −14.0678 | −0.509957 | −0.254979 | − | 0.966947i | \(-0.582068\pi\) | ||||
−0.254979 | + | 0.966947i | \(0.582068\pi\) | |||||||
\(762\) | 4.29016 | + | 24.6744i | 0.155416 | + | 0.893858i | ||||
\(763\) | 38.8384 | + | 19.7223i | 1.40605 | + | 0.713995i | ||||
\(764\) | 24.2354i | 0.876807i | ||||||||
\(765\) | 5.73274 | + | 4.85709i | 0.207268 | + | 0.175608i | ||||
\(766\) | −28.6508 | − | 16.5416i | −1.03520 | − | 0.597671i | ||||
\(767\) | − | 5.50294i | − | 0.198700i | ||||||
\(768\) | 0.596273 | − | 1.62618i | 0.0215161 | − | 0.0586797i | ||||
\(769\) | −12.1581 | − | 7.01950i | −0.438434 | − | 0.253130i | 0.264499 | − | 0.964386i | \(-0.414793\pi\) |
−0.702933 | + | 0.711256i | \(0.748127\pi\) | |||||||
\(770\) | −11.4655 | − | 5.82221i | −0.413187 | − | 0.209818i | ||||
\(771\) | 26.4299 | + | 31.6507i | 0.951848 | + | 1.13987i | ||||
\(772\) | −0.308738 | + | 0.534750i | −0.0111117 | + | 0.0192461i | ||||
\(773\) | −8.57207 | + | 14.8473i | −0.308316 | + | 0.534019i | −0.977994 | − | 0.208632i | \(-0.933099\pi\) |
0.669678 | + | 0.742652i | \(0.266432\pi\) | |||||||
\(774\) | 21.4126 | + | 3.88092i | 0.769659 | + | 0.139497i | ||||
\(775\) | 6.40644 | − | 3.69876i | 0.230126 | − | 0.132863i | ||||
\(776\) | 8.64760 | + | 14.9781i | 0.310431 | + | 0.537682i | ||||
\(777\) | −15.9542 | − | 4.89539i | −0.572353 | − | 0.175621i | ||||
\(778\) | 18.2241 | − | 31.5651i | 0.653366 | − | 1.13166i | ||||
\(779\) | 8.69031i | 0.311363i | ||||||||
\(780\) | 5.25229 | − | 4.38591i | 0.188062 | − | 0.157041i | ||||
\(781\) | −46.9689 | −1.68068 | ||||||||
\(782\) | −4.13760 | − | 7.16653i | −0.147960 | − | 0.256275i | ||||
\(783\) | −11.2611 | + | 19.1867i | −0.402439 | + | 0.685678i | ||||
\(784\) | 2.82965 | − | 6.40258i | 0.101059 | − | 0.228664i | ||||
\(785\) | −7.00637 | + | 4.04513i | −0.250068 | + | 0.144377i | ||||
\(786\) | −3.91200 | − | 22.4995i | −0.139537 | − | 0.802529i | ||||
\(787\) | 28.6382 | − | 16.5343i | 1.02084 | − | 0.589384i | 0.106495 | − | 0.994313i | \(-0.466037\pi\) |
0.914348 | + | 0.404929i | \(0.132704\pi\) | |||||||
\(788\) | −1.98016 | + | 1.14325i | −0.0705405 | + | 0.0407266i | ||||
\(789\) | 10.1004 | − | 8.43429i | 0.359583 | − | 0.300269i | ||||
\(790\) | −6.78809 | + | 3.91911i | −0.241509 | + | 0.139436i | ||||
\(791\) | 4.03840 | − | 7.95268i | 0.143589 | − | 0.282765i | ||||
\(792\) | 2.60033 | − | 14.3470i | 0.0923988 | − | 0.509800i | ||||
\(793\) | −18.1803 | − | 31.4893i | −0.645603 | − | 1.11822i | ||||
\(794\) | −15.3958 | −0.546375 | ||||||||
\(795\) | 1.68660 | + | 9.70031i | 0.0598177 | + | 0.344035i | ||||
\(796\) | − | 4.16341i | − | 0.147568i | ||||||
\(797\) | −9.84860 | + | 17.0583i | −0.348855 | + | 0.604235i | −0.986046 | − | 0.166471i | \(-0.946763\pi\) |
