Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,3,Mod(55,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.55");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.f (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.82836056527\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.119023932416481.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} - 3 x^{10} + 11 x^{9} - 5 x^{8} - 14 x^{7} + 29 x^{6} - 28 x^{5} - 20 x^{4} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 55.6 | ||
Root | \(-1.40311 + 0.176844i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.55 |
Dual form | 324.3.f.r.271.6 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.82144 | + | 0.826041i | 0.910722 | + | 0.413020i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.63531 | + | 3.00917i | 0.658828 | + | 0.752293i | ||||
\(5\) | 3.61903 | + | 6.26834i | 0.723805 | + | 1.25367i | 0.959464 | + | 0.281832i | \(0.0909420\pi\) |
−0.235659 | + | 0.971836i | \(0.575725\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.95847 | + | 3.44013i | 0.851211 | + | 0.491447i | 0.861059 | − | 0.508505i | \(-0.169802\pi\) |
−0.00984858 | + | 0.999952i | \(0.503135\pi\) | |||||||
\(8\) | 2.31438 | + | 7.65792i | 0.289297 | + | 0.957239i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.41395 | + | 14.4069i | 0.141395 | + | 1.44069i | ||||
\(11\) | −15.5474 | − | 8.97632i | −1.41340 | − | 0.816029i | −0.417697 | − | 0.908586i | \(-0.637163\pi\) |
−0.995707 | + | 0.0925568i | \(0.970496\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.83763 | − | 6.64697i | −0.295202 | − | 0.511305i | 0.679830 | − | 0.733370i | \(-0.262054\pi\) |
−0.975032 | + | 0.222065i | \(0.928720\pi\) | |||||||
\(14\) | 8.01134 | + | 11.1879i | 0.572239 | + | 0.799138i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.11024 | + | 15.8602i | −0.131890 | + | 0.991264i | ||||
\(17\) | 1.43720 | 0.0845413 | 0.0422707 | − | 0.999106i | \(-0.486541\pi\) | ||||
0.0422707 | + | 0.999106i | \(0.486541\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 13.8943i | − | 0.731281i | −0.930756 | − | 0.365641i | \(-0.880850\pi\) | ||
0.930756 | − | 0.365641i | \(-0.119150\pi\) | |||||||
\(20\) | −9.32524 | + | 27.4093i | −0.466262 | + | 1.37047i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −20.9040 | − | 29.1927i | −0.950182 | − | 1.32694i | ||||
\(23\) | 14.3608 | − | 8.29122i | 0.624384 | − | 0.360488i | −0.154190 | − | 0.988041i | \(-0.549277\pi\) |
0.778574 | + | 0.627553i | \(0.215943\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −13.6947 | + | 23.7199i | −0.547788 | + | 0.948797i | ||||
\(26\) | −1.49936 | − | 15.2771i | −0.0576676 | − | 0.587581i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.35051 | + | 26.9959i | 0.191090 | + | 0.964139i | ||||
\(29\) | −18.7509 | + | 32.4776i | −0.646584 | + | 1.11992i | 0.337349 | + | 0.941380i | \(0.390470\pi\) |
−0.983933 | + | 0.178537i | \(0.942864\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 46.7583 | − | 26.9959i | 1.50833 | − | 0.870835i | 0.508378 | − | 0.861134i | \(-0.330245\pi\) |
0.999953 | − | 0.00970102i | \(-0.00308798\pi\) | |||||||
\(32\) | −16.9449 | + | 27.1454i | −0.529528 | + | 0.848293i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.61778 | + | 1.18719i | 0.0769936 | + | 0.0349173i | ||||
\(35\) | 49.7996i | 1.42285i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 44.4415 | 1.20112 | 0.600560 | − | 0.799580i | \(-0.294944\pi\) | ||||
0.600560 | + | 0.799580i | \(0.294944\pi\) | |||||||
\(38\) | 11.4773 | − | 25.3078i | 0.302034 | − | 0.665994i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −39.6266 | + | 42.2215i | −0.990665 | + | 1.05554i | ||||
\(41\) | 28.4956 | + | 49.3558i | 0.695014 | + | 1.20380i | 0.970176 | + | 0.242401i | \(0.0779350\pi\) |
−0.275162 | + | 0.961398i | \(0.588732\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −58.5593 | − | 33.8092i | −1.36184 | − | 0.786261i | −0.371975 | − | 0.928243i | \(-0.621319\pi\) |
−0.989869 | + | 0.141982i | \(0.954653\pi\) | |||||||
\(44\) | −13.9611 | − | 70.4404i | −0.317298 | − | 1.60092i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 33.0063 | − | 3.23938i | 0.717529 | − | 0.0704212i | ||||
\(47\) | 8.17054 | + | 4.71726i | 0.173841 | + | 0.100367i | 0.584396 | − | 0.811469i | \(-0.301332\pi\) |
−0.410555 | + | 0.911836i | \(0.634665\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.831061 | − | 1.43944i | −0.0169604 | − | 0.0293763i | ||||
\(50\) | −44.5378 | + | 31.8921i | −0.890755 | + | 0.637843i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 9.88852 | − | 29.0649i | 0.190164 | − | 0.558941i | ||||
\(53\) | 7.82662 | 0.147672 | 0.0738360 | − | 0.997270i | \(-0.476476\pi\) | ||||
0.0738360 | + | 0.997270i | \(0.476476\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 129.942i | − | 2.36259i | ||||||
\(56\) | −12.5540 | + | 53.5912i | −0.224179 | + | 0.956986i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −60.9816 | + | 43.6670i | −1.05141 | + | 0.752880i | ||||
\(59\) | 19.4098 | − | 11.2062i | 0.328979 | − | 0.189936i | −0.326409 | − | 0.945229i | \(-0.605839\pi\) |
0.655388 | + | 0.755293i | \(0.272505\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 33.5907 | − | 58.1808i | 0.550667 | − | 0.953783i | −0.447559 | − | 0.894254i | \(-0.647707\pi\) |
0.998227 | − | 0.0595292i | \(-0.0189599\pi\) | |||||||
\(62\) | 107.467 | − | 10.5473i | 1.73334 | − | 0.170117i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −53.2873 | + | 35.4466i | −0.832614 | + | 0.553853i | ||||
\(65\) | 27.7770 | − | 48.1111i | 0.427338 | − | 0.740171i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 59.9324 | − | 34.6020i | 0.894514 | − | 0.516448i | 0.0190978 | − | 0.999818i | \(-0.493921\pi\) |
0.875416 | + | 0.483370i | \(0.160587\pi\) | |||||||
\(68\) | 3.78748 | + | 4.32479i | 0.0556982 | + | 0.0635999i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −41.1365 | + | 90.7072i | −0.587665 | + | 1.29582i | ||||
\(71\) | 7.14792i | 0.100675i | 0.998732 | + | 0.0503375i | \(0.0160297\pi\) | ||||
−0.998732 | + | 0.0503375i | \(0.983970\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −80.4410 | −1.10193 | −0.550965 | − | 0.834528i | \(-0.685740\pi\) | ||||
−0.550965 | + | 0.834528i | \(0.685740\pi\) | |||||||
\(74\) | 80.9476 | + | 36.7104i | 1.09389 | + | 0.496087i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 41.8105 | − | 36.6159i | 0.550138 | − | 0.481789i | ||||
\(77\) | −61.7594 | − | 106.970i | −0.802070 | − | 1.38923i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 40.5680 | + | 23.4219i | 0.513519 | + | 0.296480i | 0.734279 | − | 0.678848i | \(-0.237520\pi\) |
−0.220760 | + | 0.975328i | \(0.570854\pi\) | |||||||
\(80\) | −107.054 | + | 44.1709i | −1.33818 | + | 0.552136i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 11.1332 | + | 113.437i | 0.135771 | + | 1.38338i | ||||
\(83\) | −123.148 | − | 71.0994i | −1.48371 | − | 0.856619i | −0.483879 | − | 0.875135i | \(-0.660772\pi\) |
−0.999829 | + | 0.0185165i | \(0.994106\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.20128 | + | 9.00887i | 0.0611915 | + | 0.105987i | ||||
\(86\) | −78.7347 | − | 109.954i | −0.915519 | − | 1.27853i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 32.7573 | − | 139.836i | 0.372242 | − | 1.58904i | ||||
\(89\) | −42.1078 | −0.473122 | −0.236561 | − | 0.971617i | \(-0.576020\pi\) | ||||
−0.236561 | + | 0.971617i | \(0.576020\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 52.8077i | − | 0.580304i | ||||||
\(92\) | 62.7950 | + | 21.3642i | 0.682554 | + | 0.232220i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.9855 | + | 15.3414i | 0.116867 | + | 0.163207i | ||||
\(95\) | 87.0944 | − | 50.2840i | 0.916783 | − | 0.529305i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −31.4478 | + | 54.4691i | −0.324204 | + | 0.561538i | −0.981351 | − | 0.192225i | \(-0.938430\pi\) |
0.657147 | + | 0.753762i | \(0.271763\pi\) | |||||||
\(98\) | −0.324695 | − | 3.30835i | −0.00331321 | − | 0.0337586i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −107.467 | + | 21.2997i | −1.07467 | + | 0.212997i | ||||
\(101\) | 23.8072 | − | 41.2352i | 0.235715 | − | 0.408270i | −0.723766 | − | 0.690046i | \(-0.757590\pi\) |
0.959480 | + | 0.281776i | \(0.0909236\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −46.5264 | + | 26.8621i | −0.451713 | + | 0.260797i | −0.708553 | − | 0.705657i | \(-0.750652\pi\) |
0.256840 | + | 0.966454i | \(0.417319\pi\) | |||||||
\(104\) | 42.0202 | − | 44.7718i | 0.404040 | − | 0.430498i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 14.2557 | + | 6.46511i | 0.134488 | + | 0.0609916i | ||||
\(107\) | − | 26.4708i | − | 0.247390i | −0.992320 | − | 0.123695i | \(-0.960525\pi\) | ||
0.992320 | − | 0.123695i | \(-0.0394745\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 83.0647 | 0.762061 | 0.381031 | − | 0.924562i | \(-0.375569\pi\) | ||||
