Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [35,5,Mod(8,35)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(35, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("35.8");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 35 = 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 35.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: | \(3.61794870793\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 22.8 | ||
Character | \(\chi\) | \(=\) | 35.22 |
Dual form | 35.5.g.a.8.8 |
$q$-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 \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.48373 | + | 1.48373i | 0.370932 | + | 0.370932i | 0.867817 | − | 0.496884i | \(-0.165523\pi\) |
−0.496884 | + | 0.867817i | \(0.665523\pi\) | |||||||
\(3\) | 2.63880 | − | 2.63880i | 0.293200 | − | 0.293200i | −0.545143 | − | 0.838343i | \(-0.683525\pi\) |
0.838343 | + | 0.545143i | \(0.183525\pi\) | |||||||
\(4\) | − | 11.5971i | − | 0.724818i | ||||||
\(5\) | 8.51221 | − | 23.5062i | 0.340488 | − | 0.940249i | ||||
\(6\) | 7.83054 | 0.217515 | ||||||||
\(7\) | 13.0958 | + | 13.0958i | 0.267261 | + | 0.267261i | ||||
\(8\) | 40.9466 | − | 40.9466i | 0.639791 | − | 0.639791i | ||||
\(9\) | 67.0734i | 0.828067i | ||||||||
\(10\) | 47.5067 | − | 22.2471i | 0.475067 | − | 0.222471i | ||||
\(11\) | 18.0812 | 0.149431 | 0.0747155 | − | 0.997205i | \(-0.476195\pi\) | ||||
0.0747155 | + | 0.997205i | \(0.476195\pi\) | |||||||
\(12\) | −30.6025 | − | 30.6025i | −0.212517 | − | 0.212517i | ||||
\(13\) | −1.78021 | + | 1.78021i | −0.0105338 | + | 0.0105338i | −0.712354 | − | 0.701820i | \(-0.752371\pi\) |
0.701820 | + | 0.712354i | \(0.252371\pi\) | |||||||
\(14\) | 38.8613i | 0.198272i | ||||||||
\(15\) | −39.5662 | − | 84.4904i | −0.175850 | − | 0.375513i | ||||
\(16\) | −64.0460 | −0.250180 | ||||||||
\(17\) | 8.06293 | + | 8.06293i | 0.0278994 | + | 0.0278994i | 0.720919 | − | 0.693019i | \(-0.243720\pi\) |
−0.693019 | + | 0.720919i | \(0.743720\pi\) | |||||||
\(18\) | −99.5188 | + | 99.5188i | −0.307157 | + | 0.307157i | ||||
\(19\) | 201.172i | 0.557262i | 0.960398 | + | 0.278631i | \(0.0898807\pi\) | ||||
−0.960398 | + | 0.278631i | \(0.910119\pi\) | |||||||
\(20\) | −272.604 | − | 98.7169i | −0.681509 | − | 0.246792i | ||||
\(21\) | 69.1145 | 0.156722 | ||||||||
\(22\) | 26.8275 | + | 26.8275i | 0.0554288 | + | 0.0554288i | ||||
\(23\) | −414.713 | + | 414.713i | −0.783956 | + | 0.783956i | −0.980496 | − | 0.196540i | \(-0.937030\pi\) |
0.196540 | + | 0.980496i | \(0.437030\pi\) | |||||||
\(24\) | − | 216.100i | − | 0.375174i | ||||||
\(25\) | −480.085 | − | 400.180i | −0.768135 | − | 0.640288i | ||||
\(26\) | −5.28271 | −0.00781466 | ||||||||
\(27\) | 390.737 | + | 390.737i | 0.535990 | + | 0.535990i | ||||
\(28\) | 151.873 | − | 151.873i | 0.193716 | − | 0.193716i | ||||
\(29\) | 1065.57i | 1.26703i | 0.773729 | + | 0.633516i | \(0.218389\pi\) | ||||
−0.773729 | + | 0.633516i | \(0.781611\pi\) | |||||||
\(30\) | 66.6552 | − | 184.066i | 0.0740614 | − | 0.204518i | ||||
\(31\) | 1360.48 | 1.41569 | 0.707845 | − | 0.706368i | \(-0.249668\pi\) | ||||
0.707845 | + | 0.706368i | \(0.249668\pi\) | |||||||
\(32\) | −750.173 | − | 750.173i | −0.732591 | − | 0.732591i | ||||
\(33\) | 47.7126 | − | 47.7126i | 0.0438133 | − | 0.0438133i | ||||
\(34\) | 23.9264i | 0.0206976i | ||||||||
\(35\) | 419.307 | − | 196.359i | 0.342291 | − | 0.160293i | ||||
\(36\) | 777.857 | 0.600198 | ||||||||
\(37\) | −848.868 | − | 848.868i | −0.620065 | − | 0.620065i | 0.325483 | − | 0.945548i | \(-0.394473\pi\) |
−0.945548 | + | 0.325483i | \(0.894473\pi\) | |||||||
\(38\) | −298.484 | + | 298.484i | −0.206707 | + | 0.206707i | ||||
\(39\) | 9.39527i | 0.00617704i | ||||||||
\(40\) | −613.954 | − | 1311.05i | −0.383721 | − | 0.819404i | ||||
\(41\) | 2808.50 | 1.67073 | 0.835366 | − | 0.549694i | \(-0.185256\pi\) | ||||
0.835366 | + | 0.549694i | \(0.185256\pi\) | |||||||
\(42\) | 102.547 | + | 102.547i | 0.0581334 | + | 0.0581334i | ||||
\(43\) | 322.020 | − | 322.020i | 0.174159 | − | 0.174159i | −0.614645 | − | 0.788804i | \(-0.710701\pi\) |
0.788804 | + | 0.614645i | \(0.210701\pi\) | |||||||
\(44\) | − | 209.689i | − | 0.108310i | ||||||
\(45\) | 1576.64 | + | 570.943i | 0.778589 | + | 0.281947i | ||||
\(46\) | −1230.64 | −0.581590 | ||||||||
\(47\) | −907.451 | − | 907.451i | −0.410797 | − | 0.410797i | 0.471219 | − | 0.882016i | \(-0.343814\pi\) |
−0.882016 | + | 0.471219i | \(0.843814\pi\) | |||||||
\(48\) | −169.005 | + | 169.005i | −0.0733528 | + | 0.0733528i | ||||
\(49\) | 343.000i | 0.142857i | ||||||||
\(50\) | −118.557 | − | 1306.07i | −0.0474229 | − | 0.522430i | ||||
\(51\) | 42.5530 | 0.0163602 | ||||||||
\(52\) | 20.6453 | + | 20.6453i | 0.00763510 | + | 0.00763510i | ||||
\(53\) | −3087.31 | + | 3087.31i | −1.09908 | + | 1.09908i | −0.104558 | + | 0.994519i | \(0.533343\pi\) |
−0.994519 | + | 0.104558i | \(0.966657\pi\) | |||||||
\(54\) | 1159.50i | 0.397632i | ||||||||
\(55\) | 153.911 | − | 425.020i | 0.0508795 | − | 0.140502i | ||||
\(56\) | 1072.46 | 0.341983 | ||||||||
\(57\) | 530.853 | + | 530.853i | 0.163390 | + | 0.163390i | ||||
\(58\) | −1581.02 | + | 1581.02i | −0.469983 | + | 0.469983i | ||||
\(59\) | 1711.53i | 0.491678i | 0.969311 | + | 0.245839i | \(0.0790635\pi\) | ||||
−0.969311 | + | 0.245839i | \(0.920936\pi\) | |||||||
\(60\) | −979.843 | + | 458.853i | −0.272178 | + | 0.127459i | ||||
\(61\) | −4951.60 | −1.33072 | −0.665358 | − | 0.746524i | \(-0.731721\pi\) | ||||
−0.665358 | + | 0.746524i | \(0.731721\pi\) | |||||||
\(62\) | 2018.58 | + | 2018.58i | 0.525125 | + | 0.525125i | ||||
\(63\) | −878.380 | + | 878.380i | −0.221310 | + | 0.221310i | ||||
\(64\) | − | 1201.37i | − | 0.293304i | ||||||
\(65\) | 26.6925 | + | 56.9996i | 0.00631776 | + | 0.0134910i | ||||
\(66\) | 141.585 | 0.0325035 | ||||||||
\(67\) | −5329.83 | − | 5329.83i | −1.18731 | − | 1.18731i | −0.977808 | − | 0.209502i | \(-0.932816\pi\) |
−0.209502 | − | 0.977808i | \(-0.567184\pi\) | |||||||
\(68\) | 93.5065 | − | 93.5065i | 0.0202220 | − | 0.0202220i | ||||
\(69\) | 2188.69i | 0.459713i | ||||||||
\(70\) | 913.481 | + | 330.795i | 0.186425 | + | 0.0675092i | ||||
\(71\) | 3843.45 | 0.762439 | 0.381219 | − | 0.924485i | \(-0.375504\pi\) | ||||
0.381219 | + | 0.924485i | \(0.375504\pi\) | |||||||
\(72\) | 2746.43 | + | 2746.43i | 0.529790 | + | 0.529790i | ||||
\(73\) | 3299.35 | − | 3299.35i | 0.619132 | − | 0.619132i | −0.326177 | − | 0.945309i | \(-0.605761\pi\) |
0.945309 | + | 0.326177i | \(0.105761\pi\) | |||||||
\(74\) | − | 2518.98i | − | 0.460004i | ||||||
\(75\) | −2322.85 | + | 210.853i | −0.412950 | + | 0.0374850i | ||||
\(76\) | 2333.01 | 0.403914 | ||||||||
\(77\) | 236.787 | + | 236.787i | 0.0399371 | + | 0.0399371i | ||||
\(78\) | −13.9400 | + | 13.9400i | −0.00229126 | + | 0.00229126i | ||||
\(79\) | − | 9899.41i | − | 1.58619i | −0.609099 | − | 0.793094i | \(-0.708469\pi\) | ||
0.609099 | − | 0.793094i | \(-0.291531\pi\) | |||||||
\(80\) | −545.173 | + | 1505.48i | −0.0851833 | + | 0.235231i | ||||
\(81\) | −3370.79 | −0.513762 | ||||||||
\(82\) | 4167.06 | + | 4167.06i | 0.619729 | + | 0.619729i | ||||
\(83\) | 5254.07 | − | 5254.07i | 0.762676 | − | 0.762676i | −0.214130 | − | 0.976805i | \(-0.568692\pi\) |
0.976805 | + | 0.214130i | \(0.0686915\pi\) | |||||||
\(84\) | − | 801.527i | − | 0.113595i | ||||||
\(85\) | 258.162 | − | 120.896i | 0.0357318 | − | 0.0167330i | ||||
\(86\) | 955.582 | 0.129203 | ||||||||
\(87\) | 2811.84 | + | 2811.84i | 0.371495 | + | 0.371495i | ||||
\(88\) | 740.362 | − | 740.362i | 0.0956046 | − | 0.0956046i | ||||
\(89\) | 3691.22i | 0.466004i | 0.972476 | + | 0.233002i | \(0.0748548\pi\) | ||||
−0.972476 | + | 0.233002i | \(0.925145\pi\) | |||||||
\(90\) | 1492.19 | + | 3186.44i | 0.184221 | + | 0.393387i | ||||
\(91\) | −46.6266 | −0.00563056 | ||||||||
\(92\) | 4809.46 | + | 4809.46i | 0.568226 | + | 0.568226i | ||||
\(93\) | 3590.03 | − | 3590.03i | 0.415081 | − | 0.415081i | ||||
\(94\) | − | 2692.82i | − | 0.304756i | ||||||
\(95\) | 4728.79 | + | 1712.42i | 0.523965 | + | 0.189741i | ||||
\(96\) | −3959.12 | −0.429592 | ||||||||
\(97\) | −9933.45 | − | 9933.45i | −1.05574 | − | 1.05574i | −0.998352 | − | 0.0573876i | \(-0.981723\pi\) |
−0.0573876 | − | 0.998352i | \(-0.518277\pi\) | |||||||
\(98\) | −508.919 | + | 508.919i | −0.0529903 | + | 0.0529903i | ||||
\(99\) | 1212.77i | 0.123739i | ||||||||
\(100\) | −4640.92 | + | 5567.58i | −0.464092 | + | 0.556758i | ||||
\(101\) | −16631.2 | −1.63035 | −0.815174 | − | 0.579217i | \(-0.803358\pi\) | ||||
−0.815174 | + | 0.579217i | \(0.803358\pi\) | |||||||
\(102\) | 63.1371 | + | 63.1371i | 0.00606854 | + | 0.00606854i | ||||
\(103\) | 7782.56 | − | 7782.56i | 0.733581 | − | 0.733581i | −0.237747 | − | 0.971327i | \(-0.576409\pi\) |
0.971327 | + | 0.237747i | \(0.0764088\pi\) | |||||||
\(104\) | 145.787i | 0.0134789i | ||||||||
\(105\) | 588.317 | − | 1624.62i | 0.0533621 | − | 0.147358i | ||||
\(106\) | −9161.46 | −0.815367 | ||||||||
\(107\) | 6893.44 | + | 6893.44i | 0.602100 | + | 0.602100i | 0.940869 | − | 0.338770i | \(-0.110011\pi\) |
−0.338770 | + | 0.940869i | \(0.610011\pi\) | |||||||
\(108\) | 4531.41 | − | 4531.41i | 0.388495 | − | 0.388495i | ||||
\(109\) | 12312.6i | 1.03632i | 0.855283 | + | 0.518162i | \(0.173383\pi\) | ||||
−0.855283 | + | 0.518162i | \(0.826617\pi\) | |||||||
\(110\) | 858.976 | − | 402.252i | 0.0709897 | − | 0.0332440i | ||||
