Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [70,3,Mod(69,70)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(70, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("70.69");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 70 = 2 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 70.d (of order \(2\), degree \(1\), 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: | \(1.90736185052\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.211319484596224.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 2x^{6} - 48x^{5} - 23x^{4} - 48x^{3} + 1226x^{2} - 7512x + 24408 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 69.7 | ||
Root | \(-1.28865 + 3.99943i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 70.69 |
Dual form | 70.3.d.a.69.3 |
$q$-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 \(\left(\mathbb{Z}/70\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(57\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421i | 0.707107i | ||||||||
\(3\) | 2.07875 | 0.692918 | 0.346459 | − | 0.938065i | \(-0.387384\pi\) | ||||
0.346459 | + | 0.938065i | \(0.387384\pi\) | |||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 4.65605 | − | 1.82242i | 0.931210 | − | 0.364484i | ||||
\(6\) | 2.93980i | 0.489967i | ||||||||
\(7\) | 3.36740 | + | 6.13682i | 0.481057 | + | 0.876689i | ||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | −4.67878 | −0.519864 | ||||||||
\(10\) | 2.57729 | + | 6.58465i | 0.257729 | + | 0.658465i | ||||
\(11\) | 1.67878 | 0.152616 | 0.0763082 | − | 0.997084i | \(-0.475687\pi\) | ||||
0.0763082 | + | 0.997084i | \(0.475687\pi\) | |||||||
\(12\) | −4.15751 | −0.346459 | ||||||||
\(13\) | −9.81063 | −0.754664 | −0.377332 | − | 0.926078i | \(-0.623158\pi\) | ||||
−0.377332 | + | 0.926078i | \(0.623158\pi\) | |||||||
\(14\) | −8.67878 | + | 4.76222i | −0.619913 | + | 0.340159i | ||||
\(15\) | 9.67878 | − | 3.78837i | 0.645252 | − | 0.252558i | ||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 0.498539 | 0.0293258 | 0.0146629 | − | 0.999892i | \(-0.495332\pi\) | ||||
0.0146629 | + | 0.999892i | \(0.495332\pi\) | |||||||
\(18\) | − | 6.61679i | − | 0.367600i | ||||||
\(19\) | − | 32.2182i | − | 1.69569i | −0.530241 | − | 0.847847i | \(-0.677898\pi\) | ||
0.530241 | − | 0.847847i | \(-0.322102\pi\) | |||||||
\(20\) | −9.31210 | + | 3.64484i | −0.465605 | + | 0.182242i | ||||
\(21\) | 7.00000 | + | 12.7570i | 0.333333 | + | 0.607474i | ||||
\(22\) | 2.37415i | 0.107916i | ||||||||
\(23\) | 3.78837i | 0.164712i | 0.996603 | + | 0.0823558i | \(0.0262444\pi\) | ||||
−0.996603 | + | 0.0823558i | \(0.973756\pi\) | |||||||
\(24\) | − | 5.87961i | − | 0.244984i | ||||||
\(25\) | 18.3576 | − | 16.9706i | 0.734302 | − | 0.678823i | ||||
\(26\) | − | 13.8743i | − | 0.533628i | ||||||
\(27\) | −28.4348 | −1.05314 | ||||||||
\(28\) | −6.73480 | − | 12.2736i | −0.240529 | − | 0.438345i | ||||
\(29\) | −39.0363 | −1.34608 | −0.673040 | − | 0.739606i | \(-0.735012\pi\) | ||||
−0.673040 | + | 0.739606i | \(0.735012\pi\) | |||||||
\(30\) | 5.35756 | + | 13.6879i | 0.178585 | + | 0.456262i | ||||
\(31\) | − | 24.9285i | − | 0.804145i | −0.915608 | − | 0.402073i | \(-0.868290\pi\) | ||
0.915608 | − | 0.402073i | \(-0.131710\pi\) | |||||||
\(32\) | 5.65685i | 0.176777i | ||||||||
\(33\) | 3.48977 | 0.105751 | ||||||||
\(34\) | 0.705040i | 0.0207365i | ||||||||
\(35\) | 26.8627 | + | 22.4365i | 0.767505 | + | 0.641043i | ||||
\(36\) | 9.35756 | 0.259932 | ||||||||
\(37\) | − | 16.0620i | − | 0.434109i | −0.976160 | − | 0.217054i | \(-0.930355\pi\) | ||
0.976160 | − | 0.217054i | \(-0.0696449\pi\) | |||||||
\(38\) | 45.5634 | 1.19904 | ||||||||
\(39\) | −20.3939 | −0.522920 | ||||||||
\(40\) | −5.15459 | − | 13.1693i | −0.128865 | − | 0.329232i | ||||
\(41\) | 71.1407i | 1.73514i | 0.497317 | + | 0.867569i | \(0.334319\pi\) | ||||
−0.497317 | + | 0.867569i | \(0.665681\pi\) | |||||||
\(42\) | −18.0411 | + | 9.89949i | −0.429549 | + | 0.235702i | ||||
\(43\) | 37.7295i | 0.877430i | 0.898626 | + | 0.438715i | \(0.144566\pi\) | ||||
−0.898626 | + | 0.438715i | \(0.855434\pi\) | |||||||
\(44\) | −3.35756 | −0.0763082 | ||||||||
\(45\) | −21.7846 | + | 8.52671i | −0.484103 | + | 0.189482i | ||||
\(46\) | −5.35756 | −0.116469 | ||||||||
\(47\) | 71.4209 | 1.51959 | 0.759797 | − | 0.650160i | \(-0.225298\pi\) | ||||
0.759797 | + | 0.650160i | \(0.225298\pi\) | |||||||
\(48\) | 8.31502 | 0.173230 | ||||||||
\(49\) | −26.3212 | + | 41.3303i | −0.537168 | + | 0.843475i | ||||
\(50\) | 24.0000 | + | 25.9615i | 0.480000 | + | 0.519230i | ||||
\(51\) | 1.03634 | 0.0203204 | ||||||||
\(52\) | 19.6213 | 0.377332 | ||||||||
\(53\) | 83.0357i | 1.56671i | 0.621574 | + | 0.783356i | \(0.286494\pi\) | ||||
−0.621574 | + | 0.783356i | \(0.713506\pi\) | |||||||
\(54\) | − | 40.2129i | − | 0.744684i | ||||||
\(55\) | 7.81648 | − | 3.05944i | 0.142118 | − | 0.0556263i | ||||
\(56\) | 17.3576 | − | 9.52445i | 0.309956 | − | 0.170079i | ||||
\(57\) | − | 66.9737i | − | 1.17498i | ||||||
\(58\) | − | 55.2057i | − | 0.951823i | ||||||
\(59\) | − | 36.4484i | − | 0.617770i | −0.951099 | − | 0.308885i | \(-0.900044\pi\) | ||
0.951099 | − | 0.308885i | \(-0.0999558\pi\) | |||||||
\(60\) | −19.3576 | + | 7.57673i | −0.322626 | + | 0.126279i | ||||
\(61\) | − | 50.4424i | − | 0.826925i | −0.910521 | − | 0.413462i | \(-0.864319\pi\) | ||
0.910521 | − | 0.413462i | \(-0.135681\pi\) | |||||||
\(62\) | 35.2542 | 0.568617 | ||||||||
\(63\) | −15.7553 | − | 28.7128i | −0.250085 | − | 0.455760i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | −45.6788 | + | 17.8791i | −0.702750 | + | 0.275063i | ||||
\(66\) | 4.93528i | 0.0747770i | ||||||||
\(67\) | − | 12.2736i | − | 0.183189i | −0.995796 | − | 0.0915944i | \(-0.970804\pi\) | ||
0.995796 | − | 0.0915944i | \(-0.0291963\pi\) | |||||||
\(68\) | −0.997077 | −0.0146629 | ||||||||
\(69\) | 7.87508i | 0.114132i | ||||||||
\(70\) | −31.7300 | + | 37.9895i | −0.453286 | + | 0.542708i | ||||
\(71\) | 44.6424 | 0.628767 | 0.314383 | − | 0.949296i | \(-0.398202\pi\) | ||||
0.314383 | + | 0.949296i | \(0.398202\pi\) | |||||||
\(72\) | 13.2336i | 0.183800i | ||||||||
\(73\) | −102.433 | −1.40319 | −0.701596 | − | 0.712575i | \(-0.747529\pi\) | ||||
−0.701596 | + | 0.712575i | \(0.747529\pi\) | |||||||
\(74\) | 22.7151 | 0.306961 | ||||||||
\(75\) | 38.1609 | − | 35.2776i | 0.508811 | − | 0.470368i | ||||
\(76\) | 64.4364i | 0.847847i | ||||||||
\(77\) | 5.65313 | + | 10.3024i | 0.0734172 | + | 0.133797i | ||||
\(78\) | − | 28.8413i | − | 0.369761i | ||||||
\(79\) | 132.394 | 1.67587 | 0.837936 | − | 0.545768i | \(-0.183762\pi\) | ||||
0.837936 | + | 0.545768i | \(0.183762\pi\) | |||||||
\(80\) | 18.6242 | − | 7.28969i | 0.232802 | − | 0.0911211i | ||||
\(81\) | −17.0000 | −0.209877 | ||||||||
\(82\) | −100.608 | −1.22693 | ||||||||
\(83\) | −8.72896 | −0.105168 | −0.0525841 | − | 0.998617i | \(-0.516746\pi\) | ||||
−0.0525841 | + | 0.998617i | \(0.516746\pi\) | |||||||
\(84\) | −14.0000 | − | 25.5139i | −0.166667 | − | 0.303737i | ||||
\(85\) | 2.32122 | − | 0.908548i | 0.0273085 | − | 0.0106888i | ||||
\(86\) | −53.3576 | −0.620437 | ||||||||
\(87\) | −81.1470 | −0.932724 | ||||||||
\(88\) | − | 4.74831i | − | 0.0539580i | ||||||
\(89\) | 54.0872i | 0.607722i | 0.952716 | + | 0.303861i | \(0.0982758\pi\) | ||||
−0.952716 | + | 0.303861i | \(0.901724\pi\) | |||||||
\(90\) | −12.0586 | − | 30.8081i | −0.133984 | − | 0.342312i | ||||
\(91\) | −33.0363 | − | 60.2061i | −0.363037 | − | 0.661606i | ||||
\(92\) | − | 7.57673i | − | 0.0823558i | ||||||
\(93\) | − | 51.8202i | − | 0.557207i | ||||||
\(94\) | 101.004i | 1.07452i | ||||||||
\(95\) | −58.7151 | − | 150.009i | −0.618054 | − | 1.57905i | ||||
\(96\) | 11.7592i | 0.122492i | ||||||||
\(97\) | 41.7352 | 0.430260 | 0.215130 | − | 0.976585i | \(-0.430982\pi\) | ||||
0.215130 | + | 0.976585i | \(0.430982\pi\) | |||||||
\(98\) | −58.4499 | − | 37.2238i | −0.596427 | − | 0.379835i | ||||
\(99\) | −7.85464 | −0.0793398 | ||||||||
\(100\) | −36.7151 | + | 33.9411i | −0.367151 | + | 0.339411i | ||||
\(101\) | − | 103.944i | − | 1.02915i | −0.857445 | − | 0.514576i | \(-0.827950\pi\) | ||
0.857445 | − | 0.514576i | \(-0.172050\pi\) | |||||||
\(102\) | 1.46561i | 0.0143687i | ||||||||
\(103\) | 50.8026 | 0.493229 | 0.246614 | − | 0.969114i | \(-0.420682\pi\) | ||||
0.246614 | + | 0.969114i | \(0.420682\pi\) | |||||||
\(104\) | 27.7487i | 0.266814i | ||||||||
\(105\) | 55.8409 | + | 46.6400i | 0.531818 | + | 0.444191i | ||||
\(106\) | −117.430 | −1.10783 | ||||||||
\(107\) | 110.463i | 1.03236i | 0.856479 | + | 0.516181i | \(0.172647\pi\) | ||||
−0.856479 | + | 0.516181i | \(0.827353\pi\) | |||||||
\(108\) | 56.8696 | 0.526571 | ||||||||
\(109\) | 141.182 | 1.29524 | 0.647622 | − | 0.761961i | \(-0.275763\pi\) | ||||
