Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,2,Mod(227,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.227");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.l (of order \(6\), degree \(2\), 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: | \(7.04280545828\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 227.2 | ||
Character | \(\chi\) | \(=\) | 882.227 |
Dual form | 882.2.l.c.509.14 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | −1.63594 | − | 0.568941i | −0.944512 | − | 0.328478i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.55389 | − | 2.69141i | 0.694919 | − | 1.20364i | −0.275288 | − | 0.961362i | \(-0.588773\pi\) |
0.970208 | − | 0.242274i | \(-0.0778933\pi\) | |||||||
\(6\) | −0.568941 | + | 1.63594i | −0.232269 | + | 0.667871i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 2.35261 | + | 1.86151i | 0.784204 | + | 0.620503i | ||||
\(10\) | −2.69141 | − | 1.55389i | −0.851099 | − | 0.491382i | ||||
\(11\) | 1.07339 | − | 0.619720i | 0.323638 | − | 0.186853i | −0.329375 | − | 0.944199i | \(-0.606838\pi\) |
0.653013 | + | 0.757347i | \(0.273505\pi\) | |||||||
\(12\) | 1.63594 | + | 0.568941i | 0.472256 | + | 0.164239i | ||||
\(13\) | 4.97533 | − | 2.87251i | 1.37991 | − | 0.796690i | 0.387759 | − | 0.921761i | \(-0.373249\pi\) |
0.992148 | + | 0.125071i | \(0.0399159\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.07332 | + | 3.51892i | −1.05173 | + | 0.908582i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.783943 | − | 1.35783i | 0.190134 | − | 0.329322i | −0.755160 | − | 0.655540i | \(-0.772441\pi\) |
0.945295 | + | 0.326218i | \(0.105774\pi\) | |||||||
\(18\) | 1.86151 | − | 2.35261i | 0.438762 | − | 0.554516i | ||||
\(19\) | 5.82814 | − | 3.36488i | 1.33707 | − | 0.771956i | 0.350695 | − | 0.936490i | \(-0.385945\pi\) |
0.986371 | + | 0.164534i | \(0.0526121\pi\) | |||||||
\(20\) | −1.55389 | + | 2.69141i | −0.347460 | + | 0.601818i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.619720 | − | 1.07339i | −0.132125 | − | 0.228847i | ||||
\(23\) | −1.52367 | − | 0.879693i | −0.317708 | − | 0.183429i | 0.332663 | − | 0.943046i | \(-0.392053\pi\) |
−0.650370 | + | 0.759617i | \(0.725386\pi\) | |||||||
\(24\) | 0.568941 | − | 1.63594i | 0.116135 | − | 0.333935i | ||||
\(25\) | −2.32913 | − | 4.03417i | −0.465826 | − | 0.806835i | ||||
\(26\) | −2.87251 | − | 4.97533i | −0.563345 | − | 0.975742i | ||||
\(27\) | −2.78965 | − | 4.38382i | −0.536869 | − | 0.843666i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.46914 | − | 2.00291i | −0.644203 | − | 0.371931i | 0.142029 | − | 0.989862i | \(-0.454637\pi\) |
−0.786232 | + | 0.617932i | \(0.787971\pi\) | |||||||
\(30\) | 3.51892 | + | 4.07332i | 0.642465 | + | 0.743684i | ||||
\(31\) | 9.94737i | 1.78660i | 0.449461 | + | 0.893300i | \(0.351616\pi\) | ||||
−0.449461 | + | 0.893300i | \(0.648384\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | −2.10858 | + | 0.403133i | −0.367057 | + | 0.0701764i | ||||
\(34\) | −1.35783 | − | 0.783943i | −0.232866 | − | 0.134445i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.35261 | − | 1.86151i | −0.392102 | − | 0.310251i | ||||
\(37\) | 2.63234 | + | 4.55934i | 0.432753 | + | 0.749551i | 0.997109 | − | 0.0759809i | \(-0.0242088\pi\) |
−0.564356 | + | 0.825532i | \(0.690875\pi\) | |||||||
\(38\) | −3.36488 | − | 5.82814i | −0.545855 | − | 0.945449i | ||||
\(39\) | −9.77363 | + | 1.86859i | −1.56503 | + | 0.299213i | ||||
\(40\) | 2.69141 | + | 1.55389i | 0.425550 | + | 0.245691i | ||||
\(41\) | −5.70540 | − | 9.88204i | −0.891034 | − | 1.54332i | −0.838638 | − | 0.544690i | \(-0.816647\pi\) |
−0.0523962 | − | 0.998626i | \(-0.516686\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.38634 | + | 2.40121i | −0.211415 | + | 0.366181i | −0.952158 | − | 0.305608i | \(-0.901140\pi\) |
0.740743 | + | 0.671789i | \(0.234474\pi\) | |||||||
\(44\) | −1.07339 | + | 0.619720i | −0.161819 | + | 0.0934263i | ||||
\(45\) | 8.66578 | − | 3.43928i | 1.29182 | − | 0.512697i | ||||
\(46\) | −0.879693 | + | 1.52367i | −0.129704 | + | 0.224653i | ||||
\(47\) | −0.263735 | −0.0384698 | −0.0192349 | − | 0.999815i | \(-0.506123\pi\) | ||||
−0.0192349 | + | 0.999815i | \(0.506123\pi\) | |||||||
\(48\) | −1.63594 | − | 0.568941i | −0.236128 | − | 0.0821195i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.03417 | + | 2.32913i | −0.570518 | + | 0.329389i | ||||
\(51\) | −2.05501 | + | 1.77531i | −0.287759 | + | 0.248593i | ||||
\(52\) | −4.97533 | + | 2.87251i | −0.689953 | + | 0.398345i | ||||
\(53\) | 10.4795 | + | 6.05036i | 1.43947 | + | 0.831081i | 0.997813 | − | 0.0661005i | \(-0.0210558\pi\) |
0.441662 | + | 0.897182i | \(0.354389\pi\) | |||||||
\(54\) | −4.38382 | + | 2.78965i | −0.596562 | + | 0.379623i | ||||
\(55\) | − | 3.85190i | − | 0.519390i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.4489 | + | 2.18888i | −1.51645 | + | 0.289924i | ||||
\(58\) | −2.00291 | + | 3.46914i | −0.262995 | + | 0.455520i | ||||
\(59\) | −10.7630 | −1.40122 | −0.700609 | − | 0.713545i | \(-0.747088\pi\) | ||||
−0.700609 | + | 0.713545i | \(0.747088\pi\) | |||||||
\(60\) | 4.07332 | − | 3.51892i | 0.525864 | − | 0.454291i | ||||
\(61\) | − | 9.36774i | − | 1.19942i | −0.800219 | − | 0.599708i | \(-0.795283\pi\) | ||
0.800219 | − | 0.599708i | \(-0.204717\pi\) | |||||||
\(62\) | 9.94737 | 1.26332 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 17.8542i | − | 2.21454i | ||||||
\(66\) | 0.403133 | + | 2.10858i | 0.0496222 | + | 0.259549i | ||||
\(67\) | −2.83202 | −0.345987 | −0.172993 | − | 0.984923i | \(-0.555344\pi\) | ||||
−0.172993 | + | 0.984923i | \(0.555344\pi\) | |||||||
\(68\) | −0.783943 | + | 1.35783i | −0.0950670 | + | 0.164661i | ||||
\(69\) | 1.99215 | + | 2.30601i | 0.239826 | + | 0.277611i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 0.534528i | − | 0.0634368i | −0.999497 | − | 0.0317184i | \(-0.989902\pi\) | ||
0.999497 | − | 0.0317184i | \(-0.0100980\pi\) | |||||||
\(72\) | −1.86151 | + | 2.35261i | −0.219381 | + | 0.277258i | ||||
\(73\) | −8.05423 | − | 4.65011i | −0.942676 | − | 0.544254i | −0.0518779 | − | 0.998653i | \(-0.516521\pi\) |
−0.890798 | + | 0.454399i | \(0.849854\pi\) | |||||||
\(74\) | 4.55934 | − | 2.63234i | 0.530012 | − | 0.306003i | ||||
\(75\) | 1.51512 | + | 7.92481i | 0.174951 | + | 0.915078i | ||||
\(76\) | −5.82814 | + | 3.36488i | −0.668533 | + | 0.385978i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.86859 | + | 9.77363i | 0.211576 | + | 1.10665i | ||||
\(79\) | −16.3298 | −1.83725 | −0.918625 | − | 0.395130i | \(-0.870700\pi\) | ||||
−0.918625 | + | 0.395130i | \(0.870700\pi\) | |||||||
\(80\) | 1.55389 | − | 2.69141i | 0.173730 | − | 0.300909i | ||||
\(81\) | 2.06958 | + | 8.75882i | 0.229953 | + | 0.973202i | ||||
\(82\) | −9.88204 | + | 5.70540i | −1.09129 | + | 0.630056i | ||||
\(83\) | −4.82027 | + | 8.34895i | −0.529093 | + | 0.916416i | 0.470331 | + | 0.882490i | \(0.344134\pi\) |
−0.999424 | + | 0.0339263i | \(0.989199\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.43632 | − | 4.21982i | −0.264256 | − | 0.457704i | ||||
\(86\) | 2.40121 | + | 1.38634i | 0.258929 | + | 0.149493i | ||||
\(87\) | 4.53577 | + | 5.25037i | 0.486286 | + | 0.562899i | ||||
\(88\) | 0.619720 | + | 1.07339i | 0.0660624 | + | 0.114423i | ||||
\(89\) | 3.06418 | + | 5.30732i | 0.324802 | + | 0.562574i | 0.981472 | − | 0.191604i | \(-0.0613688\pi\) |
−0.656670 | + | 0.754178i | \(0.728036\pi\) | |||||||
\(90\) | −3.43928 | − | 8.66578i | −0.362532 | − | 0.913453i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.52367 | + | 0.879693i | 0.158854 | + | 0.0917143i | ||||
\(93\) | 5.65946 | − | 16.2733i | 0.586859 | − | 1.68746i | ||||
\(94\) | 0.263735i | 0.0272022i | ||||||||
\(95\) | − | 20.9146i | − | 2.14579i | ||||||
\(96\) | −0.568941 | + | 1.63594i | −0.0580673 | + | 0.166968i | ||||
\(97\) | 1.29936 | + | 0.750184i | 0.131930 | + | 0.0761697i | 0.564512 | − | 0.825425i | \(-0.309064\pi\) |
−0.432583 | + | 0.901594i | \(0.642398\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.67888 | + | 0.540156i | 0.369741 | + | 0.0542878i | ||||
\(100\) | 2.32913 | + | 4.03417i | 0.232913 | + | 0.403417i | ||||
\(101\) | −3.42652 | − | 5.93491i | −0.340952 | − | 0.590546i | 0.643658 | − | 0.765313i | \(-0.277416\pi\) |
−0.984610 | + | 0.174767i | \(0.944083\pi\) | |||||||
\(102\) | 1.77531 | + | 2.05501i | 0.175782 | + | 0.203476i | ||||
\(103\) | 4.74363 | + | 2.73874i | 0.467404 | + | 0.269856i | 0.715152 | − | 0.698969i | \(-0.246357\pi\) |
−0.247748 | + | 0.968824i | \(0.579691\pi\) | |||||||
\(104\) | 2.87251 | + | 4.97533i | 0.281672 | + | 0.487871i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.05036 | − | 10.4795i | 0.587663 | − | 1.01786i | ||||
\(107\) | 14.5748 | − | 8.41476i | 1.40900 | − | 0.813485i | 0.413706 | − | 0.910411i | \(-0.364234\pi\) |
0.995292 | + | 0.0969253i | \(0.0309008\pi\) | |||||||
\(108\) | 2.78965 | + | 4.38382i | 0.268434 | + | 0.421833i | ||||
\(109\) | −0.690425 | + | 1.19585i | −0.0661307 | + | 0.114542i | −0.897195 | − | 0.441635i | \(-0.854399\pi\) |
0.831064 | + | 0.556176i | \(0.187732\pi\) | |||||||
\(110\) | −3.85190 | −0.367264 | ||||||||
\(111\) | −1.71235 | − | 8.95646i | −0.162530 | − | 0.850109i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.9568 | − | 6.32593i | 1.03073 | − | 0.595093i | 0.113537 | − | 0.993534i | \(-0.463782\pi\) |
0.917194 | + | 0.398441i | \(0.130449\pi\) | |||||||
\(114\) | 2.18888 | + | 11.4489i | 0.205007 | + | 1.07229i | ||||
\(115\) | −4.73523 | + | 2.73389i | −0.441563 | + | 0.254936i | ||||
