Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [351,2,Mod(64,351)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(351, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("351.64");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 351 = 3^{3} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 351.t (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: | \(2.80274911095\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{20} - 6x^{16} + 9x^{14} + 54x^{12} + 81x^{10} + 486x^{8} + 729x^{6} - 4374x^{4} + 59049 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{9} \) |
Twist minimal: | no (minimal twist has level 117) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 181.6 | ||
Root | \(-0.219737 + 1.71806i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 351.181 |
Dual form | 351.2.t.c.64.6 |
$q$-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 \(\left(\mathbb{Z}/351\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(326\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.784270 | + | 0.452798i | 0.554562 | + | 0.320177i | 0.750960 | − | 0.660348i | \(-0.229591\pi\) |
−0.196398 | + | 0.980524i | \(0.562924\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.589947 | − | 1.02182i | −0.294974 | − | 0.510909i | ||||
\(5\) | −1.94254 | + | 1.12153i | −0.868732 | + | 0.501563i | −0.866927 | − | 0.498436i | \(-0.833908\pi\) |
−0.00180550 | + | 0.999998i | \(0.500575\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.97576 | − | 1.71806i | −1.12473 | − | 0.649364i | −0.182127 | − | 0.983275i | \(-0.558298\pi\) |
−0.942605 | + | 0.333911i | \(0.891632\pi\) | |||||||
\(8\) | − | 2.87970i | − | 1.01813i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.03130 | −0.642355 | ||||||||
\(11\) | −3.20133 | − | 1.84829i | −0.965236 | − | 0.557279i | −0.0674557 | − | 0.997722i | \(-0.521488\pi\) |
−0.897781 | + | 0.440443i | \(0.854821\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.351567 | − | 3.58837i | 0.0975072 | − | 0.995235i | ||||
\(14\) | −1.55587 | − | 2.69484i | −0.415823 | − | 0.720226i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.124029 | − | 0.214825i | 0.0310073 | − | 0.0537063i | ||||
\(17\) | 4.21120 | 1.02137 | 0.510683 | − | 0.859769i | \(-0.329393\pi\) | ||||
0.510683 | + | 0.859769i | \(0.329393\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.25298i | 0.975701i | 0.872927 | + | 0.487851i | \(0.162219\pi\) | ||||
−0.872927 | + | 0.487851i | \(0.837781\pi\) | |||||||
\(20\) | 2.29200 | + | 1.32329i | 0.512506 | + | 0.295896i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.67380 | − | 2.89911i | −0.356856 | − | 0.618092i | ||||
\(23\) | −1.89162 | − | 3.27639i | −0.394431 | − | 0.683174i | 0.598598 | − | 0.801050i | \(-0.295725\pi\) |
−0.993028 | + | 0.117876i | \(0.962392\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.0156524 | − | 0.0271108i | 0.00313048 | − | 0.00542215i | ||||
\(26\) | 1.90053 | − | 2.65506i | 0.372725 | − | 0.520700i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.05425i | 0.766181i | ||||||||
\(29\) | 1.18945 | − | 2.06020i | 0.220876 | − | 0.382569i | −0.734198 | − | 0.678935i | \(-0.762442\pi\) |
0.955074 | + | 0.296367i | \(0.0957750\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.37163 | + | 3.67866i | −1.14438 | + | 0.660707i | −0.947511 | − | 0.319723i | \(-0.896410\pi\) |
−0.196868 | + | 0.980430i | \(0.563077\pi\) | |||||||
\(32\) | −4.79325 | + | 2.76738i | −0.847334 | + | 0.489209i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.30272 | + | 1.90682i | 0.566411 | + | 0.327018i | ||||
\(35\) | 7.70739 | 1.30279 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 5.49928i | − | 0.904076i | −0.891999 | − | 0.452038i | \(-0.850697\pi\) | ||
0.891999 | − | 0.452038i | \(-0.149303\pi\) | |||||||
\(38\) | −1.92574 | + | 3.33549i | −0.312397 | + | 0.541087i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.22967 | + | 5.59395i | 0.510655 | + | 0.884481i | ||||
\(41\) | 6.86085 | − | 3.96111i | 1.07148 | − | 0.618622i | 0.142898 | − | 0.989737i | \(-0.454358\pi\) |
0.928587 | + | 0.371116i | \(0.121025\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.450266 | + | 0.779883i | −0.0686649 | + | 0.118931i | −0.898314 | − | 0.439354i | \(-0.855207\pi\) |
0.829649 | + | 0.558285i | \(0.188541\pi\) | |||||||
\(44\) | 4.36157i | 0.657531i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 3.42609i | − | 0.505150i | ||||||
\(47\) | 4.80060 | + | 2.77163i | 0.700239 | + | 0.404283i | 0.807436 | − | 0.589955i | \(-0.200854\pi\) |
−0.107197 | + | 0.994238i | \(0.534188\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.40343 | + | 4.16287i | 0.343347 | + | 0.594695i | ||||
\(50\) | 0.0245514 | − | 0.0141748i | 0.00347209 | − | 0.00200461i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.87407 | + | 1.75771i | −0.537237 | + | 0.243751i | ||||
\(53\) | −7.59566 | −1.04334 | −0.521672 | − | 0.853146i | \(-0.674692\pi\) | ||||
−0.521672 | + | 0.853146i | \(0.674692\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.29163 | 1.11804 | ||||||||
\(56\) | −4.94749 | + | 8.56930i | −0.661136 | + | 1.14512i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.86571 | − | 1.07717i | 0.244979 | − | 0.141439i | ||||
\(59\) | −4.44379 | + | 2.56562i | −0.578532 | + | 0.334016i | −0.760550 | − | 0.649279i | \(-0.775071\pi\) |
0.182018 | + | 0.983295i | \(0.441737\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.50907 | − | 11.2740i | 0.833401 | − | 1.44349i | −0.0619247 | − | 0.998081i | \(-0.519724\pi\) |
0.895326 | − | 0.445412i | \(-0.146943\pi\) | |||||||
\(62\) | −6.66277 | −0.846173 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.50838 | −0.688547 | ||||||||
\(65\) | 3.34152 | + | 7.36486i | 0.414465 | + | 0.913499i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.7002 | − | 6.75511i | 1.42941 | − | 0.825269i | 0.432333 | − | 0.901714i | \(-0.357690\pi\) |
0.997074 | + | 0.0764454i | \(0.0243571\pi\) | |||||||
\(68\) | −2.48439 | − | 4.30308i | −0.301276 | − | 0.521825i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.04468 | + | 3.48989i | 0.722477 | + | 0.417122i | ||||
\(71\) | − | 2.65506i | − | 0.315098i | −0.987511 | − | 0.157549i | \(-0.949641\pi\) | ||
0.987511 | − | 0.157549i | \(-0.0503592\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 5.45741i | − | 0.638741i | −0.947630 | − | 0.319371i | \(-0.896528\pi\) | ||
0.947630 | − | 0.319371i | \(-0.103472\pi\) | |||||||
\(74\) | 2.49006 | − | 4.31292i | 0.289464 | − | 0.501366i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.34578 | − | 2.50904i | 0.498495 | − | 0.287806i | ||||
\(77\) | 6.35092 | + | 11.0001i | 0.723755 | + | 1.25358i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.46886 | + | 9.47234i | −0.615294 | + | 1.06572i | 0.375038 | + | 0.927009i | \(0.377630\pi\) |
−0.990333 | + | 0.138712i | \(0.955704\pi\) | |||||||
\(80\) | 0.556410i | 0.0622085i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.17434 | 0.792273 | ||||||||
\(83\) | −0.465547 | − | 0.268784i | −0.0511004 | − | 0.0295029i | 0.474232 | − | 0.880400i | \(-0.342726\pi\) |
−0.525333 | + | 0.850897i | \(0.676059\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.18044 | + | 4.72298i | −0.887294 | + | 0.512279i | ||||
\(86\) | −0.706259 | + | 0.407759i | −0.0761579 | + | 0.0439698i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.32252 | + | 9.21887i | −0.567382 | + | 0.982735i | ||||
\(89\) | − | 5.75227i | − | 0.609739i | −0.952394 | − | 0.304870i | \(-0.901387\pi\) | ||
0.952394 | − | 0.304870i | \(-0.0986129\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.21120 | + | 10.0741i | −0.755939 | + | 1.05605i | ||||
\(92\) | −2.23192 | + | 3.86579i | −0.232693 | + | 0.403037i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.50998 | + | 4.34740i | 0.258884 | + | 0.448401i | ||||