0.647622 | + | 0.761961i | \(0.275763\pi\) | |||||||
\(110\) | 4.32671 | + | 11.0542i | 0.0393337 | + | 0.100492i | ||||
\(111\) | − | 33.3890i | − | 0.300802i | ||||||
\(112\) | 13.4696 | + | 24.5473i | 0.120264 | + | 0.219172i | ||||
\(113\) | 82.1272i | 0.726789i | 0.931635 | + | 0.363395i | \(0.118382\pi\) | ||||
−0.931635 | + | 0.363395i | \(0.881618\pi\) | |||||||
\(114\) | 94.7151 | 0.830834 | ||||||||
\(115\) | 6.90400 | + | 17.6388i | 0.0600348 | + | 0.153381i | ||||
\(116\) | 78.0727 | 0.673040 | ||||||||
\(117\) | 45.9018 | 0.392323 | ||||||||
\(118\) | 51.5459 | 0.436829 | ||||||||
\(119\) | 1.67878 | + | 3.05944i | 0.0141074 | + | 0.0257096i | ||||
\(120\) | −10.7151 | − | 27.3757i | −0.0892927 | − | 0.228131i | ||||
\(121\) | −118.182 | −0.976708 | ||||||||
\(122\) | 71.3363 | 0.584724 | ||||||||
\(123\) | 147.884i | 1.20231i | ||||||||
\(124\) | 49.8570i | 0.402073i | ||||||||
\(125\) | 54.5462 | − | 112.471i | 0.436369 | − | 0.899768i | ||||
\(126\) | 40.6061 | − | 22.2814i | 0.322271 | − | 0.176837i | ||||
\(127\) | 78.3388i | 0.616841i | 0.951250 | + | 0.308420i | \(0.0998004\pi\) | ||||
−0.951250 | + | 0.308420i | \(0.900200\pi\) | |||||||
\(128\) | − | 11.3137i | − | 0.0883883i | ||||||
\(129\) | 78.4304i | 0.607987i | ||||||||
\(130\) | −25.2849 | − | 64.5996i | −0.194499 | − | 0.496920i | ||||
\(131\) | 233.988i | 1.78617i | 0.449892 | + | 0.893083i | \(0.351463\pi\) | ||||
−0.449892 | + | 0.893083i | \(0.648537\pi\) | |||||||
\(132\) | −6.97954 | −0.0528753 | ||||||||
\(133\) | 197.717 | − | 108.492i | 1.48660 | − | 0.815726i | ||||
\(134\) | 17.3576 | 0.129534 | ||||||||
\(135\) | −132.394 | + | 51.8202i | −0.980696 | + | 0.383854i | ||||
\(136\) | − | 1.41008i | − | 0.0103682i | ||||||
\(137\) | − | 151.827i | − | 1.10822i | −0.832443 | − | 0.554111i | \(-0.813058\pi\) | ||
0.832443 | − | 0.554111i | \(-0.186942\pi\) | |||||||
\(138\) | −11.1371 | −0.0807033 | ||||||||
\(139\) | − | 80.1865i | − | 0.576882i | −0.957498 | − | 0.288441i | \(-0.906863\pi\) | ||
0.957498 | − | 0.288441i | \(-0.0931368\pi\) | |||||||
\(140\) | −53.7253 | − | 44.8730i | −0.383752 | − | 0.320522i | ||||
\(141\) | 148.467 | 1.05295 | ||||||||
\(142\) | 63.1339i | 0.444605i | ||||||||
\(143\) | −16.4699 | −0.115174 | ||||||||
\(144\) | −18.7151 | −0.129966 | ||||||||
\(145\) | −181.755 | + | 71.1407i | −1.25348 | + | 0.490625i | ||||
\(146\) | − | 144.862i | − | 0.992207i | ||||||
\(147\) | −54.7154 | + | 85.9155i | −0.372213 | + | 0.584459i | ||||
\(148\) | 32.1240i | 0.217054i | ||||||||
\(149\) | 91.3576 | 0.613138 | 0.306569 | − | 0.951848i | \(-0.400819\pi\) | ||||
0.306569 | + | 0.951848i | \(0.400819\pi\) | |||||||
\(150\) | 49.8901 | + | 53.9676i | 0.332601 | + | 0.359784i | ||||
\(151\) | −174.467 | −1.15541 | −0.577704 | − | 0.816246i | \(-0.696051\pi\) | ||||
−0.577704 | + | 0.816246i | \(0.696051\pi\) | |||||||
\(152\) | −91.1268 | −0.599518 | ||||||||
\(153\) | −2.33255 | −0.0152454 | ||||||||
\(154\) | −14.5698 | + | 7.99473i | −0.0946088 | + | 0.0519138i | ||||
\(155\) | −45.4302 | − | 116.068i | −0.293098 | − | 0.748828i | ||||
\(156\) | 40.7878 | 0.261460 | ||||||||
\(157\) | 38.5839 | 0.245757 | 0.122879 | − | 0.992422i | \(-0.460787\pi\) | ||||
0.122879 | + | 0.992422i | \(0.460787\pi\) | |||||||
\(158\) | 187.233i | 1.18502i | ||||||||
\(159\) | 172.611i | 1.08560i | ||||||||
\(160\) | 10.3092 | + | 26.3386i | 0.0644323 | + | 0.164616i | ||||
\(161\) | −23.2485 | + | 12.7570i | −0.144401 | + | 0.0792357i | ||||
\(162\) | − | 24.0416i | − | 0.148405i | ||||||
\(163\) | − | 291.379i | − | 1.78760i | −0.448462 | − | 0.893802i | \(-0.648028\pi\) | ||
0.448462 | − | 0.893802i | \(-0.351972\pi\) | |||||||
\(164\) | − | 142.281i | − | 0.867569i | ||||||
\(165\) | 16.2485 | − | 6.35983i | 0.0984760 | − | 0.0385444i | ||||
\(166\) | − | 12.3446i | − | 0.0743651i | ||||||
\(167\) | −205.458 | −1.23029 | −0.615145 | − | 0.788414i | \(-0.710902\pi\) | ||||
−0.615145 | + | 0.788414i | \(0.710902\pi\) | |||||||
\(168\) | 36.0821 | − | 19.7990i | 0.214774 | − | 0.117851i | ||||
\(169\) | −72.7515 | −0.430482 | ||||||||
\(170\) | 1.28488 | + | 3.28270i | 0.00755812 | + | 0.0193100i | ||||
\(171\) | 150.742i | 0.881531i | ||||||||
\(172\) | − | 75.4590i | − | 0.438715i | ||||||
\(173\) | −173.102 | −1.00059 | −0.500294 | − | 0.865856i | \(-0.666775\pi\) | ||||
−0.500294 | + | 0.865856i | \(0.666775\pi\) | |||||||
\(174\) | − | 114.759i | − | 0.659535i | ||||||
\(175\) | 165.963 | + | 55.5104i | 0.948358 | + | 0.317202i | ||||
\(176\) | 6.71512 | 0.0381541 | ||||||||
\(177\) | − | 75.7673i | − | 0.428064i | ||||||
\(178\) | −76.4909 | −0.429724 | ||||||||
\(179\) | −14.0727 | −0.0786183 | −0.0393092 | − | 0.999227i | \(-0.512516\pi\) | ||||
−0.0393092 | + | 0.999227i | \(0.512516\pi\) | |||||||
\(180\) | 43.5692 | − | 17.0534i | 0.242051 | − | 0.0947412i | ||||
\(181\) | − | 170.269i | − | 0.940714i | −0.882476 | − | 0.470357i | \(-0.844125\pi\) | ||
0.882476 | − | 0.470357i | \(-0.155875\pi\) | |||||||
\(182\) | 85.1443 | − | 46.7204i | 0.467826 | − | 0.256706i | ||||
\(183\) | − | 104.857i | − | 0.572991i | ||||||
\(184\) | 10.7151 | 0.0582343 | ||||||||
\(185\) | −29.2718 | − | 74.7855i | −0.158226 | − | 0.404246i | ||||
\(186\) | 73.2849 | 0.394005 | ||||||||
\(187\) | 0.836937 | 0.00447560 | ||||||||
\(188\) | −142.842 | −0.759797 | ||||||||
\(189\) | −95.7515 | − | 174.500i | −0.506621 | − | 0.923278i | ||||
\(190\) | 212.145 | − | 83.0357i | 1.11655 | − | 0.437030i | ||||
\(191\) | 151.254 | 0.791908 | 0.395954 | − | 0.918270i | \(-0.370414\pi\) | ||||
0.395954 | + | 0.918270i | \(0.370414\pi\) | |||||||
\(192\) | −16.6300 | −0.0866148 | ||||||||
\(193\) | 336.686i | 1.74449i | 0.489074 | + | 0.872243i | \(0.337335\pi\) | ||||
−0.489074 | + | 0.872243i | \(0.662665\pi\) | |||||||
\(194\) | 59.0225i | 0.304240i | ||||||||
\(195\) | −94.9550 | + | 37.1663i | −0.486949 | + | 0.190596i | ||||
\(196\) | 52.6424 | − | 82.6606i | 0.268584 | − | 0.421738i | ||||
\(197\) | 2.72564i | 0.0138358i | 0.999976 | + | 0.00691788i | \(0.00220205\pi\) | ||||
−0.999976 | + | 0.00691788i | \(0.997798\pi\) | |||||||
\(198\) | − | 11.1081i | − | 0.0561017i | ||||||
\(199\) | 87.4762i | 0.439579i | 0.975547 | + | 0.219790i | \(0.0705371\pi\) | ||||
−0.975547 | + | 0.219790i | \(0.929463\pi\) | |||||||
\(200\) | −48.0000 | − | 51.9230i | −0.240000 | − | 0.259615i | ||||
\(201\) | − | 25.5139i | − | 0.126935i | ||||||
\(202\) | 146.999 | 0.727720 | ||||||||
\(203\) | −131.451 | − | 239.559i | −0.647542 | − | 1.18009i | ||||
\(204\) | −2.07268 | −0.0101602 | ||||||||
\(205\) | 129.648 | + | 331.234i | 0.632431 | + | 1.61578i | ||||
\(206\) | 71.8457i | 0.348766i | ||||||||
\(207\) | − | 17.7249i | − | 0.0856277i | ||||||
\(208\) | −39.2425 | −0.188666 | ||||||||
\(209\) | − | 54.0872i | − | 0.258791i | ||||||
\(210\) | −65.9589 | + | 78.9709i | −0.314090 | + | 0.376052i | ||||
\(211\) | −14.6119 | −0.0692509 | −0.0346254 | − | 0.999400i | \(-0.511024\pi\) | ||||
−0.0346254 | + | 0.999400i | \(0.511024\pi\) | |||||||
\(212\) | − | 166.071i | − | 0.783356i | ||||||
\(213\) | 92.8007 | 0.435684 | ||||||||
\(214\) | −156.218 | −0.729991 | ||||||||
\(215\) | 68.7590 | + | 175.670i | 0.319809 | + | 0.817071i | ||||
\(216\) | 80.4258i | 0.372342i | ||||||||
\(217\) | 152.982 | − | 83.9443i | 0.704985 | − | 0.386840i | ||||
\(218\) | 199.661i | 0.915876i | ||||||||
\(219\) | −212.933 | −0.972298 | ||||||||
\(220\) | −15.6330 | + | 6.11889i | −0.0710589 | + | 0.0278131i | ||||
\(221\) | −4.89098 | −0.0221311 | ||||||||
\(222\) | 47.2192 | 0.212699 | ||||||||
\(223\) | 129.964 | 0.582800 | 0.291400 | − | 0.956601i | \(-0.405879\pi\) | ||||
0.291400 | + | 0.956601i | \(0.405879\pi\) | |||||||
\(224\) | −34.7151 | + | 19.0489i | −0.154978 | + | 0.0850397i | ||||
\(225\) | −85.8910 | + | 79.4015i | −0.381738 | + | 0.352896i | ||||
\(226\) | −116.145 | −0.513918 | ||||||||
\(227\) | 133.276 | 0.587119 | 0.293559 | − | 0.955941i | \(-0.405160\pi\) | ||||
0.293559 | + | 0.955941i | \(0.405160\pi\) | |||||||
\(228\) | 133.947i | 0.587489i | ||||||||
\(229\) | − | 220.579i | − | 0.963228i | −0.876383 | − | 0.481614i | \(-0.840051\pi\) | ||
0.876383 | − | 0.481614i | \(-0.159949\pi\) | |||||||
\(230\) | −24.9451 | + | 9.76373i | −0.108457 | + | 0.0424510i | ||||
\(231\) | 11.7515 | + | 21.4161i | 0.0508721 | + | 0.0927104i | ||||
\(232\) | 110.411i | 0.475911i | ||||||||
\(233\) | − | 216.983i | − | 0.931258i | −0.884980 | − | 0.465629i | \(-0.845828\pi\) | ||
0.884980 | − | 0.465629i | \(-0.154172\pi\) | |||||||
\(234\) | 64.9149i | 0.277414i | ||||||||
\(235\) | 332.539 | − | 130.159i | 1.41506 | − | 0.553868i | ||||
\(236\) | 72.8969i | 0.308885i | ||||||||
