Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [95,2,Mod(18,95)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(95, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("95.18");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 95 = 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 95.g (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.758578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 35x^{8} + 223x^{4} + 289 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 18.5 | ||
Root | \(1.10924 - 1.10924i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 95.18 |
Dual form | 95.2.g.b.37.5 |
$q$-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 \(\left(\mathbb{Z}/95\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.10924 | + | 1.10924i | 0.784349 | + | 0.784349i | 0.980561 | − | 0.196213i | \(-0.0628643\pi\) |
−0.196213 | + | 0.980561i | \(0.562864\pi\) | |||||||
\(3\) | 1.29790 | − | 1.29790i | 0.749344 | − | 0.749344i | −0.225012 | − | 0.974356i | \(-0.572242\pi\) |
0.974356 | + | 0.225012i | \(0.0722420\pi\) | |||||||
\(4\) | 0.460811i | 0.230406i | ||||||||
\(5\) | −2.17009 | + | 0.539189i | −0.970492 | + | 0.241133i | ||||
\(6\) | 2.87936 | 1.17549 | ||||||||
\(7\) | −1.53919 | + | 1.53919i | −0.581759 | + | 0.581759i | −0.935386 | − | 0.353628i | \(-0.884948\pi\) |
0.353628 | + | 0.935386i | \(0.384948\pi\) | |||||||
\(8\) | 1.70732 | − | 1.70732i | 0.603630 | − | 0.603630i | ||||
\(9\) | − | 0.369102i | − | 0.123034i | ||||||
\(10\) | −3.00523 | − | 1.80905i | −0.950336 | − | 0.572072i | ||||
\(11\) | −2.63090 | −0.793245 | −0.396623 | − | 0.917982i | \(-0.629818\pi\) | ||||
−0.396623 | + | 0.917982i | \(0.629818\pi\) | |||||||
\(12\) | 0.598088 | + | 0.598088i | 0.172653 | + | 0.172653i | ||||
\(13\) | −1.29790 | + | 1.29790i | −0.359973 | + | 0.359973i | −0.863803 | − | 0.503830i | \(-0.831924\pi\) |
0.503830 | + | 0.863803i | \(0.331924\pi\) | |||||||
\(14\) | −3.41465 | −0.912603 | ||||||||
\(15\) | −2.11675 | + | 3.51638i | −0.546542 | + | 0.907924i | ||||
\(16\) | 4.70928 | 1.17732 | ||||||||
\(17\) | −0.709275 | + | 0.709275i | −0.172025 | + | 0.172025i | −0.787868 | − | 0.615844i | \(-0.788815\pi\) |
0.615844 | + | 0.787868i | \(0.288815\pi\) | |||||||
\(18\) | 0.409422 | − | 0.409422i | 0.0965017 | − | 0.0965017i | ||||
\(19\) | 3.41465 | − | 2.70928i | 0.783374 | − | 0.621550i | ||||
\(20\) | −0.248464 | − | 1.00000i | −0.0555583 | − | 0.223607i | ||||
\(21\) | 3.99543i | 0.871875i | ||||||||
\(22\) | −2.91829 | − | 2.91829i | −0.622181 | − | 0.622181i | ||||
\(23\) | −1.53919 | − | 1.53919i | −0.320943 | − | 0.320943i | 0.528186 | − | 0.849129i | \(-0.322872\pi\) |
−0.849129 | + | 0.528186i | \(0.822872\pi\) | |||||||
\(24\) | − | 4.43188i | − | 0.904654i | ||||||
\(25\) | 4.41855 | − | 2.34017i | 0.883710 | − | 0.468035i | ||||
\(26\) | −2.87936 | −0.564689 | ||||||||
\(27\) | 3.41465 | + | 3.41465i | 0.657149 | + | 0.657149i | ||||
\(28\) | −0.709275 | − | 0.709275i | −0.134040 | − | 0.134040i | ||||
\(29\) | −1.84114 | −0.341891 | −0.170946 | − | 0.985280i | \(-0.554682\pi\) | ||||
−0.170946 | + | 0.985280i | \(0.554682\pi\) | |||||||
\(30\) | −6.24846 | + | 1.55252i | −1.14081 | + | 0.283450i | ||||
\(31\) | − | 10.8247i | − | 1.94418i | −0.234610 | − | 0.972090i | \(-0.575381\pi\) | ||
0.234610 | − | 0.972090i | \(-0.424619\pi\) | |||||||
\(32\) | 1.80905 | + | 1.80905i | 0.319798 | + | 0.319798i | ||||
\(33\) | −3.41465 | + | 3.41465i | −0.594414 | + | 0.594414i | ||||
\(34\) | −1.57351 | −0.269854 | ||||||||
\(35\) | 2.51026 | − | 4.17009i | 0.424311 | − | 0.704873i | ||||
\(36\) | 0.170086 | 0.0283477 | ||||||||
\(37\) | 3.51638 | + | 3.51638i | 0.578089 | + | 0.578089i | 0.934376 | − | 0.356288i | \(-0.115958\pi\) |
−0.356288 | + | 0.934376i | \(0.615958\pi\) | |||||||
\(38\) | 6.79288 | + | 0.782426i | 1.10195 | + | 0.126926i | ||||
\(39\) | 3.36910i | 0.539488i | ||||||||
\(40\) | −2.78447 | + | 4.62561i | −0.440264 | + | 0.731373i | ||||
\(41\) | − | 5.83658i | − | 0.911520i | −0.890103 | − | 0.455760i | \(-0.849368\pi\) | ||
0.890103 | − | 0.455760i | \(-0.150632\pi\) | |||||||
\(42\) | −4.43188 | + | 4.43188i | −0.683854 | + | 0.683854i | ||||
\(43\) | 8.21953 | + | 8.21953i | 1.25347 | + | 1.25347i | 0.954155 | + | 0.299312i | \(0.0967571\pi\) |
0.299312 | + | 0.954155i | \(0.403243\pi\) | |||||||
\(44\) | − | 1.21235i | − | 0.182768i | ||||||
\(45\) | 0.199016 | + | 0.800984i | 0.0296675 | + | 0.119404i | ||||
\(46\) | − | 3.41465i | − | 0.503463i | ||||||
\(47\) | −6.80098 | + | 6.80098i | −0.992025 | + | 0.992025i | −0.999968 | − | 0.00794297i | \(-0.997472\pi\) |
0.00794297 | + | 0.999968i | \(0.497472\pi\) | |||||||
\(48\) | 6.11218 | − | 6.11218i | 0.882217 | − | 0.882217i | ||||
\(49\) | 2.26180i | 0.323114i | ||||||||
\(50\) | 7.49702 | + | 2.30541i | 1.06024 | + | 0.326035i | ||||
\(51\) | 1.84114i | 0.257811i | ||||||||
\(52\) | −0.598088 | − | 0.598088i | −0.0829399 | − | 0.0829399i | ||||
\(53\) | −6.11218 | + | 6.11218i | −0.839573 | + | 0.839573i | −0.988803 | − | 0.149230i | \(-0.952321\pi\) |
0.149230 | + | 0.988803i | \(0.452321\pi\) | |||||||
\(54\) | 7.57531i | 1.03087i | ||||||||
\(55\) | 5.70928 | − | 1.41855i | 0.769839 | − | 0.191277i | ||||
\(56\) | 5.25579i | 0.702334i | ||||||||
\(57\) | 0.915506 | − | 7.94826i | 0.121262 | − | 1.05277i | ||||
\(58\) | −2.04226 | − | 2.04226i | −0.268162 | − | 0.268162i | ||||
\(59\) | 5.83658 | 0.759857 | 0.379929 | − | 0.925016i | \(-0.375949\pi\) | ||||
0.379929 | + | 0.925016i | \(0.375949\pi\) | |||||||
\(60\) | −1.62038 | − | 0.975420i | −0.209191 | − | 0.125926i | ||||
\(61\) | −10.2062 | −1.30677 | −0.653385 | − | 0.757026i | \(-0.726652\pi\) | ||||
−0.653385 | + | 0.757026i | \(0.726652\pi\) | |||||||
\(62\) | 12.0072 | − | 12.0072i | 1.52491 | − | 1.52491i | ||||
\(63\) | 0.568118 | + | 0.568118i | 0.0715762 | + | 0.0715762i | ||||
\(64\) | − | 5.40522i | − | 0.675652i | ||||||
\(65\) | 2.11675 | − | 3.51638i | 0.262550 | − | 0.436153i | ||||
\(66\) | −7.57531 | −0.932456 | ||||||||
\(67\) | −1.67523 | − | 1.67523i | −0.204663 | − | 0.204663i | 0.597332 | − | 0.801994i | \(-0.296228\pi\) |
−0.801994 | + | 0.597332i | \(0.796228\pi\) | |||||||
\(68\) | −0.326842 | − | 0.326842i | −0.0396354 | − | 0.0396354i | ||||
\(69\) | −3.99543 | −0.480994 | ||||||||
\(70\) | 7.41008 | − | 1.84114i | 0.885674 | − | 0.220058i | ||||
\(71\) | 3.99543i | 0.474171i | 0.971489 | + | 0.237085i | \(0.0761921\pi\) | ||||
−0.971489 | + | 0.237085i | \(0.923808\pi\) | |||||||
\(72\) | −0.630178 | − | 0.630178i | −0.0742671 | − | 0.0742671i | ||||
\(73\) | −7.38962 | − | 7.38962i | −0.864890 | − | 0.864890i | 0.127011 | − | 0.991901i | \(-0.459461\pi\) |
−0.991901 | + | 0.127011i | \(0.959461\pi\) | |||||||
\(74\) | 7.80098i | 0.906846i | ||||||||
\(75\) | 2.69753 | − | 8.77217i | 0.311484 | − | 1.01292i | ||||
\(76\) | 1.24846 | + | 1.57351i | 0.143209 | + | 0.180494i | ||||
\(77\) | 4.04945 | − | 4.04945i | 0.461477 | − | 0.461477i | ||||
\(78\) | −3.73713 | + | 3.73713i | −0.423147 | + | 0.423147i | ||||
\(79\) | 12.6659 | 1.42502 | 0.712511 | − | 0.701661i | \(-0.247558\pi\) | ||||
0.712511 | + | 0.701661i | \(0.247558\pi\) | |||||||
\(80\) | −10.2195 | + | 2.53919i | −1.14258 | + | 0.283890i | ||||
\(81\) | 9.97107 | 1.10790 | ||||||||
\(82\) | 6.47414 | − | 6.47414i | 0.714949 | − | 0.714949i | ||||
\(83\) | 2.51026 | + | 2.51026i | 0.275537 | + | 0.275537i | 0.831324 | − | 0.555788i | \(-0.187583\pi\) |
−0.555788 | + | 0.831324i | \(0.687583\pi\) | |||||||
\(84\) | −1.84114 | −0.200885 | ||||||||
\(85\) | 1.15676 | − | 1.92162i | 0.125468 | − | 0.208429i | ||||
\(86\) | 18.2348i | 1.96631i | ||||||||
\(87\) | −2.38962 | + | 2.38962i | −0.256194 | + | 0.256194i | ||||
\(88\) | −4.49180 | + | 4.49180i | −0.478827 | + | 0.478827i | ||||
\(89\) | −16.6613 | −1.76610 | −0.883048 | − | 0.469284i | \(-0.844512\pi\) | ||||
−0.883048 | + | 0.469284i | \(0.844512\pi\) | |||||||
\(90\) | −0.667725 | + | 1.10924i | −0.0703844 | + | 0.116924i | ||||
\(91\) | − | 3.99543i | − | 0.418835i | ||||||
\(92\) | 0.709275 | − | 0.709275i | 0.0739471 | − | 0.0739471i | ||||
\(93\) | −14.0494 | − | 14.0494i | −1.45686 | − | 1.45686i | ||||
\(94\) | −15.0878 | −1.55619 | ||||||||
\(95\) | −5.94927 | + | 7.72050i | −0.610382 | + | 0.792107i | ||||
\(96\) | 4.69594 | 0.479278 | ||||||||
\(97\) | −9.14950 | − | 9.14950i | −0.928991 | − | 0.928991i | 0.0686501 | − | 0.997641i | \(-0.478131\pi\) |
−0.997641 | + | 0.0686501i | \(0.978131\pi\) | |||||||
\(98\) | −2.50887 | + | 2.50887i | −0.253434 | + | 0.253434i | ||||
\(99\) | 0.971071i | 0.0975963i | ||||||||
\(100\) | 1.07838 | + | 2.03612i | 0.107838 | + | 0.203612i | ||||
\(101\) | 4.04945 | 0.402935 | 0.201468 | − | 0.979495i | \(-0.435429\pi\) | ||||
0.201468 | + | 0.979495i | \(0.435429\pi\) | |||||||
\(102\) | −2.04226 | + | 2.04226i | −0.202214 | + | 0.202214i | ||||
\(103\) | −0.717117 | + | 0.717117i | −0.0706596 | + | 0.0706596i | −0.741553 | − | 0.670894i | \(-0.765911\pi\) |
0.670894 | + | 0.741553i | \(0.265911\pi\) | |||||||
\(104\) | 4.43188i | 0.434582i | ||||||||
\(105\) | −2.15429 | − | 8.67044i | −0.210238 | − | 0.846148i | ||||
\(106\) | −13.5597 | −1.31704 | ||||||||
\(107\) | 0.479059 | + | 0.479059i | 0.0463124 | + | 0.0463124i | 0.729884 | − | 0.683571i | \(-0.239574\pi\) |
−0.683571 | + | 0.729884i | \(0.739574\pi\) | |||||||
\(108\) | −1.57351 | + | 1.57351i | −0.151411 | + | 0.151411i | ||||
\(109\) | 10.8247 | 1.03682 | 0.518411 | − | 0.855132i | \(-0.326524\pi\) | ||||