0.381031 | + | 0.924562i | \(0.375569\pi\) | |||||||
\(110\) | 107.338 | − | 236.682i | 0.975796 | − | 2.15166i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −67.1350 | + | 87.2433i | −0.599420 | + | 0.778958i | ||||
\(113\) | −7.76382 | − | 13.4473i | −0.0687064 | − | 0.119003i | 0.829626 | − | 0.558320i | \(-0.188554\pi\) |
−0.898332 | + | 0.439317i | \(0.855220\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 103.944 | + | 60.0123i | 0.903864 | + | 0.521846i | ||||
\(116\) | −147.145 | + | 29.1638i | −1.26849 | + | 0.251412i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 44.6106 | − | 4.37827i | 0.378056 | − | 0.0371039i | ||||
\(119\) | 8.56354 | + | 4.94416i | 0.0719625 | + | 0.0415476i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 100.649 | + | 174.329i | 0.831808 | + | 1.44073i | ||||
\(122\) | 109.243 | − | 78.2257i | 0.895436 | − | 0.641195i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 204.458 | + | 69.5610i | 1.64885 | + | 0.560976i | ||||
\(125\) | −17.2947 | −0.138358 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 157.463i | 1.23987i | 0.784654 | + | 0.619934i | \(0.212841\pi\) | ||||
−0.784654 | + | 0.619934i | \(0.787159\pi\) | |||||||
\(128\) | −126.340 | + | 20.5465i | −0.987033 | + | 0.160519i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 90.3359 | − | 64.6868i | 0.694891 | − | 0.497590i | ||||
\(131\) | −40.7545 | + | 23.5296i | −0.311103 | + | 0.179615i | −0.647420 | − | 0.762133i | \(-0.724152\pi\) |
0.336317 | + | 0.941749i | \(0.390819\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 47.7983 | − | 82.7891i | 0.359386 | − | 0.622474i | ||||
\(134\) | 137.746 | − | 13.5190i | 1.02796 | − | 0.100888i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.32623 | + | 11.0060i | 0.0244576 | + | 0.0809263i | ||||
\(137\) | 58.7486 | − | 101.756i | 0.428822 | − | 0.742742i | −0.567947 | − | 0.823065i | \(-0.692262\pi\) |
0.996769 | + | 0.0803237i | \(0.0255954\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 34.3777 | − | 19.8480i | 0.247322 | − | 0.142791i | −0.371216 | − | 0.928547i | \(-0.621059\pi\) |
0.618537 | + | 0.785756i | \(0.287726\pi\) | |||||||
\(140\) | −149.856 | + | 131.238i | −1.07040 | + | 0.937412i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.90447 | + | 13.0195i | −0.0415808 | + | 0.0916869i | ||||
\(143\) | 137.791i | 0.963575i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −271.441 | −1.87200 | ||||||||
\(146\) | −146.519 | − | 66.4475i | −1.00355 | − | 0.455120i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 117.117 | + | 133.732i | 0.791332 | + | 0.903595i | ||||
\(149\) | −57.4136 | − | 99.4432i | −0.385326 | − | 0.667404i | 0.606488 | − | 0.795092i | \(-0.292578\pi\) |
−0.991814 | + | 0.127688i | \(0.959244\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −138.670 | − | 80.0610i | −0.918343 | − | 0.530206i | −0.0352370 | − | 0.999379i | \(-0.511219\pi\) |
−0.883106 | + | 0.469173i | \(0.844552\pi\) | |||||||
\(152\) | 106.402 | − | 32.1567i | 0.700011 | − | 0.211557i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −24.1293 | − | 245.856i | −0.156684 | − | 1.59647i | ||||
\(155\) | 338.439 | + | 195.398i | 2.18348 | + | 1.26063i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −112.668 | − | 195.148i | −0.717634 | − | 1.24298i | −0.961935 | − | 0.273279i | \(-0.911892\pi\) |
0.244301 | − | 0.969699i | \(-0.421441\pi\) | |||||||
\(158\) | 54.5448 | + | 76.1725i | 0.345220 | + | 0.482105i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −231.480 | − | 7.97645i | −1.44675 | − | 0.0498528i | ||||
\(161\) | 114.091 | 0.708643 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 147.165i | 0.902850i | 0.892309 | + | 0.451425i | \(0.149084\pi\) | ||||
−0.892309 | + | 0.451425i | \(0.850916\pi\) | |||||||
\(164\) | −73.4253 | + | 215.816i | −0.447715 | + | 1.31595i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −165.576 | − | 231.228i | −0.997443 | − | 1.39294i | ||||
\(167\) | −91.7504 | + | 52.9721i | −0.549403 | + | 0.317198i | −0.748881 | − | 0.662704i | \(-0.769409\pi\) |
0.199478 | + | 0.979902i | \(0.436075\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 55.0452 | − | 95.3411i | 0.325711 | − | 0.564149i | ||||
\(170\) | 2.03213 | + | 20.7056i | 0.0119537 | + | 0.121798i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −52.5843 | − | 265.313i | −0.305723 | − | 1.54252i | ||||
\(173\) | −93.2118 | + | 161.448i | −0.538797 | + | 0.933223i | 0.460172 | + | 0.887830i | \(0.347788\pi\) |
−0.998969 | + | 0.0453938i | \(0.985546\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −163.199 | + | 94.2231i | −0.932566 | + | 0.538417i | ||||
\(176\) | 175.175 | − | 227.644i | 0.995315 | − | 1.29343i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −76.6970 | − | 34.7828i | −0.430882 | − | 0.195409i | ||||
\(179\) | − | 191.597i | − | 1.07037i | −0.844734 | − | 0.535187i | \(-0.820241\pi\) | ||
0.844734 | − | 0.535187i | \(-0.179759\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 204.960 | 1.13237 | 0.566187 | − | 0.824277i | \(-0.308418\pi\) | ||||
0.566187 | + | 0.824277i | \(0.308418\pi\) | |||||||
\(182\) | 43.6213 | − | 96.1863i | 0.239678 | − | 0.528496i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 96.7298 | + | 90.7849i | 0.525706 | + | 0.493396i | ||||
\(185\) | 160.835 | + | 278.574i | 0.869377 | + | 1.50581i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −22.3448 | − | 12.9008i | −0.119491 | − | 0.0689882i | ||||
\(188\) | 7.33688 | + | 37.0180i | 0.0390259 | + | 0.196904i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 200.174 | − | 19.6459i | 1.05355 | − | 0.103400i | ||||
\(191\) | −77.7825 | − | 44.9078i | −0.407238 | − | 0.235119i | 0.282364 | − | 0.959307i | \(-0.408881\pi\) |
−0.689602 | + | 0.724188i | \(0.742215\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −83.7981 | − | 145.143i | −0.434187 | − | 0.752034i | 0.563042 | − | 0.826428i | \(-0.309631\pi\) |
−0.997229 | + | 0.0743944i | \(0.976298\pi\) | |||||||
\(194\) | −102.274 | + | 73.2353i | −0.527186 | + | 0.377502i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.14142 | − | 6.29418i | 0.0109256 | − | 0.0321132i | ||||
\(197\) | −185.277 | −0.940492 | −0.470246 | − | 0.882535i | \(-0.655835\pi\) | ||||
−0.470246 | + | 0.882535i | \(0.655835\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 137.625i | 0.691585i | 0.938311 | + | 0.345793i | \(0.112390\pi\) | ||||
−0.938311 | + | 0.345793i | \(0.887610\pi\) | |||||||
\(200\) | −213.340 | − | 49.9761i | −1.06670 | − | 0.249880i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 77.4254 | − | 55.4419i | 0.383294 | − | 0.274465i | ||||
\(203\) | −223.454 | + | 129.011i | −1.10076 | + | 0.635523i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −206.252 | + | 357.240i | −1.00611 | + | 1.74263i | ||||
\(206\) | −106.934 | + | 10.4950i | −0.519099 | + | 0.0509465i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 113.521 | − | 46.8389i | 0.545773 | − | 0.225187i | ||||
\(209\) | −124.720 | + | 216.022i | −0.596747 | + | 1.03360i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −264.357 | + | 152.627i | −1.25288 | + | 0.723350i | −0.971680 | − | 0.236300i | \(-0.924065\pi\) |
−0.281198 | + | 0.959650i | \(0.590732\pi\) | |||||||
\(212\) | 20.6256 | + | 23.5517i | 0.0972906 | + | 0.111093i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 21.8659 | − | 48.2150i | 0.102177 | − | 0.225304i | ||||
\(215\) | − | 489.426i | − | 2.27640i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 371.477 | 1.71188 | ||||||||
\(218\) | 151.298 | + | 68.6148i | 0.694026 | + | 0.314747i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 391.019 | − | 342.439i | 1.77736 | − | 1.55654i | ||||
\(221\) | −5.51545 | − | 9.55304i | −0.0249568 | − | 0.0432264i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.9150 | + | 8.61118i | 0.0668834 | + | 0.0386152i | 0.533069 | − | 0.846072i | \(-0.321039\pi\) |
−0.466185 | + | 0.884687i | \(0.654372\pi\) | |||||||
\(224\) | −194.349 | + | 103.452i | −0.867630 | + | 0.461841i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.03332 | − | 30.9068i | −0.0134218 | − | 0.136756i | ||||
\(227\) | −35.4937 | − | 20.4923i | −0.156360 | − | 0.0902744i | 0.419779 | − | 0.907627i | \(-0.362108\pi\) |
−0.576138 | + | 0.817352i | \(0.695441\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 66.7264 | + | 115.573i | 0.291381 | + | 0.504687i | 0.974137 | − | 0.225960i | \(-0.0725518\pi\) |
−0.682755 | + | 0.730647i | \(0.739218\pi\) | |||||||
\(230\) | 139.756 | + | 195.171i | 0.607636 | + | 0.848571i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −292.107 | − | 68.4278i | −1.25908 | − | 0.294947i | ||||
\(233\) | 368.345 | 1.58088 | 0.790441 | − | 0.612539i | \(-0.209852\pi\) | ||||
0.790441 | + | 0.612539i | \(0.209852\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 68.2876i | 0.290586i | ||||||||