\(237\) | 275.214 | 1.16124 | ||||||||
\(238\) | −4.32671 | + | 2.37415i | −0.0181794 | + | 0.00997543i | ||||
\(239\) | −315.897 | −1.32174 | −0.660872 | − | 0.750499i | \(-0.729813\pi\) | ||||
−0.660872 | + | 0.750499i | \(0.729813\pi\) | |||||||
\(240\) | 38.7151 | − | 15.1535i | 0.161313 | − | 0.0631394i | ||||
\(241\) | 228.001i | 0.946064i | 0.881045 | + | 0.473032i | \(0.156840\pi\) | ||||
−0.881045 | + | 0.473032i | \(0.843160\pi\) | |||||||
\(242\) | − | 167.134i | − | 0.690637i | ||||||
\(243\) | 220.575 | 0.907714 | ||||||||
\(244\) | 100.885i | 0.413462i | ||||||||
\(245\) | −47.2316 | + | 240.404i | −0.192782 | + | 0.981242i | ||||
\(246\) | −209.140 | −0.850161 | ||||||||
\(247\) | 316.081i | 1.27968i | ||||||||
\(248\) | −70.5085 | −0.284308 | ||||||||
\(249\) | −18.1454 | −0.0728729 | ||||||||
\(250\) | 159.058 | + | 77.1399i | 0.636232 | + | 0.308560i | ||||
\(251\) | − | 83.9638i | − | 0.334517i | −0.985913 | − | 0.167259i | \(-0.946509\pi\) | ||
0.985913 | − | 0.167259i | \(-0.0534915\pi\) | |||||||
\(252\) | 31.5107 | + | 57.4257i | 0.125042 | + | 0.227880i | ||||
\(253\) | 6.35983i | 0.0251377i | ||||||||
\(254\) | −110.788 | −0.436172 | ||||||||
\(255\) | 4.82525 | − | 1.88865i | 0.0189225 | − | 0.00740646i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −174.597 | −0.679367 | −0.339683 | − | 0.940540i | \(-0.610320\pi\) | ||||
−0.339683 | + | 0.940540i | \(0.610320\pi\) | |||||||
\(258\) | −110.917 | −0.429912 | ||||||||
\(259\) | 98.5698 | − | 54.0872i | 0.380578 | − | 0.208831i | ||||
\(260\) | 91.3576 | − | 35.7582i | 0.351375 | − | 0.137532i | ||||
\(261\) | 182.642 | 0.699779 | ||||||||
\(262\) | −330.909 | −1.26301 | ||||||||
\(263\) | 151.672i | 0.576701i | 0.957525 | + | 0.288350i | \(0.0931068\pi\) | ||||
−0.957525 | + | 0.288350i | \(0.906893\pi\) | |||||||
\(264\) | − | 9.87056i | − | 0.0373885i | ||||||
\(265\) | 151.326 | + | 386.618i | 0.571042 | + | 1.45894i | ||||
\(266\) | 153.430 | + | 279.615i | 0.576805 | + | 1.05118i | ||||
\(267\) | 112.434i | 0.421102i | ||||||||
\(268\) | 24.5473i | 0.0915944i | ||||||||
\(269\) | − | 440.120i | − | 1.63613i | −0.575123 | − | 0.818067i | \(-0.695046\pi\) | ||
0.575123 | − | 0.818067i | \(-0.304954\pi\) | |||||||
\(270\) | −73.2849 | − | 187.233i | −0.271425 | − | 0.693456i | ||||
\(271\) | − | 376.269i | − | 1.38845i | −0.719760 | − | 0.694223i | \(-0.755748\pi\) | ||
0.719760 | − | 0.694223i | \(-0.244252\pi\) | |||||||
\(272\) | 1.99415 | 0.00733145 | ||||||||
\(273\) | −68.6744 | − | 125.154i | −0.251555 | − | 0.458439i | ||||
\(274\) | 214.715 | 0.783632 | ||||||||
\(275\) | 30.8183 | − | 28.4898i | 0.112067 | − | 0.103599i | ||||
\(276\) | − | 15.7502i | − | 0.0570658i | ||||||
\(277\) | − | 333.960i | − | 1.20563i | −0.797880 | − | 0.602816i | \(-0.794045\pi\) | ||
0.797880 | − | 0.602816i | \(-0.205955\pi\) | |||||||
\(278\) | 113.401 | 0.407917 | ||||||||
\(279\) | 116.635i | 0.418047i | ||||||||
\(280\) | 63.4601 | − | 75.9791i | 0.226643 | − | 0.271354i | ||||
\(281\) | 378.612 | 1.34737 | 0.673687 | − | 0.739017i | \(-0.264710\pi\) | ||||
0.673687 | + | 0.739017i | \(0.264710\pi\) | |||||||
\(282\) | 209.963i | 0.744551i | ||||||||
\(283\) | 279.447 | 0.987447 | 0.493723 | − | 0.869619i | \(-0.335636\pi\) | ||||
0.493723 | + | 0.869619i | \(0.335636\pi\) | |||||||
\(284\) | −89.2849 | −0.314383 | ||||||||
\(285\) | −122.054 | − | 311.833i | −0.428261 | − | 1.09415i | ||||
\(286\) | − | 23.2919i | − | 0.0814404i | ||||||
\(287\) | −436.578 | + | 239.559i | −1.52118 | + | 0.834701i | ||||
\(288\) | − | 26.4672i | − | 0.0918999i | ||||||
\(289\) | −288.751 | −0.999140 | ||||||||
\(290\) | −100.608 | − | 257.040i | −0.346924 | − | 0.886346i | ||||
\(291\) | 86.7573 | 0.298135 | ||||||||
\(292\) | 204.866 | 0.701596 | ||||||||
\(293\) | 235.954 | 0.805303 | 0.402651 | − | 0.915353i | \(-0.368089\pi\) | ||||
0.402651 | + | 0.915353i | \(0.368089\pi\) | |||||||
\(294\) | −121.503 | − | 77.3792i | −0.413275 | − | 0.263195i | ||||
\(295\) | −66.4244 | − | 169.706i | −0.225167 | − | 0.575273i | ||||
\(296\) | −45.4302 | −0.153481 | ||||||||
\(297\) | −47.7358 | −0.160727 | ||||||||
\(298\) | 129.199i | 0.433554i | ||||||||
\(299\) | − | 37.1663i | − | 0.124302i | ||||||
\(300\) | −76.3217 | + | 70.5553i | −0.254406 | + | 0.235184i | ||||
\(301\) | −231.539 | + | 127.050i | −0.769233 | + | 0.422094i | ||||
\(302\) | − | 246.733i | − | 0.816997i | ||||||
\(303\) | − | 216.075i | − | 0.713117i | ||||||
\(304\) | − | 128.873i | − | 0.423924i | ||||||
\(305\) | −91.9273 | − | 234.862i | −0.301401 | − | 0.770040i | ||||
\(306\) | − | 3.29873i | − | 0.0107802i | ||||||
\(307\) | −425.450 | −1.38583 | −0.692915 | − | 0.721019i | \(-0.743674\pi\) | ||||
−0.692915 | + | 0.721019i | \(0.743674\pi\) | |||||||
\(308\) | −11.3063 | − | 20.6048i | −0.0367086 | − | 0.0668986i | ||||
\(309\) | 105.606 | 0.341767 | ||||||||
\(310\) | 164.145 | − | 64.2481i | 0.529501 | − | 0.207252i | ||||
\(311\) | − | 199.881i | − | 0.642704i | −0.946960 | − | 0.321352i | \(-0.895863\pi\) | ||
0.946960 | − | 0.321352i | \(-0.104137\pi\) | |||||||
\(312\) | 57.6827i | 0.184880i | ||||||||
\(313\) | −412.243 | −1.31707 | −0.658535 | − | 0.752550i | \(-0.728824\pi\) | ||||
−0.658535 | + | 0.752550i | \(0.728824\pi\) | |||||||
\(314\) | 54.5658i | 0.173776i | ||||||||
\(315\) | −125.684 | − | 104.976i | −0.398998 | − | 0.333256i | ||||
\(316\) | −264.788 | −0.837936 | ||||||||
\(317\) | 107.891i | 0.340351i | 0.985414 | + | 0.170176i | \(0.0544335\pi\) | ||||
−0.985414 | + | 0.170176i | \(0.945566\pi\) | |||||||
\(318\) | −244.109 | −0.767637 | ||||||||
\(319\) | −65.5334 | −0.205434 | ||||||||
\(320\) | −37.2484 | + | 14.5794i | −0.116401 | + | 0.0455605i | ||||
\(321\) | 229.625i | 0.715343i | ||||||||
\(322\) | −18.0411 | − | 32.8784i | −0.0560281 | − | 0.102107i | ||||
\(323\) | − | 16.0620i | − | 0.0497276i | ||||||
\(324\) | 34.0000 | 0.104938 | ||||||||
\(325\) | −180.099 | + | 166.492i | −0.554152 | + | 0.512283i | ||||
\(326\) | 412.073 | 1.26403 | ||||||||
\(327\) | 293.482 | 0.897499 | ||||||||
\(328\) | 201.216 | 0.613464 | ||||||||
\(329\) | 240.503 | + | 438.298i | 0.731012 | + | 1.33221i | ||||
\(330\) | 8.99416 | + | 22.9789i | 0.0272550 | + | 0.0696331i | ||||
\(331\) | −38.0727 | −0.115023 | −0.0575116 | − | 0.998345i | \(-0.518317\pi\) | ||||
−0.0575116 | + | 0.998345i | \(0.518317\pi\) | |||||||
\(332\) | 17.4579 | 0.0525841 | ||||||||
\(333\) | 75.1506i | 0.225678i | ||||||||
\(334\) | − | 290.562i | − | 0.869946i | ||||||
\(335\) | −22.3678 | − | 57.1467i | −0.0667694 | − | 0.170587i | ||||
\(336\) | 28.0000 | + | 51.0278i | 0.0833333 | + | 0.151868i | ||||
\(337\) | − | 260.626i | − | 0.773372i | −0.922211 | − | 0.386686i | \(-0.873620\pi\) | ||
0.922211 | − | 0.386686i | \(-0.126380\pi\) | |||||||
\(338\) | − | 102.886i | − | 0.304397i | ||||||
\(339\) | 170.722i | 0.503605i | ||||||||
\(340\) | −4.64244 | + | 1.81710i | −0.0136542 | + | 0.00534440i | ||||
\(341\) | − | 41.8495i | − | 0.122726i | ||||||
\(342\) | −213.181 | −0.623337 | ||||||||
\(343\) | −342.271 | − | 22.3530i | −0.997874 | − | 0.0651691i | ||||
\(344\) | 106.715 | 0.310218 | ||||||||
\(345\) | 14.3517 | + | 36.6668i | 0.0415992 | + | 0.106280i | ||||
\(346\) | − | 244.803i | − | 0.707522i | ||||||
\(347\) | 390.785i | 1.12618i | 0.826395 | + | 0.563091i | \(0.190388\pi\) | ||||
−0.826395 | + | 0.563091i | \(0.809612\pi\) | |||||||
\(348\) | 162.294 | 0.466362 | ||||||||
\(349\) | 561.118i | 1.60779i | 0.594773 | + | 0.803894i | \(0.297242\pi\) | ||||
−0.594773 | + | 0.803894i | \(0.702758\pi\) | |||||||
\(350\) | −78.5036 | + | 234.707i | −0.224296 | + | 0.670590i | ||||
\(351\) | 278.964 | 0.794768 | ||||||||
\(352\) | 9.49661i | 0.0269790i | ||||||||
\(353\) | 254.916 | 0.722143 | 0.361071 | − | 0.932538i | \(-0.382411\pi\) | ||||
0.361071 | + | 0.932538i | \(0.382411\pi\) | |||||||
\(354\) | 107.151 | 0.302687 | ||||||||
\(355\) | 207.857 | − | 81.3573i | 0.585514 | − | 0.229176i | ||||
\(356\) | − | 108.174i | − | 0.303861i | ||||||
\(357\) | 3.48977 | + | 6.35983i | 0.00977527 | + | 0.0178147i | ||||
\(358\) | − | 19.9018i | − | 0.0555915i | ||||||
\(359\) | 36.9332 | 0.102878 | 0.0514389 | − | 0.998676i | \(-0.483619\pi\) | ||||
0.0514389 | + | 0.998676i | \(0.483619\pi\) | |||||||
\(360\) | 24.1172 | + | 61.6162i | 0.0669922 | + | 0.171156i | ||||
\(361\) | −677.012 | −1.87538 | ||||||||
\(362\) | 240.797 | 0.665185 | ||||||||
\(363\) | −245.671 | −0.676779 | ||||||||
\(364\) | 66.0727 | + | 120.412i | 0.181518 | + | 0.330803i | ||||
\(365\) | −476.933 | + | 186.676i | −1.30667 | + | 0.511442i | ||||
\(366\) | 148.291 | 0.405166 | ||||||||
\(367\) | 267.483 | 0.728835 | 0.364418 | − | 0.931236i | \(-0.381268\pi\) | ||||