\(116\) | 3.46914 | + | 2.00291i | 0.322101 | + | 0.185965i | ||||
\(117\) | 17.0522 | + | 2.50372i | 1.57648 | + | 0.231469i | ||||
\(118\) | 10.7630i | 0.990811i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.51892 | − | 4.07332i | −0.321232 | − | 0.371842i | ||||
\(121\) | −4.73189 | + | 8.19588i | −0.430172 | + | 0.745080i | ||||
\(122\) | −9.36774 | −0.848116 | ||||||||
\(123\) | 3.71141 | + | 19.4125i | 0.334646 | + | 1.75036i | ||||
\(124\) | − | 9.94737i | − | 0.893300i | ||||||
\(125\) | 1.06204 | 0.0949921 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.7906 | 0.957513 | 0.478756 | − | 0.877948i | \(-0.341088\pi\) | ||||
0.478756 | + | 0.877948i | \(0.341088\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 3.63412 | − | 3.13950i | 0.319966 | − | 0.276417i | ||||
\(130\) | −17.8542 | −1.56592 | ||||||||
\(131\) | −1.87338 | + | 3.24479i | −0.163678 | + | 0.283499i | −0.936185 | − | 0.351507i | \(-0.885669\pi\) |
0.772507 | + | 0.635006i | \(0.219003\pi\) | |||||||
\(132\) | 2.10858 | − | 0.403133i | 0.183529 | − | 0.0350882i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.83202i | 0.244650i | ||||||||
\(135\) | −16.1335 | + | 0.696141i | −1.38855 | + | 0.0599143i | ||||
\(136\) | 1.35783 | + | 0.783943i | 0.116433 | + | 0.0672225i | ||||
\(137\) | −0.987927 | + | 0.570380i | −0.0844043 | + | 0.0487308i | −0.541608 | − | 0.840631i | \(-0.682184\pi\) |
0.457204 | + | 0.889362i | \(0.348851\pi\) | |||||||
\(138\) | 2.30601 | − | 1.99215i | 0.196300 | − | 0.169583i | ||||
\(139\) | 9.69504 | − | 5.59744i | 0.822323 | − | 0.474768i | −0.0288941 | − | 0.999582i | \(-0.509199\pi\) |
0.851217 | + | 0.524814i | \(0.175865\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.431456 | + | 0.150050i | 0.0363351 | + | 0.0126365i | ||||
\(142\) | −0.534528 | −0.0448566 | ||||||||
\(143\) | 3.56030 | − | 6.16662i | 0.297727 | − | 0.515678i | ||||
\(144\) | 2.35261 | + | 1.86151i | 0.196051 | + | 0.155126i | ||||
\(145\) | −10.7813 | + | 6.22458i | −0.895338 | + | 0.516924i | ||||
\(146\) | −4.65011 | + | 8.05423i | −0.384846 | + | 0.666573i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.63234 | − | 4.55934i | −0.216377 | − | 0.374775i | ||||
\(149\) | 5.73752 | + | 3.31256i | 0.470036 | + | 0.271375i | 0.716255 | − | 0.697839i | \(-0.245855\pi\) |
−0.246219 | + | 0.969214i | \(0.579188\pi\) | |||||||
\(150\) | 7.92481 | − | 1.51512i | 0.647058 | − | 0.123709i | ||||
\(151\) | 0.0942803 | + | 0.163298i | 0.00767242 | + | 0.0132890i | 0.869836 | − | 0.493341i | \(-0.164224\pi\) |
−0.862164 | + | 0.506630i | \(0.830891\pi\) | |||||||
\(152\) | 3.36488 | + | 5.82814i | 0.272928 | + | 0.472724i | ||||
\(153\) | 4.37192 | − | 1.73513i | 0.353449 | − | 0.140277i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 26.7725 | + | 15.4571i | 2.15042 | + | 1.24154i | ||||
\(156\) | 9.77363 | − | 1.86859i | 0.782517 | − | 0.149607i | ||||
\(157\) | 14.3413i | 1.14456i | 0.820060 | + | 0.572278i | \(0.193940\pi\) | ||||
−0.820060 | + | 0.572278i | \(0.806060\pi\) | |||||||
\(158\) | 16.3298i | 1.29913i | ||||||||
\(159\) | −13.7016 | − | 15.8603i | −1.08661 | − | 1.25780i | ||||
\(160\) | −2.69141 | − | 1.55389i | −0.212775 | − | 0.122846i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 8.75882 | − | 2.06958i | 0.688158 | − | 0.162601i | ||||
\(163\) | 4.92077 | + | 8.52302i | 0.385424 | + | 0.667575i | 0.991828 | − | 0.127582i | \(-0.0407217\pi\) |
−0.606404 | + | 0.795157i | \(0.707388\pi\) | |||||||
\(164\) | 5.70540 | + | 9.88204i | 0.445517 | + | 0.771658i | ||||
\(165\) | −2.19150 | + | 6.30149i | −0.170608 | + | 0.490570i | ||||
\(166\) | 8.34895 | + | 4.82027i | 0.648004 | + | 0.374125i | ||||
\(167\) | 0.261517 | + | 0.452961i | 0.0202368 | + | 0.0350512i | 0.875966 | − | 0.482372i | \(-0.160225\pi\) |
−0.855730 | + | 0.517423i | \(0.826891\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.0026 | − | 17.3250i | 0.769429 | − | 1.33269i | ||||
\(170\) | −4.21982 | + | 2.43632i | −0.323646 | + | 0.186857i | ||||
\(171\) | 19.9751 | + | 2.93287i | 1.52753 | + | 0.224282i | ||||
\(172\) | 1.38634 | − | 2.40121i | 0.105707 | − | 0.183091i | ||||
\(173\) | −3.73085 | −0.283651 | −0.141826 | − | 0.989892i | \(-0.545297\pi\) | ||||
−0.141826 | + | 0.989892i | \(0.545297\pi\) | |||||||
\(174\) | 5.25037 | − | 4.53577i | 0.398030 | − | 0.343856i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.07339 | − | 0.619720i | 0.0809096 | − | 0.0467132i | ||||
\(177\) | 17.6076 | + | 6.12349i | 1.32347 | + | 0.460270i | ||||
\(178\) | 5.30732 | − | 3.06418i | 0.397800 | − | 0.229670i | ||||
\(179\) | −6.53507 | − | 3.77303i | −0.488454 | − | 0.282009i | 0.235479 | − | 0.971880i | \(-0.424334\pi\) |
−0.723933 | + | 0.689870i | \(0.757668\pi\) | |||||||
\(180\) | −8.66578 | + | 3.43928i | −0.645909 | + | 0.256349i | ||||
\(181\) | 16.6098i | 1.23460i | 0.786729 | + | 0.617299i | \(0.211773\pi\) | ||||
−0.786729 | + | 0.617299i | \(0.788227\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.32969 | + | 15.3251i | −0.393982 | + | 1.13286i | ||||
\(184\) | 0.879693 | − | 1.52367i | 0.0648518 | − | 0.112327i | ||||
\(185\) | 16.3614 | 1.20291 | ||||||||
\(186\) | −16.2733 | − | 5.65946i | −1.19322 | − | 0.414972i | ||||
\(187\) | − | 1.94330i | − | 0.142108i | ||||||
\(188\) | 0.263735 | 0.0192349 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −20.9146 | −1.51730 | ||||||||
\(191\) | − | 5.64208i | − | 0.408246i | −0.978945 | − | 0.204123i | \(-0.934566\pi\) | ||
0.978945 | − | 0.204123i | \(-0.0654343\pi\) | |||||||
\(192\) | 1.63594 | + | 0.568941i | 0.118064 | + | 0.0410598i | ||||
\(193\) | 9.42027 | 0.678086 | 0.339043 | − | 0.940771i | \(-0.389897\pi\) | ||||
0.339043 | + | 0.940771i | \(0.389897\pi\) | |||||||
\(194\) | 0.750184 | − | 1.29936i | 0.0538601 | − | 0.0932884i | ||||
\(195\) | −10.1580 | + | 29.2084i | −0.727428 | + | 2.09166i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 19.6757i | − | 1.40184i | −0.713242 | − | 0.700918i | \(-0.752774\pi\) | ||
0.713242 | − | 0.700918i | \(-0.247226\pi\) | |||||||
\(198\) | 0.540156 | − | 3.67888i | 0.0383872 | − | 0.261446i | ||||
\(199\) | 12.6517 | + | 7.30448i | 0.896858 | + | 0.517801i | 0.876179 | − | 0.481985i | \(-0.160084\pi\) |
0.0206785 | + | 0.999786i | \(0.493417\pi\) | |||||||
\(200\) | 4.03417 | − | 2.32913i | 0.285259 | − | 0.164694i | ||||
\(201\) | 4.63303 | + | 1.61125i | 0.326788 | + | 0.113649i | ||||
\(202\) | −5.93491 | + | 3.42652i | −0.417579 | + | 0.241089i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.05501 | − | 1.77531i | 0.143879 | − | 0.124297i | ||||
\(205\) | −35.4622 | −2.47679 | ||||||||
\(206\) | 2.73874 | − | 4.74363i | 0.190817 | − | 0.330504i | ||||
\(207\) | −1.94706 | − | 4.90591i | −0.135330 | − | 0.340984i | ||||
\(208\) | 4.97533 | − | 2.87251i | 0.344977 | − | 0.199172i | ||||
\(209\) | 4.17056 | − | 7.22363i | 0.288484 | − | 0.499669i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.90946 | + | 13.6996i | 0.544510 | + | 0.943118i | 0.998638 | + | 0.0521819i | \(0.0166176\pi\) |
−0.454128 | + | 0.890936i | \(0.650049\pi\) | |||||||
\(212\) | −10.4795 | − | 6.05036i | −0.719737 | − | 0.415541i | ||||
\(213\) | −0.304115 | + | 0.874457i | −0.0208376 | + | 0.0599168i | ||||
\(214\) | −8.41476 | − | 14.5748i | −0.575221 | − | 0.996312i | ||||
\(215\) | 4.30843 | + | 7.46242i | 0.293832 | + | 0.508933i | ||||
\(216\) | 4.38382 | − | 2.78965i | 0.298281 | − | 0.189812i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.19585 | + | 0.690425i | 0.0809933 | + | 0.0467615i | ||||
\(219\) | 10.5306 | + | 12.1897i | 0.711593 | + | 0.823703i | ||||
\(220\) | 3.85190i | 0.259695i | ||||||||
\(221\) | − | 9.00752i | − | 0.605911i | ||||||
\(222\) | −8.95646 | + | 1.71235i | −0.601118 | + | 0.114926i | ||||
\(223\) | 1.09788 | + | 0.633859i | 0.0735192 | + | 0.0424463i | 0.536309 | − | 0.844022i | \(-0.319818\pi\) |
−0.462790 | + | 0.886468i | \(0.653152\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.03010 | − | 13.8265i | 0.135340 | − | 0.921770i | ||||
\(226\) | −6.32593 | − | 10.9568i | −0.420794 | − | 0.728837i | ||||
\(227\) | −8.55423 | − | 14.8164i | −0.567764 | − | 0.983396i | −0.996787 | − | 0.0801026i | \(-0.974475\pi\) |
0.429022 | − | 0.903294i | \(-0.358858\pi\) | |||||||
\(228\) | 11.4489 | − | 2.18888i | 0.758223 | − | 0.144962i | ||||
\(229\) | −9.54337 | − | 5.50987i | −0.630644 | − | 0.364102i | 0.150358 | − | 0.988632i | \(-0.451957\pi\) |
−0.781001 | + | 0.624529i | \(0.785291\pi\) | |||||||
\(230\) | 2.73389 | + | 4.73523i | 0.180267 | + | 0.312232i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.00291 | − | 3.46914i | 0.131497 | − | 0.227760i | ||||
\(233\) | −19.8834 | + | 11.4797i | −1.30261 | + | 0.752060i | −0.980850 | − | 0.194763i | \(-0.937606\pi\) |
−0.321756 | + | 0.946823i | \(0.604273\pi\) | |||||||
\(234\) | 2.50372 | − | 17.0522i | 0.163673 | − | 1.11474i | ||||
\(235\) | −0.409815 | + | 0.709821i | −0.0267334 | + | 0.0463036i | ||||
\(236\) | 10.7630 | 0.700609 | ||||||||
\(237\) | 26.7147 | + | 9.29071i | 1.73530 | + | 0.603496i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.63609 | + | 5.56340i | −0.623307 | + | 0.359866i | −0.778155 | − | 0.628072i | \(-0.783844\pi\) |
0.154849 | + | 0.987938i | \(0.450511\pi\) | |||||||
\(240\) | −4.07332 | + | 3.51892i | −0.262932 | + | 0.227146i | ||||
\(241\) | 0.384876 | − | 0.222208i | 0.0247920 | − | 0.0143137i | −0.487553 | − | 0.873094i | \(-0.662110\pi\) |
0.512345 | + | 0.858780i | \(0.328777\pi\) | |||||||
\(242\) | 8.19588 | + | 4.73189i | 0.526851 | + | 0.304178i | ||||
\(243\) | 1.59754 | − | 15.5064i | 0.102482 | − | 0.994735i | ||||
