Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(131,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.131");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.z (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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 131.13 | ||
Character | \(\chi\) | \(=\) | 546.131 |
Dual form | 546.2.z.a.521.13 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | 0.305007 | − | 1.70498i | 0.176096 | − | 0.984373i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 1.04730 | − | 1.81398i | 0.468367 | − | 0.811236i | −0.530979 | − | 0.847385i | \(-0.678176\pi\) |
0.999346 | + | 0.0361491i | \(0.0115091\pi\) | |||||||
\(6\) | 1.11664 | − | 1.32406i | 0.455865 | − | 0.540544i | ||||
\(7\) | 1.84957 | − | 1.89185i | 0.699072 | − | 0.715052i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −2.81394 | − | 1.04007i | −0.937980 | − | 0.346688i | ||||
\(10\) | 1.81398 | − | 1.04730i | 0.573630 | − | 0.331186i | ||||
\(11\) | −1.67306 | + | 0.965940i | −0.504446 | + | 0.291242i | −0.730548 | − | 0.682862i | \(-0.760735\pi\) |
0.226102 | + | 0.974104i | \(0.427402\pi\) | |||||||
\(12\) | 1.62906 | − | 0.588348i | 0.470270 | − | 0.169841i | ||||
\(13\) | − | 1.00000i | − | 0.277350i | ||||||
\(14\) | 2.54770 | − | 0.713604i | 0.680901 | − | 0.190719i | ||||
\(15\) | −2.77337 | − | 2.33891i | −0.716081 | − | 0.603903i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0.345960 | + | 0.599220i | 0.0839076 | + | 0.145332i | 0.904925 | − | 0.425571i | \(-0.139927\pi\) |
−0.821018 | + | 0.570903i | \(0.806593\pi\) | |||||||
\(18\) | −1.91691 | − | 2.30769i | −0.451820 | − | 0.543929i | ||||
\(19\) | 2.08687 | + | 1.20485i | 0.478760 | + | 0.276412i | 0.719900 | − | 0.694078i | \(-0.244188\pi\) |
−0.241140 | + | 0.970490i | \(0.577521\pi\) | |||||||
\(20\) | 2.09460 | 0.468367 | ||||||||
\(21\) | −2.66144 | − | 3.73052i | −0.580774 | − | 0.814065i | ||||
\(22\) | −1.93188 | −0.411878 | ||||||||
\(23\) | −3.14870 | − | 1.81790i | −0.656550 | − | 0.379059i | 0.134411 | − | 0.990926i | \(-0.457086\pi\) |
−0.790961 | + | 0.611866i | \(0.790419\pi\) | |||||||
\(24\) | 1.70498 | + | 0.305007i | 0.348028 | + | 0.0622594i | ||||
\(25\) | 0.306322 | + | 0.530566i | 0.0612645 | + | 0.106113i | ||||
\(26\) | 0.500000 | − | 0.866025i | 0.0980581 | − | 0.169842i | ||||
\(27\) | −2.63157 | + | 4.48050i | −0.506445 | + | 0.862272i | ||||
\(28\) | 2.56317 | + | 0.655850i | 0.484394 | + | 0.123944i | ||||
\(29\) | − | 3.88157i | − | 0.720790i | −0.932800 | − | 0.360395i | \(-0.882642\pi\) | ||
0.932800 | − | 0.360395i | \(-0.117358\pi\) | |||||||
\(30\) | −1.23235 | − | 3.41224i | −0.224996 | − | 0.622987i | ||||
\(31\) | 0.817770 | − | 0.472140i | 0.146876 | − | 0.0847988i | −0.424761 | − | 0.905305i | \(-0.639642\pi\) |
0.571637 | + | 0.820507i | \(0.306309\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 1.13662 | + | 3.14716i | 0.197860 | + | 0.547849i | ||||
\(34\) | 0.691920i | 0.118663i | ||||||||
\(35\) | −1.49472 | − | 5.33641i | −0.252653 | − | 0.902019i | ||||
\(36\) | −0.506247 | − | 2.95698i | −0.0843746 | − | 0.492830i | ||||
\(37\) | −3.57753 | + | 6.19647i | −0.588142 | + | 1.01869i | 0.406333 | + | 0.913725i | \(0.366807\pi\) |
−0.994476 | + | 0.104968i | \(0.966526\pi\) | |||||||
\(38\) | 1.20485 | + | 2.08687i | 0.195453 | + | 0.338534i | ||||
\(39\) | −1.70498 | − | 0.305007i | −0.273016 | − | 0.0488403i | ||||
\(40\) | 1.81398 | + | 1.04730i | 0.286815 | + | 0.165593i | ||||
\(41\) | 8.66067 | 1.35257 | 0.676285 | − | 0.736640i | \(-0.263589\pi\) | ||||
0.676285 | + | 0.736640i | \(0.263589\pi\) | |||||||
\(42\) | −0.439616 | − | 4.56144i | −0.0678342 | − | 0.703846i | ||||
\(43\) | 8.01907 | 1.22290 | 0.611449 | − | 0.791284i | \(-0.290587\pi\) | ||||
0.611449 | + | 0.791284i | \(0.290587\pi\) | |||||||
\(44\) | −1.67306 | − | 0.965940i | −0.252223 | − | 0.145621i | ||||
\(45\) | −4.83370 | + | 4.01517i | −0.720565 | + | 0.598546i | ||||
\(46\) | −1.81790 | − | 3.14870i | −0.268035 | − | 0.464251i | ||||
\(47\) | −2.19759 | + | 3.80633i | −0.320551 | + | 0.555210i | −0.980602 | − | 0.196010i | \(-0.937201\pi\) |
0.660051 | + | 0.751221i | \(0.270535\pi\) | |||||||
\(48\) | 1.32406 | + | 1.11664i | 0.191111 | + | 0.161173i | ||||
\(49\) | −0.158181 | − | 6.99821i | −0.0225973 | − | 0.999745i | ||||
\(50\) | 0.612645i | 0.0866410i | ||||||||
\(51\) | 1.12718 | − | 0.407090i | 0.157837 | − | 0.0570040i | ||||
\(52\) | 0.866025 | − | 0.500000i | 0.120096 | − | 0.0693375i | ||||
\(53\) | 4.81192 | − | 2.77816i | 0.660968 | − | 0.381610i | −0.131678 | − | 0.991293i | \(-0.542036\pi\) |
0.792646 | + | 0.609683i | \(0.208703\pi\) | |||||||
\(54\) | −4.51925 | + | 2.56444i | −0.614992 | + | 0.348976i | ||||
\(55\) | 4.04652i | 0.545633i | ||||||||
\(56\) | 1.89185 | + | 1.84957i | 0.252809 | + | 0.247159i | ||||
\(57\) | 2.69076 | − | 3.19058i | 0.356400 | − | 0.422603i | ||||
\(58\) | 1.94079 | − | 3.36154i | 0.254838 | − | 0.441392i | ||||
\(59\) | 5.21237 | + | 9.02810i | 0.678593 | + | 1.17536i | 0.975405 | + | 0.220422i | \(0.0707434\pi\) |
−0.296811 | + | 0.954936i | \(0.595923\pi\) | |||||||
\(60\) | 0.638869 | − | 3.57126i | 0.0824776 | − | 0.461048i | ||||
\(61\) | 2.92469 | + | 1.68857i | 0.374469 | + | 0.216200i | 0.675409 | − | 0.737443i | \(-0.263967\pi\) |
−0.300940 | + | 0.953643i | \(0.597300\pi\) | |||||||
\(62\) | 0.944280 | 0.119924 | ||||||||
\(63\) | −7.17223 | + | 3.39988i | −0.903616 | + | 0.428344i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −1.81398 | − | 1.04730i | −0.224996 | − | 0.129902i | ||||
\(66\) | −0.589238 | + | 3.29383i | −0.0725302 | + | 0.405442i | ||||
\(67\) | −4.98074 | − | 8.62689i | −0.608494 | − | 1.05394i | −0.991489 | − | 0.130192i | \(-0.958441\pi\) |
0.382995 | − | 0.923751i | \(-0.374893\pi\) | |||||||
\(68\) | −0.345960 | + | 0.599220i | −0.0419538 | + | 0.0726661i | ||||
\(69\) | −4.05987 | + | 4.81401i | −0.488752 | + | 0.579539i | ||||
\(70\) | 1.37375 | − | 5.36883i | 0.164194 | − | 0.641698i | ||||
\(71\) | 3.58456i | 0.425409i | 0.977117 | + | 0.212705i | \(0.0682272\pi\) | ||||
−0.977117 | + | 0.212705i | \(0.931773\pi\) | |||||||
\(72\) | 1.04007 | − | 2.81394i | 0.122573 | − | 0.331626i | ||||
\(73\) | 7.46660 | − | 4.31085i | 0.873900 | − | 0.504546i | 0.00525772 | − | 0.999986i | \(-0.498326\pi\) |
0.868642 | + | 0.495440i | \(0.164993\pi\) | |||||||
\(74\) | −6.19647 | + | 3.57753i | −0.720324 | + | 0.415880i | ||||
\(75\) | 0.998037 | − | 0.360448i | 0.115243 | − | 0.0416210i | ||||
\(76\) | 2.40970i | 0.276412i | ||||||||
\(77\) | −1.26702 | + | 4.95175i | −0.144391 | + | 0.564304i | ||||
\(78\) | −1.32406 | − | 1.11664i | −0.149920 | − | 0.126434i | ||||
\(79\) | −8.33482 | + | 14.4363i | −0.937741 | + | 1.62421i | −0.168069 | + | 0.985775i | \(0.553753\pi\) |
−0.769672 | + | 0.638439i | \(0.779580\pi\) | |||||||
\(80\) | 1.04730 | + | 1.81398i | 0.117092 | + | 0.202809i | ||||
\(81\) | 6.83653 | + | 5.85337i | 0.759614 | + | 0.650374i | ||||
\(82\) | 7.50036 | + | 4.33034i | 0.828277 | + | 0.478206i | ||||
\(83\) | −12.5850 | −1.38138 | −0.690691 | − | 0.723150i | \(-0.742694\pi\) | ||||
−0.690691 | + | 0.723150i | \(0.742694\pi\) | |||||||
\(84\) | 1.90000 | − | 4.17013i | 0.207307 | − | 0.454999i | ||||
\(85\) | 1.44930 | 0.157198 | ||||||||
\(86\) | 6.94472 | + | 4.00954i | 0.748868 | + | 0.432359i | ||||
\(87\) | −6.61802 | − | 1.18391i | −0.709526 | − | 0.126928i | ||||
\(88\) | −0.965940 | − | 1.67306i | −0.102970 | − | 0.178349i | ||||
\(89\) | −7.45988 | + | 12.9209i | −0.790746 | + | 1.36961i | 0.134760 | + | 0.990878i | \(0.456974\pi\) |
−0.925506 | + | 0.378734i | \(0.876360\pi\) | |||||||
\(90\) | −6.19369 | + | 1.06039i | −0.652872 | + | 0.111775i | ||||
\(91\) | −1.89185 | − | 1.84957i | −0.198320 | − | 0.193888i | ||||
\(92\) | − | 3.63581i | − | 0.379059i | ||||||
\(93\) | −0.555565 | − | 1.53829i | −0.0576094 | − | 0.159513i | ||||
\(94\) | −3.80633 | + | 2.19759i | −0.392593 | + | 0.226664i | ||||
\(95\) | 4.37115 | − | 2.52369i | 0.448471 | − | 0.258925i | ||||
\(96\) | 0.588348 | + | 1.62906i | 0.0600480 | + | 0.166266i | ||||
\(97\) | − | 2.33951i | − | 0.237541i | −0.992922 | − | 0.118770i | \(-0.962105\pi\) | ||
0.992922 | − | 0.118770i | \(-0.0378952\pi\) | |||||||
\(98\) | 3.36212 | − | 6.13972i | 0.339625 | − | 0.620205i | ||||
\(99\) | 5.71253 | − | 0.978010i | 0.574131 | − | 0.0982937i | ||||
\(100\) | −0.306322 | + | 0.530566i | −0.0306322 | + | 0.0530566i | ||||
\(101\) | 7.51343 | + | 13.0136i | 0.747615 | + | 1.29491i | 0.948963 | + | 0.315387i | \(0.102134\pi\) |
−0.201349 | + | 0.979520i | \(0.564532\pi\) | |||||||
\(102\) | 1.17971 | + | 0.211041i | 0.116809 | + | 0.0208961i | ||||
\(103\) | −16.1762 | − | 9.33933i | −1.59389 | − | 0.920231i | −0.992631 | − | 0.121174i | \(-0.961334\pi\) |
−0.601256 | − | 0.799057i | \(-0.705333\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | −9.55440 | + | 0.920820i | −0.932414 | + | 0.0898629i | ||||
\(106\) | 5.55632 | 0.539678 | ||||||||
\(107\) | 1.30018 | + | 0.750662i | 0.125694 | + | 0.0725692i | 0.561528 | − | 0.827457i | \(-0.310214\pi\) |
−0.435835 | + | 0.900027i | \(0.643547\pi\) | |||||||
\(108\) | −5.19601 | − | 0.0387561i | −0.499986 | − | 0.00372931i | ||||
\(109\) | −1.87726 | − | 3.25151i | −0.179809 | − | 0.311438i | 0.762006 | − | 0.647570i | \(-0.224215\pi\) |
−0.941815 | + | 0.336132i | \(0.890881\pi\) | |||||||
\(110\) | −2.02326 | + | 3.50439i | −0.192910 | + | 0.334130i | ||||
\(111\) | 9.47370 | + | 7.98960i | 0.899204 | + | 0.758339i | ||||
\(112\) | 0.713604 | + | 2.54770i | 0.0674292 | + | 0.240735i | ||||
\(113\) | 8.66137i | 0.814793i | 0.913251 | + | 0.407396i | \(0.133563\pi\) | ||||
−0.913251 | + | 0.407396i | \(0.866437\pi\) | |||||||
\(114\) | 3.92556 | − | 1.41774i | 0.367663 | − | 0.132784i | ||||
\(115\) | −6.59528 | + | 3.80778i | −0.615013 | + | 0.355078i | ||||
\(116\) | 3.36154 | − | 1.94079i | 0.312111 | − | 0.180197i | ||||
\(117\) | −1.04007 | + | 2.81394i | −0.0961541 | + | 0.260149i | ||||