\(236\) | 84.8723 | + | 28.8754i | 0.359628 | + | 0.122353i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 11.5139 | + | 16.0793i | 0.0483778 | + | 0.0675602i | ||||
\(239\) | −249.901 | + | 144.280i | −1.04561 | + | 0.603683i | −0.921417 | − | 0.388576i | \(-0.872967\pi\) |
−0.124192 | + | 0.992258i | \(0.539634\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 51.4937 | − | 89.1897i | 0.213667 | − | 0.370082i | −0.739193 | − | 0.673494i | \(-0.764793\pi\) |
0.952859 | + | 0.303412i | \(0.0981260\pi\) | |||||||
\(242\) | 39.3234 | + | 400.670i | 0.162493 | + | 1.65566i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 263.598 | − | 52.2444i | 1.08032 | − | 0.214116i | ||||
\(245\) | 6.01526 | − | 10.4187i | 0.0245521 | − | 0.0425255i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −92.3552 | + | 53.3213i | −0.373908 | + | 0.215876i | ||||
\(248\) | 314.948 | + | 295.592i | 1.26995 | + | 1.19190i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −31.5014 | − | 14.2861i | −0.126005 | − | 0.0571446i | ||||
\(251\) | 69.9866i | 0.278831i | 0.990234 | + | 0.139416i | \(0.0445224\pi\) | ||||
−0.990234 | + | 0.139416i | \(0.955478\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −297.699 | −1.17668 | ||||||||
\(254\) | −130.071 | + | 286.810i | −0.512091 | + | 1.12917i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −247.094 | − | 66.9379i | −0.965210 | − | 0.261476i | ||||
\(257\) | 48.5410 | + | 84.0754i | 0.188875 | + | 0.327142i | 0.944876 | − | 0.327430i | \(-0.106182\pi\) |
−0.756000 | + | 0.654571i | \(0.772849\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 264.803 | + | 152.884i | 1.02241 | + | 0.590287i | ||||
\(260\) | 217.976 | − | 43.2022i | 0.838368 | − | 0.166162i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −93.6684 | + | 9.19301i | −0.357513 | + | 0.0350878i | ||||
\(263\) | 7.27870 | + | 4.20236i | 0.0276757 | + | 0.0159785i | 0.513774 | − | 0.857926i | \(-0.328247\pi\) |
−0.486098 | + | 0.873904i | \(0.661580\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 28.3247 | + | 49.0599i | 0.106886 | + | 0.185132i | ||||
\(266\) | 155.449 | − | 111.312i | 0.584395 | − | 0.418467i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 262.064 | + | 89.1599i | 0.977852 | + | 0.332686i | ||||
\(269\) | −281.198 | −1.04535 | −0.522673 | − | 0.852533i | \(-0.675065\pi\) | ||||
−0.522673 | + | 0.852533i | \(0.675065\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 369.456i | 1.36331i | 0.731675 | + | 0.681654i | \(0.238739\pi\) | ||||
−0.731675 | + | 0.681654i | \(0.761261\pi\) | |||||||
\(272\) | −3.03285 | + | 22.7944i | −0.0111502 | + | 0.0838028i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 191.062 | − | 136.813i | 0.697305 | − | 0.499319i | ||||
\(275\) | 425.836 | − | 245.856i | 1.54849 | − | 0.894023i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −66.4546 | + | 115.103i | −0.239908 | + | 0.415533i | −0.960688 | − | 0.277631i | \(-0.910451\pi\) |
0.720779 | + | 0.693164i | \(0.243784\pi\) | |||||||
\(278\) | 79.0123 | − | 7.75459i | 0.284217 | − | 0.0278942i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −381.361 | + | 115.255i | −1.36200 | + | 0.411625i | ||||
\(281\) | 18.6577 | − | 32.3160i | 0.0663974 | − | 0.115004i | −0.830916 | − | 0.556398i | \(-0.812183\pi\) |
0.897313 | + | 0.441395i | \(0.145516\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −135.246 | + | 78.0842i | −0.477900 | + | 0.275916i | −0.719541 | − | 0.694450i | \(-0.755648\pi\) |
0.241641 | + | 0.970366i | \(0.422314\pi\) | |||||||
\(284\) | −21.5093 | + | 18.8370i | −0.0757371 | + | 0.0663275i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −113.821 | + | 250.979i | −0.397976 | + | 0.877548i | ||||
\(287\) | 392.113i | 1.36625i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −286.934 | −0.992853 | ||||||||
\(290\) | −494.414 | − | 224.221i | −1.70487 | − | 0.773176i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −211.987 | − | 242.061i | −0.725983 | − | 0.828975i | ||||
\(293\) | 12.9881 | + | 22.4961i | 0.0443280 | + | 0.0767784i | 0.887338 | − | 0.461119i | \(-0.152552\pi\) |
−0.843010 | + | 0.537898i | \(0.819219\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 140.489 | + | 81.1113i | 0.476233 | + | 0.274954i | ||||
\(296\) | 102.854 | + | 340.329i | 0.347481 | + | 1.14976i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −22.4314 | − | 228.556i | −0.0752733 | − | 0.766967i | ||||
\(299\) | −110.223 | − | 63.6373i | −0.368639 | − | 0.212834i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −232.616 | − | 402.903i | −0.772811 | − | 1.33855i | ||||
\(302\) | −186.446 | − | 260.374i | −0.617369 | − | 0.862164i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 220.367 | + | 29.3204i | 0.724893 | + | 0.0964488i | ||||
\(305\) | 486.262 | 1.59430 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 111.670i | 0.363745i | 0.983322 | + | 0.181872i | \(0.0582158\pi\) | ||||
−0.983322 | + | 0.181872i | \(0.941784\pi\) | |||||||
\(308\) | 159.137 | − | 467.745i | 0.516679 | − | 1.51865i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 455.041 | + | 635.470i | 1.46787 | + | 2.04990i | ||||
\(311\) | −280.368 | + | 161.871i | −0.901506 | + | 0.520485i | −0.877689 | − | 0.479232i | \(-0.840915\pi\) |
−0.0238176 | + | 0.999716i | \(0.507582\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 183.090 | − | 317.122i | 0.584953 | − | 1.01317i | −0.409928 | − | 0.912118i | \(-0.634446\pi\) |
0.994881 | − | 0.101050i | \(-0.0322203\pi\) | |||||||
\(314\) | −44.0195 | − | 448.519i | −0.140189 | − | 1.42840i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 36.4287 | + | 183.800i | 0.115281 | + | 0.581646i | ||||
\(317\) | 32.5014 | − | 56.2941i | 0.102528 | − | 0.177584i | −0.810197 | − | 0.586157i | \(-0.800640\pi\) |
0.912726 | + | 0.408573i | \(0.133973\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 583.059 | − | 336.629i | 1.82777 | − | 1.05526i | ||||
\(320\) | −415.039 | − | 205.741i | −1.29700 | − | 0.642940i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 207.811 | + | 94.2442i | 0.645376 | + | 0.292684i | ||||
\(323\) | − | 19.9690i | − | 0.0618235i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 210.221 | 0.646833 | ||||||||
\(326\) | −121.564 | + | 268.052i | −0.372895 | + | 0.822245i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −312.013 | + | 332.444i | −0.951258 | + | 1.01355i | ||||
\(329\) | 32.4560 | + | 56.2154i | 0.0986504 | + | 0.170867i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −380.566 | − | 219.720i | −1.14975 | − | 0.663807i | −0.200922 | − | 0.979607i | \(-0.564394\pi\) |
−0.948826 | + | 0.315800i | \(0.897727\pi\) | |||||||
\(332\) | −110.583 | − | 557.942i | −0.333080 | − | 1.68055i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −210.875 | + | 20.6962i | −0.631363 | + | 0.0619645i | ||||
\(335\) | 433.794 | + | 250.451i | 1.29491 | + | 0.747616i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 187.409 | + | 324.602i | 0.556109 | + | 0.963210i | 0.997816 | + | 0.0660503i | \(0.0210398\pi\) |
−0.441707 | + | 0.897159i | \(0.645627\pi\) | |||||||
\(338\) | 179.017 | − | 128.189i | 0.529637 | − | 0.379257i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −13.4023 | + | 39.3927i | −0.0394184 | + | 0.115861i | ||||
\(341\) | −969.295 | −2.84251 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 348.568i | − | 1.01623i | ||||||
\(344\) | 123.380 | − | 526.689i | 0.358663 | − | 1.53107i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −303.142 | + | 217.071i | −0.876134 | + | 0.627373i | ||||
\(347\) | 284.948 | − | 164.515i | 0.821177 | − | 0.474107i | −0.0296454 | − | 0.999560i | \(-0.509438\pi\) |
0.850822 | + | 0.525454i | \(0.176104\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −186.253 | + | 322.599i | −0.533676 | + | 0.924354i | 0.465550 | + | 0.885021i | \(0.345856\pi\) |
−0.999226 | + | 0.0393323i | \(0.987477\pi\) | |||||||
\(350\) | −375.090 | + | 36.8129i | −1.07169 | + | 0.105180i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 507.115 | − | 269.938i | 1.44067 | − | 0.766871i | ||||
\(353\) | 108.879 | − | 188.584i | 0.308440 | − | 0.534233i | −0.669582 | − | 0.742738i | \(-0.733527\pi\) |
0.978021 | + | 0.208505i | \(0.0668599\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −44.8056 | + | 25.8685i | −0.126213 | + | 0.0728691i | ||||
\(356\) | −110.967 | − | 126.710i | −0.311706 | − | 0.355926i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 158.267 | − | 348.983i | 0.442086 | − | 0.974812i | ||||
\(359\) | 145.576i | 0.405505i | 0.979230 | + | 0.202753i | \(0.0649887\pi\) | ||||
−0.979230 | + | 0.202753i | \(0.935011\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 167.947 | 0.465228 | ||||||||
\(362\) | 373.323 | + | 169.305i | 1.03128 | + | 0.467694i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 158.908 | − | 139.165i | 0.436559 | − | 0.382321i | ||||