\(244\) | 9.36774i | 0.599708i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 19.4125 | − | 3.71141i | 1.23769 | − | 0.236631i | ||||
\(247\) | 19.3313 | − | 33.4827i | 1.23002 | − | 2.13045i | ||||
\(248\) | −9.94737 | −0.631659 | ||||||||
\(249\) | 12.6357 | − | 10.9160i | 0.800757 | − | 0.691770i | ||||
\(250\) | − | 1.06204i | − | 0.0671696i | ||||||
\(251\) | −18.9568 | −1.19655 | −0.598273 | − | 0.801292i | \(-0.704146\pi\) | ||||
−0.598273 | + | 0.801292i | \(0.704146\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.18065 | −0.137096 | ||||||||
\(254\) | − | 10.7906i | − | 0.677064i | ||||||
\(255\) | 1.58484 | + | 8.28951i | 0.0992467 | + | 0.519109i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.66124 | − | 15.0017i | 0.540273 | − | 0.935781i | −0.458615 | − | 0.888635i | \(-0.651654\pi\) |
0.998888 | − | 0.0471456i | \(-0.0150125\pi\) | |||||||
\(258\) | −3.13950 | − | 3.63412i | −0.195456 | − | 0.226250i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 17.8542i | 1.10727i | ||||||||
\(261\) | −4.43311 | − | 11.1699i | −0.274403 | − | 0.691399i | ||||
\(262\) | 3.24479 | + | 1.87338i | 0.200464 | + | 0.115738i | ||||
\(263\) | 2.43723 | − | 1.40713i | 0.150286 | − | 0.0867675i | −0.422971 | − | 0.906143i | \(-0.639013\pi\) |
0.573257 | + | 0.819375i | \(0.305680\pi\) | |||||||
\(264\) | −0.403133 | − | 2.10858i | −0.0248111 | − | 0.129774i | ||||
\(265\) | 32.5680 | − | 18.8032i | 2.00064 | − | 1.15507i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.99327 | − | 10.4258i | −0.121986 | − | 0.638049i | ||||
\(268\) | 2.83202 | 0.172993 | ||||||||
\(269\) | 12.6555 | − | 21.9200i | 0.771620 | − | 1.33648i | −0.165055 | − | 0.986284i | \(-0.552780\pi\) |
0.936675 | − | 0.350200i | \(-0.113886\pi\) | |||||||
\(270\) | 0.696141 | + | 16.1335i | 0.0423658 | + | 0.981851i | ||||
\(271\) | −24.2642 | + | 14.0089i | −1.47394 | + | 0.850982i | −0.999569 | − | 0.0293402i | \(-0.990659\pi\) |
−0.474375 | + | 0.880323i | \(0.657326\pi\) | |||||||
\(272\) | 0.783943 | − | 1.35783i | 0.0475335 | − | 0.0823304i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.570380 | + | 0.987927i | 0.0344579 | + | 0.0596828i | ||||
\(275\) | −5.00012 | − | 2.88682i | −0.301518 | − | 0.174082i | ||||
\(276\) | −1.99215 | − | 2.30601i | −0.119913 | − | 0.138805i | ||||
\(277\) | −1.85995 | − | 3.22152i | −0.111753 | − | 0.193562i | 0.804724 | − | 0.593649i | \(-0.202313\pi\) |
−0.916477 | + | 0.400087i | \(0.868980\pi\) | |||||||
\(278\) | −5.59744 | − | 9.69504i | −0.335712 | − | 0.581470i | ||||
\(279\) | −18.5171 | + | 23.4023i | −1.10859 | + | 1.40106i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.40645 | + | 3.69877i | 0.382177 | + | 0.220650i | 0.678765 | − | 0.734356i | \(-0.262516\pi\) |
−0.296588 | + | 0.955005i | \(0.595849\pi\) | |||||||
\(282\) | 0.150050 | − | 0.431456i | 0.00893534 | − | 0.0256928i | ||||
\(283\) | 13.5292i | 0.804226i | 0.915590 | + | 0.402113i | \(0.131724\pi\) | ||||
−0.915590 | + | 0.402113i | \(0.868276\pi\) | |||||||
\(284\) | 0.534528i | 0.0317184i | ||||||||
\(285\) | −11.8991 | + | 34.2150i | −0.704844 | + | 2.02672i | ||||
\(286\) | −6.16662 | − | 3.56030i | −0.364640 | − | 0.210525i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.86151 | − | 2.35261i | 0.109690 | − | 0.138629i | ||||
\(289\) | 7.27087 | + | 12.5935i | 0.427698 | + | 0.740795i | ||||
\(290\) | 6.22458 | + | 10.7813i | 0.365520 | + | 0.633099i | ||||
\(291\) | −1.69886 | − | 1.96652i | −0.0995891 | − | 0.115279i | ||||
\(292\) | 8.05423 | + | 4.65011i | 0.471338 | + | 0.272127i | ||||
\(293\) | 2.50771 | + | 4.34349i | 0.146502 | + | 0.253749i | 0.929932 | − | 0.367731i | \(-0.119865\pi\) |
−0.783430 | + | 0.621480i | \(0.786532\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.7244 | + | 28.9676i | −0.973734 | + | 1.68656i | ||||
\(296\) | −4.55934 | + | 2.63234i | −0.265006 | + | 0.153001i | ||||
\(297\) | −5.71111 | − | 2.97673i | −0.331392 | − | 0.172727i | ||||
\(298\) | 3.31256 | − | 5.73752i | 0.191891 | − | 0.332366i | ||||
\(299\) | −10.1077 | −0.584543 | ||||||||
\(300\) | −1.51512 | − | 7.92481i | −0.0874754 | − | 0.457539i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.163298 | − | 0.0942803i | 0.00939676 | − | 0.00542522i | ||||
\(303\) | 2.22898 | + | 11.6587i | 0.128052 | + | 0.669773i | ||||
\(304\) | 5.82814 | − | 3.36488i | 0.334267 | − | 0.192989i | ||||
\(305\) | −25.2125 | − | 14.5564i | −1.44366 | − | 0.833498i | ||||
\(306\) | −1.73513 | − | 4.37192i | −0.0991907 | − | 0.249926i | ||||
\(307\) | − | 10.7290i | − | 0.612334i | −0.951978 | − | 0.306167i | \(-0.900953\pi\) | ||
0.951978 | − | 0.306167i | \(-0.0990466\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.20213 | − | 7.17926i | −0.352827 | − | 0.408414i | ||||
\(310\) | 15.4571 | − | 26.7725i | 0.877904 | − | 1.52057i | ||||
\(311\) | 1.07969 | 0.0612236 | 0.0306118 | − | 0.999531i | \(-0.490254\pi\) | ||||
0.0306118 | + | 0.999531i | \(0.490254\pi\) | |||||||
\(312\) | −1.86859 | − | 9.77363i | −0.105788 | − | 0.553323i | ||||
\(313\) | 23.8521i | 1.34820i | 0.738639 | + | 0.674101i | \(0.235469\pi\) | ||||
−0.738639 | + | 0.674101i | \(0.764531\pi\) | |||||||
\(314\) | 14.3413 | 0.809324 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.3298 | 0.918625 | ||||||||
\(317\) | 22.0867i | 1.24051i | 0.784399 | + | 0.620256i | \(0.212971\pi\) | ||||
−0.784399 | + | 0.620256i | \(0.787029\pi\) | |||||||
\(318\) | −15.8603 | + | 13.7016i | −0.889400 | + | 0.768348i | ||||
\(319\) | −4.96497 | −0.277985 | ||||||||
\(320\) | −1.55389 | + | 2.69141i | −0.0868649 | + | 0.150454i | ||||
\(321\) | −28.6310 | + | 5.47386i | −1.59803 | + | 0.305521i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 10.5515i | − | 0.587100i | ||||||
\(324\) | −2.06958 | − | 8.75882i | −0.114976 | − | 0.486601i | ||||
\(325\) | −23.1764 | − | 13.3809i | −1.28559 | − | 0.742238i | ||||
\(326\) | 8.52302 | − | 4.92077i | 0.472047 | − | 0.272536i | ||||
\(327\) | 1.80986 | − | 1.56353i | 0.100086 | − | 0.0864635i | ||||
\(328\) | 9.88204 | − | 5.70540i | 0.545645 | − | 0.315028i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 6.30149 | + | 2.19150i | 0.346885 | + | 0.120638i | ||||
\(331\) | 14.3102 | 0.786561 | 0.393281 | − | 0.919418i | \(-0.371340\pi\) | ||||
0.393281 | + | 0.919418i | \(0.371340\pi\) | |||||||
\(332\) | 4.82027 | − | 8.34895i | 0.264547 | − | 0.458208i | ||||
\(333\) | −2.29438 | + | 15.6265i | −0.125731 | + | 0.856325i | ||||
\(334\) | 0.452961 | − | 0.261517i | 0.0247849 | − | 0.0143096i | ||||
\(335\) | −4.40064 | + | 7.62214i | −0.240433 | + | 0.416442i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.0707 | − | 17.4430i | −0.548588 | − | 0.950182i | −0.998372 | − | 0.0570449i | \(-0.981832\pi\) |
0.449783 | − | 0.893138i | \(-0.351501\pi\) | |||||||
\(338\) | −17.3250 | − | 10.0026i | −0.942354 | − | 0.544068i | ||||
\(339\) | −21.5238 | + | 4.11506i | −1.16901 | + | 0.223500i | ||||
\(340\) | 2.43632 | + | 4.21982i | 0.132128 | + | 0.228852i | ||||
\(341\) | 6.16458 | + | 10.6774i | 0.333831 | + | 0.578212i | ||||
\(342\) | 2.93287 | − | 19.9751i | 0.158592 | − | 1.08013i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.40121 | − | 1.38634i | −0.129465 | − | 0.0747464i | ||||
\(345\) | 9.30198 | − | 1.77842i | 0.500802 | − | 0.0957467i | ||||
\(346\) | 3.73085i | 0.200572i | ||||||||
\(347\) | 13.4117i | 0.719975i | 0.932957 | + | 0.359988i | \(0.117219\pi\) | ||||
−0.932957 | + | 0.359988i | \(0.882781\pi\) | |||||||
\(348\) | −4.53577 | − | 5.25037i | −0.243143 | − | 0.281450i | ||||
\(349\) | −16.4018 | − | 9.46958i | −0.877968 | − | 0.506895i | −0.00798005 | − | 0.999968i | \(-0.502540\pi\) |
−0.869988 | + | 0.493073i | \(0.835873\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −26.4720 | − | 13.7976i | −1.41297 | − | 0.736463i | ||||
\(352\) | −0.619720 | − | 1.07339i | −0.0330312 | − | 0.0572117i | ||||
\(353\) | 12.5947 | + | 21.8147i | 0.670349 | + | 1.16108i | 0.977805 | + | 0.209516i | \(0.0671889\pi\) |
−0.307456 | + | 0.951562i | \(0.599478\pi\) | |||||||
\(354\) | 6.12349 | − | 17.6076i | 0.325460 | − | 0.935832i | ||||
\(355\) | −1.43863 | − | 0.830596i | −0.0763548 | − | 0.0440835i | ||||
\(356\) | −3.06418 | − | 5.30732i | −0.162401 | − | 0.281287i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.77303 | + | 6.53507i | −0.199411 | + | 0.345389i | ||||
\(359\) | 6.33158 | − | 3.65554i | 0.334168 | − | 0.192932i | −0.323522 | − | 0.946221i | \(-0.604867\pi\) |
0.657690 | + | 0.753289i | \(0.271534\pi\) | |||||||
\(360\) | 3.43928 | + | 8.66578i | 0.181266 | + | 0.456727i | ||||
\(361\) | 13.1448 | − | 22.7674i | 0.691831 | − | 1.19829i | ||||
\(362\) | 16.6098 | 0.872992 | ||||||||
\(363\) | 12.4041 | − | 10.7158i | 0.651045 | − | 0.562435i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −25.0307 | + | 14.4515i | −1.31017 | + | 0.756426i | ||||
\(366\) | 15.3251 | + | 5.32969i | 0.801055 | + | 0.278587i | ||||
\(367\) | 22.6702 | − | 13.0886i | 1.18337 | − | 0.683220i | 0.226580 | − | 0.973993i | \(-0.427245\pi\) |
0.956792 | + | 0.290772i | \(0.0939122\pi\) | |||||||
\(368\) | −1.52367 | − | 0.879693i | −0.0794269 | − | 0.0458572i | ||||
\(369\) | 4.97291 | − | 33.8693i | 0.258879 | − | 1.76316i | ||||
\(370\) | − | 16.3614i | − | 0.850589i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −5.65946 | + | 16.2733i | −0.293429 | + | 0.843732i | ||||
\(373\) | −10.5412 | + | 18.2578i | −0.545801 | + | 0.945355i | 0.452755 | + | 0.891635i | \(0.350441\pi\) |
−0.998556 | + | 0.0537204i | \(0.982892\pi\) | |||||||