\(95\) | −4.76984 | − | 8.26161i | −0.489375 | − | 0.847623i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.87585 | − | 3.39243i | −0.596603 | − | 0.344449i | 0.171101 | − | 0.985253i | \(-0.445267\pi\) |
−0.767704 | + | 0.640805i | \(0.778601\pi\) | |||||||
\(98\) | 4.35308i | 0.439727i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.0369364 | −0.00369364 | ||||||||
\(101\) | −2.48116 | + | 4.29749i | −0.246884 | + | 0.427616i | −0.962660 | − | 0.270715i | \(-0.912740\pi\) |
0.715776 | + | 0.698330i | \(0.246073\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.05587 | − | 1.82881i | −0.104038 | − | 0.180198i | 0.809307 | − | 0.587386i | \(-0.199843\pi\) |
−0.913345 | + | 0.407188i | \(0.866510\pi\) | |||||||
\(104\) | −10.3334 | − | 1.01241i | −1.01328 | − | 0.0992748i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.95705 | − | 3.43930i | −0.578600 | − | 0.334055i | ||||
\(107\) | 8.07404 | 0.780547 | 0.390274 | − | 0.920699i | \(-0.372380\pi\) | ||||
0.390274 | + | 0.920699i | \(0.372380\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 10.0020i | − | 0.958021i | −0.877809 | − | 0.479011i | \(-0.840996\pi\) | ||
0.877809 | − | 0.479011i | \(-0.159004\pi\) | |||||||
\(110\) | 6.50287 | + | 3.75443i | 0.620024 | + | 0.357971i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.738163 | + | 0.426179i | −0.0697498 | + | 0.0402701i | ||||
\(113\) | 9.71733 | + | 16.8309i | 0.914130 | + | 1.58332i | 0.808171 | + | 0.588948i | \(0.200458\pi\) |
0.105959 | + | 0.994371i | \(0.466209\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.34912 | + | 4.24302i | 0.685309 | + | 0.395664i | ||||
\(116\) | −2.80686 | −0.260611 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.64684 | −0.427776 | ||||||||
\(119\) | −12.5315 | − | 7.23508i | −1.14876 | − | 0.663238i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.33233 | + | 2.30766i | 0.121121 | + | 0.209787i | ||||
\(122\) | 10.2097 | − | 5.89459i | 0.924346 | − | 0.533671i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.51786 | + | 4.34044i | 0.675123 | + | 0.389783i | ||||
\(125\) | − | 11.1451i | − | 0.996845i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.76413 | −0.156541 | −0.0782704 | − | 0.996932i | \(-0.524940\pi\) | ||||
−0.0782704 | + | 0.996932i | \(0.524940\pi\) | |||||||
\(128\) | 5.26644 | + | 3.04058i | 0.465492 | + | 0.268752i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.714140 | + | 7.28907i | −0.0626342 | + | 0.639294i | ||||
\(131\) | −3.56490 | − | 6.17458i | −0.311466 | − | 0.539476i | 0.667214 | − | 0.744866i | \(-0.267487\pi\) |
−0.978680 | + | 0.205391i | \(0.934153\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.30686 | − | 12.6559i | 0.633585 | − | 1.09740i | ||||
\(134\) | 12.2348 | 1.05693 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 12.1270i | − | 1.03988i | ||||||
\(137\) | −3.91494 | − | 2.26029i | −0.334476 | − | 0.193110i | 0.323351 | − | 0.946279i | \(-0.395191\pi\) |
−0.657826 | + | 0.753170i | \(0.728524\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.05496 | − | 12.2195i | −0.598394 | − | 1.03645i | −0.993058 | − | 0.117623i | \(-0.962472\pi\) |
0.394664 | − | 0.918825i | \(-0.370861\pi\) | |||||||
\(140\) | −4.54696 | − | 7.87556i | −0.384288 | − | 0.665606i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.20221 | − | 2.08228i | 0.100887 | − | 0.174741i | ||||
\(143\) | −7.75782 | + | 10.8377i | −0.648741 | + | 0.906298i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.33603i | 0.443133i | ||||||||
\(146\) | 2.47111 | − | 4.28008i | 0.204510 | − | 0.354222i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.61927 | + | 3.24428i | −0.461901 | + | 0.266679i | ||||
\(149\) | 5.02499 | − | 2.90118i | 0.411663 | − | 0.237674i | −0.279841 | − | 0.960046i | \(-0.590282\pi\) |
0.691504 | + | 0.722372i | \(0.256948\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.44018 | + | 4.87294i | 0.686852 | + | 0.396554i | 0.802432 | − | 0.596744i | \(-0.203539\pi\) |
−0.115580 | + | 0.993298i | \(0.536873\pi\) | |||||||
\(152\) | 12.2473 | 0.993389 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 11.5027i | 0.926917i | ||||||||
\(155\) | 8.25145 | − | 14.2919i | 0.662773 | − | 1.14796i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.539798 | + | 0.934957i | 0.0430806 | + | 0.0746177i | 0.886762 | − | 0.462227i | \(-0.152949\pi\) |
−0.843681 | + | 0.536845i | \(0.819616\pi\) | |||||||
\(158\) | −8.57812 | + | 4.95258i | −0.682438 | + | 0.394006i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.20739 | − | 10.7515i | 0.490738 | − | 0.849982i | ||||
\(161\) | 12.9997i | 1.02452i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.54857i | 0.434598i | 0.976105 | + | 0.217299i | \(0.0697247\pi\) | ||||
−0.976105 | + | 0.217299i | \(0.930275\pi\) | |||||||
\(164\) | −8.09508 | − | 4.67370i | −0.632120 | − | 0.364954i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.243410 | − | 0.421598i | −0.0188923 | − | 0.0327223i | ||||
\(167\) | 11.5515 | − | 6.66925i | 0.893880 | − | 0.516082i | 0.0186702 | − | 0.999826i | \(-0.494057\pi\) |
0.875210 | + | 0.483744i | \(0.160723\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7528 | − | 2.52311i | −0.980985 | − | 0.194085i | ||||
\(170\) | −8.55423 | −0.656079 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.06253 | 0.0810173 | ||||||||
\(173\) | 3.72080 | − | 6.44461i | 0.282887 | − | 0.489975i | −0.689208 | − | 0.724564i | \(-0.742041\pi\) |
0.972095 | + | 0.234589i | \(0.0753745\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.0931556 | + | 0.0537834i | −0.00704190 | + | 0.00406564i | ||||
\(176\) | −0.794117 | + | 0.458484i | −0.0598588 | + | 0.0345595i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.60462 | − | 4.51133i | 0.195224 | − | 0.338138i | ||||
\(179\) | −23.2047 | −1.73440 | −0.867202 | − | 0.497957i | \(-0.834084\pi\) | ||||
−0.867202 | + | 0.497957i | \(0.834084\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.18439 | 0.385353 | 0.192676 | − | 0.981262i | \(-0.438283\pi\) | ||||
0.192676 | + | 0.981262i | \(0.438283\pi\) | |||||||
\(182\) | −10.2171 | + | 4.63560i | −0.757339 | + | 0.343614i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −9.43502 | + | 5.44731i | −0.695559 | + | 0.401581i | ||||
\(185\) | 6.16760 | + | 10.6826i | 0.453451 | + | 0.785400i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.4814 | − | 7.78351i | −0.985860 | − | 0.569186i | ||||
\(188\) | − | 6.54045i | − | 0.477012i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 8.63911i | − | 0.626747i | ||||||
\(191\) | 8.07057 | − | 13.9786i | 0.583966 | − | 1.01146i | −0.411037 | − | 0.911619i | \(-0.634833\pi\) |
0.995003 | − | 0.0998406i | \(-0.0318333\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.83991 | + | 1.63962i | −0.204421 | + | 0.118023i | −0.598716 | − | 0.800961i | \(-0.704322\pi\) |
0.394295 | + | 0.918984i | \(0.370989\pi\) | |||||||
\(194\) | −3.07217 | − | 5.32115i | −0.220569 | − | 0.382037i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.83580 | − | 4.91174i | 0.202557 | − | 0.350839i | ||||
\(197\) | 7.11249i | 0.506744i | 0.967369 | + | 0.253372i | \(0.0815396\pi\) | ||||
−0.967369 | + | 0.253372i | \(0.918460\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.8449 | −0.981437 | −0.490719 | − | 0.871318i | \(-0.663266\pi\) | ||||
−0.490719 | + | 0.871318i | \(0.663266\pi\) | |||||||
\(200\) | −0.0780709 | − | 0.0450743i | −0.00552045 | − | 0.00318723i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.89179 | + | 2.24693i | −0.273825 | + | 0.158093i | ||||
\(203\) | −7.07906 | + | 4.08710i | −0.496853 | + | 0.286858i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.88500 | + | 15.3893i | −0.620555 | + | 1.07483i | ||||