0.364418 | + | 0.931236i | \(0.381268\pi\) | |||||||
\(368\) | 15.1535i | 0.0411779i | ||||||||
\(369\) | − | 332.852i | − | 0.902037i | ||||||
\(370\) | 105.763 | − | 41.3965i | 0.285845 | − | 0.111882i | ||||
\(371\) | −509.576 | + | 279.615i | −1.37352 | + | 0.753678i | ||||
\(372\) | 103.640i | 0.278603i | ||||||||
\(373\) | − | 126.971i | − | 0.340404i | −0.985409 | − | 0.170202i | \(-0.945558\pi\) | ||
0.985409 | − | 0.170202i | \(-0.0544421\pi\) | |||||||
\(374\) | 1.18361i | 0.00316473i | ||||||||
\(375\) | 113.388 | − | 233.800i | 0.302368 | − | 0.623465i | ||||
\(376\) | − | 202.009i | − | 0.537258i | ||||||
\(377\) | 382.971 | 1.01584 | ||||||||
\(378\) | 246.780 | − | 135.413i | 0.652856 | − | 0.358235i | ||||
\(379\) | 519.939 | 1.37187 | 0.685935 | − | 0.727662i | \(-0.259393\pi\) | ||||
0.685935 | + | 0.727662i | \(0.259393\pi\) | |||||||
\(380\) | 117.430 | + | 300.019i | 0.309027 | + | 0.789523i | ||||
\(381\) | 162.847i | 0.427420i | ||||||||
\(382\) | 213.906i | 0.559963i | ||||||||
\(383\) | 393.703 | 1.02795 | 0.513973 | − | 0.857806i | \(-0.328173\pi\) | ||||
0.513973 | + | 0.857806i | \(0.328173\pi\) | |||||||
\(384\) | − | 23.5184i | − | 0.0612459i | ||||||
\(385\) | 45.0965 | + | 37.6660i | 0.117134 | + | 0.0978337i | ||||
\(386\) | −476.145 | −1.23354 | ||||||||
\(387\) | − | 176.528i | − | 0.456145i | ||||||
\(388\) | −83.4705 | −0.215130 | ||||||||
\(389\) | 106.031 | 0.272572 | 0.136286 | − | 0.990670i | \(-0.456483\pi\) | ||||
0.136286 | + | 0.990670i | \(0.456483\pi\) | |||||||
\(390\) | −52.5611 | − | 134.287i | −0.134772 | − | 0.344325i | ||||
\(391\) | 1.88865i | 0.00483030i | ||||||||
\(392\) | 116.900 | + | 74.4477i | 0.298214 | + | 0.189917i | ||||
\(393\) | 486.403i | 1.23767i | ||||||||
\(394\) | −3.85464 | −0.00978335 | ||||||||
\(395\) | 616.432 | − | 241.277i | 1.56059 | − | 0.610829i | ||||
\(396\) | 15.7093 | 0.0396699 | ||||||||
\(397\) | −391.625 | −0.986460 | −0.493230 | − | 0.869899i | \(-0.664184\pi\) | ||||
−0.493230 | + | 0.869899i | \(0.664184\pi\) | |||||||
\(398\) | −123.710 | −0.310829 | ||||||||
\(399\) | 411.006 | − | 225.527i | 1.03009 | − | 0.565231i | ||||
\(400\) | 73.4302 | − | 67.8823i | 0.183576 | − | 0.169706i | ||||
\(401\) | 41.1090 | 0.102516 | 0.0512581 | − | 0.998685i | \(-0.483677\pi\) | ||||
0.0512581 | + | 0.998685i | \(0.483677\pi\) | |||||||
\(402\) | 36.0821 | 0.0897565 | ||||||||
\(403\) | 244.564i | 0.606860i | ||||||||
\(404\) | 207.889i | 0.514576i | ||||||||
\(405\) | −79.1528 | + | 30.9812i | −0.195439 | + | 0.0764967i | ||||
\(406\) | 338.788 | − | 185.900i | 0.834453 | − | 0.457881i | ||||
\(407\) | − | 26.9646i | − | 0.0662521i | ||||||
\(408\) | − | 2.93121i | − | 0.00718434i | ||||||
\(409\) | 511.846i | 1.25146i | 0.780041 | + | 0.625729i | \(0.215198\pi\) | ||||
−0.780041 | + | 0.625729i | \(0.784802\pi\) | |||||||
\(410\) | −468.436 | + | 183.350i | −1.14253 | + | 0.447196i | ||||
\(411\) | − | 315.610i | − | 0.767908i | ||||||
\(412\) | −101.605 | −0.246614 | ||||||||
\(413\) | 223.678 | − | 122.736i | 0.541592 | − | 0.297183i | ||||
\(414\) | 25.0668 | 0.0605479 | ||||||||
\(415\) | −40.6424 | + | 15.9078i | −0.0979336 | + | 0.0383321i | ||||
\(416\) | − | 55.4973i | − | 0.133407i | ||||||
\(417\) | − | 166.688i | − | 0.399732i | ||||||
\(418\) | 76.4909 | 0.182993 | ||||||||
\(419\) | − | 82.5281i | − | 0.196965i | −0.995139 | − | 0.0984823i | \(-0.968601\pi\) | ||
0.995139 | − | 0.0984823i | \(-0.0313988\pi\) | |||||||
\(420\) | −111.682 | − | 93.2800i | −0.265909 | − | 0.222095i | ||||
\(421\) | −227.400 | −0.540142 | −0.270071 | − | 0.962840i | \(-0.587047\pi\) | ||||
−0.270071 | + | 0.962840i | \(0.587047\pi\) | |||||||
\(422\) | − | 20.6644i | − | 0.0489678i | ||||||
\(423\) | −334.163 | −0.789983 | ||||||||
\(424\) | 234.860 | 0.553916 | ||||||||
\(425\) | 9.15195 | − | 8.46048i | 0.0215340 | − | 0.0199070i | ||||
\(426\) | 131.240i | 0.308075i | ||||||||
\(427\) | 309.556 | − | 169.860i | 0.724956 | − | 0.397798i | ||||
\(428\) | − | 220.926i | − | 0.516181i | ||||||
\(429\) | −34.2369 | −0.0798062 | ||||||||
\(430\) | −248.435 | + | 97.2400i | −0.577757 | + | 0.226139i | ||||
\(431\) | 254.964 | 0.591563 | 0.295782 | − | 0.955256i | \(-0.404420\pi\) | ||||
0.295782 | + | 0.955256i | \(0.404420\pi\) | |||||||
\(432\) | −113.739 | −0.263285 | ||||||||
\(433\) | −675.154 | −1.55925 | −0.779624 | − | 0.626248i | \(-0.784590\pi\) | ||||
−0.779624 | + | 0.626248i | \(0.784590\pi\) | |||||||
\(434\) | 118.715 | + | 216.349i | 0.273537 | + | 0.498500i | ||||
\(435\) | −377.824 | + | 147.884i | −0.868561 | + | 0.339963i | ||||
\(436\) | −282.363 | −0.647622 | ||||||||
\(437\) | 122.054 | 0.279300 | ||||||||
\(438\) | − | 301.133i | − | 0.687518i | ||||||
\(439\) | − | 3.77730i | − | 0.00860432i | −0.999991 | − | 0.00430216i | \(-0.998631\pi\) | ||
0.999991 | − | 0.00430216i | \(-0.00136942\pi\) | |||||||
\(440\) | −8.65342 | − | 22.1083i | −0.0196669 | − | 0.0502462i | ||||
\(441\) | 123.151 | − | 193.375i | 0.279254 | − | 0.438493i | ||||
\(442\) | − | 6.91689i | − | 0.0156491i | ||||||
\(443\) | 273.500i | 0.617382i | 0.951162 | + | 0.308691i | \(0.0998909\pi\) | ||||
−0.951162 | + | 0.308691i | \(0.900109\pi\) | |||||||
\(444\) | 66.7780i | 0.150401i | ||||||||
\(445\) | 98.5698 | + | 251.833i | 0.221505 | + | 0.565916i | ||||
\(446\) | 183.797i | 0.412102i | ||||||||
\(447\) | 189.910 | 0.424854 | ||||||||
\(448\) | −26.9392 | − | 49.0946i | −0.0601322 | − | 0.109586i | ||||
\(449\) | 232.042 | 0.516798 | 0.258399 | − | 0.966038i | \(-0.416805\pi\) | ||||
0.258399 | + | 0.966038i | \(0.416805\pi\) | |||||||
\(450\) | −112.291 | − | 121.468i | −0.249535 | − | 0.269929i | ||||
\(451\) | 119.430i | 0.264810i | ||||||||
\(452\) | − | 164.254i | − | 0.363395i | ||||||
\(453\) | −362.673 | −0.800603 | ||||||||
\(454\) | 188.481i | 0.415156i | ||||||||
\(455\) | −263.540 | − | 220.117i | −0.579208 | − | 0.483773i | ||||
\(456\) | −189.430 | −0.415417 | ||||||||
\(457\) | − | 371.243i | − | 0.812349i | −0.913796 | − | 0.406174i | \(-0.866863\pi\) | ||
0.913796 | − | 0.406174i | \(-0.133137\pi\) | |||||||
\(458\) | 311.946 | 0.681105 | ||||||||
\(459\) | −14.1759 | −0.0308842 | ||||||||
\(460\) | −13.8080 | − | 35.2776i | −0.0300174 | − | 0.0766905i | ||||
\(461\) | 12.2378i | 0.0265462i | 0.999912 | + | 0.0132731i | \(0.00422508\pi\) | ||||
−0.999912 | + | 0.0132731i | \(0.995775\pi\) | |||||||
\(462\) | −30.2870 | + | 16.6191i | −0.0655562 | + | 0.0359720i | ||||
\(463\) | 266.232i | 0.575015i | 0.957778 | + | 0.287507i | \(0.0928266\pi\) | ||||
−0.957778 | + | 0.287507i | \(0.907173\pi\) | |||||||
\(464\) | −156.145 | −0.336520 | ||||||||
\(465\) | −94.4383 | − | 241.277i | −0.203093 | − | 0.518876i | ||||
\(466\) | 306.860 | 0.658499 | ||||||||
\(467\) | −287.932 | −0.616556 | −0.308278 | − | 0.951296i | \(-0.599753\pi\) | ||||
−0.308278 | + | 0.951296i | \(0.599753\pi\) | |||||||
\(468\) | −91.8036 | −0.196162 | ||||||||
\(469\) | 75.3212 | − | 41.3303i | 0.160600 | − | 0.0881243i | ||||
\(470\) | 184.073 | + | 470.282i | 0.391644 | + | 1.00060i | ||||
\(471\) | 80.2064 | 0.170290 | ||||||||
\(472\) | −103.092 | −0.218415 | ||||||||
\(473\) | 63.3395i | 0.133910i | ||||||||
\(474\) | 389.212i | 0.821122i | ||||||||
\(475\) | −546.761 | − | 591.447i | −1.15108 | − | 1.24515i | ||||
\(476\) | −3.35756 | − | 6.11889i | −0.00705370 | − | 0.0128548i | ||||
\(477\) | − | 388.506i | − | 0.814478i | ||||||
\(478\) | − | 446.746i | − | 0.934614i | ||||||
\(479\) | − | 235.159i | − | 0.490937i | −0.969405 | − | 0.245468i | \(-0.921058\pi\) | ||
0.969405 | − | 0.245468i | \(-0.0789417\pi\) | |||||||
\(480\) | 21.4302 | + | 54.7514i | 0.0446463 | + | 0.114066i | ||||
\(481\) | 157.579i | 0.327606i | ||||||||
\(482\) | −322.443 | −0.668968 | ||||||||
\(483\) | −48.3280 | + | 26.5186i | −0.100058 | + | 0.0549039i | ||||
\(484\) | 236.363 | 0.488354 | ||||||||
\(485\) | 194.321 | − | 76.0592i | 0.400662 | − | 0.156823i | ||||
\(486\) | 311.940i | 0.641851i | ||||||||
\(487\) | − | 291.379i | − | 0.598315i | −0.954204 | − | 0.299157i | \(-0.903294\pi\) | ||
0.954204 | − | 0.299157i | \(-0.0967056\pi\) | |||||||
\(488\) | −142.673 | −0.292362 | ||||||||
\(489\) | − | 605.706i | − | 1.23866i | ||||||
\(490\) | −339.983 | − | 66.7956i | −0.693843 | − | 0.136318i | ||||
\(491\) | 610.260 | 1.24289 | 0.621446 | − | 0.783457i | \(-0.286545\pi\) | ||||
0.621446 | + | 0.783457i | \(0.286545\pi\) | |||||||
\(492\) | − | 295.768i | − | 0.601154i | ||||||
\(493\) | −19.4611 | −0.0394749 | ||||||||
\(494\) | −447.006 | −0.904870 | ||||||||
\(495\) | −36.5716 | + | 14.3145i | −0.0738820 | + | 0.0289181i | ||||
\(496\) | − | 99.7140i | − | 0.201036i | ||||||
\(497\) | 150.329 | + | 273.963i | 0.302473 | + | 0.551233i | ||||