\(365\) | −291.118 | − | 504.231i | −0.797583 | − | 1.38146i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 46.3123 | + | 26.7384i | 0.126192 | + | 0.0728568i | 0.561767 | − | 0.827295i | \(-0.310122\pi\) |
−0.435575 | + | 0.900152i | \(0.643455\pi\) | |||||||
\(368\) | 101.196 | + | 245.262i | 0.274989 | + | 0.666474i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 62.8380 | + | 640.263i | 0.169833 | + | 1.73044i | ||||
\(371\) | 46.6347 | + | 26.9246i | 0.125700 | + | 0.0725729i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 170.752 | + | 295.751i | 0.457781 | + | 0.792899i | 0.998843 | − | 0.0480829i | \(-0.0153112\pi\) |
−0.541063 | + | 0.840982i | \(0.681978\pi\) | |||||||
\(374\) | −30.0433 | − | 41.9558i | −0.0803296 | − | 0.112181i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −17.2147 | + | 73.4868i | −0.0457838 | + | 0.195444i | ||||
\(377\) | 287.837 | 0.763492 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 220.189i | − | 0.580972i | −0.956879 | − | 0.290486i | \(-0.906183\pi\) | ||
0.956879 | − | 0.290486i | \(-0.0938170\pi\) | |||||||
\(380\) | 380.834 | + | 129.568i | 1.00220 | + | 0.340969i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −104.581 | − | 146.048i | −0.273772 | − | 0.382326i | ||||
\(383\) | 581.167 | − | 335.537i | 1.51741 | − | 0.876075i | 0.517616 | − | 0.855613i | \(-0.326820\pi\) |
0.999791 | − | 0.0204616i | \(-0.00651358\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 447.018 | − | 774.257i | 1.16108 | − | 2.01106i | ||||
\(386\) | −32.7399 | − | 333.590i | −0.0848183 | − | 0.864222i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −246.782 | + | 48.9115i | −0.636036 | + | 0.126061i | ||||
\(389\) | 242.462 | − | 419.957i | 0.623296 | − | 1.07958i | −0.365572 | − | 0.930783i | \(-0.619127\pi\) |
0.988868 | − | 0.148797i | \(-0.0475401\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.6394 | − | 11.9162i | 0.0527862 | − | 0.0304761i | ||||
\(392\) | 9.09972 | − | 9.69560i | 0.0232136 | − | 0.0247337i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −337.472 | − | 153.046i | −0.856527 | − | 0.388442i | ||||
\(395\) | 339.058i | 0.858376i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −279.373 | −0.703711 | −0.351855 | − | 0.936054i | \(-0.614449\pi\) | ||||
−0.351855 | + | 0.936054i | \(0.614449\pi\) | |||||||
\(398\) | −113.684 | + | 250.677i | −0.285639 | + | 0.629842i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −347.304 | − | 267.256i | −0.868261 | − | 0.668140i | ||||
\(401\) | −291.099 | − | 504.199i | −0.725934 | − | 1.25735i | −0.958589 | − | 0.284795i | \(-0.908075\pi\) |
0.232655 | − | 0.972559i | \(-0.425259\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −358.882 | − | 207.200i | −0.890525 | − | 0.514145i | ||||
\(404\) | 186.823 | − | 37.0279i | 0.462434 | − | 0.0916531i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −513.577 | + | 50.4046i | −1.26497 | + | 0.124149i | ||||
\(407\) | −690.951 | − | 398.921i | −1.69767 | − | 0.980150i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 218.330 | + | 378.160i | 0.533815 | + | 0.924595i | 0.999220 | + | 0.0394972i | \(0.0125756\pi\) |
−0.465404 | + | 0.885098i | \(0.654091\pi\) | |||||||
\(410\) | −670.771 | + | 480.319i | −1.63603 | + | 1.17151i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −203.444 | − | 69.2162i | −0.493797 | − | 0.168000i | ||||
\(413\) | 154.203 | 0.373374 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 1029.24i | − | 2.48010i | ||||||
\(416\) | 245.463 | + | 8.45825i | 0.590054 | + | 0.0203323i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −405.613 | + | 290.447i | −0.970367 | + | 0.694850i | ||||
\(419\) | −656.682 | + | 379.135i | −1.56726 | + | 0.904858i | −0.570773 | + | 0.821108i | \(0.693356\pi\) |
−0.996487 | + | 0.0837495i | \(0.973310\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −261.674 | + | 453.232i | −0.621553 | + | 1.07656i | 0.367644 | + | 0.929967i | \(0.380165\pi\) |
−0.989197 | + | 0.146595i | \(0.953169\pi\) | |||||||
\(422\) | −607.588 | + | 59.6312i | −1.43978 | + | 0.141306i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 18.1137 | + | 59.9356i | 0.0427211 | + | 0.141358i | ||||
\(425\) | −19.6821 | + | 34.0904i | −0.0463108 | + | 0.0802126i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 400.299 | − | 231.112i | 0.937467 | − | 0.541247i | ||||
\(428\) | 79.6551 | − | 69.7588i | 0.186110 | − | 0.162988i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 404.286 | − | 891.462i | 0.940199 | − | 2.07317i | ||||
\(431\) | − | 729.146i | − | 1.69176i | −0.533377 | − | 0.845878i | \(-0.679077\pi\) | ||
0.533377 | − | 0.845878i | \(-0.320923\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −491.219 | −1.13445 | −0.567227 | − | 0.823561i | \(-0.691984\pi\) | ||||
−0.567227 | + | 0.823561i | \(0.691984\pi\) | |||||||
\(434\) | 676.625 | + | 306.855i | 1.55904 | + | 0.707040i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 218.901 | + | 249.956i | 0.502068 | + | 0.573293i | ||||
\(437\) | −115.201 | − | 199.534i | −0.263618 | − | 0.456600i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 163.413 | + | 94.3467i | 0.372240 | + | 0.214913i | 0.674436 | − | 0.738333i | \(-0.264387\pi\) |
−0.302197 | + | 0.953246i | \(0.597720\pi\) | |||||||
\(440\) | 995.087 | − | 300.735i | 2.26156 | − | 0.683489i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.15488 | − | 21.9563i | −0.00487530 | − | 0.0496749i | ||||
\(443\) | −357.848 | − | 206.604i | −0.807784 | − | 0.466375i | 0.0384015 | − | 0.999262i | \(-0.487773\pi\) |
−0.846186 | + | 0.532888i | \(0.821107\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −152.389 | − | 263.946i | −0.342448 | − | 0.593137i | ||||
\(446\) | 20.0537 | + | 28.0052i | 0.0449633 | + | 0.0627919i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −439.452 | + | 27.8925i | −0.980919 | + | 0.0622600i | ||||
\(449\) | 638.253 | 1.42150 | 0.710749 | − | 0.703446i | \(-0.248356\pi\) | ||||
0.710749 | + | 0.703446i | \(0.248356\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 1023.14i | − | 2.26861i | ||||||
\(452\) | 20.0052 | − | 58.8006i | 0.0442594 | − | 0.130090i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −47.7223 | − | 66.6448i | −0.105115 | − | 0.146795i | ||||
\(455\) | 331.017 | − | 191.112i | 0.727509 | − | 0.420027i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 115.344 | − | 199.781i | 0.252393 | − | 0.437157i | −0.711791 | − | 0.702391i | \(-0.752116\pi\) |
0.964184 | + | 0.265234i | \(0.0854492\pi\) | |||||||
\(458\) | 26.0699 | + | 265.629i | 0.0569213 | + | 0.579976i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 93.3386 | + | 470.938i | 0.202910 | + | 1.02378i | ||||
\(461\) | −200.094 | + | 346.573i | −0.434044 | + | 0.751786i | −0.997217 | − | 0.0745529i | \(-0.976247\pi\) |
0.563173 | + | 0.826339i | \(0.309580\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −256.912 | + | 148.328i | −0.554886 | + | 0.320363i | −0.751090 | − | 0.660200i | \(-0.770472\pi\) |
0.196205 | + | 0.980563i | \(0.437138\pi\) | |||||||
\(464\) | −475.533 | − | 365.930i | −1.02486 | − | 0.788642i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 670.920 | + | 304.268i | 1.43974 | + | 0.652936i | ||||
\(467\) | 127.057i | 0.272070i | 0.990704 | + | 0.136035i | \(0.0434359\pi\) | ||||
−0.990704 | + | 0.136035i | \(0.956564\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 476.141 | 1.01523 | ||||||||
\(470\) | −56.4084 | + | 124.382i | −0.120018 | + | 0.264643i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 130.738 | + | 122.703i | 0.276987 | + | 0.259964i | ||||
\(473\) | 606.965 | + | 1051.29i | 1.28322 | + | 2.22261i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 329.573 | + | 190.279i | 0.693837 | + | 0.400587i | ||||
\(476\) | 7.68977 | + | 38.7986i | 0.0161550 | + | 0.0815096i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −574.361 | + | 56.3701i | −1.20159 | + | 0.117929i | ||||
\(479\) | 10.6651 | + | 6.15749i | 0.0222653 | + | 0.0128549i | 0.511091 | − | 0.859526i | \(-0.329241\pi\) |
−0.488826 | + | 0.872381i | \(0.662575\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −170.550 | − | 295.401i | −0.354573 | − | 0.614139i | ||||
\(482\) | 167.467 | − | 119.918i | 0.347442 | − | 0.248793i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −259.344 | + | 762.281i | −0.535836 | + | 1.57496i | ||||
\(485\) | −455.241 | −0.938642 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 181.054i | 0.371773i | 0.982571 | + | 0.185887i | \(0.0595157\pi\) | ||||
−0.982571 | + | 0.185887i | \(0.940484\pi\) | |||||||
\(488\) | 523.285 | + | 122.582i | 1.07231 | + | 0.251194i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 19.5628 | − | 14.0083i | 0.0399240 | − | 0.0285884i | ||||
\(491\) | 430.484 | − | 248.540i | 0.876749 | − | 0.506191i | 0.00716404 | − | 0.999974i | \(-0.497720\pi\) |