\(118\) | 10.4247i | 0.959676i | ||||||||
\(119\) | 1.77351 | + | 0.453796i | 0.162578 | + | 0.0415994i | ||||
\(120\) | 2.33891 | − | 2.77337i | 0.213512 | − | 0.253173i | ||||
\(121\) | −3.63392 | + | 6.29413i | −0.330356 | + | 0.572194i | ||||
\(122\) | 1.68857 | + | 2.92469i | 0.152876 | + | 0.264789i | ||||
\(123\) | 2.64157 | − | 14.7663i | 0.238182 | − | 1.33143i | ||||
\(124\) | 0.817770 | + | 0.472140i | 0.0734379 | + | 0.0423994i | ||||
\(125\) | 11.7563 | 1.05151 | ||||||||
\(126\) | −7.91127 | − | 0.641735i | −0.704792 | − | 0.0571703i | ||||
\(127\) | −2.17602 | −0.193091 | −0.0965454 | − | 0.995329i | \(-0.530779\pi\) | ||||
−0.0965454 | + | 0.995329i | \(0.530779\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 2.44588 | − | 13.6724i | 0.215347 | − | 1.20379i | ||||
\(130\) | −1.04730 | − | 1.81398i | −0.0918544 | − | 0.159096i | ||||
\(131\) | 3.27646 | − | 5.67499i | 0.286265 | − | 0.495826i | −0.686650 | − | 0.726988i | \(-0.740919\pi\) |
0.972915 | + | 0.231162i | \(0.0742528\pi\) | |||||||
\(132\) | −2.15721 | + | 2.55792i | −0.187761 | + | 0.222638i | ||||
\(133\) | 6.13920 | − | 1.71957i | 0.532336 | − | 0.149106i | ||||
\(134\) | − | 9.96148i | − | 0.860541i | ||||||
\(135\) | 5.37148 | + | 9.46603i | 0.462303 | + | 0.814706i | ||||
\(136\) | −0.599220 | + | 0.345960i | −0.0513827 | + | 0.0296658i | ||||
\(137\) | 12.3253 | − | 7.11601i | 1.05302 | − | 0.607962i | 0.129527 | − | 0.991576i | \(-0.458654\pi\) |
0.923494 | + | 0.383614i | \(0.125321\pi\) | |||||||
\(138\) | −5.92296 | + | 2.13912i | −0.504196 | + | 0.182094i | ||||
\(139\) | 8.44011i | 0.715881i | 0.933744 | + | 0.357940i | \(0.116521\pi\) | ||||
−0.933744 | + | 0.357940i | \(0.883479\pi\) | |||||||
\(140\) | 3.87411 | − | 3.96267i | 0.327422 | − | 0.334907i | ||||
\(141\) | 5.81945 | + | 4.90781i | 0.490086 | + | 0.413312i | ||||
\(142\) | −1.79228 | + | 3.10432i | −0.150405 | + | 0.260509i | ||||
\(143\) | 0.965940 | + | 1.67306i | 0.0807760 | + | 0.139908i | ||||
\(144\) | 2.30769 | − | 1.91691i | 0.192308 | − | 0.159743i | ||||
\(145\) | −7.04109 | − | 4.06517i | −0.584731 | − | 0.337594i | ||||
\(146\) | 8.62169 | 0.713536 | ||||||||
\(147\) | −11.9801 | − | 1.86481i | −0.988101 | − | 0.153807i | ||||
\(148\) | −7.15506 | −0.588142 | ||||||||
\(149\) | −0.0334409 | − | 0.0193071i | −0.00273959 | − | 0.00158170i | 0.498630 | − | 0.866815i | \(-0.333837\pi\) |
−0.501369 | + | 0.865233i | \(0.667170\pi\) | |||||||
\(150\) | 1.04455 | + | 0.186861i | 0.0852871 | + | 0.0152572i | ||||
\(151\) | −10.4122 | − | 18.0344i | −0.847329 | − | 1.46762i | −0.883583 | − | 0.468274i | \(-0.844876\pi\) |
0.0362546 | − | 0.999343i | \(-0.488457\pi\) | |||||||
\(152\) | −1.20485 | + | 2.08687i | −0.0977264 | + | 0.169267i | ||||
\(153\) | −0.350283 | − | 2.04599i | −0.0283187 | − | 0.165409i | ||||
\(154\) | −3.57315 | + | 3.65483i | −0.287933 | + | 0.294514i | ||||
\(155\) | − | 1.97789i | − | 0.158868i | ||||||
\(156\) | −0.588348 | − | 1.62906i | −0.0471055 | − | 0.130429i | ||||
\(157\) | 3.98152 | − | 2.29873i | 0.317760 | − | 0.183459i | −0.332634 | − | 0.943056i | \(-0.607937\pi\) |
0.650394 | + | 0.759597i | \(0.274604\pi\) | |||||||
\(158\) | −14.4363 | + | 8.33482i | −1.14849 | + | 0.663083i | ||||
\(159\) | −3.26905 | − | 9.05160i | −0.259253 | − | 0.717839i | ||||
\(160\) | 2.09460i | 0.165593i | ||||||||
\(161\) | −9.26294 | + | 2.59453i | −0.730022 | + | 0.204477i | ||||
\(162\) | 2.99392 | + | 8.48743i | 0.235225 | + | 0.666835i | ||||
\(163\) | −9.93799 | + | 17.2131i | −0.778404 | + | 1.34823i | 0.154458 | + | 0.987999i | \(0.450637\pi\) |
−0.932862 | + | 0.360235i | \(0.882696\pi\) | |||||||
\(164\) | 4.33034 | + | 7.50036i | 0.338143 | + | 0.585680i | ||||
\(165\) | 6.89925 | + | 1.23422i | 0.537106 | + | 0.0960838i | ||||
\(166\) | −10.8989 | − | 6.29250i | −0.845921 | − | 0.488393i | ||||
\(167\) | 5.36254 | 0.414965 | 0.207483 | − | 0.978239i | \(-0.433473\pi\) | ||||
0.207483 | + | 0.978239i | \(0.433473\pi\) | |||||||
\(168\) | 3.73052 | − | 2.66144i | 0.287815 | − | 0.205334i | ||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 1.25513 | + | 0.724648i | 0.0962639 | + | 0.0555780i | ||||
\(171\) | −4.61919 | − | 5.56086i | −0.353238 | − | 0.425250i | ||||
\(172\) | 4.00954 | + | 6.94472i | 0.305724 | + | 0.529530i | ||||
\(173\) | 0.0694333 | − | 0.120262i | 0.00527892 | − | 0.00914335i | −0.863374 | − | 0.504565i | \(-0.831653\pi\) |
0.868653 | + | 0.495421i | \(0.164986\pi\) | |||||||
\(174\) | −5.13942 | − | 4.33430i | −0.389618 | − | 0.328583i | ||||
\(175\) | 1.57031 | + | 0.401803i | 0.118705 | + | 0.0303735i | ||||
\(176\) | − | 1.93188i | − | 0.145621i | ||||||
\(177\) | 16.9826 | − | 6.13338i | 1.27649 | − | 0.461013i | ||||
\(178\) | −12.9209 | + | 7.45988i | −0.968462 | + | 0.559142i | ||||
\(179\) | −12.4682 | + | 7.19850i | −0.931914 | + | 0.538041i | −0.887416 | − | 0.460969i | \(-0.847502\pi\) |
−0.0444976 | + | 0.999009i | \(0.514169\pi\) | |||||||
\(180\) | −5.89408 | − | 2.17852i | −0.439319 | − | 0.162377i | ||||
\(181\) | − | 9.27914i | − | 0.689713i | −0.938655 | − | 0.344856i | \(-0.887928\pi\) | ||
0.938655 | − | 0.344856i | \(-0.112072\pi\) | |||||||
\(182\) | −0.713604 | − | 2.54770i | −0.0528958 | − | 0.188848i | ||||
\(183\) | 3.77104 | − | 4.47153i | 0.278764 | − | 0.330545i | ||||
\(184\) | 1.81790 | − | 3.14870i | 0.134018 | − | 0.232125i | ||||
\(185\) | 7.49350 | + | 12.9791i | 0.550933 | + | 0.954244i | ||||
\(186\) | 0.288012 | − | 1.60998i | 0.0211181 | − | 0.118050i | ||||
\(187\) | −1.15762 | − | 0.668353i | −0.0846537 | − | 0.0488748i | ||||
\(188\) | −4.39517 | −0.320551 | ||||||||
\(189\) | 3.60915 | + | 13.2655i | 0.262527 | + | 0.964925i | ||||
\(190\) | 5.04737 | 0.366175 | ||||||||
\(191\) | 2.93538 | + | 1.69474i | 0.212397 | + | 0.122627i | 0.602425 | − | 0.798176i | \(-0.294201\pi\) |
−0.390028 | + | 0.920803i | \(0.627535\pi\) | |||||||
\(192\) | −0.305007 | + | 1.70498i | −0.0220120 | + | 0.123047i | ||||
\(193\) | −6.28558 | − | 10.8869i | −0.452446 | − | 0.783659i | 0.546091 | − | 0.837726i | \(-0.316115\pi\) |
−0.998537 | + | 0.0540663i | \(0.982782\pi\) | |||||||
\(194\) | 1.16975 | − | 2.02607i | 0.0839833 | − | 0.145463i | ||||
\(195\) | −2.33891 | + | 2.77337i | −0.167493 | + | 0.198605i | ||||
\(196\) | 5.98154 | − | 3.63610i | 0.427253 | − | 0.259721i | ||||
\(197\) | − | 12.0271i | − | 0.856894i | −0.903567 | − | 0.428447i | \(-0.859061\pi\) | ||
0.903567 | − | 0.428447i | \(-0.140939\pi\) | |||||||
\(198\) | 5.43620 | + | 2.00928i | 0.386334 | + | 0.142793i | ||||
\(199\) | −13.0591 | + | 7.53965i | −0.925732 | + | 0.534472i | −0.885459 | − | 0.464717i | \(-0.846156\pi\) |
−0.0402727 | + | 0.999189i | \(0.512823\pi\) | |||||||
\(200\) | −0.530566 | + | 0.306322i | −0.0375167 | + | 0.0216603i | ||||
\(201\) | −16.2279 | + | 5.86081i | −1.14463 | + | 0.413390i | ||||
\(202\) | 15.0269i | 1.05729i | ||||||||
\(203\) | −7.34335 | − | 7.17924i | −0.515402 | − | 0.503884i | ||||
\(204\) | 0.916141 | + | 0.772623i | 0.0641427 | + | 0.0540944i | ||||
\(205\) | 9.07033 | − | 15.7103i | 0.633499 | − | 1.09725i | ||||
\(206\) | −9.33933 | − | 16.1762i | −0.650702 | − | 1.12705i | ||||
\(207\) | 6.96952 | + | 8.39033i | 0.484415 | + | 0.583168i | ||||
\(208\) | 0.866025 | + | 0.500000i | 0.0600481 | + | 0.0346688i | ||||
\(209\) | −4.65526 | −0.322011 | ||||||||
\(210\) | −8.73476 | − | 3.97975i | −0.602756 | − | 0.274629i | ||||
\(211\) | 11.0298 | 0.759324 | 0.379662 | − | 0.925125i | \(-0.376040\pi\) | ||||
0.379662 | + | 0.925125i | \(0.376040\pi\) | |||||||
\(212\) | 4.81192 | + | 2.77816i | 0.330484 | + | 0.190805i | ||||
\(213\) | 6.11162 | + | 1.09332i | 0.418761 | + | 0.0749129i | ||||
\(214\) | 0.750662 | + | 1.30018i | 0.0513142 | + | 0.0888788i | ||||
\(215\) | 8.39838 | − | 14.5464i | 0.572765 | − | 0.992058i | ||||
\(216\) | −4.48050 | − | 2.63157i | −0.304859 | − | 0.179056i | ||||
\(217\) | 0.619306 | − | 2.42035i | 0.0420412 | − | 0.164304i | ||||
\(218\) | − | 3.75452i | − | 0.254288i | ||||||
\(219\) | −5.07255 | − | 14.0453i | −0.342771 | − | 0.949092i | ||||
\(220\) | −3.50439 | + | 2.02326i | −0.236266 | + | 0.136408i | ||||
\(221\) | 0.599220 | − | 0.345960i | 0.0403079 | − | 0.0232718i | ||||
\(222\) | 4.20967 | + | 11.6560i | 0.282534 | + | 0.782303i | ||||
\(223\) | − | 14.2894i | − | 0.956889i | −0.878118 | − | 0.478444i | \(-0.841201\pi\) | ||
0.878118 | − | 0.478444i | \(-0.158799\pi\) | |||||||
\(224\) | −0.655850 | + | 2.56317i | −0.0438209 | + | 0.171259i | ||||
\(225\) | −0.310150 | − | 1.81158i | −0.0206767 | − | 0.120772i | ||||
\(226\) | −4.33068 | + | 7.50096i | −0.288073 | + | 0.498957i | ||||
\(227\) | −10.4107 | − | 18.0319i | −0.690983 | − | 1.19682i | −0.971516 | − | 0.236973i | \(-0.923845\pi\) |
0.280534 | − | 0.959844i | \(-0.409489\pi\) | |||||||
\(228\) | 4.10851 | + | 0.734978i | 0.272093 | + | 0.0486751i | ||||
\(229\) | −0.284143 | − | 0.164050i | −0.0187767 | − | 0.0108407i | 0.490582 | − | 0.871395i | \(-0.336784\pi\) |
−0.509359 | + | 0.860554i | \(0.670117\pi\) | |||||||
\(230\) | −7.61557 | −0.502156 | ||||||||
\(231\) | 8.05620 | + | 3.67058i | 0.530059 | + | 0.241506i | ||||
\(232\) | 3.88157 | 0.254838 | ||||||||
\(233\) | −7.80411 | − | 4.50571i | −0.511264 | − | 0.295179i | 0.222089 | − | 0.975026i | \(-0.428713\pi\) |
−0.733353 | + | 0.679848i | \(0.762046\pi\) | |||||||
\(234\) | −2.30769 | + | 1.91691i | −0.150859 | + | 0.125312i | ||||
\(235\) | 4.60307 | + | 7.97275i | 0.300271 | + | 0.520085i | ||||
\(236\) | −5.21237 | + | 9.02810i | −0.339297 | + | 0.587679i | ||||
\(237\) | 22.0715 | + | 18.6139i | 1.43370 | + | 1.20910i | ||||
\(238\) | 1.30901 | + | 1.27975i | 0.0848504 | + | 0.0829542i | ||||
\(239\) | − | 28.2160i | − | 1.82514i | −0.408922 | − | 0.912569i | \(-0.634095\pi\) | ||
0.408922 | − | 0.912569i | \(-0.365905\pi\) | |||||||
\(240\) | 3.41224 | − | 1.23235i | 0.220259 | − | 0.0795481i | ||||