\(111\) | −4480.00 | −0.363606 | ||||||||
\(112\) | −838.734 | − | 838.734i | −0.0668634 | − | 0.0668634i | ||||
\(113\) | −4571.88 | + | 4571.88i | −0.358045 | + | 0.358045i | −0.863092 | − | 0.505047i | \(-0.831475\pi\) |
0.505047 | + | 0.863092i | \(0.331475\pi\) | |||||||
\(114\) | 1575.28i | 0.121213i | ||||||||
\(115\) | 6218.21 | + | 13278.5i | 0.470186 | + | 1.00404i | ||||
\(116\) | 12357.6 | 0.918368 | ||||||||
\(117\) | −119.405 | − | 119.405i | −0.00872270 | − | 0.00872270i | ||||
\(118\) | −2539.45 | + | 2539.45i | −0.182379 | + | 0.182379i | ||||
\(119\) | 211.181i | 0.0149129i | ||||||||
\(120\) | −5079.70 | − | 1839.49i | −0.352757 | − | 0.127742i | ||||
\(121\) | −14314.1 | −0.977670 | ||||||||
\(122\) | −7346.83 | − | 7346.83i | −0.493606 | − | 0.493606i | ||||
\(123\) | 7411.09 | − | 7411.09i | 0.489860 | − | 0.489860i | ||||
\(124\) | − | 15777.6i | − | 1.02612i | ||||||
\(125\) | −13493.3 | + | 7878.56i | −0.863571 | + | 0.504228i | ||||
\(126\) | −2606.56 | −0.164182 | ||||||||
\(127\) | −756.980 | − | 756.980i | −0.0469328 | − | 0.0469328i | 0.683251 | − | 0.730184i | \(-0.260566\pi\) |
−0.730184 | + | 0.683251i | \(0.760566\pi\) | |||||||
\(128\) | −10220.3 | + | 10220.3i | −0.623795 | + | 0.623795i | ||||
\(129\) | − | 1699.50i | − | 0.102127i | ||||||
\(130\) | −44.9676 | + | 124.177i | −0.00266080 | + | 0.00734773i | ||||
\(131\) | 4951.67 | 0.288542 | 0.144271 | − | 0.989538i | \(-0.453916\pi\) | ||||
0.144271 | + | 0.989538i | \(0.453916\pi\) | |||||||
\(132\) | −553.328 | − | 553.328i | −0.0317566 | − | 0.0317566i | ||||
\(133\) | −2634.50 | + | 2634.50i | −0.148935 | + | 0.148935i | ||||
\(134\) | − | 15816.1i | − | 0.880824i | ||||||
\(135\) | 12510.8 | − | 5858.71i | 0.686462 | − | 0.321466i | ||||
\(136\) | 660.299 | 0.0356996 | ||||||||
\(137\) | 13415.6 | + | 13415.6i | 0.714774 | + | 0.714774i | 0.967530 | − | 0.252756i | \(-0.0813369\pi\) |
−0.252756 | + | 0.967530i | \(0.581337\pi\) | |||||||
\(138\) | −3247.43 | + | 3247.43i | −0.170522 | + | 0.170522i | ||||
\(139\) | 6023.08i | 0.311738i | 0.987778 | + | 0.155869i | \(0.0498177\pi\) | ||||
−0.987778 | + | 0.155869i | \(0.950182\pi\) | |||||||
\(140\) | −2277.19 | − | 4862.74i | −0.116183 | − | 0.248099i | ||||
\(141\) | −4789.17 | −0.240892 | ||||||||
\(142\) | 5702.65 | + | 5702.65i | 0.282813 | + | 0.282813i | ||||
\(143\) | −32.1883 | + | 32.1883i | −0.00157408 | + | 0.00157408i | ||||
\(144\) | − | 4295.79i | − | 0.207166i | ||||||
\(145\) | 25047.6 | + | 9070.39i | 1.19133 | + | 0.431410i | ||||
\(146\) | 9790.70 | 0.459312 | ||||||||
\(147\) | 905.110 | + | 905.110i | 0.0418858 | + | 0.0418858i | ||||
\(148\) | −9844.41 | + | 9844.41i | −0.449434 | + | 0.449434i | ||||
\(149\) | − | 15207.8i | − | 0.685003i | −0.939517 | − | 0.342502i | \(-0.888726\pi\) | ||
0.939517 | − | 0.342502i | \(-0.111274\pi\) | |||||||
\(150\) | −3759.32 | − | 3133.63i | −0.167081 | − | 0.139272i | ||||
\(151\) | 38369.4 | 1.68279 | 0.841397 | − | 0.540417i | \(-0.181734\pi\) | ||||
0.841397 | + | 0.540417i | \(0.181734\pi\) | |||||||
\(152\) | 8237.30 | + | 8237.30i | 0.356531 | + | 0.356531i | ||||
\(153\) | −540.808 | + | 540.808i | −0.0231026 | + | 0.0231026i | ||||
\(154\) | 702.656i | 0.0296280i | ||||||||
\(155\) | 11580.7 | − | 31979.7i | 0.482026 | − | 1.33110i | ||||
\(156\) | 108.958 | 0.00447723 | ||||||||
\(157\) | −4024.99 | − | 4024.99i | −0.163292 | − | 0.163292i | 0.620731 | − | 0.784023i | \(-0.286836\pi\) |
−0.784023 | + | 0.620731i | \(0.786836\pi\) | |||||||
\(158\) | 14688.0 | − | 14688.0i | 0.588369 | − | 0.588369i | ||||
\(159\) | 16293.6i | 0.644500i | ||||||||
\(160\) | −24019.4 | + | 11248.1i | −0.938256 | + | 0.439379i | ||||
\(161\) | −10862.0 | −0.419042 | ||||||||
\(162\) | −5001.34 | − | 5001.34i | −0.190571 | − | 0.190571i | ||||
\(163\) | 7525.01 | − | 7525.01i | 0.283225 | − | 0.283225i | −0.551169 | − | 0.834394i | \(-0.685818\pi\) |
0.834394 | + | 0.551169i | \(0.185818\pi\) | |||||||
\(164\) | − | 32570.5i | − | 1.21098i | ||||||
\(165\) | −715.404 | − | 1527.68i | −0.0262774 | − | 0.0561133i | ||||
\(166\) | 15591.2 | 0.565802 | ||||||||
\(167\) | −34535.2 | − | 34535.2i | −1.23831 | − | 1.23831i | −0.960692 | − | 0.277615i | \(-0.910456\pi\) |
−0.277615 | − | 0.960692i | \(-0.589544\pi\) | |||||||
\(168\) | 2830.01 | − | 2830.01i | 0.100269 | − | 0.100269i | ||||
\(169\) | 28554.7i | 0.999778i | ||||||||
\(170\) | 562.419 | + | 203.667i | 0.0194609 | + | 0.00704729i | ||||
\(171\) | −13493.3 | −0.461451 | ||||||||
\(172\) | −3734.50 | − | 3734.50i | −0.126234 | − | 0.126234i | ||||
\(173\) | −23342.7 | + | 23342.7i | −0.779937 | + | 0.779937i | −0.979820 | − | 0.199883i | \(-0.935944\pi\) |
0.199883 | + | 0.979820i | \(0.435944\pi\) | |||||||
\(174\) | 8344.03i | 0.275599i | ||||||||
\(175\) | −1046.42 | − | 11527.8i | −0.0341687 | − | 0.376417i | ||||
\(176\) | −1158.03 | −0.0373846 | ||||||||
\(177\) | 4516.40 | + | 4516.40i | 0.144160 | + | 0.144160i | ||||
\(178\) | −5476.77 | + | 5476.77i | −0.172856 | + | 0.172856i | ||||
\(179\) | 28472.1i | 0.888614i | 0.895875 | + | 0.444307i | \(0.146550\pi\) | ||||
−0.895875 | + | 0.444307i | \(0.853450\pi\) | |||||||
\(180\) | 6621.28 | − | 18284.5i | 0.204360 | − | 0.564335i | ||||
\(181\) | 40886.7 | 1.24803 | 0.624015 | − | 0.781412i | \(-0.285500\pi\) | ||||
0.624015 | + | 0.781412i | \(0.285500\pi\) | |||||||
\(182\) | −69.1813 | − | 69.1813i | −0.00208856 | − | 0.00208856i | ||||
\(183\) | −13066.3 | + | 13066.3i | −0.390167 | + | 0.390167i | ||||
\(184\) | 33962.2i | 1.00314i | ||||||||
\(185\) | −27179.4 | + | 12727.9i | −0.794140 | + | 0.371890i | ||||
\(186\) | 10653.3 | 0.307934 | ||||||||
\(187\) | 145.787 | + | 145.787i | 0.00416904 | + | 0.00416904i | ||||
\(188\) | −10523.8 | + | 10523.8i | −0.297753 | + | 0.297753i | ||||
\(189\) | 10234.0i | 0.286499i | ||||||||
\(190\) | 4475.48 | + | 9557.00i | 0.123974 | + | 0.264737i | ||||
\(191\) | −15424.7 | −0.422814 | −0.211407 | − | 0.977398i | \(-0.567804\pi\) | ||||
−0.211407 | + | 0.977398i | \(0.567804\pi\) | |||||||
\(192\) | −3170.18 | − | 3170.18i | −0.0859968 | − | 0.0859968i | ||||
\(193\) | −6739.80 | + | 6739.80i | −0.180939 | + | 0.180939i | −0.791765 | − | 0.610826i | \(-0.790838\pi\) |
0.610826 | + | 0.791765i | \(0.290838\pi\) | |||||||
\(194\) | − | 29477.1i | − | 0.783216i | ||||||
\(195\) | 220.847 | + | 79.9745i | 0.00580795 | + | 0.00210321i | ||||
\(196\) | 3977.80 | 0.103545 | ||||||||
\(197\) | −21.4403 | − | 21.4403i | −0.000552458 | − | 0.000552458i | 0.706830 | − | 0.707383i | \(-0.250124\pi\) |
−0.707383 | + | 0.706830i | \(0.750124\pi\) | |||||||
\(198\) | −1799.42 | + | 1799.42i | −0.0458988 | + | 0.0458988i | ||||
\(199\) | 61587.1i | 1.55519i | 0.628765 | + | 0.777596i | \(0.283561\pi\) | ||||
−0.628765 | + | 0.777596i | \(0.716439\pi\) | |||||||
\(200\) | −36043.9 | + | 3271.83i | −0.901096 | + | 0.0817958i | ||||
\(201\) | −28128.8 | −0.696240 | ||||||||
\(202\) | −24676.2 | − | 24676.2i | −0.604749 | − | 0.604749i | ||||
\(203\) | −13954.5 | + | 13954.5i | −0.338629 | + | 0.338629i | ||||
\(204\) | − | 493.491i | − | 0.0118582i | ||||||
\(205\) | 23906.6 | − | 66017.3i | 0.568865 | − | 1.57090i | ||||
\(206\) | 23094.4 | 0.544218 | ||||||||
\(207\) | −27816.2 | − | 27816.2i | −0.649168 | − | 0.649168i | ||||
\(208\) | 114.016 | − | 114.016i | 0.00263535 | − | 0.00263535i | ||||
\(209\) | 3637.42i | 0.0832723i | ||||||||
\(210\) | 3283.40 | − | 1537.59i | 0.0744536 | − | 0.0348661i | ||||
\(211\) | 7989.99 | 0.179466 | 0.0897328 | − | 0.995966i | \(-0.471399\pi\) | ||||
0.0897328 | + | 0.995966i | \(0.471399\pi\) | |||||||
\(212\) | 35803.8 | + | 35803.8i | 0.796631 | + | 0.796631i | ||||
\(213\) | 10142.1 | − | 10142.1i | 0.223547 | − | 0.223547i | ||||
\(214\) | 20456.0i | 0.446676i | ||||||||
\(215\) | −4828.37 | − | 10310.6i | −0.104454 | − | 0.223052i | ||||
\(216\) | 31998.7 | 0.685843 | ||||||||
\(217\) | 17816.5 | + | 17816.5i | 0.378359 | + | 0.378359i | ||||
\(218\) | −18268.5 | + | 18268.5i | −0.384406 | + | 0.384406i | ||||
\(219\) | − | 17412.7i | − | 0.363059i | ||||||
\(220\) | −4928.99 | − | 1784.92i | −0.101839 | − | 0.0368784i | ||||
\(221\) | −28.7075 | −0.000587774 | ||||||||
\(222\) | −6647.10 | − | 6647.10i | −0.134873 | − | 0.134873i | ||||
\(223\) | 68789.7 | − | 68789.7i | 1.38329 | − | 1.38329i | 0.544589 | − | 0.838703i | \(-0.316686\pi\) |
0.838703 | − | 0.544589i | \(-0.183314\pi\) | |||||||
\(224\) | − | 19648.2i | − | 0.391586i | ||||||
\(225\) | 26841.4 | − | 32200.9i | 0.530201 | − | 0.636067i | ||||
\(226\) | −13566.9 | −0.265621 | ||||||||
\(227\) | 10650.0 | + | 10650.0i | 0.206680 | + | 0.206680i | 0.802855 | − | 0.596175i | \(-0.203314\pi\) |
−0.596175 | + | 0.802855i | \(0.703314\pi\) | |||||||
\(228\) | 6156.35 | − | 6156.35i | 0.118428 | − | 0.118428i | ||||
\(229\) | − | 21675.8i | − | 0.413336i | −0.978411 | − | 0.206668i | \(-0.933738\pi\) | ||
0.978411 | − | 0.206668i | \(-0.0662620\pi\) | |||||||
\(230\) | −10475.5 | + | 28927.8i | −0.198025 | + | 0.546839i | ||||
\(231\) | 1249.67 | 0.0234192 | ||||||||
\(232\) | 43631.7 | + | 43631.7i | 0.810636 | + | 0.810636i | ||||
\(233\) | 14316.4 | − | 14316.4i | 0.263707 | − | 0.263707i | −0.562851 | − | 0.826558i | \(-0.690296\pi\) |
0.826558 | + | 0.562851i | \(0.190296\pi\) | |||||||
\(234\) | − | 354.330i | − | 0.00647106i | ||||||