0.637191 | + | 0.770706i | \(0.280096\pi\) | |||||||
\(798\) | −3.72801 | + | 3.46936i | −0.131970 | + | 0.122814i | ||||
\(799\) | 14.6331 | + | 25.3453i | 0.517682 | + | 0.896652i | ||||
\(800\) | −0.866025 | + | 0.500000i | −0.0306186 | + | 0.0176777i | ||||
\(801\) | −42.3229 | + | 15.1763i | −1.49541 | + | 0.536227i | ||||
\(802\) | −8.20364 | + | 14.2091i | −0.289681 | + | 0.501742i | ||||
\(803\) | −33.8329 | + | 58.6004i | −1.19394 | + | 2.06796i | ||||
\(804\) | 10.2634 | − | 1.78451i | 0.361962 | − | 0.0629348i | ||||
\(805\) | −8.72906 | + | 0.469446i | −0.307659 | + | 0.0165458i | ||||
\(806\) | 25.3096 | + | 14.6125i | 0.891491 | + | 0.514703i | ||||
\(807\) | −12.2399 | + | 2.12816i | −0.430863 | + | 0.0749146i | ||||
\(808\) | 2.93286i | 0.103178i | ||||||||
\(809\) | 21.6772 | + | 12.5154i | 0.762131 | + | 0.440017i | 0.830060 | − | 0.557674i | \(-0.188306\pi\) |
−0.0679294 | + | 0.997690i | \(0.521639\pi\) | |||||||
\(810\) | 5.71911 | + | 6.94923i | 0.200949 | + | 0.244171i | ||||
\(811\) | 12.0504i | 0.423146i | 0.977362 | + | 0.211573i | \(0.0678586\pi\) | ||||
−0.977362 | + | 0.211573i | \(0.932141\pi\) | |||||||
\(812\) | 5.12889 | − | 10.1001i | 0.179989 | − | 0.354446i | ||||
\(813\) | −6.00516 | − | 2.20192i | −0.210610 | − | 0.0772247i | ||||
\(814\) | 17.6996 | 0.620370 | ||||||||
\(815\) | 0.616736 | + | 1.06822i | 0.0216033 | + | 0.0374180i | ||||
\(816\) | 1.49340 | − | 4.07287i | 0.0522796 | − | 0.142579i | ||||
\(817\) | 6.98113 | + | 4.03056i | 0.244239 | + | 0.141011i | ||||
\(818\) | −21.1331 | −0.738900 | ||||||||
\(819\) | 24.9788 | + | 18.9563i | 0.872828 | + | 0.662385i | ||||
\(820\) | −7.81999 | −0.273086 | ||||||||
\(821\) | −36.2762 | − | 20.9441i | −1.26605 | − | 0.730953i | −0.291811 | − | 0.956476i | \(-0.594258\pi\) |
−0.974238 | + | 0.225523i | \(0.927591\pi\) | |||||||
\(822\) | 17.7088 | − | 3.07904i | 0.617664 | − | 0.107394i | ||||
\(823\) | −13.8411 | − | 23.9735i | −0.482470 | − | 0.835663i | 0.517327 | − | 0.855788i | \(-0.326927\pi\) |
−0.999797 | + | 0.0201248i | \(0.993594\pi\) | |||||||
\(824\) | 2.58519 | 0.0900595 | ||||||||
\(825\) | −6.46161 | + | 5.39575i | −0.224964 | + | 0.187856i | ||||
\(826\) | −3.68001 | + | 0.197910i | −0.128044 | + | 0.00688616i | ||||
\(827\) | 36.8335i | 1.28083i | 0.768031 | + | 0.640413i | \(0.221237\pi\) | ||||
−0.768031 | + | 0.640413i | \(0.778763\pi\) | |||||||
\(828\) | −3.34572 | − | 9.33041i | −0.116272 | − | 0.324254i | ||||
\(829\) | 44.8357 | + | 25.8859i | 1.55721 | + | 0.899055i | 0.997522 | + | 0.0703515i | \(0.0224121\pi\) |
0.559687 | + | 0.828704i | \(0.310921\pi\) | |||||||
\(830\) | 0.787736i | 0.0273427i | ||||||||
\(831\) | 27.6533 | + | 33.1159i | 0.959284 | + | 1.14878i | ||||