\(206\) | − | 1.91238i | − | 0.133242i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.727267 | − | 0.520589i | −0.0504269 | − | 0.0360963i | ||||
\(209\) | 7.86073 | − | 13.6152i | 0.543738 | − | 0.941782i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.21695 | − | 12.5001i | −0.496836 | − | 0.860545i | 0.503158 | − | 0.864195i | \(-0.332171\pi\) |
−0.999993 | + | 0.00365007i | \(0.998838\pi\) | |||||||
\(212\) | 4.48104 | + | 7.76139i | 0.307759 | + | 0.533055i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.33223 | + | 3.65591i | 0.432862 | + | 0.249913i | ||||
\(215\) | − | 2.01994i | − | 0.137759i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 25.2806 | 1.71616 | ||||||||
\(218\) | 4.52890 | − | 7.84429i | 0.306736 | − | 0.531283i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.89162 | − | 8.47254i | −0.329793 | − | 0.571219i | ||||
\(221\) | 1.48052 | − | 15.1113i | 0.0995905 | − | 1.01650i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.52959 | − | 5.50191i | −0.638149 | − | 0.368435i | 0.145752 | − | 0.989321i | \(-0.453440\pi\) |
−0.783901 | + | 0.620886i | \(0.786773\pi\) | |||||||
\(224\) | 19.0181 | 1.27070 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 17.6000i | 1.17073i | ||||||||
\(227\) | −7.03055 | − | 4.05909i | −0.466634 | − | 0.269411i | 0.248196 | − | 0.968710i | \(-0.420162\pi\) |
−0.714830 | + | 0.699299i | \(0.753496\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.65740 | − | 2.68895i | 0.307769 | − | 0.177691i | −0.338158 | − | 0.941089i | \(-0.609804\pi\) |
0.645928 | + | 0.763398i | \(0.276471\pi\) | |||||||
\(230\) | 3.84246 | + | 6.65534i | 0.253365 | + | 0.438840i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.93275 | − | 3.42528i | −0.389504 | − | 0.224880i | ||||
\(233\) | −20.0992 | −1.31675 | −0.658373 | − | 0.752692i | \(-0.728755\pi\) | ||||
−0.658373 | + | 0.752692i | \(0.728755\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.4338 | −0.811094 | ||||||||
\(236\) | 5.24321 | + | 3.02717i | 0.341304 | + | 0.197052i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.55206 | − | 11.3485i | −0.424707 | − | 0.735614i | ||||
\(239\) | −12.2635 | + | 7.08034i | −0.793261 | + | 0.457989i | −0.841109 | − | 0.540865i | \(-0.818097\pi\) |
0.0478485 | + | 0.998855i | \(0.484764\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.2041 | + | 15.1289i | 1.68795 | + | 0.974539i | 0.956084 | + | 0.293092i | \(0.0946842\pi\) |
0.731867 | + | 0.681447i | \(0.238649\pi\) | |||||||
\(242\) | 2.41310i | 0.155120i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −15.3600 | −0.983326 | ||||||||
\(245\) | −9.33754 | − | 5.39103i | −0.596554 | − | 0.344421i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.2613 | + | 1.49521i | 0.971052 | + | 0.0951379i | ||||
\(248\) | 10.5935 | + | 18.3484i | 0.672685 | + | 1.16512i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.04647 | − | 8.74074i | 0.319167 | − | 0.552813i | ||||
\(251\) | 17.5085 | 1.10512 | 0.552562 | − | 0.833472i | \(-0.313650\pi\) | ||||
0.552562 | + | 0.833472i | \(0.313650\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.9850i | 0.879232i | ||||||||
\(254\) | −1.38355 | − | 0.798793i | −0.0868117 | − | 0.0501208i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.26192 | + | 14.3101i | 0.516370 | + | 0.894379i | ||||
\(257\) | 9.15211 | + | 15.8519i | 0.570893 | + | 0.988815i | 0.996475 | + | 0.0838952i | \(0.0267361\pi\) |
−0.425582 | + | 0.904920i | \(0.639931\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.44807 | + | 16.3645i | −0.587074 | + | 1.01684i | ||||
\(260\) | 5.55423 | − | 7.75931i | 0.344459 | − | 0.481212i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 6.45672i | − | 0.398897i | ||||||
\(263\) | −4.19661 | + | 7.26875i | −0.258774 | + | 0.448210i | −0.965914 | − | 0.258864i | \(-0.916652\pi\) |
0.707140 | + | 0.707074i | \(0.249985\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.7549 | − | 8.51875i | 0.906387 | − | 0.523303i | ||||
\(266\) | 11.4611 | − | 6.61707i | 0.702725 | − | 0.405719i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −13.8050 | − | 7.97032i | −0.843275 | − | 0.486865i | ||||
\(269\) | −21.3238 | −1.30014 | −0.650069 | − | 0.759875i | \(-0.725260\pi\) | ||||
−0.650069 | + | 0.759875i | \(0.725260\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 18.4587i | − | 1.12129i | −0.828057 | − | 0.560643i | \(-0.810554\pi\) | ||
0.828057 | − | 0.560643i | \(-0.189446\pi\) | |||||||
\(272\) | 0.522312 | − | 0.904671i | 0.0316698 | − | 0.0548538i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.04691 | − | 3.54535i | −0.123658 | − | 0.214183i | ||||
\(275\) | −0.100217 | + | 0.0578603i | −0.00604331 | + | 0.00348911i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.31390 | − | 7.47189i | 0.259197 | − | 0.448943i | −0.706830 | − | 0.707383i | \(-0.749875\pi\) |
0.966027 | + | 0.258441i | \(0.0832087\pi\) | |||||||
\(278\) | − | 12.7779i | − | 0.766367i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − | 22.1950i | − | 1.32640i | ||||||
\(281\) | 3.00928 | + | 1.73741i | 0.179518 | + | 0.103645i | 0.587066 | − | 0.809539i | \(-0.300283\pi\) |
−0.407548 | + | 0.913184i | \(0.633616\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.89178 | + | 11.9369i | 0.409674 | + | 0.709576i | 0.994853 | − | 0.101328i | \(-0.0323091\pi\) |
−0.585179 | + | 0.810904i | \(0.698976\pi\) | |||||||
\(284\) | −2.71299 | + | 1.56635i | −0.160986 | + | 0.0929456i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10.9915 | + | 4.98699i | −0.649943 | + | 0.294887i | ||||
\(287\) | −27.2217 | −1.60684 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.734202 | 0.0431884 | ||||||||
\(290\) | −2.41615 | + | 4.18489i | −0.141881 | + | 0.245745i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.57648 | + | 3.21958i | −0.326339 | + | 0.188412i | ||||
\(293\) | 24.6911 | − | 14.2554i | 1.44247 | − | 0.832810i | 0.444455 | − | 0.895801i | \(-0.353397\pi\) |
0.998014 | + | 0.0629917i | \(0.0200642\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.75484 | − | 9.96768i | 0.335060 | − | 0.580341i | ||||
\(296\) | −15.8363 | −0.920465 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.25460 | 0.304391 | ||||||||
\(299\) | −12.4219 | + | 5.63597i | −0.718378 | + | 0.325937i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.67977 | − | 1.54716i | 0.154459 | − | 0.0891770i | ||||
\(302\) | 4.41292 | + | 7.64340i | 0.253935 | + | 0.439828i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.913648 | + | 0.527495i | 0.0524013 | + | 0.0302539i | ||||
\(305\) | 29.2004i | 1.67201i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.8137i | 1.24497i | 0.782631 | + | 0.622486i | \(0.213877\pi\) | ||||
−0.782631 | + | 0.622486i | \(0.786123\pi\) | |||||||
\(308\) | 7.49342 | − | 12.9790i | 0.426977 | − | 0.739546i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 12.9427 | − | 7.47249i | 0.735097 | − | 0.424409i | ||||
\(311\) | −3.48161 | − | 6.03032i | −0.197424 | − | 0.341948i | 0.750268 | − | 0.661133i | \(-0.229924\pi\) |
−0.947692 | + | 0.319185i | \(0.896591\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.2253 | + | 19.4428i | −0.634491 | + | 1.09897i | 0.352131 | + | 0.935951i | \(0.385457\pi\) |
−0.986623 | + | 0.163020i | \(0.947876\pi\) | |||||||
\(314\) | 0.977678i | 0.0551736i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.9054 | 0.725983 | ||||||||
\(317\) | −8.84739 | − | 5.10804i | −0.496919 | − | 0.286896i | 0.230522 | − | 0.973067i | \(-0.425957\pi\) |
−0.727440 | + | 0.686171i | \(0.759290\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.61567 | + | 4.39691i | −0.426395 | + | 0.246180i | ||||