\(235\) | −29055.1 | + | 13606.3i | −0.526123 | + | 0.246380i | ||||
\(236\) | 19848.8 | 0.356377 | ||||||||
\(237\) | −26122.6 | − | 26122.6i | −0.465071 | − | 0.465071i | ||||
\(238\) | −313.336 | + | 313.336i | −0.00553166 | + | 0.00553166i | ||||
\(239\) | − | 80312.5i | − | 1.40601i | −0.711187 | − | 0.703003i | \(-0.751842\pi\) | ||
0.711187 | − | 0.703003i | \(-0.248158\pi\) | |||||||
\(240\) | 2534.06 | + | 5411.27i | 0.0439941 | + | 0.0939457i | ||||
\(241\) | 14965.1 | 0.257659 | 0.128829 | − | 0.991667i | \(-0.458878\pi\) | ||||
0.128829 | + | 0.991667i | \(0.458878\pi\) | |||||||
\(242\) | −21238.2 | − | 21238.2i | −0.362650 | − | 0.362650i | ||||
\(243\) | −40544.5 | + | 40544.5i | −0.686625 | + | 0.686625i | ||||
\(244\) | 57424.1i | 0.964528i | ||||||||
\(245\) | 8062.63 | + | 2919.69i | 0.134321 | + | 0.0486412i | ||||
\(246\) | 21992.1 | 0.363410 | ||||||||
\(247\) | −358.129 | − | 358.129i | −0.00587009 | − | 0.00587009i | ||||
\(248\) | 55707.0 | − | 55707.0i | 0.905745 | − | 0.905745i | ||||
\(249\) | − | 27728.9i | − | 0.447234i | ||||||
\(250\) | −31710.1 | − | 8330.75i | −0.507361 | − | 0.133292i | ||||
\(251\) | 49620.5 | 0.787614 | 0.393807 | − | 0.919193i | \(-0.371158\pi\) | ||||
0.393807 | + | 0.919193i | \(0.371158\pi\) | |||||||
\(252\) | 10186.7 | + | 10186.7i | 0.160410 | + | 0.160410i | ||||
\(253\) | −7498.49 | + | 7498.49i | −0.117147 | + | 0.117147i | ||||
\(254\) | − | 2246.31i | − | 0.0348178i | ||||||
\(255\) | 362.220 | − | 1000.26i | 0.00557047 | − | 0.0153827i | ||||
\(256\) | −49550.1 | −0.756075 | ||||||||
\(257\) | 61440.3 | + | 61440.3i | 0.930222 | + | 0.930222i | 0.997719 | − | 0.0674972i | \(-0.0215014\pi\) |
−0.0674972 | + | 0.997719i | \(0.521501\pi\) | |||||||
\(258\) | 2521.59 | − | 2521.59i | 0.0378822 | − | 0.0378822i | ||||
\(259\) | − | 22233.2i | − | 0.331438i | ||||||
\(260\) | 661.030 | − | 309.556i | 0.00977855 | − | 0.00457923i | ||||
\(261\) | −71471.7 | −1.04919 | ||||||||
\(262\) | 7346.94 | + | 7346.94i | 0.107030 | + | 0.107030i | ||||
\(263\) | −30152.4 | + | 30152.4i | −0.435924 | + | 0.435924i | −0.890638 | − | 0.454713i | \(-0.849742\pi\) |
0.454713 | + | 0.890638i | \(0.349742\pi\) | |||||||
\(264\) | − | 3907.34i | − | 0.0560627i | ||||||
\(265\) | 46291.1 | + | 98850.7i | 0.659183 | + | 1.40763i | ||||
\(266\) | −7817.79 | −0.110489 | ||||||||
\(267\) | 9740.40 | + | 9740.40i | 0.136633 | + | 0.136633i | ||||
\(268\) | −61810.6 | + | 61810.6i | −0.860584 | + | 0.860584i | ||||
\(269\) | − | 27372.8i | − | 0.378282i | −0.981950 | − | 0.189141i | \(-0.939430\pi\) | ||
0.981950 | − | 0.189141i | \(-0.0605703\pi\) | |||||||
\(270\) | 27255.4 | + | 9869.87i | 0.373873 | + | 0.135389i | ||||
\(271\) | −107491. | −1.46364 | −0.731821 | − | 0.681497i | \(-0.761329\pi\) | ||||
−0.731821 | + | 0.681497i | \(0.761329\pi\) | |||||||
\(272\) | −516.398 | − | 516.398i | −0.00697987 | − | 0.00697987i | ||||
\(273\) | −123.039 | + | 123.039i | −0.00165088 | + | 0.00165088i | ||||
\(274\) | 39810.3i | 0.530266i | ||||||||
\(275\) | −8680.48 | − | 7235.71i | −0.114783 | − | 0.0956788i | ||||
\(276\) | 25382.5 | 0.333208 | ||||||||
\(277\) | −90987.9 | − | 90987.9i | −1.18583 | − | 1.18583i | −0.978208 | − | 0.207626i | \(-0.933426\pi\) |
−0.207626 | − | 0.978208i | \(-0.566574\pi\) | |||||||
\(278\) | −8936.62 | + | 8936.62i | −0.115634 | + | 0.115634i | ||||
\(279\) | 91251.9i | 1.17229i | ||||||||
\(280\) | 9128.99 | − | 25209.4i | 0.116441 | − | 0.321549i | ||||
\(281\) | −81617.1 | −1.03364 | −0.516819 | − | 0.856095i | \(-0.672884\pi\) | ||||
−0.516819 | + | 0.856095i | \(0.672884\pi\) | |||||||
\(282\) | −7105.83 | − | 7105.83i | −0.0893546 | − | 0.0893546i | ||||
\(283\) | −25062.7 | + | 25062.7i | −0.312936 | + | 0.312936i | −0.846046 | − | 0.533110i | \(-0.821023\pi\) |
0.533110 | + | 0.846046i | \(0.321023\pi\) | |||||||
\(284\) | − | 44572.9i | − | 0.552629i | ||||||
\(285\) | 16997.1 | − | 7959.61i | 0.209259 | − | 0.0979946i | ||||
\(286\) | −95.5175 | −0.00116775 | ||||||||
\(287\) | 36779.6 | + | 36779.6i | 0.446522 | + | 0.446522i | ||||
\(288\) | 50316.7 | − | 50316.7i | 0.606634 | − | 0.606634i | ||||
\(289\) | − | 83391.0i | − | 0.998443i | ||||||
\(290\) | 23705.9 | + | 50621.9i | 0.281877 | + | 0.601925i | ||||
\(291\) | −52424.9 | −0.619087 | ||||||||
\(292\) | −38262.9 | − | 38262.9i | −0.448758 | − | 0.448758i | ||||
\(293\) | 53618.1 | − | 53618.1i | 0.624562 | − | 0.624562i | −0.322132 | − | 0.946695i | \(-0.604400\pi\) |
0.946695 | + | 0.322132i | \(0.104400\pi\) | |||||||
\(294\) | 2685.88i | 0.0310736i | ||||||||
\(295\) | 40231.7 | + | 14568.9i | 0.462300 | + | 0.167411i | ||||
\(296\) | −69516.6 | −0.793424 | ||||||||
\(297\) | 7064.97 | + | 7064.97i | 0.0800936 | + | 0.0800936i | ||||
\(298\) | 22564.2 | − | 22564.2i | 0.254090 | − | 0.254090i | ||||
\(299\) | − | 1476.56i | − | 0.0165161i | ||||||
\(300\) | 2445.28 | + | 26938.2i | 0.0271698 | + | 0.299314i | ||||
\(301\) | 8434.23 | 0.0930920 | ||||||||
\(302\) | 56929.8 | + | 56929.8i | 0.624203 | + | 0.624203i | ||||
\(303\) | −43886.4 | + | 43886.4i | −0.478019 | + | 0.478019i | ||||
\(304\) | − | 12884.2i | − | 0.139416i | ||||||
\(305\) | −42149.0 | + | 116393.i | −0.453094 | + | 1.25120i | ||||
\(306\) | −1604.83 | −0.0171390 | ||||||||
\(307\) | −76759.5 | − | 76759.5i | −0.814433 | − | 0.814433i | 0.170862 | − | 0.985295i | \(-0.445345\pi\) |
−0.985295 | + | 0.170862i | \(0.945345\pi\) | |||||||
\(308\) | 2746.04 | − | 2746.04i | 0.0289472 | − | 0.0289472i | ||||
\(309\) | − | 41073.3i | − | 0.430172i | ||||||
\(310\) | 64631.8 | − | 30266.6i | 0.672547 | − | 0.314949i | ||||
\(311\) | 157851. | 1.63203 | 0.816014 | − | 0.578033i | \(-0.196179\pi\) | ||||
0.816014 | + | 0.578033i | \(0.196179\pi\) | |||||||
\(312\) | 384.705 | + | 384.705i | 0.00395201 | + | 0.00395201i | ||||
\(313\) | 75579.4 | − | 75579.4i | 0.771463 | − | 0.771463i | −0.206899 | − | 0.978362i | \(-0.566337\pi\) |
0.978362 | + | 0.206899i | \(0.0663373\pi\) | |||||||
\(314\) | − | 11944.0i | − | 0.121141i | ||||||
\(315\) | 13170.4 | + | 28124.4i | 0.132733 | + | 0.283440i | ||||
\(316\) | −114804. | −1.14970 | ||||||||
\(317\) | 51889.2 | + | 51889.2i | 0.516367 | + | 0.516367i | 0.916470 | − | 0.400103i | \(-0.131026\pi\) |
−0.400103 | + | 0.916470i | \(0.631026\pi\) | |||||||
\(318\) | −24175.3 | + | 24175.3i | −0.239066 | + | 0.239066i | ||||
\(319\) | 19266.8i | 0.189334i | ||||||||
\(320\) | −28239.7 | − | 10226.3i | −0.275778 | − | 0.0998665i | ||||
\(321\) | 36380.9 | 0.353072 | ||||||||
\(322\) | −16116.3 | − | 16116.3i | −0.155436 | − | 0.155436i | ||||
\(323\) | −1622.03 | + | 1622.03i | −0.0155473 | + | 0.0155473i | ||||
\(324\) | 39091.4i | 0.372384i | ||||||||
\(325\) | 1567.06 | − | 142.248i | 0.0148361 | − | 0.00134672i | ||||
\(326\) | 22330.2 | 0.210115 | ||||||||
\(327\) | 32490.4 | + | 32490.4i | 0.303851 | + | 0.303851i | ||||
\(328\) | 114999. | − | 114999.i | 1.06892 | − | 1.06892i | ||||
\(329\) | − | 23767.6i | − | 0.219580i | ||||||
\(330\) | 1205.20 | − | 3328.13i | 0.0110671 | − | 0.0305614i | ||||
\(331\) | 53202.6 | 0.485598 | 0.242799 | − | 0.970077i | \(-0.421935\pi\) | ||||
0.242799 | + | 0.970077i | \(0.421935\pi\) | |||||||
\(332\) | −60932.0 | − | 60932.0i | −0.552801 | − | 0.552801i | ||||
\(333\) | 56936.5 | − | 56936.5i | 0.513455 | − | 0.513455i | ||||
\(334\) | − | 102482.i | − | 0.918657i | ||||||
\(335\) | −170653. | + | 79915.6i | −1.52063 | + | 0.712101i | ||||
\(336\) | −4426.51 | −0.0392087 | ||||||||
\(337\) | 95083.4 | + | 95083.4i | 0.837231 | + | 0.837231i | 0.988494 | − | 0.151263i | \(-0.0483340\pi\) |
−0.151263 | + | 0.988494i | \(0.548334\pi\) | |||||||
\(338\) | −42367.4 | + | 42367.4i | −0.370850 | + | 0.370850i | ||||
\(339\) | 24128.6i | 0.209958i | ||||||||
\(340\) | −1402.04 | − | 2993.93i | −0.0121284 | − | 0.0258991i | ||||
\(341\) | 24599.0 | 0.211548 | ||||||||
\(342\) | −20020.4 | − | 20020.4i | −0.171167 | − | 0.171167i | ||||
\(343\) | −4491.86 | + | 4491.86i | −0.0381802 | + | 0.0381802i | ||||
\(344\) | − | 26371.3i | − | 0.222851i | ||||||
\(345\) | 51447.9 | + | 18630.6i | 0.432244 | + | 0.156527i | ||||
\(346\) | −69268.6 | −0.578608 | ||||||||
\(347\) | 74352.3 | + | 74352.3i | 0.617498 | + | 0.617498i | 0.944889 | − | 0.327391i | \(-0.106169\pi\) |
−0.327391 | + | 0.944889i | \(0.606169\pi\) | |||||||
\(348\) | 32609.2 | − | 32609.2i | 0.269266 | − | 0.269266i | ||||
\(349\) | − | 100857.i | − | 0.828045i | −0.910267 | − | 0.414022i | \(-0.864124\pi\) | ||
0.910267 | − | 0.414022i | \(-0.135876\pi\) | |||||||
\(350\) | 15551.5 | − | 18656.7i | 0.126951 | − | 0.152300i | ||||
\(351\) | −1391.19 | −0.0112920 | ||||||||
\(352\) | −13564.0 | − | 13564.0i | −0.109472 | − | 0.109472i | ||||
\(353\) | −30072.1 | + | 30072.1i | −0.241332 | + | 0.241332i | −0.817401 | − | 0.576069i | \(-0.804586\pi\) |
0.576069 | + | 0.817401i | \(0.304586\pi\) | |||||||
\(354\) | 13402.2i | 0.106947i | ||||||||
\(355\) | 32716.3 | − | 90345.1i | 0.259602 | − | 0.716882i | ||||
\(356\) | 42807.4 | 0.337768 | ||||||||
\(357\) | 557.265 | + | 557.265i | 0.00437246 | + | 0.00437246i | ||||
\(358\) | −42244.9 | + | 42244.9i | −0.329616 | + | 0.329616i | ||||
\(359\) | − | 12797.6i | − | 0.0992974i | −0.998767 | − | 0.0496487i | \(-0.984190\pi\) | ||
0.998767 | − | 0.0496487i | \(-0.0158102\pi\) | |||||||
\(360\) | 87936.4 | − | 41180.0i | 0.678522 | − | 0.317747i | ||||