\(498\) | − | 25.6614i | − | 0.0515289i | ||||||
\(499\) | 49.6788 | 0.0995567 | 0.0497783 | − | 0.998760i | \(-0.484149\pi\) | ||||
0.0497783 | + | 0.998760i | \(0.484149\pi\) | |||||||
\(500\) | −109.092 | + | 224.942i | −0.218185 | + | 0.449884i | ||||
\(501\) | −427.097 | −0.852490 | ||||||||
\(502\) | 118.743 | 0.236539 | ||||||||
\(503\) | 441.083 | 0.876904 | 0.438452 | − | 0.898755i | \(-0.355527\pi\) | ||||
0.438452 | + | 0.898755i | \(0.355527\pi\) | |||||||
\(504\) | −81.2122 | + | 44.5628i | −0.161135 | + | 0.0884183i | ||||
\(505\) | −189.430 | − | 483.969i | −0.375109 | − | 0.958355i | ||||
\(506\) | −8.99416 | −0.0177750 | ||||||||
\(507\) | −151.232 | −0.298289 | ||||||||
\(508\) | − | 156.678i | − | 0.308420i | ||||||
\(509\) | 420.460i | 0.826051i | 0.910719 | + | 0.413026i | \(0.135528\pi\) | ||||
−0.910719 | + | 0.413026i | \(0.864472\pi\) | |||||||
\(510\) | 2.67095 | + | 6.82393i | 0.00523716 | + | 0.0133803i | ||||
\(511\) | −344.933 | − | 628.614i | −0.675016 | − | 1.23016i | ||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | 916.119i | 1.78581i | ||||||||
\(514\) | − | 246.918i | − | 0.480385i | ||||||
\(515\) | 236.539 | − | 92.5837i | 0.459300 | − | 0.179774i | ||||
\(516\) | − | 156.861i | − | 0.303994i | ||||||
\(517\) | 119.900 | 0.231915 | ||||||||
\(518\) | 76.4909 | + | 139.399i | 0.147666 | + | 0.269109i | ||||
\(519\) | −359.836 | −0.693325 | ||||||||
\(520\) | 50.5698 | + | 129.199i | 0.0972495 | + | 0.248460i | ||||
\(521\) | − | 698.451i | − | 1.34060i | −0.742092 | − | 0.670298i | \(-0.766166\pi\) | ||
0.742092 | − | 0.670298i | \(-0.233834\pi\) | |||||||
\(522\) | 258.295i | 0.494819i | ||||||||
\(523\) | 434.940 | 0.831625 | 0.415813 | − | 0.909450i | \(-0.363497\pi\) | ||||
0.415813 | + | 0.909450i | \(0.363497\pi\) | |||||||
\(524\) | − | 467.976i | − | 0.893083i | ||||||
\(525\) | 344.996 | + | 115.393i | 0.657134 | + | 0.219795i | ||||
\(526\) | −214.497 | −0.407789 | ||||||||
\(527\) | − | 12.4278i | − | 0.0235822i | ||||||
\(528\) | 13.9591 | 0.0264377 | ||||||||
\(529\) | 514.648 | 0.972870 | ||||||||
\(530\) | −546.761 | + | 214.007i | −1.03162 | + | 0.403788i | ||||
\(531\) | 170.534i | 0.321157i | ||||||||
\(532\) | −395.435 | + | 216.983i | −0.743298 | + | 0.407863i | ||||
\(533\) | − | 697.935i | − | 1.30945i | ||||||
\(534\) | −159.006 | −0.297764 | ||||||||
\(535\) | 201.310 | + | 514.320i | 0.376280 | + | 0.961346i | ||||
\(536\) | −34.7151 | −0.0647670 | ||||||||
\(537\) | −29.2536 | −0.0544761 | ||||||||
\(538\) | 622.424 | 1.15692 | ||||||||
\(539\) | −44.1875 | + | 69.3845i | −0.0819806 | + | 0.128728i | ||||
\(540\) | 264.788 | − | 103.640i | 0.490348 | − | 0.191927i | ||||
\(541\) | 769.254 | 1.42191 | 0.710956 | − | 0.703237i | \(-0.248262\pi\) | ||||
0.710956 | + | 0.703237i | \(0.248262\pi\) | |||||||
\(542\) | 532.125 | 0.981780 | ||||||||
\(543\) | − | 353.948i | − | 0.651838i | ||||||
\(544\) | 2.82016i | 0.00518412i | ||||||||
\(545\) | 657.349 | − | 257.293i | 1.20614 | − | 0.472096i | ||||
\(546\) | 176.994 | − | 97.1203i | 0.324165 | − | 0.177876i | ||||
\(547\) | 242.885i | 0.444031i | 0.975043 | + | 0.222016i | \(0.0712636\pi\) | ||||
−0.975043 | + | 0.222016i | \(0.928736\pi\) | |||||||
\(548\) | 303.653i | 0.554111i | ||||||||
\(549\) | 236.009i | 0.429889i | ||||||||
\(550\) | 40.2907 | + | 43.5837i | 0.0732558 | + | 0.0792430i | ||||
\(551\) | 1257.68i | 2.28254i | ||||||||
\(552\) | 22.2741 | 0.0403516 | ||||||||
\(553\) | 445.823 | + | 812.478i | 0.806191 | + | 1.46922i | ||||
\(554\) | 472.291 | 0.852510 | ||||||||
\(555\) | −60.8488 | − | 155.461i | −0.109637 | − | 0.280109i | ||||
\(556\) | 160.373i | 0.288441i | ||||||||
\(557\) | 766.109i | 1.37542i | 0.725985 | + | 0.687710i | \(0.241384\pi\) | ||||
−0.725985 | + | 0.687710i | \(0.758616\pi\) | |||||||
\(558\) | −164.947 | −0.295604 | ||||||||
\(559\) | − | 370.150i | − | 0.662165i | ||||||
\(560\) | 107.451 | + | 89.7461i | 0.191876 | + | 0.160261i | ||||
\(561\) | 1.73979 | 0.00310122 | ||||||||
\(562\) | 535.438i | 0.952737i | ||||||||
\(563\) | −586.605 | −1.04193 | −0.520963 | − | 0.853579i | \(-0.674427\pi\) | ||||
−0.520963 | + | 0.853579i | \(0.674427\pi\) | |||||||
\(564\) | −296.933 | −0.526477 | ||||||||
\(565\) | 149.670 | + | 382.388i | 0.264903 | + | 0.676793i | ||||
\(566\) | 395.198i | 0.698230i | ||||||||
\(567\) | −57.2458 | − | 104.326i | −0.100963 | − | 0.183996i | ||||
\(568\) | − | 126.268i | − | 0.222303i | ||||||
\(569\) | −744.375 | −1.30822 | −0.654108 | − | 0.756401i | \(-0.726956\pi\) | ||||
−0.654108 | + | 0.756401i | \(0.726956\pi\) | |||||||
\(570\) | 440.998 | − | 172.611i | 0.773681 | − | 0.302826i | ||||
\(571\) | −323.503 | −0.566555 | −0.283278 | − | 0.959038i | \(-0.591422\pi\) | ||||
−0.283278 | + | 0.959038i | \(0.591422\pi\) | |||||||
\(572\) | 32.9398 | 0.0575870 | ||||||||
\(573\) | 314.421 | 0.548727 | ||||||||
\(574\) | −338.788 | − | 617.414i | −0.590223 | − | 1.07563i | ||||
\(575\) | 64.2907 | + | 69.5452i | 0.111810 | + | 0.120948i | ||||
\(576\) | 37.4302 | 0.0649831 | ||||||||
\(577\) | −394.936 | −0.684465 | −0.342232 | − | 0.939615i | \(-0.611183\pi\) | ||||
−0.342232 | + | 0.939615i | \(0.611183\pi\) | |||||||
\(578\) | − | 408.356i | − | 0.706499i | ||||||
\(579\) | 699.887i | 1.20879i | ||||||||
\(580\) | 363.510 | − | 142.281i | 0.626742 | − | 0.245313i | ||||
\(581\) | −29.3939 | − | 53.5681i | −0.0505919 | − | 0.0921998i | ||||
\(582\) | 122.693i | 0.210813i | ||||||||
\(583\) | 139.399i | 0.239106i | ||||||||
\(584\) | 289.724i | 0.496103i | ||||||||
\(585\) | 213.721 | − | 83.6524i | 0.365335 | − | 0.142996i | ||||
\(586\) | 333.689i | 0.569435i | ||||||||
\(587\) | −63.9610 | −0.108962 | −0.0544812 | − | 0.998515i | \(-0.517351\pi\) | ||||
−0.0544812 | + | 0.998515i | \(0.517351\pi\) | |||||||
\(588\) | 109.431 | − | 171.831i | 0.186107 | − | 0.292230i | ||||
\(589\) | −803.151 | −1.36358 | ||||||||
\(590\) | 240.000 | − | 93.9383i | 0.406780 | − | 0.159217i | ||||
\(591\) | 5.66594i | 0.00958704i | ||||||||
\(592\) | − | 64.2481i | − | 0.108527i | ||||||
\(593\) | −310.432 | −0.523495 | −0.261747 | − | 0.965136i | \(-0.584299\pi\) | ||||
−0.261747 | + | 0.965136i | \(0.584299\pi\) | |||||||
\(594\) | − | 67.5086i | − | 0.113651i | ||||||
\(595\) | 13.3921 | + | 11.1855i | 0.0225077 | + | 0.0187991i | ||||
\(596\) | −182.715 | −0.306569 | ||||||||
\(597\) | 181.842i | 0.304592i | ||||||||
\(598\) | 52.5611 | 0.0878947 | ||||||||
\(599\) | −429.885 | −0.717671 | −0.358836 | − | 0.933401i | \(-0.616826\pi\) | ||||
−0.358836 | + | 0.933401i | \(0.616826\pi\) | |||||||
\(600\) | −99.7802 | − | 107.935i | −0.166300 | − | 0.179892i | ||||
\(601\) | − | 67.8163i | − | 0.112839i | −0.998407 | − | 0.0564196i | \(-0.982032\pi\) | ||
0.998407 | − | 0.0564196i | \(-0.0179684\pi\) | |||||||
\(602\) | −179.676 | − | 327.446i | −0.298466 | − | 0.543930i | ||||
\(603\) | 57.4257i | 0.0952333i | ||||||||
\(604\) | 348.933 | 0.577704 | ||||||||
\(605\) | −550.260 | + | 215.377i | −0.909520 | + | 0.355995i | ||||
\(606\) | 305.576 | 0.504250 | ||||||||
\(607\) | 389.350 | 0.641433 | 0.320716 | − | 0.947175i | \(-0.396076\pi\) | ||||
0.320716 | + | 0.947175i | \(0.396076\pi\) | |||||||
\(608\) | 182.254 | 0.299759 | ||||||||
\(609\) | −273.254 | − | 497.985i | −0.448694 | − | 0.817709i | ||||
\(610\) | 332.145 | − | 130.005i | 0.544501 | − | 0.213123i | ||||
\(611\) | −700.685 | −1.14678 | ||||||||
\(612\) | 4.66511 | 0.00762272 | ||||||||
\(613\) | − | 822.472i | − | 1.34172i | −0.741586 | − | 0.670858i | \(-0.765926\pi\) | ||
0.741586 | − | 0.670858i | \(-0.234074\pi\) | |||||||
\(614\) | − | 601.677i | − | 0.979930i | ||||||
\(615\) | 269.507 | + | 688.555i | 0.438223 | + | 1.11960i | ||||
\(616\) | 29.1395 | − | 15.9895i | 0.0473044 | − | 0.0259569i | ||||
\(617\) | 507.916i | 0.823203i | 0.911364 | + | 0.411602i | \(0.135031\pi\) | ||||
−0.911364 | + | 0.411602i | \(0.864969\pi\) | |||||||
\(618\) | 149.350i | 0.241666i | ||||||||
\(619\) | − | 167.210i | − | 0.270129i | −0.990837 | − | 0.135064i | \(-0.956876\pi\) | ||
0.990837 | − | 0.135064i | \(-0.0431242\pi\) | |||||||
\(620\) | 90.8605 | + | 232.137i | 0.146549 | + | 0.374414i | ||||
\(621\) | − | 107.722i | − | 0.173465i | ||||||
\(622\) | 282.674 | 0.454460 | ||||||||
\(623\) | −331.924 | + | 182.133i | −0.532783 | + | 0.292349i | ||||
\(624\) | −81.5756 | −0.130730 | ||||||||
\(625\) | 49.0000 | − | 623.076i | 0.0784000 | − | 0.996922i | ||||
\(626\) | − | 583.000i | − | 0.931309i | ||||||
\(627\) | − | 112.434i | − | 0.179321i | ||||||
\(628\) | −77.1677 | −0.122879 | ||||||||
\(629\) | − | 8.00754i | − | 0.0127306i | ||||||
\(630\) | 148.458 | − | 177.745i | 0.235647 | − | 0.282134i | ||||
\(631\) | 538.696 | 0.853718 | 0.426859 | − | 0.904318i | \(-0.359620\pi\) | ||||