\(320\) | 10.7003 | − | 6.17780i | 0.598163 | − | 0.345350i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.88622 | + | 10.1952i | −0.328026 | + | 0.568158i | ||||
\(323\) | 17.9102i | 0.996548i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.0917806 | − | 0.0656979i | −0.00509107 | − | 0.00364426i | ||||
\(326\) | −2.51239 | + | 4.35158i | −0.139148 | + | 0.241012i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −11.4068 | − | 19.7572i | −0.629836 | − | 1.09091i | ||||
\(329\) | −9.52362 | − | 16.4954i | −0.525054 | − | 0.909420i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.67794 | + | 2.70081i | 0.257123 | + | 0.148450i | 0.623021 | − | 0.782205i | \(-0.285905\pi\) |
−0.365898 | + | 0.930655i | \(0.619238\pi\) | |||||||
\(332\) | 0.634273i | 0.0348103i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.0793 | 0.660949 | ||||||||
\(335\) | −15.1521 | + | 26.2442i | −0.827848 | + | 1.43387i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.4621 | + | 28.5132i | 0.896749 | + | 1.55321i | 0.831625 | + | 0.555338i | \(0.187411\pi\) |
0.0651239 | + | 0.997877i | \(0.479256\pi\) | |||||||
\(338\) | −8.85918 | − | 7.75324i | −0.481876 | − | 0.421721i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9.65206 | + | 5.57262i | 0.523457 | + | 0.302218i | ||||
\(341\) | 27.1969 | 1.47279 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.53586i | 0.406898i | ||||||||
\(344\) | 2.24583 | + | 1.29663i | 0.121087 | + | 0.0699097i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.83622 | − | 3.36954i | 0.313757 | − | 0.181148i | ||||
\(347\) | 6.81390 | + | 11.8020i | 0.365789 | + | 0.633566i | 0.988902 | − | 0.148566i | \(-0.0474658\pi\) |
−0.623113 | + | 0.782132i | \(0.714132\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.76413 | + | 5.63732i | 0.522662 | + | 0.301759i | 0.738023 | − | 0.674776i | \(-0.235760\pi\) |
−0.215361 | + | 0.976534i | \(0.569093\pi\) | |||||||
\(350\) | −0.0974121 | −0.00520690 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 20.4597 | 1.09050 | ||||||||
\(353\) | 23.0629 | + | 13.3154i | 1.22751 | + | 0.708706i | 0.966509 | − | 0.256631i | \(-0.0826126\pi\) |
0.261005 | + | 0.965337i | \(0.415946\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.97773 | + | 5.15757i | 0.158041 | + | 0.273736i | ||||
\(356\) | −5.87778 | + | 3.39354i | −0.311522 | + | 0.179857i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −18.1988 | − | 10.5071i | −0.961835 | − | 0.555316i | ||||
\(359\) | 34.9036i | 1.84214i | 0.389396 | + | 0.921071i | \(0.372684\pi\) | ||||
−0.389396 | + | 0.921071i | \(0.627316\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.912132 | 0.0480069 | ||||||||
\(362\) | 4.06596 | + | 2.34748i | 0.213702 | + | 0.123381i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 14.5482 | + | 1.42534i | 0.762530 | + | 0.0747082i | ||||
\(365\) | 6.12064 | + | 10.6013i | 0.320369 | + | 0.554895i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.35716 | − | 2.35068i | 0.0708434 | − | 0.122704i | −0.828428 | − | 0.560096i | \(-0.810764\pi\) |
0.899271 | + | 0.437392i | \(0.144098\pi\) | |||||||
\(368\) | −0.938467 | −0.0489210 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 11.1707i | 0.580737i | ||||||||
\(371\) | 22.6029 | + | 13.0498i | 1.17348 | + | 0.677510i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.875481 | + | 1.51638i | 0.0453307 | + | 0.0785150i | 0.887800 | − | 0.460229i | \(-0.152233\pi\) |
−0.842470 | + | 0.538744i | \(0.818899\pi\) | |||||||
\(374\) | −7.04872 | − | 12.2087i | −0.364480 | − | 0.631299i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.98146 | − | 13.8243i | 0.411612 | − | 0.712933i | ||||
\(377\) | −6.97457 | − | 4.99250i | −0.359209 | − | 0.257127i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.90941i | 0.149446i | 0.997204 | + | 0.0747231i | \(0.0238073\pi\) | ||||
−0.997204 | + | 0.0747231i | \(0.976193\pi\) | |||||||
\(380\) | −5.62791 | + | 9.74783i | −0.288706 | + | 0.500053i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 12.6590 | − | 7.30868i | 0.647691 | − | 0.373945i | ||||
\(383\) | −17.7065 | + | 10.2229i | −0.904760 | + | 0.522363i | −0.878741 | − | 0.477298i | \(-0.841616\pi\) |
−0.0260185 | + | 0.999661i | \(0.508283\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −24.6739 | − | 14.2455i | −1.25750 | − | 0.726017i | ||||
\(386\) | −2.96968 | −0.151152 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8.00541i | 0.406413i | ||||||||
\(389\) | 6.48161 | − | 11.2265i | 0.328631 | − | 0.569205i | −0.653610 | − | 0.756832i | \(-0.726746\pi\) |
0.982240 | + | 0.187627i | \(0.0600795\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.96600 | − | 13.7975i | −0.402858 | − | 0.697771i | ||||
\(392\) | 11.9878 | − | 6.92117i | 0.605476 | − | 0.349572i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.22052 | + | 5.57811i | −0.162248 | + | 0.281021i | ||||
\(395\) | − | 24.5339i | − | 1.23444i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 29.1809i | − | 1.46455i | −0.681010 | − | 0.732274i | \(-0.738459\pi\) | ||
0.681010 | − | 0.732274i | \(-0.261541\pi\) | |||||||
\(398\) | −10.8581 | − | 6.26894i | −0.544268 | − | 0.314233i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.00388271 | − | 0.00672506i | −0.000194136 | − | 0.000336253i | ||||
\(401\) | −19.2018 | + | 11.0862i | −0.958894 | + | 0.553617i | −0.895832 | − | 0.444392i | \(-0.853420\pi\) |
−0.0630612 | + | 0.998010i | \(0.520086\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.9603 | + | 24.1571i | 0.545974 | + | 1.20335i | ||||
\(404\) | 5.85500 | 0.291297 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.40253 | −0.367381 | ||||||||
\(407\) | −10.1642 | + | 17.6050i | −0.503823 | + | 0.872647i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.81749 | + | 1.04933i | −0.0898689 | + | 0.0518858i | −0.544261 | − | 0.838916i | \(-0.683190\pi\) |
0.454392 | + | 0.890802i | \(0.349857\pi\) | |||||||
\(410\) | −13.9365 | + | 8.04623i | −0.688273 | + | 0.397375i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.24581 | + | 2.15781i | −0.0613767 | + | 0.106307i | ||||
\(413\) | 17.6315 | 0.867591 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.20579 | 0.0591901 | ||||||||
\(416\) | 8.24524 | + | 18.1729i | 0.404256 | + | 0.890998i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 12.3299 | − | 7.11865i | 0.603074 | − | 0.348185i | ||||
\(419\) | 0.195699 | + | 0.338961i | 0.00956053 | + | 0.0165593i | 0.870766 | − | 0.491697i | \(-0.163623\pi\) |
−0.861206 | + | 0.508257i | \(0.830290\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.59987 | + | 5.54249i | 0.467869 | + | 0.270124i | 0.715347 | − | 0.698769i | \(-0.246269\pi\) |
−0.247478 | + | 0.968893i | \(0.579602\pi\) | |||||||
\(422\) | − | 13.0713i | − | 0.636301i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 21.8732i | 1.06226i | ||||||||
\(425\) | 0.0659154 | − | 0.114169i | 0.00319737 | − | 0.00553800i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −38.7389 | + | 22.3659i | −1.87470 | + | 1.08236i | ||||
\(428\) | −4.76326 | − | 8.25021i | −0.230241 | − | 0.398789i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.914627 | − | 1.58418i | 0.0441072 | − | 0.0763960i | ||||
\(431\) | − | 36.4573i | − | 1.75609i | −0.478580 | − | 0.878044i | \(-0.658848\pi\) | ||
0.478580 | − | 0.878044i | \(-0.341152\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.82757 | 0.424226 | 0.212113 | − | 0.977245i | \(-0.431966\pi\) | ||||
0.212113 | + | 0.977245i | \(0.431966\pi\) | |||||||
\(434\) | 19.8268 | + | 11.4470i | 0.951717 | + | 0.549474i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.2203 | + | 5.90067i | −0.489462 | + | 0.282591i | ||||