\(361\) | 89850.9 | 0.689459 | ||||||||
\(362\) | 60664.8 | + | 60664.8i | 0.462935 | + | 0.462935i | ||||
\(363\) | −37772.0 | + | 37772.0i | −0.286653 | + | 0.286653i | ||||
\(364\) | 540.734i | 0.00408113i | ||||||||
\(365\) | −49470.5 | − | 105640.i | −0.371331 | − | 0.792945i | ||||
\(366\) | −38773.7 | −0.289451 | ||||||||
\(367\) | −62216.0 | − | 62216.0i | −0.461924 | − | 0.461924i | 0.437362 | − | 0.899286i | \(-0.355913\pi\) |
−0.899286 | + | 0.437362i | \(0.855913\pi\) | |||||||
\(368\) | 26560.7 | − | 26560.7i | 0.196130 | − | 0.196130i | ||||
\(369\) | 188376.i | 1.38348i | ||||||||
\(370\) | −59211.8 | − | 21442.1i | −0.432518 | − | 0.156626i | ||||
\(371\) | −80861.5 | −0.587481 | ||||||||
\(372\) | −41634.0 | − | 41634.0i | −0.300858 | − | 0.300858i | ||||
\(373\) | 47558.2 | − | 47558.2i | 0.341828 | − | 0.341828i | −0.515226 | − | 0.857054i | \(-0.672292\pi\) |
0.857054 | + | 0.515226i | \(0.172292\pi\) | |||||||
\(374\) | 432.617i | 0.00309286i | ||||||||
\(375\) | −14816.2 | + | 56396.1i | −0.105360 | + | 0.401039i | ||||
\(376\) | −74314.1 | −0.525649 | ||||||||
\(377\) | −1896.95 | − | 1896.95i | −0.0133467 | − | 0.0133467i | ||||
\(378\) | −15184.5 | + | 15184.5i | −0.106272 | + | 0.106272i | ||||
\(379\) | 109716.i | 0.763817i | 0.924200 | + | 0.381909i | \(0.124733\pi\) | ||||
−0.924200 | + | 0.381909i | \(0.875267\pi\) | |||||||
\(380\) | 19859.0 | − | 54840.2i | 0.137528 | − | 0.379780i | ||||
\(381\) | −3995.04 | −0.0275215 | ||||||||
\(382\) | −22886.0 | − | 22886.0i | −0.156835 | − | 0.156835i | ||||
\(383\) | −93866.2 | + | 93866.2i | −0.639899 | + | 0.639899i | −0.950530 | − | 0.310631i | \(-0.899460\pi\) |
0.310631 | + | 0.950530i | \(0.399460\pi\) | |||||||
\(384\) | 53938.5i | 0.365794i | ||||||||
\(385\) | 7581.55 | − | 3550.39i | 0.0511490 | − | 0.0239527i | ||||
\(386\) | −20000.1 | −0.134232 | ||||||||
\(387\) | 21599.0 | + | 21599.0i | 0.144215 | + | 0.144215i | ||||
\(388\) | −115199. | + | 115199.i | −0.765219 | + | 0.765219i | ||||
\(389\) | − | 111194.i | − | 0.734821i | −0.930059 | − | 0.367410i | \(-0.880244\pi\) | ||
0.930059 | − | 0.367410i | \(-0.119756\pi\) | |||||||
\(390\) | 209.017 | + | 446.338i | 0.00137421 | + | 0.00293451i | ||||
\(391\) | −6687.60 | −0.0437438 | ||||||||
\(392\) | 14044.7 | + | 14044.7i | 0.0913987 | + | 0.0913987i | ||||
\(393\) | 13066.5 | − | 13066.5i | 0.0846007 | − | 0.0846007i | ||||
\(394\) | − | 63.6233i | − | 0.000409849i | ||||||
\(395\) | −232698. | − | 84265.8i | −1.49141 | − | 0.540079i | ||||
\(396\) | 14064.5 | 0.0896882 | ||||||||
\(397\) | 56827.1 | + | 56827.1i | 0.360557 | + | 0.360557i | 0.864018 | − | 0.503461i | \(-0.167940\pi\) |
−0.503461 | + | 0.864018i | \(0.667940\pi\) | |||||||
\(398\) | −91378.7 | + | 91378.7i | −0.576871 | + | 0.576871i | ||||
\(399\) | 13903.9i | 0.0873354i | ||||||||
\(400\) | 30747.5 | + | 25629.9i | 0.192172 | + | 0.160187i | ||||
\(401\) | 160496. | 0.998104 | 0.499052 | − | 0.866572i | \(-0.333682\pi\) | ||||
0.499052 | + | 0.866572i | \(0.333682\pi\) | |||||||
\(402\) | −41735.5 | − | 41735.5i | −0.258258 | − | 0.258258i | ||||
\(403\) | −2421.94 | + | 2421.94i | −0.0149126 | + | 0.0149126i | ||||
\(404\) | 192873.i | 1.18171i | ||||||||
\(405\) | −28692.9 | + | 79234.6i | −0.174930 | + | 0.483064i | ||||
\(406\) | −41409.6 | −0.251217 | ||||||||
\(407\) | −15348.5 | − | 15348.5i | −0.0926569 | − | 0.0926569i | ||||
\(408\) | 1742.40 | − | 1742.40i | 0.0104671 | − | 0.0104671i | ||||
\(409\) | 135898.i | 0.812396i | 0.913785 | + | 0.406198i | \(0.133146\pi\) | ||||
−0.913785 | + | 0.406198i | \(0.866854\pi\) | |||||||
\(410\) | 133423. | − | 62480.9i | 0.793710 | − | 0.371689i | ||||
\(411\) | 70802.3 | 0.419144 | ||||||||
\(412\) | −90255.0 | − | 90255.0i | −0.531713 | − | 0.531713i | ||||
\(413\) | −22413.9 | + | 22413.9i | −0.131407 | + | 0.131407i | ||||
\(414\) | − | 82543.5i | − | 0.481595i | ||||||
\(415\) | −78779.6 | − | 168227.i | −0.457423 | − | 0.976787i | ||||
\(416\) | 2670.94 | 0.0154339 | ||||||||
\(417\) | 15893.7 | + | 15893.7i | 0.0914016 | + | 0.0914016i | ||||
\(418\) | −5396.94 | + | 5396.94i | −0.0308884 | + | 0.0308884i | ||||
\(419\) | − | 16910.3i | − | 0.0963216i | −0.998840 | − | 0.0481608i | \(-0.984664\pi\) | ||
0.998840 | − | 0.0481608i | \(-0.0153360\pi\) | |||||||
\(420\) | −18840.9 | − | 6822.77i | −0.106808 | − | 0.0386778i | ||||
\(421\) | −169177. | −0.954500 | −0.477250 | − | 0.878768i | \(-0.658366\pi\) | ||||
−0.477250 | + | 0.878768i | \(0.658366\pi\) | |||||||
\(422\) | 11855.0 | + | 11855.0i | 0.0665696 | + | 0.0665696i | ||||
\(423\) | 60865.8 | − | 60865.8i | 0.340168 | − | 0.340168i | ||||
\(424\) | 252830.i | 1.40636i | ||||||||
\(425\) | −644.267 | − | 7097.51i | −0.00356687 | − | 0.0392942i | ||||
\(426\) | 30096.3 | 0.165842 | ||||||||
\(427\) | −64845.1 | − | 64845.1i | −0.355649 | − | 0.355649i | ||||
\(428\) | 79943.8 | − | 79943.8i | 0.436413 | − | 0.436413i | ||||
\(429\) | 169.877i | 0.000923041i | ||||||||
\(430\) | 8134.12 | − | 22462.1i | 0.0439920 | − | 0.121483i | ||||
\(431\) | 317161. | 1.70736 | 0.853680 | − | 0.520797i | \(-0.174365\pi\) | ||||
0.853680 | + | 0.520797i | \(0.174365\pi\) | |||||||
\(432\) | −25025.1 | − | 25025.1i | −0.134094 | − | 0.134094i | ||||
\(433\) | 32567.7 | − | 32567.7i | 0.173704 | − | 0.173704i | −0.614900 | − | 0.788605i | \(-0.710804\pi\) |
0.788605 | + | 0.614900i | \(0.210804\pi\) | |||||||
\(434\) | 52869.9i | 0.280691i | ||||||||
\(435\) | 90030.8 | − | 42160.8i | 0.475787 | − | 0.222808i | ||||
\(436\) | 142790. | 0.751146 | ||||||||
\(437\) | −83428.5 | − | 83428.5i | −0.436869 | − | 0.436869i | ||||
\(438\) | 25835.7 | − | 25835.7i | 0.134671 | − | 0.134671i | ||||
\(439\) | − | 144941.i | − | 0.752078i | −0.926604 | − | 0.376039i | \(-0.877286\pi\) | ||
0.926604 | − | 0.376039i | \(-0.122714\pi\) | |||||||
\(440\) | −11101.0 | − | 23705.2i | −0.0573399 | − | 0.122444i | ||||
\(441\) | −23006.2 | −0.118295 | ||||||||
\(442\) | −42.5941 | − | 42.5941i | −0.000218024 | − | 0.000218024i | ||||
\(443\) | −122190. | + | 122190.i | −0.622625 | + | 0.622625i | −0.946202 | − | 0.323577i | \(-0.895115\pi\) |
0.323577 | + | 0.946202i | \(0.395115\pi\) | |||||||
\(444\) | 51954.9i | 0.263549i | ||||||||
\(445\) | 86766.5 | + | 31420.4i | 0.438160 | + | 0.158669i | ||||
\(446\) | 204131. | 1.02622 | ||||||||
\(447\) | −40130.3 | − | 40130.3i | −0.200843 | − | 0.200843i | ||||
\(448\) | 15732.9 | − | 15732.9i | 0.0783887 | − | 0.0783887i | ||||
\(449\) | − | 256403.i | − | 1.27184i | −0.771757 | − | 0.635918i | \(-0.780622\pi\) | ||
0.771757 | − | 0.635918i | \(-0.219378\pi\) | |||||||
\(450\) | 87602.9 | − | 7952.03i | 0.432607 | − | 0.0392693i | ||||
\(451\) | 50781.0 | 0.249659 | ||||||||
\(452\) | 53020.5 | + | 53020.5i | 0.259517 | + | 0.259517i | ||||
\(453\) | 101249. | − | 101249.i | 0.493396 | − | 0.493396i | ||||
\(454\) | 31603.4i | 0.153328i | ||||||||
\(455\) | −396.896 | + | 1096.02i | −0.00191714 | + | 0.00529412i | ||||
\(456\) | 43473.3 | 0.209070 | ||||||||
\(457\) | 161721. | + | 161721.i | 0.774344 | + | 0.774344i | 0.978863 | − | 0.204519i | \(-0.0655629\pi\) |
−0.204519 | + | 0.978863i | \(0.565563\pi\) | |||||||
\(458\) | 32161.0 | − | 32161.0i | 0.153320 | − | 0.153320i | ||||
\(459\) | 6300.96i | 0.0299076i | ||||||||
\(460\) | 153991. | − | 72113.1i | 0.727748 | − | 0.340799i | ||||
\(461\) | −15976.3 | −0.0751753 | −0.0375877 | − | 0.999293i | \(-0.511967\pi\) | ||||
−0.0375877 | + | 0.999293i | \(0.511967\pi\) | |||||||
\(462\) | 1854.17 | + | 1854.17i | 0.00868693 | + | 0.00868693i | ||||
\(463\) | −272415. | + | 272415.i | −1.27078 | + | 1.27078i | −0.325094 | + | 0.945682i | \(0.605396\pi\) |
−0.945682 | + | 0.325094i | \(0.894604\pi\) | |||||||
\(464\) | − | 68245.8i | − | 0.316986i | ||||||
\(465\) | −53829.0 | − | 114947.i | −0.248949 | − | 0.531609i | ||||
\(466\) | 42483.4 | 0.195635 | ||||||||
\(467\) | −204044. | − | 204044.i | −0.935598 | − | 0.935598i | 0.0624499 | − | 0.998048i | \(-0.480109\pi\) |
−0.998048 | + | 0.0624499i | \(0.980109\pi\) | |||||||
\(468\) | −1384.75 | + | 1384.75i | −0.00632237 | + | 0.00632237i | ||||
\(469\) | − | 139597.i | − | 0.634644i | ||||||
\(470\) | −63298.1 | − | 22921.9i | −0.286546 | − | 0.103766i | ||||
\(471\) | −21242.3 | −0.0957547 | ||||||||
\(472\) | 70081.5 | + | 70081.5i | 0.314571 | + | 0.314571i | ||||
\(473\) | 5822.50 | − | 5822.50i | 0.0260248 | − | 0.0260248i | ||||
\(474\) | − | 77517.7i | − | 0.345020i | ||||||
\(475\) | 80504.8 | − | 96579.4i | 0.356808 | − | 0.428053i | ||||
\(476\) | 2449.09 | 0.0108091 | ||||||||
\(477\) | −207076. | − | 207076.i | −0.910109 | − | 0.910109i | ||||
\(478\) | 119162. | − | 119162.i | 0.521533 | − | 0.521533i | ||||
\(479\) | 36564.3i | 0.159363i | 0.996820 | + | 0.0796813i | \(0.0253903\pi\) | ||||
−0.996820 | + | 0.0796813i | \(0.974610\pi\) | |||||||
\(480\) | −33700.9 | + | 93063.9i | −0.146271 | + | 0.403923i | ||||
\(481\) | 3022.33 | 0.0130633 | ||||||||
\(482\) | 22204.2 | + | 22204.2i | 0.0955741 | + | 0.0955741i | ||||
\(483\) | −28662.7 | + | 28662.7i | −0.122863 | + | 0.122863i | ||||
\(484\) | 166002.i | 0.708633i | ||||||||
\(485\) | −318054. | + | 148942.i | −1.35212 | + | 0.633191i | ||||
\(486\) | −120314. | −0.509383 | ||||||||
\(487\) | 76566.7 | + | 76566.7i | 0.322836 | + | 0.322836i | 0.849854 | − | 0.527018i | \(-0.176690\pi\) |
−0.527018 | + | 0.849854i | \(0.676690\pi\) | |||||||