0.518411 | + | 0.855132i | \(0.326524\pi\) | |||||||
\(110\) | 7.90644 | + | 4.75943i | 0.753850 | + | 0.453794i | ||||
\(111\) | 9.12783 | 0.866375 | ||||||||
\(112\) | −7.24846 | + | 7.24846i | −0.684915 | + | 0.684915i | ||||
\(113\) | 4.53867 | − | 4.53867i | 0.426962 | − | 0.426962i | −0.460630 | − | 0.887592i | \(-0.652376\pi\) |
0.887592 | + | 0.460630i | \(0.152376\pi\) | |||||||
\(114\) | 9.83201 | − | 7.80098i | 0.920852 | − | 0.730629i | ||||
\(115\) | 4.17009 | + | 2.51026i | 0.388863 | + | 0.234083i | ||||
\(116\) | − | 0.848418i | − | 0.0787736i | ||||||
\(117\) | 0.479059 | + | 0.479059i | 0.0442890 | + | 0.0442890i | ||||
\(118\) | 6.47414 | + | 6.47414i | 0.595993 | + | 0.595993i | ||||
\(119\) | − | 2.18342i | − | 0.200154i | ||||||
\(120\) | 2.38962 | + | 9.61757i | 0.218142 | + | 0.877960i | ||||
\(121\) | −4.07838 | −0.370762 | ||||||||
\(122\) | −11.3211 | − | 11.3211i | −1.02496 | − | 1.02496i | ||||
\(123\) | −7.57531 | − | 7.57531i | −0.683042 | − | 0.683042i | ||||
\(124\) | 4.98816 | 0.447950 | ||||||||
\(125\) | −8.32684 | + | 7.46081i | −0.744775 | + | 0.667315i | ||||
\(126\) | 1.26036i | 0.112281i | ||||||||
\(127\) | 6.93102 | + | 6.93102i | 0.615029 | + | 0.615029i | 0.944252 | − | 0.329223i | \(-0.106787\pi\) |
−0.329223 | + | 0.944252i | \(0.606787\pi\) | |||||||
\(128\) | 9.61377 | − | 9.61377i | 0.849745 | − | 0.849745i | ||||
\(129\) | 21.3363 | 1.87856 | ||||||||
\(130\) | 6.24846 | − | 1.55252i | 0.548027 | − | 0.136165i | ||||
\(131\) | 4.31351 | 0.376873 | 0.188437 | − | 0.982085i | \(-0.439658\pi\) | ||||
0.188437 | + | 0.982085i | \(0.439658\pi\) | |||||||
\(132\) | −1.57351 | − | 1.57351i | −0.136956 | − | 0.136956i | ||||
\(133\) | −1.08570 | + | 9.42588i | −0.0941424 | + | 0.817327i | ||||
\(134\) | − | 3.71646i | − | 0.321054i | ||||||
\(135\) | −9.25122 | − | 5.56894i | −0.796219 | − | 0.479298i | ||||
\(136\) | 2.42193i | 0.207678i | ||||||||
\(137\) | 6.41855 | − | 6.41855i | 0.548374 | − | 0.548374i | −0.377596 | − | 0.925970i | \(-0.623249\pi\) |
0.925970 | + | 0.377596i | \(0.123249\pi\) | |||||||
\(138\) | −4.43188 | − | 4.43188i | −0.377267 | − | 0.377267i | ||||
\(139\) | − | 10.9711i | − | 0.930554i | −0.885165 | − | 0.465277i | \(-0.845955\pi\) | ||
0.885165 | − | 0.465277i | \(-0.154045\pi\) | |||||||
\(140\) | 1.92162 | + | 1.15676i | 0.162407 | + | 0.0977637i | ||||
\(141\) | 17.6540i | 1.48674i | ||||||||
\(142\) | −4.43188 | + | 4.43188i | −0.371915 | + | 0.371915i | ||||
\(143\) | 3.41465 | − | 3.41465i | 0.285547 | − | 0.285547i | ||||
\(144\) | − | 1.73820i | − | 0.144850i | ||||||
\(145\) | 3.99543 | − | 0.992723i | 0.331803 | − | 0.0824411i | ||||
\(146\) | − | 16.3937i | − | 1.35675i | ||||||
\(147\) | 2.93559 | + | 2.93559i | 0.242123 | + | 0.242123i | ||||
\(148\) | −1.62038 | + | 1.62038i | −0.133195 | + | 0.133195i | ||||
\(149\) | − | 2.63090i | − | 0.215532i | −0.994176 | − | 0.107766i | \(-0.965630\pi\) | ||
0.994176 | − | 0.107766i | \(-0.0343697\pi\) | |||||||
\(150\) | 12.7226 | − | 6.73820i | 1.03880 | − | 0.550172i | ||||
\(151\) | 1.84114i | 0.149830i | 0.997190 | + | 0.0749150i | \(0.0238685\pi\) | ||||
−0.997190 | + | 0.0749150i | \(0.976131\pi\) | |||||||
\(152\) | 1.20430 | − | 10.4555i | 0.0976817 | − | 0.848055i | ||||
\(153\) | 0.261795 | + | 0.261795i | 0.0211649 | + | 0.0211649i | ||||
\(154\) | 8.98359 | 0.723918 | ||||||||
\(155\) | 5.83658 | + | 23.4906i | 0.468805 | + | 1.88681i | ||||
\(156\) | −1.55252 | −0.124301 | ||||||||
\(157\) | −12.1278 | + | 12.1278i | −0.967906 | + | 0.967906i | −0.999501 | − | 0.0315949i | \(-0.989941\pi\) |
0.0315949 | + | 0.999501i | \(0.489941\pi\) | |||||||
\(158\) | 14.0494 | + | 14.0494i | 1.11771 | + | 1.11771i | ||||
\(159\) | 15.8660i | 1.25826i | ||||||||
\(160\) | −4.90122 | − | 2.95038i | −0.387475 | − | 0.233248i | ||||
\(161\) | 4.73820 | 0.373423 | ||||||||
\(162\) | 11.0603 | + | 11.0603i | 0.868977 | + | 0.868977i | ||||
\(163\) | 1.98667 | + | 1.98667i | 0.155608 | + | 0.155608i | 0.780617 | − | 0.625009i | \(-0.214905\pi\) |
−0.625009 | + | 0.780617i | \(0.714905\pi\) | |||||||
\(164\) | 2.68956 | 0.210019 | ||||||||
\(165\) | 5.56894 | − | 9.25122i | 0.433542 | − | 0.720207i | ||||
\(166\) | 5.56894i | 0.432234i | ||||||||
\(167\) | −11.5714 | − | 11.5714i | −0.895424 | − | 0.895424i | 0.0996036 | − | 0.995027i | \(-0.468243\pi\) |
−0.995027 | + | 0.0996036i | \(0.968243\pi\) | |||||||
\(168\) | 6.82150 | + | 6.82150i | 0.526290 | + | 0.526290i | ||||
\(169\) | 9.63090i | 0.740838i | ||||||||
\(170\) | 3.41465 | − | 0.848418i | 0.261892 | − | 0.0650707i | ||||
\(171\) | −1.00000 | − | 1.26036i | −0.0764719 | − | 0.0963818i | ||||
\(172\) | −3.78765 | + | 3.78765i | −0.288806 | + | 0.288806i | ||||
\(173\) | 13.5223 | − | 13.5223i | 1.02808 | − | 1.02808i | 0.0284845 | − | 0.999594i | \(-0.490932\pi\) |
0.999594 | − | 0.0284845i | \(-0.00906812\pi\) | |||||||
\(174\) | −5.30131 | −0.401891 | ||||||||
\(175\) | −3.19902 | + | 10.4030i | −0.241823 | + | 0.786389i | ||||
\(176\) | −12.3896 | −0.933903 | ||||||||
\(177\) | 7.57531 | − | 7.57531i | 0.569395 | − | 0.569395i | ||||
\(178\) | −18.4813 | − | 18.4813i | −1.38523 | − | 1.38523i | ||||
\(179\) | −12.6659 | −0.946692 | −0.473346 | − | 0.880877i | \(-0.656954\pi\) | ||||
−0.473346 | + | 0.880877i | \(0.656954\pi\) | |||||||
\(180\) | −0.369102 | + | 0.0917087i | −0.0275113 | + | 0.00683557i | ||||
\(181\) | 11.6732i | 0.867658i | 0.900995 | + | 0.433829i | \(0.142838\pi\) | ||||
−0.900995 | + | 0.433829i | \(0.857162\pi\) | |||||||
\(182\) | 4.43188 | − | 4.43188i | 0.328513 | − | 0.328513i | ||||
\(183\) | −13.2467 | + | 13.2467i | −0.979221 | + | 0.979221i | ||||
\(184\) | −5.25579 | −0.387462 | ||||||||
\(185\) | −9.52683 | − | 5.73485i | −0.700426 | − | 0.421634i | ||||
\(186\) | − | 31.1683i | − | 2.28537i | ||||||
\(187\) | 1.86603 | − | 1.86603i | 0.136458 | − | 0.136458i | ||||
\(188\) | −3.13397 | − | 3.13397i | −0.228568 | − | 0.228568i | ||||
\(189\) | −10.5116 | −0.764605 | ||||||||
\(190\) | −15.1630 | + | 1.96471i | −1.10004 | + | 0.142535i | ||||
\(191\) | −2.65368 | −0.192014 | −0.0960069 | − | 0.995381i | \(-0.530607\pi\) | ||||
−0.0960069 | + | 0.995381i | \(0.530607\pi\) | |||||||
\(192\) | −7.01545 | − | 7.01545i | −0.506296 | − | 0.506296i | ||||
\(193\) | −12.9415 | + | 12.9415i | −0.931548 | + | 0.931548i | −0.997803 | − | 0.0662547i | \(-0.978895\pi\) |
0.0662547 | + | 0.997803i | \(0.478895\pi\) | |||||||
\(194\) | − | 20.2979i | − | 1.45731i | ||||||
\(195\) | −1.81658 | − | 7.31124i | −0.130088 | − | 0.523569i | ||||
\(196\) | −1.04226 | −0.0744472 | ||||||||
\(197\) | −8.80817 | + | 8.80817i | −0.627556 | + | 0.627556i | −0.947453 | − | 0.319896i | \(-0.896352\pi\) |
0.319896 | + | 0.947453i | \(0.396352\pi\) | |||||||
\(198\) | −1.07715 | + | 1.07715i | −0.0765495 | + | 0.0765495i | ||||
\(199\) | − | 4.52359i | − | 0.320669i | −0.987063 | − | 0.160334i | \(-0.948743\pi\) | ||
0.987063 | − | 0.160334i | \(-0.0512573\pi\) | |||||||
\(200\) | 3.54847 | − | 11.5393i | 0.250914 | − | 0.815954i | ||||
\(201\) | −4.34858 | −0.306725 | ||||||||
\(202\) | 4.49180 | + | 4.49180i | 0.316042 | + | 0.316042i | ||||
\(203\) | 2.83386 | − | 2.83386i | 0.198898 | − | 0.198898i | ||||
\(204\) | −0.848418 | −0.0594011 | ||||||||
\(205\) | 3.14702 | + | 12.6659i | 0.219797 | + | 0.884623i | ||||
\(206\) | −1.59090 | −0.110844 | ||||||||
\(207\) | −0.568118 | + | 0.568118i | −0.0394870 | + | 0.0394870i | ||||
\(208\) | −6.11218 | + | 6.11218i | −0.423803 | + | 0.423803i | ||||
\(209\) | −8.98359 | + | 7.12783i | −0.621408 | + | 0.493042i | ||||
\(210\) | 7.22795 | − | 12.0072i | 0.498776 | − | 0.828575i | ||||
\(211\) | − | 8.67044i | − | 0.596898i | −0.954426 | − | 0.298449i | \(-0.903531\pi\) | ||
0.954426 | − | 0.298449i | \(-0.0964692\pi\) | |||||||
\(212\) | −2.81656 | − | 2.81656i | −0.193442 | − | 0.193442i | ||||
\(213\) | 5.18568 | + | 5.18568i | 0.355317 | + | 0.355317i | ||||
\(214\) | 1.06278i | 0.0726501i | ||||||||
\(215\) | −22.2690 | − | 13.4052i | −1.51873 | − | 0.914228i | ||||
\(216\) | 11.6598 | 0.793351 | ||||||||
\(217\) | 16.6613 | + | 16.6613i | 1.13104 | + | 1.13104i | ||||
\(218\) | 12.0072 | + | 12.0072i | 0.813229 | + | 0.813229i | ||||
\(219\) | −19.1820 | −1.29620 | ||||||||
\(220\) | 0.653684 | + | 2.63090i | 0.0440714 | + | 0.177375i | ||||
\(221\) | − | 1.84114i | − | 0.123849i | ||||||
\(222\) | 10.1249 | + | 10.1249i | 0.679540 | + | 0.679540i | ||||
\(223\) | 13.9638 | − | 13.9638i | 0.935084 | − | 0.935084i | −0.0629341 | − | 0.998018i | \(-0.520046\pi\) |
0.998018 | + | 0.0629341i | \(0.0200458\pi\) | |||||||
\(224\) | −5.56894 | −0.372091 | ||||||||
\(225\) | −0.863763 | − | 1.63090i | −0.0575842 | − | 0.108727i | ||||
\(226\) | 10.0689 | 0.669775 | ||||||||
\(227\) | 19.9742 | + | 19.9742i | 1.32574 | + | 1.32574i | 0.909051 | + | 0.416685i | \(0.136808\pi\) |
0.416685 | + | 0.909051i | \(0.363192\pi\) | |||||||
\(228\) | 3.66265 | + | 0.421875i | 0.242565 | + | 0.0279394i | ||||
\(229\) | 19.7237i | 1.30338i | 0.758487 | + | 0.651688i | \(0.225939\pi\) | ||||
−0.758487 | + | 0.651688i | \(0.774061\pi\) | |||||||
\(230\) | 1.84114 | + | 7.41008i | 0.121401 | + | 0.488606i | ||||
\(231\) | − | 10.5116i | − | 0.691611i | ||||||
\(232\) | −3.14342 | + | 3.14342i | −0.206376 | + | 0.206376i | ||||
\(233\) | 3.58145 | + | 3.58145i | 0.234629 | + | 0.234629i | 0.814621 | − | 0.579993i | \(-0.196945\pi\) |
−0.579993 | + | 0.814621i | \(0.696945\pi\) | |||||||
\(234\) | 1.06278i | 0.0694761i | ||||||||
\(235\) | 11.0917 | − | 18.4257i | 0.723543 | − | 1.20196i | ||||