\(374\) | −1.94330 | −0.100486 | ||||||||
\(375\) | −1.73744 | − | 0.604240i | −0.0897212 | − | 0.0312028i | ||||
\(376\) | − | 0.263735i | − | 0.0136011i | ||||||
\(377\) | −23.0134 | −1.18525 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.68371 | −0.291953 | −0.145976 | − | 0.989288i | \(-0.546632\pi\) | ||||
−0.145976 | + | 0.989288i | \(0.546632\pi\) | |||||||
\(380\) | 20.9146i | 1.07289i | ||||||||
\(381\) | −17.6528 | − | 6.13922i | −0.904382 | − | 0.314522i | ||||
\(382\) | −5.64208 | −0.288674 | ||||||||
\(383\) | 0.0608136 | − | 0.105332i | 0.00310743 | − | 0.00538223i | −0.864468 | − | 0.502689i | \(-0.832344\pi\) |
0.867575 | + | 0.497306i | \(0.165678\pi\) | |||||||
\(384\) | 0.568941 | − | 1.63594i | 0.0290336 | − | 0.0834838i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 9.42027i | − | 0.479479i | ||||||
\(387\) | −7.73139 | + | 3.06844i | −0.393009 | + | 0.155977i | ||||
\(388\) | −1.29936 | − | 0.750184i | −0.0659649 | − | 0.0380848i | ||||
\(389\) | −23.8235 | + | 13.7545i | −1.20790 | + | 0.697381i | −0.962300 | − | 0.271991i | \(-0.912318\pi\) |
−0.245599 | + | 0.969372i | \(0.578985\pi\) | |||||||
\(390\) | 29.2084 | + | 10.1580i | 1.47903 | + | 0.514369i | ||||
\(391\) | −2.38894 | + | 1.37926i | −0.120814 | + | 0.0697521i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.91084 | − | 4.24245i | 0.247719 | − | 0.214003i | ||||
\(394\) | −19.6757 | −0.991248 | ||||||||
\(395\) | −25.3747 | + | 43.9503i | −1.27674 | + | 2.21138i | ||||
\(396\) | −3.67888 | − | 0.540156i | −0.184871 | − | 0.0271439i | ||||
\(397\) | 10.7866 | − | 6.22766i | 0.541365 | − | 0.312557i | −0.204267 | − | 0.978915i | \(-0.565481\pi\) |
0.745632 | + | 0.666358i | \(0.232148\pi\) | |||||||
\(398\) | 7.30448 | − | 12.6517i | 0.366141 | − | 0.634174i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.32913 | − | 4.03417i | −0.116457 | − | 0.201709i | ||||
\(401\) | 24.0294 | + | 13.8734i | 1.19997 | + | 0.692802i | 0.960548 | − | 0.278114i | \(-0.0897092\pi\) |
0.239421 | + | 0.970916i | \(0.423042\pi\) | |||||||
\(402\) | 1.61125 | − | 4.63303i | 0.0803620 | − | 0.231074i | ||||
\(403\) | 28.5739 | + | 49.4914i | 1.42337 | + | 2.46534i | ||||
\(404\) | 3.42652 | + | 5.93491i | 0.170476 | + | 0.295273i | ||||
\(405\) | 26.7895 | + | 8.04013i | 1.33118 | + | 0.399517i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.65103 | + | 3.26262i | 0.280111 | + | 0.161722i | ||||
\(408\) | −1.77531 | − | 2.05501i | −0.0878910 | − | 0.101738i | ||||
\(409\) | − | 11.2300i | − | 0.555286i | −0.960684 | − | 0.277643i | \(-0.910447\pi\) | ||
0.960684 | − | 0.277643i | \(-0.0895533\pi\) | |||||||
\(410\) | 35.4622i | 1.75135i | ||||||||
\(411\) | 1.94070 | − | 0.371037i | 0.0957278 | − | 0.0183019i | ||||
\(412\) | −4.74363 | − | 2.73874i | −0.233702 | − | 0.134928i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −4.90591 | + | 1.94706i | −0.241112 | + | 0.0956926i | ||||
\(415\) | 14.9803 | + | 25.9467i | 0.735354 | + | 1.27367i | ||||
\(416\) | −2.87251 | − | 4.97533i | −0.140836 | − | 0.243935i | ||||
\(417\) | −19.0451 | + | 3.64118i | −0.932644 | + | 0.178309i | ||||
\(418\) | −7.22363 | − | 4.17056i | −0.353319 | − | 0.203989i | ||||
\(419\) | 1.68086 | + | 2.91134i | 0.0821155 | + | 0.142228i | 0.904158 | − | 0.427197i | \(-0.140499\pi\) |
−0.822043 | + | 0.569425i | \(0.807166\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.08955 | + | 5.35125i | −0.150575 | + | 0.260804i | −0.931439 | − | 0.363897i | \(-0.881446\pi\) |
0.780864 | + | 0.624701i | \(0.214779\pi\) | |||||||
\(422\) | 13.6996 | − | 7.90946i | 0.666885 | − | 0.385026i | ||||
\(423\) | −0.620467 | − | 0.490946i | −0.0301682 | − | 0.0238706i | ||||
\(424\) | −6.05036 | + | 10.4795i | −0.293832 | + | 0.508931i | ||||
\(425\) | −7.30362 | −0.354278 | ||||||||
\(426\) | 0.874457 | + | 0.304115i | 0.0423676 | + | 0.0147344i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −14.5748 | + | 8.41476i | −0.704499 | + | 0.406743i | ||||
\(429\) | −9.33288 | + | 8.06263i | −0.450596 | + | 0.389267i | ||||
\(430\) | 7.46242 | − | 4.30843i | 0.359870 | − | 0.207771i | ||||
\(431\) | 11.5265 | + | 6.65482i | 0.555211 | + | 0.320551i | 0.751221 | − | 0.660050i | \(-0.229465\pi\) |
−0.196010 | + | 0.980602i | \(0.562798\pi\) | |||||||
\(432\) | −2.78965 | − | 4.38382i | −0.134217 | − | 0.210916i | ||||
\(433\) | 25.7161i | 1.23584i | 0.786242 | + | 0.617919i | \(0.212024\pi\) | ||||
−0.786242 | + | 0.617919i | \(0.787976\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 21.1790 | − | 4.04914i | 1.01545 | − | 0.194141i | ||||
\(436\) | 0.690425 | − | 1.19585i | 0.0330654 | − | 0.0572709i | ||||
\(437\) | −11.8402 | −0.566395 | ||||||||
\(438\) | 12.1897 | − | 10.5306i | 0.582446 | − | 0.503172i | ||||
\(439\) | − | 37.0419i | − | 1.76791i | −0.467570 | − | 0.883956i | \(-0.654870\pi\) | ||
0.467570 | − | 0.883956i | \(-0.345130\pi\) | |||||||
\(440\) | 3.85190 | 0.183632 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.00752 | −0.428444 | ||||||||
\(443\) | 22.9752i | 1.09158i | 0.837921 | + | 0.545792i | \(0.183771\pi\) | ||||
−0.837921 | + | 0.545792i | \(0.816229\pi\) | |||||||
\(444\) | 1.71235 | + | 8.95646i | 0.0812648 | + | 0.425055i | ||||
\(445\) | 19.0456 | 0.902846 | ||||||||
\(446\) | 0.633859 | − | 1.09788i | 0.0300141 | − | 0.0519859i | ||||
\(447\) | −7.50160 | − | 8.68347i | −0.354814 | − | 0.410714i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.217897i | 0.0102832i | 0.999987 | + | 0.00514159i | \(0.00163663\pi\) | ||||
−0.999987 | + | 0.00514159i | \(0.998363\pi\) | |||||||
\(450\) | −13.8265 | − | 2.03010i | −0.651790 | − | 0.0957000i | ||||
\(451\) | −12.2482 | − | 7.07150i | −0.576745 | − | 0.332984i | ||||
\(452\) | −10.9568 | + | 6.32593i | −0.515366 | + | 0.297546i | ||||
\(453\) | −0.0613301 | − | 0.320786i | −0.00288154 | − | 0.0150719i | ||||
\(454\) | −14.8164 | + | 8.55423i | −0.695366 | + | 0.401470i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.18888 | − | 11.4489i | −0.102504 | − | 0.536144i | ||||
\(457\) | −0.930228 | −0.0435143 | −0.0217571 | − | 0.999763i | \(-0.506926\pi\) | ||||
−0.0217571 | + | 0.999763i | \(0.506926\pi\) | |||||||
\(458\) | −5.50987 | + | 9.54337i | −0.257459 | + | 0.445932i | ||||
\(459\) | −8.13940 | + | 0.351206i | −0.379915 | + | 0.0163929i | ||||
\(460\) | 4.73523 | − | 2.73389i | 0.220781 | − | 0.127468i | ||||
\(461\) | 15.6935 | − | 27.1820i | 0.730921 | − | 1.26599i | −0.225570 | − | 0.974227i | \(-0.572424\pi\) |
0.956490 | − | 0.291764i | \(-0.0942424\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.3239 | + | 17.8816i | 0.479795 | + | 0.831028i | 0.999731 | − | 0.0231762i | \(-0.00737788\pi\) |
−0.519937 | + | 0.854205i | \(0.674045\pi\) | |||||||
\(464\) | −3.46914 | − | 2.00291i | −0.161051 | − | 0.0929826i | ||||
\(465\) | −35.0040 | − | 40.5188i | −1.62327 | − | 1.87902i | ||||
\(466\) | 11.4797 | + | 19.8834i | 0.531787 | + | 0.921082i | ||||
\(467\) | 5.27432 | + | 9.13539i | 0.244066 | + | 0.422736i | 0.961869 | − | 0.273511i | \(-0.0881852\pi\) |
−0.717802 | + | 0.696247i | \(0.754852\pi\) | |||||||
\(468\) | −17.0522 | − | 2.50372i | −0.788238 | − | 0.115734i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.709821 | + | 0.409815i | 0.0327416 | + | 0.0189034i | ||||
\(471\) | 8.15932 | − | 23.4615i | 0.375962 | − | 1.08105i | ||||
\(472\) | − | 10.7630i | − | 0.495406i | ||||||
\(473\) | 3.43657i | 0.158014i | ||||||||
\(474\) | 9.29071 | − | 26.7147i | 0.426736 | − | 1.22705i | ||||
\(475\) | −27.1490 | − | 15.6745i | −1.24568 | − | 0.719194i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.3915 | + | 33.7419i | 0.613154 | + | 1.54494i | ||||
\(478\) | 5.56340 | + | 9.63609i | 0.254464 | + | 0.440744i | ||||
\(479\) | −9.23071 | − | 15.9881i | −0.421762 | − | 0.730513i | 0.574350 | − | 0.818610i | \(-0.305255\pi\) |
−0.996112 | + | 0.0880966i | \(0.971922\pi\) | |||||||
\(480\) | 3.51892 | + | 4.07332i | 0.160616 | + | 0.185921i | ||||
\(481\) | 26.1934 | + | 15.1228i | 1.19432 | + | 0.689540i | ||||
\(482\) | −0.222208 | − | 0.384876i | −0.0101213 | − | 0.0175306i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.73189 | − | 8.19588i | 0.215086 | − | 0.372540i | ||||
\(485\) | 4.03811 | − | 2.33140i | 0.183361 | − | 0.105864i | ||||
\(486\) | −15.5064 | − | 1.59754i | −0.703384 | − | 0.0724660i | ||||
\(487\) | 19.1534 | − | 33.1747i | 0.867924 | − | 1.50329i | 0.00381071 | − | 0.999993i | \(-0.498787\pi\) |
0.864114 | − | 0.503297i | \(-0.167880\pi\) | |||||||
\(488\) | 9.36774 | 0.424058 | ||||||||
\(489\) | −3.20100 | − | 16.7428i | −0.144754 | − | 0.757135i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.32798 | − | 5.38551i | 0.420966 | − | 0.243045i | −0.274525 | − | 0.961580i | \(-0.588521\pi\) |
0.695490 | + | 0.718535i | \(0.255187\pi\) | |||||||
\(492\) | −3.71141 | − | 19.4125i | −0.167323 | − | 0.875182i | ||||
\(493\) | −5.43921 | + | 3.14033i | −0.244970 | + | 0.141433i | ||||
\(494\) | −33.4827 | − | 19.3313i | −1.50646 | − | 0.869754i | ||||
\(495\) | 7.17034 | − | 9.06203i | 0.322283 | − | 0.407308i | ||||
\(496\) | 9.94737i | 0.446650i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −10.9160 | − | 12.6357i | −0.489156 | − | 0.566221i | ||||
\(499\) | 6.11298 | − | 10.5880i | 0.273655 | − | 0.473984i | −0.696140 | − | 0.717906i | \(-0.745101\pi\) |
0.969795 | + | 0.243922i | \(0.0784341\pi\) | |||||||
\(500\) | −1.06204 | −0.0474961 | ||||||||
\(501\) | −0.170119 | − | 0.889806i | −0.00760036 | − | 0.0397536i | ||||
\(502\) | 18.9568i | 0.846086i | ||||||||
\(503\) | 4.13307 | 0.184285 | 0.0921423 | − | 0.995746i | \(-0.470629\pi\) | ||||