\(241\) | 9.92924 | − | 5.73265i | 0.639599 | − | 0.369272i | −0.144861 | − | 0.989452i | \(-0.546274\pi\) |
0.784460 | + | 0.620180i | \(0.212940\pi\) | |||||||
\(242\) | −6.29413 | + | 3.63392i | −0.404602 | + | 0.233597i | ||||
\(243\) | 12.0651 | − | 9.87085i | 0.773976 | − | 0.633215i | ||||
\(244\) | 3.37715i | 0.216200i | ||||||||
\(245\) | −12.8603 | − | 7.04230i | −0.821612 | − | 0.449916i | ||||
\(246\) | 9.67082 | − | 11.4672i | 0.616589 | − | 0.731123i | ||||
\(247\) | 1.20485 | − | 2.08687i | 0.0766629 | − | 0.132784i | ||||
\(248\) | 0.472140 | + | 0.817770i | 0.0299809 | + | 0.0519285i | ||||
\(249\) | −3.83852 | + | 21.4572i | −0.243256 | + | 1.35980i | ||||
\(250\) | 10.1812 | + | 5.87813i | 0.643917 | + | 0.371765i | ||||
\(251\) | 25.7601 | 1.62596 | 0.812982 | − | 0.582289i | \(-0.197843\pi\) | ||||
0.812982 | + | 0.582289i | \(0.197843\pi\) | |||||||
\(252\) | −6.53049 | − | 4.51139i | −0.411382 | − | 0.284191i | ||||
\(253\) | 7.02395 | 0.441592 | ||||||||
\(254\) | −1.88449 | − | 1.08801i | −0.118244 | − | 0.0682679i | ||||
\(255\) | 0.442046 | − | 2.47103i | 0.0276820 | − | 0.154742i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −6.89377 | + | 11.9404i | −0.430021 | + | 0.744819i | −0.996875 | − | 0.0789999i | \(-0.974827\pi\) |
0.566853 | + | 0.823819i | \(0.308161\pi\) | |||||||
\(258\) | 8.95439 | − | 10.6177i | 0.557476 | − | 0.661029i | ||||
\(259\) | 5.10588 | + | 18.2289i | 0.317264 | + | 1.13269i | ||||
\(260\) | − | 2.09460i | − | 0.129902i | ||||||
\(261\) | −4.03709 | + | 10.9225i | −0.249890 | + | 0.676087i | ||||
\(262\) | 5.67499 | − | 3.27646i | 0.350602 | − | 0.202420i | ||||
\(263\) | −18.5720 | + | 10.7225i | −1.14520 | + | 0.661180i | −0.947712 | − | 0.319126i | \(-0.896611\pi\) |
−0.197484 | + | 0.980306i | \(0.563277\pi\) | |||||||
\(264\) | −3.14716 | + | 1.13662i | −0.193694 | + | 0.0699540i | ||||
\(265\) | − | 11.6383i | − | 0.714934i | ||||||
\(266\) | 6.17649 | + | 1.58041i | 0.378705 | + | 0.0969009i | ||||
\(267\) | 19.7546 | + | 16.6599i | 1.20896 | + | 1.01957i | ||||
\(268\) | 4.98074 | − | 8.62689i | 0.304247 | − | 0.526971i | ||||
\(269\) | 4.76794 | + | 8.25831i | 0.290706 | + | 0.503518i | 0.973977 | − | 0.226647i | \(-0.0727764\pi\) |
−0.683271 | + | 0.730165i | \(0.739443\pi\) | |||||||
\(270\) | −0.0811787 | + | 10.8836i | −0.00494038 | + | 0.662353i | ||||
\(271\) | −22.0755 | − | 12.7453i | −1.34099 | − | 0.774221i | −0.354038 | − | 0.935231i | \(-0.615192\pi\) |
−0.986953 | + | 0.161010i | \(0.948525\pi\) | |||||||
\(272\) | −0.691920 | −0.0419538 | ||||||||
\(273\) | −3.73052 | + | 2.66144i | −0.225781 | + | 0.161078i | ||||
\(274\) | 14.2320 | 0.859788 | ||||||||
\(275\) | −1.02499 | − | 0.591778i | −0.0618092 | − | 0.0356856i | ||||
\(276\) | −6.19899 | − | 1.10895i | −0.373136 | − | 0.0667508i | ||||
\(277\) | 9.72968 | + | 16.8523i | 0.584600 | + | 1.01256i | 0.994925 | + | 0.100618i | \(0.0320819\pi\) |
−0.410325 | + | 0.911939i | \(0.634585\pi\) | |||||||
\(278\) | −4.22006 | + | 7.30935i | −0.253102 | + | 0.438386i | ||||
\(279\) | −2.79221 | + | 0.478039i | −0.167165 | + | 0.0286195i | ||||
\(280\) | 5.33641 | − | 1.49472i | 0.318912 | − | 0.0893263i | ||||
\(281\) | 8.66815i | 0.517099i | 0.965998 | + | 0.258549i | \(0.0832445\pi\) | ||||
−0.965998 | + | 0.258549i | \(0.916756\pi\) | |||||||
\(282\) | 2.58589 | + | 7.16001i | 0.153988 | + | 0.426373i | ||||
\(283\) | 19.9498 | − | 11.5180i | 1.18589 | − | 0.684676i | 0.228523 | − | 0.973539i | \(-0.426610\pi\) |
0.957371 | + | 0.288862i | \(0.0932770\pi\) | |||||||
\(284\) | −3.10432 | + | 1.79228i | −0.184208 | + | 0.106352i | ||||
\(285\) | −2.96961 | − | 8.22249i | −0.175905 | − | 0.487058i | ||||
\(286\) | 1.93188i | 0.114235i | ||||||||
\(287\) | 16.0185 | − | 16.3847i | 0.945544 | − | 0.967157i | ||||
\(288\) | 2.95698 | − | 0.506247i | 0.174242 | − | 0.0298309i | ||||
\(289\) | 8.26062 | − | 14.3078i | 0.485919 | − | 0.841636i | ||||
\(290\) | −4.06517 | − | 7.04109i | −0.238715 | − | 0.413467i | ||||
\(291\) | −3.98882 | − | 0.713566i | −0.233829 | − | 0.0418300i | ||||
\(292\) | 7.46660 | + | 4.31085i | 0.436950 | + | 0.252273i | ||||
\(293\) | 18.2447 | 1.06587 | 0.532934 | − | 0.846157i | \(-0.321089\pi\) | ||||
0.532934 | + | 0.846157i | \(0.321089\pi\) | |||||||
\(294\) | −9.44265 | − | 7.60502i | −0.550707 | − | 0.443534i | ||||
\(295\) | 21.8357 | 1.27132 | ||||||||
\(296\) | −6.19647 | − | 3.57753i | −0.360162 | − | 0.207940i | ||||
\(297\) | 0.0748722 | − | 10.0381i | 0.00434453 | − | 0.582468i | ||||
\(298\) | −0.0193071 | − | 0.0334409i | −0.00111843 | − | 0.00193718i | ||||
\(299\) | −1.81790 | + | 3.14870i | −0.105132 | + | 0.182094i | ||||
\(300\) | 0.811176 | + | 0.684101i | 0.0468333 | + | 0.0394966i | ||||
\(301\) | 14.8318 | − | 15.1709i | 0.854893 | − | 0.874434i | ||||
\(302\) | − | 20.8243i | − | 1.19830i | ||||||
\(303\) | 24.4797 | − | 8.84102i | 1.40632 | − | 0.507904i | ||||
\(304\) | −2.08687 | + | 1.20485i | −0.119690 | + | 0.0691030i | ||||
\(305\) | 6.12607 | − | 3.53689i | 0.350778 | − | 0.202522i | ||||
\(306\) | 0.719642 | − | 1.94702i | 0.0411392 | − | 0.111304i | ||||
\(307\) | 21.8510i | 1.24710i | 0.781783 | + | 0.623551i | \(0.214311\pi\) | ||||
−0.781783 | + | 0.623551i | \(0.785689\pi\) | |||||||
\(308\) | −4.92185 | + | 1.37860i | −0.280448 | + | 0.0785529i | ||||
\(309\) | −20.8573 | + | 24.7316i | −1.18653 | + | 1.40693i | ||||
\(310\) | 0.988945 | − | 1.71290i | 0.0561683 | − | 0.0972863i | ||||
\(311\) | 1.41409 | + | 2.44927i | 0.0801856 | + | 0.138885i | 0.903330 | − | 0.428947i | \(-0.141115\pi\) |
−0.823144 | + | 0.567833i | \(0.807782\pi\) | |||||||
\(312\) | 0.305007 | − | 1.70498i | 0.0172676 | − | 0.0965257i | ||||
\(313\) | −8.58082 | − | 4.95414i | −0.485017 | − | 0.280025i | 0.237488 | − | 0.971390i | \(-0.423676\pi\) |
−0.722505 | + | 0.691366i | \(0.757009\pi\) | |||||||
\(314\) | 4.59746 | 0.259450 | ||||||||
\(315\) | −1.34418 | + | 16.5710i | −0.0757359 | + | 0.933668i | ||||
\(316\) | −16.6696 | −0.937741 | ||||||||
\(317\) | −15.2159 | − | 8.78492i | −0.854612 | − | 0.493410i | 0.00759227 | − | 0.999971i | \(-0.497583\pi\) |
−0.862204 | + | 0.506561i | \(0.830917\pi\) | |||||||
\(318\) | 1.69472 | − | 9.47344i | 0.0950352 | − | 0.531244i | ||||
\(319\) | 3.74937 | + | 6.49410i | 0.209924 | + | 0.363600i | ||||
\(320\) | −1.04730 | + | 1.81398i | −0.0585459 | + | 0.101404i | ||||
\(321\) | 1.67643 | − | 1.98784i | 0.0935693 | − | 0.110950i | ||||
\(322\) | −9.31921 | − | 2.38455i | −0.519339 | − | 0.132886i | ||||
\(323\) | 1.66732i | 0.0927723i | ||||||||
\(324\) | −1.65090 | + | 8.84729i | −0.0917166 | + | 0.491516i | ||||
\(325\) | 0.530566 | − | 0.306322i | 0.0294305 | − | 0.0169917i | ||||
\(326\) | −17.2131 | + | 9.93799i | −0.953346 | + | 0.550414i | ||||
\(327\) | −6.11635 | + | 2.20896i | −0.338235 | + | 0.122156i | ||||
\(328\) | 8.66067i | 0.478206i | ||||||||
\(329\) | 3.13641 | + | 11.1976i | 0.172916 | + | 0.617342i | ||||
\(330\) | 5.35782 | + | 4.51849i | 0.294938 | + | 0.248735i | ||||
\(331\) | 7.70234 | − | 13.3408i | 0.423359 | − | 0.733279i | −0.572907 | − | 0.819621i | \(-0.694184\pi\) |
0.996266 | + | 0.0863414i | \(0.0275176\pi\) | |||||||
\(332\) | −6.29250 | − | 10.8989i | −0.345346 | − | 0.598156i | ||||
\(333\) | 16.5117 | − | 13.7156i | 0.904835 | − | 0.751611i | ||||
\(334\) | 4.64409 | + | 2.68127i | 0.254113 | + | 0.146712i | ||||
\(335\) | −20.8653 | −1.13999 | ||||||||
\(336\) | 4.56144 | − | 0.439616i | 0.248847 | − | 0.0239830i | ||||
\(337\) | 14.4566 | 0.787501 | 0.393750 | − | 0.919217i | \(-0.371177\pi\) | ||||
0.393750 | + | 0.919217i | \(0.371177\pi\) | |||||||
\(338\) | −0.866025 | − | 0.500000i | −0.0471056 | − | 0.0271964i | ||||
\(339\) | 14.7675 | + | 2.64178i | 0.802060 | + | 0.143482i | ||||
\(340\) | 0.724648 | + | 1.25513i | 0.0392996 | + | 0.0680689i | ||||
\(341\) | −0.912118 | + | 1.57983i | −0.0493939 | + | 0.0855528i | ||||
\(342\) | −1.21991 | − | 7.12544i | −0.0659650 | − | 0.385300i | ||||
\(343\) | −13.5321 | − | 12.6444i | −0.730666 | − | 0.682735i | ||||
\(344\) | 8.01907i | 0.432359i | ||||||||
\(345\) | 4.48060 | + | 12.4062i | 0.241228 | + | 0.667930i | ||||
\(346\) | 0.120262 | − | 0.0694333i | 0.00646533 | − | 0.00373276i | ||||
\(347\) | −10.8790 | + | 6.28099i | −0.584015 | + | 0.337181i | −0.762727 | − | 0.646720i | \(-0.776140\pi\) |
0.178712 | + | 0.983901i | \(0.442807\pi\) | |||||||
\(348\) | −2.28372 | − | 6.32333i | −0.122420 | − | 0.338966i | ||||
\(349\) | − | 17.7010i | − | 0.947514i | −0.880656 | − | 0.473757i | \(-0.842897\pi\) | ||
0.880656 | − | 0.473757i | \(-0.157103\pi\) | |||||||
\(350\) | 1.15903 | + | 1.13313i | 0.0619528 | + | 0.0605683i | ||||
\(351\) | 4.48050 | + | 2.63157i | 0.239151 | + | 0.140463i | ||||
\(352\) | 0.965940 | − | 1.67306i | 0.0514848 | − | 0.0891743i | ||||
\(353\) | 0.222657 | + | 0.385653i | 0.0118508 | + | 0.0205263i | 0.871890 | − | 0.489702i | \(-0.162894\pi\) |
−0.860039 | + | 0.510228i | \(0.829561\pi\) | |||||||
\(354\) | 17.7740 | + | 3.17962i | 0.944679 | + | 0.168995i | ||||
\(355\) | 6.50231 | + | 3.75411i | 0.345107 | + | 0.199248i | ||||
\(356\) | −14.9198 | −0.790746 | ||||||||
\(357\) | 1.31465 | − | 2.88540i | 0.0695786 | − | 0.152711i | ||||
\(358\) | −14.3970 | −0.760905 | ||||||||
\(359\) | −17.9004 | − | 10.3348i | −0.944745 | − | 0.545449i | −0.0533007 | − | 0.998579i | \(-0.516974\pi\) |
−0.891445 | + | 0.453130i | \(0.850308\pi\) | |||||||
\(360\) | −4.01517 | − | 4.83370i | −0.211618 | − | 0.254758i | ||||
\(361\) | −6.59666 | − | 11.4258i | −0.347193 | − | 0.601355i | ||||
\(362\) | 4.63957 | − | 8.03597i | 0.243850 | − | 0.422361i | ||||
\(363\) | 9.62302 | + | 8.11553i | 0.505078 | + | 0.425955i | ||||
\(364\) | 0.655850 | − | 2.56317i | 0.0343759 | − | 0.134347i | ||||
\(365\) | − | 18.0590i | − | 0.945252i | ||||||
\(366\) | 5.50158 | − | 1.98694i | 0.287572 | − | 0.103859i | ||||
\(367\) | −17.2106 | + | 9.93654i | −0.898385 | + | 0.518683i | −0.876676 | − | 0.481081i | \(-0.840244\pi\) |