\(236\) | 2.68956i | 0.175075i | ||||||||
\(237\) | 16.4391 | − | 16.4391i | 1.06783 | − | 1.06783i | ||||
\(238\) | 2.42193 | − | 2.42193i | 0.156990 | − | 0.156990i | ||||
\(239\) | − | 21.9155i | − | 1.41759i | −0.705412 | − | 0.708797i | \(-0.749238\pi\) | ||
0.705412 | − | 0.708797i | \(-0.250762\pi\) | |||||||
\(240\) | −9.96834 | + | 16.5596i | −0.643454 | + | 1.06892i | ||||
\(241\) | 4.67500i | 0.301143i | 0.988599 | + | 0.150572i | \(0.0481115\pi\) | ||||
−0.988599 | + | 0.150572i | \(0.951889\pi\) | |||||||
\(242\) | −4.52389 | − | 4.52389i | −0.290806 | − | 0.290806i | ||||
\(243\) | 2.69753 | − | 2.69753i | 0.173047 | − | 0.173047i | ||||
\(244\) | − | 4.70313i | − | 0.301087i | ||||||
\(245\) | −1.21953 | − | 4.90829i | −0.0779132 | − | 0.313579i | ||||
\(246\) | − | 16.8056i | − | 1.07149i | ||||||
\(247\) | −0.915506 | + | 7.94826i | −0.0582523 | + | 0.505736i | ||||
\(248\) | −18.4813 | − | 18.4813i | −1.17357 | − | 1.17357i | ||||
\(249\) | 6.51614 | 0.412944 | ||||||||
\(250\) | −17.5122 | − | 0.960633i | −1.10757 | − | 0.0607558i | ||||
\(251\) | −4.18342 | −0.264055 | −0.132027 | − | 0.991246i | \(-0.542149\pi\) | ||||
−0.132027 | + | 0.991246i | \(0.542149\pi\) | |||||||
\(252\) | −0.261795 | + | 0.261795i | −0.0164915 | + | 0.0164915i | ||||
\(253\) | 4.04945 | + | 4.04945i | 0.254587 | + | 0.254587i | ||||
\(254\) | 15.3763i | 0.964794i | ||||||||
\(255\) | −0.992723 | − | 3.99543i | −0.0621667 | − | 0.250204i | ||||
\(256\) | 10.5174 | 0.657340 | ||||||||
\(257\) | 1.36208 | + | 1.36208i | 0.0849643 | + | 0.0849643i | 0.748312 | − | 0.663347i | \(-0.230865\pi\) |
−0.663347 | + | 0.748312i | \(0.730865\pi\) | |||||||
\(258\) | 23.6670 | + | 23.6670i | 1.47344 | + | 1.47344i | ||||
\(259\) | −10.8247 | −0.672616 | ||||||||
\(260\) | 1.62038 | + | 0.975420i | 0.100492 | + | 0.0604930i | ||||
\(261\) | 0.679569i | 0.0420643i | ||||||||
\(262\) | 4.78470 | + | 4.78470i | 0.295600 | + | 0.295600i | ||||
\(263\) | 0.326842 | + | 0.326842i | 0.0201539 | + | 0.0201539i | 0.717112 | − | 0.696958i | \(-0.245464\pi\) |
−0.696958 | + | 0.717112i | \(0.745464\pi\) | |||||||
\(264\) | 11.6598i | 0.717613i | ||||||||
\(265\) | 9.96834 | − | 16.5596i | 0.612350 | − | 1.01725i | ||||
\(266\) | −11.6598 | + | 9.25122i | −0.714910 | + | 0.567229i | ||||
\(267\) | −21.6248 | + | 21.6248i | −1.32341 | + | 1.32341i | ||||
\(268\) | 0.771967 | − | 0.771967i | 0.0471554 | − | 0.0471554i | ||||
\(269\) | 11.9863 | 0.730818 | 0.365409 | − | 0.930847i | \(-0.380929\pi\) | ||||
0.365409 | + | 0.930847i | \(0.380929\pi\) | |||||||
\(270\) | −4.08452 | − | 16.4391i | −0.248576 | − | 1.00045i | ||||
\(271\) | 15.9916 | 0.971420 | 0.485710 | − | 0.874120i | \(-0.338561\pi\) | ||||
0.485710 | + | 0.874120i | \(0.338561\pi\) | |||||||
\(272\) | −3.34017 | + | 3.34017i | −0.202528 | + | 0.202528i | ||||
\(273\) | −5.18568 | − | 5.18568i | −0.313852 | − | 0.313852i | ||||
\(274\) | 14.2394 | 0.860232 | ||||||||
\(275\) | −11.6248 | + | 6.15676i | −0.700999 | + | 0.371266i | ||||
\(276\) | − | 1.84114i | − | 0.110824i | ||||||
\(277\) | 15.2062 | − | 15.2062i | 0.913652 | − | 0.913652i | −0.0829052 | − | 0.996557i | \(-0.526420\pi\) |
0.996557 | + | 0.0829052i | \(0.0264199\pi\) | |||||||
\(278\) | 12.1695 | − | 12.1695i | 0.729879 | − | 0.729879i | ||||
\(279\) | −3.99543 | −0.239200 | ||||||||
\(280\) | −2.83386 | − | 11.4055i | −0.169356 | − | 0.681610i | ||||
\(281\) | − | 15.8129i | − | 0.943318i | −0.881781 | − | 0.471659i | \(-0.843655\pi\) | ||
0.881781 | − | 0.471659i | \(-0.156345\pi\) | |||||||
\(282\) | −19.5825 | + | 19.5825i | −1.16612 | + | 1.16612i | ||||
\(283\) | 3.48133 | + | 3.48133i | 0.206944 | + | 0.206944i | 0.802967 | − | 0.596023i | \(-0.203253\pi\) |
−0.596023 | + | 0.802967i | \(0.703253\pi\) | |||||||
\(284\) | −1.84114 | −0.109252 | ||||||||
\(285\) | 2.29888 | + | 17.7420i | 0.136174 | + | 1.05095i | ||||
\(286\) | 7.57531 | 0.447937 | ||||||||
\(287\) | 8.98359 | + | 8.98359i | 0.530285 | + | 0.530285i | ||||
\(288\) | 0.667725 | − | 0.667725i | 0.0393461 | − | 0.0393461i | ||||
\(289\) | 15.9939i | 0.940815i | ||||||||
\(290\) | 5.53305 | + | 3.33072i | 0.324912 | + | 0.195586i | ||||
\(291\) | −23.7503 | −1.39227 | ||||||||
\(292\) | 3.40522 | − | 3.40522i | 0.199275 | − | 0.199275i | ||||
\(293\) | 7.54641 | − | 7.54641i | 0.440866 | − | 0.440866i | −0.451437 | − | 0.892303i | \(-0.649088\pi\) |
0.892303 | + | 0.451437i | \(0.149088\pi\) | |||||||
\(294\) | 6.51253i | 0.379818i | ||||||||
\(295\) | −12.6659 | + | 3.14702i | −0.737436 | + | 0.183226i | ||||
\(296\) | 12.0072 | 0.697904 | ||||||||
\(297\) | −8.98359 | − | 8.98359i | −0.521281 | − | 0.521281i | ||||
\(298\) | 2.91829 | − | 2.91829i | 0.169052 | − | 0.169052i | ||||
\(299\) | 3.99543 | 0.231062 | ||||||||
\(300\) | 4.04231 | + | 1.24305i | 0.233383 | + | 0.0717677i | ||||
\(301\) | −25.3028 | −1.45843 | ||||||||
\(302\) | −2.04226 | + | 2.04226i | −0.117519 | + | 0.117519i | ||||
\(303\) | 5.25579 | − | 5.25579i | 0.301937 | − | 0.301937i | ||||
\(304\) | 16.0805 | − | 12.7587i | 0.922281 | − | 0.731763i | ||||
\(305\) | 22.1483 | − | 5.50307i | 1.26821 | − | 0.315105i | ||||
\(306\) | 0.580786i | 0.0332013i | ||||||||
\(307\) | −7.51181 | − | 7.51181i | −0.428722 | − | 0.428722i | 0.459471 | − | 0.888193i | \(-0.348039\pi\) |
−0.888193 | + | 0.459471i | \(0.848039\pi\) | |||||||
\(308\) | 1.86603 | + | 1.86603i | 0.106327 | + | 0.106327i | ||||
\(309\) | 1.86150i | 0.105897i | ||||||||
\(310\) | −19.5825 | + | 32.5308i | −1.11221 | + | 1.84762i | ||||
\(311\) | 30.2472 | 1.71516 | 0.857582 | − | 0.514348i | \(-0.171966\pi\) | ||||
0.857582 | + | 0.514348i | \(0.171966\pi\) | |||||||
\(312\) | 5.75215 | + | 5.75215i | 0.325651 | + | 0.325651i | ||||
\(313\) | −0.503072 | − | 0.503072i | −0.0284353 | − | 0.0284353i | 0.692746 | − | 0.721181i | \(-0.256401\pi\) |
−0.721181 | + | 0.692746i | \(0.756401\pi\) | |||||||
\(314\) | −26.9053 | −1.51835 | ||||||||
\(315\) | −1.53919 | − | 0.926543i | −0.0867235 | − | 0.0522048i | ||||
\(316\) | 5.83658i | 0.328333i | ||||||||
\(317\) | −11.9192 | − | 11.9192i | −0.669448 | − | 0.669448i | 0.288140 | − | 0.957588i | \(-0.406963\pi\) |
−0.957588 | + | 0.288140i | \(0.906963\pi\) | |||||||
\(318\) | −17.5992 | + | 17.5992i | −0.986913 | + | 0.986913i | ||||
\(319\) | 4.84385 | 0.271204 | ||||||||
\(320\) | 2.91443 | + | 11.7298i | 0.162922 | + | 0.655715i | ||||
\(321\) | 1.24354 | 0.0694078 | ||||||||
\(322\) | 5.25579 | + | 5.25579i | 0.292894 | + | 0.292894i | ||||
\(323\) | −0.500304 | + | 4.34355i | −0.0278377 | + | 0.241682i | ||||
\(324\) | 4.59478i | 0.255266i | ||||||||
\(325\) | −2.69753 | + | 8.77217i | −0.149632 | + | 0.486592i | ||||
\(326\) | 4.40737i | 0.244102i | ||||||||
\(327\) | 14.0494 | − | 14.0494i | 0.776936 | − | 0.776936i | ||||
\(328\) | −9.96493 | − | 9.96493i | −0.550221 | − | 0.550221i | ||||
\(329\) | − | 20.9360i | − | 1.15424i | ||||||
\(330\) | 16.4391 | − | 4.08452i | 0.904941 | − | 0.224845i | ||||
\(331\) | − | 5.52342i | − | 0.303595i | −0.988412 | − | 0.151797i | \(-0.951494\pi\) | ||
0.988412 | − | 0.151797i | \(-0.0485061\pi\) | |||||||
\(332\) | −1.15676 | + | 1.15676i | −0.0634852 | + | 0.0634852i | ||||
\(333\) | 1.29790 | − | 1.29790i | 0.0711246 | − | 0.0711246i | ||||
\(334\) | − | 25.6709i | − | 1.40465i | ||||||
\(335\) | 4.53867 | + | 2.73214i | 0.247974 | + | 0.149273i | ||||
\(336\) | 18.8156i | 1.02648i | ||||||||
\(337\) | −15.6015 | − | 15.6015i | −0.849866 | − | 0.849866i | 0.140250 | − | 0.990116i | \(-0.455209\pi\) |
−0.990116 | + | 0.140250i | \(0.955209\pi\) | |||||||
\(338\) | −10.6829 | + | 10.6829i | −0.581075 | + | 0.581075i | ||||
\(339\) | − | 11.7815i | − | 0.639884i | ||||||
\(340\) | 0.885505 | + | 0.533046i | 0.0480232 | + | 0.0289085i | ||||
\(341\) | 28.4788i | 1.54221i | ||||||||
\(342\) | 0.288795 | − | 2.50727i | 0.0156163 | − | 0.135578i | ||||
\(343\) | −14.2557 | − | 14.2557i | −0.769733 | − | 0.769733i | ||||
\(344\) | 28.0668 | 1.51326 | ||||||||
\(345\) | 8.67044 | − | 2.15429i | 0.466801 | − | 0.115983i | ||||
\(346\) | 29.9988 | 1.61274 | ||||||||
\(347\) | −5.79484 | + | 5.79484i | −0.311083 | + | 0.311083i | −0.845329 | − | 0.534246i | \(-0.820596\pi\) |
0.534246 | + | 0.845329i | \(0.320596\pi\) | |||||||
\(348\) | −1.10116 | − | 1.10116i | −0.0590286 | − | 0.0590286i | ||||
\(349\) | 7.13624i | 0.381994i | 0.981591 | + | 0.190997i | \(0.0611721\pi\) | ||||
−0.981591 | + | 0.190997i | \(0.938828\pi\) | |||||||
\(350\) | −15.0878 | + | 7.99087i | −0.806477 | + | 0.427130i | ||||
\(351\) | −8.86376 | −0.473113 | ||||||||
\(352\) | −4.75943 | − | 4.75943i | −0.253678 | − | 0.253678i | ||||
\(353\) | 15.9711 | + | 15.9711i | 0.850054 | + | 0.850054i | 0.990139 | − | 0.140085i | \(-0.0447376\pi\) |
−0.140085 | + | 0.990139i | \(0.544738\pi\) | |||||||
\(354\) | 16.8056 | 0.893208 | ||||||||
\(355\) | −2.15429 | − | 8.67044i | −0.114338 | − | 0.460179i | ||||
\(356\) | − | 7.67772i | − | 0.406918i | ||||||
\(357\) | −2.83386 | − | 2.83386i | −0.149984 | − | 0.149984i | ||||
\(358\) | −14.0494 | − | 14.0494i | −0.742536 | − | 0.742536i | ||||
\(359\) | − | 27.1689i | − | 1.43392i | −0.697115 | − | 0.716959i | \(-0.745534\pi\) | ||
0.697115 | − | 0.716959i | \(-0.254466\pi\) | |||||||
\(360\) | 1.70732 | + | 1.02776i | 0.0899839 | + | 0.0541674i | ||||
\(361\) | 4.31965 | − | 18.5024i | 0.227350 | − | 0.973813i | ||||
\(362\) | −12.9483 | + | 12.9483i | −0.680547 | + | 0.680547i | ||||
\(363\) | −5.29334 | + | 5.29334i | −0.277828 | + | 0.277828i | ||||