\(437\) | 13.9344 | − | 8.04504i | 0.666574 | − | 0.384847i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.5672 | − | 30.4273i | 0.838438 | − | 1.45222i | −0.0527626 | − | 0.998607i | \(-0.516803\pi\) |
0.891200 | − | 0.453610i | \(-0.149864\pi\) | |||||||
\(440\) | − | 23.8774i | − | 1.13831i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.00352 | − | 11.1810i | 0.380688 | − | 0.531826i | ||||
\(443\) | 11.9526 | − | 20.7025i | 0.567885 | − | 0.983606i | −0.428890 | − | 0.903357i | \(-0.641095\pi\) |
0.996775 | − | 0.0802490i | \(-0.0255715\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.45133 | + | 11.1740i | 0.305822 | + | 0.529700i | ||||
\(446\) | −4.98251 | − | 8.62997i | −0.235929 | − | 0.408641i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 16.3916 | + | 9.46370i | 0.774431 | + | 0.447118i | ||||
\(449\) | − | 13.9683i | − | 0.659206i | −0.944120 | − | 0.329603i | \(-0.893085\pi\) | ||
0.944120 | − | 0.329603i | \(-0.106915\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29.2851 | −1.37898 | ||||||||
\(452\) | 11.4654 | − | 19.8587i | 0.539288 | − | 0.934075i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.67590 | − | 6.36684i | −0.172518 | − | 0.298811i | ||||
\(455\) | 2.70967 | − | 27.6570i | 0.127031 | − | 1.29658i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.0872 | + | 8.71058i | 0.705748 | + | 0.407464i | 0.809485 | − | 0.587141i | \(-0.199747\pi\) |
−0.103737 | + | 0.994605i | \(0.533080\pi\) | |||||||
\(458\) | 4.87021 | 0.227570 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 10.0126i | − | 0.466841i | ||||||
\(461\) | −20.6691 | − | 11.9333i | −0.962658 | − | 0.555791i | −0.0656678 | − | 0.997842i | \(-0.520918\pi\) |
−0.896990 | + | 0.442051i | \(0.854251\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.12555 | + | 5.26864i | −0.424100 | + | 0.244854i | −0.696830 | − | 0.717236i | \(-0.745407\pi\) |
0.272730 | + | 0.962091i | \(0.412074\pi\) | |||||||
\(464\) | −0.295055 | − | 0.511049i | −0.0136976 | − | 0.0237249i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15.7632 | − | 9.10090i | −0.730217 | − | 0.421591i | ||||
\(467\) | 8.40923 | 0.389133 | 0.194566 | − | 0.980889i | \(-0.437670\pi\) | ||||
0.194566 | + | 0.980889i | \(0.437670\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −46.4227 | −2.14360 | ||||||||
\(470\) | −9.75148 | − | 5.63002i | −0.449802 | − | 0.259693i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.38823 | + | 12.7968i | 0.340071 | + | 0.589020i | ||||
\(473\) | 2.88290 | − | 1.66444i | 0.132556 | − | 0.0765310i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.115302 | + | 0.0665694i | 0.00529040 | + | 0.00305441i | ||||
\(476\) | 17.0733i | 0.782551i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12.8239 | −0.586550 | ||||||||
\(479\) | 13.6025 | + | 7.85338i | 0.621512 | + | 0.358830i | 0.777457 | − | 0.628935i | \(-0.216509\pi\) |
−0.155945 | + | 0.987766i | \(0.549842\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19.7334 | − | 1.93337i | −0.899768 | − | 0.0881539i | ||||
\(482\) | 13.7007 | + | 23.7303i | 0.624050 | + | 1.08089i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.57201 | − | 2.72280i | 0.0714549 | − | 0.123764i | ||||
\(485\) | 15.2188 | 0.691051 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 37.8948i | − | 1.71718i | −0.512666 | − | 0.858588i | \(-0.671342\pi\) | ||
0.512666 | − | 0.858588i | \(-0.328658\pi\) | |||||||
\(488\) | −32.4659 | − | 18.7442i | −1.46966 | − | 0.848509i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.88210 | − | 8.45605i | −0.220551 | − | 0.382005i | ||||
\(491\) | −1.88027 | − | 3.25672i | −0.0848553 | − | 0.146974i | 0.820474 | − | 0.571684i | \(-0.193709\pi\) |
−0.905330 | + | 0.424710i | \(0.860376\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.00903 | − | 8.67590i | 0.225595 | − | 0.390743i | ||||
\(494\) | 11.2919 | + | 8.08293i | 0.508048 | + | 0.363668i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.82505i | 0.0819471i | ||||||||
\(497\) | −4.56154 | + | 7.90082i | −0.204613 | + | 0.354400i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.15464 | + | 4.13073i | −0.320286 | + | 0.184917i | −0.651520 | − | 0.758632i | \(-0.725868\pi\) |
0.331234 | + | 0.943549i | \(0.392535\pi\) | |||||||
\(500\) | −11.3882 | + | 6.57500i | −0.509298 | + | 0.294043i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.7314 | + | 7.92780i | 0.612860 | + | 0.353835i | ||||
\(503\) | 12.9954 | 0.579434 | 0.289717 | − | 0.957112i | \(-0.406439\pi\) | ||||
0.289717 | + | 0.957112i | \(0.406439\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 11.1307i | − | 0.495312i | ||||||
\(506\) | −6.33241 | + | 10.9680i | −0.281510 | + | 0.487589i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.04074 | + | 1.80262i | 0.0461754 | + | 0.0799782i | ||||
\(509\) | −23.2712 | + | 13.4356i | −1.03148 | + | 0.595524i | −0.917408 | − | 0.397949i | \(-0.869722\pi\) |
−0.114070 | + | 0.993473i | \(0.536389\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.37613 | + | 16.2399i | −0.414776 | + | 0.718413i | ||||
\(512\) | 2.80162i | 0.123815i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 16.5762i | 0.731146i | ||||||||
\(515\) | 4.10213 | + | 2.36837i | 0.180761 | + | 0.104363i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.2455 | − | 17.7458i | −0.450597 | − | 0.780458i | ||||
\(518\) | −14.8197 | + | 8.55614i | −0.651139 | + | 0.375935i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 21.2086 | − | 9.62260i | 0.930059 | − | 0.421979i | ||||
\(521\) | −14.2080 | −0.622464 | −0.311232 | − | 0.950334i | \(-0.600742\pi\) | ||||
−0.311232 | + | 0.950334i | \(0.600742\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.07846 | 0.309519 | 0.154760 | − | 0.987952i | \(-0.450540\pi\) | ||||
0.154760 | + | 0.987952i | \(0.450540\pi\) | |||||||
\(524\) | −4.20620 | + | 7.28536i | −0.183749 | + | 0.318262i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.58255 | + | 3.80044i | −0.287013 | + | 0.165707i | ||||
\(527\) | −26.8322 | + | 15.4916i | −1.16883 | + | 0.674824i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.34352 | − | 7.52320i | 0.188849 | − | 0.327096i | ||||
\(530\) | 15.4291 | 0.670198 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −17.2427 | −0.747564 | ||||||||
\(533\) | −11.8019 | − | 26.0119i | −0.511197 | − | 1.12670i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.6842 | + | 9.05527i | −0.678086 | + | 0.391493i | ||||
\(536\) | −19.4527 | − | 33.6931i | −0.840229 | − | 1.45532i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −16.7236 | − | 9.65540i | −0.721007 | − | 0.416274i | ||||
\(539\) | − | 17.7689i | − | 0.765362i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.18897i | 0.309078i | 0.987987 | + | 0.154539i | \(0.0493892\pi\) | ||||
−0.987987 | + | 0.154539i | \(0.950611\pi\) | |||||||
\(542\) | 8.35807 | − | 14.4766i | 0.359010 | − | 0.621823i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −20.1853 | + | 11.6540i | −0.865438 | + | 0.499661i | ||||
\(545\) | 11.2176 | + | 19.4294i | 0.480508 | + | 0.832264i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.8887 | − | 27.5201i | 0.679353 | − | 1.17667i | −0.295823 | − | 0.955243i | \(-0.595594\pi\) |
0.975176 | − | 0.221431i | \(-0.0710729\pi\) | |||||||
\(548\) | 5.33381i | 0.227849i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.104796 | −0.00446852 | ||||||||
\(551\) | 8.76198 | + | 5.05873i | 0.373273 | + | 0.215509i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 32.5480 | − | 18.7916i | 1.38408 | − | 0.799100i | ||||
\(554\) | 6.76652 | − | 3.90665i | 0.287482 | − | 0.165978i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.32411 | + | 14.4178i | −0.353021 | + | 0.611450i | ||||
\(557\) | 32.2223i | 1.36530i | 0.730745 | + | 0.682650i | \(0.239173\pi\) | ||||