−0.0217093 | + | 0.999764i | \(0.506911\pi\) | |||||||
\(368\) | 3.14870 | − | 1.81790i | 0.164137 | − | 0.0947648i | ||||
\(369\) | −24.3706 | − | 9.00767i | −1.26868 | − | 0.468920i | ||||
\(370\) | 14.9870i | 0.779137i | ||||||||
\(371\) | 3.64412 | − | 14.2418i | 0.189193 | − | 0.739399i | ||||
\(372\) | 1.05442 | − | 1.25028i | 0.0546690 | − | 0.0648239i | ||||
\(373\) | 7.64212 | − | 13.2365i | 0.395694 | − | 0.685362i | −0.597496 | − | 0.801872i | \(-0.703838\pi\) |
0.993189 | + | 0.116510i | \(0.0371708\pi\) | |||||||
\(374\) | −0.668353 | − | 1.15762i | −0.0345597 | − | 0.0598592i | ||||
\(375\) | 3.58574 | − | 20.0442i | 0.185167 | − | 1.03508i | ||||
\(376\) | −3.80633 | − | 2.19759i | −0.196297 | − | 0.113332i | ||||
\(377\) | −3.88157 | −0.199911 | ||||||||
\(378\) | −3.50714 | + | 13.2929i | −0.180388 | + | 0.683711i | ||||
\(379\) | −23.8814 | −1.22670 | −0.613352 | − | 0.789810i | \(-0.710179\pi\) | ||||
−0.613352 | + | 0.789810i | \(0.710179\pi\) | |||||||
\(380\) | 4.37115 | + | 2.52369i | 0.224235 | + | 0.129462i | ||||
\(381\) | −0.663703 | + | 3.71009i | −0.0340025 | + | 0.190073i | ||||
\(382\) | 1.69474 | + | 2.93538i | 0.0867106 | + | 0.150187i | ||||
\(383\) | 18.7955 | − | 32.5547i | 0.960404 | − | 1.66347i | 0.238916 | − | 0.971040i | \(-0.423208\pi\) |
0.721488 | − | 0.692427i | \(-0.243459\pi\) | |||||||
\(384\) | −1.11664 | + | 1.32406i | −0.0569831 | + | 0.0675679i | ||||
\(385\) | 7.65540 | + | 7.48432i | 0.390155 | + | 0.381436i | ||||
\(386\) | − | 12.5712i | − | 0.639855i | ||||||
\(387\) | −22.5652 | − | 8.34036i | −1.14705 | − | 0.423964i | ||||
\(388\) | 2.02607 | − | 1.16975i | 0.102858 | − | 0.0593852i | ||||
\(389\) | −25.5296 | + | 14.7395i | −1.29440 | + | 0.747322i | −0.979431 | − | 0.201780i | \(-0.935327\pi\) |
−0.314969 | + | 0.949102i | \(0.601994\pi\) | |||||||
\(390\) | −3.41224 | + | 1.23235i | −0.172785 | + | 0.0624027i | ||||
\(391\) | − | 2.51569i | − | 0.127224i | ||||||
\(392\) | 6.99821 | − | 0.158181i | 0.353463 | − | 0.00798935i | ||||
\(393\) | −8.67642 | − | 7.31722i | −0.437668 | − | 0.369105i | ||||
\(394\) | 6.01354 | − | 10.4158i | 0.302958 | − | 0.524739i | ||||
\(395\) | 17.4581 | + | 30.2384i | 0.878414 | + | 1.52146i | ||||
\(396\) | 3.70324 | + | 4.45819i | 0.186095 | + | 0.224032i | ||||
\(397\) | 16.3264 | + | 9.42604i | 0.819398 | + | 0.473079i | 0.850209 | − | 0.526446i | \(-0.176476\pi\) |
−0.0308110 | + | 0.999525i | \(0.509809\pi\) | |||||||
\(398\) | −15.0793 | −0.755857 | ||||||||
\(399\) | −1.05934 | − | 10.9917i | −0.0530336 | − | 0.550275i | ||||
\(400\) | −0.612645 | −0.0306322 | ||||||||
\(401\) | −9.99593 | − | 5.77115i | −0.499173 | − | 0.288198i | 0.229199 | − | 0.973380i | \(-0.426389\pi\) |
−0.728372 | + | 0.685182i | \(0.759723\pi\) | |||||||
\(402\) | −16.9842 | − | 3.03832i | −0.847093 | − | 0.151538i | ||||
\(403\) | −0.472140 | − | 0.817770i | −0.0235190 | − | 0.0407360i | ||||
\(404\) | −7.51343 | + | 13.0136i | −0.373807 | + | 0.647453i | ||||
\(405\) | 17.7778 | − | 6.27108i | 0.883385 | − | 0.311612i | ||||
\(406\) | −2.76991 | − | 9.88908i | −0.137468 | − | 0.490787i | ||||
\(407\) | − | 13.8227i | − | 0.685167i | ||||||
\(408\) | 0.407090 | + | 1.12718i | 0.0201539 | + | 0.0558038i | ||||
\(409\) | −20.8221 | + | 12.0217i | −1.02959 | + | 0.594433i | −0.916867 | − | 0.399194i | \(-0.869290\pi\) |
−0.112721 | + | 0.993627i | \(0.535957\pi\) | |||||||
\(410\) | 15.7103 | − | 9.07033i | 0.775875 | − | 0.447952i | ||||
\(411\) | −8.37338 | − | 23.1849i | −0.413028 | − | 1.14363i | ||||
\(412\) | − | 18.6787i | − | 0.920231i | ||||||
\(413\) | 26.7204 | + | 6.83707i | 1.31483 | + | 0.336430i | ||||
\(414\) | 1.84062 | + | 10.7510i | 0.0904615 | + | 0.528383i | ||||
\(415\) | −13.1803 | + | 22.8289i | −0.646994 | + | 1.12063i | ||||
\(416\) | 0.500000 | + | 0.866025i | 0.0245145 | + | 0.0424604i | ||||
\(417\) | 14.3903 | + | 2.57430i | 0.704694 | + | 0.126064i | ||||
\(418\) | −4.03158 | − | 2.32763i | −0.197191 | − | 0.113848i | ||||
\(419\) | −3.63647 | −0.177653 | −0.0888267 | − | 0.996047i | \(-0.528312\pi\) | ||||
−0.0888267 | + | 0.996047i | \(0.528312\pi\) | |||||||
\(420\) | −5.57465 | − | 7.81394i | −0.272015 | − | 0.381281i | ||||
\(421\) | −0.0321368 | −0.00156625 | −0.000783127 | − | 1.00000i | \(-0.500249\pi\) | ||||
−0.000783127 | 1.00000i | \(0.500249\pi\) | ||||||||
\(422\) | 9.55210 | + | 5.51491i | 0.464989 | + | 0.268461i | ||||
\(423\) | 10.1427 | − | 8.42516i | 0.493155 | − | 0.409645i | ||||
\(424\) | 2.77816 | + | 4.81192i | 0.134919 | + | 0.233687i | ||||
\(425\) | −0.211951 | + | 0.367109i | −0.0102811 | + | 0.0178074i | ||||
\(426\) | 4.74616 | + | 4.00265i | 0.229952 | + | 0.193929i | ||||
\(427\) | 8.60395 | − | 2.40994i | 0.416374 | − | 0.116625i | ||||
\(428\) | 1.50132i | 0.0725692i | ||||||||
\(429\) | 3.14716 | − | 1.13662i | 0.151946 | − | 0.0548764i | ||||
\(430\) | 14.5464 | − | 8.39838i | 0.701491 | − | 0.405006i | ||||
\(431\) | −14.3401 | + | 8.27924i | −0.690737 | + | 0.398797i | −0.803888 | − | 0.594781i | \(-0.797239\pi\) |
0.113151 | + | 0.993578i | \(0.463906\pi\) | |||||||
\(432\) | −2.56444 | − | 4.51925i | −0.123382 | − | 0.217433i | ||||
\(433\) | 23.5650i | 1.13246i | 0.824247 | + | 0.566231i | \(0.191599\pi\) | ||||
−0.824247 | + | 0.566231i | \(0.808401\pi\) | |||||||
\(434\) | 1.74651 | − | 1.78643i | 0.0838352 | − | 0.0857516i | ||||
\(435\) | −9.07864 | + | 10.7650i | −0.435288 | + | 0.516144i | ||||
\(436\) | 1.87726 | − | 3.25151i | 0.0899045 | − | 0.155719i | ||||
\(437\) | −4.38061 | − | 7.58744i | −0.209553 | − | 0.362957i | ||||
\(438\) | 2.62968 | − | 14.6998i | 0.125651 | − | 0.702386i | ||||
\(439\) | −1.10437 | − | 0.637611i | −0.0527089 | − | 0.0304315i | 0.473414 | − | 0.880840i | \(-0.343021\pi\) |
−0.526123 | + | 0.850409i | \(0.676355\pi\) | |||||||
\(440\) | −4.04652 | −0.192910 | ||||||||
\(441\) | −6.83349 | + | 19.8571i | −0.325404 | + | 0.945575i | ||||
\(442\) | 0.691920 | 0.0329113 | ||||||||
\(443\) | −5.80498 | − | 3.35151i | −0.275803 | − | 0.159235i | 0.355719 | − | 0.934593i | \(-0.384236\pi\) |
−0.631522 | + | 0.775358i | \(0.717569\pi\) | |||||||
\(444\) | −2.18235 | + | 12.1993i | −0.103570 | + | 0.578952i | ||||
\(445\) | 15.6255 | + | 27.0641i | 0.740719 | + | 1.28296i | ||||
\(446\) | 7.14470 | − | 12.3750i | 0.338311 | − | 0.585972i | ||||
\(447\) | −0.0431181 | + | 0.0511275i | −0.00203942 | + | 0.00241825i | ||||
\(448\) | −1.84957 | + | 1.89185i | −0.0873840 | + | 0.0893814i | ||||
\(449\) | − | 11.4423i | − | 0.539997i | −0.962861 | − | 0.269998i | \(-0.912977\pi\) | ||
0.962861 | − | 0.269998i | \(-0.0870232\pi\) | |||||||
\(450\) | 0.637191 | − | 1.72395i | 0.0300375 | − | 0.0812676i | ||||
\(451\) | −14.4898 | + | 8.36569i | −0.682298 | + | 0.393925i | ||||
\(452\) | −7.50096 | + | 4.33068i | −0.352816 | + | 0.203698i | ||||
\(453\) | −33.9241 | + | 12.2519i | −1.59389 | + | 0.575646i | ||||
\(454\) | − | 20.8214i | − | 0.977197i | ||||||
\(455\) | −5.33641 | + | 1.49472i | −0.250175 | + | 0.0700733i | ||||
\(456\) | 3.19058 | + | 2.69076i | 0.149413 | + | 0.126007i | ||||
\(457\) | −15.9902 | + | 27.6958i | −0.747989 | + | 1.29556i | 0.200796 | + | 0.979633i | \(0.435647\pi\) |
−0.948785 | + | 0.315922i | \(0.897686\pi\) | |||||||
\(458\) | −0.164050 | − | 0.284143i | −0.00766554 | − | 0.0132771i | ||||
\(459\) | −3.59522 | − | 0.0268161i | −0.167811 | − | 0.00125167i | ||||
\(460\) | −6.59528 | − | 3.80778i | −0.307506 | − | 0.177539i | ||||
\(461\) | −7.66318 | −0.356910 | −0.178455 | − | 0.983948i | \(-0.557110\pi\) | ||||
−0.178455 | + | 0.983948i | \(0.557110\pi\) | |||||||
\(462\) | 5.14158 | + | 7.20691i | 0.239208 | + | 0.335296i | ||||
\(463\) | −33.6757 | −1.56504 | −0.782522 | − | 0.622623i | \(-0.786067\pi\) | ||||
−0.782522 | + | 0.622623i | \(0.786067\pi\) | |||||||
\(464\) | 3.36154 | + | 1.94079i | 0.156056 | + | 0.0900987i | ||||
\(465\) | −3.37227 | − | 0.603271i | −0.156385 | − | 0.0279760i | ||||
\(466\) | −4.50571 | − | 7.80411i | −0.208723 | − | 0.361519i | ||||
\(467\) | 9.89478 | − | 17.1383i | 0.457876 | − | 0.793064i | −0.540973 | − | 0.841040i | \(-0.681944\pi\) |
0.998848 | + | 0.0479760i | \(0.0152771\pi\) | |||||||
\(468\) | −2.95698 | + | 0.506247i | −0.136686 | + | 0.0234013i | ||||
\(469\) | −25.5330 | − | 6.53324i | −1.17900 | − | 0.301677i | ||||
\(470\) | 9.20613i | 0.424647i | ||||||||
\(471\) | −2.70491 | − | 7.48956i | −0.124636 | − | 0.345101i | ||||
\(472\) | −9.02810 | + | 5.21237i | −0.415552 | + | 0.239919i | ||||
\(473\) | −13.4164 | + | 7.74595i | −0.616885 | + | 0.356159i | ||||
\(474\) | 9.80755 | + | 27.1559i | 0.450476 | + | 1.24731i | ||||
\(475\) | 1.47629i | 0.0677370i | ||||||||
\(476\) | 0.493757 | + | 1.76280i | 0.0226313 | + | 0.0807980i | ||||
\(477\) | −16.4299 | + | 2.81287i | −0.752275 | + | 0.128793i | ||||
\(478\) | 14.1080 | − | 24.4357i | 0.645284 | − | 1.11766i | ||||
\(479\) | 10.3981 | + | 18.0101i | 0.475102 | + | 0.822900i | 0.999593 | − | 0.0285153i | \(-0.00907794\pi\) |
−0.524492 | + | 0.851416i | \(0.675745\pi\) | |||||||
\(480\) | 3.57126 | + | 0.638869i | 0.163005 | + | 0.0291602i | ||||
\(481\) | 6.19647 | + | 3.57753i | 0.282534 | + | 0.163121i | ||||
\(482\) | 11.4653 | 0.522230 | ||||||||
\(483\) | 1.59836 | + | 16.5845i | 0.0727279 | + | 0.754622i | ||||
\(484\) | −7.26784 | −0.330356 | ||||||||
\(485\) | −4.24381 | − | 2.45017i | −0.192702 | − | 0.111256i | ||||
\(486\) | 15.3841 | − | 2.51586i | 0.697837 | − | 0.114122i | ||||
\(487\) | 2.80203 | + | 4.85326i | 0.126972 | + | 0.219922i | 0.922502 | − | 0.385992i | \(-0.126141\pi\) |
−0.795530 | + | 0.605914i | \(0.792807\pi\) | |||||||
\(488\) | −1.68857 | + | 2.92469i | −0.0764381 | + | 0.132395i | ||||
\(489\) | 26.3169 | + | 22.1942i | 1.19009 | + | 1.00366i | ||||
\(490\) | −7.61617 | − | 12.5289i | −0.344063 | − | 0.566000i | ||||
\(491\) | 19.4106i | 0.875989i | 0.898978 | + | 0.437994i | \(0.144311\pi\) | ||||
−0.898978 | + | 0.437994i | \(0.855689\pi\) | |||||||