\(364\) | 1.84114 | 0.0965020 | ||||||||
\(365\) | 20.0205 | + | 12.0517i | 1.04792 | + | 0.630816i | ||||
\(366\) | −29.3874 | −1.53610 | ||||||||
\(367\) | −1.09171 | + | 1.09171i | −0.0569867 | + | 0.0569867i | −0.735026 | − | 0.678039i | \(-0.762830\pi\) |
0.678039 | + | 0.735026i | \(0.262830\pi\) | |||||||
\(368\) | −7.24846 | − | 7.24846i | −0.377852 | − | 0.377852i | ||||
\(369\) | −2.15429 | −0.112148 | ||||||||
\(370\) | −4.20620 | − | 16.9288i | −0.218670 | − | 0.880087i | ||||
\(371\) | − | 18.8156i | − | 0.976857i | ||||||
\(372\) | 6.47414 | − | 6.47414i | 0.335669 | − | 0.335669i | ||||
\(373\) | 2.87141 | − | 2.87141i | 0.148676 | − | 0.148676i | −0.628850 | − | 0.777526i | \(-0.716474\pi\) |
0.777526 | + | 0.628850i | \(0.216474\pi\) | |||||||
\(374\) | 4.13974 | 0.214061 | ||||||||
\(375\) | −1.12402 | + | 20.4908i | −0.0580443 | + | 1.05814i | ||||
\(376\) | 23.2230i | 1.19763i | ||||||||
\(377\) | 2.38962 | − | 2.38962i | 0.123072 | − | 0.123072i | ||||
\(378\) | −11.6598 | − | 11.6598i | −0.599717 | − | 0.599717i | ||||
\(379\) | −29.6403 | −1.52252 | −0.761261 | − | 0.648446i | \(-0.775419\pi\) | ||||
−0.761261 | + | 0.648446i | \(0.775419\pi\) | |||||||
\(380\) | −3.55769 | − | 2.74149i | −0.182506 | − | 0.140636i | ||||
\(381\) | 17.9916 | 0.921737 | ||||||||
\(382\) | −2.94356 | − | 2.94356i | −0.150606 | − | 0.150606i | ||||
\(383\) | 0.275606 | − | 0.275606i | 0.0140828 | − | 0.0140828i | −0.700030 | − | 0.714113i | \(-0.746830\pi\) |
0.714113 | + | 0.700030i | \(0.246830\pi\) | |||||||
\(384\) | − | 24.9555i | − | 1.27350i | ||||||
\(385\) | −6.60424 | + | 10.9711i | −0.336583 | + | 0.559138i | ||||
\(386\) | −28.7103 | −1.46132 | ||||||||
\(387\) | 3.03385 | − | 3.03385i | 0.154219 | − | 0.154219i | ||||
\(388\) | 4.21619 | − | 4.21619i | 0.214045 | − | 0.214045i | ||||
\(389\) | − | 10.2557i | − | 0.519982i | −0.965611 | − | 0.259991i | \(-0.916280\pi\) | ||
0.965611 | − | 0.259991i | \(-0.0837196\pi\) | |||||||
\(390\) | 6.09488 | − | 10.1249i | 0.308626 | − | 0.512695i | ||||
\(391\) | 2.18342 | 0.110420 | ||||||||
\(392\) | 3.86162 | + | 3.86162i | 0.195041 | + | 0.195041i | ||||
\(393\) | 5.59852 | − | 5.59852i | 0.282408 | − | 0.282408i | ||||
\(394\) | −19.5407 | −0.984446 | ||||||||
\(395\) | −27.4860 | + | 6.82930i | −1.38297 | + | 0.343619i | ||||
\(396\) | −0.447480 | −0.0224867 | ||||||||
\(397\) | −11.4741 | + | 11.4741i | −0.575871 | + | 0.575871i | −0.933763 | − | 0.357892i | \(-0.883496\pi\) |
0.357892 | + | 0.933763i | \(0.383496\pi\) | |||||||
\(398\) | 5.01773 | − | 5.01773i | 0.251516 | − | 0.251516i | ||||
\(399\) | 10.8247 | + | 13.6430i | 0.541914 | + | 0.683005i | ||||
\(400\) | 20.8082 | − | 11.0205i | 1.04041 | − | 0.551026i | ||||
\(401\) | 32.1610i | 1.60605i | 0.595948 | + | 0.803023i | \(0.296776\pi\) | ||||
−0.595948 | + | 0.803023i | \(0.703224\pi\) | |||||||
\(402\) | −4.82361 | − | 4.82361i | −0.240580 | − | 0.240580i | ||||
\(403\) | 14.0494 | + | 14.0494i | 0.699853 | + | 0.699853i | ||||
\(404\) | 1.86603i | 0.0928385i | ||||||||
\(405\) | −21.6381 | + | 5.37629i | −1.07521 | + | 0.267150i | ||||
\(406\) | 6.28685 | 0.312011 | ||||||||
\(407\) | −9.25122 | − | 9.25122i | −0.458566 | − | 0.458566i | ||||
\(408\) | 3.14342 | + | 3.14342i | 0.155623 | + | 0.155623i | ||||
\(409\) | 24.4833 | 1.21062 | 0.605311 | − | 0.795989i | \(-0.293049\pi\) | ||||
0.605311 | + | 0.795989i | \(0.293049\pi\) | |||||||
\(410\) | −10.5587 | + | 17.5402i | −0.521455 | + | 0.866250i | ||||
\(411\) | − | 16.6613i | − | 0.821842i | ||||||
\(412\) | −0.330455 | − | 0.330455i | −0.0162804 | − | 0.0162804i | ||||
\(413\) | −8.98359 | + | 8.98359i | −0.442054 | + | 0.442054i | ||||
\(414\) | −1.26036 | −0.0619431 | ||||||||
\(415\) | −6.80098 | − | 4.09398i | −0.333847 | − | 0.200965i | ||||
\(416\) | −4.69594 | −0.230238 | ||||||||
\(417\) | −14.2394 | − | 14.2394i | −0.697305 | − | 0.697305i | ||||
\(418\) | −17.8714 | − | 2.05848i | −0.874117 | − | 0.100684i | ||||
\(419\) | 24.8059i | 1.21185i | 0.795523 | + | 0.605924i | \(0.207196\pi\) | ||||
−0.795523 | + | 0.605924i | \(0.792804\pi\) | |||||||
\(420\) | 3.99543 | − | 0.992723i | 0.194957 | − | 0.0484399i | ||||
\(421\) | − | 13.8274i | − | 0.673908i | −0.941521 | − | 0.336954i | \(-0.890603\pi\) | ||
0.941521 | − | 0.336954i | \(-0.109397\pi\) | |||||||
\(422\) | 9.61757 | − | 9.61757i | 0.468176 | − | 0.468176i | ||||
\(423\) | 2.51026 | + | 2.51026i | 0.122053 | + | 0.122053i | ||||
\(424\) | 20.8710i | 1.01358i | ||||||||
\(425\) | −1.47414 | + | 4.79380i | −0.0715064 | + | 0.232533i | ||||
\(426\) | 11.5043i | 0.557385i | ||||||||
\(427\) | 15.7093 | − | 15.7093i | 0.760225 | − | 0.760225i | ||||
\(428\) | −0.220756 | + | 0.220756i | −0.0106706 | + | 0.0106706i | ||||
\(429\) | − | 8.86376i | − | 0.427947i | ||||||
\(430\) | −9.83201 | − | 39.5711i | −0.474142 | − | 1.90829i | ||||
\(431\) | 17.8229i | 0.858498i | 0.903186 | + | 0.429249i | \(0.141222\pi\) | ||||
−0.903186 | + | 0.429249i | \(0.858778\pi\) | |||||||
\(432\) | 16.0805 | + | 16.0805i | 0.773674 | + | 0.773674i | ||||
\(433\) | 2.38438 | − | 2.38438i | 0.114586 | − | 0.114586i | −0.647489 | − | 0.762075i | \(-0.724181\pi\) |
0.762075 | + | 0.647489i | \(0.224181\pi\) | |||||||
\(434\) | 36.9627i | 1.77426i | ||||||||
\(435\) | 3.89723 | − | 6.47414i | 0.186858 | − | 0.310411i | ||||
\(436\) | 4.98816i | 0.238889i | ||||||||
\(437\) | −9.42588 | − | 1.08570i | −0.450901 | − | 0.0519362i | ||||
\(438\) | −21.2774 | − | 21.2774i | −1.01667 | − | 1.01667i | ||||
\(439\) | −23.8038 | −1.13609 | −0.568046 | − | 0.822997i | \(-0.692300\pi\) | ||||
−0.568046 | + | 0.822997i | \(0.692300\pi\) | |||||||
\(440\) | 7.32566 | − | 12.1695i | 0.349237 | − | 0.580159i | ||||
\(441\) | 0.834834 | 0.0397540 | ||||||||
\(442\) | 2.04226 | − | 2.04226i | 0.0971404 | − | 0.0971404i | ||||
\(443\) | 20.3268 | + | 20.3268i | 0.965757 | + | 0.965757i | 0.999433 | − | 0.0336754i | \(-0.0107212\pi\) |
−0.0336754 | + | 0.999433i | \(0.510721\pi\) | |||||||
\(444\) | 4.20620i | 0.199618i | ||||||||
\(445\) | 36.1565 | − | 8.98359i | 1.71398 | − | 0.425863i | ||||
\(446\) | 30.9783 | 1.46686 | ||||||||
\(447\) | −3.41465 | − | 3.41465i | −0.161507 | − | 0.161507i | ||||
\(448\) | 8.31965 | + | 8.31965i | 0.393067 | + | 0.393067i | ||||
\(449\) | 13.9717 | 0.659368 | 0.329684 | − | 0.944091i | \(-0.393058\pi\) | ||||
0.329684 | + | 0.944091i | \(0.393058\pi\) | |||||||
\(450\) | 0.850933 | − | 2.76717i | 0.0401134 | − | 0.130446i | ||||
\(451\) | 15.3554i | 0.723059i | ||||||||
\(452\) | 2.09147 | + | 2.09147i | 0.0983745 | + | 0.0983745i | ||||
\(453\) | 2.38962 | + | 2.38962i | 0.112274 | + | 0.112274i | ||||
\(454\) | 44.3123i | 2.07968i | ||||||||
\(455\) | 2.15429 | + | 8.67044i | 0.100995 | + | 0.406476i | ||||
\(456\) | −12.0072 | − | 15.1333i | −0.562288 | − | 0.708683i | ||||
\(457\) | 7.83710 | − | 7.83710i | 0.366604 | − | 0.366604i | −0.499633 | − | 0.866237i | \(-0.666532\pi\) |
0.866237 | + | 0.499633i | \(0.166532\pi\) | |||||||
\(458\) | −21.8782 | + | 21.8782i | −1.02230 | + | 1.02230i | ||||
\(459\) | −4.84385 | −0.226092 | ||||||||
\(460\) | −1.15676 | + | 1.92162i | −0.0539340 | + | 0.0895961i | ||||
\(461\) | −32.2557 | −1.50230 | −0.751148 | − | 0.660134i | \(-0.770499\pi\) | ||||
−0.751148 | + | 0.660134i | \(0.770499\pi\) | |||||||
\(462\) | 11.6598 | − | 11.6598i | 0.542464 | − | 0.542464i | ||||
\(463\) | −1.40910 | − | 1.40910i | −0.0654862 | − | 0.0654862i | 0.673605 | − | 0.739091i | \(-0.264745\pi\) |
−0.739091 | + | 0.673605i | \(0.764745\pi\) | |||||||
\(464\) | −8.67044 | −0.402515 | ||||||||
\(465\) | 38.0638 | + | 22.9132i | 1.76517 | + | 1.06257i | ||||
\(466\) | 7.94535i | 0.368061i | ||||||||
\(467\) | 15.6647 | − | 15.6647i | 0.724878 | − | 0.724878i | −0.244717 | − | 0.969595i | \(-0.578695\pi\) |
0.969595 | + | 0.244717i | \(0.0786949\pi\) | |||||||
\(468\) | −0.220756 | + | 0.220756i | −0.0102044 | + | 0.0102044i | ||||
\(469\) | 5.15701 | 0.238128 | ||||||||
\(470\) | 32.7418 | − | 8.13517i | 1.51027 | − | 0.375248i | ||||
\(471\) | 31.4815i | 1.45059i | ||||||||
\(472\) | 9.96493 | − | 9.96493i | 0.458673 | − | 0.458673i | ||||
\(473\) | −21.6248 | − | 21.6248i | −0.994307 | − | 0.994307i | ||||
\(474\) | 36.4696 | 1.67511 | ||||||||
\(475\) | 8.74763 | − | 19.9619i | 0.401369 | − | 0.915917i | ||||
\(476\) | 1.00614 | 0.0461165 | ||||||||
\(477\) | 2.25602 | + | 2.25602i | 0.103296 | + | 0.103296i | ||||
\(478\) | 24.3094 | − | 24.3094i | 1.11189 | − | 1.11189i | ||||
\(479\) | − | 3.28458i | − | 0.150076i | −0.997181 | − | 0.0750382i | \(-0.976092\pi\) | ||
0.997181 | − | 0.0750382i | \(-0.0239079\pi\) | |||||||
\(480\) | −10.1906 | + | 2.53200i | −0.465135 | + | 0.115570i | ||||
\(481\) | −9.12783 | −0.416193 | ||||||||
\(482\) | −5.18568 | + | 5.18568i | −0.236201 | + | 0.236201i | ||||
\(483\) | 6.14973 | − | 6.14973i | 0.279822 | − | 0.279822i | ||||
\(484\) | − | 1.87936i | − | 0.0854255i | ||||||
\(485\) | 24.7885 | + | 14.9219i | 1.12559 | + | 0.677568i | ||||
\(486\) | 5.98440 | 0.271458 | ||||||||
\(487\) | −0.682512 | − | 0.682512i | −0.0309276 | − | 0.0309276i | 0.691474 | − | 0.722401i | \(-0.256962\pi\) |
−0.722401 | + | 0.691474i | \(0.756962\pi\) | |||||||
\(488\) | −17.4253 | + | 17.4253i | −0.788806 | + | 0.788806i | ||||
\(489\) | 5.15701 | 0.233208 | ||||||||
\(490\) | 4.09170 | − | 6.79721i | 0.184844 | − | 0.307067i | ||||
\(491\) | −7.02052 | −0.316832 | −0.158416 | − | 0.987372i | \(-0.550639\pi\) | ||||
−0.158416 | + | 0.987372i | \(0.550639\pi\) | |||||||