−0.730745 | + | 0.682650i | \(0.760827\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.64021 | + | 1.88990i | 0.111669 | + | 0.0799343i | ||||
\(560\) | 0.955943 | − | 1.65574i | 0.0403960 | − | 0.0699679i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.57339 | + | 2.72519i | 0.0663694 | + | 0.114955i | ||||
\(563\) | −16.8257 | − | 29.1430i | −0.709119 | − | 1.22823i | −0.965184 | − | 0.261571i | \(-0.915760\pi\) |
0.256065 | − | 0.966659i | \(-0.417574\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −37.7527 | − | 21.7965i | −1.58827 | − | 0.916987i | ||||
\(566\) | 12.4824i | 0.524672i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.64578 | −0.320810 | ||||||||
\(569\) | −5.66793 | + | 9.81715i | −0.237612 | + | 0.411556i | −0.960029 | − | 0.279902i | \(-0.909698\pi\) |
0.722416 | + | 0.691458i | \(0.243031\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.127260 | + | 0.220421i | 0.00532568 | + | 0.00922435i | 0.868676 | − | 0.495381i | \(-0.164971\pi\) |
−0.863350 | + | 0.504605i | \(0.831638\pi\) | |||||||
\(572\) | 15.6509 | + | 1.53338i | 0.654398 | + | 0.0641140i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −21.3491 | − | 12.3259i | −0.891095 | − | 0.514474i | ||||
\(575\) | −0.118434 | −0.00493903 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 1.91400i | − | 0.0796807i | −0.999206 | − | 0.0398403i | \(-0.987315\pi\) | ||
0.999206 | − | 0.0398403i | \(-0.0126849\pi\) | |||||||
\(578\) | 0.575812 | + | 0.332445i | 0.0239506 | + | 0.0138279i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.45246 | − | 3.14798i | 0.226401 | − | 0.130713i | ||||
\(581\) | 0.923571 | + | 1.59967i | 0.0383162 | + | 0.0663656i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.3162 | + | 14.0390i | 1.00707 | + | 0.581435i | ||||
\(584\) | −15.7157 | −0.650321 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 25.8193 | 1.06659 | ||||||||
\(587\) | 7.69412 | + | 4.44220i | 0.317570 | + | 0.183349i | 0.650309 | − | 0.759670i | \(-0.274639\pi\) |
−0.332739 | + | 0.943019i | \(0.607973\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.6453 | − | 27.0984i | −0.644653 | − | 1.11657i | ||||
\(590\) | 9.02670 | − | 5.21156i | 0.371623 | − | 0.214557i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.18138 | − | 0.682072i | −0.0485545 | − | 0.0280330i | ||||
\(593\) | − | 43.1136i | − | 1.77046i | −0.465152 | − | 0.885231i | \(-0.654000\pi\) | ||
0.465152 | − | 0.885231i | \(-0.346000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 32.4574 | 1.33062 | ||||||||
\(596\) | −5.92896 | − | 3.42309i | −0.242860 | − | 0.140215i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −12.2941 | − | 1.20450i | −0.502743 | − | 0.0492558i | ||||
\(599\) | −5.59868 | − | 9.69720i | −0.228756 | − | 0.396217i | 0.728684 | − | 0.684850i | \(-0.240132\pi\) |
−0.957440 | + | 0.288634i | \(0.906799\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.96273 | + | 5.13159i | −0.120852 | + | 0.209322i | −0.920104 | − | 0.391674i | \(-0.871896\pi\) |
0.799252 | + | 0.600996i | \(0.205229\pi\) | |||||||
\(602\) | 2.80221 | 0.114210 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 11.4991i | − | 0.467892i | ||||||
\(605\) | −5.17622 | − | 2.98849i | −0.210443 | − | 0.121499i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.53470 | − | 4.39022i | −0.102880 | − | 0.178194i | 0.809990 | − | 0.586444i | \(-0.199472\pi\) |
−0.912870 | + | 0.408250i | \(0.866139\pi\) | |||||||
\(608\) | −11.7696 | − | 20.3856i | −0.477321 | − | 0.826745i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −13.2219 | + | 22.9010i | −0.535339 | + | 0.927235i | ||||
\(611\) | 11.6334 | − | 16.2519i | 0.470635 | − | 0.657482i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.6393i | 0.995173i | 0.867414 | + | 0.497587i | \(0.165780\pi\) | ||||
−0.867414 | + | 0.497587i | \(0.834220\pi\) | |||||||
\(614\) | −9.87719 | + | 17.1078i | −0.398611 | + | 0.690414i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 31.6771 | − | 18.2888i | 1.27630 | − | 0.736875i | ||||
\(617\) | 38.0933 | − | 21.9932i | 1.53358 | − | 0.885413i | 0.534387 | − | 0.845240i | \(-0.320543\pi\) |
0.999193 | − | 0.0401727i | \(-0.0127908\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.7979 | − | 10.2756i | −0.715358 | − | 0.413012i | 0.0976839 | − | 0.995217i | \(-0.468857\pi\) |
−0.813042 | + | 0.582206i | \(0.802190\pi\) | |||||||
\(620\) | −19.4717 | −0.782002 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 6.30587i | − | 0.252842i | ||||||
\(623\) | −9.88272 | + | 17.1174i | −0.395943 | + | 0.685793i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.5778 | + | 21.7853i | 0.503111 | + | 0.871414i | ||||
\(626\) | −17.6073 | + | 10.1656i | −0.703730 | + | 0.406299i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.636905 | − | 1.10315i | 0.0254153 | − | 0.0440205i | ||||
\(629\) | − | 23.1586i | − | 0.923392i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.1460i | 1.00105i | 0.865723 | + | 0.500523i | \(0.166859\pi\) | ||||
−0.865723 | + | 0.500523i | \(0.833141\pi\) | |||||||
\(632\) | 27.2775 | + | 15.7487i | 1.08504 | + | 0.626449i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.62582 | − | 8.01216i | −0.183715 | − | 0.318204i | ||||
\(635\) | 3.42689 | − | 1.97852i | 0.135992 | − | 0.0785151i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.7829 | − | 7.16088i | 0.625340 | − | 0.283724i | ||||
\(638\) | −7.96365 | −0.315284 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −13.6404 | −0.539183 | ||||||||
\(641\) | −16.6711 | + | 28.8751i | −0.658467 | + | 1.14050i | 0.322545 | + | 0.946554i | \(0.395462\pi\) |
−0.981012 | + | 0.193945i | \(0.937872\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.1759 | − | 15.6900i | 1.07171 | − | 0.618754i | 0.143065 | − | 0.989713i | \(-0.454304\pi\) |
0.928649 | + | 0.370959i | \(0.120971\pi\) | |||||||
\(644\) | 13.2833 | − | 7.66911i | 0.523435 | − | 0.302205i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.10969 | + | 14.0464i | −0.319072 | + | 0.552648i | ||||
\(647\) | 47.5495 | 1.86936 | 0.934681 | − | 0.355486i | \(-0.115685\pi\) | ||||
0.934681 | + | 0.355486i | \(0.115685\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.9680 | 0.744561 | ||||||||
\(650\) | −0.0422328 | − | 0.0930829i | −0.00165651 | − | 0.00365101i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.66964 | − | 3.27337i | 0.222040 | − | 0.128195i | ||||
\(653\) | −13.8728 | − | 24.0284i | −0.542884 | − | 0.940302i | −0.998737 | − | 0.0502473i | \(-0.983999\pi\) |
0.455853 | − | 0.890055i | \(-0.349334\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.8499 | + | 7.99627i | 0.541162 | + | 0.312440i | ||||
\(656\) | − | 1.96518i | − | 0.0767273i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 17.2491i | − | 0.672440i | ||||||
\(659\) | 7.80940 | − | 13.5263i | 0.304211 | − | 0.526909i | −0.672874 | − | 0.739757i | \(-0.734940\pi\) |
0.977085 | + | 0.212848i | \(0.0682738\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.5161 | + | 8.95822i | −0.603506 | + | 0.348434i | −0.770420 | − | 0.637537i | \(-0.779953\pi\) |
0.166914 | + | 0.985972i | \(0.446620\pi\) | |||||||
\(662\) | 2.44585 | + | 4.23633i | 0.0950605 | + | 0.164650i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.774017 | + | 1.34064i | −0.0300377 | + | 0.0520268i | ||||
\(665\) | 32.7794i | 1.27113i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.00000 | −0.348481 | ||||||||
\(668\) | −13.6295 | − | 7.86901i | −0.527342 | − | 0.304461i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −23.7667 | + | 13.7217i | −0.918187 | + | 0.530115i | ||||