\(488\) | −202751. | + | 202751.i | −0.851381 | + | 0.851381i | ||||
\(489\) | − | 39714.0i | − | 0.166083i | ||||||
\(490\) | 7630.74 | + | 16294.8i | 0.0317815 | + | 0.0678667i | ||||
\(491\) | 399454. | 1.65693 | 0.828464 | − | 0.560043i | \(-0.189215\pi\) | ||||
0.828464 | + | 0.560043i | \(0.189215\pi\) | |||||||
\(492\) | −85947.1 | − | 85947.1i | −0.355059 | − | 0.355059i | ||||
\(493\) | −8591.65 | + | 8591.65i | −0.0353494 | + | 0.0353494i | ||||
\(494\) | − | 1062.73i | − | 0.00435482i | ||||||
\(495\) | 28507.5 | + | 10323.3i | 0.116345 | + | 0.0421317i | ||||
\(496\) | −87133.2 | −0.354177 | ||||||||
\(497\) | 50333.1 | + | 50333.1i | 0.203770 | + | 0.203770i | ||||
\(498\) | 41142.2 | − | 41142.2i | 0.165893 | − | 0.165893i | ||||
\(499\) | − | 17571.0i | − | 0.0705658i | −0.999377 | − | 0.0352829i | \(-0.988767\pi\) | ||
0.999377 | − | 0.0352829i | \(-0.0112332\pi\) | |||||||
\(500\) | 91368.4 | + | 156483.i | 0.365473 | + | 0.625932i | ||||
\(501\) | −182263. | −0.726145 | ||||||||
\(502\) | 73623.4 | + | 73623.4i | 0.292152 | + | 0.292152i | ||||
\(503\) | −131869. | + | 131869.i | −0.521202 | + | 0.521202i | −0.917934 | − | 0.396732i | \(-0.870144\pi\) |
0.396732 | + | 0.917934i | \(0.370144\pi\) | |||||||
\(504\) | 71933.4i | 0.283185i | ||||||||
\(505\) | −141568. | + | 390936.i | −0.555114 | + | 1.53293i | ||||
\(506\) | −22251.5 | −0.0869075 | ||||||||
\(507\) | 75350.2 | + | 75350.2i | 0.293135 | + | 0.293135i | ||||
\(508\) | −8778.76 | + | 8778.76i | −0.0340178 | + | 0.0340178i | ||||
\(509\) | − | 127171.i | − | 0.490855i | −0.969415 | − | 0.245427i | \(-0.921072\pi\) | ||
0.969415 | − | 0.245427i | \(-0.0789283\pi\) | |||||||
\(510\) | 2021.55 | − | 946.678i | 0.00777221 | − | 0.00363967i | ||||
\(511\) | 86415.4 | 0.330940 | ||||||||
\(512\) | 90005.1 | + | 90005.1i | 0.343342 | + | 0.343342i | ||||
\(513\) | −78605.2 | + | 78605.2i | −0.298687 | + | 0.298687i | ||||
\(514\) | 182321.i | 0.690099i | ||||||||
\(515\) | −116692. | − | 249185.i | −0.439973 | − | 0.939524i | ||||
\(516\) | −19709.2 | −0.0740236 | ||||||||
\(517\) | −16407.8 | − | 16407.8i | −0.0613858 | − | 0.0613858i | ||||
\(518\) | 32988.1 | − | 32988.1i | 0.122941 | − | 0.122941i | ||||
\(519\) | 123194.i | 0.457356i | ||||||||
\(520\) | 3426.91 | + | 1240.97i | 0.0126735 | + | 0.00458940i | ||||
\(521\) | −91618.7 | −0.337527 | −0.168764 | − | 0.985657i | \(-0.553977\pi\) | ||||
−0.168764 | + | 0.985657i | \(0.553977\pi\) | |||||||
\(522\) | −106045. | − | 106045.i | −0.389178 | − | 0.389178i | ||||
\(523\) | 103824. | − | 103824.i | 0.379573 | − | 0.379573i | −0.491375 | − | 0.870948i | \(-0.663506\pi\) |
0.870948 | + | 0.491375i | \(0.163506\pi\) | |||||||
\(524\) | − | 57425.0i | − | 0.209141i | ||||||
\(525\) | −33180.8 | − | 27658.2i | −0.120384 | − | 0.100347i | ||||
\(526\) | −89476.2 | −0.323397 | ||||||||
\(527\) | 10969.4 | + | 10969.4i | 0.0394969 | + | 0.0394969i | ||||
\(528\) | −3055.80 | + | 3055.80i | −0.0109612 | + | 0.0109612i | ||||
\(529\) | − | 64132.6i | − | 0.229175i | ||||||
\(530\) | −77984.3 | + | 215351.i | −0.277623 | + | 0.766648i | ||||
\(531\) | −114798. | −0.407143 | ||||||||
\(532\) | 30552.6 | + | 30552.6i | 0.107951 | + | 0.107951i | ||||
\(533\) | −4999.73 | + | 4999.73i | −0.0175992 | + | 0.0175992i | ||||
\(534\) | 28904.2i | 0.101363i | ||||||||
\(535\) | 220717. | − | 103360.i | 0.771131 | − | 0.361115i | ||||
\(536\) | −436477. | −1.51926 | ||||||||
\(537\) | 75132.2 | + | 75132.2i | 0.260542 | + | 0.260542i | ||||
\(538\) | 40613.9 | − | 40613.9i | 0.140317 | − | 0.140317i | ||||
\(539\) | 6201.84i | 0.0213473i | ||||||||
\(540\) | −67944.0 | − | 145089.i | −0.233004 | − | 0.497560i | ||||
\(541\) | −334086. | −1.14147 | −0.570735 | − | 0.821135i | \(-0.693342\pi\) | ||||
−0.570735 | + | 0.821135i | \(0.693342\pi\) | |||||||
\(542\) | −159488. | − | 159488.i | −0.542912 | − | 0.542912i | ||||
\(543\) | 107892. | − | 107892.i | 0.365923 | − | 0.365923i | ||||
\(544\) | − | 12097.2i | − | 0.0408777i | ||||||
\(545\) | 289422. | + | 104807.i | 0.974402 | + | 0.352856i | ||||
\(546\) | −365.112 | −0.00122473 | ||||||||
\(547\) | 190383. | + | 190383.i | 0.636287 | + | 0.636287i | 0.949637 | − | 0.313351i | \(-0.101452\pi\) |
−0.313351 | + | 0.949637i | \(0.601452\pi\) | |||||||
\(548\) | 155582. | − | 155582.i | 0.518082 | − | 0.518082i | ||||
\(549\) | − | 332121.i | − | 1.10192i | ||||||
\(550\) | −2143.65 | − | 23615.3i | −0.00708645 | − | 0.0780672i | ||||
\(551\) | −214363. | −0.706069 | ||||||||
\(552\) | 89619.6 | + | 89619.6i | 0.294120 | + | 0.294120i | ||||
\(553\) | 129641. | − | 129641.i | 0.423927 | − | 0.423927i | ||||
\(554\) | − | 270003.i | − | 0.879729i | ||||||
\(555\) | −38134.7 | + | 105308.i | −0.123804 | + | 0.341880i | ||||
\(556\) | 69850.2 | 0.225953 | ||||||||
\(557\) | −77060.8 | − | 77060.8i | −0.248384 | − | 0.248384i | 0.571923 | − | 0.820307i | \(-0.306197\pi\) |
−0.820307 | + | 0.571923i | \(0.806197\pi\) | |||||||
\(558\) | −135393. | + | 135393.i | −0.434839 | + | 0.434839i | ||||
\(559\) | 1146.53i | 0.00366912i | ||||||||
\(560\) | −26854.9 | + | 12576.0i | −0.0856344 | + | 0.0401020i | ||||
\(561\) | 769.407 | 0.00244473 | ||||||||
\(562\) | −121098. | − | 121098.i | −0.383410 | − | 0.383410i | ||||
\(563\) | 285556. | − | 285556.i | 0.900897 | − | 0.900897i | −0.0946167 | − | 0.995514i | \(-0.530163\pi\) |
0.995514 | + | 0.0946167i | \(0.0301625\pi\) | |||||||
\(564\) | 55540.4i | 0.174603i | ||||||||
\(565\) | 68550.7 | + | 146384.i | 0.214741 | + | 0.458561i | ||||
\(566\) | −74372.7 | −0.232156 | ||||||||
\(567\) | −44143.2 | − | 44143.2i | −0.137309 | − | 0.137309i | ||||
\(568\) | 157376. | − | 157376.i | 0.487801 | − | 0.487801i | ||||
\(569\) | 281883.i | 0.870650i | 0.900273 | + | 0.435325i | \(0.143367\pi\) | ||||
−0.900273 | + | 0.435325i | \(0.856633\pi\) | |||||||
\(570\) | 37029.0 | + | 13409.1i | 0.113970 | + | 0.0412716i | ||||
\(571\) | −191251. | −0.586585 | −0.293292 | − | 0.956023i | \(-0.594751\pi\) | ||||
−0.293292 | + | 0.956023i | \(0.594751\pi\) | |||||||
\(572\) | 373.291 | + | 373.291i | 0.00114092 | + | 0.00114092i | ||||
\(573\) | −40702.7 | + | 40702.7i | −0.123969 | + | 0.123969i | ||||
\(574\) | 109142.i | 0.331259i | ||||||||
\(575\) | 365057. | − | 33137.6i | 1.10414 | − | 0.100227i | ||||
\(576\) | 80580.1 | 0.242875 | ||||||||
\(577\) | 394966. | + | 394966.i | 1.18634 | + | 1.18634i | 0.978072 | + | 0.208265i | \(0.0667817\pi\) |
0.208265 | + | 0.978072i | \(0.433218\pi\) | |||||||
\(578\) | 123730. | − | 123730.i | 0.370355 | − | 0.370355i | ||||
\(579\) | 35570.0i | 0.106103i | ||||||||
\(580\) | 105190. | − | 290480.i | 0.312694 | − | 0.863495i | ||||
\(581\) | 137613. | 0.407667 | ||||||||
\(582\) | −77784.4 | − | 77784.4i | −0.229639 | − | 0.229639i | ||||
\(583\) | −55822.1 | + | 55822.1i | −0.164236 | + | 0.164236i | ||||
\(584\) | − | 270195.i | − | 0.792230i | ||||||
\(585\) | −3823.16 | + | 1790.36i | −0.0111715 | + | 0.00523153i | ||||
\(586\) | 159109. | 0.463341 | ||||||||
\(587\) | 434613. | + | 434613.i | 1.26132 | + | 1.26132i | 0.950452 | + | 0.310871i | \(0.100621\pi\) |
0.310871 | + | 0.950452i | \(0.399379\pi\) | |||||||
\(588\) | 10496.6 | − | 10496.6i | 0.0303596 | − | 0.0303596i | ||||
\(589\) | 273690.i | 0.788910i | ||||||||
\(590\) | 38076.6 | + | 81309.3i | 0.109384 | + | 0.233580i | ||||
\(591\) | −113.154 | −0.000323962 | ||||||||
\(592\) | 54366.6 | + | 54366.6i | 0.155128 | + | 0.155128i | ||||
\(593\) | 149520. | − | 149520.i | 0.425197 | − | 0.425197i | −0.461792 | − | 0.886988i | \(-0.652793\pi\) |
0.886988 | + | 0.461792i | \(0.152793\pi\) | |||||||
\(594\) | 20965.0i | 0.0594186i | ||||||||
\(595\) | 4964.07 | + | 1797.62i | 0.0140218 | + | 0.00507766i | ||||
\(596\) | −176366. | −0.496503 | ||||||||
\(597\) | 162516. | + | 162516.i | 0.455983 | + | 0.455983i | ||||
\(598\) | 2190.81 | − | 2190.81i | 0.00612635 | − | 0.00612635i | ||||
\(599\) | − | 251890.i | − | 0.702033i | −0.936369 | − | 0.351017i | \(-0.885836\pi\) | ||
0.936369 | − | 0.351017i | \(-0.114164\pi\) | |||||||
\(600\) | −86478.9 | + | 103746.i | −0.240219 | + | 0.288184i | ||||
\(601\) | −46644.1 | −0.129136 | −0.0645681 | − | 0.997913i | \(-0.520567\pi\) | ||||
−0.0645681 | + | 0.997913i | \(0.520567\pi\) | |||||||
\(602\) | 12514.1 | + | 12514.1i | 0.0345308 | + | 0.0345308i | ||||
\(603\) | 357490. | − | 357490.i | 0.983172 | − | 0.983172i | ||||
\(604\) | − | 444973.i | − | 1.21972i | ||||||
\(605\) | −121844. | + | 336470.i | −0.332885 | + | 0.919253i | ||||
\(606\) | −130231. | −0.354625 | ||||||||
\(607\) | −404387. | − | 404387.i | −1.09754 | − | 1.09754i | −0.994698 | − | 0.102841i | \(-0.967207\pi\) |
−0.102841 | − | 0.994698i | \(-0.532793\pi\) | |||||||
\(608\) | 150914. | − | 150914.i | 0.408245 | − | 0.408245i | ||||
\(609\) | 73646.6i | 0.198572i | ||||||||
\(610\) | −235234. | + | 110158.i | −0.632180 | + | 0.296045i | ||||
\(611\) | 3230.91 | 0.00865452 | ||||||||
\(612\) | 6271.80 | + | 6271.80i | 0.0167452 | + | 0.0167452i | ||||
\(613\) | −425304. | + | 425304.i | −1.13182 | + | 1.13182i | −0.141950 | + | 0.989874i | \(0.545337\pi\) |
−0.989874 | + | 0.141950i | \(0.954663\pi\) | |||||||
\(614\) | − | 227781.i | − | 0.604199i | ||||||
\(615\) | −111122. | − | 237291.i | −0.293798 | − | 0.627381i | ||||
\(616\) | 19391.3 | 0.0511028 | ||||||||