\(492\) | 3.49079 | − | 3.49079i | 0.157377 | − | 0.157377i | ||||
\(493\) | 1.30588 | − | 1.30588i | 0.0588137 | − | 0.0588137i | ||||
\(494\) | −9.83201 | + | 7.80098i | −0.442363 | + | 0.350983i | ||||
\(495\) | −0.523590 | − | 2.10731i | −0.0235336 | − | 0.0947164i | ||||
\(496\) | − | 50.9766i | − | 2.28892i | ||||||
\(497\) | −6.14973 | − | 6.14973i | −0.275853 | − | 0.275853i | ||||
\(498\) | 7.22795 | + | 7.22795i | 0.323892 | + | 0.323892i | ||||
\(499\) | 18.0228i | 0.806811i | 0.915021 | + | 0.403405i | \(0.132174\pi\) | ||||
−0.915021 | + | 0.403405i | \(0.867826\pi\) | |||||||
\(500\) | −3.43802 | − | 3.83710i | −0.153753 | − | 0.171600i | ||||
\(501\) | −30.0372 | −1.34196 | ||||||||
\(502\) | −4.64040 | − | 4.64040i | −0.207111 | − | 0.207111i | ||||
\(503\) | −13.7226 | − | 13.7226i | −0.611861 | − | 0.611861i | 0.331570 | − | 0.943431i | \(-0.392422\pi\) |
−0.943431 | + | 0.331570i | \(0.892422\pi\) | |||||||
\(504\) | 1.93992 | 0.0864111 | ||||||||
\(505\) | −8.78765 | + | 2.18342i | −0.391045 | + | 0.0971608i | ||||
\(506\) | 8.98359i | 0.399369i | ||||||||
\(507\) | 12.5000 | + | 12.5000i | 0.555143 | + | 0.555143i | ||||
\(508\) | −3.19389 | + | 3.19389i | −0.141706 | + | 0.141706i | ||||
\(509\) | 8.67044 | 0.384310 | 0.192155 | − | 0.981365i | \(-0.438452\pi\) | ||||
0.192155 | + | 0.981365i | \(0.438452\pi\) | |||||||
\(510\) | 3.33072 | − | 5.53305i | 0.147487 | − | 0.245007i | ||||
\(511\) | 22.7480 | 1.00631 | ||||||||
\(512\) | −7.56120 | − | 7.56120i | −0.334161 | − | 0.334161i | ||||
\(513\) | 20.9111 | + | 2.40860i | 0.923245 | + | 0.106342i | ||||
\(514\) | 3.02174i | 0.133283i | ||||||||
\(515\) | 1.16954 | − | 1.94287i | 0.0515363 | − | 0.0856130i | ||||
\(516\) | 9.83201i | 0.432830i | ||||||||
\(517\) | 17.8927 | − | 17.8927i | 0.786920 | − | 0.786920i | ||||
\(518\) | −12.0072 | − | 12.0072i | −0.527566 | − | 0.527566i | ||||
\(519\) | − | 35.1012i | − | 1.54077i | ||||||
\(520\) | −2.38962 | − | 9.61757i | −0.104792 | − | 0.421758i | ||||
\(521\) | − | 35.3081i | − | 1.54687i | −0.633873 | − | 0.773437i | \(-0.718536\pi\) | ||
0.633873 | − | 0.773437i | \(-0.281464\pi\) | |||||||
\(522\) | −0.753803 | + | 0.753803i | −0.0329931 | + | 0.0329931i | ||||
\(523\) | −9.83998 | + | 9.83998i | −0.430272 | + | 0.430272i | −0.888721 | − | 0.458449i | \(-0.848405\pi\) |
0.458449 | + | 0.888721i | \(0.348405\pi\) | |||||||
\(524\) | 1.98771i | 0.0868337i | ||||||||
\(525\) | 9.35001 | + | 17.6540i | 0.408068 | + | 0.770485i | ||||
\(526\) | 0.725090i | 0.0316154i | ||||||||
\(527\) | 7.67772 | + | 7.67772i | 0.334447 | + | 0.334447i | ||||
\(528\) | −16.0805 | + | 16.0805i | −0.699815 | + | 0.699815i | ||||
\(529\) | − | 18.2618i | − | 0.793991i | ||||||
\(530\) | 29.4257 | − | 7.31124i | 1.27817 | − | 0.317580i | ||||
\(531\) | − | 2.15429i | − | 0.0934884i | ||||||
\(532\) | −4.34355 | − | 0.500304i | −0.188317 | − | 0.0216909i | ||||
\(533\) | 7.57531 | + | 7.57531i | 0.328123 | + | 0.328123i | ||||
\(534\) | −47.9739 | −2.07604 | ||||||||
\(535\) | −1.29790 | − | 0.781296i | −0.0561132 | − | 0.0337784i | ||||
\(536\) | −5.72034 | −0.247081 | ||||||||
\(537\) | −16.4391 | + | 16.4391i | −0.709398 | + | 0.709398i | ||||
\(538\) | 13.2956 | + | 13.2956i | 0.573216 | + | 0.573216i | ||||
\(539\) | − | 5.95055i | − | 0.256308i | ||||||
\(540\) | 2.56623 | − | 4.26307i | 0.110433 | − | 0.183453i | ||||
\(541\) | −9.79380 | −0.421068 | −0.210534 | − | 0.977587i | \(-0.567520\pi\) | ||||
−0.210534 | + | 0.977587i | \(0.567520\pi\) | |||||||
\(542\) | 17.7385 | + | 17.7385i | 0.761932 | + | 0.761932i | ||||
\(543\) | 15.1506 | + | 15.1506i | 0.650175 | + | 0.650175i | ||||
\(544\) | −2.56623 | −0.110026 | ||||||||
\(545\) | −23.4906 | + | 5.83658i | −1.00623 | + | 0.250011i | ||||
\(546\) | − | 11.5043i | − | 0.492339i | ||||||
\(547\) | −6.72757 | − | 6.72757i | −0.287650 | − | 0.287650i | 0.548500 | − | 0.836150i | \(-0.315199\pi\) |
−0.836150 | + | 0.548500i | \(0.815199\pi\) | |||||||
\(548\) | 2.95774 | + | 2.95774i | 0.126348 | + | 0.126348i | ||||
\(549\) | 3.76713i | 0.160777i | ||||||||
\(550\) | −19.7239 | − | 6.06530i | −0.841030 | − | 0.258625i | ||||
\(551\) | −6.28685 | + | 4.98816i | −0.267829 | + | 0.212503i | ||||
\(552\) | −6.82150 | + | 6.82150i | −0.290342 | + | 0.290342i | ||||
\(553\) | −19.4952 | + | 19.4952i | −0.829019 | + | 0.829019i | ||||
\(554\) | 33.7346 | 1.43324 | ||||||||
\(555\) | −19.8082 | + | 4.92162i | −0.840810 | + | 0.208911i | ||||
\(556\) | 5.05559 | 0.214405 | ||||||||
\(557\) | −10.3379 | + | 10.3379i | −0.438031 | + | 0.438031i | −0.891349 | − | 0.453318i | \(-0.850240\pi\) |
0.453318 | + | 0.891349i | \(0.350240\pi\) | |||||||
\(558\) | −4.43188 | − | 4.43188i | −0.187617 | − | 0.187617i | ||||
\(559\) | −21.3363 | −0.902430 | ||||||||
\(560\) | 11.8215 | − | 19.6381i | 0.499550 | − | 0.829861i | ||||
\(561\) | − | 4.84385i | − | 0.204508i | ||||||
\(562\) | 17.5402 | − | 17.5402i | 0.739890 | − | 0.739890i | ||||
\(563\) | 9.28877 | − | 9.28877i | 0.391475 | − | 0.391475i | −0.483738 | − | 0.875213i | \(-0.660721\pi\) |
0.875213 | + | 0.483738i | \(0.160721\pi\) | |||||||
\(564\) | −8.13517 | −0.342553 | ||||||||
\(565\) | −7.40211 | + | 12.2965i | −0.311409 | + | 0.517318i | ||||
\(566\) | 7.72324i | 0.324632i | ||||||||
\(567\) | −15.3474 | + | 15.3474i | −0.644529 | + | 0.644529i | ||||
\(568\) | 6.82150 | + | 6.82150i | 0.286224 | + | 0.286224i | ||||
\(569\) | 14.5070 | 0.608166 | 0.304083 | − | 0.952646i | \(-0.401650\pi\) | ||||
0.304083 | + | 0.952646i | \(0.401650\pi\) | |||||||
\(570\) | −17.1301 | + | 22.2301i | −0.717501 | + | 0.931117i | ||||
\(571\) | −21.6658 | −0.906685 | −0.453343 | − | 0.891336i | \(-0.649769\pi\) | ||||
−0.453343 | + | 0.891336i | \(0.649769\pi\) | |||||||
\(572\) | 1.57351 | + | 1.57351i | 0.0657917 | + | 0.0657917i | ||||
\(573\) | −3.44422 | + | 3.44422i | −0.143884 | + | 0.143884i | ||||
\(574\) | 19.9299i | 0.831856i | ||||||||
\(575\) | −10.4030 | − | 3.19902i | −0.433833 | − | 0.133408i | ||||
\(576\) | −1.99508 | −0.0831283 | ||||||||
\(577\) | −1.68035 | + | 1.68035i | −0.0699537 | + | 0.0699537i | −0.741218 | − | 0.671264i | \(-0.765752\pi\) |
0.671264 | + | 0.741218i | \(0.265752\pi\) | |||||||
\(578\) | −17.7410 | + | 17.7410i | −0.737927 | + | 0.737927i | ||||
\(579\) | 33.5936i | 1.39610i | ||||||||
\(580\) | 0.457458 | + | 1.84114i | 0.0189949 | + | 0.0764492i | ||||
\(581\) | −7.72753 | −0.320592 | ||||||||
\(582\) | −26.3447 | − | 26.3447i | −1.09202 | − | 1.09202i | ||||
\(583\) | 16.0805 | − | 16.0805i | 0.665987 | − | 0.665987i | ||||
\(584\) | −25.2330 | −1.04415 | ||||||||
\(585\) | −1.29790 | − | 0.781296i | −0.0536617 | − | 0.0323026i | ||||
\(586\) | 16.7415 | 0.691586 | ||||||||
\(587\) | −0.850432 | + | 0.850432i | −0.0351011 | + | 0.0351011i | −0.724439 | − | 0.689338i | \(-0.757901\pi\) |
0.689338 | + | 0.724439i | \(0.257901\pi\) | |||||||
\(588\) | −1.35275 | + | 1.35275i | −0.0557866 | + | 0.0557866i | ||||
\(589\) | −29.3272 | − | 36.9627i | −1.20841 | − | 1.52302i | ||||
\(590\) | −17.5402 | − | 10.5587i | −0.722120 | − | 0.434693i | ||||
\(591\) | 22.8643i | 0.940512i | ||||||||
\(592\) | 16.5596 | + | 16.5596i | 0.680595 | + | 0.680595i | ||||
\(593\) | −20.2618 | − | 20.2618i | −0.832052 | − | 0.832052i | 0.155745 | − | 0.987797i | \(-0.450222\pi\) |
−0.987797 | + | 0.155745i | \(0.950222\pi\) | |||||||
\(594\) | − | 19.9299i | − | 0.817732i | ||||||
\(595\) | 1.17727 | + | 4.73820i | 0.0482635 | + | 0.194247i | ||||
\(596\) | 1.21235 | 0.0496597 | ||||||||
\(597\) | −5.87118 | − | 5.87118i | −0.240291 | − | 0.240291i | ||||
\(598\) | 4.43188 | + | 4.43188i | 0.181233 | + | 0.181233i | ||||
\(599\) | 12.6659 | 0.517514 | 0.258757 | − | 0.965943i | \(-0.416687\pi\) | ||||
0.258757 | + | 0.965943i | \(0.416687\pi\) | |||||||
\(600\) | −10.3714 | − | 19.5825i | −0.423409 | − | 0.799452i | ||||
\(601\) | 20.1215i | 0.820772i | 0.911912 | + | 0.410386i | \(0.134606\pi\) | ||||
−0.911912 | + | 0.410386i | \(0.865394\pi\) | |||||||
\(602\) | −28.0668 | − | 28.0668i | −1.14392 | − | 1.14392i | ||||
\(603\) | −0.618333 | + | 0.618333i | −0.0251805 | + | 0.0251805i | ||||
\(604\) | −0.848418 | −0.0345216 | ||||||||
\(605\) | 8.85043 | − | 2.19902i | 0.359821 | − | 0.0894027i | ||||
\(606\) | 11.6598 | 0.473648 | ||||||||
\(607\) | −5.35752 | − | 5.35752i | −0.217455 | − | 0.217455i | 0.589970 | − | 0.807425i | \(-0.299139\pi\) |
−0.807425 | + | 0.589970i | \(0.799139\pi\) | |||||||
\(608\) | 11.0785 | + | 1.27606i | 0.449292 | + | 0.0517509i | ||||
\(609\) | − | 7.35616i | − | 0.298087i | ||||||
\(610\) | 30.6720 | + | 18.4635i | 1.24187 | + | 0.747567i | ||||
\(611\) | − | 17.6540i | − | 0.714206i | ||||||
\(612\) | −0.120638 | + | 0.120638i | −0.00487651 | + | 0.00487651i | ||||
\(613\) | 16.7009 | + | 16.7009i | 0.674542 | + | 0.674542i | 0.958760 | − | 0.284218i | \(-0.0917340\pi\) |
−0.284218 | + | 0.958760i | \(0.591734\pi\) | |||||||
\(614\) | − | 16.6647i | − | 0.672534i | ||||||
\(615\) | 20.5236 | + | 12.3545i | 0.827591 | + | 0.498183i | ||||
\(616\) | − | 13.8274i | − | 0.557124i | ||||||
\(617\) | −10.8394 | + | 10.8394i | −0.436377 | + | 0.436377i | −0.890791 | − | 0.454414i | \(-0.849849\pi\) |
0.454414 | + | 0.890791i | \(0.349849\pi\) | |||||||
\(618\) | −2.06484 | + | 2.06484i | −0.0830600 | + | 0.0830600i | ||||
\(619\) | 0.0350725i | 0.00140968i | 1.00000 | 0.000704841i | \(0.000224358\pi\) | |||||
−1.00000 | 0.000704841i | \(0.999776\pi\) | ||||||||
\(620\) | −10.8247 | + | 2.68956i | −0.434732 | + | 0.108015i | ||||