0.426859 | + | 0.904318i | \(0.359620\pi\) | |||||||
\(632\) | − | 374.466i | − | 0.592510i | ||||||
\(633\) | −30.3746 | −0.0479852 | ||||||||
\(634\) | −152.581 | −0.240665 | ||||||||
\(635\) | 142.766 | + | 364.749i | 0.224829 | + | 0.574408i | ||||
\(636\) | − | 345.222i | − | 0.542801i | ||||||
\(637\) | 258.228 | − | 405.476i | 0.405381 | − | 0.636541i | ||||
\(638\) | − | 92.6783i | − | 0.145264i | ||||||
\(639\) | −208.872 | −0.326873 | ||||||||
\(640\) | −20.6183 | − | 52.6772i | −0.0322162 | − | 0.0823081i | ||||
\(641\) | 520.788 | 0.812461 | 0.406231 | − | 0.913771i | \(-0.366843\pi\) | ||||
0.406231 | + | 0.913771i | \(0.366843\pi\) | |||||||
\(642\) | −324.739 | −0.505824 | ||||||||
\(643\) | −547.317 | −0.851192 | −0.425596 | − | 0.904913i | \(-0.639936\pi\) | ||||
−0.425596 | + | 0.904913i | \(0.639936\pi\) | |||||||
\(644\) | 46.4971 | − | 25.5139i | 0.0722004 | − | 0.0396179i | ||||
\(645\) | 142.933 | + | 365.175i | 0.221602 | + | 0.566163i | ||||
\(646\) | 22.7151 | 0.0351627 | ||||||||
\(647\) | −639.806 | −0.988881 | −0.494441 | − | 0.869211i | \(-0.664627\pi\) | ||||
−0.494441 | + | 0.869211i | \(0.664627\pi\) | |||||||
\(648\) | 48.0833i | 0.0742026i | ||||||||
\(649\) | − | 61.1889i | − | 0.0942818i | ||||||
\(650\) | −235.455 | − | 254.699i | −0.362239 | − | 0.391844i | ||||
\(651\) | 318.012 | − | 174.500i | 0.488497 | − | 0.268048i | ||||
\(652\) | 582.759i | 0.893802i | ||||||||
\(653\) | − | 386.397i | − | 0.591726i | −0.955230 | − | 0.295863i | \(-0.904393\pi\) | ||
0.955230 | − | 0.295863i | \(-0.0956071\pi\) | |||||||
\(654\) | 415.046i | 0.634627i | ||||||||
\(655\) | 426.424 | + | 1089.46i | 0.651030 | + | 1.66330i | ||||
\(656\) | 284.563i | 0.433785i | ||||||||
\(657\) | 479.262 | 0.729470 | ||||||||
\(658\) | −619.847 | + | 340.122i | −0.942016 | + | 0.516903i | ||||
\(659\) | −684.042 | −1.03800 | −0.519000 | − | 0.854774i | \(-0.673696\pi\) | ||||
−0.519000 | + | 0.854774i | \(0.673696\pi\) | |||||||
\(660\) | −32.4971 | + | 12.7197i | −0.0492380 | + | 0.0192722i | ||||
\(661\) | 36.5809i | 0.0553417i | 0.999617 | + | 0.0276709i | \(0.00880903\pi\) | ||||
−0.999617 | + | 0.0276709i | \(0.991191\pi\) | |||||||
\(662\) | − | 53.8429i | − | 0.0813337i | ||||||
\(663\) | −10.1671 | −0.0153351 | ||||||||
\(664\) | 24.6892i | 0.0371826i | ||||||||
\(665\) | 722.864 | − | 865.466i | 1.08701 | − | 1.30145i | ||||
\(666\) | −106.279 | −0.159578 | ||||||||
\(667\) | − | 147.884i | − | 0.221715i | ||||||
\(668\) | 410.917 | 0.615145 | ||||||||
\(669\) | 270.164 | 0.403833 | ||||||||
\(670\) | 80.8176 | − | 31.6328i | 0.120623 | − | 0.0472131i | ||||
\(671\) | − | 84.6817i | − | 0.126202i | ||||||
\(672\) | −72.1642 | + | 39.5980i | −0.107387 | + | 0.0589256i | ||||
\(673\) | − | 85.1447i | − | 0.126515i | −0.997997 | − | 0.0632575i | \(-0.979851\pi\) | ||
0.997997 | − | 0.0632575i | \(-0.0201490\pi\) | |||||||
\(674\) | 368.581 | 0.546857 | ||||||||
\(675\) | −521.994 | + | 482.555i | −0.773324 | + | 0.714896i | ||||
\(676\) | 145.503 | 0.215241 | ||||||||
\(677\) | −623.768 | −0.921371 | −0.460686 | − | 0.887563i | \(-0.652396\pi\) | ||||
−0.460686 | + | 0.887563i | \(0.652396\pi\) | |||||||
\(678\) | −241.438 | −0.356103 | ||||||||
\(679\) | 140.539 | + | 256.122i | 0.206980 | + | 0.377204i | ||||
\(680\) | −2.56976 | − | 6.56540i | −0.00377906 | − | 0.00965500i | ||||
\(681\) | 277.048 | 0.406825 | ||||||||
\(682\) | 59.1841 | 0.0867802 | ||||||||
\(683\) | − | 898.085i | − | 1.31491i | −0.753493 | − | 0.657456i | \(-0.771632\pi\) | ||
0.753493 | − | 0.657456i | \(-0.228368\pi\) | |||||||
\(684\) | − | 301.484i | − | 0.440766i | ||||||
\(685\) | −276.692 | − | 706.912i | −0.403930 | − | 1.03199i | ||||
\(686\) | 31.6119 | − | 484.044i | 0.0460815 | − | 0.705604i | ||||
\(687\) | − | 458.530i | − | 0.667438i | ||||||
\(688\) | 150.918i | 0.219358i | ||||||||
\(689\) | − | 814.633i | − | 1.18234i | ||||||
\(690\) | −51.8546 | + | 20.2964i | −0.0751517 | + | 0.0294151i | ||||
\(691\) | 487.503i | 0.705504i | 0.935717 | + | 0.352752i | \(0.114754\pi\) | ||||
−0.935717 | + | 0.352752i | \(0.885246\pi\) | |||||||
\(692\) | 346.203 | 0.500294 | ||||||||
\(693\) | −26.4497 | − | 48.2026i | −0.0381670 | − | 0.0695564i | ||||
\(694\) | −552.654 | −0.796332 | ||||||||
\(695\) | −146.134 | − | 373.352i | −0.210264 | − | 0.537198i | ||||
\(696\) | 229.518i | 0.329768i | ||||||||
\(697\) | 35.4664i | 0.0508843i | ||||||||
\(698\) | −793.540 | −1.13688 | ||||||||
\(699\) | − | 451.055i | − | 0.645286i | ||||||
\(700\) | −331.925 | − | 111.021i | −0.474179 | − | 0.158601i | ||||
\(701\) | 399.170 | 0.569429 | 0.284715 | − | 0.958612i | \(-0.408101\pi\) | ||||
0.284715 | + | 0.958612i | \(0.408101\pi\) | |||||||
\(702\) | 394.514i | 0.561986i | ||||||||
\(703\) | −517.489 | −0.736115 | ||||||||
\(704\) | −13.4302 | −0.0190770 | ||||||||
\(705\) | 691.267 | − | 270.569i | 0.980521 | − | 0.383785i | ||||
\(706\) | 360.506i | 0.510632i | ||||||||
\(707\) | 637.888 | − | 350.022i | 0.902246 | − | 0.495081i | ||||
\(708\) | 151.535i | 0.214032i | ||||||||
\(709\) | −241.751 | −0.340975 | −0.170488 | − | 0.985360i | \(-0.554534\pi\) | ||||
−0.170488 | + | 0.985360i | \(0.554534\pi\) | |||||||
\(710\) | 115.057 | + | 293.955i | 0.162052 | + | 0.414021i | ||||
\(711\) | −619.442 | −0.871226 | ||||||||
\(712\) | 152.982 | 0.214862 | ||||||||
\(713\) | 94.4383 | 0.132452 | ||||||||
\(714\) | −8.99416 | + | 4.93528i | −0.0125969 | + | 0.00691216i | ||||
\(715\) | −76.6846 | + | 30.0151i | −0.107251 | + | 0.0419791i | ||||
\(716\) | 28.1454 | 0.0393092 | ||||||||
\(717\) | −656.672 | −0.915860 | ||||||||
\(718\) | 52.2314i | 0.0727456i | ||||||||
\(719\) | − | 544.197i | − | 0.756880i | −0.925626 | − | 0.378440i | \(-0.876461\pi\) | ||
0.925626 | − | 0.378440i | \(-0.123539\pi\) | |||||||
\(720\) | −87.1385 | + | 34.1068i | −0.121026 | + | 0.0473706i | ||||
\(721\) | 171.073 | + | 311.767i | 0.237271 | + | 0.432409i | ||||
\(722\) | − | 957.439i | − | 1.32609i | ||||||
\(723\) | 473.959i | 0.655545i | ||||||||
\(724\) | 340.539i | 0.470357i | ||||||||
\(725\) | −716.612 | + | 662.469i | −0.988430 | + | 0.913750i | ||||
\(726\) | − | 347.431i | − | 0.478555i | ||||||
\(727\) | −211.414 | −0.290803 | −0.145401 | − | 0.989373i | \(-0.546447\pi\) | ||||
−0.145401 | + | 0.989373i | \(0.546447\pi\) | |||||||
\(728\) | −170.289 | + | 93.4409i | −0.233913 | + | 0.128353i | ||||
\(729\) | 611.520 | 0.838848 | ||||||||
\(730\) | −264.000 | − | 674.485i | −0.361644 | − | 0.923953i | ||||
\(731\) | 18.8096i | 0.0257313i | ||||||||
\(732\) | 209.715i | 0.286496i | ||||||||
\(733\) | 1085.37 | 1.48072 | 0.740359 | − | 0.672211i | \(-0.234655\pi\) | ||||
0.740359 | + | 0.672211i | \(0.234655\pi\) | |||||||
\(734\) | 378.277i | 0.515364i | ||||||||
\(735\) | −98.1830 | + | 499.741i | −0.133582 | + | 0.679920i | ||||
\(736\) | −21.4302 | −0.0291172 | ||||||||
\(737\) | − | 20.6048i | − | 0.0279576i | ||||||
\(738\) | 470.723 | 0.637836 | ||||||||
\(739\) | −671.193 | −0.908245 | −0.454123 | − | 0.890939i | \(-0.650047\pi\) | ||||
−0.454123 | + | 0.890939i | \(0.650047\pi\) | |||||||
\(740\) | 58.5435 | + | 149.571i | 0.0791129 | + | 0.202123i | ||||
\(741\) | 657.054i | 0.886713i | ||||||||
\(742\) | −395.435 | − | 720.649i | −0.532931 | − | 0.971225i | ||||
\(743\) | − | 194.699i | − | 0.262044i | −0.991379 | − | 0.131022i | \(-0.958174\pi\) | ||
0.991379 | − | 0.131022i | \(-0.0418259\pi\) | |||||||
\(744\) | −146.570 | −0.197002 | ||||||||
\(745\) | 425.365 | − | 166.492i | 0.570960 | − | 0.223479i | ||||
\(746\) | 179.564 | 0.240702 | ||||||||
\(747\) | 40.8409 | 0.0546732 | ||||||||
\(748\) | −1.67387 | −0.00223780 | ||||||||
\(749\) | −677.891 | + | 371.973i | −0.905061 | + | 0.496626i | ||||
\(750\) | 330.642 | + | 160.355i | 0.440857 | + | 0.213807i | ||||
\(751\) | 218.115 | 0.290433 | 0.145216 | − | 0.989400i | \(-0.453612\pi\) | ||||
0.145216 | + | 0.989400i | \(0.453612\pi\) | |||||||
\(752\) | 285.684 | 0.379899 | ||||||||
\(753\) | − | 174.540i | − | 0.231793i | ||||||
\(754\) | 541.603i | 0.718307i | ||||||||
\(755\) | −812.325 | + | 317.952i | −1.07593 | + | 0.421128i | ||||
\(756\) | 191.503 | + | 348.999i | 0.253311 | + | 0.461639i | ||||
\(757\) | 1248.55i | 1.64934i | 0.565611 | + | 0.824672i | \(0.308640\pi\) | ||||
−0.565611 | + | 0.824672i | \(0.691360\pi\) | |||||||
\(758\) | 735.305i | 0.970059i | ||||||||
\(759\) | 13.2205i | 0.0174184i | ||||||||
\(760\) | −424.291 | + | 166.071i | −0.558277 | + | 0.218515i | ||||
\(761\) | − | 947.736i | − | 1.24538i | −0.782468 | − | 0.622691i | \(-0.786039\pi\) | ||
0.782468 | − | 0.622691i | \(-0.213961\pi\) | |||||||
\(762\) | −230.301 | −0.302232 | ||||||||