0.869585 | + | 0.493783i | \(0.164386\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −26.9489 | + | 46.6769i | −0.0546631 | + | 0.0946792i | ||||
\(494\) | −212.265 | + | 20.8326i | −0.429687 | + | 0.0421712i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 329.490 | + | 798.565i | 0.664294 | + | 1.61001i | ||||
\(497\) | −24.5898 | + | 42.5907i | −0.0494764 | + | 0.0856956i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 660.403 | − | 381.284i | 1.32345 | − | 0.764096i | 0.339175 | − | 0.940723i | \(-0.389852\pi\) |
0.984278 | + | 0.176628i | \(0.0565189\pi\) | |||||||
\(500\) | −45.5770 | − | 52.0428i | −0.0911540 | − | 0.104086i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −57.8118 | + | 127.477i | −0.115163 | + | 0.253938i | ||||
\(503\) | 994.596i | 1.97733i | 0.150146 | + | 0.988664i | \(0.452026\pi\) | ||||
−0.150146 | + | 0.988664i | \(0.547974\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 344.635 | 0.682446 | ||||||||
\(506\) | −542.242 | − | 245.911i | −1.07162 | − | 0.485991i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −473.834 | + | 414.965i | −0.932744 | + | 0.816860i | ||||
\(509\) | 26.8655 | + | 46.5325i | 0.0527810 | + | 0.0914194i | 0.891209 | − | 0.453593i | \(-0.149858\pi\) |
−0.838428 | + | 0.545013i | \(0.816525\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −479.305 | − | 276.727i | −0.937975 | − | 0.541540i | ||||
\(512\) | −394.774 | − | 326.033i | −0.771043 | − | 0.636783i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18.9649 | + | 193.235i | 0.0368967 | + | 0.375944i | ||||
\(515\) | −336.761 | − | 194.429i | −0.653905 | − | 0.377532i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −84.6874 | − | 146.683i | −0.163805 | − | 0.283719i | ||||
\(518\) | 356.036 | + | 497.208i | 0.687327 | + | 0.959861i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 432.717 | + | 101.366i | 0.832148 | + | 0.194935i | ||||
\(521\) | −616.206 | −1.18274 | −0.591369 | − | 0.806401i | \(-0.701412\pi\) | ||||
−0.591369 | + | 0.806401i | \(0.701412\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 683.938i | 1.30772i | 0.756615 | + | 0.653860i | \(0.226852\pi\) | ||||
−0.756615 | + | 0.653860i | \(0.773148\pi\) | |||||||
\(524\) | −178.206 | − | 60.6294i | −0.340087 | − | 0.115705i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.78642 | + | 13.6669i | 0.0186054 | + | 0.0259826i | ||||
\(527\) | 67.2011 | − | 38.7986i | 0.127516 | − | 0.0736216i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −127.011 | + | 219.990i | −0.240097 | + | 0.415860i | ||||
\(530\) | 11.0665 | + | 112.757i | 0.0208801 | + | 0.212749i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 375.090 | − | 74.3418i | 0.705057 | − | 0.139740i | ||||
\(533\) | 218.711 | − | 378.818i | 0.410339 | − | 0.710728i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 165.928 | − | 95.7984i | 0.310145 | − | 0.179062i | ||||
\(536\) | 403.686 | + | 378.876i | 0.753145 | + | 0.706857i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −512.187 | − | 232.281i | −0.952020 | − | 0.431749i | ||||
\(539\) | 29.8395i | 0.0553608i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 518.000 | 0.957486 | 0.478743 | − | 0.877955i | \(-0.341093\pi\) | ||||
0.478743 | + | 0.877955i | \(0.341093\pi\) | |||||||
\(542\) | −305.186 | + | 672.944i | −0.563073 | + | 1.24159i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −24.3532 | + | 39.0134i | −0.0447670 | + | 0.0717158i | ||||
\(545\) | 300.613 | + | 520.677i | 0.551584 | + | 0.955371i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 254.839 | + | 147.131i | 0.465885 | + | 0.268979i | 0.714515 | − | 0.699620i | \(-0.246647\pi\) |
−0.248631 | + | 0.968598i | \(0.579981\pi\) | |||||||
\(548\) | 461.021 | − | 91.3732i | 0.841280 | − | 0.166739i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 978.723 | − | 96.0559i | 1.77950 | − | 0.174647i | ||||
\(551\) | 451.254 | + | 260.532i | 0.818974 | + | 0.472835i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 161.149 | + | 279.118i | 0.291408 | + | 0.504734i | ||||
\(554\) | −216.123 | + | 154.759i | −0.390113 | + | 0.279348i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 150.322 | + | 51.1428i | 0.270363 | + | 0.0919834i | ||||
\(557\) | −395.706 | −0.710424 | −0.355212 | − | 0.934786i | \(-0.615591\pi\) | ||||
−0.355212 | + | 0.934786i | \(0.615591\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 518.989i | 0.928424i | ||||||||
\(560\) | −789.834 | − | 105.089i | −1.41042 | − | 0.187660i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 60.6783 | − | 43.4499i | 0.107968 | − | 0.0773129i | ||||
\(563\) | −224.519 | + | 129.626i | −0.398791 | + | 0.230242i | −0.685962 | − | 0.727637i | \(-0.740618\pi\) |
0.287171 | + | 0.957879i | \(0.407285\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 56.1950 | − | 97.3325i | 0.0994601 | − | 0.172270i | ||||
\(566\) | −310.843 | + | 30.5074i | −0.549193 | + | 0.0539001i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −54.7382 | + | 16.5430i | −0.0963700 | + | 0.0291250i | ||||
\(569\) | −123.594 | + | 214.071i | −0.217213 | + | 0.376224i | −0.953955 | − | 0.299950i | \(-0.903030\pi\) |
0.736742 | + | 0.676174i | \(0.236363\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 520.747 | − | 300.654i | 0.911992 | − | 0.526539i | 0.0309205 | − | 0.999522i | \(-0.490156\pi\) |
0.881072 | + | 0.472983i | \(0.156823\pi\) | |||||||
\(572\) | −414.637 | + | 363.123i | −0.724891 | + | 0.634830i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −323.902 | + | 714.212i | −0.564288 | + | 1.24427i | ||||
\(575\) | 454.184i | 0.789885i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −754.648 | −1.30788 | −0.653941 | − | 0.756545i | \(-0.726886\pi\) | ||||
−0.653941 | + | 0.756545i | \(0.726886\pi\) | |||||||
\(578\) | −522.635 | − | 237.020i | −0.904213 | − | 0.410068i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −715.331 | − | 816.812i | −1.23333 | − | 1.40830i | ||||
\(581\) | −489.182 | − | 847.287i | −0.841965 | − | 1.45833i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −121.684 | − | 70.2543i | −0.208720 | − | 0.120505i | ||||
\(584\) | −186.171 | − | 616.010i | −0.318785 | − | 1.05481i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.07445 | + | 51.7040i | 0.00865946 | + | 0.0882321i | ||||
\(587\) | 211.142 | + | 121.903i | 0.359696 | + | 0.207671i | 0.668948 | − | 0.743310i | \(-0.266745\pi\) |
−0.309251 | + | 0.950980i | \(0.600078\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −375.090 | − | 649.675i | −0.636825 | − | 1.10301i | ||||
\(590\) | 188.891 | + | 263.789i | 0.320155 | + | 0.447100i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −93.7823 | + | 704.852i | −0.158416 | + | 1.19063i | ||||
\(593\) | 1091.73 | 1.84103 | 0.920516 | − | 0.390704i | \(-0.127768\pi\) | ||||
0.920516 | + | 0.390704i | \(0.127768\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 71.5722i | 0.120289i | ||||||||
\(596\) | 147.939 | − | 434.831i | 0.248220 | − | 0.729583i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −148.198 | − | 206.960i | −0.247823 | − | 0.346088i | ||||
\(599\) | 814.688 | − | 470.361i | 1.36008 | − | 0.785243i | 0.370447 | − | 0.928854i | \(-0.379205\pi\) |
0.989634 | + | 0.143611i | \(0.0458713\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −526.113 | + | 911.255i | −0.875396 | + | 1.51623i | −0.0190566 | + | 0.999818i | \(0.506066\pi\) |
−0.856340 | + | 0.516413i | \(0.827267\pi\) | |||||||
\(602\) | −90.8829 | − | 926.015i | −0.150968 | − | 1.53823i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −124.521 | − | 628.267i | −0.206160 | − | 1.04018i | ||||
\(605\) | −728.501 | + | 1261.80i | −1.20413 | + | 2.08562i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −380.876 | + | 219.899i | −0.627474 | + | 0.362272i | −0.779773 | − | 0.626062i | \(-0.784666\pi\) |
0.152299 | + | 0.988334i | \(0.451332\pi\) | |||||||
\(608\) | 377.167 | + | 235.438i | 0.620340 | + | 0.387233i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 885.700 | + | 401.673i | 1.45197 | + | 0.658480i | ||||
\(611\) | − | 72.4124i | − | 0.118515i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 449.866 | 0.733876 | 0.366938 | − | 0.930245i | \(-0.380406\pi\) | ||||
0.366938 | + | 0.930245i | \(0.380406\pi\) | |||||||
\(614\) | −92.2436 | + | 203.400i | −0.150234 | + | 0.331270i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 676.236 | − | 720.518i | 1.09779 | − | 1.16967i | ||||
\(617\) | 424.268 | + | 734.854i | 0.687630 | + | 1.19101i | 0.972602 | + | 0.232475i | \(0.0746823\pi\) |
−0.284972 | + | 0.958536i | \(0.591984\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 467.583 | + | 269.959i | 0.755384 | + | 0.436121i | 0.827636 | − | 0.561265i | \(-0.189685\pi\) |
−0.0722522 | + | 0.997386i | \(0.523019\pi\) | |||||||