\(832\) | −3.42136 | − | 1.97532i | −0.118614 | − | 0.0684820i | ||||
\(833\) | 7.08704 | − | 16.0357i | 0.245551 | − | 0.555604i | ||||
\(834\) | 5.45645 | − | 14.8811i | 0.188942 | − | 0.515289i | ||||
\(835\) | −5.43643 | + | 9.41617i | −0.188135 | + | 0.325860i | ||||
\(836\) | 2.70059 | − | 4.67756i | 0.0934019 | − | 0.161777i | ||||
\(837\) | −19.4568 | + | 33.1506i | −0.672525 | + | 1.14585i | ||||
\(838\) | 4.00254 | − | 2.31087i | 0.138265 | − | 0.0798276i | ||||
\(839\) | 4.77807 | + | 8.27587i | 0.164957 | + | 0.285715i | 0.936640 | − | 0.350293i | \(-0.113918\pi\) |
−0.771683 | + | 0.636008i | \(0.780585\pi\) | |||||||
\(840\) | −3.12191 | − | 3.35465i | −0.107716 | − | 0.115747i | ||||
\(841\) | −5.33439 | + | 9.23943i | −0.183944 | + | 0.318601i | ||||
\(842\) | 2.31111i | 0.0796461i | ||||||||
\(843\) | −23.8221 | − | 8.73486i | −0.820475 | − | 0.300845i | ||||
\(844\) | 2.53146 | 0.0871365 | ||||||||
\(845\) | −1.30379 | − | 2.25823i | −0.0448518 | − | 0.0776855i | ||||
\(846\) | 11.8325 | + | 32.9981i | 0.406811 | + | 1.13450i | ||||
\(847\) | 1.79339 | + | 33.3469i | 0.0616214 | + | 1.14581i | ||||
\(848\) | 4.92292 | − | 2.84225i | 0.169054 | − | 0.0976033i | ||||
\(849\) | 10.3262 | + | 3.78630i | 0.354393 | + | 0.129946i | ||||
\(850\) | −2.16902 | + | 1.25228i | −0.0743967 | + | 0.0429529i | ||||
\(851\) | 10.4203 | − | 6.01616i | 0.357203 | − | 0.206231i | ||||
\(852\) | −15.7152 | − | 5.76230i | −0.538393 | − | 0.197413i | ||||
\(853\) | 6.13810 | − | 3.54384i | 0.210165 | − | 0.121339i | −0.391223 | − | 0.920296i | \(-0.627948\pi\) |
0.601388 | + | 0.798957i | \(0.294615\pi\) | |||||||
\(854\) | −20.4041 | + | 13.2903i | −0.698215 | + | 0.454786i | ||||
\(855\) | 1.12531 | + | 3.13822i | 0.0384848 | + | 0.107325i | ||||
\(856\) | −3.73486 | − | 6.46896i | −0.127655 | − | 0.221104i | ||||
\(857\) | −37.5025 | −1.28106 | −0.640531 | − | 0.767932i | \(-0.721286\pi\) | ||||
−0.640531 | + | 0.767932i | \(0.721286\pi\) | |||||||
\(858\) | −31.2245 | − | 11.4491i | −1.06599 | − | 0.390867i | ||||
\(859\) | 11.6835i | 0.398636i | 0.979935 | + | 0.199318i | \(0.0638726\pi\) | ||||
−0.979935 | + | 0.199318i | \(0.936127\pi\) | |||||||
\(860\) | −3.62690 | + | 6.28198i | −0.123676 | + | 0.214214i | ||||
\(861\) | −8.02584 | − | 34.9254i | −0.273520 | − | 1.19025i | ||||
\(862\) | −12.3175 | − | 21.3345i | −0.419536 | − | 0.726657i | ||||
\(863\) | 41.4770 | − | 23.9467i | 1.41189 | − | 0.815157i | 0.416326 | − | 0.909215i | \(-0.363317\pi\) |
0.995567 | + | 0.0940587i | \(0.0299841\pi\) | |||||||
\(864\) | 2.63018 | − | 4.48131i | 0.0894805 | − | 0.152457i | ||||
\(865\) | −2.88695 | + | 5.00034i | −0.0981592 | + | 0.170017i | ||||
\(866\) | 3.27886 | − | 5.67916i | 0.111420 | − | 0.192986i | ||||