\(617\) | −249065. | − | 249065.i | −0.654247 | − | 0.654247i | 0.299766 | − | 0.954013i | \(-0.403092\pi\) |
−0.954013 | + | 0.299766i | \(0.903092\pi\) | |||||||
\(618\) | 60941.7 | − | 60941.7i | 0.159565 | − | 0.159565i | ||||
\(619\) | − | 63129.3i | − | 0.164759i | −0.996601 | − | 0.0823796i | \(-0.973748\pi\) | ||
0.996601 | − | 0.0823796i | \(-0.0262520\pi\) | |||||||
\(620\) | −370871. | − | 134302.i | −0.964806 | − | 0.349381i | ||||
\(621\) | −324087. | −0.840386 | ||||||||
\(622\) | 234209. | + | 234209.i | 0.605372 | + | 0.605372i | ||||
\(623\) | −48339.4 | + | 48339.4i | −0.124545 | + | 0.124545i | ||||
\(624\) | − | 601.730i | − | 0.00154537i | ||||||
\(625\) | 70337.3 | + | 384240.i | 0.180064 | + | 0.983655i | ||||
\(626\) | 224279. | 0.572321 | ||||||||
\(627\) | 9598.43 | + | 9598.43i | 0.0244155 | + | 0.0244155i | ||||
\(628\) | −46678.2 | + | 46678.2i | −0.118357 | + | 0.118357i | ||||
\(629\) | − | 13688.7i | − | 0.0345989i | ||||||
\(630\) | −22187.6 | + | 61270.3i | −0.0559022 | + | 0.154372i | ||||
\(631\) | 603122. | 1.51477 | 0.757385 | − | 0.652969i | \(-0.226477\pi\) | ||||
0.757385 | + | 0.652969i | \(0.226477\pi\) | |||||||
\(632\) | −405347. | − | 405347.i | −1.01483 | − | 1.01483i | ||||
\(633\) | 21084.0 | − | 21084.0i | 0.0526194 | − | 0.0526194i | ||||
\(634\) | 153979.i | 0.383075i | ||||||||
\(635\) | −24237.3 | + | 11350.2i | −0.0601086 | + | 0.0281484i | ||||
\(636\) | 188958. | 0.467145 | ||||||||
\(637\) | −610.613 | − | 610.613i | −0.00150483 | − | 0.00150483i | ||||
\(638\) | −28586.7 | + | 28586.7i | −0.0702301 | + | 0.0702301i | ||||
\(639\) | 257794.i | 0.631350i | ||||||||
\(640\) | 153243. | + | 327237.i | 0.374127 | + | 0.798917i | ||||
\(641\) | −405370. | −0.986587 | −0.493293 | − | 0.869863i | \(-0.664207\pi\) | ||||
−0.493293 | + | 0.869863i | \(0.664207\pi\) | |||||||
\(642\) | 53979.4 | + | 53979.4i | 0.130966 | + | 0.130966i | ||||
\(643\) | −167231. | + | 167231.i | −0.404478 | + | 0.404478i | −0.879808 | − | 0.475330i | \(-0.842329\pi\) |
0.475330 | + | 0.879808i | \(0.342329\pi\) | |||||||
\(644\) | 125968.i | 0.303729i | ||||||||
\(645\) | −39948.7 | − | 14466.5i | −0.0960249 | − | 0.0347731i | ||||
\(646\) | −4813.32 | −0.0115340 | ||||||||
\(647\) | 318214. | + | 318214.i | 0.760170 | + | 0.760170i | 0.976353 | − | 0.216183i | \(-0.0693607\pi\) |
−0.216183 | + | 0.976353i | \(0.569361\pi\) | |||||||
\(648\) | −138023. | + | 138023.i | −0.328700 | + | 0.328700i | ||||
\(649\) | 30946.5i | 0.0734720i | ||||||||
\(650\) | 2536.15 | + | 2114.03i | 0.00600272 | + | 0.00500363i | ||||
\(651\) | 94028.7 | 0.221870 | ||||||||
\(652\) | −87268.2 | − | 87268.2i | −0.205287 | − | 0.205287i | ||||
\(653\) | 517979. | − | 517979.i | 1.21475 | − | 1.21475i | 0.245300 | − | 0.969447i | \(-0.421113\pi\) |
0.969447 | − | 0.245300i | \(-0.0788866\pi\) | |||||||
\(654\) | 96414.1i | 0.225416i | ||||||||
\(655\) | 42149.7 | − | 116395.i | 0.0982452 | − | 0.271301i | ||||
\(656\) | −179873. | −0.417984 | ||||||||
\(657\) | 221299. | + | 221299.i | 0.512683 | + | 0.512683i | ||||
\(658\) | 35264.7 | − | 35264.7i | 0.0814495 | − | 0.0814495i | ||||
\(659\) | 378556.i | 0.871686i | 0.900023 | + | 0.435843i | \(0.143550\pi\) | ||||
−0.900023 | + | 0.435843i | \(0.856450\pi\) | |||||||
\(660\) | −17716.7 | + | 8296.60i | −0.0406719 | + | 0.0190464i | ||||
\(661\) | −793156. | −1.81533 | −0.907666 | − | 0.419694i | \(-0.862137\pi\) | ||||
−0.907666 | + | 0.419694i | \(0.862137\pi\) | |||||||
\(662\) | 78938.2 | + | 78938.2i | 0.180124 | + | 0.180124i | ||||
\(663\) | −75.7534 | + | 75.7534i | −0.000172336 | + | 0.000172336i | ||||
\(664\) | − | 430273.i | − | 0.975906i | ||||||
\(665\) | 39501.8 | + | 84352.7i | 0.0893251 | + | 0.190746i | ||||
\(666\) | 168957. | 0.380914 | ||||||||
\(667\) | −441907. | − | 441907.i | −0.993298 | − | 0.993298i | ||||
\(668\) | −400507. | + | 400507.i | −0.897548 | + | 0.897548i | ||||
\(669\) | − | 363045.i | − | 0.811164i | ||||||
\(670\) | −371776. | − | 134630.i | −0.828193 | − | 0.299910i | ||||
\(671\) | −89530.6 | −0.198850 | ||||||||
\(672\) | −51847.8 | − | 51847.8i | −0.114813 | − | 0.114813i | ||||
\(673\) | −277903. | + | 277903.i | −0.613570 | + | 0.613570i | −0.943874 | − | 0.330305i | \(-0.892848\pi\) |
0.330305 | + | 0.943874i | \(0.392848\pi\) | |||||||
\(674\) | 282156.i | 0.621112i | ||||||||
\(675\) | −31221.7 | − | 343952.i | −0.0685251 | − | 0.754901i | ||||
\(676\) | 331151. | 0.724657 | ||||||||
\(677\) | −244917. | − | 244917.i | −0.534369 | − | 0.534369i | 0.387501 | − | 0.921869i | \(-0.373338\pi\) |
−0.921869 | + | 0.387501i | \(0.873338\pi\) | |||||||
\(678\) | −35800.3 | + | 35800.3i | −0.0778802 | + | 0.0778802i | ||||
\(679\) | − | 260173.i | − | 0.564317i | ||||||
\(680\) | 5620.61 | − | 15521.1i | 0.0121553 | − | 0.0335665i | ||||
\(681\) | 56206.5 | 0.121197 | ||||||||
\(682\) | 36498.3 | + | 36498.3i | 0.0784700 | + | 0.0784700i | ||||
\(683\) | −504443. | + | 504443.i | −1.08136 | + | 1.08136i | −0.0849785 | + | 0.996383i | \(0.527082\pi\) |
−0.996383 | + | 0.0849785i | \(0.972918\pi\) | |||||||
\(684\) | 156483.i | 0.334468i | ||||||||
\(685\) | 429547. | − | 201154.i | 0.915438 | − | 0.428693i | ||||
\(686\) | −13329.4 | −0.0283245 | ||||||||
\(687\) | −57198.1 | − | 57198.1i | −0.121190 | − | 0.121190i | ||||
\(688\) | −20624.1 | + | 20624.1i | −0.0435711 | + | 0.0435711i | ||||
\(689\) | − | 10992.1i | − | 0.0231549i | ||||||
\(690\) | 48692.0 | + | 103978.i | 0.102273 | + | 0.218394i | ||||
\(691\) | 452722. | 0.948146 | 0.474073 | − | 0.880486i | \(-0.342783\pi\) | ||||
0.474073 | + | 0.880486i | \(0.342783\pi\) | |||||||
\(692\) | 270708. | + | 270708.i | 0.565312 | + | 0.565312i | ||||
\(693\) | −15882.1 | + | 15882.1i | −0.0330706 | + | 0.0330706i | ||||
\(694\) | 220638.i | 0.458100i | ||||||||
\(695\) | 141580. | + | 51269.7i | 0.293111 | + | 0.106143i | ||||
\(696\) | 230271. | 0.475358 | ||||||||
\(697\) | 22644.7 | + | 22644.7i | 0.0466124 | + | 0.0466124i | ||||
\(698\) | 149644. | − | 149644.i | 0.307149 | − | 0.307149i | ||||
\(699\) | − | 75556.4i | − | 0.154638i | ||||||
\(700\) | −133689. | + | 12135.4i | −0.272834 | + | 0.0247661i | ||||
\(701\) | −430640. | −0.876352 | −0.438176 | − | 0.898889i | \(-0.644375\pi\) | ||||
−0.438176 | + | 0.898889i | \(0.644375\pi\) | |||||||
\(702\) | −2064.15 | − | 2064.15i | −0.00418858 | − | 0.00418858i | ||||
\(703\) | 170768. | − | 170768.i | 0.345539 | − | 0.345539i | ||||
\(704\) | − | 21722.2i | − | 0.0438287i | ||||||
\(705\) | −40766.4 | + | 112575.i | −0.0820209 | + | 0.226498i | ||||
\(706\) | −89237.7 | −0.179035 | ||||||||
\(707\) | −217798. | − | 217798.i | −0.435729 | − | 0.435729i | ||||
\(708\) | 52377.1 | − | 52377.1i | 0.104490 | − | 0.104490i | ||||
\(709\) | 232388.i | 0.462298i | 0.972918 | + | 0.231149i | \(0.0742484\pi\) | ||||
−0.972918 | + | 0.231149i | \(0.925752\pi\) | |||||||
\(710\) | 182590. | − | 85505.5i | 0.362209 | − | 0.169620i | ||||
\(711\) | 663987. | 1.31347 | ||||||||
\(712\) | 151143. | + | 151143.i | 0.298145 | + | 0.298145i | ||||
\(713\) | −564208. | + | 564208.i | −1.10984 | + | 1.10984i | ||||
\(714\) | 1653.66i | 0.00324377i | ||||||||
\(715\) | 482.632 | + | 1030.62i | 0.000944070 | + | 0.00201598i | ||||
\(716\) | 330193. | 0.644084 | ||||||||
\(717\) | −211929. | − | 211929.i | −0.412242 | − | 0.412242i | ||||
\(718\) | 18988.1 | − | 18988.1i | 0.0368326 | − | 0.0368326i | ||||
\(719\) | 684958.i | 1.32497i | 0.749075 | + | 0.662485i | \(0.230498\pi\) | ||||
−0.749075 | + | 0.662485i | \(0.769502\pi\) | |||||||
\(720\) | −100978. | − | 36566.6i | −0.194787 | − | 0.0705375i | ||||
\(721\) | 203838. | 0.392115 | ||||||||
\(722\) | 133315. | + | 133315.i | 0.255743 | + | 0.255743i | ||||
\(723\) | 39489.9 | − | 39489.9i | 0.0755457 | − | 0.0755457i | ||||
\(724\) | − | 474167.i | − | 0.904595i | ||||||
\(725\) | 426421. | − | 511566.i | 0.811265 | − | 0.973252i | ||||
\(726\) | −112087. | −0.212658 | ||||||||
\(727\) | −344257. | − | 344257.i | −0.651350 | − | 0.651350i | 0.301968 | − | 0.953318i | \(-0.402356\pi\) |
−0.953318 | + | 0.301968i | \(0.902356\pi\) | |||||||
\(728\) | −1909.20 | + | 1909.20i | −0.00360238 | + | 0.00360238i | ||||
\(729\) | − | 59055.9i | − | 0.111124i | ||||||
\(730\) | 83340.5 | − | 230142.i | 0.156390 | − | 0.431868i | ||||
\(731\) | 5192.85 | 0.00971787 | ||||||||
\(732\) | 151531. | + | 151531.i | 0.282800 | + | 0.282800i | ||||
\(733\) | 458945. | − | 458945.i | 0.854186 | − | 0.854186i | −0.136460 | − | 0.990646i | \(-0.543572\pi\) |
0.990646 | + | 0.136460i | \(0.0435724\pi\) | |||||||
\(734\) | − | 184624.i | − | 0.342685i | ||||||
\(735\) | 28980.2 | − | 13571.2i | 0.0536447 | − | 0.0251214i | ||||
\(736\) | 622213. | 1.14864 | ||||||||
\(737\) | −96369.6 | − | 96369.6i | −0.177421 | − | 0.177421i | ||||
\(738\) | −279499. | + | 279499.i | −0.513177 | + | 0.513177i | ||||
\(739\) | − | 61500.0i | − | 0.112612i | −0.998414 | − | 0.0563062i | \(-0.982068\pi\) | ||
0.998414 | − | 0.0563062i | \(-0.0179323\pi\) | |||||||
\(740\) | 147607. | + | 315202.i | 0.269553 | + | 0.575607i | ||||
\(741\) | −1890.06 | −0.00344223 | ||||||||
\(742\) | −119977. | − | 119977.i | −0.217916 | − | 0.217916i | ||||
\(743\) | 33421.8 | − | 33421.8i | 0.0605414 | − | 0.0605414i | −0.676188 | − | 0.736729i | \(-0.736369\pi\) |
0.736729 | + | 0.676188i | \(0.236369\pi\) | |||||||
\(744\) | − | 294000.i | − | 0.531130i | ||||||