\(620\) | 303.907 | + | 1533.35i | 0.490172 | + | 2.47315i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −644.387 | + | 63.2428i | −1.03599 | + | 0.101677i | ||||
\(623\) | −250.898 | − | 144.856i | −0.402726 | − | 0.232514i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 279.778 | + | 484.589i | 0.447644 | + | 0.775343i | ||||
\(626\) | 595.444 | − | 426.379i | 0.951188 | − | 0.681117i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 290.316 | − | 853.314i | 0.462286 | − | 1.35878i | ||||
\(629\) | 63.8714 | 0.101544 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 43.6036i | − | 0.0691024i | −0.999403 | − | 0.0345512i | \(-0.989000\pi\) | ||
0.999403 | − | 0.0345512i | \(-0.0110002\pi\) | |||||||
\(632\) | −85.4736 | + | 364.873i | −0.135243 | + | 0.577331i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 105.701 | − | 75.6891i | 0.166720 | − | 0.119383i | ||||
\(635\) | −987.033 | + | 569.864i | −1.55438 | + | 0.897423i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.37860 | + | 11.0481i | −0.0100135 | + | 0.0173439i | ||||
\(638\) | 1340.08 | − | 131.521i | 2.10043 | − | 0.206145i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −586.021 | − | 717.585i | −0.915657 | − | 1.12123i | ||||
\(641\) | 83.6313 | − | 144.854i | 0.130470 | − | 0.225981i | −0.793388 | − | 0.608716i | \(-0.791685\pi\) |
0.923858 | + | 0.382736i | \(0.125018\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −645.855 | + | 372.885i | −1.00444 | + | 0.579914i | −0.909559 | − | 0.415574i | \(-0.863581\pi\) |
−0.0948816 | + | 0.995489i | \(0.530247\pi\) | |||||||
\(644\) | 300.667 | + | 343.321i | 0.466874 | + | 0.533107i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 16.4952 | − | 36.3724i | 0.0255344 | − | 0.0563040i | ||||
\(647\) | − | 596.836i | − | 0.922467i | −0.887279 | − | 0.461233i | \(-0.847407\pi\) | ||
0.887279 | − | 0.461233i | \(-0.152593\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −402.363 | −0.619974 | ||||||||
\(650\) | 382.905 | + | 173.651i | 0.589085 | + | 0.267155i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −442.844 | + | 387.825i | −0.679208 | + | 0.594823i | ||||
\(653\) | 395.435 | + | 684.914i | 0.605567 | + | 1.04887i | 0.991962 | + | 0.126540i | \(0.0403871\pi\) |
−0.386394 | + | 0.922334i | \(0.626280\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −294.983 | − | 170.309i | −0.450356 | − | 0.260013i | ||||
\(656\) | −842.926 | + | 347.793i | −1.28495 | + | 0.530173i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 12.6805 | + | 129.203i | 0.0192713 | + | 0.196357i | ||||
\(659\) | 348.635 | + | 201.284i | 0.529036 | + | 0.305439i | 0.740624 | − | 0.671920i | \(-0.234530\pi\) |
−0.211588 | + | 0.977359i | \(0.567863\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −243.272 | − | 421.359i | −0.368036 | − | 0.637457i | 0.621222 | − | 0.783634i | \(-0.286636\pi\) |
−0.989258 | + | 0.146177i | \(0.953303\pi\) | |||||||
\(662\) | −511.682 | − | 714.571i | −0.772934 | − | 1.07941i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 259.463 | − | 1107.61i | 0.390757 | − | 1.66808i | ||||
\(665\) | 691.933 | 1.04050 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 621.873i | 0.932343i | ||||||||
\(668\) | −401.193 | − | 136.495i | −0.600589 | − | 0.204333i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 583.249 | + | 814.514i | 0.870521 | + | 1.21569i | ||||
\(671\) | −1044.50 | + | 603.042i | −1.55663 | + | 0.898721i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 85.8636 | − | 148.720i | 0.127583 | − | 0.220981i | −0.795156 | − | 0.606404i | \(-0.792611\pi\) |
0.922740 | + | 0.385423i | \(0.125945\pi\) | |||||||
\(674\) | 73.2205 | + | 746.051i | 0.108636 | + | 1.10690i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 431.959 | − | 85.6132i | 0.638993 | − | 0.126647i | ||||
\(677\) | −106.547 | + | 184.546i | −0.157382 | + | 0.272593i | −0.933924 | − | 0.357472i | \(-0.883639\pi\) |
0.776542 | + | 0.630065i | \(0.216972\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −374.761 | + | 216.369i | −0.551931 | + | 0.318658i | ||||
\(680\) | −56.9515 | + | 60.6809i | −0.0837522 | + | 0.0892365i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1765.52 | − | 800.677i | −2.58873 | − | 1.17401i | ||||
\(683\) | − | 602.265i | − | 0.881794i | −0.897558 | − | 0.440897i | \(-0.854660\pi\) | ||
0.897558 | − | 0.440897i | \(-0.145340\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 850.451 | 1.24153 | ||||||||
\(686\) | 287.931 | − | 634.897i | 0.419725 | − | 0.925506i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 659.796 | − | 857.418i | 0.959006 | − | 1.24625i | ||||
\(689\) | −30.0357 | − | 52.0233i | −0.0435931 | − | 0.0755055i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1062.89 | − | 613.657i | −1.53818 | − | 0.888071i | −0.998945 | − | 0.0459192i | \(-0.985378\pi\) |
−0.539240 | − | 0.842152i | \(-0.681288\pi\) | |||||||
\(692\) | −731.466 | + | 144.975i | −1.05703 | + | 0.209501i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 654.913 | − | 64.2759i | 0.943679 | − | 0.0926166i | ||||
\(695\) | 248.828 | + | 143.661i | 0.358025 | + | 0.206706i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 40.9539 | + | 70.9342i | 0.0587574 | + | 0.101771i | ||||
\(698\) | −605.729 | + | 433.744i | −0.867807 | + | 0.621410i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −713.614 | − | 242.787i | −1.01945 | − | 0.346839i | ||||
\(701\) | −133.314 | −0.190176 | −0.0950882 | − | 0.995469i | \(-0.530313\pi\) | ||||
−0.0950882 | + | 0.995469i | \(0.530313\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 617.485i | − | 0.878357i | ||||||
\(704\) | 1146.66 | − | 72.7798i | 1.62878 | − | 0.103380i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 354.095 | − | 253.557i | 0.501552 | − | 0.359146i | ||||
\(707\) | 283.709 | − | 163.799i | 0.401285 | − | 0.231682i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 305.128 | − | 528.497i | 0.430364 | − | 0.745412i | −0.566541 | − | 0.824034i | \(-0.691719\pi\) |
0.996905 | + | 0.0786216i | \(0.0250519\pi\) | |||||||
\(710\) | −102.979 | + | 10.1068i | −0.145041 | + | 0.0142349i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −97.4534 | − | 322.458i | −0.136873 | − | 0.452891i | ||||
\(713\) | 447.658 | − | 775.366i | 0.627851 | − | 1.08747i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −863.722 | + | 498.670i | −1.20800 | + | 0.697440i | ||||
\(716\) | 576.548 | − | 504.918i | 0.805235 | − | 0.705192i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −120.252 | + | 265.159i | −0.167482 | + | 0.369303i | ||||
\(719\) | − | 967.279i | − | 1.34531i | −0.739956 | − | 0.672656i | \(-0.765154\pi\) | ||
0.739956 | − | 0.672656i | \(-0.234846\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −369.635 | −0.512671 | ||||||||
\(722\) | 305.907 | + | 138.731i | 0.423693 | + | 0.192149i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 540.133 | + | 616.759i | 0.746040 | + | 0.851877i | ||||
\(725\) | −513.577 | − | 889.542i | −0.708382 | − | 1.22695i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1209.48 | + | 698.296i | 1.66366 | + | 0.960517i | 0.970942 | + | 0.239313i | \(0.0769223\pi\) |
0.692722 | + | 0.721204i | \(0.256411\pi\) | |||||||
\(728\) | 404.397 | − | 122.217i | 0.555490 | − | 0.167880i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −113.740 | − | 1158.90i | −0.155808 | − | 1.58754i | ||||
\(731\) | −84.1616 | − | 48.5907i | −0.115132 | − | 0.0664716i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 153.115 | + | 265.202i | 0.208888 | + | 0.361804i | 0.951364 | − | 0.308068i | \(-0.0996823\pi\) |
−0.742477 | + | 0.669872i | \(0.766349\pi\) | |||||||
\(734\) | 62.2683 | + | 86.9584i | 0.0848341 | + | 0.118472i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −18.2741 | + | 530.324i | −0.0248290 | + | 0.720548i | ||||
\(737\) | −1242.40 | −1.68575 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 463.182i | 0.626769i | 0.949626 | + | 0.313384i | \(0.101463\pi\) | ||||
−0.949626 | + | 0.313384i | \(0.898537\pi\) | |||||||
\(740\) | −414.427 | + | 1218.11i | −0.560037 | + | 1.64609i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 62.7017 | + | 87.5637i | 0.0845036 | + | 0.118010i | ||||
\(743\) | −702.085 | + | 405.349i | −0.944932 | + | 0.545557i | −0.891503 | − | 0.453015i | \(-0.850348\pi\) |
−0.0534291 | + | 0.998572i | \(0.517015\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 415.562 | − | 719.775i | 0.557802 | − | 0.966141i | ||||
\(746\) | 66.7128 | + | 679.743i | 0.0894273 | + | 0.911183i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −20.0649 | − | 101.237i | −0.0268248 | − | 0.135344i | ||||
\(749\) | 91.0628 | − | 157.725i | 0.121579 | − | 0.210581i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −858.169 | + | 495.464i | −1.14270 | + | 0.659739i | −0.947098 | − | 0.320944i | \(-0.896000\pi\) |
−0.195603 | + | 0.980683i | \(0.562666\pi\) | |||||||