\(867\) | −6.39631 | + | 17.4443i | −0.217230 | + | 0.592438i | ||||
\(868\) | 8.86163 | − | 17.4509i | 0.300783 | − | 0.592323i | ||||
\(869\) | 32.9919 | + | 19.0479i | 1.11917 | + | 0.646155i | ||||
\(870\) | −4.75322 | − | 5.69215i | −0.161149 | − | 0.192982i | ||||
\(871\) | − | 23.7611i | − | 0.805113i | ||||||
\(872\) | −14.2581 | − | 8.23189i | −0.482839 | − | 0.278767i | ||||
\(873\) | 17.5134 | + | 48.8405i | 0.592737 | + | 1.65300i | ||||
\(874\) | − | 3.67176i | − | 0.124199i | ||||||
\(875\) | 0.142082 | + | 2.64193i | 0.00480326 | + | 0.0893137i | ||||
\(876\) | −18.5093 | + | 15.4562i | −0.625373 | + | 0.522216i | ||||
\(877\) | −33.2605 | −1.12313 | −0.561564 | − | 0.827433i | \(-0.689800\pi\) | ||||
−0.561564 | + | 0.827433i | \(0.689800\pi\) | |||||||
\(878\) | 16.2145 | + | 28.0844i | 0.547214 | + | 0.947803i | ||||
\(879\) | 6.12638 | − | 1.06520i | 0.206638 | − | 0.0359283i | ||||
\(880\) | 4.20911 | + | 2.43013i | 0.141889 | + | 0.0819197i | ||||
\(881\) | −39.7345 | −1.33869 | −0.669344 | − | 0.742953i | \(-0.733425\pi\) | ||||
−0.669344 | + | 0.742953i | \(0.733425\pi\) | |||||||
\(882\) | 11.7784 | − | 17.3859i | 0.396598 | − | 0.585414i | ||||
\(883\) | −20.3226 | −0.683910 | −0.341955 | − | 0.939716i | \(-0.611089\pi\) | ||||
−0.341955 | + | 0.939716i | \(0.611089\pi\) | |||||||
\(884\) | −8.56901 | − | 4.94732i | −0.288207 | − | 0.166396i | ||||
\(885\) | −0.830562 | + | 2.26514i | −0.0279190 | + | 0.0761419i | ||||
\(886\) | 0.117843 | + | 0.204110i | 0.00395901 | + | 0.00685720i | ||||
\(887\) | −2.71826 | −0.0912703 | −0.0456351 | − | 0.998958i | \(-0.514531\pi\) | ||||
−0.0456351 | + | 0.998958i | \(0.514531\pi\) | |||||||
\(888\) | 5.92205 | + | 2.17144i | 0.198731 | + | 0.0728689i | ||||
\(889\) | −2.05444 | − | 38.2010i | −0.0689036 | − | 1.28122i | ||||
\(890\) | − | 14.9872i | − | 0.502373i | ||||||
\(891\) | 15.3519 | − | 40.9599i | 0.514307 | − | 1.37221i | ||||
\(892\) | −9.62445 | − | 5.55668i | −0.322250 | − | 0.186051i | ||||
\(893\) | 12.9856i | 0.434548i | ||||||||
\(894\) | −41.2684 | + | 7.17538i | −1.38022 | + | 0.239980i | ||||
\(895\) | 4.85812 | + | 2.80484i | 0.162389 | + | 0.0937554i | ||||
\(896\) | −1.19792 | + | 2.35902i | −0.0400197 | + | 0.0788094i | ||||
\(897\) | −22.2744 | + | 3.87288i | −0.743722 | + | 0.129312i | ||||
\(898\) | 9.40341 | − | 16.2872i | 0.313796 | − | 0.543510i | ||||
\(899\) | 15.8362 | − | 27.4292i | 0.528168 | − | 0.914813i | ||||
\(900\) | −2.82394 | + | 1.01261i | −0.0941312 | + | 0.0337538i | ||||
\(901\) | 12.3298 | − | 7.11861i | 0.410765 | − | 0.237155i | ||||
\(902\) | 19.0036 | + | 32.9152i | 0.632751 | + | 1.09596i | ||||
\(903\) | −31.7788 | − | 9.75102i | −1.05753 | − | 0.324494i | ||||
\(904\) | −1.68559 | + | 2.91952i | −0.0560618 | + | 0.0971019i | ||||