\(621\) | − | 10.5116i | − | 0.421815i | ||||||
\(622\) | 33.5513 | + | 33.5513i | 1.34529 | + | 1.34529i | ||||
\(623\) | 25.6449 | − | 25.6449i | 1.02744 | − | 1.02744i | ||||
\(624\) | 15.8660i | 0.635150i | ||||||||
\(625\) | 14.0472 | − | 20.6803i | 0.561887 | − | 0.827214i | ||||
\(626\) | − | 1.11605i | − | 0.0446064i | ||||||
\(627\) | −2.40860 | + | 20.9111i | −0.0961903 | + | 0.835107i | ||||
\(628\) | −5.58864 | − | 5.58864i | −0.223011 | − | 0.223011i | ||||
\(629\) | −4.98816 | −0.198891 | ||||||||
\(630\) | −0.679569 | − | 2.73508i | −0.0270747 | − | 0.108968i | ||||
\(631\) | −26.3630 | −1.04949 | −0.524746 | − | 0.851259i | \(-0.675840\pi\) | ||||
−0.524746 | + | 0.851259i | \(0.675840\pi\) | |||||||
\(632\) | 21.6248 | − | 21.6248i | 0.860187 | − | 0.860187i | ||||
\(633\) | −11.2534 | − | 11.2534i | −0.447282 | − | 0.447282i | ||||
\(634\) | − | 26.4424i | − | 1.05016i | ||||||
\(635\) | −18.7781 | − | 11.3038i | −0.745184 | − | 0.448577i | ||||
\(636\) | −7.31124 | −0.289910 | ||||||||
\(637\) | −2.93559 | − | 2.93559i | −0.116312 | − | 0.116312i | ||||
\(638\) | 5.37298 | + | 5.37298i | 0.212718 | + | 0.212718i | ||||
\(639\) | 1.47472 | 0.0583392 | ||||||||
\(640\) | −15.6791 | + | 26.0463i | −0.619770 | + | 1.02957i | ||||
\(641\) | − | 22.6422i | − | 0.894313i | −0.894456 | − | 0.447156i | \(-0.852437\pi\) | ||
0.894456 | − | 0.447156i | \(-0.147563\pi\) | |||||||
\(642\) | 1.37938 | + | 1.37938i | 0.0544399 | + | 0.0544399i | ||||
\(643\) | −29.1555 | − | 29.1555i | −1.14978 | − | 1.14978i | −0.986595 | − | 0.163187i | \(-0.947823\pi\) |
−0.163187 | − | 0.986595i | \(-0.552177\pi\) | |||||||
\(644\) | 2.18342i | 0.0860387i | ||||||||
\(645\) | −46.3016 | + | 11.5043i | −1.82313 | + | 0.452981i | ||||
\(646\) | −5.37298 | + | 4.26307i | −0.211397 | + | 0.167728i | ||||
\(647\) | −18.9083 | + | 18.9083i | −0.743362 | + | 0.743362i | −0.973223 | − | 0.229862i | \(-0.926173\pi\) |
0.229862 | + | 0.973223i | \(0.426173\pi\) | |||||||
\(648\) | 17.0239 | − | 17.0239i | 0.668760 | − | 0.668760i | ||||
\(649\) | −15.3554 | −0.602753 | ||||||||
\(650\) | −12.7226 | + | 6.73820i | −0.499022 | + | 0.264294i | ||||
\(651\) | 43.2495 | 1.69508 | ||||||||
\(652\) | −0.915479 | + | 0.915479i | −0.0358529 | + | 0.0358529i | ||||
\(653\) | 12.9688 | + | 12.9688i | 0.507508 | + | 0.507508i | 0.913761 | − | 0.406252i | \(-0.133165\pi\) |
−0.406252 | + | 0.913761i | \(0.633165\pi\) | |||||||
\(654\) | 31.1683 | 1.21878 | ||||||||
\(655\) | −9.36069 | + | 2.32580i | −0.365752 | + | 0.0908764i | ||||
\(656\) | − | 27.4860i | − | 1.07315i | ||||||
\(657\) | −2.72753 | + | 2.72753i | −0.106411 | + | 0.106411i | ||||
\(658\) | 23.2230 | − | 23.2230i | 0.905326 | − | 0.905326i | ||||
\(659\) | 39.1592 | 1.52543 | 0.762713 | − | 0.646737i | \(-0.223867\pi\) | ||||
0.762713 | + | 0.646737i | \(0.223867\pi\) | |||||||
\(660\) | 4.26307 | + | 2.56623i | 0.165940 | + | 0.0998904i | ||||
\(661\) | 41.6799i | 1.62116i | 0.585628 | + | 0.810580i | \(0.300848\pi\) | ||||
−0.585628 | + | 0.810580i | \(0.699152\pi\) | |||||||
\(662\) | 6.12678 | − | 6.12678i | 0.238124 | − | 0.238124i | ||||
\(663\) | −2.38962 | − | 2.38962i | −0.0928052 | − | 0.0928052i | ||||
\(664\) | 8.57165 | 0.332645 | ||||||||
\(665\) | −2.72626 | − | 21.0404i | −0.105720 | − | 0.815910i | ||||
\(666\) | 2.87936 | 0.111573 | ||||||||
\(667\) | 2.83386 | + | 2.83386i | 0.109728 | + | 0.109728i | ||||
\(668\) | 5.33224 | − | 5.33224i | 0.206311 | − | 0.206311i | ||||
\(669\) | − | 36.2472i | − | 1.40140i | ||||||
\(670\) | 2.00388 | + | 8.06505i | 0.0774165 | + | 0.311580i | ||||
\(671\) | 26.8515 | 1.03659 | ||||||||
\(672\) | −7.22795 | + | 7.22795i | −0.278824 | + | 0.278824i | ||||
\(673\) | −28.7839 | + | 28.7839i | −1.10954 | + | 1.10954i | −0.116329 | + | 0.993211i | \(0.537113\pi\) |
−0.993211 | + | 0.116329i | \(0.962887\pi\) | |||||||
\(674\) | − | 34.6114i | − | 1.33318i | ||||||
\(675\) | 23.0787 | + | 7.09693i | 0.888298 | + | 0.273161i | ||||
\(676\) | −4.43802 | −0.170693 | ||||||||
\(677\) | 23.0115 | + | 23.0115i | 0.884406 | + | 0.884406i | 0.993979 | − | 0.109573i | \(-0.0349484\pi\) |
−0.109573 | + | 0.993979i | \(0.534948\pi\) | |||||||
\(678\) | 13.0685 | − | 13.0685i | 0.501892 | − | 0.501892i | ||||
\(679\) | 28.1656 | 1.08090 | ||||||||
\(680\) | −1.30588 | − | 5.25579i | −0.0500780 | − | 0.201550i | ||||
\(681\) | 51.8492 | 1.98687 | ||||||||
\(682\) | −31.5897 | + | 31.5897i | −1.20963 | + | 1.20963i | ||||
\(683\) | −4.53867 | + | 4.53867i | −0.173667 | + | 0.173667i | −0.788589 | − | 0.614921i | \(-0.789188\pi\) |
0.614921 | + | 0.788589i | \(0.289188\pi\) | |||||||
\(684\) | 0.580786 | − | 0.460811i | 0.0222069 | − | 0.0176196i | ||||
\(685\) | −10.4680 | + | 17.3896i | −0.399962 | + | 0.664423i | ||||
\(686\) | − | 31.6258i | − | 1.20748i | ||||||
\(687\) | 25.5994 | + | 25.5994i | 0.976677 | + | 0.976677i | ||||
\(688\) | 38.7081 | + | 38.7081i | 1.47573 | + | 1.47573i | ||||
\(689\) | − | 15.8660i | − | 0.604448i | ||||||
\(690\) | 12.0072 | + | 7.22795i | 0.457106 | + | 0.275163i | ||||
\(691\) | 21.1012 | 0.802726 | 0.401363 | − | 0.915919i | \(-0.368537\pi\) | ||||
0.401363 | + | 0.915919i | \(0.368537\pi\) | |||||||
\(692\) | 6.23121 | + | 6.23121i | 0.236875 | + | 0.236875i | ||||
\(693\) | −1.49466 | − | 1.49466i | −0.0567775 | − | 0.0567775i | ||||
\(694\) | −12.8557 | −0.487996 | ||||||||
\(695\) | 5.91548 | + | 23.8082i | 0.224387 | + | 0.903095i | ||||
\(696\) | 8.15972i | 0.309293i | ||||||||
\(697\) | 4.13974 | + | 4.13974i | 0.156804 | + | 0.156804i | ||||
\(698\) | −7.91577 | + | 7.91577i | −0.299616 | + | 0.299616i | ||||
\(699\) | 9.29674 | 0.351635 | ||||||||
\(700\) | −4.79380 | − | 1.47414i | −0.181188 | − | 0.0557173i | ||||
\(701\) | −0.729794 | −0.0275639 | −0.0137820 | − | 0.999905i | \(-0.504387\pi\) | ||||
−0.0137820 | + | 0.999905i | \(0.504387\pi\) | |||||||
\(702\) | −9.83201 | − | 9.83201i | −0.371085 | − | 0.371085i | ||||
\(703\) | 21.5340 | + | 2.48036i | 0.812171 | + | 0.0935485i | ||||
\(704\) | 14.2206i | 0.535958i | ||||||||
\(705\) | −9.51886 | − | 38.3108i | −0.358501 | − | 1.44287i | ||||
\(706\) | 35.4314i | 1.33348i | ||||||||
\(707\) | −6.23287 | + | 6.23287i | −0.234411 | + | 0.234411i | ||||
\(708\) | 3.49079 | + | 3.49079i | 0.131192 | + | 0.131192i | ||||
\(709\) | 24.3812i | 0.915656i | 0.889041 | + | 0.457828i | \(0.151372\pi\) | ||||
−0.889041 | + | 0.457828i | \(0.848628\pi\) | |||||||
\(710\) | 7.22795 | − | 12.0072i | 0.271260 | − | 0.450622i | ||||
\(711\) | − | 4.67500i | − | 0.175326i | ||||||
\(712\) | −28.4463 | + | 28.4463i | −1.06607 | + | 1.06607i | ||||
\(713\) | −16.6613 | + | 16.6613i | −0.623971 | + | 0.623971i | ||||
\(714\) | − | 6.28685i | − | 0.235279i | ||||||
\(715\) | −5.56894 | + | 9.25122i | −0.208267 | + | 0.345976i | ||||
\(716\) | − | 5.83658i | − | 0.218123i | ||||||
\(717\) | −28.4442 | − | 28.4442i | −1.06227 | − | 1.06227i | ||||
\(718\) | 30.1367 | − | 30.1367i | 1.12469 | − | 1.12469i | ||||
\(719\) | 43.6970i | 1.62962i | 0.579726 | + | 0.814811i | \(0.303160\pi\) | ||||
−0.579726 | + | 0.814811i | \(0.696840\pi\) | |||||||
\(720\) | 0.937221 | + | 3.77205i | 0.0349282 | + | 0.140576i | ||||
\(721\) | − | 2.20756i | − | 0.0822137i | ||||||
\(722\) | 25.3151 | − | 15.7321i | 0.942131 | − | 0.585487i | ||||
\(723\) | 6.06770 | + | 6.06770i | 0.225660 | + | 0.225660i | ||||
\(724\) | −5.37912 | −0.199913 | ||||||||
\(725\) | −8.13517 | + | 4.30859i | −0.302133 | + | 0.160017i | ||||
\(726\) | −11.7431 | −0.435828 | ||||||||
\(727\) | 18.7081 | − | 18.7081i | 0.693843 | − | 0.693843i | −0.269232 | − | 0.963075i | \(-0.586770\pi\) |
0.963075 | + | 0.269232i | \(0.0867699\pi\) | |||||||
\(728\) | −6.82150 | − | 6.82150i | −0.252822 | − | 0.252822i | ||||
\(729\) | 22.9109i | 0.848553i | ||||||||
\(730\) | 8.83929 | + | 35.5757i | 0.327157 | + | 1.31672i | ||||
\(731\) | −11.6598 | −0.431254 | ||||||||
\(732\) | −6.10421 | − | 6.10421i | −0.225618 | − | 0.225618i | ||||
\(733\) | −30.6742 | − | 30.6742i | −1.13298 | − | 1.13298i | −0.989680 | − | 0.143298i | \(-0.954229\pi\) |
−0.143298 | − | 0.989680i | \(-0.545771\pi\) | |||||||
\(734\) | −2.42193 | −0.0893949 | ||||||||
\(735\) | −7.95332 | − | 4.78765i | −0.293363 | − | 0.176595i | ||||
\(736\) | − | 5.56894i | − | 0.205274i | ||||||
\(737\) | 4.40737 | + | 4.40737i | 0.162348 | + | 0.162348i | ||||
\(738\) | −2.38962 | − | 2.38962i | −0.0879632 | − | 0.0879632i | ||||
\(739\) | 13.6163i | 0.500885i | 0.968131 | + | 0.250443i | \(0.0805762\pi\) | ||||
−0.968131 | + | 0.250443i | \(0.919424\pi\) | |||||||
\(740\) | 2.64268 | − | 4.39007i | 0.0971469 | − | 0.161382i | ||||
\(741\) | 9.12783 | + | 11.5043i | 0.335319 | + | 0.422621i | ||||
\(742\) | 20.8710 | − | 20.8710i | 0.766197 | − | 0.766197i | ||||
\(743\) | 23.4826 | − | 23.4826i | 0.861494 | − | 0.861494i | −0.130017 | − | 0.991512i | \(-0.541503\pi\) |
0.991512 | + | 0.130017i | \(0.0415033\pi\) | |||||||
\(744\) | −47.9739 | −1.75881 | ||||||||
\(745\) | 1.41855 | + | 5.70928i | 0.0519717 | + | 0.209172i | ||||
\(746\) | 6.37015 | 0.233228 | ||||||||
\(747\) | 0.926543 | − | 0.926543i | 0.0339004 | − | 0.0339004i | ||||
\(748\) | 0.859888 | + | 0.859888i | 0.0314406 | + | 0.0314406i | ||||
\(749\) | −1.47472 | −0.0538853 | ||||||||
\(750\) | −23.9760 | + | 21.4824i | −0.875479 | + | 0.784425i | ||||
\(751\) | − | 20.9699i | − | 0.765202i | −0.923914 | − | 0.382601i | \(-0.875028\pi\) | ||
0.923914 | − | 0.382601i | \(-0.124972\pi\) | |||||||