\(492\) | 14.1088 | − | 5.09549i | 0.636073 | − | 0.229722i | ||||
\(493\) | 2.32592 | − | 1.34287i | 0.104754 | − | 0.0604798i | ||||
\(494\) | 2.08687 | − | 1.20485i | 0.0938925 | − | 0.0542089i | ||||
\(495\) | 4.20865 | − | 11.3867i | 0.189165 | − | 0.511793i | ||||
\(496\) | 0.944280i | 0.0423994i | ||||||||
\(497\) | 6.78145 | + | 6.62990i | 0.304189 | + | 0.297391i | ||||
\(498\) | −14.0529 | + | 16.6632i | −0.629724 | + | 0.746698i | ||||
\(499\) | −12.1481 | + | 21.0412i | −0.543825 | + | 0.941932i | 0.454855 | + | 0.890565i | \(0.349691\pi\) |
−0.998680 | + | 0.0513667i | \(0.983642\pi\) | |||||||
\(500\) | 5.87813 | + | 10.1812i | 0.262878 | + | 0.455318i | ||||
\(501\) | 1.63561 | − | 9.14304i | 0.0730738 | − | 0.408481i | ||||
\(502\) | 22.3089 | + | 12.8801i | 0.995695 | + | 0.574865i | ||||
\(503\) | −7.56087 | −0.337123 | −0.168561 | − | 0.985691i | \(-0.553912\pi\) | ||||
−0.168561 | + | 0.985691i | \(0.553912\pi\) | |||||||
\(504\) | −3.39988 | − | 7.17223i | −0.151443 | − | 0.319476i | ||||
\(505\) | 31.4753 | 1.40063 | ||||||||
\(506\) | 6.08292 | + | 3.51197i | 0.270419 | + | 0.156126i | ||||
\(507\) | −0.305007 | + | 1.70498i | −0.0135459 | + | 0.0757210i | ||||
\(508\) | −1.08801 | − | 1.88449i | −0.0482727 | − | 0.0836108i | ||||
\(509\) | 17.0560 | − | 29.5418i | 0.755992 | − | 1.30942i | −0.188888 | − | 0.981999i | \(-0.560488\pi\) |
0.944880 | − | 0.327417i | \(-0.106178\pi\) | |||||||
\(510\) | 1.61834 | − | 1.91895i | 0.0716612 | − | 0.0849725i | ||||
\(511\) | 5.65454 | − | 22.0989i | 0.250142 | − | 0.977598i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −10.8901 | + | 6.17954i | −0.480808 | + | 0.272834i | ||||
\(514\) | −11.9404 | + | 6.89377i | −0.526666 | + | 0.304071i | ||||
\(515\) | −33.8827 | + | 19.5622i | −1.49305 | + | 0.862012i | ||||
\(516\) | 13.0636 | − | 4.71800i | 0.575092 | − | 0.207699i | ||||
\(517\) | − | 8.49095i | − | 0.373431i | ||||||
\(518\) | −4.69265 | + | 18.3397i | −0.206183 | + | 0.805799i | ||||
\(519\) | −0.183867 | − | 0.155063i | −0.00807087 | − | 0.00680653i | ||||
\(520\) | 1.04730 | − | 1.81398i | 0.0459272 | − | 0.0795482i | ||||
\(521\) | 16.1589 | + | 27.9881i | 0.707935 | + | 1.22618i | 0.965622 | + | 0.259951i | \(0.0837064\pi\) |
−0.257687 | + | 0.966229i | \(0.582960\pi\) | |||||||
\(522\) | −8.95748 | + | 7.44063i | −0.392058 | + | 0.325668i | ||||
\(523\) | 24.1399 | + | 13.9372i | 1.05556 | + | 0.609430i | 0.924202 | − | 0.381904i | \(-0.124732\pi\) |
0.131362 | + | 0.991334i | \(0.458065\pi\) | |||||||
\(524\) | 6.55291 | 0.286265 | ||||||||
\(525\) | 1.16403 | − | 2.55481i | 0.0508023 | − | 0.111501i | ||||
\(526\) | −21.4451 | −0.935049 | ||||||||
\(527\) | 0.565831 | + | 0.326683i | 0.0246480 | + | 0.0142305i | ||||
\(528\) | −3.29383 | − | 0.589238i | −0.143345 | − | 0.0256433i | ||||
\(529\) | −4.89045 | − | 8.47051i | −0.212628 | − | 0.368283i | ||||
\(530\) | 5.81914 | − | 10.0791i | 0.252767 | − | 0.437806i | ||||
\(531\) | −5.27750 | − | 30.8257i | −0.229024 | − | 1.33772i | ||||
\(532\) | 4.55880 | + | 4.45692i | 0.197649 | + | 0.193232i | ||||
\(533\) | − | 8.66067i | − | 0.375135i | ||||||
\(534\) | 8.77801 | + | 24.3052i | 0.379862 | + | 1.05179i | ||||
\(535\) | 2.72337 | − | 1.57234i | 0.117741 | − | 0.0679781i | ||||
\(536\) | 8.62689 | − | 4.98074i | 0.372625 | − | 0.215135i | ||||
\(537\) | 8.47044 | + | 23.4536i | 0.365526 | + | 1.01210i | ||||
\(538\) | 9.53588i | 0.411121i | ||||||||
\(539\) | 7.02450 | + | 11.5556i | 0.302567 | + | 0.497736i | ||||
\(540\) | −5.51209 | + | 9.38486i | −0.237202 | + | 0.403860i | ||||
\(541\) | −15.0677 | + | 26.0980i | −0.647810 | + | 1.12204i | 0.335835 | + | 0.941921i | \(0.390982\pi\) |
−0.983645 | + | 0.180119i | \(0.942352\pi\) | |||||||
\(542\) | −12.7453 | − | 22.0755i | −0.547457 | − | 0.948224i | ||||
\(543\) | −15.8208 | − | 2.83021i | −0.678935 | − | 0.121456i | ||||
\(544\) | −0.599220 | − | 0.345960i | −0.0256914 | − | 0.0148329i | ||||
\(545\) | −7.86423 | −0.336866 | ||||||||
\(546\) | −4.56144 | + | 0.439616i | −0.195212 | + | 0.0188138i | ||||
\(547\) | −7.84538 | −0.335444 | −0.167722 | − | 0.985834i | \(-0.553641\pi\) | ||||
−0.167722 | + | 0.985834i | \(0.553641\pi\) | |||||||
\(548\) | 12.3253 | + | 7.11601i | 0.526511 | + | 0.303981i | ||||
\(549\) | −6.47369 | − | 7.79342i | −0.276290 | − | 0.332615i | ||||
\(550\) | −0.591778 | − | 1.02499i | −0.0252335 | − | 0.0437057i | ||||
\(551\) | 4.67672 | − | 8.10032i | 0.199235 | − | 0.345085i | ||||
\(552\) | −4.81401 | − | 4.05987i | −0.204898 | − | 0.172800i | ||||
\(553\) | 11.8955 | + | 42.4692i | 0.505849 | + | 1.80598i | ||||
\(554\) | 19.4594i | 0.826749i | ||||||||
\(555\) | 24.4148 | − | 8.81757i | 1.03635 | − | 0.374285i | ||||
\(556\) | −7.30935 | + | 4.22006i | −0.309986 | + | 0.178970i | ||||
\(557\) | 10.8446 | − | 6.26115i | 0.459502 | − | 0.265294i | −0.252333 | − | 0.967640i | \(-0.581198\pi\) |
0.711835 | + | 0.702347i | \(0.247864\pi\) | |||||||
\(558\) | −2.65715 | − | 0.982113i | −0.112486 | − | 0.0415761i | ||||
\(559\) | − | 8.01907i | − | 0.339171i | ||||||
\(560\) | 5.36883 | + | 1.37375i | 0.226874 | + | 0.0580513i | ||||
\(561\) | −1.49262 | + | 1.76987i | −0.0630183 | + | 0.0747242i | ||||
\(562\) | −4.33408 | + | 7.50684i | −0.182822 | + | 0.316657i | ||||
\(563\) | −6.12663 | − | 10.6116i | −0.258207 | − | 0.447227i | 0.707555 | − | 0.706658i | \(-0.249798\pi\) |
−0.965762 | + | 0.259431i | \(0.916465\pi\) | |||||||
\(564\) | −1.34056 | + | 7.49370i | −0.0564478 | + | 0.315542i | ||||
\(565\) | 15.7115 | + | 9.07106i | 0.660989 | + | 0.381622i | ||||
\(566\) | 23.0361 | 0.968278 | ||||||||
\(567\) | 23.7183 | − | 2.10746i | 0.996076 | − | 0.0885052i | ||||
\(568\) | −3.58456 | −0.150405 | ||||||||
\(569\) | −34.2211 | − | 19.7576i | −1.43462 | − | 0.828281i | −0.437155 | − | 0.899386i | \(-0.644014\pi\) |
−0.997469 | + | 0.0711052i | \(0.977347\pi\) | |||||||
\(570\) | 1.53949 | − | 8.60569i | 0.0644820 | − | 0.360453i | ||||
\(571\) | 16.5630 | + | 28.6880i | 0.693141 | + | 1.20056i | 0.970803 | + | 0.239877i | \(0.0771071\pi\) |
−0.277662 | + | 0.960679i | \(0.589560\pi\) | |||||||
\(572\) | −0.965940 | + | 1.67306i | −0.0403880 | + | 0.0699541i | ||||
\(573\) | 3.78482 | − | 4.48787i | 0.158113 | − | 0.187483i | ||||
\(574\) | 22.0648 | − | 6.18029i | 0.920967 | − | 0.257960i | ||||
\(575\) | − | 2.22746i | − | 0.0928915i | ||||||
\(576\) | 2.81394 | + | 1.04007i | 0.117248 | + | 0.0433361i | ||||
\(577\) | 23.3130 | − | 13.4597i | 0.970531 | − | 0.560337i | 0.0711331 | − | 0.997467i | \(-0.477338\pi\) |
0.899398 | + | 0.437130i | \(0.144005\pi\) | |||||||
\(578\) | 14.3078 | − | 8.26062i | 0.595127 | − | 0.343597i | ||||
\(579\) | −20.4792 | + | 7.39621i | −0.851087 | + | 0.307376i | ||||
\(580\) | − | 8.13035i | − | 0.337594i | ||||||
\(581\) | −23.2768 | + | 23.8089i | −0.965686 | + | 0.987760i | ||||
\(582\) | −3.09764 | − | 2.61238i | −0.128401 | − | 0.108286i | ||||
\(583\) | −5.36708 | + | 9.29605i | −0.222282 | + | 0.385003i | ||||
\(584\) | 4.31085 | + | 7.46660i | 0.178384 | + | 0.308970i | ||||
\(585\) | 4.01517 | + | 4.83370i | 0.166007 | + | 0.199849i | ||||
\(586\) | 15.8004 | + | 9.12237i | 0.652709 | + | 0.376842i | ||||
\(587\) | −22.5994 | −0.932778 | −0.466389 | − | 0.884580i | \(-0.654445\pi\) | ||||
−0.466389 | + | 0.884580i | \(0.654445\pi\) | |||||||
\(588\) | −4.37507 | − | 11.3075i | −0.180425 | − | 0.466312i | ||||
\(589\) | 2.27544 | 0.0937577 | ||||||||
\(590\) | 18.9103 | + | 10.9178i | 0.778523 | + | 0.449481i | ||||
\(591\) | −20.5060 | − | 3.66835i | −0.843504 | − | 0.150896i | ||||
\(592\) | −3.57753 | − | 6.19647i | −0.147036 | − | 0.254673i | ||||
\(593\) | −16.5789 | + | 28.7155i | −0.680814 | + | 1.17920i | 0.293919 | + | 0.955830i | \(0.405040\pi\) |
−0.974733 | + | 0.223374i | \(0.928293\pi\) | |||||||
\(594\) | 5.08387 | − | 8.65579i | 0.208594 | − | 0.355151i | ||||
\(595\) | 2.68058 | − | 2.74185i | 0.109893 | − | 0.112405i | ||||
\(596\) | − | 0.0386143i | − | 0.00158170i | ||||||
\(597\) | 8.87187 | + | 24.5651i | 0.363102 | + | 1.00538i | ||||
\(598\) | −3.14870 | + | 1.81790i | −0.128760 | + | 0.0743396i | ||||
\(599\) | 39.7724 | − | 22.9626i | 1.62506 | − | 0.938227i | 0.639518 | − | 0.768776i | \(-0.279134\pi\) |
0.985539 | − | 0.169451i | \(-0.0541994\pi\) | |||||||
\(600\) | 0.360448 | + | 0.998037i | 0.0147152 | + | 0.0407447i | ||||
\(601\) | − | 17.7850i | − | 0.725466i | −0.931893 | − | 0.362733i | \(-0.881844\pi\) | ||
0.931893 | − | 0.362733i | \(-0.118156\pi\) | |||||||
\(602\) | 20.4302 | − | 5.72244i | 0.832672 | − | 0.233229i | ||||
\(603\) | 5.04297 | + | 29.4559i | 0.205366 | + | 1.19954i | ||||
\(604\) | 10.4122 | − | 18.0344i | 0.423664 | − | 0.733808i | ||||
\(605\) | 7.61161 | + | 13.1837i | 0.309456 | + | 0.535993i | ||||
\(606\) | 25.6206 | + | 4.58331i | 1.04076 | + | 0.186184i | ||||
\(607\) | 23.5234 | + | 13.5812i | 0.954785 | + | 0.551245i | 0.894564 | − | 0.446940i | \(-0.147486\pi\) |
0.0602210 | + | 0.998185i | \(0.480819\pi\) | |||||||
\(608\) | −2.40970 | −0.0977264 | ||||||||
\(609\) | −14.4803 | + | 10.3306i | −0.586770 | + | 0.418616i | ||||
\(610\) | 7.07377 | 0.286409 | ||||||||
\(611\) | 3.80633 | + | 2.19759i | 0.153988 | + | 0.0889048i | ||||
\(612\) | 1.59674 | − | 1.32635i | 0.0645444 | − | 0.0536145i | ||||
\(613\) | −11.4277 | − | 19.7933i | −0.461559 | − | 0.799444i | 0.537480 | − | 0.843277i | \(-0.319376\pi\) |
−0.999039 | + | 0.0438328i | \(0.986043\pi\) | |||||||
\(614\) | −10.9255 | + | 18.9235i | −0.440917 | + | 0.763691i | ||||
\(615\) | −24.0192 | − | 20.2565i | −0.968549 | − | 0.816822i | ||||
\(616\) | −4.95175 | − | 1.26702i | −0.199512 | − | 0.0510499i | ||||
\(617\) | − | 31.8388i | − | 1.28178i | −0.767632 | − | 0.640891i | \(-0.778565\pi\) | ||
0.767632 | − | 0.640891i | \(-0.221435\pi\) | |||||||
\(618\) | −30.4287 | + | 10.9895i | −1.22402 | + | 0.442064i | ||||
\(619\) | −25.4744 | + | 14.7077i | −1.02390 | + | 0.591151i | −0.915232 | − | 0.402926i | \(-0.867993\pi\) |