\(905\) | 24.0589i | 0.799744i | ||||||||
\(906\) | −6.82285 | − | 39.2409i | −0.226674 | − | 1.30369i | ||||
\(907\) | −46.2654 | −1.53622 | −0.768109 | − | 0.640320i | \(-0.778802\pi\) | ||||
−0.768109 | + | 0.640320i | \(0.778802\pi\) | |||||||
\(908\) | −5.76421 | − | 9.98390i | −0.191292 | − | 0.331327i | ||||
\(909\) | −1.56914 | + | 8.65753i | −0.0520449 | + | 0.287152i | ||||
\(910\) | −8.75834 | + | 5.70478i | −0.290336 | + | 0.189112i | ||||
\(911\) | −33.8272 | + | 19.5301i | −1.12074 | + | 0.647062i | −0.941591 | − | 0.336759i | \(-0.890669\pi\) |
−0.179154 | + | 0.983821i | \(0.557336\pi\) | |||||||
\(912\) | 1.47744 | − | 1.23373i | 0.0489229 | − | 0.0408529i | ||||
\(913\) | 3.31567 | − | 1.91430i | 0.109733 | − | 0.0633541i | ||||
\(914\) | 16.1182 | − | 9.30583i | 0.533142 | − | 0.307810i | ||||
\(915\) | 2.73077 | + | 15.7057i | 0.0902764 | + | 0.519215i | ||||
\(916\) | −22.7387 | + | 13.1282i | −0.751308 | + | 0.433768i | ||||
\(917\) | 1.87335 | + | 34.8338i | 0.0618635 | + | 1.15031i | ||||
\(918\) | 6.58746 | − | 11.2237i | 0.217418 | − | 0.370439i | ||||
\(919\) | 19.6509 | + | 34.0363i | 0.648223 | + | 1.12276i | 0.983547 | + | 0.180652i | \(0.0578209\pi\) |
−0.335324 | + | 0.942103i | \(0.608846\pi\) | |||||||
\(920\) | 3.30404 | 0.108931 | ||||||||
\(921\) | 14.7026 | − | 12.2773i | 0.484466 | − | 0.404552i | ||||
\(922\) | 27.5440i | 0.907113i | ||||||||
\(923\) | −19.0892 | + | 33.0635i | −0.628330 | + | 1.08830i | ||||
\(924\) | −6.53347 | + | 21.2927i | −0.214935 | + | 0.700478i | ||||
\(925\) | −1.82085 | − | 3.15380i | −0.0598691 | − | 0.103696i | ||||
\(926\) | 0.414241 | − | 0.239162i | 0.0136128 | − | 0.00785935i | ||||
\(927\) | 7.63125 | + | 1.38313i | 0.250643 | + | 0.0454279i | ||||
\(928\) | −2.14075 | + | 3.70789i | −0.0702735 | + | 0.121717i | ||||
\(929\) | 22.8771 | − | 39.6243i | 0.750574 | − | 1.30003i | −0.196971 | − | 0.980409i | \(-0.563111\pi\) |
0.947545 | − | 0.319622i | \(-0.103556\pi\) | |||||||
\(930\) | −8.21255 | − | 9.83483i | −0.269300 | − | 0.322497i | ||||
\(931\) | 6.28085 | − | 4.58962i | 0.205847 | − | 0.150419i | ||||
\(932\) | −0.657636 | − | 0.379686i | −0.0215416 | − | 0.0124370i | ||||
\(933\) | 8.31482 | − | 22.6765i | 0.272215 | − | 0.742395i | ||||
\(934\) | − | 12.1697i | − | 0.398205i | ||||||
\(935\) | 10.5420 | + | 6.08642i | 0.344760 | + | 0.199047i | ||||
\(936\) | −9.04269 | − | 7.66146i | −0.295570 | − | 0.250423i | ||||
\(937\) | 52.1498i | 1.70366i | 0.523819 | + | 0.851830i | \(0.324507\pi\) | ||||
−0.523819 | + | 0.851830i | \(0.675493\pi\) | |||||||
\(938\) | −15.8899 | + | 0.854551i | −0.518822 | + | 0.0279021i | ||||
\(939\) | 3.93758 | + | 22.6465i | 0.128498 | + | 0.739042i | ||||
\(940\) | −11.6852 | −0.381128 | ||||||||