0.0921423 | + | 0.995746i | \(0.470629\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.2977 | −0.947736 | ||||||||
\(506\) | 2.18065i | 0.0969419i | ||||||||
\(507\) | −26.2205 | + | 22.6518i | −1.16449 | + | 1.00600i | ||||
\(508\) | −10.7906 | −0.478756 | ||||||||
\(509\) | −5.57958 | + | 9.66411i | −0.247310 | + | 0.428354i | −0.962779 | − | 0.270291i | \(-0.912880\pi\) |
0.715468 | + | 0.698645i | \(0.246213\pi\) | |||||||
\(510\) | 8.28951 | − | 1.58484i | 0.367066 | − | 0.0701780i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −31.0095 | − | 16.1627i | −1.36910 | − | 0.713599i | ||||
\(514\) | −15.0017 | − | 8.66124i | −0.661697 | − | 0.382031i | ||||
\(515\) | 14.7421 | − | 8.51138i | 0.649616 | − | 0.375056i | ||||
\(516\) | −3.63412 | + | 3.13950i | −0.159983 | + | 0.138209i | ||||
\(517\) | −0.283090 | + | 0.163442i | −0.0124503 | + | 0.00718818i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.10345 | + | 2.12263i | 0.267912 | + | 0.0931732i | ||||
\(520\) | 17.8542 | 0.782958 | ||||||||
\(521\) | −2.62310 | + | 4.54334i | −0.114920 | + | 0.199047i | −0.917748 | − | 0.397164i | \(-0.869995\pi\) |
0.802828 | + | 0.596211i | \(0.203328\pi\) | |||||||
\(522\) | −11.1699 | + | 4.43311i | −0.488893 | + | 0.194032i | ||||
\(523\) | −13.6454 | + | 7.87819i | −0.596673 | + | 0.344489i | −0.767732 | − | 0.640772i | \(-0.778615\pi\) |
0.171059 | + | 0.985261i | \(0.445281\pi\) | |||||||
\(524\) | 1.87338 | − | 3.24479i | 0.0818391 | − | 0.141749i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.40713 | − | 2.43723i | −0.0613539 | − | 0.106268i | ||||
\(527\) | 13.5068 | + | 7.79817i | 0.588366 | + | 0.339693i | ||||
\(528\) | −2.10858 | + | 0.403133i | −0.0917643 | + | 0.0175441i | ||||
\(529\) | −9.95228 | − | 17.2379i | −0.432708 | − | 0.749472i | ||||
\(530\) | −18.8032 | − | 32.5680i | −0.816757 | − | 1.41466i | ||||
\(531\) | −25.3211 | − | 20.0353i | −1.09884 | − | 0.869460i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −56.7724 | − | 32.7776i | −2.45909 | − | 1.41975i | ||||
\(534\) | −10.4258 | + | 1.99327i | −0.451168 | + | 0.0862574i | ||||
\(535\) | − | 52.3023i | − | 2.26123i | ||||||
\(536\) | − | 2.83202i | − | 0.122325i | ||||||
\(537\) | 8.54437 | + | 9.89052i | 0.368717 | + | 0.426807i | ||||
\(538\) | −21.9200 | − | 12.6555i | −0.945037 | − | 0.545617i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 16.1335 | − | 0.696141i | 0.694273 | − | 0.0299572i | ||||
\(541\) | −3.03172 | − | 5.25109i | −0.130344 | − | 0.225762i | 0.793465 | − | 0.608615i | \(-0.208275\pi\) |
−0.923809 | + | 0.382853i | \(0.874941\pi\) | |||||||
\(542\) | 14.0089 | + | 24.2642i | 0.601735 | + | 1.04224i | ||||
\(543\) | 9.45000 | − | 27.1727i | 0.405538 | − | 1.16609i | ||||
\(544\) | −1.35783 | − | 0.783943i | −0.0582164 | − | 0.0336113i | ||||
\(545\) | 2.14569 | + | 3.71644i | 0.0919110 | + | 0.159195i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.412740 | − | 0.714887i | 0.0176475 | − | 0.0305663i | −0.857067 | − | 0.515205i | \(-0.827716\pi\) |
0.874714 | + | 0.484639i | \(0.161049\pi\) | |||||||
\(548\) | 0.987927 | − | 0.570380i | 0.0422021 | − | 0.0243654i | ||||
\(549\) | 17.4381 | − | 22.0387i | 0.744241 | − | 0.940588i | ||||
\(550\) | −2.88682 | + | 5.00012i | −0.123094 | + | 0.213206i | ||||
\(551\) | −26.9581 | −1.14846 | ||||||||
\(552\) | −2.30601 | + | 1.99215i | −0.0981501 | + | 0.0847914i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.22152 | + | 1.85995i | −0.136869 | + | 0.0790215i | ||||
\(555\) | −26.7663 | − | 9.30867i | −1.13617 | − | 0.395131i | ||||
\(556\) | −9.69504 | + | 5.59744i | −0.411161 | + | 0.237384i | ||||
\(557\) | 19.2191 | + | 11.0961i | 0.814339 | + | 0.470159i | 0.848460 | − | 0.529259i | \(-0.177530\pi\) |
−0.0341214 | + | 0.999418i | \(0.510863\pi\) | |||||||
\(558\) | 23.4023 | + | 18.5171i | 0.990699 | + | 0.783892i | ||||
\(559\) | 15.9291i | 0.673728i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.10562 | + | 3.17913i | −0.0466794 | + | 0.134223i | ||||
\(562\) | 3.69877 | − | 6.40645i | 0.156023 | − | 0.270240i | ||||
\(563\) | −1.96694 | −0.0828968 | −0.0414484 | − | 0.999141i | \(-0.513197\pi\) | ||||
−0.0414484 | + | 0.999141i | \(0.513197\pi\) | |||||||
\(564\) | −0.431456 | − | 0.150050i | −0.0181676 | − | 0.00631824i | ||||
\(565\) | − | 39.3191i | − | 1.65417i | ||||||
\(566\) | 13.5292 | 0.568674 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.534528 | 0.0224283 | ||||||||
\(569\) | 26.0453i | 1.09188i | 0.837825 | + | 0.545938i | \(0.183827\pi\) | ||||
−0.837825 | + | 0.545938i | \(0.816173\pi\) | |||||||
\(570\) | 34.2150 | + | 11.8991i | 1.43311 | + | 0.498400i | ||||
\(571\) | −6.64910 | −0.278256 | −0.139128 | − | 0.990274i | \(-0.544430\pi\) | ||||
−0.139128 | + | 0.990274i | \(0.544430\pi\) | |||||||
\(572\) | −3.56030 | + | 6.16662i | −0.148864 | + | 0.257839i | ||||
\(573\) | −3.21001 | + | 9.23011i | −0.134100 | + | 0.385593i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.19568i | 0.341784i | ||||||||
\(576\) | −2.35261 | − | 1.86151i | −0.0980255 | − | 0.0775628i | ||||
\(577\) | 1.79600 | + | 1.03692i | 0.0747683 | + | 0.0431675i | 0.536918 | − | 0.843634i | \(-0.319588\pi\) |
−0.462150 | + | 0.886802i | \(0.652922\pi\) | |||||||
\(578\) | 12.5935 | − | 7.27087i | 0.523821 | − | 0.302428i | ||||
\(579\) | −15.4110 | − | 5.35957i | −0.640460 | − | 0.222736i | ||||
\(580\) | 10.7813 | − | 6.22458i | 0.447669 | − | 0.258462i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1.96652 | + | 1.69886i | −0.0815147 | + | 0.0704201i | ||||
\(583\) | 14.9981 | 0.621159 | ||||||||
\(584\) | 4.65011 | − | 8.05423i | 0.192423 | − | 0.333286i | ||||
\(585\) | 33.2357 | − | 42.0040i | 1.37413 | − | 1.73665i | ||||
\(586\) | 4.34349 | − | 2.50771i | 0.179428 | − | 0.103593i | ||||
\(587\) | 5.82360 | − | 10.0868i | 0.240366 | − | 0.416326i | −0.720453 | − | 0.693504i | \(-0.756066\pi\) |
0.960818 | + | 0.277178i | \(0.0893993\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 33.4717 | + | 57.9746i | 1.37918 | + | 2.38880i | ||||
\(590\) | 28.9676 | + | 16.7244i | 1.19258 | + | 0.688534i | ||||
\(591\) | −11.1943 | + | 32.1883i | −0.460473 | + | 1.32405i | ||||
\(592\) | 2.63234 | + | 4.55934i | 0.108188 | + | 0.187388i | ||||
\(593\) | 12.3939 | + | 21.4669i | 0.508956 | + | 0.881538i | 0.999946 | + | 0.0103731i | \(0.00330192\pi\) |
−0.490990 | + | 0.871165i | \(0.663365\pi\) | |||||||
\(594\) | −2.97673 | + | 5.71111i | −0.122137 | + | 0.234330i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.73752 | − | 3.31256i | −0.235018 | − | 0.135688i | ||||
\(597\) | −16.5417 | − | 19.1478i | −0.677006 | − | 0.783667i | ||||
\(598\) | 10.1077i | 0.413334i | ||||||||
\(599\) | − | 42.8086i | − | 1.74911i | −0.484926 | − | 0.874555i | \(-0.661153\pi\) | ||
0.484926 | − | 0.874555i | \(-0.338847\pi\) | |||||||
\(600\) | −7.92481 | + | 1.51512i | −0.323529 | + | 0.0618544i | ||||
\(601\) | 9.72891 | + | 5.61699i | 0.396851 | + | 0.229122i | 0.685124 | − | 0.728426i | \(-0.259748\pi\) |
−0.288274 | + | 0.957548i | \(0.593081\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.66265 | − | 5.27183i | −0.271324 | − | 0.214686i | ||||
\(604\) | −0.0942803 | − | 0.163298i | −0.00383621 | − | 0.00664451i | ||||
\(605\) | 14.7057 | + | 25.4710i | 0.597870 | + | 1.03554i | ||||
\(606\) | 11.6587 | − | 2.22898i | 0.473601 | − | 0.0905461i | ||||
\(607\) | −2.61469 | − | 1.50959i | −0.106127 | − | 0.0612724i | 0.445997 | − | 0.895034i | \(-0.352849\pi\) |
−0.552124 | + | 0.833762i | \(0.686182\pi\) | |||||||
\(608\) | −3.36488 | − | 5.82814i | −0.136464 | − | 0.236362i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14.5564 | + | 25.2125i | −0.589372 | + | 1.02082i | ||||
\(611\) | −1.31217 | + | 0.757581i | −0.0530847 | + | 0.0306485i | ||||
\(612\) | −4.37192 | + | 1.73513i | −0.176724 | + | 0.0701384i | ||||
\(613\) | −15.8207 | + | 27.4022i | −0.638990 | + | 1.10676i | 0.346664 | + | 0.937989i | \(0.387314\pi\) |
−0.985655 | + | 0.168774i | \(0.946019\pi\) | |||||||
\(614\) | −10.7290 | −0.432986 | ||||||||
\(615\) | 58.0141 | + | 20.1759i | 2.33935 | + | 0.813570i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.34373 | − | 4.23990i | 0.295647 | − | 0.170692i | −0.344839 | − | 0.938662i | \(-0.612066\pi\) |
0.640486 | + | 0.767970i | \(0.278733\pi\) | |||||||
\(618\) | −7.17926 | + | 6.20213i | −0.288792 | + | 0.249486i | ||||
\(619\) | 33.0186 | − | 19.0633i | 1.32713 | − | 0.766218i | 0.342274 | − | 0.939600i | \(-0.388803\pi\) |
0.984855 | + | 0.173382i | \(0.0554694\pi\) | |||||||
\(620\) | −26.7725 | − | 15.4571i | −1.07521 | − | 0.620772i | ||||
\(621\) | 0.394102 | + | 9.13354i | 0.0158148 | + | 0.366516i | ||||
\(622\) | − | 1.07969i | − | 0.0432916i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −9.77363 | + | 1.86859i | −0.391258 | + | 0.0748034i | ||||
\(625\) | 13.2960 | − | 23.0293i | 0.531838 | − | 0.921171i | ||||
\(626\) | 23.8521 | 0.953323 | ||||||||
\(627\) | −10.9326 | + | 9.44463i | −0.436607 | + | 0.377182i | ||||
\(628\) | − | 14.3413i | − | 0.572278i | ||||||
\(629\) | 8.25440 | 0.329124 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.1860 | −0.604547 | −0.302273 | − | 0.953221i | \(-0.597746\pi\) | ||||
−0.302273 | + | 0.953221i | \(0.597746\pi\) | |||||||
\(632\) | − | 16.3298i | − | 0.649566i | ||||||
\(633\) | −5.14517 | − | 26.9117i | −0.204502 | − | 1.06965i | ||||
\(634\) | 22.0867 | 0.877175 | ||||||||
\(635\) | 16.7674 | − | 29.0420i | 0.665394 | − | 1.15250i | ||||