\(763\) | 475.415 | + | 866.407i | 0.623087 | + | 1.13553i | ||||
\(764\) | −302.509 | −0.395954 | ||||||||
\(765\) | −10.8605 | + | 4.25089i | −0.0141967 | + | 0.00555673i | ||||
\(766\) | 556.781i | 0.726868i | ||||||||
\(767\) | 357.582i | 0.466209i | ||||||||
\(768\) | 33.2601 | 0.0433074 | ||||||||
\(769\) | 127.967i | 0.166407i | 0.996533 | + | 0.0832034i | \(0.0265151\pi\) | ||||
−0.996533 | + | 0.0832034i | \(0.973485\pi\) | |||||||
\(770\) | −53.2677 | + | 63.7761i | −0.0691789 | + | 0.0828261i | ||||
\(771\) | −362.945 | −0.470746 | ||||||||
\(772\) | − | 673.371i | − | 0.872243i | ||||||
\(773\) | 698.585 | 0.903733 | 0.451866 | − | 0.892086i | \(-0.350758\pi\) | ||||
0.451866 | + | 0.892086i | \(0.350758\pi\) | |||||||
\(774\) | 249.648 | 0.322543 | ||||||||
\(775\) | −423.051 | − | 457.626i | −0.545872 | − | 0.590486i | ||||
\(776\) | − | 118.045i | − | 0.152120i | ||||||
\(777\) | 204.902 | − | 112.434i | 0.263710 | − | 0.144703i | ||||
\(778\) | 149.950i | 0.192738i | ||||||||
\(779\) | 2292.02 | 2.94226 | ||||||||
\(780\) | 189.910 | − | 74.3326i | 0.243474 | − | 0.0952982i | ||||
\(781\) | 74.9448 | 0.0959601 | ||||||||
\(782\) | −2.67095 | −0.00341554 | ||||||||
\(783\) | 1109.99 | 1.41761 | ||||||||
\(784\) | −105.285 | + | 165.321i | −0.134292 | + | 0.210869i | ||||
\(785\) | 179.648 | − | 70.3161i | 0.228851 | − | 0.0895746i | ||||
\(786\) | −687.878 | −0.875163 | ||||||||
\(787\) | 1450.29 | 1.84281 | 0.921403 | − | 0.388609i | \(-0.127044\pi\) | ||||
0.921403 | + | 0.388609i | \(0.127044\pi\) | |||||||
\(788\) | − | 5.45129i | − | 0.00691788i | ||||||
\(789\) | 315.290i | 0.399607i | ||||||||
\(790\) | 341.218 | + | 871.767i | 0.431921 | + | 1.10350i | ||||
\(791\) | −504.000 | + | 276.555i | −0.637168 | + | 0.349627i | ||||
\(792\) | 22.2163i | 0.0280509i | ||||||||
\(793\) | 494.872i | 0.624050i | ||||||||
\(794\) | − | 553.841i | − | 0.697533i | ||||||
\(795\) | 314.570 | + | 803.684i | 0.395685 | + | 1.01092i | ||||
\(796\) | − | 174.952i | − | 0.219790i | ||||||
\(797\) | −742.137 | −0.931163 | −0.465581 | − | 0.885005i | \(-0.654155\pi\) | ||||
−0.465581 | + | 0.885005i | \(0.654155\pi\) | |||||||
\(798\) | 318.944 | + | 581.250i | 0.399679 | + | 0.728383i | ||||
\(799\) | 35.6061 | 0.0445633 | ||||||||
\(800\) | 96.0000 | + | 103.846i | 0.120000 | + | 0.129808i | ||||
\(801\) | − | 253.062i | − | 0.315933i | ||||||
\(802\) | 58.1369i | 0.0724899i | ||||||||
\(803\) | −171.963 | −0.214150 | ||||||||
\(804\) | 51.0278i | 0.0634674i | ||||||||
\(805\) | −84.9978 | + | 101.766i | −0.105587 | + | 0.126417i | ||||
\(806\) | −345.866 | −0.429115 | ||||||||
\(807\) | − | 914.902i | − | 1.13371i | ||||||
\(808\) | −293.999 | −0.363860 | ||||||||
\(809\) | 884.551 | 1.09339 | 0.546694 | − | 0.837332i | \(-0.315886\pi\) | ||||
0.546694 | + | 0.837332i | \(0.315886\pi\) | |||||||
\(810\) | −43.8140 | − | 111.939i | −0.0540913 | − | 0.138196i | ||||
\(811\) | − | 472.924i | − | 0.583136i | −0.956550 | − | 0.291568i | \(-0.905823\pi\) | ||
0.956550 | − | 0.291568i | \(-0.0941770\pi\) | |||||||
\(812\) | 262.902 | + | 479.118i | 0.323771 | + | 0.590047i | ||||
\(813\) | − | 782.171i | − | 0.962080i | ||||||
\(814\) | 38.1337 | 0.0468473 | ||||||||
\(815\) | −531.016 | − | 1356.68i | −0.651553 | − | 1.66463i | ||||
\(816\) | 4.14536 | 0.00508010 | ||||||||
\(817\) | 1215.58 | 1.48785 | ||||||||
\(818\) | −723.860 | −0.884914 | ||||||||
\(819\) | 154.570 | + | 281.691i | 0.188730 | + | 0.343945i | ||||
\(820\) | −259.297 | − | 662.469i | −0.316215 | − | 0.807889i | ||||
\(821\) | −1091.40 | −1.32935 | −0.664677 | − | 0.747131i | \(-0.731431\pi\) | ||||
−0.664677 | + | 0.747131i | \(0.731431\pi\) | |||||||
\(822\) | 446.340 | 0.542993 | ||||||||
\(823\) | − | 749.909i | − | 0.911190i | −0.890187 | − | 0.455595i | \(-0.849427\pi\) | ||
0.890187 | − | 0.455595i | \(-0.150573\pi\) | |||||||
\(824\) | − | 143.691i | − | 0.174383i | ||||||
\(825\) | 64.0637 | − | 59.2234i | 0.0776529 | − | 0.0717859i | ||||
\(826\) | 173.576 | + | 316.328i | 0.210140 | + | 0.382964i | ||||
\(827\) | − | 511.380i | − | 0.618355i | −0.951004 | − | 0.309178i | \(-0.899946\pi\) | ||
0.951004 | − | 0.309178i | \(-0.100054\pi\) | |||||||
\(828\) | 35.4499i | 0.0428139i | ||||||||
\(829\) | 200.919i | 0.242363i | 0.992630 | + | 0.121182i | \(0.0386684\pi\) | ||||
−0.992630 | + | 0.121182i | \(0.961332\pi\) | |||||||
\(830\) | −22.4971 | − | 57.4771i | −0.0271049 | − | 0.0692495i | ||||
\(831\) | − | 694.221i | − | 0.835404i | ||||||
\(832\) | 78.4851 | 0.0943330 | ||||||||
\(833\) | −13.1221 | + | 20.6048i | −0.0157529 | + | 0.0247356i | ||||
\(834\) | 235.733 | 0.282653 | ||||||||
\(835\) | −956.624 | + | 374.432i | −1.14566 | + | 0.448421i | ||||
\(836\) | 108.174i | 0.129395i | ||||||||
\(837\) | 708.838i | 0.846879i | ||||||||
\(838\) | 116.712 | 0.139275 | ||||||||
\(839\) | 1403.47i | 1.67279i | 0.548124 | + | 0.836397i | \(0.315342\pi\) | ||||
−0.548124 | + | 0.836397i | \(0.684658\pi\) | |||||||
\(840\) | 131.918 | − | 157.942i | 0.157045 | − | 0.188026i | ||||
\(841\) | 682.836 | 0.811933 | ||||||||
\(842\) | − | 321.592i | − | 0.381938i | ||||||
\(843\) | 787.041 | 0.933620 | ||||||||
\(844\) | 29.2239 | 0.0346254 | ||||||||
\(845\) | −338.734 | + | 132.584i | −0.400869 | + | 0.156904i | ||||
\(846\) | − | 472.578i | − | 0.558602i | ||||||
\(847\) | −397.965 | − | 725.260i | −0.469853 | − | 0.856270i | ||||
\(848\) | 332.143i | 0.391678i | ||||||||
\(849\) | 580.903 | 0.684220 | ||||||||
\(850\) | 11.9649 | + | 12.9428i | 0.0140764 | + | 0.0152268i | ||||
\(851\) | 60.8488 | 0.0715027 | ||||||||
\(852\) | −185.601 | −0.217842 | ||||||||
\(853\) | −1221.54 | −1.43205 | −0.716026 | − | 0.698074i | \(-0.754041\pi\) | ||||
−0.716026 | + | 0.698074i | \(0.754041\pi\) | |||||||
\(854\) | 240.218 | + | 437.779i | 0.281286 | + | 0.512621i | ||||
\(855\) | 274.715 | + | 701.861i | 0.321304 | + | 0.820890i | ||||
\(856\) | 312.436 | 0.364995 | ||||||||
\(857\) | −541.135 | −0.631429 | −0.315715 | − | 0.948854i | \(-0.602244\pi\) | ||||
−0.315715 | + | 0.948854i | \(0.602244\pi\) | |||||||
\(858\) | − | 48.4182i | − | 0.0564315i | ||||||
\(859\) | − | 1175.60i | − | 1.36857i | −0.729213 | − | 0.684287i | \(-0.760114\pi\) | ||
0.729213 | − | 0.684287i | \(-0.239886\pi\) | |||||||
\(860\) | −137.518 | − | 351.341i | −0.159905 | − | 0.408536i | ||||
\(861\) | −907.538 | + | 497.985i | −1.05405 | + | 0.578379i | ||||
\(862\) | 360.573i | 0.418298i | ||||||||
\(863\) | 1155.08i | 1.33844i | 0.743062 | + | 0.669222i | \(0.233373\pi\) | ||||
−0.743062 | + | 0.669222i | \(0.766627\pi\) | |||||||
\(864\) | − | 160.852i | − | 0.186171i | ||||||
\(865\) | −805.969 | + | 315.464i | −0.931757 | + | 0.364698i | ||||
\(866\) | − | 954.812i | − | 1.10255i | ||||||
\(867\) | −600.243 | −0.692322 | ||||||||
\(868\) | −305.964 | + | 167.889i | −0.352493 | + | 0.193420i | ||||
\(869\) | 222.260 | 0.255765 | ||||||||
\(870\) | −209.140 | − | 534.324i | −0.240390 | − | 0.614166i | ||||
\(871\) | 120.412i | 0.138246i | ||||||||
\(872\) | − | 399.322i | − | 0.457938i | ||||||
\(873\) | −195.270 | −0.223677 | ||||||||
\(874\) | 172.611i | 0.197495i | ||||||||
\(875\) | 873.893 | − | 43.9947i | 0.998735 | − | 0.0502796i | ||||
\(876\) | 425.866 | 0.486149 | ||||||||
\(877\) | 993.086i | 1.13237i | 0.824279 | + | 0.566184i | \(0.191581\pi\) | ||||
−0.824279 | + | 0.566184i | \(0.808419\pi\) | |||||||
\(878\) | 5.34190 | 0.00608417 | ||||||||
\(879\) | 490.490 | 0.558009 | ||||||||
\(880\) | 31.2659 | − | 12.2378i | 0.0355295 | − | 0.0139066i | ||||
\(881\) | − | 431.925i | − | 0.490266i | −0.969489 | − | 0.245133i | \(-0.921168\pi\) | ||
0.969489 | − | 0.245133i | \(-0.0788317\pi\) | |||||||
\(882\) | 273.474 | + | 174.162i | 0.310061 | + | 0.197463i | ||||
\(883\) | − | 1064.16i | − | 1.20516i | −0.798058 | − | 0.602580i | \(-0.794139\pi\) | ||
0.798058 | − | 0.602580i | \(-0.205861\pi\) | |||||||
\(884\) | 9.78196 | 0.0110656 | ||||||||
\(885\) | −138.080 | − | 352.776i | −0.156023 | − | 0.398617i | ||||
\(886\) | −386.788 | −0.436555 | ||||||||
\(887\) | 367.743 | 0.414592 | 0.207296 | − | 0.978278i | \(-0.433534\pi\) | ||||
0.207296 | + | 0.978278i | \(0.433534\pi\) | |||||||
\(888\) | −94.4383 | −0.106349 | ||||||||
\(889\) | −480.751 | + | 263.798i | −0.540778 | + | 0.296736i | ||||
\(890\) | −356.145 | + | 139.399i | −0.400163 | + | 0.156628i | ||||
\(891\) | −28.5393 | −0.0320306 | ||||||||
\(892\) | −259.929 | −0.291400 | ||||||||
\(893\) | − | 2301.05i | − | 2.57677i | ||||||
\(894\) | 268.573i | 0.300417i | ||||||||
\(895\) | −65.5231 | + | 25.6464i | −0.0732101 | + | 0.0286551i | ||||
\(896\) | 69.4302 | − | 38.0978i | 0.0774891 | − | 0.0425199i | ||||
\(897\) | − | 77.2596i | − | 0.0861311i | ||||||
\(898\) | 328.157i | 0.365431i | ||||||||