\(941\) | 13.3755 | + | 23.1671i | 0.436029 | + | 0.755224i | 0.997379 | − | 0.0723541i | \(-0.0230512\pi\) |
−0.561350 | + | 0.827579i | \(0.689718\pi\) | |||||||
\(942\) | 8.98161 | + | 10.7558i | 0.292637 | + | 0.350443i | ||||
\(943\) | 22.3760 | + | 12.9188i | 0.728663 | + | 0.420694i | ||||
\(944\) | 1.39292 | 0.0453358 | ||||||||
\(945\) | −7.42077 | − | 11.5729i | −0.241398 | − | 0.376467i | ||||
\(946\) | 35.2554 | 1.14625 | ||||||||
\(947\) | 8.53441 | + | 4.92734i | 0.277331 | + | 0.160117i | 0.632214 | − | 0.774793i | \(-0.282146\pi\) |
−0.354884 | + | 0.934911i | \(0.615479\pi\) | |||||||
\(948\) | 8.70180 | + | 10.4207i | 0.282621 | + | 0.338449i | ||||
\(949\) | 27.5010 | + | 47.6331i | 0.892719 | + | 1.54623i | ||||
\(950\) | −1.11129 | −0.0360551 | ||||||||
\(951\) | 1.32049 | + | 7.59464i | 0.0428197 | + | 0.246273i | ||||
\(952\) | −3.00027 | + | 5.90833i | −0.0972393 | + | 0.191490i | ||||
\(953\) | − | 18.8568i | − | 0.610830i | −0.952219 | − | 0.305415i | \(-0.901205\pi\) | ||
0.952219 | − | 0.305415i | \(-0.0987952\pi\) | |||||||
\(954\) | 16.0527 | − | 5.75621i | 0.519724 | − | 0.186364i | ||||
\(955\) | −20.9885 | − | 12.1177i | −0.679172 | − | 0.392120i | ||||
\(956\) | − | 24.5895i | − | 0.795280i | ||||||
\(957\) | −12.4080 | + | 33.8395i | −0.401093 | + | 1.09388i | ||||
\(958\) | −34.9474 | − | 20.1769i | −1.12910 | − | 0.651886i | ||||
\(959\) | −27.4168 | + | 1.47447i | −0.885334 | + | 0.0476130i | ||||
\(960\) | 1.11018 | + | 1.32948i | 0.0358308 | + | 0.0429087i | ||||
\(961\) | 11.8616 | − | 20.5450i | 0.382633 | − | 0.662741i | ||||
\(962\) | 7.19352 | − | 12.4595i | 0.231928 | − | 0.401712i | ||||
\(963\) | −7.56393 | − | 21.0940i | −0.243744 | − | 0.679744i | ||||
\(964\) | 11.6664 | − | 6.73558i | 0.375749 | − | 0.216939i | ||||
\(965\) | −0.308738 | − | 0.534750i | −0.00993863 | − | 0.0172142i | ||||
\(966\) | 3.39102 | + | 14.7564i | 0.109104 | + | 0.474780i | ||||
\(967\) | 27.7839 | − | 48.1232i | 0.893471 | − | 1.54754i | 0.0577849 | − | 0.998329i | \(-0.481596\pi\) |
0.835686 | − | 0.549208i | \(-0.185070\pi\) | |||||||
\(968\) | − | 12.6222i | − | 0.405691i | ||||||
\(969\) | 3.70034 | − | 3.08996i | 0.118872 | − | 0.0992639i | ||||
\(970\) | −17.2952 | −0.555316 | ||||||||
\(971\) | 26.8589 | + | 46.5210i | 0.861944 | + | 1.49293i | 0.870050 | + | 0.492963i | \(0.164086\pi\) |
−0.00810628 | + | 0.999967i | \(0.502580\pi\) | |||||||
\(972\) | 10.1616 | − | 11.8212i | 0.325934 | − | 0.379166i | ||||
\(973\) | −10.9621 | + | 21.5873i | −0.351428 | + | 0.692056i | ||||
\(974\) | −7.12353 | + | 4.11277i | −0.228253 | + | 0.131782i | ||||
\(975\) | 1.17216 | + | 6.74157i | 0.0375393 | + | 0.215903i | ||||
\(976\) | 7.97067 | − | 4.60187i | 0.255135 | − | 0.147302i | ||||