\(671\) | −41.6753 | + | 24.0613i | −1.60886 | + | 0.928875i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.94960 | − | 5.10885i | 0.113699 | − | 0.196932i | −0.803560 | − | 0.595224i | \(-0.797064\pi\) |
0.917259 | + | 0.398292i | \(0.130397\pi\) | |||||||
\(674\) | 29.8161i | 1.14847i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.94532 | + | 14.5196i | 0.190205 | + | 0.558444i | ||||
\(677\) | 13.7045 | − | 23.7369i | 0.526707 | − | 0.912283i | −0.472809 | − | 0.881165i | \(-0.656760\pi\) |
0.999516 | − | 0.0311180i | \(-0.00990678\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.6568 | + | 20.1901i | 0.447345 | + | 0.774825i | ||||
\(680\) | 13.6008 | + | 23.5572i | 0.521566 | + | 0.903379i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 21.3297 | + | 12.3147i | 0.816757 | + | 0.471555i | ||||
\(683\) | − | 16.0989i | − | 0.616006i | −0.951385 | − | 0.308003i | \(-0.900339\pi\) | ||
0.951385 | − | 0.308003i | \(-0.0996607\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.1399 | 0.387427 | ||||||||
\(686\) | −3.41223 | + | 5.91015i | −0.130279 | + | 0.225651i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.111692 | + | 0.193457i | 0.00425823 | + | 0.00737547i | ||||
\(689\) | −2.67039 | + | 27.2561i | −0.101734 | + | 1.03837i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.9736 | − | 13.8412i | −0.912000 | − | 0.526543i | −0.0309256 | − | 0.999522i | \(-0.509845\pi\) |
−0.881074 | + | 0.472979i | \(0.843179\pi\) | |||||||
\(692\) | −8.78030 | −0.333777 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.3413i | 0.468469i | ||||||||
\(695\) | 27.4091 | + | 15.8247i | 1.03969 | + | 0.600264i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 28.8924 | − | 16.6810i | 1.09438 | − | 0.631839i | ||||
\(698\) | 5.10514 | + | 8.84236i | 0.193232 | + | 0.334688i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.109914 | + | 0.0634588i | 0.00415435 | + | 0.00239852i | ||||
\(701\) | 10.0776 | 0.380624 | 0.190312 | − | 0.981724i | \(-0.439050\pi\) | ||||
0.190312 | + | 0.981724i | \(0.439050\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23.3883 | 0.882108 | ||||||||
\(704\) | 17.6341 | + | 10.1811i | 0.664611 | + | 0.383713i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.0584 | + | 20.8857i | 0.453822 | + | 0.786043i | ||||
\(707\) | 14.7666 | − | 8.52553i | 0.555357 | − | 0.320635i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.79484 | − | 1.61360i | −0.104962 | − | 0.0606000i | 0.446600 | − | 0.894734i | \(-0.352635\pi\) |
−0.551562 | + | 0.834134i | \(0.685968\pi\) | |||||||
\(710\) | 5.39324i | 0.202405i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −16.5648 | −0.620793 | ||||||||
\(713\) | 24.1055 | + | 13.9173i | 0.902756 | + | 0.521207i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.91506 | − | 29.7534i | 0.109017 | − | 1.11271i | ||||
\(716\) | 13.6896 | + | 23.7110i | 0.511604 | + | 0.886123i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −15.8043 | + | 27.3738i | −0.589811 | + | 1.02158i | ||||
\(719\) | 30.0712 | 1.12147 | 0.560733 | − | 0.827996i | \(-0.310519\pi\) | ||||
0.560733 | + | 0.827996i | \(0.310519\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.25614i | 0.270233i | ||||||||
\(722\) | 0.715357 | + | 0.413012i | 0.0266228 | + | 0.0153707i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.05852 | − | 5.29751i | −0.113669 | − | 0.196880i | ||||
\(725\) | −0.0372356 | − | 0.0644940i | −0.00138290 | − | 0.00239525i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.68860 | − | 16.7811i | 0.359330 | − | 0.622378i | −0.628519 | − | 0.777794i | \(-0.716339\pi\) |
0.987849 | + | 0.155416i | \(0.0496719\pi\) | |||||||
\(728\) | 29.0105 | + | 20.7661i | 1.07520 | + | 0.769643i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 11.0857i | 0.410299i | ||||||||
\(731\) | −1.89616 | + | 3.28424i | −0.0701320 | + | 0.121472i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.1938 | + | 12.2362i | −0.782810 | + | 0.451955i | −0.837425 | − | 0.546552i | \(-0.815940\pi\) |
0.0546155 | + | 0.998507i | \(0.482607\pi\) | |||||||
\(734\) | 2.12877 | − | 1.22904i | 0.0785742 | − | 0.0453648i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 18.1340 | + | 10.4697i | 0.668429 | + | 0.385918i | ||||
\(737\) | −49.9416 | −1.83962 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 3.30687i | − | 0.121645i | −0.998149 | − | 0.0608226i | \(-0.980628\pi\) | ||
0.998149 | − | 0.0608226i | \(-0.0193724\pi\) | |||||||
\(740\) | 7.27712 | − | 12.6043i | 0.267512 | − | 0.463344i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.8178 | + | 20.4691i | 0.433846 | + | 0.751444i | ||||
\(743\) | 15.1394 | − | 8.74076i | 0.555412 | − | 0.320667i | −0.195890 | − | 0.980626i | \(-0.562760\pi\) |
0.751302 | + | 0.659959i | \(0.229426\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.50751 | + | 11.2713i | −0.238417 | + | 0.412950i | ||||
\(746\) | 1.58566i | 0.0580553i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 18.3674i | 0.671580i | ||||||||
\(749\) | −24.0264 | − | 13.8717i | −0.877906 | − | 0.506859i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.2922 | + | 24.7548i | 0.521528 | + | 0.903314i | 0.999686 | + | 0.0250400i | \(0.00797130\pi\) |
−0.478158 | + | 0.878274i | \(0.658695\pi\) | |||||||
\(752\) | 1.19083 | − | 0.687526i | 0.0434251 | − | 0.0250715i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.20935 | − | 7.07354i | −0.116878 | − | 0.257603i | ||||
\(755\) | −21.8606 | −0.795587 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.9611 | 0.434733 | 0.217367 | − | 0.976090i | \(-0.430253\pi\) | ||||
0.217367 | + | 0.976090i | \(0.430253\pi\) | |||||||
\(758\) | −1.31737 | + | 2.28176i | −0.0478492 | + | 0.0828772i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −23.7910 | + | 13.7357i | −0.862989 | + | 0.498247i | ||||
\(761\) | 1.84327 | − | 1.06421i | 0.0668185 | − | 0.0385777i | −0.466219 | − | 0.884670i | \(-0.654384\pi\) |
0.533037 | + | 0.846092i | \(0.321051\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.1841 | + | 29.7637i | −0.622105 | + | 1.07752i | ||||
\(764\) | −19.0449 | −0.689019 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.5156 | −0.668994 | ||||||||
\(767\) | 7.64412 | + | 16.8480i | 0.276013 | + | 0.608345i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.62584 | − | 3.82543i | 0.238934 | − | 0.137949i | −0.375753 | − | 0.926720i | \(-0.622616\pi\) |
0.614687 | + | 0.788771i | \(0.289282\pi\) | |||||||
\(770\) | −12.9007 | − | 22.3446i | −0.464907 | − | 0.805243i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.35080 | + | 1.93458i | 0.120598 | + | 0.0696272i | ||||
\(773\) | 24.6440i | 0.886383i | 0.896427 | + | 0.443191i | \(0.146154\pi\) | ||||
−0.896427 | + | 0.443191i | \(0.853846\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.230320i | 0.00827333i | ||||||||
\(776\) | −9.76918 | + | 16.9207i | −0.350693 | + | 0.607418i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.1667 | − | 5.86972i | 0.364492 | − | 0.210440i | ||||
\(779\) | 16.8465 | + | 29.1791i | 0.603590 | + | 1.04545i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.90731 | + | 8.49972i | −0.175598 | + | 0.304144i | ||||
\(782\) | − | 14.4280i | − | 0.515943i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.19238 | 0.0425851 | ||||||||
\(785\) | −2.09716 | − | 1.21080i | −0.0748509 | − | 0.0432152i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.2586 | − | 20.9339i | 1.29248 | − | 0.746214i | 0.313388 | − | 0.949625i | \(-0.398536\pi\) |
0.979093 | + | 0.203411i | \(0.0652027\pi\) | |||||||
\(788\) | 7.26768 | − | 4.19599i | 0.258900 | − | 0.149476i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 11.1089 | − | 19.2412i | 0.395237 | − | 0.684571i | ||||
\(791\) | − | 66.7797i | − | 2.37441i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38.1671 | − | 27.3205i | −1.35535 | − | 0.970181i | ||||