\(636\) | 13.7016 | + | 15.8603i | 0.543304 | + | 0.628901i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.96497i | 0.196565i | ||||||||
\(639\) | 0.995028 | − | 1.25754i | 0.0393627 | − | 0.0497474i | ||||
\(640\) | 2.69141 | + | 1.55389i | 0.106387 | + | 0.0614228i | ||||
\(641\) | −25.0395 | + | 14.4566i | −0.989002 | + | 0.571001i | −0.904976 | − | 0.425463i | \(-0.860111\pi\) |
−0.0840262 | + | 0.996464i | \(0.526778\pi\) | |||||||
\(642\) | 5.47386 | + | 28.6310i | 0.216036 | + | 1.12998i | ||||
\(643\) | −26.4809 | + | 15.2888i | −1.04431 | + | 0.602930i | −0.921050 | − | 0.389445i | \(-0.872667\pi\) |
−0.123256 | + | 0.992375i | \(0.539334\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.80267 | − | 14.6593i | −0.110355 | − | 0.577210i | ||||
\(646\) | −10.5515 | −0.415142 | ||||||||
\(647\) | −13.6686 | + | 23.6747i | −0.537368 | + | 0.930749i | 0.461676 | + | 0.887048i | \(0.347248\pi\) |
−0.999045 | + | 0.0437008i | \(0.986085\pi\) | |||||||
\(648\) | −8.75882 | + | 2.06958i | −0.344079 | + | 0.0813006i | ||||
\(649\) | −11.5528 | + | 6.67002i | −0.453488 | + | 0.261821i | ||||
\(650\) | −13.3809 | + | 23.1764i | −0.524841 | + | 0.909052i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.92077 | − | 8.52302i | −0.192712 | − | 0.333787i | ||||
\(653\) | 0.875223 | + | 0.505310i | 0.0342501 | + | 0.0197743i | 0.517027 | − | 0.855969i | \(-0.327039\pi\) |
−0.482777 | + | 0.875743i | \(0.660372\pi\) | |||||||
\(654\) | −1.56353 | − | 1.80986i | −0.0611389 | − | 0.0707713i | ||||
\(655\) | 5.82205 | + | 10.0841i | 0.227486 | + | 0.394018i | ||||
\(656\) | −5.70540 | − | 9.88204i | −0.222758 | − | 0.385829i | ||||
\(657\) | −10.2923 | − | 25.9329i | −0.401539 | − | 1.01174i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.4827 | − | 15.8671i | −1.07057 | − | 0.618096i | −0.142236 | − | 0.989833i | \(-0.545429\pi\) |
−0.928338 | + | 0.371737i | \(0.878762\pi\) | |||||||
\(660\) | 2.19150 | − | 6.30149i | 0.0853041 | − | 0.245285i | ||||
\(661\) | − | 3.85538i | − | 0.149957i | −0.997185 | − | 0.0749784i | \(-0.976111\pi\) | ||
0.997185 | − | 0.0749784i | \(-0.0238888\pi\) | |||||||
\(662\) | − | 14.3102i | − | 0.556183i | ||||||
\(663\) | −5.12474 | + | 14.7358i | −0.199029 | + | 0.572290i | ||||
\(664\) | −8.34895 | − | 4.82027i | −0.324002 | − | 0.187063i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 15.6265 | + | 2.29438i | 0.605513 | + | 0.0889054i | ||||
\(667\) | 3.52389 | + | 6.10355i | 0.136445 | + | 0.236330i | ||||
\(668\) | −0.261517 | − | 0.452961i | −0.0101184 | − | 0.0175256i | ||||
\(669\) | −1.43543 | − | 1.66158i | −0.0554971 | − | 0.0642405i | ||||
\(670\) | 7.62214 | + | 4.40064i | 0.294469 | + | 0.170012i | ||||
\(671\) | −5.80538 | − | 10.0552i | −0.224114 | − | 0.388177i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.0025 | − | 32.9132i | 0.732491 | − | 1.26871i | −0.223324 | − | 0.974744i | \(-0.571691\pi\) |
0.955815 | − | 0.293968i | \(-0.0949760\pi\) | |||||||
\(674\) | −17.4430 | + | 10.0707i | −0.671880 | + | 0.387910i | ||||
\(675\) | −11.1876 | + | 21.4644i | −0.430611 | + | 0.826166i | ||||
\(676\) | −10.0026 | + | 17.3250i | −0.384714 | + | 0.666345i | ||||
\(677\) | 15.4397 | 0.593397 | 0.296698 | − | 0.954971i | \(-0.404114\pi\) | ||||
0.296698 | + | 0.954971i | \(0.404114\pi\) | |||||||
\(678\) | 4.11506 | + | 21.5238i | 0.158038 | + | 0.826617i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.21982 | − | 2.43632i | 0.161823 | − | 0.0934285i | ||||
\(681\) | 5.56459 | + | 29.1056i | 0.213236 | + | 1.11533i | ||||
\(682\) | 10.6774 | − | 6.16458i | 0.408858 | − | 0.236054i | ||||
\(683\) | 14.3519 | + | 8.28608i | 0.549161 | + | 0.317058i | 0.748784 | − | 0.662815i | \(-0.230638\pi\) |
−0.199623 | + | 0.979873i | \(0.563972\pi\) | |||||||
\(684\) | −19.9751 | − | 2.93287i | −0.763767 | − | 0.112141i | ||||
\(685\) | 3.54522i | 0.135456i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.4776 | + | 14.4434i | 0.476051 | + | 0.551051i | ||||
\(688\) | −1.38634 | + | 2.40121i | −0.0528537 | + | 0.0915453i | ||||
\(689\) | 69.5188 | 2.64845 | ||||||||
\(690\) | −1.77842 | − | 9.30198i | −0.0677031 | − | 0.354121i | ||||
\(691\) | 9.17558i | 0.349056i | 0.984652 | + | 0.174528i | \(0.0558399\pi\) | ||||
−0.984652 | + | 0.174528i | \(0.944160\pi\) | |||||||
\(692\) | 3.73085 | 0.141826 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13.4117 | 0.509100 | ||||||||
\(695\) | − | 34.7911i | − | 1.31970i | ||||||
\(696\) | −5.25037 | + | 4.53577i | −0.199015 | + | 0.171928i | ||||
\(697\) | −17.8908 | −0.677663 | ||||||||
\(698\) | −9.46958 | + | 16.4018i | −0.358429 | + | 0.620817i | ||||
\(699\) | 39.0594 | − | 7.46763i | 1.47736 | − | 0.282452i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 16.6900i | − | 0.630371i | −0.949030 | − | 0.315185i | \(-0.897933\pi\) | ||
0.949030 | − | 0.315185i | \(-0.102067\pi\) | |||||||
\(702\) | −13.7976 | + | 26.4720i | −0.520758 | + | 0.999120i | ||||
\(703\) | 30.6832 | + | 17.7150i | 1.15724 | + | 0.668133i | ||||
\(704\) | −1.07339 | + | 0.619720i | −0.0404548 | + | 0.0233566i | ||||
\(705\) | 1.07428 | − | 0.928065i | 0.0404597 | − | 0.0349529i | ||||
\(706\) | 21.8147 | − | 12.5947i | 0.821006 | − | 0.474008i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −17.6076 | − | 6.12349i | −0.661733 | − | 0.230135i | ||||
\(709\) | 41.8842 | 1.57299 | 0.786497 | − | 0.617594i | \(-0.211893\pi\) | ||||
0.786497 | + | 0.617594i | \(0.211893\pi\) | |||||||
\(710\) | −0.830596 | + | 1.43863i | −0.0311717 | + | 0.0539910i | ||||
\(711\) | −38.4178 | − | 30.3981i | −1.44078 | − | 1.14002i | ||||
\(712\) | −5.30732 | + | 3.06418i | −0.198900 | + | 0.114835i | ||||
\(713\) | 8.75063 | − | 15.1565i | 0.327714 | − | 0.567617i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.0646 | − | 19.1645i | −0.413793 | − | 0.716710i | ||||
\(716\) | 6.53507 | + | 3.77303i | 0.244227 | + | 0.141005i | ||||
\(717\) | 18.9293 | − | 3.61903i | 0.706929 | − | 0.135155i | ||||
\(718\) | −3.65554 | − | 6.33158i | −0.136424 | − | 0.236292i | ||||
\(719\) | −22.4982 | − | 38.9680i | −0.839042 | − | 1.45326i | −0.890697 | − | 0.454598i | \(-0.849783\pi\) |
0.0516552 | − | 0.998665i | \(-0.483550\pi\) | |||||||
\(720\) | 8.66578 | − | 3.43928i | 0.322955 | − | 0.128174i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −22.7674 | − | 13.1448i | −0.847316 | − | 0.489198i | ||||
\(723\) | −0.756058 | + | 0.144548i | −0.0281181 | + | 0.00537580i | ||||
\(724\) | − | 16.6098i | − | 0.617299i | ||||||
\(725\) | 18.6601i | 0.693020i | ||||||||
\(726\) | −10.7158 | − | 12.4041i | −0.397701 | − | 0.460358i | ||||
\(727\) | 14.5491 | + | 8.39992i | 0.539596 | + | 0.311536i | 0.744915 | − | 0.667159i | \(-0.232490\pi\) |
−0.205319 | + | 0.978695i | \(0.565823\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11.4357 | + | 24.4586i | −0.423544 | + | 0.905875i | ||||
\(730\) | 14.4515 | + | 25.0307i | 0.534874 | + | 0.926429i | ||||
\(731\) | 2.17362 | + | 3.76482i | 0.0803943 | + | 0.139247i | ||||
\(732\) | 5.32969 | − | 15.3251i | 0.196991 | − | 0.566432i | ||||
\(733\) | 36.7850 | + | 21.2378i | 1.35868 | + | 0.784436i | 0.989446 | − | 0.144899i | \(-0.0462857\pi\) |
0.369237 | + | 0.929335i | \(0.379619\pi\) | |||||||
\(734\) | −13.0886 | − | 22.6702i | −0.483110 | − | 0.836771i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.879693 | + | 1.52367i | −0.0324259 | + | 0.0561633i | ||||
\(737\) | −3.03986 | + | 1.75506i | −0.111975 | + | 0.0646485i | ||||
\(738\) | −33.8693 | − | 4.97291i | −1.24675 | − | 0.183055i | ||||
\(739\) | −6.22722 | + | 10.7859i | −0.229072 | + | 0.396764i | −0.957533 | − | 0.288323i | \(-0.906902\pi\) |
0.728461 | + | 0.685087i | \(0.240236\pi\) | |||||||
\(740\) | −16.3614 | −0.601457 | ||||||||
\(741\) | −50.6745 | + | 43.7774i | −1.86157 | + | 1.60820i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.5057 | − | 13.5710i | 0.862339 | − | 0.497872i | −0.00245578 | − | 0.999997i | \(-0.500782\pi\) |
0.864795 | + | 0.502125i | \(0.167448\pi\) | |||||||
\(744\) | 16.2733 | + | 5.65946i | 0.596609 | + | 0.207486i | ||||
\(745\) | 17.8309 | − | 10.2947i | 0.653274 | − | 0.377168i | ||||
\(746\) | 18.2578 | + | 10.5412i | 0.668467 | + | 0.385940i | ||||
\(747\) | −26.8819 | + | 10.6689i | −0.983556 | + | 0.390354i | ||||
\(748\) | 1.94330i | 0.0710541i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.604240 | + | 1.73744i | −0.0220637 | + | 0.0634425i | ||||
\(751\) | 7.09292 | − | 12.2853i | 0.258824 | − | 0.448297i | −0.707103 | − | 0.707111i | \(-0.749998\pi\) |
0.965927 | + | 0.258814i | \(0.0833316\pi\) | |||||||
\(752\) | −0.263735 | −0.00961744 | ||||||||
\(753\) | 31.0123 | + | 10.7853i | 1.13015 | + | 0.393039i | ||||
\(754\) | 23.0134i | 0.838100i | ||||||||
\(755\) | 0.586004 | 0.0213269 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.83604 | 0.357497 | 0.178748 | − | 0.983895i | \(-0.442795\pi\) | ||||
0.178748 | + | 0.983895i | \(0.442795\pi\) | |||||||
\(758\) | 5.68371i | 0.206442i | ||||||||
\(759\) | 3.56742 | + | 1.24066i | 0.129489 | + | 0.0450332i | ||||
\(760\) | 20.9146 | 0.758651 | ||||||||
\(761\) | −24.4276 | + | 42.3098i | −0.885499 | + | 1.53373i | −0.0403574 | + | 0.999185i | \(0.512850\pi\) |
−0.845141 | + | 0.534543i | \(0.820484\pi\) | |||||||
\(762\) | −6.13922 | + | 17.6528i | −0.222401 | + | 0.639494i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 5.64208i | 0.204123i | ||||||||
\(765\) | 2.12353 | − | 14.4628i | 0.0767763 | − | 0.522905i | ||||
\(766\) | −0.105332 | − | 0.0608136i | −0.00380581 | − | 0.00219728i | ||||
\(767\) | −53.5492 | + | 30.9167i | −1.93355 | + | 1.11634i | ||||