\(745\) | −357477. | − | 129452.i | −0.644073 | − | 0.233236i | ||||
\(746\) | 141127. | 0.253590 | ||||||||
\(747\) | 352409. | + | 352409.i | 0.631546 | + | 0.631546i | ||||
\(748\) | 1690.71 | − | 1690.71i | 0.00302179 | − | 0.00302179i | ||||
\(749\) | 180550.i | 0.321836i | ||||||||
\(750\) | −105660. | + | 61693.4i | −0.187840 | + | 0.109677i | ||||
\(751\) | 257993. | 0.457434 | 0.228717 | − | 0.973493i | \(-0.426547\pi\) | ||||
0.228717 | + | 0.973493i | \(0.426547\pi\) | |||||||
\(752\) | 58118.6 | + | 58118.6i | 0.102773 | + | 0.102773i | ||||
\(753\) | 130939. | − | 130939.i | 0.230929 | − | 0.230929i | ||||
\(754\) | − | 5629.12i | − | 0.00990143i | ||||||
\(755\) | 326608. | − | 901919.i | 0.572972 | − | 1.58225i | ||||
\(756\) | 118685. | 0.207660 | ||||||||
\(757\) | −783812. | − | 783812.i | −1.36779 | − | 1.36779i | −0.863581 | − | 0.504211i | \(-0.831783\pi\) |
−0.504211 | − | 0.863581i | \(-0.668217\pi\) | |||||||
\(758\) | −162788. | + | 162788.i | −0.283325 | + | 0.283325i | ||||
\(759\) | 39574.1i | 0.0686954i | ||||||||
\(760\) | 263745. | − | 123510.i | 0.456623 | − | 0.213833i | ||||
\(761\) | 614396. | 1.06091 | 0.530456 | − | 0.847713i | \(-0.322021\pi\) | ||||
0.530456 | + | 0.847713i | \(0.322021\pi\) | |||||||
\(762\) | −5927.56 | − | 5927.56i | −0.0102086 | − | 0.0102086i | ||||
\(763\) | −161243. | + | 161243.i | −0.276969 | + | 0.276969i | ||||
\(764\) | 178881.i | 0.306463i | ||||||||
\(765\) | 8108.88 | + | 17315.8i | 0.0138560 | + | 0.0295883i | ||||
\(766\) | −278544. | −0.474719 | ||||||||
\(767\) | −3046.89 | − | 3046.89i | −0.00517925 | − | 0.00517925i | ||||
\(768\) | −130753. | + | 130753.i | −0.221682 | + | 0.221682i | ||||
\(769\) | 232260.i | 0.392755i | 0.980528 | + | 0.196377i | \(0.0629177\pi\) | ||||
−0.980528 | + | 0.196377i | \(0.937082\pi\) | |||||||
\(770\) | 16516.8 | + | 5981.16i | 0.0278576 | + | 0.0100880i | ||||
\(771\) | 324258. | 0.545483 | ||||||||
\(772\) | 78162.1 | + | 78162.1i | 0.131148 | + | 0.131148i | ||||
\(773\) | 654735. | − | 654735.i | 1.09574 | − | 1.09574i | 0.100834 | − | 0.994903i | \(-0.467849\pi\) |
0.994903 | − | 0.100834i | \(-0.0321510\pi\) | |||||||
\(774\) | 64094.2i | 0.106988i | ||||||||
\(775\) | −653144. | − | 544436.i | −1.08744 | − | 0.906448i | ||||
\(776\) | −813483. | −1.35091 | ||||||||
\(777\) | −58669.1 | − | 58669.1i | −0.0971779 | − | 0.0971779i | ||||
\(778\) | 164982. | − | 164982.i | 0.272569 | − | 0.272569i | ||||
\(779\) | 564991.i | 0.931036i | ||||||||
\(780\) | 927.472 | − | 2561.19i | 0.00152444 | − | 0.00420971i | ||||
\(781\) | 69494.1 | 0.113932 | ||||||||
\(782\) | −9922.59 | − | 9922.59i | −0.0162260 | − | 0.0162260i | ||||
\(783\) | −416359. | + | 416359.i | −0.679117 | + | 0.679117i | ||||
\(784\) | − | 21967.8i | − | 0.0357400i | ||||||
\(785\) | −128874. | + | 60350.7i | −0.209134 | + | 0.0979362i | ||||
\(786\) | 38774.3 | 0.0627623 | ||||||||
\(787\) | 95570.1 | + | 95570.1i | 0.154302 | + | 0.154302i | 0.780036 | − | 0.625734i | \(-0.215200\pi\) |
−0.625734 | + | 0.780036i | \(0.715200\pi\) | |||||||
\(788\) | −248.645 | + | 248.645i | −0.000400431 | + | 0.000400431i | ||||
\(789\) | 159133.i | 0.255626i | ||||||||
\(790\) | −220233. | − | 470288.i | −0.352880 | − | 0.753546i | ||||
\(791\) | −119745. | −0.191383 | ||||||||
\(792\) | 49658.6 | + | 49658.6i | 0.0791670 | + | 0.0791670i | ||||
\(793\) | 8814.90 | − | 8814.90i | 0.0140175 | − | 0.0140175i | ||||
\(794\) | 168632.i | 0.267485i | ||||||||
\(795\) | 383001. | + | 138695.i | 0.605990 | + | 0.219445i | ||||
\(796\) | 714232. | 1.12723 | ||||||||
\(797\) | 319866. | + | 319866.i | 0.503560 | + | 0.503560i | 0.912542 | − | 0.408983i | \(-0.134116\pi\) |
−0.408983 | + | 0.912542i | \(0.634116\pi\) | |||||||
\(798\) | −20629.6 | + | 20629.6i | −0.0323955 | + | 0.0323955i | ||||
\(799\) | − | 14633.4i | − | 0.0229220i | ||||||
\(800\) | 59942.4 | + | 660351.i | 0.0936600 | + | 1.03180i | ||||
\(801\) | −247583. | −0.385882 | ||||||||
\(802\) | 238133. | + | 238133.i | 0.370229 | + | 0.370229i | ||||
\(803\) | 59656.1 | − | 59656.1i | 0.0925175 | − | 0.0925175i | ||||
\(804\) | 326212.i | 0.504647i | ||||||||
\(805\) | −92459.6 | + | 255324.i | −0.142679 | + | 0.394004i | ||||
\(806\) | −7187.01 | −0.0110631 | ||||||||
\(807\) | −72231.6 | − | 72231.6i | −0.110912 | − | 0.110912i | ||||
\(808\) | −680990. | + | 680990.i | −1.04308 | + | 1.04308i | ||||
\(809\) | 243401.i | 0.371899i | 0.982559 | + | 0.185950i | \(0.0595361\pi\) | ||||
−0.982559 | + | 0.185950i | \(0.940464\pi\) | |||||||
\(810\) | −160135. | + | 74990.2i | −0.244071 | + | 0.114297i | ||||
\(811\) | −1.18528e6 | −1.80210 | −0.901049 | − | 0.433717i | \(-0.857202\pi\) | ||||
−0.901049 | + | 0.433717i | \(0.857202\pi\) | |||||||
\(812\) | 161832. | + | 161832.i | 0.245444 | + | 0.245444i | ||||
\(813\) | −283649. | + | 283649.i | −0.429141 | + | 0.429141i | ||||
\(814\) | − | 45546.1i | − | 0.0687389i | ||||||
\(815\) | −112830. | − | 240939.i | −0.169867 | − | 0.362737i | ||||
\(816\) | −2725.35 | −0.00409300 | ||||||||
\(817\) | 64781.4 | + | 64781.4i | 0.0970523 | + | 0.0970523i | ||||
\(818\) | −201636. | + | 201636.i | −0.301344 | + | 0.301344i | ||||
\(819\) | − | 3127.41i | − | 0.00466248i | ||||||
\(820\) | −765608. | − | 277247.i | −1.13862 | − | 0.412324i | ||||
\(821\) | 155906. | 0.231300 | 0.115650 | − | 0.993290i | \(-0.463105\pi\) | ||||
0.115650 | + | 0.993290i | \(0.463105\pi\) | |||||||
\(822\) | 105051. | + | 105051.i | 0.155474 | + | 0.155474i | ||||
\(823\) | 128790. | − | 128790.i | 0.190144 | − | 0.190144i | −0.605614 | − | 0.795758i | \(-0.707073\pi\) |
0.795758 | + | 0.605614i | \(0.207073\pi\) | |||||||
\(824\) | − | 637339.i | − | 0.938677i | ||||||
\(825\) | −41999.7 | + | 3812.47i | −0.0617076 | + | 0.00560142i | ||||
\(826\) | −66512.3 | −0.0974859 | ||||||||
\(827\) | −355578. | − | 355578.i | −0.519905 | − | 0.519905i | 0.397637 | − | 0.917543i | \(-0.369830\pi\) |
−0.917543 | + | 0.397637i | \(0.869830\pi\) | |||||||
\(828\) | −322587. | + | 322587.i | −0.470529 | + | 0.470529i | ||||
\(829\) | − | 180229.i | − | 0.262250i | −0.991366 | − | 0.131125i | \(-0.958141\pi\) | ||
0.991366 | − | 0.131125i | \(-0.0418590\pi\) | |||||||
\(830\) | 132716. | − | 366491.i | 0.192649 | − | 0.531995i | ||||
\(831\) | −480198. | −0.695374 | ||||||||
\(832\) | 2138.70 | + | 2138.70i | 0.00308960 | + | 0.00308960i | ||||
\(833\) | −2765.58 | + | 2765.58i | −0.00398563 | + | 0.00398563i | ||||
\(834\) | 47164.0i | 0.0678076i | ||||||||
\(835\) | −1.10576e6 | + | 517820.i | −1.58595 | + | 0.742688i | ||||
\(836\) | 42183.5 | 0.0603573 | ||||||||
\(837\) | 531589. | + | 531589.i | 0.758796 | + | 0.758796i | ||||
\(838\) | 25090.3 | − | 25090.3i | 0.0357288 | − | 0.0357288i | ||||
\(839\) | 246879.i | 0.350720i | 0.984504 | + | 0.175360i | \(0.0561089\pi\) | ||||
−0.984504 | + | 0.175360i | \(0.943891\pi\) | |||||||
\(840\) | −42433.1 | − | 90612.3i | −0.0601377 | − | 0.128419i | ||||
\(841\) | −428168. | −0.605371 | ||||||||
\(842\) | −251012. | − | 251012.i | −0.354055 | − | 0.354055i | ||||
\(843\) | −215371. | + | 215371.i | −0.303063 | + | 0.303063i | ||||
\(844\) | − | 92660.6i | − | 0.130080i | ||||||
\(845\) | 671212. | + | 243063.i | 0.940040 | + | 0.340413i | ||||
\(846\) | 180617. | 0.252358 | ||||||||
\(847\) | −187454. | − | 187454.i | −0.261293 | − | 0.261293i | ||||
\(848\) | 197730. | − | 197730.i | 0.274967 | − | 0.274967i | ||||
\(849\) | 132271.i | 0.183506i | ||||||||
\(850\) | 9574.87 | − | 11486.7i | 0.0132524 | − | 0.0158985i | ||||
\(851\) | 704073. | 0.972207 | ||||||||
\(852\) | −117619. | − | 117619.i | −0.162031 | − | 0.162031i | ||||
\(853\) | 427394. | − | 427394.i | 0.587395 | − | 0.587395i | −0.349530 | − | 0.936925i | \(-0.613659\pi\) |
0.936925 | + | 0.349530i | \(0.113659\pi\) | |||||||
\(854\) | − | 192425.i | − | 0.263844i | ||||||
\(855\) | −114858. | + | 317176.i | −0.157119 | + | 0.433878i | ||||
\(856\) | 564526. | 0.770436 | ||||||||
\(857\) | −345769. | − | 345769.i | −0.470787 | − | 0.470787i | 0.431382 | − | 0.902169i | \(-0.358026\pi\) |
−0.902169 | + | 0.431382i | \(0.858026\pi\) | |||||||
\(858\) | −252.052 | + | 252.052i | −0.000342386 | + | 0.000342386i | ||||
\(859\) | 298325.i | 0.404299i | 0.979355 | + | 0.202150i | \(0.0647927\pi\) | ||||
−0.979355 | + | 0.202150i | \(0.935207\pi\) | |||||||
\(860\) | −119573. | + | 55995.1i | −0.161672 | + | 0.0757100i | ||||
\(861\) | 194108. | 0.261841 | ||||||||
\(862\) | 470581. | + | 470581.i | 0.633315 | + | 0.633315i | ||||
\(863\) | 232266. | − | 232266.i | 0.311863 | − | 0.311863i | −0.533768 | − | 0.845631i | \(-0.679225\pi\) |
0.845631 | + | 0.533768i | \(0.179225\pi\) | |||||||
\(864\) | − | 586240.i | − | 0.785323i | ||||||
\(865\) | 350001. | + | 747397.i | 0.467775 | + | 0.998894i | ||||
\(866\) | 96643.2 | 0.128865 | ||||||||
\(867\) | −220052. | − | 220052.i | −0.292744 | − | 0.292744i | ||||
\(868\) | 206620. | − | 206620.i | 0.274241 | − | 0.274241i | ||||
\(869\) | − | 178993.i | − | 0.237026i | ||||||
\(870\) | 196137. | + | 71026.1i | 0.259131 | + | 0.0938382i | ||||
\(871\) | 18976.5 | 0.0250138 | ||||||||
\(872\) | 504158. | + | 504158.i | 0.663031 | + | 0.663031i | ||||
\(873\) | 666271. | − | 666271.i | 0.874223 | − | 0.874223i | ||||
\(874\) | − | 247571.i | − | 0.324098i | ||||||
\(875\) | −279882. | − | 73529.5i | −0.365560 | − | 0.0960385i | ||||
\(876\) | −201937. | −0.263152 | ||||||||