−0.108672 | + | 0.994078i | \(0.534660\pi\) | |||||||
\(620\) | 1.71290 | − | 0.988945i | 0.0687918 | − | 0.0397170i | ||||
\(621\) | 16.4311 | − | 9.32381i | 0.659359 | − | 0.374152i | ||||
\(622\) | 2.82818i | 0.113400i | ||||||||
\(623\) | 10.6468 | + | 38.0111i | 0.426555 | + | 1.52288i | ||||
\(624\) | 1.11664 | − | 1.32406i | 0.0447012 | − | 0.0530047i | ||||
\(625\) | 10.7807 | − | 18.6728i | 0.431229 | − | 0.746910i | ||||
\(626\) | −4.95414 | − | 8.58082i | −0.198007 | − | 0.342959i | ||||
\(627\) | −1.41989 | + | 7.93715i | −0.0567049 | + | 0.316979i | ||||
\(628\) | 3.98152 | + | 2.29873i | 0.158880 | + | 0.0917294i | ||||
\(629\) | −4.95073 | −0.197399 | ||||||||
\(630\) | −9.44957 | + | 13.6788i | −0.376480 | + | 0.544976i | ||||
\(631\) | 20.0601 | 0.798581 | 0.399291 | − | 0.916824i | \(-0.369256\pi\) | ||||
0.399291 | + | 0.916824i | \(0.369256\pi\) | |||||||
\(632\) | −14.4363 | − | 8.33482i | −0.574247 | − | 0.331541i | ||||
\(633\) | 3.36417 | − | 18.8057i | 0.133714 | − | 0.747458i | ||||
\(634\) | −8.78492 | − | 15.2159i | −0.348894 | − | 0.604302i | ||||
\(635\) | −2.27895 | + | 3.94726i | −0.0904374 | + | 0.156642i | ||||
\(636\) | 6.20439 | − | 7.35688i | 0.246020 | − | 0.291719i | ||||
\(637\) | −6.99821 | + | 0.158181i | −0.277279 | + | 0.00626736i | ||||
\(638\) | 7.49874i | 0.296878i | ||||||||
\(639\) | 3.72818 | − | 10.0867i | 0.147484 | − | 0.399025i | ||||
\(640\) | −1.81398 | + | 1.04730i | −0.0717038 | + | 0.0413982i | ||||
\(641\) | −39.6565 | + | 22.8957i | −1.56634 | + | 0.904326i | −0.569749 | + | 0.821819i | \(0.692960\pi\) |
−0.996590 | + | 0.0825076i | \(0.973707\pi\) | |||||||
\(642\) | 2.44575 | − | 0.883300i | 0.0965261 | − | 0.0348611i | ||||
\(643\) | 21.5260i | 0.848904i | 0.905450 | + | 0.424452i | \(0.139533\pi\) | ||||
−0.905450 | + | 0.424452i | \(0.860467\pi\) | |||||||
\(644\) | −6.87840 | − | 6.72468i | −0.271047 | − | 0.264990i | ||||
\(645\) | −22.2398 | − | 18.7559i | −0.875693 | − | 0.738512i | ||||
\(646\) | −0.833662 | + | 1.44394i | −0.0328000 | + | 0.0568112i | ||||
\(647\) | −7.06767 | − | 12.2416i | −0.277859 | − | 0.481265i | 0.692994 | − | 0.720944i | \(-0.256291\pi\) |
−0.970852 | + | 0.239678i | \(0.922958\pi\) | |||||||
\(648\) | −5.85337 | + | 6.83653i | −0.229942 | + | 0.268564i | ||||
\(649\) | −17.4412 | − | 10.0697i | −0.684627 | − | 0.395270i | ||||
\(650\) | 0.612645 | 0.0240299 | ||||||||
\(651\) | −3.93777 | − | 1.79413i | −0.154333 | − | 0.0703176i | ||||
\(652\) | −19.8760 | −0.778404 | ||||||||
\(653\) | 14.0019 | + | 8.08399i | 0.547936 | + | 0.316351i | 0.748289 | − | 0.663373i | \(-0.230876\pi\) |
−0.200353 | + | 0.979724i | \(0.564209\pi\) | |||||||
\(654\) | −6.40140 | − | 1.14516i | −0.250314 | − | 0.0447792i | ||||
\(655\) | −6.86287 | − | 11.8868i | −0.268155 | − | 0.464457i | ||||
\(656\) | −4.33034 | + | 7.50036i | −0.169071 | + | 0.292840i | ||||
\(657\) | −25.4941 | + | 4.36471i | −0.994621 | + | 0.170284i | ||||
\(658\) | −2.88258 | + | 11.2656i | −0.112374 | + | 0.439178i | ||||
\(659\) | 42.0011i | 1.63613i | 0.575126 | + | 0.818065i | \(0.304953\pi\) | ||||
−0.575126 | + | 0.818065i | \(0.695047\pi\) | |||||||
\(660\) | 2.38076 | + | 6.59204i | 0.0926710 | + | 0.256595i | ||||
\(661\) | 4.44931 | − | 2.56881i | 0.173058 | − | 0.0999152i | −0.410969 | − | 0.911649i | \(-0.634810\pi\) |
0.584027 | + | 0.811734i | \(0.301476\pi\) | |||||||
\(662\) | 13.3408 | − | 7.70234i | 0.518507 | − | 0.299360i | ||||
\(663\) | −0.407090 | − | 1.12718i | −0.0158101 | − | 0.0437761i | ||||
\(664\) | − | 12.5850i | − | 0.488393i | ||||||
\(665\) | 3.31032 | − | 12.9373i | 0.128369 | − | 0.501687i | ||||
\(666\) | 21.1574 | − | 3.62223i | 0.819831 | − | 0.140359i | ||||
\(667\) | −7.05633 | + | 12.2219i | −0.273222 | + | 0.473235i | ||||
\(668\) | 2.68127 | + | 4.64409i | 0.103741 | + | 0.179685i | ||||
\(669\) | −24.3632 | − | 4.35837i | −0.941936 | − | 0.168504i | ||||
\(670\) | −18.0699 | − | 10.4327i | −0.698101 | − | 0.403049i | ||||
\(671\) | −6.52424 | −0.251866 | ||||||||
\(672\) | 4.17013 | + | 1.90000i | 0.160866 | + | 0.0732941i | ||||
\(673\) | −37.9013 | −1.46099 | −0.730494 | − | 0.682919i | \(-0.760710\pi\) | ||||
−0.730494 | + | 0.682919i | \(0.760710\pi\) | |||||||
\(674\) | 12.5198 | + | 7.22830i | 0.482244 | + | 0.278424i | ||||
\(675\) | −3.18331 | − | 0.0237437i | −0.122526 | − | 0.000913897i | ||||
\(676\) | −0.500000 | − | 0.866025i | −0.0192308 | − | 0.0333087i | ||||
\(677\) | 13.4434 | − | 23.2847i | 0.516672 | − | 0.894902i | −0.483141 | − | 0.875543i | \(-0.660504\pi\) |
0.999813 | − | 0.0193592i | \(-0.00616261\pi\) | |||||||
\(678\) | 11.4681 | + | 9.67160i | 0.440431 | + | 0.371435i | ||||
\(679\) | −4.42599 | − | 4.32708i | −0.169854 | − | 0.166058i | ||||
\(680\) | 1.44930i | 0.0555780i | ||||||||
\(681\) | −33.9194 | + | 12.2502i | −1.29979 | + | 0.469430i | ||||
\(682\) | −1.57983 | + | 0.912118i | −0.0604950 | + | 0.0349268i | ||||
\(683\) | −8.54705 | + | 4.93464i | −0.327044 | + | 0.188819i | −0.654528 | − | 0.756038i | \(-0.727133\pi\) |
0.327484 | + | 0.944857i | \(0.393799\pi\) | |||||||
\(684\) | 2.50625 | − | 6.78077i | 0.0958289 | − | 0.259269i | ||||
\(685\) | − | 29.8104i | − | 1.13900i | ||||||
\(686\) | −5.39695 | − | 17.7165i | −0.206056 | − | 0.676418i | ||||
\(687\) | −0.366368 | + | 0.434422i | −0.0139778 | + | 0.0165742i | ||||
\(688\) | −4.00954 | + | 6.94472i | −0.152862 | + | 0.264765i | ||||
\(689\) | −2.77816 | − | 4.81192i | −0.105840 | − | 0.183319i | ||||
\(690\) | −2.32280 | + | 12.9844i | −0.0884277 | + | 0.494309i | ||||
\(691\) | 10.7402 | + | 6.20088i | 0.408578 | + | 0.235893i | 0.690179 | − | 0.723639i | \(-0.257532\pi\) |
−0.281601 | + | 0.959532i | \(0.590865\pi\) | |||||||
\(692\) | 0.138867 | 0.00527892 | ||||||||
\(693\) | 8.71547 | − | 12.6161i | 0.331073 | − | 0.479247i | ||||
\(694\) | −12.5620 | −0.476846 | ||||||||
\(695\) | 15.3102 | + | 8.83933i | 0.580748 | + | 0.335295i | ||||
\(696\) | 1.18391 | − | 6.61802i | 0.0448759 | − | 0.250855i | ||||
\(697\) | 2.99625 | + | 5.18965i | 0.113491 | + | 0.196572i | ||||
\(698\) | 8.85051 | − | 15.3295i | 0.334997 | − | 0.580232i | ||||
\(699\) | −10.0625 | + | 11.9316i | −0.380598 | + | 0.451295i | ||||
\(700\) | 0.437186 | + | 1.56083i | 0.0165241 | + | 0.0589940i | ||||
\(701\) | − | 2.73572i | − | 0.103327i | −0.998665 | − | 0.0516634i | \(-0.983548\pi\) | ||
0.998665 | − | 0.0516634i | \(-0.0164523\pi\) | |||||||
\(702\) | 2.56444 | + | 4.51925i | 0.0967886 | + | 0.170568i | ||||
\(703\) | −14.9317 | + | 8.62079i | −0.563158 | + | 0.325139i | ||||
\(704\) | 1.67306 | − | 0.965940i | 0.0630557 | − | 0.0364052i | ||||
\(705\) | 14.9974 | − | 5.41641i | 0.564834 | − | 0.203994i | ||||
\(706\) | 0.445314i | 0.0167596i | ||||||||
\(707\) | 38.5165 | + | 9.85538i | 1.44856 | + | 0.370650i | ||||
\(708\) | 13.8029 | + | 11.6406i | 0.518746 | + | 0.437482i | ||||
\(709\) | 4.28476 | − | 7.42143i | 0.160918 | − | 0.278718i | −0.774280 | − | 0.632843i | \(-0.781888\pi\) |
0.935198 | + | 0.354125i | \(0.115221\pi\) | |||||||
\(710\) | 3.75411 | + | 6.50231i | 0.140889 | + | 0.244028i | ||||
\(711\) | 38.4684 | − | 31.9542i | 1.44268 | − | 1.19838i | ||||
\(712\) | −12.9209 | − | 7.45988i | −0.484231 | − | 0.279571i | ||||
\(713\) | −3.43322 | −0.128575 | ||||||||
\(714\) | 2.58122 | − | 1.84150i | 0.0965997 | − | 0.0689165i | ||||
\(715\) | 4.04652 | 0.151331 | ||||||||
\(716\) | −12.4682 | − | 7.19850i | −0.465957 | − | 0.269020i | ||||
\(717\) | −48.1078 | − | 8.60608i | −1.79662 | − | 0.321400i | ||||
\(718\) | −10.3348 | − | 17.9004i | −0.385691 | − | 0.668036i | ||||
\(719\) | 12.6631 | − | 21.9332i | 0.472255 | − | 0.817969i | −0.527241 | − | 0.849716i | \(-0.676774\pi\) |
0.999496 | + | 0.0317464i | \(0.0101069\pi\) | |||||||
\(720\) | −1.06039 | − | 6.19369i | −0.0395183 | − | 0.230825i | ||||
\(721\) | −47.5876 | + | 13.3292i | −1.77225 | + | 0.496404i | ||||
\(722\) | − | 13.1933i | − | 0.491005i | ||||||
\(723\) | −6.74559 | − | 18.6777i | −0.250871 | − | 0.694631i | ||||
\(724\) | 8.03597 | − | 4.63957i | 0.298654 | − | 0.172428i | ||||
\(725\) | 2.05943 | − | 1.18901i | 0.0764853 | − | 0.0441588i | ||||
\(726\) | 4.27602 | + | 11.8398i | 0.158698 | + | 0.439415i | ||||
\(727\) | − | 48.9569i | − | 1.81571i | −0.419284 | − | 0.907855i | \(-0.637719\pi\) | ||
0.419284 | − | 0.907855i | \(-0.362281\pi\) | |||||||
\(728\) | 1.84957 | − | 1.89185i | 0.0685496 | − | 0.0701166i | ||||
\(729\) | −13.1497 | − | 23.5815i | −0.487026 | − | 0.873387i | ||||
\(730\) | 9.02951 | − | 15.6396i | 0.334197 | − | 0.578846i | ||||
\(731\) | 2.77428 | + | 4.80519i | 0.102610 | + | 0.177726i | ||||
\(732\) | 5.75798 | + | 1.03005i | 0.212821 | + | 0.0380719i | ||||
\(733\) | 43.4681 | + | 25.0963i | 1.60553 | + | 0.926954i | 0.990353 | + | 0.138566i | \(0.0442494\pi\) |
0.615179 | + | 0.788388i | \(0.289084\pi\) | |||||||
\(734\) | −19.8731 | −0.733528 | ||||||||
\(735\) | −15.9295 | + | 19.7786i | −0.587568 | + | 0.729545i | ||||
\(736\) | 3.63581 | 0.134018 | ||||||||
\(737\) | 16.6661 | + | 9.62219i | 0.613905 | + | 0.354438i | ||||
\(738\) | −16.6017 | − | 19.9862i | −0.611119 | − | 0.735702i | ||||
\(739\) | −8.36739 | − | 14.4927i | −0.307799 | − | 0.533124i | 0.670081 | − | 0.742288i | \(-0.266259\pi\) |
−0.977881 | + | 0.209164i | \(0.932926\pi\) | |||||||
\(740\) | −7.49350 | + | 12.9791i | −0.275467 | + | 0.477122i | ||||
\(741\) | −3.19058 | − | 2.69076i | −0.117209 | − | 0.0988477i | ||||
\(742\) | 10.2768 | − | 10.5117i | 0.377274 | − | 0.385898i | ||||
\(743\) | − | 6.98714i | − | 0.256333i | −0.991753 | − | 0.128167i | \(-0.959091\pi\) | ||
0.991753 | − | 0.128167i | \(-0.0409092\pi\) | |||||||
\(744\) | 1.53829 | − | 0.555565i | 0.0563965 | − | 0.0203680i | ||||
\(745\) | −0.0700454 | + | 0.0404408i | −0.00256627 | + | 0.00148163i | ||||
\(746\) | 13.2365 | − | 7.64212i | 0.484624 | − | 0.279798i | ||||
\(747\) | 35.4134 | + | 13.0892i | 1.29571 | + | 0.478910i | ||||