\(768\) | −1.63594 | − | 0.568941i | −0.0590320 | − | 0.0205299i | ||||
\(769\) | 12.4959 | − | 7.21451i | 0.450614 | − | 0.260162i | −0.257476 | − | 0.966285i | \(-0.582891\pi\) |
0.708089 | + | 0.706123i | \(0.249557\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.7044 | + | 19.6142i | −0.817678 | + | 0.706388i | ||||
\(772\) | −9.42027 | −0.339043 | ||||||||
\(773\) | −14.1371 | + | 24.4861i | −0.508475 | + | 0.880705i | 0.491477 | + | 0.870891i | \(0.336457\pi\) |
−0.999952 | + | 0.00981408i | \(0.996876\pi\) | |||||||
\(774\) | 3.06844 | + | 7.73139i | 0.110293 | + | 0.277899i | ||||
\(775\) | 40.1294 | − | 23.1687i | 1.44149 | − | 0.832245i | ||||
\(776\) | −0.750184 | + | 1.29936i | −0.0269300 | + | 0.0466442i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.7545 | + | 23.8235i | 0.493123 | + | 0.854113i | ||||
\(779\) | −66.5037 | − | 38.3959i | −2.38274 | − | 1.37568i | ||||
\(780\) | 10.1580 | − | 29.2084i | 0.363714 | − | 1.04583i | ||||
\(781\) | −0.331258 | − | 0.573755i | −0.0118533 | − | 0.0205306i | ||||
\(782\) | 1.37926 | + | 2.38894i | 0.0493222 | + | 0.0854285i | ||||
\(783\) | 0.897302 | + | 20.7955i | 0.0320670 | + | 0.743170i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 38.5982 | + | 22.2847i | 1.37763 | + | 0.795375i | ||||
\(786\) | −4.24245 | − | 4.91084i | −0.151323 | − | 0.175164i | ||||
\(787\) | 24.7123i | 0.880898i | 0.897778 | + | 0.440449i | \(0.145181\pi\) | ||||
−0.897778 | + | 0.440449i | \(0.854819\pi\) | |||||||
\(788\) | 19.6757i | 0.700918i | ||||||||
\(789\) | −4.78774 | + | 0.915351i | −0.170448 | + | 0.0325874i | ||||
\(790\) | 43.9503 | + | 25.3747i | 1.56368 | + | 0.902792i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.540156 | + | 3.67888i | −0.0191936 | + | 0.130723i | ||||
\(793\) | −26.9089 | − | 46.6076i | −0.955563 | − | 1.65508i | ||||
\(794\) | −6.22766 | − | 10.7866i | −0.221011 | − | 0.382803i | ||||
\(795\) | −63.9773 | + | 12.2316i | −2.26904 | + | 0.433810i | ||||
\(796\) | −12.6517 | − | 7.30448i | −0.448429 | − | 0.258901i | ||||
\(797\) | 14.3076 | + | 24.7815i | 0.506802 | + | 0.877807i | 0.999969 | + | 0.00787254i | \(0.00250593\pi\) |
−0.493167 | + | 0.869935i | \(0.664161\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.206753 | + | 0.358107i | −0.00731441 | + | 0.0126689i | ||||
\(800\) | −4.03417 | + | 2.32913i | −0.142630 | + | 0.0823472i | ||||
\(801\) | −2.67078 | + | 18.1901i | −0.0943674 | + | 0.642714i | ||||
\(802\) | 13.8734 | − | 24.0294i | 0.489885 | − | 0.848506i | ||||
\(803\) | −11.5271 | −0.406781 | ||||||||
\(804\) | −4.63303 | − | 1.61125i | −0.163394 | − | 0.0568245i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 49.4914 | − | 28.5739i | 1.74326 | − | 1.00647i | ||||
\(807\) | −33.1748 | + | 28.6596i | −1.16781 | + | 1.00886i | ||||
\(808\) | 5.93491 | − | 3.42652i | 0.208790 | − | 0.120545i | ||||
\(809\) | 33.7618 | + | 19.4924i | 1.18700 | + | 0.685317i | 0.957624 | − | 0.288020i | \(-0.0929971\pi\) |
0.229379 | + | 0.973337i | \(0.426330\pi\) | |||||||
\(810\) | 8.04013 | − | 26.7895i | 0.282502 | − | 0.941286i | ||||
\(811\) | 1.94541i | 0.0683126i | 0.999417 | + | 0.0341563i | \(0.0108744\pi\) | ||||
−0.999417 | + | 0.0341563i | \(0.989126\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 47.6651 | − | 9.11292i | 1.67169 | − | 0.319604i | ||||
\(814\) | 3.26262 | − | 5.65103i | 0.114355 | − | 0.198068i | ||||
\(815\) | 30.5853 | 1.07136 | ||||||||
\(816\) | −2.05501 | + | 1.77531i | −0.0719397 | + | 0.0621483i | ||||
\(817\) | 18.6594i | 0.652811i | ||||||||
\(818\) | −11.2300 | −0.392647 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 35.4622 | 1.23839 | ||||||||
\(821\) | 18.7810i | 0.655461i | 0.944771 | + | 0.327730i | \(0.106284\pi\) | ||||
−0.944771 | + | 0.327730i | \(0.893716\pi\) | |||||||
\(822\) | −0.371037 | − | 1.94070i | −0.0129414 | − | 0.0676898i | ||||
\(823\) | 16.0214 | 0.558471 | 0.279235 | − | 0.960223i | \(-0.409919\pi\) | ||||
0.279235 | + | 0.960223i | \(0.409919\pi\) | |||||||
\(824\) | −2.73874 | + | 4.74363i | −0.0954084 | + | 0.165252i | ||||
\(825\) | 6.53747 | + | 7.56744i | 0.227606 | + | 0.263464i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.59187i | 0.229222i | 0.993410 | + | 0.114611i | \(0.0365621\pi\) | ||||
−0.993410 | + | 0.114611i | \(0.963438\pi\) | |||||||
\(828\) | 1.94706 | + | 4.90591i | 0.0676649 | + | 0.170492i | ||||
\(829\) | 4.17189 | + | 2.40864i | 0.144896 | + | 0.0836556i | 0.570695 | − | 0.821162i | \(-0.306674\pi\) |
−0.425800 | + | 0.904818i | \(0.640007\pi\) | |||||||
\(830\) | 25.9467 | − | 14.9803i | 0.900622 | − | 0.519974i | ||||
\(831\) | 1.20991 | + | 6.32842i | 0.0419713 | + | 0.219530i | ||||
\(832\) | −4.97533 | + | 2.87251i | −0.172488 | + | 0.0995862i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 3.64118 | + | 19.0451i | 0.126084 | + | 0.659479i | ||||
\(835\) | 1.62547 | 0.0562518 | ||||||||
\(836\) | −4.17056 | + | 7.22363i | −0.144242 | + | 0.249834i | ||||
\(837\) | 43.6074 | − | 27.7497i | 1.50729 | − | 0.959169i | ||||
\(838\) | 2.91134 | − | 1.68086i | 0.100570 | − | 0.0580644i | ||||
\(839\) | −22.1980 | + | 38.4480i | −0.766360 | + | 1.32737i | 0.173165 | + | 0.984893i | \(0.444601\pi\) |
−0.939525 | + | 0.342481i | \(0.888733\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.47673 | − | 11.2180i | −0.223335 | − | 0.386828i | ||||
\(842\) | 5.35125 | + | 3.08955i | 0.184416 | + | 0.106473i | ||||
\(843\) | −8.37620 | − | 9.69586i | −0.288492 | − | 0.333943i | ||||
\(844\) | −7.90946 | − | 13.6996i | −0.272255 | − | 0.471559i | ||||
\(845\) | −31.0857 | − | 53.8421i | −1.06938 | − | 1.85222i | ||||
\(846\) | −0.490946 | + | 0.620467i | −0.0168791 | + | 0.0213321i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 10.4795 | + | 6.05036i | 0.359869 | + | 0.207770i | ||||
\(849\) | 7.69730 | − | 22.1329i | 0.264171 | − | 0.759601i | ||||
\(850\) | 7.30362i | 0.250512i | ||||||||
\(851\) | − | 9.26259i | − | 0.317517i | ||||||
\(852\) | 0.304115 | − | 0.874457i | 0.0104188 | − | 0.0299584i | ||||
\(853\) | −9.69461 | − | 5.59718i | −0.331937 | − | 0.191644i | 0.324764 | − | 0.945795i | \(-0.394715\pi\) |
−0.656701 | + | 0.754151i | \(0.728049\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 38.9326 | − | 49.2039i | 1.33147 | − | 1.68274i | ||||
\(856\) | 8.41476 | + | 14.5748i | 0.287610 | + | 0.498156i | ||||
\(857\) | −0.915956 | − | 1.58648i | −0.0312885 | − | 0.0541932i | 0.849957 | − | 0.526852i | \(-0.176628\pi\) |
−0.881246 | + | 0.472659i | \(0.843294\pi\) | |||||||
\(858\) | 8.06263 | + | 9.33288i | 0.275254 | + | 0.318619i | ||||
\(859\) | 34.4844 | + | 19.9096i | 1.17659 | + | 0.679306i | 0.955224 | − | 0.295884i | \(-0.0956141\pi\) |
0.221369 | + | 0.975190i | \(0.428947\pi\) | |||||||
\(860\) | −4.30843 | − | 7.46242i | −0.146916 | − | 0.254466i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.65482 | − | 11.5265i | 0.226664 | − | 0.392594i | ||||
\(863\) | −30.3578 | + | 17.5271i | −1.03339 | + | 0.596629i | −0.917954 | − | 0.396686i | \(-0.870160\pi\) |
−0.115437 | + | 0.993315i | \(0.536827\pi\) | |||||||
\(864\) | −4.38382 | + | 2.78965i | −0.149140 | + | 0.0949058i | ||||
\(865\) | −5.79732 | + | 10.0412i | −0.197115 | + | 0.341413i | ||||
\(866\) | 25.7161 | 0.873869 | ||||||||
\(867\) | −4.72976 | − | 24.7389i | −0.160631 | − | 0.840179i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.5282 | + | 10.1199i | −0.594604 | + | 0.343295i | ||||
\(870\) | −4.04914 | − | 21.1790i | −0.137279 | − | 0.718035i | ||||
\(871\) | −14.0902 | + | 8.13500i | −0.477429 | + | 0.275644i | ||||
\(872\) | −1.19585 | − | 0.690425i | −0.0404966 | − | 0.0233807i | ||||
\(873\) | 1.66041 | + | 4.18366i | 0.0561964 | + | 0.141595i | ||||
\(874\) | 11.8402i | 0.400502i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.5306 | − | 12.1897i | −0.355796 | − | 0.411851i | ||||
\(877\) | 15.6443 | − | 27.0967i | 0.528270 | − | 0.914990i | −0.471187 | − | 0.882033i | \(-0.656174\pi\) |
0.999457 | − | 0.0329569i | \(-0.0104924\pi\) | |||||||
\(878\) | −37.0419 | −1.25010 | ||||||||
\(879\) | −1.63129 | − | 8.53243i | −0.0550219 | − | 0.287792i | ||||
\(880\) | − | 3.85190i | − | 0.129848i | ||||||
\(881\) | −17.8567 | −0.601609 | −0.300805 | − | 0.953686i | \(-0.597255\pi\) | ||||
−0.300805 | + | 0.953686i | \(0.597255\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 52.2623 | 1.75877 | 0.879383 | − | 0.476115i | \(-0.157955\pi\) | ||||
0.879383 | + | 0.476115i | \(0.157955\pi\) | |||||||
\(884\) | 9.00752i | 0.302956i | ||||||||
\(885\) | 43.8410 | − | 37.8740i | 1.47370 | − | 1.27312i | ||||
\(886\) | 22.9752 | 0.771867 | ||||||||
\(887\) | 25.6962 | − | 44.5072i | 0.862796 | − | 1.49441i | −0.00642400 | − | 0.999979i | \(-0.502045\pi\) |
0.869220 | − | 0.494426i | \(-0.164622\pi\) | |||||||
\(888\) | 8.95646 | − | 1.71235i | 0.300559 | − | 0.0574629i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 19.0456i | − | 0.638409i | ||||||
\(891\) | 7.64947 | + | 8.11904i | 0.256267 | + | 0.271998i | ||||
\(892\) | −1.09788 | − | 0.633859i | −0.0367596 | − | 0.0212232i | ||||
\(893\) | −1.53709 | + | 0.887437i | −0.0514366 | + | 0.0296970i | ||||
\(894\) | −8.68347 | + | 7.50160i | −0.290419 | + | 0.250891i | ||||
\(895\) | −20.3095 | + | 11.7257i | −0.678873 | + | 0.391947i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.5356 | + | 5.75068i | 0.552107 | + | 0.192010i | ||||
\(898\) | 0.217897 | 0.00727131 | ||||||||
\(899\) | 19.9237 | − | 34.5088i | 0.664491 | − | 1.15093i | ||||
\(900\) | −2.03010 | + | 13.8265i | −0.0676701 | + | 0.460885i | ||||