\(877\) | 220910. | + | 220910.i | 0.287221 | + | 0.287221i | 0.835980 | − | 0.548759i | \(-0.184900\pi\) |
−0.548759 | + | 0.835980i | \(0.684900\pi\) | |||||||
\(878\) | 215054. | − | 215054.i | 0.278970 | − | 0.278970i | ||||
\(879\) | − | 282975.i | − | 0.366244i | ||||||
\(880\) | −9857.36 | + | 27220.8i | −0.0127290 | + | 0.0351508i | ||||
\(881\) | −219463. | −0.282754 | −0.141377 | − | 0.989956i | \(-0.545153\pi\) | ||||
−0.141377 | + | 0.989956i | \(0.545153\pi\) | |||||||
\(882\) | −34135.0 | − | 34135.0i | −0.0438796 | − | 0.0438796i | ||||
\(883\) | 351509. | − | 351509.i | 0.450833 | − | 0.450833i | −0.444798 | − | 0.895631i | \(-0.646725\pi\) |
0.895631 | + | 0.444798i | \(0.146725\pi\) | |||||||
\(884\) | 332.923i | 0.000426029i | ||||||||
\(885\) | 144608. | − | 67718.9i | 0.184631 | − | 0.0864616i | ||||
\(886\) | −362593. | −0.461904 | ||||||||
\(887\) | −51300.9 | − | 51300.9i | −0.0652045 | − | 0.0652045i | 0.673753 | − | 0.738957i | \(-0.264681\pi\) |
−0.738957 | + | 0.673753i | \(0.764681\pi\) | |||||||
\(888\) | −183441. | + | 183441.i | −0.232632 | + | 0.232632i | ||||
\(889\) | − | 19826.5i | − | 0.0250867i | ||||||
\(890\) | 82118.7 | + | 175357.i | 0.103672 | + | 0.221383i | ||||
\(891\) | −60947.8 | −0.0767720 | ||||||||
\(892\) | −797761. | − | 797761.i | −1.00264 | − | 1.00264i | ||||
\(893\) | 182553. | − | 182553.i | 0.228922 | − | 0.228922i | ||||
\(894\) | − | 119085.i | − | 0.148999i | ||||||
\(895\) | 669271. | + | 242360.i | 0.835518 | + | 0.302563i | ||||
\(896\) | −267685. | −0.333432 | ||||||||
\(897\) | −3896.34 | − | 3896.34i | −0.00484253 | − | 0.00484253i | ||||
\(898\) | 380433. | − | 380433.i | 0.471765 | − | 0.471765i | ||||
\(899\) | 1.44969e6i | 1.79372i | ||||||||
\(900\) | −373437. | − | 311282.i | −0.461033 | − | 0.384299i | ||||
\(901\) | −49785.5 | −0.0613272 | ||||||||
\(902\) | 75345.2 | + | 75345.2i | 0.0926067 | + | 0.0926067i | ||||
\(903\) | 22256.3 | − | 22256.3i | 0.0272946 | − | 0.0272946i | ||||
\(904\) | 374406.i | 0.458148i | ||||||||
\(905\) | 348036. | − | 961092.i | 0.424940 | − | 1.17346i | ||||
\(906\) | 300453. | 0.366033 | ||||||||
\(907\) | −382253. | − | 382253.i | −0.464662 | − | 0.464662i | 0.435518 | − | 0.900180i | \(-0.356565\pi\) |
−0.900180 | + | 0.435518i | \(0.856565\pi\) | |||||||
\(908\) | 123509. | − | 123509.i | 0.149805 | − | 0.149805i | ||||
\(909\) | − | 1.11551e6i | − | 1.35004i | ||||||
\(910\) | −2215.08 | + | 1037.31i | −0.00267489 | + | 0.00125263i | ||||
\(911\) | 220039. | 0.265133 | 0.132566 | − | 0.991174i | \(-0.457678\pi\) | ||||
0.132566 | + | 0.991174i | \(0.457678\pi\) | |||||||
\(912\) | −33999.0 | − | 33999.0i | −0.0408768 | − | 0.0408768i | ||||
\(913\) | 94999.7 | − | 94999.7i | 0.113967 | − | 0.113967i | ||||
\(914\) | 479900.i | 0.574459i | ||||||||
\(915\) | 195916. | + | 418362.i | 0.234007 | + | 0.499701i | ||||
\(916\) | −251376. | −0.299594 | ||||||||
\(917\) | 64846.1 | + | 64846.1i | 0.0771161 | + | 0.0771161i | ||||
\(918\) | −9348.93 | + | 9348.93i | −0.0110937 | + | 0.0110937i | ||||
\(919\) | − | 923186.i | − | 1.09310i | −0.837428 | − | 0.546548i | \(-0.815942\pi\) | ||
0.837428 | − | 0.546548i | \(-0.184058\pi\) | |||||||
\(920\) | 798323. | + | 289093.i | 0.943198 | + | 0.341556i | ||||
\(921\) | −405106. | −0.477584 | ||||||||
\(922\) | −23704.6 | − | 23704.6i | −0.0278850 | − | 0.0278850i | ||||
\(923\) | −6842.17 | + | 6842.17i | −0.00803138 | + | 0.00803138i | ||||
\(924\) | − | 14492.5i | − | 0.0169746i | ||||||
\(925\) | 67828.7 | + | 747229.i | 0.0792738 | + | 0.873313i | ||||
\(926\) | −808380. | −0.942744 | ||||||||
\(927\) | 522003. | + | 522003.i | 0.607454 | + | 0.607454i | ||||
\(928\) | 799365. | − | 799365.i | 0.928216 | − | 0.928216i | ||||
\(929\) | 340275.i | 0.394275i | 0.980376 | + | 0.197137i | \(0.0631645\pi\) | ||||
−0.980376 | + | 0.197137i | \(0.936836\pi\) | |||||||
\(930\) | 90683.0 | − | 250418.i | 0.104848 | − | 0.289534i | ||||
\(931\) | −69001.9 | −0.0796089 | ||||||||
\(932\) | −166029. | − | 166029.i | −0.191140 | − | 0.191140i | ||||
\(933\) | 416539. | − | 416539.i | 0.478511 | − | 0.478511i | ||||
\(934\) | − | 605491.i | − | 0.694087i | ||||||
\(935\) | 4667.87 | − | 2185.93i | 0.00533944 | − | 0.00250042i | ||||
\(936\) | −9778.47 | −0.0111614 | ||||||||
\(937\) | 1.13011e6 | + | 1.13011e6i | 1.28718 | + | 1.28718i | 0.936490 | + | 0.350695i | \(0.114055\pi\) |
0.350695 | + | 0.936490i | \(0.385945\pi\) | |||||||
\(938\) | 207124. | − | 207124.i | 0.235410 | − | 0.235410i | ||||
\(939\) | − | 398879.i | − | 0.452387i | ||||||
\(940\) | 157794. | + | 336955.i | 0.178581 | + | 0.381344i | ||||
\(941\) | −690085. | −0.779334 | −0.389667 | − | 0.920956i | \(-0.627410\pi\) | ||||
−0.389667 | + | 0.920956i | \(0.627410\pi\) | |||||||
\(942\) | −31517.9 | − | 31517.9i | −0.0355185 | − | 0.0355185i | ||||
\(943\) | −1.16472e6 | + | 1.16472e6i | −1.30978 | + | 1.30978i | ||||
\(944\) | − | 109617.i | − | 0.123008i | ||||||
\(945\) | 240563. | + | 87114.1i | 0.269380 | + | 0.0975495i | ||||
\(946\) | 17278.0 | 0.0193069 | ||||||||
\(947\) | −312697. | − | 312697.i | −0.348677 | − | 0.348677i | 0.510940 | − | 0.859617i | \(-0.329298\pi\) |
−0.859617 | + | 0.510940i | \(0.829298\pi\) | |||||||
\(948\) | −302946. | + | 302946.i | −0.337092 | + | 0.337092i | ||||
\(949\) | 11747.1i | 0.0130436i | ||||||||
\(950\) | 262745. | − | 23850.3i | 0.291130 | − | 0.0264270i | ||||
\(951\) | 273851. | 0.302798 | ||||||||
\(952\) | 8647.15 | + | 8647.15i | 0.00954111 | + | 0.00954111i | ||||
\(953\) | 163152. | − | 163152.i | 0.179642 | − | 0.179642i | −0.611558 | − | 0.791200i | \(-0.709457\pi\) |
0.791200 | + | 0.611558i | \(0.209457\pi\) | |||||||
\(954\) | − | 614491.i | − | 0.675178i | ||||||
\(955\) | −131298. | + | 362576.i | −0.143963 | + | 0.397550i | ||||
\(956\) | −931391. | −1.01910 | ||||||||
\(957\) | 50841.4 | + | 50841.4i | 0.0555128 | + | 0.0555128i | ||||
\(958\) | −54251.5 | + | 54251.5i | −0.0591127 | + | 0.0591127i | ||||
\(959\) | 351376.i | 0.382063i | ||||||||
\(960\) | −101504. | + | 47533.8i | −0.110139 | + | 0.0515774i | ||||
\(961\) | 927378. | 1.00418 | ||||||||
\(962\) | 4484.33 | + | 4484.33i | 0.00484560 | + | 0.00484560i | ||||
\(963\) | −462366. | + | 462366.i | −0.498579 | + | 0.498579i | ||||
\(964\) | − | 173552.i | − | 0.186756i | ||||||
\(965\) | 101057. | + | 215798.i | 0.108520 | + | 0.231736i | ||||
\(966\) | −85055.3 | −0.0911480 | ||||||||
\(967\) | 366124. | + | 366124.i | 0.391540 | + | 0.391540i | 0.875236 | − | 0.483696i | \(-0.160706\pi\) |
−0.483696 | + | 0.875236i | \(0.660706\pi\) | |||||||
\(968\) | −586113. | + | 586113.i | −0.625505 | + | 0.625505i | ||||
\(969\) | 8560.45i | 0.00911694i | ||||||||
\(970\) | −692896. | − | 250915.i | −0.736418 | − | 0.266676i | ||||
\(971\) | −597720. | −0.633956 | −0.316978 | − | 0.948433i | \(-0.602668\pi\) | ||||
−0.316978 | + | 0.948433i | \(0.602668\pi\) | |||||||
\(972\) | 470199. | + | 470199.i | 0.497679 | + | 0.497679i | ||||
\(973\) | −78877.1 | + | 78877.1i | −0.0833154 | + | 0.0833154i | ||||
\(974\) | 227209.i | 0.239501i | ||||||||
\(975\) | 3759.80 | − | 4510.52i | 0.00395508 | − | 0.00474480i | ||||
\(976\) | 317130. | 0.332918 | ||||||||
\(977\) | −299471. | − | 299471.i | −0.313737 | − | 0.313737i | 0.532618 | − | 0.846356i | \(-0.321208\pi\) |
−0.846356 | + | 0.532618i | \(0.821208\pi\) | |||||||
\(978\) | 58924.9 | − | 58924.9i | 0.0616058 | − | 0.0616058i | ||||
\(979\) | 66741.5i | 0.0696354i | ||||||||
\(980\) | 33859.9 | − | 93503.1i | 0.0352560 | − | 0.0973585i | ||||
\(981\) | −825846. | −0.858145 | ||||||||
\(982\) | 592681. | + | 592681.i | 0.614608 | + | 0.614608i | ||||
\(983\) | −16044.9 | + | 16044.9i | −0.0166046 | + | 0.0166046i | −0.715360 | − | 0.698756i | \(-0.753737\pi\) |
0.698756 | + | 0.715360i | \(0.253737\pi\) | |||||||
\(984\) | − | 606918.i | − | 0.626816i | ||||||
\(985\) | −686.486 | + | 321.476i | −0.000707553 | + | 0.000331342i | ||||
\(986\) | −25495.4 | −0.0262245 | ||||||||
\(987\) | −62718.0 | − | 62718.0i | −0.0643810 | − | 0.0643810i | ||||
\(988\) | −4153.25 | + | 4153.25i | −0.00425475 | + | 0.00425475i | ||||
\(989\) | 267092.i | 0.273066i | ||||||||
\(990\) | 26980.5 | + | 57614.5i | 0.0275283 | + | 0.0587843i | ||||
\(991\) | −1.35587e6 | −1.38061 | −0.690307 | − | 0.723517i | \(-0.742525\pi\) | ||||
−0.690307 | + | 0.723517i | \(0.742525\pi\) | |||||||
\(992\) | −1.02059e6 | − | 1.02059e6i | −1.03712 | − | 1.03712i | ||||
\(993\) | 140391. | − | 140391.i | 0.142377 | − | 0.142377i | ||||
\(994\) | 149361.i | 0.151170i | ||||||||
\(995\) | 1.44768e6 | + | 524243.i | 1.46227 | + | 0.529525i | ||||
\(996\) | −321575. | −0.324163 | ||||||||
\(997\) | 833075. | + | 833075.i | 0.838096 | + | 0.838096i | 0.988608 | − | 0.150513i | \(-0.0480924\pi\) |
−0.150513 | + | 0.988608i | \(0.548092\pi\) | |||||||
\(998\) | 26070.6 | − | 26070.6i | 0.0261752 | − | 0.0261752i | ||||
\(999\) | − | 663368.i | − | 0.664697i |
(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 | 35.5.g.a.22.8 | yes | 24 | |
5.2 | odd | 4 | 175.5.g.c.43.5 | 24 | |||
5.3 | odd | 4 | inner | 35.5.g.a.8.8 | ✓ | 24 | |
5.4 | even | 2 | 175.5.g.c.57.5 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.5.g.a.8.8 | ✓ | 24 | 5.3 | odd | 4 | inner | |
35.5.g.a.22.8 | yes | 24 | 1.1 | even | 1 | trivial | |
175.5.g.c.43.5 | 24 | 5.2 | odd | 4 | |||
175.5.g.c.57.5 | 24 | 5.4 | even | 2 |