\(748\) | − | 1.33671i | − | 0.0488748i | ||||||
\(749\) | 3.82492 | − | 1.07135i | 0.139760 | − | 0.0391463i | ||||
\(750\) | 13.1275 | − | 15.5659i | 0.479347 | − | 0.568388i | ||||
\(751\) | 0.680716 | − | 1.17903i | 0.0248397 | − | 0.0430236i | −0.853338 | − | 0.521358i | \(-0.825426\pi\) |
0.878178 | + | 0.478334i | \(0.158759\pi\) | |||||||
\(752\) | −2.19759 | − | 3.80633i | −0.0801377 | − | 0.138803i | ||||
\(753\) | 7.85702 | − | 43.9206i | 0.286326 | − | 1.60055i | ||||
\(754\) | −3.36154 | − | 1.94079i | −0.122420 | − | 0.0706793i | ||||
\(755\) | −43.6186 | −1.58744 | ||||||||
\(756\) | −9.68370 | + | 9.75838i | −0.352193 | + | 0.354909i | ||||
\(757\) | −17.6138 | −0.640186 | −0.320093 | − | 0.947386i | \(-0.603714\pi\) | ||||
−0.320093 | + | 0.947386i | \(0.603714\pi\) | |||||||
\(758\) | −20.6819 | − | 11.9407i | −0.751200 | − | 0.433705i | ||||
\(759\) | 2.14236 | − | 11.9757i | 0.0777626 | − | 0.434691i | ||||
\(760\) | 2.52369 | + | 4.37115i | 0.0915437 | + | 0.158558i | ||||
\(761\) | 10.6541 | − | 18.4534i | 0.386210 | − | 0.668935i | −0.605727 | − | 0.795673i | \(-0.707117\pi\) |
0.991936 | + | 0.126738i | \(0.0404508\pi\) | |||||||
\(762\) | −2.42983 | + | 2.88118i | −0.0880233 | + | 0.104374i | ||||
\(763\) | −9.62349 | − | 2.46240i | −0.348394 | − | 0.0891450i | ||||
\(764\) | 3.38949i | 0.122627i | ||||||||
\(765\) | −4.07824 | − | 1.50736i | −0.147449 | − | 0.0544988i | ||||
\(766\) | 32.5547 | − | 18.7955i | 1.17625 | − | 0.679108i | ||||
\(767\) | 9.02810 | − | 5.21237i | 0.325986 | − | 0.188208i | ||||
\(768\) | −1.62906 | + | 0.588348i | −0.0587838 | + | 0.0212302i | ||||
\(769\) | − | 49.2139i | − | 1.77470i | −0.461099 | − | 0.887349i | \(-0.652545\pi\) | ||
0.461099 | − | 0.887349i | \(-0.347455\pi\) | |||||||
\(770\) | 2.88761 | + | 10.3093i | 0.104062 | + | 0.371522i | ||||
\(771\) | 18.2555 | + | 15.3957i | 0.657454 | + | 0.554461i | ||||
\(772\) | 6.28558 | − | 10.8869i | 0.226223 | − | 0.391830i | ||||
\(773\) | −14.9637 | − | 25.9179i | −0.538208 | − | 0.932203i | −0.999001 | − | 0.0446955i | \(-0.985768\pi\) |
0.460793 | − | 0.887508i | \(-0.347565\pi\) | |||||||
\(774\) | −15.3719 | − | 18.5056i | −0.552530 | − | 0.665169i | ||||
\(775\) | 0.501003 | + | 0.289254i | 0.0179965 | + | 0.0103903i | ||||
\(776\) | 2.33951 | 0.0839833 | ||||||||
\(777\) | 32.6374 | − | 3.14548i | 1.17086 | − | 0.112843i | ||||
\(778\) | −29.4790 | −1.05687 | ||||||||
\(779\) | 18.0737 | + | 10.4348i | 0.647556 | + | 0.373867i | ||||
\(780\) | −3.57126 | − | 0.638869i | −0.127872 | − | 0.0228752i | ||||
\(781\) | −3.46247 | − | 5.99718i | −0.123897 | − | 0.214596i | ||||
\(782\) | 1.25784 | − | 2.17865i | 0.0449804 | − | 0.0779084i | ||||
\(783\) | 17.3914 | + | 10.2146i | 0.621517 | + | 0.365041i | ||||
\(784\) | 6.13972 | + | 3.36212i | 0.219276 | + | 0.120076i | ||||
\(785\) | − | 9.62985i | − | 0.343704i | ||||||
\(786\) | −3.85539 | − | 10.6751i | −0.137517 | − | 0.380769i | ||||
\(787\) | 17.6377 | − | 10.1831i | 0.628715 | − | 0.362989i | −0.151539 | − | 0.988451i | \(-0.548423\pi\) |
0.780254 | + | 0.625462i | \(0.215090\pi\) | |||||||
\(788\) | 10.4158 | − | 6.01354i | 0.371046 | − | 0.214224i | ||||
\(789\) | 12.6172 | + | 34.9354i | 0.449183 | + | 1.24373i | ||||
\(790\) | 34.9163i | 1.24226i | ||||||||
\(791\) | 16.3860 | + | 16.0198i | 0.582619 | + | 0.569599i | ||||
\(792\) | 0.978010 | + | 5.71253i | 0.0347521 | + | 0.202986i | ||||
\(793\) | 1.68857 | − | 2.92469i | 0.0599630 | − | 0.103859i | ||||
\(794\) | 9.42604 | + | 16.3264i | 0.334518 | + | 0.579402i | ||||
\(795\) | −19.8431 | − | 3.54976i | −0.703762 | − | 0.125897i | ||||
\(796\) | −13.0591 | − | 7.53965i | −0.462866 | − | 0.267236i | ||||
\(797\) | 14.7873 | 0.523792 | 0.261896 | − | 0.965096i | \(-0.415652\pi\) | ||||
0.261896 | + | 0.965096i | \(0.415652\pi\) | |||||||
\(798\) | 4.57844 | − | 10.0488i | 0.162075 | − | 0.355723i | ||||
\(799\) | −3.04111 | −0.107587 | ||||||||
\(800\) | −0.530566 | − | 0.306322i | −0.0187583 | − | 0.0108301i | ||||
\(801\) | 34.4302 | − | 28.5999i | 1.21653 | − | 1.01053i | ||||
\(802\) | −5.77115 | − | 9.99593i | −0.203786 | − | 0.352968i | ||||
\(803\) | −8.32804 | + | 14.4246i | −0.293890 | + | 0.509033i | ||||
\(804\) | −13.1896 | − | 11.1233i | −0.465160 | − | 0.392290i | ||||
\(805\) | −4.99467 | + | 19.5200i | −0.176039 | + | 0.687991i | ||||
\(806\) | − | 0.944280i | − | 0.0332608i | ||||||
\(807\) | 15.5346 | − | 5.61041i | 0.546842 | − | 0.197496i | ||||
\(808\) | −13.0136 | + | 7.51343i | −0.457819 | + | 0.264322i | ||||
\(809\) | 35.4312 | − | 20.4562i | 1.24569 | − | 0.719202i | 0.275446 | − | 0.961317i | \(-0.411174\pi\) |
0.970248 | + | 0.242115i | \(0.0778411\pi\) | |||||||
\(810\) | 18.5315 | + | 3.45798i | 0.651132 | + | 0.121501i | ||||
\(811\) | − | 15.0715i | − | 0.529231i | −0.964354 | − | 0.264616i | \(-0.914755\pi\) | ||
0.964354 | − | 0.264616i | \(-0.0852451\pi\) | |||||||
\(812\) | 2.54573 | − | 9.94915i | 0.0893377 | − | 0.349147i | ||||
\(813\) | −28.4637 | + | 33.7510i | −0.998266 | + | 1.18370i | ||||
\(814\) | 6.91136 | − | 11.9708i | 0.242243 | − | 0.419577i | ||||
\(815\) | 20.8161 | + | 36.0546i | 0.729157 | + | 1.26294i | ||||
\(816\) | −0.211041 | + | 1.17971i | −0.00738790 | + | 0.0412982i | ||||
\(817\) | 16.7347 | + | 9.66180i | 0.585474 | + | 0.338024i | ||||
\(818\) | −24.0433 | −0.840655 | ||||||||
\(819\) | 3.39988 | + | 7.17223i | 0.118801 | + | 0.250618i | ||||
\(820\) | 18.1407 | 0.633499 | ||||||||
\(821\) | −14.4930 | − | 8.36756i | −0.505811 | − | 0.292030i | 0.225299 | − | 0.974290i | \(-0.427664\pi\) |
−0.731110 | + | 0.682260i | \(0.760997\pi\) | |||||||
\(822\) | 4.34087 | − | 24.2654i | 0.151405 | − | 0.846352i | ||||
\(823\) | 26.3860 | + | 45.7019i | 0.919757 | + | 1.59307i | 0.799783 | + | 0.600290i | \(0.204948\pi\) |
0.119975 | + | 0.992777i | \(0.461719\pi\) | |||||||
\(824\) | 9.33933 | − | 16.1762i | 0.325351 | − | 0.563524i | ||||
\(825\) | −1.32160 | + | 1.56709i | −0.0460123 | + | 0.0545592i | ||||
\(826\) | 19.7220 | + | 19.2813i | 0.686218 | + | 0.670882i | ||||
\(827\) | 35.5394i | 1.23583i | 0.786246 | + | 0.617913i | \(0.212022\pi\) | ||||
−0.786246 | + | 0.617913i | \(0.787978\pi\) | |||||||
\(828\) | −3.78148 | + | 10.2309i | −0.131415 | + | 0.355550i | ||||
\(829\) | 23.3896 | − | 13.5040i | 0.812354 | − | 0.469013i | −0.0354185 | − | 0.999373i | \(-0.511276\pi\) |
0.847773 | + | 0.530360i | \(0.177943\pi\) | |||||||
\(830\) | −22.8289 | + | 13.1803i | −0.792403 | + | 0.457494i | ||||
\(831\) | 31.7005 | − | 11.4489i | 1.09968 | − | 0.397157i | ||||
\(832\) | 1.00000i | 0.0346688i | ||||||||
\(833\) | 4.13875 | − | 2.51589i | 0.143399 | − | 0.0871703i | ||||
\(834\) | 11.1752 | + | 9.42453i | 0.386965 | + | 0.326345i | ||||
\(835\) | 5.61619 | − | 9.72752i | 0.194356 | − | 0.336635i | ||||
\(836\) | −2.32763 | − | 4.03158i | −0.0805028 | − | 0.139435i | ||||
\(837\) | −0.0365966 | + | 4.90648i | −0.00126496 | + | 0.169593i | ||||
\(838\) | −3.14928 | − | 1.81824i | −0.108790 | − | 0.0628099i | ||||
\(839\) | −12.4473 | −0.429730 | −0.214865 | − | 0.976644i | \(-0.568931\pi\) | ||||
−0.214865 | + | 0.976644i | \(0.568931\pi\) | |||||||
\(840\) | −0.920820 | − | 9.55440i | −0.0317713 | − | 0.329658i | ||||
\(841\) | 13.9334 | 0.480462 | ||||||||
\(842\) | −0.0278313 | − | 0.0160684i | −0.000959130 | − | 0.000553754i | ||||
\(843\) | 14.7791 | + | 2.64385i | 0.509018 | + | 0.0910591i | ||||
\(844\) | 5.51491 | + | 9.55210i | 0.189831 | + | 0.328797i | ||||
\(845\) | −1.04730 | + | 1.81398i | −0.0360282 | + | 0.0624027i | ||||
\(846\) | 12.9964 | − | 2.22504i | 0.446826 | − | 0.0764986i | ||||
\(847\) | 5.18636 | + | 18.5163i | 0.178205 | + | 0.636226i | ||||
\(848\) | 5.55632i | 0.190805i | ||||||||
\(849\) | −13.5532 | − | 37.5272i | −0.465145 | − | 1.28793i | ||||
\(850\) | −0.367109 | + | 0.211951i | −0.0125917 | + | 0.00726984i | ||||
\(851\) | 22.5292 | − | 13.0072i | 0.772290 | − | 0.445882i | ||||
\(852\) | 2.10897 | + | 5.83948i | 0.0722521 | + | 0.200057i | ||||
\(853\) | 37.5892i | 1.28703i | 0.765433 | + | 0.643515i | \(0.222525\pi\) | ||||
−0.765433 | + | 0.643515i | \(0.777475\pi\) | |||||||
\(854\) | 8.65621 | + | 2.21490i | 0.296209 | + | 0.0757924i | ||||
\(855\) | −14.9250 | + | 2.55522i | −0.510423 | + | 0.0873866i | ||||
\(856\) | −0.750662 | + | 1.30018i | −0.0256571 | + | 0.0444394i | ||||
\(857\) | −6.33608 | − | 10.9744i | −0.216436 | − | 0.374879i | 0.737280 | − | 0.675588i | \(-0.236110\pi\) |
−0.953716 | + | 0.300709i | \(0.902777\pi\) | |||||||
\(858\) | 3.29383 | + | 0.589238i | 0.112449 | + | 0.0201162i | ||||
\(859\) | −10.2996 | − | 5.94647i | −0.351417 | − | 0.202891i | 0.313892 | − | 0.949459i | \(-0.398367\pi\) |
−0.665309 | + | 0.746568i | \(0.731700\pi\) | |||||||
\(860\) | 16.7968 | 0.572765 | ||||||||
\(861\) | −23.0499 | − | 32.3088i | −0.785537 | − | 1.10108i | ||||
\(862\) | −16.5585 | −0.563984 | ||||||||
\(863\) | 14.3740 | + | 8.29886i | 0.489298 | + | 0.282496i | 0.724283 | − | 0.689502i | \(-0.242171\pi\) |
−0.234985 | + | 0.971999i | \(0.575504\pi\) | |||||||
\(864\) | 0.0387561 | − | 5.19601i | 0.00131851 | − | 0.176772i | ||||
\(865\) | −0.145435 | − | 0.251901i | −0.00494494 | − | 0.00856489i | ||||
\(866\) | −11.7825 | + | 20.4079i | −0.400385 | + | 0.693488i | ||||
\(867\) | −21.8751 | − | 18.4482i | −0.742916 | − | 0.626534i | ||||
\(868\) | 2.40574 | − | 0.673841i | 0.0816561 | − | 0.0228717i | ||||
\(869\) | − | 32.2038i | − | 1.09244i | ||||||
\(870\) | −13.2449 | + | 4.78347i | −0.449042 | + | 0.162175i | ||||
\(871\) | −8.62689 | + | 4.98074i | −0.292311 | + | 0.168766i | ||||
\(872\) | 3.25151 | − | 1.87726i | 0.110110 | − | 0.0635721i | ||||
\(873\) | −2.43324 | + | 6.58323i | −0.0823526 | + | 0.222809i | ||||
\(874\) | − | 8.76123i | − | 0.296353i | ||||||
\(875\) | 21.7440 | − | 22.2411i | 0.735082 | − | 0.751885i | ||||
\(876\) | 9.62729 | − | 11.4156i | 0.325276 | − | 0.385697i | ||||
\(877\) | 18.9926 | − | 32.8962i | 0.641336 | − | 1.11083i | −0.343799 | − | 0.939043i | \(-0.611714\pi\) |