\(901\) | 16.4307 | − | 9.48627i | 0.547386 | − | 0.316034i | ||||
\(902\) | −7.07150 | + | 12.2482i | −0.235455 | + | 0.407820i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.32593 | + | 10.9568i | 0.210397 | + | 0.364419i | ||||
\(905\) | 44.7038 | + | 25.8098i | 1.48601 | + | 0.857946i | ||||
\(906\) | −0.320786 | + | 0.0613301i | −0.0106574 | + | 0.00203756i | ||||
\(907\) | 15.4685 | + | 26.7922i | 0.513624 | + | 0.889622i | 0.999875 | + | 0.0158032i | \(0.00503052\pi\) |
−0.486252 | + | 0.873819i | \(0.661636\pi\) | |||||||
\(908\) | 8.55423 | + | 14.8164i | 0.283882 | + | 0.491698i | ||||
\(909\) | 2.98661 | − | 20.3411i | 0.0990594 | − | 0.674670i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.92291 | − | 1.68755i | −0.0968405 | − | 0.0559109i | 0.450798 | − | 0.892626i | \(-0.351140\pi\) |
−0.547638 | + | 0.836715i | \(0.684473\pi\) | |||||||
\(912\) | −11.4489 | + | 2.18888i | −0.379111 | + | 0.0724810i | ||||
\(913\) | 11.9489i | 0.395450i | ||||||||
\(914\) | 0.930228i | 0.0307692i | ||||||||
\(915\) | 32.9644 | + | 38.1579i | 1.08977 | + | 1.26146i | ||||
\(916\) | 9.54337 | + | 5.50987i | 0.315322 | + | 0.182051i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.351206 | + | 8.13940i | 0.0115915 | + | 0.268640i | ||||
\(919\) | 20.4737 | + | 35.4615i | 0.675366 | + | 1.16977i | 0.976362 | + | 0.216143i | \(0.0693477\pi\) |
−0.300996 | + | 0.953625i | \(0.597319\pi\) | |||||||
\(920\) | −2.73389 | − | 4.73523i | −0.0901336 | − | 0.156116i | ||||
\(921\) | −6.10414 | + | 17.5520i | −0.201138 | + | 0.578357i | ||||
\(922\) | −27.1820 | − | 15.6935i | −0.895191 | − | 0.516839i | ||||
\(923\) | −1.53543 | − | 2.65945i | −0.0505394 | − | 0.0875369i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.2621 | − | 21.2386i | 0.403176 | − | 0.698321i | ||||
\(926\) | 17.8816 | − | 10.3239i | 0.587626 | − | 0.339266i | ||||
\(927\) | 6.06175 | + | 15.2735i | 0.199094 | + | 0.501647i | ||||
\(928\) | −2.00291 | + | 3.46914i | −0.0657486 | + | 0.113880i | ||||
\(929\) | −3.10096 | −0.101739 | −0.0508696 | − | 0.998705i | \(-0.516199\pi\) | ||||
−0.0508696 | + | 0.998705i | \(0.516199\pi\) | |||||||
\(930\) | −40.5188 | + | 35.0040i | −1.32867 | + | 1.14783i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 19.8834 | − | 11.4797i | 0.651303 | − | 0.376030i | ||||
\(933\) | −1.76631 | − | 0.614279i | −0.0578264 | − | 0.0201106i | ||||
\(934\) | 9.13539 | − | 5.27432i | 0.298919 | − | 0.172581i | ||||
\(935\) | −5.23022 | − | 3.01967i | −0.171046 | − | 0.0987537i | ||||
\(936\) | −2.50372 | + | 17.0522i | −0.0818365 | + | 0.557369i | ||||
\(937\) | − | 50.5048i | − | 1.64992i | −0.565190 | − | 0.824960i | \(-0.691197\pi\) | ||
0.565190 | − | 0.824960i | \(-0.308803\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.5704 | − | 39.0207i | 0.442855 | − | 1.27339i | ||||
\(940\) | 0.409815 | − | 0.709821i | 0.0133667 | − | 0.0231518i | ||||
\(941\) | −2.65547 | −0.0865659 | −0.0432830 | − | 0.999063i | \(-0.513782\pi\) | ||||
−0.0432830 | + | 0.999063i | \(0.513782\pi\) | |||||||
\(942\) | −23.4615 | − | 8.15932i | −0.764416 | − | 0.265845i | ||||
\(943\) | 20.0760i | 0.653765i | ||||||||
\(944\) | −10.7630 | −0.350305 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.43657 | 0.111732 | ||||||||
\(947\) | − | 46.6605i | − | 1.51626i | −0.652103 | − | 0.758131i | \(-0.726113\pi\) | ||
0.652103 | − | 0.758131i | \(-0.273887\pi\) | |||||||
\(948\) | −26.7147 | − | 9.29071i | −0.867652 | − | 0.301748i | ||||
\(949\) | −53.4299 | −1.73441 | ||||||||
\(950\) | −15.6745 | + | 27.1490i | −0.508547 | + | 0.880830i | ||||
\(951\) | 12.5660 | − | 36.1326i | 0.407481 | − | 1.17168i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.0100i | 1.23127i | 0.788033 | + | 0.615633i | \(0.211100\pi\) | ||||
−0.788033 | + | 0.615633i | \(0.788900\pi\) | |||||||
\(954\) | 33.7419 | − | 13.3915i | 1.09243 | − | 0.433565i | ||||
\(955\) | −15.1852 | − | 8.76715i | −0.491380 | − | 0.283698i | ||||
\(956\) | 9.63609 | − | 5.56340i | 0.311653 | − | 0.179933i | ||||
\(957\) | 8.12240 | + | 2.82477i | 0.262560 | + | 0.0913119i | ||||
\(958\) | −15.9881 | + | 9.23071i | −0.516551 | + | 0.298231i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 4.07332 | − | 3.51892i | 0.131466 | − | 0.113573i | ||||
\(961\) | −67.9501 | −2.19194 | ||||||||
\(962\) | 15.1228 | − | 26.1934i | 0.487578 | − | 0.844511i | ||||
\(963\) | 49.9530 | + | 7.33442i | 1.60971 | + | 0.236348i | ||||
\(964\) | −0.384876 | + | 0.222208i | −0.0123960 | + | 0.00715684i | ||||
\(965\) | 14.6380 | − | 25.3538i | 0.471215 | − | 0.816168i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.3800 | − | 21.4428i | −0.398115 | − | 0.689555i | 0.595379 | − | 0.803445i | \(-0.297002\pi\) |
−0.993493 | + | 0.113891i | \(0.963669\pi\) | |||||||
\(968\) | −8.19588 | − | 4.73189i | −0.263426 | − | 0.152089i | ||||
\(969\) | −6.00317 | + | 17.2616i | −0.192850 | + | 0.554523i | ||||
\(970\) | −2.33140 | − | 4.03811i | −0.0748568 | − | 0.129656i | ||||
\(971\) | 28.8119 | + | 49.9037i | 0.924619 | + | 1.60149i | 0.792173 | + | 0.610296i | \(0.208950\pi\) |
0.132445 | + | 0.991190i | \(0.457717\pi\) | |||||||
\(972\) | −1.59754 | + | 15.5064i | −0.0512412 | + | 0.497367i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −33.1747 | − | 19.1534i | −1.06299 | − | 0.613715i | ||||
\(975\) | 30.3023 | + | 35.0763i | 0.970449 | + | 1.12334i | ||||
\(976\) | − | 9.36774i | − | 0.299854i | ||||||
\(977\) | 32.6571i | 1.04479i | 0.852703 | + | 0.522396i | \(0.174962\pi\) | ||||
−0.852703 | + | 0.522396i | \(0.825038\pi\) | |||||||
\(978\) | −16.7428 | + | 3.20100i | −0.535376 | + | 0.102357i | ||||
\(979\) | 6.57810 | + | 3.79787i | 0.210237 | + | 0.121380i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.85039 | + | 1.52814i | −0.122933 | + | 0.0487899i | ||||
\(982\) | −5.38551 | − | 9.32798i | −0.171859 | − | 0.297668i | ||||
\(983\) | −5.43038 | − | 9.40569i | −0.173202 | − | 0.299995i | 0.766335 | − | 0.642441i | \(-0.222078\pi\) |
−0.939538 | + | 0.342446i | \(0.888745\pi\) | |||||||
\(984\) | −19.4125 | + | 3.71141i | −0.618847 | + | 0.118315i | ||||
\(985\) | −52.9554 | − | 30.5738i | −1.68730 | − | 0.974163i | ||||
\(986\) | 3.14033 | + | 5.43921i | 0.100008 | + | 0.173220i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −19.3313 | + | 33.4827i | −0.615009 | + | 1.06523i | ||||
\(989\) | 4.22465 | − | 2.43911i | 0.134336 | − | 0.0775590i | ||||
\(990\) | −9.06203 | − | 7.17034i | −0.288010 | − | 0.227888i | ||||
\(991\) | −23.6511 | + | 40.9649i | −0.751302 | + | 1.30129i | 0.195890 | + | 0.980626i | \(0.437240\pi\) |
−0.947192 | + | 0.320667i | \(0.896093\pi\) | |||||||
\(992\) | 9.94737 | 0.315829 | ||||||||
\(993\) | −23.4107 | − | 8.14167i | −0.742916 | − | 0.258368i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 39.3187 | − | 22.7007i | 1.24649 | − | 0.719660i | ||||
\(996\) | −12.6357 | + | 10.9160i | −0.400379 | + | 0.345885i | ||||
\(997\) | −50.5561 | + | 29.1886i | −1.60113 | + | 0.924411i | −0.609865 | + | 0.792505i | \(0.708776\pi\) |
−0.991262 | + | 0.131906i | \(0.957890\pi\) | |||||||
\(998\) | −10.5880 | − | 6.11298i | −0.335157 | − | 0.193503i | ||||
\(999\) | 12.6440 | − | 24.2586i | 0.400039 | − | 0.767509i |
(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 | 882.2.l.c.227.2 | 48 | ||
3.2 | odd | 2 | 2646.2.l.c.521.19 | 48 | |||
7.2 | even | 3 | 882.2.t.c.803.8 | 48 | |||
7.3 | odd | 6 | 882.2.m.c.587.17 | yes | 48 | ||
7.4 | even | 3 | 882.2.m.c.587.20 | yes | 48 | ||
7.5 | odd | 6 | 882.2.t.c.803.5 | 48 | |||
7.6 | odd | 2 | inner | 882.2.l.c.227.11 | 48 | ||
9.4 | even | 3 | 2646.2.t.c.2285.23 | 48 | |||
9.5 | odd | 6 | 882.2.t.c.815.5 | 48 | |||
21.2 | odd | 6 | 2646.2.t.c.1979.24 | 48 | |||
21.5 | even | 6 | 2646.2.t.c.1979.23 | 48 | |||
21.11 | odd | 6 | 2646.2.m.c.1763.5 | 48 | |||
21.17 | even | 6 | 2646.2.m.c.1763.6 | 48 | |||
21.20 | even | 2 | 2646.2.l.c.521.20 | 48 | |||
63.4 | even | 3 | 2646.2.m.c.881.6 | 48 | |||
63.5 | even | 6 | inner | 882.2.l.c.509.14 | 48 | ||
63.13 | odd | 6 | 2646.2.t.c.2285.24 | 48 | |||
63.23 | odd | 6 | inner | 882.2.l.c.509.23 | 48 | ||
63.31 | odd | 6 | 2646.2.m.c.881.5 | 48 | |||
63.32 | odd | 6 | 882.2.m.c.293.17 | ✓ | 48 | ||
63.40 | odd | 6 | 2646.2.l.c.1097.19 | 48 | |||
63.41 | even | 6 | 882.2.t.c.815.8 | 48 | |||
63.58 | even | 3 | 2646.2.l.c.1097.20 | 48 | |||
63.59 | even | 6 | 882.2.m.c.293.20 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
882.2.l.c.227.2 | 48 | 1.1 | even | 1 | trivial | ||
882.2.l.c.227.11 | 48 | 7.6 | odd | 2 | inner | ||
882.2.l.c.509.14 | 48 | 63.5 | even | 6 | inner | ||
882.2.l.c.509.23 | 48 | 63.23 | odd | 6 | inner | ||
882.2.m.c.293.17 | ✓ | 48 | 63.32 | odd | 6 | ||
882.2.m.c.293.20 | yes | 48 | 63.59 | even | 6 | ||
882.2.m.c.587.17 | yes | 48 | 7.3 | odd | 6 | ||
882.2.m.c.587.20 | yes | 48 | 7.4 | even | 3 | ||
882.2.t.c.803.5 | 48 | 7.5 | odd | 6 | |||
882.2.t.c.803.8 | 48 | 7.2 | even | 3 | |||
882.2.t.c.815.5 | 48 | 9.5 | odd | 6 | |||
882.2.t.c.815.8 | 48 | 63.41 | even | 6 | |||
2646.2.l.c.521.19 | 48 | 3.2 | odd | 2 | |||
2646.2.l.c.521.20 | 48 | 21.20 | even | 2 | |||
2646.2.l.c.1097.19 | 48 | 63.40 | odd | 6 | |||
2646.2.l.c.1097.20 | 48 | 63.58 | even | 3 | |||
2646.2.m.c.881.5 | 48 | 63.31 | odd | 6 | |||
2646.2.m.c.881.6 | 48 | 63.4 | even | 3 | |||
2646.2.m.c.1763.5 | 48 | 21.11 | odd | 6 | |||
2646.2.m.c.1763.6 | 48 | 21.17 | even | 6 | |||
2646.2.t.c.1979.23 | 48 | 21.5 | even | 6 | |||
2646.2.t.c.1979.24 | 48 | 21.2 | odd | 6 | |||
2646.2.t.c.2285.23 | 48 | 9.4 | even | 3 | |||
2646.2.t.c.2285.24 | 48 | 63.13 | odd | 6 |