\(752\) | −32.0277 | + | 32.0277i | −1.16793 | + | 1.16793i | ||||
\(753\) | −5.42967 | + | 5.42967i | −0.197868 | + | 0.197868i | ||||
\(754\) | 5.30131 | 0.193062 | ||||||||
\(755\) | −0.992723 | − | 3.99543i | −0.0361289 | − | 0.145409i | ||||
\(756\) | − | 4.84385i | − | 0.176169i | ||||||
\(757\) | −4.02893 | + | 4.02893i | −0.146434 | + | 0.146434i | −0.776523 | − | 0.630089i | \(-0.783018\pi\) |
0.630089 | + | 0.776523i | \(0.283018\pi\) | |||||||
\(758\) | −32.8781 | − | 32.8781i | −1.19419 | − | 1.19419i | ||||
\(759\) | 10.5116 | 0.381546 | ||||||||
\(760\) | 3.02406 | + | 23.3387i | 0.109694 | + | 0.846585i | ||||
\(761\) | 48.1939 | 1.74703 | 0.873514 | − | 0.486799i | \(-0.161836\pi\) | ||||
0.873514 | + | 0.486799i | \(0.161836\pi\) | |||||||
\(762\) | 19.9569 | + | 19.9569i | 0.722963 | + | 0.722963i | ||||
\(763\) | −16.6613 | + | 16.6613i | −0.603180 | + | 0.603180i | ||||
\(764\) | − | 1.22285i | − | 0.0442411i | ||||||
\(765\) | −0.709275 | − | 0.426961i | −0.0256439 | − | 0.0154368i | ||||
\(766\) | 0.611424 | 0.0220916 | ||||||||
\(767\) | −7.57531 | + | 7.57531i | −0.273528 | + | 0.273528i | ||||
\(768\) | 13.6506 | − | 13.6506i | 0.492574 | − | 0.492574i | ||||
\(769\) | − | 14.0494i | − | 0.506636i | −0.967383 | − | 0.253318i | \(-0.918478\pi\) | ||
0.967383 | − | 0.253318i | \(-0.0815219\pi\) | |||||||
\(770\) | −19.4952 | + | 4.84385i | −0.702557 | + | 0.174560i | ||||
\(771\) | 3.53570 | 0.127335 | ||||||||
\(772\) | −5.96358 | − | 5.96358i | −0.214634 | − | 0.214634i | ||||
\(773\) | −2.29063 | + | 2.29063i | −0.0823881 | + | 0.0823881i | −0.747100 | − | 0.664712i | \(-0.768554\pi\) |
0.664712 | + | 0.747100i | \(0.268554\pi\) | |||||||
\(774\) | 6.73051 | 0.241923 | ||||||||
\(775\) | −25.3317 | − | 47.8296i | −0.909943 | − | 1.71809i | ||||
\(776\) | −31.2423 | −1.12153 | ||||||||
\(777\) | −14.0494 | + | 14.0494i | −0.504021 | + | 0.504021i | ||||
\(778\) | 11.3759 | − | 11.3759i | 0.407847 | − | 0.407847i | ||||
\(779\) | −15.8129 | − | 19.9299i | −0.566556 | − | 0.714061i | ||||
\(780\) | 3.36910 | − | 0.837101i | 0.120633 | − | 0.0299730i | ||||
\(781\) | − | 10.5116i | − | 0.376134i | ||||||
\(782\) | 2.42193 | + | 2.42193i | 0.0866079 | + | 0.0866079i | ||||
\(783\) | −6.28685 | − | 6.28685i | −0.224674 | − | 0.224674i | ||||
\(784\) | 10.6514i | 0.380408i | ||||||||
\(785\) | 19.7792 | − | 32.8576i | 0.705951 | − | 1.17274i | ||||
\(786\) | 12.4202 | 0.443012 | ||||||||
\(787\) | −3.04529 | − | 3.04529i | −0.108553 | − | 0.108553i | 0.650744 | − | 0.759297i | \(-0.274457\pi\) |
−0.759297 | + | 0.650744i | \(0.774457\pi\) | |||||||
\(788\) | −4.05890 | − | 4.05890i | −0.144592 | − | 0.144592i | ||||
\(789\) | 0.848418 | 0.0302045 | ||||||||
\(790\) | −38.0638 | − | 22.9132i | −1.35425 | − | 0.815215i | ||||
\(791\) | 13.9717i | 0.496778i | ||||||||
\(792\) | 1.65793 | + | 1.65793i | 0.0589121 | + | 0.0589121i | ||||
\(793\) | 13.2467 | − | 13.2467i | 0.470403 | − | 0.470403i | ||||
\(794\) | −25.4551 | −0.903367 | ||||||||
\(795\) | −8.55479 | − | 34.4307i | −0.303407 | − | 1.22113i | ||||
\(796\) | 2.08452 | 0.0738839 | ||||||||
\(797\) | −2.32020 | − | 2.32020i | −0.0821857 | − | 0.0821857i | 0.664819 | − | 0.747005i | \(-0.268509\pi\) |
−0.747005 | + | 0.664819i | \(0.768509\pi\) | |||||||
\(798\) | −3.12613 | + | 27.1405i | −0.110664 | + | 0.960764i | ||||
\(799\) | − | 9.64754i | − | 0.341305i | ||||||
\(800\) | 12.2269 | + | 3.75989i | 0.432285 | + | 0.132932i | ||||
\(801\) | 6.14973i | 0.217290i | ||||||||
\(802\) | −35.6742 | + | 35.6742i | −1.25970 | + | 1.25970i | ||||
\(803\) | 19.4413 | + | 19.4413i | 0.686070 | + | 0.686070i | ||||
\(804\) | − | 2.00388i | − | 0.0706712i | ||||||
\(805\) | −10.2823 | + | 2.55479i | −0.362404 | + | 0.0900444i | ||||
\(806\) | 31.1683i | 1.09786i | ||||||||
\(807\) | 15.5571 | − | 15.5571i | 0.547634 | − | 0.547634i | ||||
\(808\) | 6.91372 | − | 6.91372i | 0.243224 | − | 0.243224i | ||||
\(809\) | 36.2122i | 1.27315i | 0.771214 | + | 0.636576i | \(0.219650\pi\) | ||||
−0.771214 | + | 0.636576i | \(0.780350\pi\) | |||||||
\(810\) | −29.9653 | − | 18.0382i | −1.05287 | − | 0.633797i | ||||
\(811\) | 0.313153i | 0.0109963i | 0.999985 | + | 0.00549815i | \(0.00175012\pi\) | ||||
−0.999985 | + | 0.00549815i | \(0.998250\pi\) | |||||||
\(812\) | 1.30588 | + | 1.30588i | 0.0458273 | + | 0.0458273i | ||||
\(813\) | 20.7555 | − | 20.7555i | 0.727928 | − | 0.727928i | ||||
\(814\) | − | 20.5236i | − | 0.719351i | ||||||
\(815\) | −5.38243 | − | 3.24005i | −0.188538 | − | 0.113494i | ||||
\(816\) | 8.67044i | 0.303526i | ||||||||
\(817\) | 50.3358 | + | 5.79784i | 1.76103 | + | 0.202841i | ||||
\(818\) | 27.1578 | + | 27.1578i | 0.949550 | + | 0.949550i | ||||
\(819\) | −1.47472 | −0.0515310 | ||||||||
\(820\) | −5.83658 | + | 1.45018i | −0.203822 | + | 0.0506425i | ||||
\(821\) | 16.2557 | 0.567326 | 0.283663 | − | 0.958924i | \(-0.408450\pi\) | ||||
0.283663 | + | 0.958924i | \(0.408450\pi\) | |||||||
\(822\) | 18.4813 | − | 18.4813i | 0.644610 | − | 0.644610i | ||||
\(823\) | 2.46922 | + | 2.46922i | 0.0860717 | + | 0.0860717i | 0.748832 | − | 0.662760i | \(-0.230615\pi\) |
−0.662760 | + | 0.748832i | \(0.730615\pi\) | |||||||
\(824\) | 2.44870i | 0.0853046i | ||||||||
\(825\) | −7.09693 | + | 23.0787i | −0.247083 | + | 0.803496i | ||||
\(826\) | −19.9299 | −0.693448 | ||||||||
\(827\) | 4.24147 | + | 4.24147i | 0.147490 | + | 0.147490i | 0.776996 | − | 0.629506i | \(-0.216743\pi\) |
−0.629506 | + | 0.776996i | \(0.716743\pi\) | |||||||
\(828\) | −0.261795 | − | 0.261795i | −0.00909801 | − | 0.00909801i | ||||
\(829\) | −9.66316 | −0.335615 | −0.167808 | − | 0.985820i | \(-0.553669\pi\) | ||||
−0.167808 | + | 0.985820i | \(0.553669\pi\) | |||||||
\(830\) | −3.00271 | − | 12.0851i | −0.104226 | − | 0.419480i | ||||
\(831\) | − | 39.4723i | − | 1.36928i | ||||||
\(832\) | 7.01545 | + | 7.01545i | 0.243217 | + | 0.243217i | ||||
\(833\) | −1.60424 | − | 1.60424i | −0.0555835 | − | 0.0555835i | ||||
\(834\) | − | 31.5897i | − | 1.09386i | ||||||
\(835\) | 31.3502 | + | 18.8718i | 1.08492 | + | 0.653086i | ||||
\(836\) | −3.28458 | − | 4.13974i | −0.113600 | − | 0.143176i | ||||
\(837\) | 36.9627 | − | 36.9627i | 1.27762 | − | 1.27762i | ||||
\(838\) | −27.5156 | + | 27.5156i | −0.950511 | + | 0.950511i | ||||
\(839\) | −48.5092 | −1.67472 | −0.837362 | − | 0.546649i | \(-0.815903\pi\) | ||||
−0.837362 | + | 0.546649i | \(0.815903\pi\) | |||||||
\(840\) | −18.4813 | − | 11.1252i | −0.637666 | − | 0.383855i | ||||
\(841\) | −25.6102 | −0.883110 | ||||||||
\(842\) | 15.3379 | − | 15.3379i | 0.528579 | − | 0.528579i | ||||
\(843\) | −20.5236 | − | 20.5236i | −0.706870 | − | 0.706870i | ||||
\(844\) | 3.99543 | 0.137529 | ||||||||
\(845\) | −5.19287 | − | 20.8999i | −0.178640 | − | 0.718978i | ||||
\(846\) | 5.56894i | 0.191464i | ||||||||
\(847\) | 6.27739 | − | 6.27739i | 0.215694 | − | 0.215694i | ||||
\(848\) | −28.7839 | + | 28.7839i | −0.988445 | + | 0.988445i | ||||
\(849\) | 9.03685 | 0.310144 | ||||||||
\(850\) | −6.95263 | + | 3.68228i | −0.238473 | + | 0.126301i | ||||
\(851\) | − | 10.8247i | − | 0.371067i | ||||||
\(852\) | −2.38962 | + | 2.38962i | −0.0818671 | + | 0.0818671i | ||||
\(853\) | 4.23513 | + | 4.23513i | 0.145008 | + | 0.145008i | 0.775884 | − | 0.630876i | \(-0.217304\pi\) |
−0.630876 | + | 0.775884i | \(0.717304\pi\) | |||||||
\(854\) | 34.8506 | 1.19256 | ||||||||
\(855\) | 2.84966 | + | 2.19589i | 0.0974562 | + | 0.0750979i | ||||
\(856\) | 1.63582 | 0.0559111 | ||||||||
\(857\) | 9.18410 | + | 9.18410i | 0.313723 | + | 0.313723i | 0.846350 | − | 0.532627i | \(-0.178795\pi\) |
−0.532627 | + | 0.846350i | \(0.678795\pi\) | |||||||
\(858\) | 9.83201 | − | 9.83201i | 0.335659 | − | 0.335659i | ||||
\(859\) | 17.1194i | 0.584107i | 0.956402 | + | 0.292053i | \(0.0943385\pi\) | ||||
−0.956402 | + | 0.292053i | \(0.905661\pi\) | |||||||
\(860\) | 6.17727 | − | 10.2618i | 0.210643 | − | 0.349924i | ||||
\(861\) | 23.3197 | 0.794732 | ||||||||
\(862\) | −19.7698 | + | 19.7698i | −0.673362 | + | 0.673362i | ||||
\(863\) | 11.2742 | − | 11.2742i | 0.383779 | − | 0.383779i | −0.488683 | − | 0.872462i | \(-0.662522\pi\) |
0.872462 | + | 0.488683i | \(0.162522\pi\) | |||||||
\(864\) | 12.3545i | 0.420310i | ||||||||
\(865\) | −22.0534 | + | 36.6355i | −0.749839 | + | 1.24565i | ||||
\(866\) | 5.28968 | 0.179751 | ||||||||
\(867\) | 20.7585 | + | 20.7585i | 0.704995 | + | 0.704995i | ||||
\(868\) | −7.67772 | + | 7.67772i | −0.260599 | + | 0.260599i | ||||
\(869\) | −33.3226 | −1.13039 | ||||||||
\(870\) | 11.5043 | − | 2.85841i | 0.390032 | − | 0.0969091i | ||||
\(871\) | 4.34858 | 0.147346 | ||||||||
\(872\) | 18.4813 | − | 18.4813i | 0.625857 | − | 0.625857i | ||||
\(873\) | −3.37710 | + | 3.37710i | −0.114298 | + | 0.114298i | ||||
\(874\) | −9.25122 | − | 11.6598i | −0.312927 | − | 0.394400i | ||||
\(875\) | 1.33299 | − | 24.3002i | 0.0450631 | − | 0.821496i | ||||
\(876\) | − | 8.83929i | − | 0.298652i | ||||||
\(877\) | −23.8008 | − | 23.8008i | −0.803696 | − | 0.803696i | 0.179975 | − | 0.983671i | \(-0.442398\pi\) |
−0.983671 | + | 0.179975i | \(0.942398\pi\) | |||||||
\(878\) | −26.4040 | − | 26.4040i | −0.891092 | − | 0.891092i | ||||
\(879\) | − | 19.5890i | − | 0.660721i | ||||||
\(880\) | 26.8865 | − | 6.68035i | 0.906345 | − | 0.225194i | ||||
\(881\) | −31.7359 | −1.06921 | −0.534605 | − | 0.845102i | \(-0.679540\pi\) | ||||
−0.534605 | + | 0.845102i | \(0.679540\pi\) | |||||||
\(882\) | 0.926028 | + | 0.926028i | 0.0311810 | + | 0.0311810i | ||||