\(899\) | 973.117i | 1.08244i | ||||||||
\(900\) | 171.782 | − | 158.803i | 0.190869 | − | 0.176448i | ||||
\(901\) | 41.3965i | 0.0459451i | ||||||||
\(902\) | −168.899 | −0.187249 | ||||||||
\(903\) | −481.313 | + | 264.106i | −0.533016 | + | 0.292477i | ||||
\(904\) | 232.291 | 0.256959 | ||||||||
\(905\) | −310.302 | − | 792.782i | −0.342876 | − | 0.876002i | ||||
\(906\) | − | 512.897i | − | 0.566112i | ||||||
\(907\) | − | 872.646i | − | 0.962123i | −0.876687 | − | 0.481062i | \(-0.840251\pi\) | ||
0.876687 | − | 0.481062i | \(-0.159749\pi\) | |||||||
\(908\) | −266.552 | −0.293559 | ||||||||
\(909\) | 486.332i | 0.535019i | ||||||||
\(910\) | 311.292 | − | 372.701i | 0.342079 | − | 0.409562i | ||||
\(911\) | −467.939 | −0.513654 | −0.256827 | − | 0.966457i | \(-0.582677\pi\) | ||||
−0.256827 | + | 0.966457i | \(0.582677\pi\) | |||||||
\(912\) | − | 267.895i | − | 0.293744i | ||||||
\(913\) | −14.6540 | −0.0160504 | ||||||||
\(914\) | 525.018 | 0.574417 | ||||||||
\(915\) | −191.094 | − | 488.221i | −0.208846 | − | 0.533575i | ||||
\(916\) | 441.158i | 0.481614i | ||||||||
\(917\) | −1435.94 | + | 787.931i | −1.56591 | + | 0.859248i | ||||
\(918\) | − | 20.0477i | − | 0.0218384i | ||||||
\(919\) | 254.964 | 0.277436 | 0.138718 | − | 0.990332i | \(-0.455702\pi\) | ||||
0.138718 | + | 0.990332i | \(0.455702\pi\) | |||||||
\(920\) | 49.8901 | − | 19.5275i | 0.0542284 | − | 0.0212255i | ||||
\(921\) | −884.406 | −0.960267 | ||||||||
\(922\) | −17.3068 | −0.0187710 | ||||||||
\(923\) | −437.971 | −0.474508 | ||||||||
\(924\) | −23.5029 | − | 42.8322i | −0.0254361 | − | 0.0463552i | ||||
\(925\) | −272.581 | − | 294.859i | −0.294683 | − | 0.318767i | ||||
\(926\) | −376.509 | −0.406597 | ||||||||
\(927\) | −237.694 | −0.256412 | ||||||||
\(928\) | − | 220.823i | − | 0.237956i | ||||||
\(929\) | − | 21.7366i | − | 0.0233979i | −0.999932 | − | 0.0116989i | \(-0.996276\pi\) | ||
0.999932 | − | 0.0116989i | \(-0.00372397\pi\) | |||||||
\(930\) | 341.218 | − | 133.556i | 0.366901 | − | 0.143609i | ||||
\(931\) | 1331.59 | + | 848.022i | 1.43028 | + | 0.910872i | ||||
\(932\) | 433.966i | 0.465629i | ||||||||
\(933\) | − | 415.503i | − | 0.445341i | ||||||
\(934\) | − | 407.197i | − | 0.435971i | ||||||
\(935\) | 3.89682 | − | 1.52525i | 0.00416772 | − | 0.00163129i | ||||
\(936\) | − | 129.830i | − | 0.138707i | ||||||
\(937\) | −1089.71 | −1.16298 | −0.581490 | − | 0.813554i | \(-0.697530\pi\) | ||||
−0.581490 | + | 0.813554i | \(0.697530\pi\) | |||||||
\(938\) | 58.4499 | + | 106.520i | 0.0623133 | + | 0.113561i | ||||
\(939\) | −856.952 | −0.912622 | ||||||||
\(940\) | −665.079 | + | 260.318i | −0.707530 | + | 0.276934i | ||||
\(941\) | 1017.39i | 1.08117i | 0.841288 | + | 0.540587i | \(0.181798\pi\) | ||||
−0.841288 | + | 0.540587i | \(0.818202\pi\) | |||||||
\(942\) | 113.429i | 0.120413i | ||||||||
\(943\) | −269.507 | −0.285797 | ||||||||
\(944\) | − | 145.794i | − | 0.154443i | ||||||
\(945\) | −763.835 | − | 637.979i | −0.808291 | − | 0.675110i | ||||
\(946\) | −89.5756 | −0.0946888 | ||||||||
\(947\) | − | 260.781i | − | 0.275376i | −0.990476 | − | 0.137688i | \(-0.956033\pi\) | ||
0.990476 | − | 0.137688i | \(-0.0439670\pi\) | |||||||
\(948\) | −550.429 | −0.580621 | ||||||||
\(949\) | 1004.93 | 1.05894 | ||||||||
\(950\) | 836.433 | − | 773.237i | 0.880456 | − | 0.813933i | ||||
\(951\) | 224.280i | 0.235836i | ||||||||
\(952\) | 8.65342 | − | 4.74831i | 0.00908972 | − | 0.00498772i | ||||
\(953\) | 862.773i | 0.905323i | 0.891682 | + | 0.452662i | \(0.149525\pi\) | ||||
−0.891682 | + | 0.452662i | \(0.850475\pi\) | |||||||
\(954\) | 549.430 | 0.575923 | ||||||||
\(955\) | 704.248 | − | 275.649i | 0.737432 | − | 0.288638i | ||||
\(956\) | 631.794 | 0.660872 | ||||||||
\(957\) | −136.228 | −0.142349 | ||||||||
\(958\) | 332.564 | 0.347145 | ||||||||
\(959\) | 931.733 | − | 511.261i | 0.971567 | − | 0.533119i | ||||
\(960\) | −77.4302 | + | 30.3069i | −0.0806565 | + | 0.0315697i | ||||
\(961\) | 339.570 | 0.353350 | ||||||||
\(962\) | −222.850 | −0.231653 | ||||||||
\(963\) | − | 516.831i | − | 0.536689i | ||||||
\(964\) | − | 456.003i | − | 0.473032i | ||||||
\(965\) | 613.583 | + | 1567.62i | 0.635837 | + | 1.62448i | ||||
\(966\) | −37.5029 | − | 68.3461i | −0.0388229 | − | 0.0707517i | ||||
\(967\) | 948.088i | 0.980443i | 0.871598 | + | 0.490222i | \(0.163084\pi\) | ||||
−0.871598 | + | 0.490222i | \(0.836916\pi\) | |||||||
\(968\) | 334.268i | 0.345319i | ||||||||
\(969\) | − | 33.3890i | − | 0.0344572i | ||||||
\(970\) | 107.564 | + | 274.812i | 0.110891 | + | 0.283311i | ||||
\(971\) | − | 1415.45i | − | 1.45772i | −0.684662 | − | 0.728860i | \(-0.740050\pi\) | ||
0.684662 | − | 0.728860i | \(-0.259950\pi\) | |||||||
\(972\) | −441.149 | −0.453857 | ||||||||
\(973\) | 492.091 | − | 270.020i | 0.505746 | − | 0.277513i | ||||
\(974\) | 412.073 | 0.423073 | ||||||||
\(975\) | −374.382 | + | 346.096i | −0.383982 | + | 0.354970i | ||||
\(976\) | − | 201.770i | − | 0.206731i | ||||||
\(977\) | 925.821i | 0.947616i | 0.880628 | + | 0.473808i | \(0.157121\pi\) | ||||
−0.880628 | + | 0.473808i | \(0.842879\pi\) | |||||||
\(978\) | 856.598 | 0.875867 | ||||||||
\(979\) | 90.8006i | 0.0927483i | ||||||||
\(980\) | 94.4633 | − | 480.808i | 0.0963911 | − | 0.490621i | ||||
\(981\) | −660.558 | −0.673352 | ||||||||
\(982\) | 863.038i | 0.878858i | ||||||||
\(983\) | −1048.06 | −1.06619 | −0.533093 | − | 0.846057i | \(-0.678970\pi\) | ||||
−0.533093 | + | 0.846057i | \(0.678970\pi\) | |||||||
\(984\) | 418.279 | 0.425080 | ||||||||
\(985\) | 4.96727 | + | 12.6907i | 0.00504291 | + | 0.0128840i | ||||
\(986\) | − | 27.5222i | − | 0.0279130i | ||||||
\(987\) | 499.947 | + | 911.113i | 0.506531 | + | 0.923114i | ||||
\(988\) | − | 632.162i | − | 0.639840i | ||||||
\(989\) | −142.933 | −0.144523 | ||||||||
\(990\) | −20.2437 | − | 51.7200i | −0.0204482 | − | 0.0522425i | ||||
\(991\) | 1014.10 | 1.02331 | 0.511653 | − | 0.859192i | \(-0.329033\pi\) | ||||
0.511653 | + | 0.859192i | \(0.329033\pi\) | |||||||
\(992\) | 141.017 | 0.142154 | ||||||||
\(993\) | −79.1438 | −0.0797017 | ||||||||
\(994\) | −387.442 | + | 212.597i | −0.389781 | + | 0.213881i | ||||
\(995\) | 159.419 | + | 407.294i | 0.160220 | + | 0.409340i | ||||
\(996\) | 36.2907 | 0.0364365 | ||||||||
\(997\) | 459.819 | 0.461202 | 0.230601 | − | 0.973048i | \(-0.425931\pi\) | ||||
0.230601 | + | 0.973048i | \(0.425931\pi\) | |||||||
\(998\) | 70.2564i | 0.0703972i | ||||||||
\(999\) | 456.721i | 0.457178i |
(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 | 70.3.d.a.69.7 | yes | 8 | |
3.2 | odd | 2 | 630.3.h.d.559.1 | 8 | |||
4.3 | odd | 2 | 560.3.p.g.209.3 | 8 | |||
5.2 | odd | 4 | 350.3.b.c.251.2 | 8 | |||
5.3 | odd | 4 | 350.3.b.c.251.7 | 8 | |||
5.4 | even | 2 | inner | 70.3.d.a.69.2 | ✓ | 8 | |
7.2 | even | 3 | 490.3.h.a.129.6 | 16 | |||
7.3 | odd | 6 | 490.3.h.a.19.3 | 16 | |||
7.4 | even | 3 | 490.3.h.a.19.2 | 16 | |||
7.5 | odd | 6 | 490.3.h.a.129.7 | 16 | |||
7.6 | odd | 2 | inner | 70.3.d.a.69.6 | yes | 8 | |
15.14 | odd | 2 | 630.3.h.d.559.8 | 8 | |||
20.19 | odd | 2 | 560.3.p.g.209.5 | 8 | |||
21.20 | even | 2 | 630.3.h.d.559.4 | 8 | |||
28.27 | even | 2 | 560.3.p.g.209.6 | 8 | |||
35.4 | even | 6 | 490.3.h.a.19.7 | 16 | |||
35.9 | even | 6 | 490.3.h.a.129.3 | 16 | |||
35.13 | even | 4 | 350.3.b.c.251.6 | 8 | |||
35.19 | odd | 6 | 490.3.h.a.129.2 | 16 | |||
35.24 | odd | 6 | 490.3.h.a.19.6 | 16 | |||
35.27 | even | 4 | 350.3.b.c.251.3 | 8 | |||
35.34 | odd | 2 | inner | 70.3.d.a.69.3 | yes | 8 | |
105.104 | even | 2 | 630.3.h.d.559.5 | 8 | |||
140.139 | even | 2 | 560.3.p.g.209.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.3.d.a.69.2 | ✓ | 8 | 5.4 | even | 2 | inner | |
70.3.d.a.69.3 | yes | 8 | 35.34 | odd | 2 | inner | |
70.3.d.a.69.6 | yes | 8 | 7.6 | odd | 2 | inner | |
70.3.d.a.69.7 | yes | 8 | 1.1 | even | 1 | trivial | |
350.3.b.c.251.2 | 8 | 5.2 | odd | 4 | |||
350.3.b.c.251.3 | 8 | 35.27 | even | 4 | |||
350.3.b.c.251.6 | 8 | 35.13 | even | 4 | |||
350.3.b.c.251.7 | 8 | 5.3 | odd | 4 | |||
490.3.h.a.19.2 | 16 | 7.4 | even | 3 | |||
490.3.h.a.19.3 | 16 | 7.3 | odd | 6 | |||
490.3.h.a.19.6 | 16 | 35.24 | odd | 6 | |||
490.3.h.a.19.7 | 16 | 35.4 | even | 6 | |||
490.3.h.a.129.2 | 16 | 35.19 | odd | 6 | |||
490.3.h.a.129.3 | 16 | 35.9 | even | 6 | |||
490.3.h.a.129.6 | 16 | 7.2 | even | 3 | |||
490.3.h.a.129.7 | 16 | 7.5 | odd | 6 | |||
560.3.p.g.209.3 | 8 | 4.3 | odd | 2 | |||
560.3.p.g.209.4 | 8 | 140.139 | even | 2 | |||
560.3.p.g.209.5 | 8 | 20.19 | odd | 2 | |||
560.3.p.g.209.6 | 8 | 28.27 | even | 2 | |||
630.3.h.d.559.1 | 8 | 3.2 | odd | 2 | |||
630.3.h.d.559.4 | 8 | 21.20 | even | 2 | |||
630.3.h.d.559.5 | 8 | 105.104 | even | 2 | |||
630.3.h.d.559.8 | 8 | 15.14 | odd | 2 |