0.985135 | − | 0.171783i | \(-0.0549528\pi\) | |||||||
\(878\) | −0.637611 | − | 1.10437i | −0.0215183 | − | 0.0372708i | ||||
\(879\) | 5.56478 | − | 31.1070i | 0.187695 | − | 1.04921i | ||||
\(880\) | −3.50439 | − | 2.02326i | −0.118133 | − | 0.0682041i | ||||
\(881\) | 52.5629 | 1.77089 | 0.885444 | − | 0.464746i | \(-0.153854\pi\) | ||||
0.885444 | + | 0.464746i | \(0.153854\pi\) | |||||||
\(882\) | −15.8465 | + | 13.7800i | −0.533580 | + | 0.463996i | ||||
\(883\) | 21.4529 | 0.721948 | 0.360974 | − | 0.932576i | \(-0.382444\pi\) | ||||
0.360974 | + | 0.932576i | \(0.382444\pi\) | |||||||
\(884\) | 0.599220 | + | 0.345960i | 0.0201540 | + | 0.0116359i | ||||
\(885\) | 6.66005 | − | 37.2295i | 0.223875 | − | 1.25146i | ||||
\(886\) | −3.35151 | − | 5.80498i | −0.112596 | − | 0.195022i | ||||
\(887\) | −5.84800 | + | 10.1290i | −0.196357 | + | 0.340099i | −0.947344 | − | 0.320217i | \(-0.896244\pi\) |
0.750988 | + | 0.660316i | \(0.229578\pi\) | |||||||
\(888\) | −7.98960 | + | 9.47370i | −0.268113 | + | 0.317917i | ||||
\(889\) | −4.02471 | + | 4.11671i | −0.134984 | + | 0.138070i | ||||
\(890\) | 31.2510i | 1.04753i | ||||||||
\(891\) | −17.0919 | − | 3.18934i | −0.572600 | − | 0.106847i | ||||
\(892\) | 12.3750 | − | 7.14470i | 0.414345 | − | 0.239222i | ||||
\(893\) | −9.17213 | + | 5.29553i | −0.306934 | + | 0.177208i | ||||
\(894\) | −0.0629051 | + | 0.0227186i | −0.00210386 | + | 0.000759824i | ||||
\(895\) | 30.1560i | 1.00800i | ||||||||
\(896\) | −2.54770 | + | 0.713604i | −0.0851126 | + | 0.0238398i | ||||
\(897\) | 4.81401 | + | 4.05987i | 0.160735 | + | 0.135555i | ||||
\(898\) | 5.72116 | − | 9.90935i | 0.190918 | − | 0.330679i | ||||
\(899\) | −1.83265 | − | 3.17423i | −0.0611221 | − | 0.105867i | ||||
\(900\) | 1.41380 | − | 1.17439i | 0.0471265 | − | 0.0391462i | ||||
\(901\) | 3.32946 | + | 1.92227i | 0.110920 | + | 0.0640400i | ||||
\(902\) | −16.7314 | −0.557094 | ||||||||
\(903\) | −21.3423 | − | 29.9153i | −0.710226 | − | 0.995518i | ||||
\(904\) | −8.66137 | −0.288073 | ||||||||
\(905\) | −16.8322 | − | 9.71805i | −0.559520 | − | 0.323039i | ||||
\(906\) | −35.5051 | − | 6.35157i | −1.17958 | − | 0.211017i | ||||
\(907\) | 25.5815 | + | 44.3084i | 0.849419 | + | 1.47124i | 0.881727 | + | 0.471759i | \(0.156381\pi\) |
−0.0323084 | + | 0.999478i | \(0.510286\pi\) | |||||||
\(908\) | 10.4107 | − | 18.0319i | 0.345491 | − | 0.598409i | ||||
\(909\) | −7.60731 | − | 44.4341i | −0.252319 | − | 1.47379i | ||||
\(910\) | −5.36883 | − | 1.37375i | −0.177975 | − | 0.0455392i | ||||
\(911\) | 43.0375i | 1.42589i | 0.701218 | + | 0.712947i | \(0.252640\pi\) | ||||
−0.701218 | + | 0.712947i | \(0.747360\pi\) | |||||||
\(912\) | 1.41774 | + | 3.92556i | 0.0469462 | + | 0.129988i | ||||
\(913\) | 21.0554 | − | 12.1564i | 0.696833 | − | 0.402317i | ||||
\(914\) | −27.6958 | + | 15.9902i | −0.916096 | + | 0.528908i | ||||
\(915\) | −4.16184 | − | 11.5236i | −0.137586 | − | 0.380959i | ||||
\(916\) | − | 0.328100i | − | 0.0108407i | ||||||
\(917\) | −4.67618 | − | 16.6949i | −0.154421 | − | 0.551313i | ||||
\(918\) | −3.10015 | − | 1.82083i | −0.102320 | − | 0.0600965i | ||||
\(919\) | −18.7861 | + | 32.5385i | −0.619696 | + | 1.07335i | 0.369845 | + | 0.929094i | \(0.379411\pi\) |
−0.989541 | + | 0.144252i | \(0.953922\pi\) | |||||||
\(920\) | −3.80778 | − | 6.59528i | −0.125539 | − | 0.217440i | ||||
\(921\) | 37.2556 | + | 6.66471i | 1.22761 | + | 0.219610i | ||||
\(922\) | −6.63651 | − | 3.83159i | −0.218562 | − | 0.126187i | ||||
\(923\) | 3.58456 | 0.117987 | ||||||||
\(924\) | 0.849286 | + | 8.81216i | 0.0279395 | + | 0.289899i | ||||
\(925\) | −4.38351 | −0.144129 | ||||||||
\(926\) | −29.1640 | − | 16.8379i | −0.958390 | − | 0.553327i | ||||
\(927\) | 35.8053 | + | 43.1046i | 1.17600 | + | 1.41574i | ||||
\(928\) | 1.94079 | + | 3.36154i | 0.0637094 | + | 0.110348i | ||||
\(929\) | −1.73163 | + | 2.99926i | −0.0568128 | + | 0.0984026i | −0.893033 | − | 0.449991i | \(-0.851427\pi\) |
0.836220 | + | 0.548394i | \(0.184760\pi\) | |||||||
\(930\) | −2.61884 | − | 2.20858i | −0.0858750 | − | 0.0724223i | ||||
\(931\) | 8.10171 | − | 14.7949i | 0.265523 | − | 0.484884i | ||||
\(932\) | − | 9.01141i | − | 0.295179i | ||||||
\(933\) | 4.60728 | − | 1.66395i | 0.150835 | − | 0.0544753i | ||||
\(934\) | 17.1383 | − | 9.89478i | 0.560781 | − | 0.323767i | ||||
\(935\) | −2.42476 | + | 1.39993i | −0.0792980 | + | 0.0457827i | ||||
\(936\) | −2.81394 | − | 1.04007i | −0.0919765 | − | 0.0339956i | ||||
\(937\) | − | 26.4458i | − | 0.863948i | −0.901886 | − | 0.431974i | \(-0.857817\pi\) | ||
0.901886 | − | 0.431974i | \(-0.142183\pi\) | |||||||
\(938\) | −18.8456 | − | 18.4244i | −0.615331 | − | 0.601580i | ||||
\(939\) | −11.0639 | + | 13.1191i | −0.361058 | + | 0.428126i | ||||
\(940\) | −4.60307 | + | 7.97275i | −0.150135 | + | 0.260042i | ||||
\(941\) | 16.9152 | + | 29.2979i | 0.551418 | + | 0.955084i | 0.998173 | + | 0.0604278i | \(0.0192465\pi\) |
−0.446754 | + | 0.894657i | \(0.647420\pi\) | |||||||
\(942\) | 1.40226 | − | 7.83860i | 0.0456881 | − | 0.255395i | ||||
\(943\) | −27.2699 | − | 15.7443i | −0.888030 | − | 0.512704i | ||||
\(944\) | −10.4247 | −0.339297 | ||||||||
\(945\) | 27.8432 | + | 7.34607i | 0.905740 | + | 0.238968i | ||||
\(946\) | −15.4919 | −0.503685 | ||||||||
\(947\) | −0.430364 | − | 0.248471i | −0.0139849 | − | 0.00807421i | 0.492991 | − | 0.870034i | \(-0.335903\pi\) |
−0.506976 | + | 0.861960i | \(0.669237\pi\) | |||||||
\(948\) | −5.08436 | + | 28.4215i | −0.165132 | + | 0.923087i | ||||
\(949\) | −4.31085 | − | 7.46660i | −0.139936 | − | 0.242376i | ||||
\(950\) | −0.738147 | + | 1.27851i | −0.0239486 | + | 0.0414803i | ||||
\(951\) | −19.6191 | + | 23.2635i | −0.636194 | + | 0.754369i | ||||
\(952\) | −0.453796 | + | 1.77351i | −0.0147076 | + | 0.0574798i | ||||
\(953\) | − | 41.4342i | − | 1.34219i | −0.741373 | − | 0.671093i | \(-0.765825\pi\) | ||
0.741373 | − | 0.671093i | \(-0.234175\pi\) | |||||||
\(954\) | −15.6352 | − | 5.77894i | −0.506207 | − | 0.187100i | ||||
\(955\) | 6.14846 | − | 3.54981i | 0.198959 | − | 0.114869i | ||||
\(956\) | 24.4357 | − | 14.1080i | 0.790308 | − | 0.456285i | ||||
\(957\) | 12.2159 | − | 4.41187i | 0.394884 | − | 0.142615i | ||||
\(958\) | 20.7962i | 0.671895i | ||||||||
\(959\) | 9.33408 | − | 36.4792i | 0.301413 | − | 1.17797i | ||||
\(960\) | 2.77337 | + | 2.33891i | 0.0895101 | + | 0.0754879i | ||||
\(961\) | −15.0542 | + | 26.0746i | −0.485618 | + | 0.841116i | ||||
\(962\) | 3.57753 | + | 6.19647i | 0.115344 | + | 0.199782i | ||||
\(963\) | −2.87790 | − | 3.46459i | −0.0927392 | − | 0.111645i | ||||
\(964\) | 9.92924 | + | 5.73265i | 0.319799 | + | 0.184636i | ||||
\(965\) | −26.3316 | −0.847643 | ||||||||
\(966\) | −6.90804 | + | 15.1618i | −0.222263 | + | 0.487823i | ||||
\(967\) | 53.6640 | 1.72572 | 0.862859 | − | 0.505444i | \(-0.168671\pi\) | ||||
0.862859 | + | 0.505444i | \(0.168671\pi\) | |||||||
\(968\) | −6.29413 | − | 3.63392i | −0.202301 | − | 0.116799i | ||||
\(969\) | 2.84276 | + | 0.508546i | 0.0913226 | + | 0.0163368i | ||||
\(970\) | −2.45017 | − | 4.24381i | −0.0786701 | − | 0.136261i | ||||
\(971\) | −26.9806 | + | 46.7317i | −0.865848 | + | 1.49969i | 0.000355104 | 1.00000i | \(0.499887\pi\) | |
−0.866203 | + | 0.499692i | \(0.833446\pi\) | |||||||
\(972\) | 14.5810 | + | 5.51325i | 0.467684 | + | 0.176837i | ||||
\(973\) | 15.9674 | + | 15.6106i | 0.511892 | + | 0.500452i | ||||
\(974\) | 5.60406i | 0.179566i | ||||||||
\(975\) | −0.360448 | − | 0.998037i | −0.0115436 | − | 0.0319628i | ||||
\(976\) | −2.92469 | + | 1.68857i | −0.0936172 | + | 0.0540499i | ||||
\(977\) | 52.5754 | − | 30.3544i | 1.68203 | − | 0.971123i | 0.721728 | − | 0.692177i | \(-0.243348\pi\) |
0.960307 | − | 0.278946i | \(-0.0899851\pi\) | |||||||
\(978\) | 11.6940 | + | 32.3792i | 0.373933 | + | 1.03537i | ||||
\(979\) | − | 28.8232i | − | 0.921194i | ||||||
\(980\) | −0.331326 | − | 14.6585i | −0.0105838 | − | 0.468248i | ||||
\(981\) | 1.90072 | + | 11.1020i | 0.0606852 | + | 0.354461i | ||||
\(982\) | −9.70531 | + | 16.8101i | −0.309709 | + | 0.536431i | ||||
\(983\) | −9.30310 | − | 16.1134i | −0.296723 | − | 0.513939i | 0.678661 | − | 0.734451i | \(-0.262560\pi\) |
−0.975384 | + | 0.220512i | \(0.929227\pi\) | |||||||
\(984\) | 14.7663 | + | 2.64157i | 0.470733 | + | 0.0842102i | ||||
\(985\) | −21.8169 | − | 12.5960i | −0.695143 | − | 0.401341i | ||||
\(986\) | 2.68574 | 0.0855313 | ||||||||
\(987\) | 20.0483 | − | 1.93219i | 0.638145 | − | 0.0615022i | ||||
\(988\) | 2.40970 | 0.0766629 | ||||||||
\(989\) | −25.2497 | − | 14.5779i | −0.802893 | − | 0.463550i | ||||
\(990\) | 9.33813 | − | 7.75682i | 0.296785 | − | 0.246528i | ||||
\(991\) | −13.6603 | − | 23.6603i | −0.433934 | − | 0.751596i | 0.563274 | − | 0.826270i | \(-0.309542\pi\) |
−0.997208 | + | 0.0746745i | \(0.976208\pi\) | |||||||
\(992\) | −0.472140 | + | 0.817770i | −0.0149905 | + | 0.0259642i | ||||
\(993\) | −20.3967 | − | 17.2014i | −0.647268 | − | 0.545871i | ||||
\(994\) | 2.55796 | + | 9.13238i | 0.0811334 | + | 0.289662i | ||||
\(995\) | 31.5851i | 1.00132i | ||||||||
\(996\) | −20.5018 | + | 7.40436i | −0.649623 | + | 0.234616i | ||||
\(997\) | −24.8479 | + | 14.3459i | −0.786940 | + | 0.454340i | −0.838884 | − | 0.544310i | \(-0.816792\pi\) |
0.0519442 | + | 0.998650i | \(0.483458\pi\) | |||||||
\(998\) | −21.0412 | + | 12.1481i | −0.666047 | + | 0.384542i | ||||
\(999\) | −18.3487 | − | 32.3355i | −0.580528 | − | 1.02305i |
(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 | 546.2.z.a.131.13 | ✓ | 32 | |
3.2 | odd | 2 | 546.2.z.b.131.8 | yes | 32 | ||
7.3 | odd | 6 | 546.2.z.b.521.8 | yes | 32 | ||
21.17 | even | 6 | inner | 546.2.z.a.521.13 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.z.a.131.13 | ✓ | 32 | 1.1 | even | 1 | trivial | |
546.2.z.a.521.13 | yes | 32 | 21.17 | even | 6 | inner | |
546.2.z.b.131.8 | yes | 32 | 3.2 | odd | 2 | ||
546.2.z.b.521.8 | yes | 32 | 7.3 | odd | 6 |