\(883\) | 4.93495 | + | 4.93495i | 0.166074 | + | 0.166074i | 0.785251 | − | 0.619177i | \(-0.212534\pi\) |
−0.619177 | + | 0.785251i | \(0.712534\pi\) | |||||||
\(884\) | 0.848418 | 0.0285354 | ||||||||
\(885\) | −12.3545 | + | 20.5236i | −0.415294 | + | 0.689893i | ||||
\(886\) | 45.0945i | 1.51498i | ||||||||
\(887\) | −10.6588 | − | 10.6588i | −0.357888 | − | 0.357888i | 0.505146 | − | 0.863034i | \(-0.331439\pi\) |
−0.863034 | + | 0.505146i | \(0.831439\pi\) | |||||||
\(888\) | 15.5842 | − | 15.5842i | 0.522970 | − | 0.522970i | ||||
\(889\) | −21.3363 | −0.715597 | ||||||||
\(890\) | 50.0710 | + | 30.1412i | 1.67838 | + | 1.01033i | ||||
\(891\) | −26.2329 | −0.878834 | ||||||||
\(892\) | 6.43466 | + | 6.43466i | 0.215448 | + | 0.215448i | ||||
\(893\) | −4.79723 | + | 41.6487i | −0.160533 | + | 1.39372i | ||||
\(894\) | − | 7.57531i | − | 0.253356i | ||||||
\(895\) | 27.4860 | − | 6.82930i | 0.918757 | − | 0.228278i | ||||
\(896\) | 29.5948i | 0.988693i | ||||||||
\(897\) | 5.18568 | − | 5.18568i | 0.173145 | − | 0.173145i | ||||
\(898\) | 15.4980 | + | 15.4980i | 0.517174 | + | 0.517174i | ||||
\(899\) | 19.9299i | 0.664698i | ||||||||
\(900\) | 0.751536 | − | 0.398032i | 0.0250512 | − | 0.0132677i | ||||
\(901\) | − | 8.67044i | − | 0.288854i | ||||||
\(902\) | −17.0328 | + | 17.0328i | −0.567130 | + | 0.567130i | ||||
\(903\) | −32.8406 | + | 32.8406i | −1.09287 | + | 1.09287i | ||||
\(904\) | − | 15.4980i | − | 0.515455i | ||||||
\(905\) | −6.29403 | − | 25.3317i | −0.209221 | − | 0.842056i | ||||
\(906\) | 5.30131i | 0.176124i | ||||||||
\(907\) | −23.8600 | − | 23.8600i | −0.792257 | − | 0.792257i | 0.189604 | − | 0.981861i | \(-0.439280\pi\) |
−0.981861 | + | 0.189604i | \(0.939280\pi\) | |||||||
\(908\) | −9.20435 | + | 9.20435i | −0.305457 | + | 0.305457i | ||||
\(909\) | − | 1.49466i | − | 0.0495748i | ||||||
\(910\) | −7.22795 | + | 12.0072i | −0.239604 | + | 0.398034i | ||||
\(911\) | − | 32.3053i | − | 1.07032i | −0.844749 | − | 0.535162i | \(-0.820251\pi\) | ||
0.844749 | − | 0.535162i | \(-0.179749\pi\) | |||||||
\(912\) | 4.31137 | − | 37.4305i | 0.142764 | − | 1.23945i | ||||
\(913\) | −6.60424 | − | 6.60424i | −0.218568 | − | 0.218568i | ||||
\(914\) | 17.3864 | 0.575091 | ||||||||
\(915\) | 21.6039 | − | 35.8888i | 0.714204 | − | 1.18645i | ||||
\(916\) | −9.08888 | −0.300305 | ||||||||
\(917\) | −6.63931 | + | 6.63931i | −0.219249 | + | 0.219249i | ||||
\(918\) | −5.37298 | − | 5.37298i | −0.177335 | − | 0.177335i | ||||
\(919\) | − | 5.86991i | − | 0.193630i | −0.995302 | − | 0.0968152i | \(-0.969134\pi\) | ||
0.995302 | − | 0.0968152i | \(-0.0308656\pi\) | |||||||
\(920\) | 11.4055 | − | 2.83386i | 0.376029 | − | 0.0934297i | ||||
\(921\) | −19.4992 | −0.642520 | ||||||||
\(922\) | −35.7791 | − | 35.7791i | −1.17832 | − | 1.17832i | ||||
\(923\) | −5.18568 | − | 5.18568i | −0.170689 | − | 0.170689i | ||||
\(924\) | 4.84385 | 0.159351 | ||||||||
\(925\) | 23.7662 | + | 7.30836i | 0.781428 | + | 0.240297i | ||||
\(926\) | − | 3.12604i | − | 0.102728i | ||||||
\(927\) | 0.264690 | + | 0.264690i | 0.00869355 | + | 0.00869355i | ||||
\(928\) | −3.33072 | − | 3.33072i | −0.109336 | − | 0.109336i | ||||
\(929\) | 58.6369i | 1.92381i | 0.273379 | + | 0.961907i | \(0.411859\pi\) | ||||
−0.273379 | + | 0.961907i | \(0.588141\pi\) | |||||||
\(930\) | 16.8056 | + | 67.6380i | 0.551078 | + | 2.21794i | ||||
\(931\) | 6.12783 | + | 7.72324i | 0.200831 | + | 0.253119i | ||||
\(932\) | −1.65037 | + | 1.65037i | −0.0540597 | + | 0.0540597i | ||||
\(933\) | 39.2580 | − | 39.2580i | 1.28525 | − | 1.28525i | ||||
\(934\) | 34.7518 | 1.13711 | ||||||||
\(935\) | −3.04331 | + | 5.05559i | −0.0995267 | + | 0.165336i | ||||
\(936\) | 1.63582 | 0.0534684 | ||||||||
\(937\) | −14.4413 | + | 14.4413i | −0.471778 | + | 0.471778i | −0.902490 | − | 0.430712i | \(-0.858263\pi\) |
0.430712 | + | 0.902490i | \(0.358263\pi\) | |||||||
\(938\) | 5.72034 | + | 5.72034i | 0.186776 | + | 0.186776i | ||||
\(939\) | −1.30588 | −0.0426156 | ||||||||
\(940\) | 8.49079 | + | 5.11118i | 0.276939 | + | 0.166708i | ||||
\(941\) | − | 47.5165i | − | 1.54899i | −0.632578 | − | 0.774496i | \(-0.718003\pi\) | ||
0.632578 | − | 0.774496i | \(-0.281997\pi\) | |||||||
\(942\) | −34.9204 | + | 34.9204i | −1.13777 | + | 1.13777i | ||||
\(943\) | −8.98359 | + | 8.98359i | −0.292546 | + | 0.292546i | ||||
\(944\) | 27.4860 | 0.894594 | ||||||||
\(945\) | 22.8110 | − | 5.66773i | 0.742043 | − | 0.184371i | ||||
\(946\) | − | 47.9739i | − | 1.55977i | ||||||
\(947\) | 11.2218 | − | 11.2218i | 0.364660 | − | 0.364660i | −0.500866 | − | 0.865525i | \(-0.666985\pi\) |
0.865525 | + | 0.500866i | \(0.166985\pi\) | |||||||
\(948\) | 7.57531 | + | 7.57531i | 0.246035 | + | 0.246035i | ||||
\(949\) | 19.1820 | 0.622675 | ||||||||
\(950\) | 31.8457 | − | 12.4393i | 1.03321 | − | 0.403585i | ||||
\(951\) | −30.9399 | −1.00329 | ||||||||
\(952\) | −3.72780 | − | 3.72780i | −0.120819 | − | 0.120819i | ||||
\(953\) | −23.4531 | + | 23.4531i | −0.759719 | + | 0.759719i | −0.976271 | − | 0.216552i | \(-0.930519\pi\) |
0.216552 | + | 0.976271i | \(0.430519\pi\) | |||||||
\(954\) | 5.00492i | 0.162040i | ||||||||
\(955\) | 5.75872 | − | 1.43084i | 0.186348 | − | 0.0463008i | ||||
\(956\) | 10.0989 | 0.326622 | ||||||||
\(957\) | 6.28685 | − | 6.28685i | 0.203225 | − | 0.203225i | ||||
\(958\) | 3.64338 | − | 3.64338i | 0.117712 | − | 0.117712i | ||||
\(959\) | 19.7587i | 0.638042i | ||||||||
\(960\) | 19.0068 | + | 11.4415i | 0.613441 | + | 0.369272i | ||||
\(961\) | −86.1748 | −2.77983 | ||||||||
\(962\) | −10.1249 | − | 10.1249i | −0.326440 | − | 0.326440i | ||||
\(963\) | 0.176822 | − | 0.176822i | 0.00569800 | − | 0.00569800i | ||||
\(964\) | −2.15429 | −0.0693851 | ||||||||
\(965\) | 21.1062 | − | 35.0620i | 0.679433 | − | 1.12869i | ||||
\(966\) | 13.6430 | 0.438957 | ||||||||
\(967\) | 8.98440 | − | 8.98440i | 0.288919 | − | 0.288919i | −0.547734 | − | 0.836653i | \(-0.684509\pi\) |
0.836653 | + | 0.547734i | \(0.184509\pi\) | |||||||
\(968\) | −6.96311 | + | 6.96311i | −0.223803 | + | 0.223803i | ||||
\(969\) | 4.98816 | + | 6.28685i | 0.160243 | + | 0.201963i | ||||
\(970\) | 10.9444 | + | 44.0482i | 0.351404 | + | 1.41430i | ||||
\(971\) | 15.0423i | 0.482730i | 0.970434 | + | 0.241365i | \(0.0775950\pi\) | ||||
−0.970434 | + | 0.241365i | \(0.922405\pi\) | |||||||
\(972\) | 1.24305 | + | 1.24305i | 0.0398709 | + | 0.0398709i | ||||
\(973\) | 16.8865 | + | 16.8865i | 0.541358 | + | 0.541358i | ||||
\(974\) | − | 1.51414i | − | 0.0485160i | ||||||
\(975\) | 7.88428 | + | 14.8865i | 0.252499 | + | 0.476751i | ||||
\(976\) | −48.0638 | −1.53849 | ||||||||
\(977\) | 18.5450 | + | 18.5450i | 0.593308 | + | 0.593308i | 0.938523 | − | 0.345216i | \(-0.112194\pi\) |
−0.345216 | + | 0.938523i | \(0.612194\pi\) | |||||||
\(978\) | 5.72034 | + | 5.72034i | 0.182916 | + | 0.182916i | ||||
\(979\) | 43.8342 | 1.40095 | ||||||||
\(980\) | 2.26180 | − | 0.561975i | 0.0722504 | − | 0.0179516i | ||||
\(981\) | − | 3.99543i | − | 0.127564i | ||||||
\(982\) | −7.78742 | − | 7.78742i | −0.248506 | − | 0.248506i | ||||
\(983\) | −25.0561 | + | 25.0561i | −0.799167 | + | 0.799167i | −0.982964 | − | 0.183797i | \(-0.941161\pi\) |
0.183797 | + | 0.982964i | \(0.441161\pi\) | |||||||
\(984\) | −25.8670 | −0.824610 | ||||||||
\(985\) | 14.3652 | − | 23.8638i | 0.457714 | − | 0.760363i | ||||
\(986\) | 2.89705 | 0.0922609 | ||||||||
\(987\) | −27.1729 | − | 27.1729i | −0.864923 | − | 0.864923i | ||||
\(988\) | −3.66265 | − | 0.421875i | −0.116524 | − | 0.0134216i | ||||
\(989\) | − | 25.3028i | − | 0.804583i | ||||||
\(990\) | 1.75672 | − | 2.91829i | 0.0558321 | − | 0.0927493i | ||||
\(991\) | 4.36185i | 0.138559i | 0.997597 | + | 0.0692794i | \(0.0220700\pi\) | ||||
−0.997597 | + | 0.0692794i | \(0.977930\pi\) | |||||||
\(992\) | 19.5825 | − | 19.5825i | 0.621745 | − | 0.621745i | ||||
\(993\) | −7.16886 | − | 7.16886i | −0.227497 | − | 0.227497i | ||||
\(994\) | − | 13.6430i | − | 0.432730i | ||||||
\(995\) | 2.43907 | + | 9.81658i | 0.0773237 | + | 0.311207i | ||||
\(996\) | 3.00271i | 0.0951446i | ||||||||
\(997\) | 7.18342 | − | 7.18342i | 0.227501 | − | 0.227501i | −0.584147 | − | 0.811648i | \(-0.698571\pi\) |
0.811648 | + | 0.584147i | \(0.198571\pi\) | |||||||
\(998\) | −19.9915 | + | 19.9915i | −0.632821 | + | 0.632821i | ||||
\(999\) | 24.0144i | 0.759781i |
(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 | 95.2.g.b.18.5 | yes | 12 | |
3.2 | odd | 2 | 855.2.p.f.208.2 | 12 | |||
5.2 | odd | 4 | inner | 95.2.g.b.37.2 | yes | 12 | |
5.3 | odd | 4 | 475.2.g.b.132.5 | 12 | |||
5.4 | even | 2 | 475.2.g.b.18.2 | 12 | |||
15.2 | even | 4 | 855.2.p.f.37.5 | 12 | |||
19.18 | odd | 2 | inner | 95.2.g.b.18.2 | ✓ | 12 | |
57.56 | even | 2 | 855.2.p.f.208.5 | 12 | |||
95.18 | even | 4 | 475.2.g.b.132.2 | 12 | |||
95.37 | even | 4 | inner | 95.2.g.b.37.5 | yes | 12 | |
95.94 | odd | 2 | 475.2.g.b.18.5 | 12 | |||
285.227 | odd | 4 | 855.2.p.f.37.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.g.b.18.2 | ✓ | 12 | 19.18 | odd | 2 | inner | |
95.2.g.b.18.5 | yes | 12 | 1.1 | even | 1 | trivial | |
95.2.g.b.37.2 | yes | 12 | 5.2 | odd | 4 | inner | |
95.2.g.b.37.5 | yes | 12 | 95.37 | even | 4 | inner | |
475.2.g.b.18.2 | 12 | 5.4 | even | 2 | |||
475.2.g.b.18.5 | 12 | 95.94 | odd | 2 | |||
475.2.g.b.132.2 | 12 | 95.18 | even | 4 | |||
475.2.g.b.132.5 | 12 | 5.3 | odd | 4 | |||
855.2.p.f.37.2 | 12 | 285.227 | odd | 4 | |||
855.2.p.f.37.5 | 12 | 15.2 | even | 4 | |||
855.2.p.f.208.2 | 12 | 3.2 | odd | 2 | |||
855.2.p.f.208.5 | 12 | 57.56 | even | 2 |