\(977\) | 14.8925 | − | 8.59820i | 0.476454 | − | 0.275081i | −0.242484 | − | 0.970155i | \(-0.577962\pi\) |
0.718937 | + | 0.695075i | \(0.244629\pi\) | |||||||
\(978\) | 1.63987 | − | 1.36937i | 0.0524373 | − | 0.0437876i | ||||
\(979\) | −63.0829 | + | 36.4209i | −2.01614 | + | 1.16402i | ||||
\(980\) | 4.12998 | + | 5.65184i | 0.131927 | + | 0.180541i | ||||
\(981\) | −37.6842 | − | 31.9281i | −1.20317 | − | 1.01939i | ||||
\(982\) | 5.26190 | + | 9.11388i | 0.167914 | + | 0.290835i | ||||
\(983\) | −28.5735 | −0.911352 | −0.455676 | − | 0.890146i | \(-0.650602\pi\) | ||||
−0.455676 | + | 0.890146i | \(0.650602\pi\) | |||||||
\(984\) | 2.32021 | + | 13.3444i | 0.0739655 | + | 0.425404i | ||||
\(985\) | − | 2.28650i | − | 0.0728539i | ||||||
\(986\) | −5.36165 | + | 9.28664i | −0.170750 | + | 0.295747i | ||||
\(987\) | −11.9927 | − | 52.1879i | −0.381733 | − | 1.66116i | ||||
\(988\) | −2.19516 | − | 3.80213i | −0.0698374 | − | 0.120962i | ||||
\(989\) | 20.7559 | − | 11.9834i | 0.660001 | − | 0.381052i | ||||
\(990\) | 11.1247 | + | 9.42548i | 0.353567 | + | 0.299561i | ||||
\(991\) | −9.29023 | + | 16.0912i | −0.295114 | + | 0.511152i | −0.975011 | − | 0.222155i | \(-0.928691\pi\) |
0.679897 | + | 0.733307i | \(0.262024\pi\) | |||||||
\(992\) | −3.69876 | + | 6.40644i | −0.117436 | + | 0.203405i | ||||
\(993\) | −13.3779 | + | 2.32602i | −0.424534 | + | 0.0738141i | ||||
\(994\) | 22.7973 | + | 11.5765i | 0.723086 | + | 0.367185i | ||||
\(995\) | 3.60562 | + | 2.08171i | 0.114306 | + | 0.0659945i | ||||
\(996\) | 1.34423 | − | 0.233723i | 0.0425936 | − | 0.00740579i | ||||
\(997\) | − | 7.73126i | − | 0.244851i | −0.992478 | − | 0.122426i | \(-0.960933\pi\) | ||
0.992478 | − | 0.122426i | \(-0.0390673\pi\) | |||||||
\(998\) | 0.736540 | + | 0.425242i | 0.0233148 | + | 0.0134608i | ||||
\(999\) | 16.3196 | + | 9.57831i | 0.516328 | + | 0.303044i |
(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 | 630.2.t.b.311.13 | ✓ | 28 | |
3.2 | odd | 2 | 1890.2.t.b.1151.7 | 28 | |||
7.5 | odd | 6 | 630.2.bk.b.131.7 | yes | 28 | ||
9.2 | odd | 6 | 630.2.bk.b.101.14 | yes | 28 | ||
9.7 | even | 3 | 1890.2.bk.b.521.3 | 28 | |||
21.5 | even | 6 | 1890.2.bk.b.341.3 | 28 | |||
63.47 | even | 6 | inner | 630.2.t.b.551.13 | yes | 28 | |
63.61 | odd | 6 | 1890.2.t.b.1601.7 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.t.b.311.13 | ✓ | 28 | 1.1 | even | 1 | trivial | |
630.2.t.b.551.13 | yes | 28 | 63.47 | even | 6 | inner | |
630.2.bk.b.101.14 | yes | 28 | 9.2 | odd | 6 | ||
630.2.bk.b.131.7 | yes | 28 | 7.5 | odd | 6 | ||
1890.2.t.b.1151.7 | 28 | 3.2 | odd | 2 | |||
1890.2.t.b.1601.7 | 28 | 63.61 | odd | 6 | |||
1890.2.bk.b.341.3 | 28 | 21.5 | even | 6 | |||
1890.2.bk.b.521.3 | 28 | 9.7 | even | 3 |