\(752\) | −92.0587 | + | 119.632i | −0.122419 | + | 0.159085i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 524.278 | + | 237.765i | 0.695329 | + | 0.315338i | ||||
\(755\) | − | 1158.97i | − | 1.53506i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −320.001 | −0.422723 | −0.211361 | − | 0.977408i | \(-0.567790\pi\) | ||||
−0.211361 | + | 0.977408i | \(0.567790\pi\) | |||||||
\(758\) | 181.885 | − | 401.061i | 0.239953 | − | 0.529104i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 586.640 | + | 550.586i | 0.771894 | + | 0.724455i | ||||
\(761\) | −317.988 | − | 550.771i | −0.417855 | − | 0.723746i | 0.577868 | − | 0.816130i | \(-0.303885\pi\) |
−0.995723 | + | 0.0923836i | \(0.970551\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 494.939 | + | 285.753i | 0.648675 | + | 0.374512i | ||||
\(764\) | −69.8461 | − | 352.407i | −0.0914217 | − | 0.461266i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1335.73 | − | 131.094i | 1.74377 | − | 0.171141i | ||||
\(767\) | −148.975 | − | 86.0107i | −0.194231 | − | 0.112139i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −152.926 | − | 264.876i | −0.198864 | − | 0.344442i | 0.749297 | − | 0.662234i | \(-0.230392\pi\) |
−0.948160 | + | 0.317793i | \(0.897058\pi\) | |||||||
\(770\) | 1453.79 | − | 1041.01i | 1.88803 | − | 1.35196i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 215.925 | − | 634.659i | 0.279695 | − | 0.822097i | ||||
\(773\) | −187.263 | −0.242255 | −0.121128 | − | 0.992637i | \(-0.538651\pi\) | ||||
−0.121128 | + | 0.992637i | \(0.538651\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1478.80i | 1.90813i | ||||||||
\(776\) | −489.902 | − | 114.762i | −0.631317 | − | 0.147890i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 788.532 | − | 564.644i | 1.01354 | − | 0.725763i | ||||
\(779\) | 685.766 | − | 395.927i | 0.880315 | − | 0.508250i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 64.1621 | − | 111.132i | 0.0821537 | − | 0.142294i | ||||
\(782\) | 47.4368 | − | 4.65564i | 0.0606608 | − | 0.00595350i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 24.5836 | − | 10.1432i | 0.0313566 | − | 0.0129378i | ||||
\(785\) | 815.501 | − | 1412.49i | 1.03885 | − | 1.79935i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −160.626 | + | 92.7376i | −0.204099 | + | 0.117837i | −0.598566 | − | 0.801073i | \(-0.704263\pi\) |
0.394467 | + | 0.918910i | \(0.370929\pi\) | |||||||
\(788\) | −488.263 | − | 557.530i | −0.619623 | − | 0.707526i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −280.076 | + | 617.576i | −0.354527 | + | 0.781741i | ||||
\(791\) | − | 106.834i | − | 0.135062i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −515.634 | −0.650232 | ||||||||
\(794\) | −508.862 | − | 230.774i | −0.640885 | − | 0.290647i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −414.139 | + | 362.686i | −0.520275 | + | 0.455636i | ||||
\(797\) | −546.202 | − | 946.049i | −0.685322 | − | 1.18701i | −0.973336 | − | 0.229386i | \(-0.926328\pi\) |
0.288014 | − | 0.957626i | \(-0.407005\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.7427 | + | 6.77967i | 0.0146968 | + | 0.00848519i | ||||
\(800\) | −411.831 | − | 773.679i | −0.514789 | − | 0.967099i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −113.732 | − | 1158.83i | −0.141811 | − | 1.44493i | ||||
\(803\) | 1250.65 | + | 722.064i | 1.55747 | + | 0.899208i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 412.900 | + | 715.164i | 0.512919 | + | 0.888402i | ||||
\(806\) | −482.527 | − | 673.855i | −0.598668 | − | 0.836048i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 370.875 | + | 86.8794i | 0.459003 | + | 0.107524i | ||||
\(809\) | 51.1143 | 0.0631821 | 0.0315911 | − | 0.999501i | \(-0.489943\pi\) | ||||
0.0315911 | + | 0.999501i | \(0.489943\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 680.159i | − | 0.838667i | −0.907832 | − | 0.419333i | \(-0.862264\pi\) | ||
0.907832 | − | 0.419333i | \(-0.137736\pi\) | |||||||
\(812\) | −977.088 | − | 332.427i | −1.20331 | − | 0.409392i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −929.004 | − | 1297.37i | −1.14128 | − | 1.59382i | ||||
\(815\) | −922.477 | + | 532.593i | −1.13187 | + | 0.653488i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −469.757 | + | 813.643i | −0.574978 | + | 0.995891i | ||||
\(818\) | 85.3016 | + | 869.146i | 0.104281 | + | 1.06253i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1618.54 | + | 320.789i | −1.97382 | + | 0.391207i | ||||
\(821\) | −62.1337 | + | 107.619i | −0.0756805 | + | 0.131082i | −0.901382 | − | 0.433025i | \(-0.857446\pi\) |
0.825702 | + | 0.564107i | \(0.190780\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 959.409 | − | 553.915i | 1.16575 | − | 0.673044i | 0.213072 | − | 0.977036i | \(-0.431653\pi\) |
0.952674 | + | 0.303992i | \(0.0983197\pi\) | |||||||
\(824\) | −313.387 | − | 294.127i | −0.380324 | − | 0.356950i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 280.873 | + | 127.378i | 0.340040 | + | 0.154211i | ||||
\(827\) | 856.831i | 1.03607i | 0.855359 | + | 0.518036i | \(0.173337\pi\) | ||||
−0.855359 | + | 0.518036i | \(0.826663\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −59.5071 | −0.0717818 | −0.0358909 | − | 0.999356i | \(-0.511427\pi\) | ||||
−0.0358909 | + | 0.999356i | \(0.511427\pi\) | |||||||
\(830\) | 850.196 | − | 1874.71i | 1.02433 | − | 2.25868i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 440.109 | + | 218.168i | 0.528977 | + | 0.262221i | ||||
\(833\) | −1.19440 | − | 2.06877i | −0.00143386 | − | 0.00248351i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −664.094 | − | 383.415i | −0.795322 | − | 0.459179i | ||||
\(836\) | −978.723 | + | 193.980i | −1.17072 | + | 0.232034i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1509.29 | + | 148.128i | −1.80106 | + | 0.176764i | ||||
\(839\) | 402.435 | + | 232.346i | 0.479660 | + | 0.276932i | 0.720275 | − | 0.693689i | \(-0.244016\pi\) |
−0.240615 | + | 0.970621i | \(0.577349\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −282.695 | − | 489.643i | −0.336142 | − | 0.582215i | ||||
\(842\) | −851.012 | + | 609.384i | −1.01070 | + | 0.723734i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1155.94 | − | 393.277i | −1.36960 | − | 0.465969i | ||||
\(845\) | 796.840 | 0.943006 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1384.98i | 1.63516i | ||||||||
\(848\) | −16.5161 | + | 124.132i | −0.0194765 | + | 0.146382i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −64.0098 | + | 45.8355i | −0.0753057 | + | 0.0539241i | ||||
\(851\) | 638.216 | − | 368.474i | 0.749960 | − | 0.432990i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 683.164 | − | 1183.28i | 0.800896 | − | 1.38719i | −0.118131 | − | 0.992998i | \(-0.537690\pi\) |
0.919027 | − | 0.394195i | \(-0.128977\pi\) | |||||||
\(854\) | 920.029 | − | 90.2955i | 1.07732 | − | 0.105732i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 202.711 | − | 61.2633i | 0.236812 | − | 0.0715693i | ||||
\(857\) | −838.799 | + | 1452.84i | −0.978762 | + | 1.69527i | −0.311846 | + | 0.950133i | \(0.600947\pi\) |
−0.666916 | + | 0.745133i | \(0.732386\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1424.63 | + | 822.513i | −1.65848 | + | 0.957524i | −0.685063 | + | 0.728484i | \(0.740225\pi\) |
−0.973417 | + | 0.229039i | \(0.926442\pi\) | |||||||
\(860\) | 1472.77 | − | 1289.79i | 1.71252 | − | 1.49976i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 602.305 | − | 1328.10i | 0.698729 | − | 1.54072i | ||||
\(863\) | 294.311i | 0.341033i | 0.985355 | + | 0.170516i | \(0.0545436\pi\) | ||||
−0.985355 | + | 0.170516i | \(0.945456\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1349.34 | −1.55994 | ||||||||
\(866\) | −894.727 | − | 405.767i | −1.03317 | − | 0.468553i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 978.959 | + | 1117.84i | 1.12783 | + | 1.28783i | ||||
\(869\) | −420.486 | − | 728.303i | −0.483873 | − | 0.838093i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −459.997 | − | 265.579i | −0.528125 | − | 0.304913i | ||||
\(872\) | 192.243 | + | 636.102i | 0.220462 | + | 0.729475i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −45.0090 | − | 458.601i | −0.0514977 | − | 0.524715i | ||||
\(875\) | −103.050 | − | 59.4960i | −0.117772 | − | 0.0679955i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −359.584 | − | 622.818i | −0.410016 | − | 0.710169i | 0.584875 | − | 0.811124i | \(-0.301144\pi\) |
−0.994891 | + | 0.100954i | \(0.967810\pi\) | |||||||
\(878\) | 219.714 | + | 306.833i | 0.250244 | + | 0.349468i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2060.91 | + | 274.210i | 2.34195 | + | 0.311602i | ||||
\(881\) | 16.3083 | 0.0185112 | 0.00925559 | − | 0.999957i | \(-0.497054\pi\) | ||||
0.00925559 | + | 0.999957i | \(0.497054\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1190.35i | 1.34807i | 0.738698 | + | 0.674036i | \(0.235441\pi\) | ||||
−0.738698 | + | 0.674036i | \(0.764559\pi\) | |||||||
\(884\) | 14.2118 | − | 41.7722i | 0.0160767 | − | 0.0472536i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −481.138 | − | 671.915i | −0.543045 | − | 0.758369i | ||||
\(887\) | 346.987 | − | 200.333i | 0.391192 | − | 0.225855i | −0.291485 | − | 0.956575i | \(-0.594149\pi\) |
0.682676 | + | 0.730721i | \(0.260816\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −541.693 | + | 938.241i | −0.609329 | + | 1.05539i | ||||
\(890\) | −59.5384 | − | 606.643i | −0.0668971 | − | 0.681621i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13.3932 | + | 67.5750i | 0.0150148 | + | 0.0757567i | ||||
\(893\) | 65.5433 | − | 113.524i | 0.0733967 | − | 0.127127i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1200.99 | − | 693.394i | 1.34189 | − | 0.774742i | ||||
\(896\) | −823.477 | − | 312.201i | −0.919059 | − | 0.348438i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1162.54 | + | 527.223i | 1.29459 | + | 0.587108i | ||||
\(899\) | 2024.79i | 2.25227i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.2484 | 0.0124844 | ||||||||
\(902\) | 845.156 | − | 1863.59i | 0.936981 | − | 2.06607i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 85.0101 | − | 90.5769i | 0.0940378 | − | 0.100196i | ||||
\(905\) | 741.755 | + | 1284.76i | 0.819618 | + | 1.41962i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1091.40 | + | 630.121i | 1.20331 | + | 0.694731i | 0.961289 | − | 0.275541i | \(-0.0888569\pi\) |
0.242019 | + | 0.970271i | \(0.422190\pi\) | |||||||
\(908\) | −31.8722 | − | 160.810i | −0.0351015 | − | 0.177104i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 760.795 | − | 74.6675i | 0.836038 | − | 0.0820522i | ||||
\(911\) | 835.193 | + | 482.199i | 0.916788 | + | 0.529308i | 0.882609 | − | 0.470108i | \(-0.155785\pi\) |
0.0341788 | + | 0.999416i | \(0.489118\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1276.42 | + | 2210.83i | 1.39805 | + | 2.42150i | ||||
\(914\) | 375.119 | − | 268.611i | 0.410414 | − | 0.293885i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −171.936 | + | 505.363i | −0.187703 | + | 0.551707i | ||||
\(917\) | −323.779 | −0.353086 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 424.406i | 0.461813i | 0.972976 | + | 0.230906i | \(0.0741691\pi\) | ||||
−0.972976 | + | 0.230906i | \(0.925831\pi\) | |||||||
\(920\) | −219.003 | + | 934.888i | −0.238047 | + | 1.01618i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −650.744 | + | 465.978i | −0.705796 | + | 0.505399i | ||||
\(923\) | 47.5120 | − | 27.4311i | 0.0514756 | − | 0.0297195i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −608.613 | + | 1054.15i | −0.657960 | + | 1.13962i | ||||
\(926\) | −590.476 | + | 57.9517i | −0.637663 | + | 0.0625829i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −563.883 | − | 1059.33i | −0.607633 | − | 1.14152i | ||||
\(929\) | 429.229 | − | 743.447i | 0.462033 | − | 0.800265i | −0.537029 | − | 0.843564i | \(-0.680453\pi\) |
0.999062 | + | 0.0432985i | \(0.0137867\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.0001 | + | 11.5470i | −0.0214823 | + | 0.0124028i | ||||
\(932\) | 970.706 | + | 1108.41i | 1.04153 | + | 1.18929i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −104.954 | + | 231.426i | −0.112370 | + | 0.247780i | ||||
\(935\) | − | 186.753i | − | 0.199736i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 858.258 | 0.915964 | 0.457982 | − | 0.888962i | \(-0.348572\pi\) | ||||
0.457982 | + | 0.888962i | \(0.348572\pi\) | |||||||
\(938\) | 867.264 | + | 393.312i | 0.924589 | + | 0.419309i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −205.489 | + | 179.959i | −0.218606 | + | 0.191446i | ||||
\(941\) | 468.553 | + | 811.558i | 0.497931 | + | 0.862442i | 0.999997 | − | 0.00238755i | \(-0.000759981\pi\) |
−0.502066 | + | 0.864829i | \(0.667427\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 818.439 | + | 472.526i | 0.867910 | + | 0.501088i | ||||
\(944\) | 136.774 | + | 331.491i | 0.144888 | + | 0.351156i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 237.141 | + | 2416.25i | 0.250677 | + | 2.55418i | ||||
\(947\) | −768.302 | − | 443.580i | −0.811301 | − | 0.468405i | 0.0361062 | − | 0.999348i | \(-0.488505\pi\) |
−0.847408 | + | 0.530943i | \(0.821838\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 308.702 | + | 534.688i | 0.325292 | + | 0.563423i | ||||
\(950\) | 443.120 | + | 618.823i | 0.466442 | + | 0.651392i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −18.0427 | + | 77.0215i | −0.0189524 | + | 0.0809049i | ||||
\(953\) | 1078.46 | 1.13164 | 0.565821 | − | 0.824528i | \(-0.308559\pi\) | ||||
0.565821 | + | 0.824528i | \(0.308559\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 650.090i | − | 0.680722i | ||||||
\(956\) | −1092.73 | − | 371.770i | −1.14302 | − | 0.388881i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 14.3395 | + | 20.0253i | 0.0149682 | + | 0.0209033i | ||||
\(959\) | 700.104 | − | 404.205i | 0.730036 | − | 0.421486i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 977.056 | − | 1692.31i | 1.01671 | − | 1.76099i | ||||
\(962\) | −66.6337 | − | 678.937i | −0.0692658 | − | 0.705756i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 404.089 | − | 80.0894i | 0.419180 | − | 0.0830803i | ||||
\(965\) | 606.535 | − | 1050.55i | 0.628534 | − | 1.08865i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 103.113 | − | 59.5324i | 0.106632 | − | 0.0615640i | −0.445736 | − | 0.895165i | \(-0.647058\pi\) |
0.552368 | + | 0.833601i | \(0.313725\pi\) | |||||||
\(968\) | −1102.06 | + | 1174.22i | −1.13849 | + | 1.21304i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −829.196 | − | 376.048i | −0.854842 | − | 0.387678i | ||||
\(971\) | − | 1516.56i | − | 1.56185i | −0.624624 | − | 0.780926i | \(-0.714748\pi\) | ||
0.624624 | − | 0.780926i | \(-0.285252\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 273.118 | 0.280697 | ||||||||
\(974\) | −149.558 | + | 329.779i | −0.153550 | + | 0.338582i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 851.876 | + | 655.532i | 0.872824 | + | 0.671651i | ||||
\(977\) | −789.151 | − | 1366.85i | −0.807729 | − | 1.39903i | −0.914434 | − | 0.404736i | \(-0.867363\pi\) |
0.106705 | − | 0.994291i | \(-0.465970\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 654.669 | + | 377.974i | 0.668712 | + | 0.386081i | ||||
\(980\) | 47.2039 | − | 9.35568i | 0.0481672 | − | 0.00954661i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 989.406 | − | 97.1044i | 1.00754 | − | 0.0988843i | ||||
\(983\) | −513.330 | − | 296.371i | −0.522207 | − | 0.301497i | 0.215630 | − | 0.976475i | \(-0.430820\pi\) |
−0.737837 | + | 0.674979i | \(0.764153\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −670.522 | − | 1161.38i | −0.680733 | − | 1.17906i | ||||
\(986\) | −87.6429 | + | 62.7584i | −0.0888873 | + | 0.0636495i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −403.838 | − | 137.394i | −0.408743 | − | 0.139063i | ||||
\(989\) | −1121.28 | −1.13375 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1896.17i | − | 1.91339i | −0.291098 | − | 0.956693i | \(-0.594020\pi\) | ||
0.291098 | − | 0.956693i | \(-0.405980\pi\) | |||||||
\(992\) | −59.4998 | + | 1726.71i | −0.0599796 | + | 1.74064i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −79.9705 | + | 57.2644i | −0.0804532 | + | 0.0576101i | ||||
\(995\) | −862.683 | + | 498.070i | −0.867018 | + | 0.500573i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.8563 | + | 60.3729i | −0.0349612 | + | 0.0605546i | −0.882977 | − | 0.469417i | \(-0.844464\pi\) |
0.848015 | + | 0.529972i | \(0.177797\pi\) | |||||||
\(998\) | 1517.84 | − | 148.967i | 1.52088 | − | 0.149266i | ||||
\(999\) | 0 | 0 |
(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 | 324.3.f.r.55.6 | 12 | ||
3.2 | odd | 2 | 324.3.f.q.55.1 | 12 | |||
4.3 | odd | 2 | inner | 324.3.f.r.55.2 | 12 | ||
9.2 | odd | 6 | 324.3.d.f.163.4 | yes | 6 | ||
9.4 | even | 3 | inner | 324.3.f.r.271.2 | 12 | ||
9.5 | odd | 6 | 324.3.f.q.271.5 | 12 | |||
9.7 | even | 3 | 324.3.d.e.163.3 | ✓ | 6 | ||
12.11 | even | 2 | 324.3.f.q.55.5 | 12 | |||
36.7 | odd | 6 | 324.3.d.e.163.4 | yes | 6 | ||
36.11 | even | 6 | 324.3.d.f.163.3 | yes | 6 | ||
36.23 | even | 6 | 324.3.f.q.271.1 | 12 | |||
36.31 | odd | 6 | inner | 324.3.f.r.271.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
324.3.d.e.163.3 | ✓ | 6 | 9.7 | even | 3 | ||
324.3.d.e.163.4 | yes | 6 | 36.7 | odd | 6 | ||
324.3.d.f.163.3 | yes | 6 | 36.11 | even | 6 | ||
324.3.d.f.163.4 | yes | 6 | 9.2 | odd | 6 | ||
324.3.f.q.55.1 | 12 | 3.2 | odd | 2 | |||
324.3.f.q.55.5 | 12 | 12.11 | even | 2 | |||
324.3.f.q.271.1 | 12 | 36.23 | even | 6 | |||
324.3.f.q.271.5 | 12 | 9.5 | odd | 6 | |||
324.3.f.r.55.2 | 12 | 4.3 | odd | 2 | inner | ||
324.3.f.r.55.6 | 12 | 1.1 | even | 1 | trivial | ||
324.3.f.r.271.2 | 12 | 9.4 | even | 3 | inner | ||
324.3.f.r.271.6 | 12 | 36.31 | odd | 6 | inner |