\(794\) | 13.2131 | − | 22.8857i | 0.468914 | − | 0.812183i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.16775 | + | 14.1470i | 0.289498 | + | 0.501426i | ||||
\(797\) | −20.8781 | − | 36.1620i | −0.739541 | − | 1.28092i | −0.952702 | − | 0.303906i | \(-0.901709\pi\) |
0.213161 | − | 0.977017i | \(-0.431624\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.2163 | + | 11.6719i | 0.715200 | + | 0.412921i | ||||
\(800\) | 0.173265i | 0.00612583i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −20.0792 | −0.709022 | ||||||||
\(803\) | −10.0869 | + | 17.4709i | −0.355957 | + | 0.616536i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.5795 | − | 25.2524i | −0.513859 | − | 0.890030i | ||||
\(806\) | −2.34241 | + | 23.9085i | −0.0825079 | + | 0.842140i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12.3755 | + | 7.14499i | 0.435368 | + | 0.251360i | ||||
\(809\) | −45.2476 | −1.59082 | −0.795410 | − | 0.606072i | \(-0.792744\pi\) | ||||
−0.795410 | + | 0.606072i | \(0.792744\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 52.8820i | − | 1.85694i | −0.371410 | − | 0.928469i | \(-0.621126\pi\) | ||
0.371410 | − | 0.928469i | \(-0.378874\pi\) | |||||||
\(812\) | 8.35255 | + | 4.82235i | 0.293117 | + | 0.169231i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −15.9430 | + | 9.20470i | −0.558802 | + | 0.322625i | ||||
\(815\) | −6.22288 | − | 10.7784i | −0.217978 | − | 0.377549i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.31683 | − | 1.91497i | −0.116041 | − | 0.0669964i | ||||
\(818\) | −1.90053 | −0.0664505 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 20.9667 | 0.732190 | ||||||||
\(821\) | −29.8105 | − | 17.2111i | −1.04039 | − | 0.600671i | −0.120449 | − | 0.992720i | \(-0.538433\pi\) |
−0.919945 | + | 0.392048i | \(0.871767\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.99853 | + | 10.3898i | 0.209096 | + | 0.362164i | 0.951430 | − | 0.307866i | \(-0.0996147\pi\) |
−0.742334 | + | 0.670030i | \(0.766281\pi\) | |||||||
\(824\) | −5.26644 | + | 3.04058i | −0.183465 | + | 0.105924i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.8279 | + | 7.98353i | 0.481134 | + | 0.277783i | ||||
\(827\) | 4.35092i | 0.151296i | 0.997135 | + | 0.0756482i | \(0.0241026\pi\) | ||||
−0.997135 | + | 0.0756482i | \(0.975897\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.6204 | 1.58446 | 0.792230 | − | 0.610222i | \(-0.208920\pi\) | ||||
0.792230 | + | 0.610222i | \(0.208920\pi\) | |||||||
\(830\) | 0.945668 | + | 0.545982i | 0.0328246 | + | 0.0189513i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.93657 | + | 19.7661i | −0.0671383 | + | 0.685266i | ||||
\(833\) | 10.1213 | + | 17.5307i | 0.350683 | + | 0.607401i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.9595 | + | 25.9106i | −0.517695 | + | 0.896674i | ||||
\(836\) | −18.5497 | −0.641554 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.354449i | 0.0122442i | ||||||||
\(839\) | 21.3626 | + | 12.3337i | 0.737520 | + | 0.425808i | 0.821167 | − | 0.570688i | \(-0.193323\pi\) |
−0.0836466 | + | 0.996495i | \(0.526657\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.6704 | + | 20.2137i | 0.402427 | + | 0.697025i | ||||
\(842\) | 5.01926 | + | 8.69361i | 0.172975 | + | 0.299602i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −8.51525 | + | 14.7488i | −0.293107 | + | 0.507676i | ||||
\(845\) | 27.6026 | − | 9.40138i | 0.949559 | − | 0.323417i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 9.15606i | − | 0.314606i | ||||||
\(848\) | −0.942085 | + | 1.63174i | −0.0323513 | + | 0.0560341i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.103391 | − | 0.0596928i | 0.00354628 | − | 0.00204744i | ||||
\(851\) | −18.0178 | + | 10.4026i | −0.617641 | + | 0.356595i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.9668 | − | 13.2599i | −0.786369 | − | 0.454010i | 0.0523138 | − | 0.998631i | \(-0.483340\pi\) |
−0.838683 | + | 0.544620i | \(0.816674\pi\) | |||||||
\(854\) | −40.5089 | −1.38619 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 23.2508i | − | 0.794697i | ||||||
\(857\) | −3.20474 | + | 5.55077i | −0.109472 | + | 0.189611i | −0.915556 | − | 0.402190i | \(-0.868249\pi\) |
0.806085 | + | 0.591800i | \(0.201583\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.7998 | − | 22.1699i | −0.436723 | − | 0.756427i | 0.560711 | − | 0.828011i | \(-0.310528\pi\) |
−0.997435 | + | 0.0715846i | \(0.977194\pi\) | |||||||
\(860\) | −2.06402 | + | 1.19166i | −0.0703824 | + | 0.0406353i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.5078 | − | 28.5924i | 0.562258 | − | 0.973860i | ||||
\(863\) | 48.4823i | 1.65036i | 0.564873 | + | 0.825178i | \(0.308925\pi\) | ||||
−0.564873 | + | 0.825178i | \(0.691075\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.6919i | 0.567542i | ||||||||
\(866\) | 6.92319 | + | 3.99711i | 0.235260 | + | 0.135827i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −14.9142 | − | 25.8322i | −0.506222 | − | 0.876802i | ||||
\(869\) | 35.0152 | − | 20.2160i | 1.18781 | − | 0.685782i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.1264 | − | 44.3595i | −0.681959 | − | 1.50307i | ||||
\(872\) | −28.8029 | −0.975389 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 14.5711 | 0.492876 | ||||||||
\(875\) | −19.1478 | + | 33.1650i | −0.647315 | + | 1.12118i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27.0023 | + | 15.5898i | −0.911801 | + | 0.526429i | −0.881010 | − | 0.473097i | \(-0.843136\pi\) |
−0.0307911 | + | 0.999526i | \(0.509803\pi\) | |||||||
\(878\) | 27.5549 | − | 15.9088i | 0.929932 | − | 0.536897i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.02840 | − | 1.78125i | 0.0346675 | − | 0.0600459i | ||||
\(881\) | 49.6614 | 1.67314 | 0.836568 | − | 0.547863i | \(-0.184558\pi\) | ||||
0.836568 | + | 0.547863i | \(0.184558\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.3523 | 1.02144 | 0.510718 | − | 0.859748i | \(-0.329380\pi\) | ||||
0.510718 | + | 0.859748i | \(0.329380\pi\) | |||||||
\(884\) | −16.3145 | + | 7.40207i | −0.548715 | + | 0.248959i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 18.7481 | − | 10.8242i | 0.629855 | − | 0.363647i | ||||
\(887\) | 6.42161 | + | 11.1226i | 0.215616 | + | 0.373459i | 0.953463 | − | 0.301510i | \(-0.0974906\pi\) |
−0.737847 | + | 0.674968i | \(0.764157\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.24962 | + | 3.03087i | 0.176066 | + | 0.101652i | ||||
\(890\) | 11.6846i | 0.391669i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12.9834i | 0.434715i | ||||||||
\(893\) | −11.7877 | + | 20.4169i | −0.394460 | + | 0.683224i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 45.0762 | − | 26.0248i | 1.50673 | − | 0.869912i | ||||
\(896\) | −10.4478 | − | 18.0961i | −0.349035 | − | 0.604547i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.32484 | − | 10.9549i | 0.211063 | − | 0.365571i | ||||
\(899\) | 17.5024i | 0.583738i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31.9869 | −1.06564 | ||||||||
\(902\) | −22.9674 | − | 13.2602i | −0.764731 | − | 0.441518i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 48.4680 | − | 27.9830i | 1.61202 | − | 0.930701i | ||||
\(905\) | −10.0709 | + | 5.81444i | −0.334768 | + | 0.193279i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.2993 | − | 17.8389i | 0.341983 | − | 0.592331i | −0.642818 | − | 0.766019i | \(-0.722235\pi\) |
0.984801 | + | 0.173688i | \(0.0555683\pi\) | |||||||
\(908\) | 9.57860i | 0.317877i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 14.6481 | − | 20.4636i | 0.485581 | − | 0.678362i | ||||
\(911\) | 21.1949 | − | 36.7107i | 0.702219 | − | 1.21628i | −0.265466 | − | 0.964120i | \(-0.585526\pi\) |
0.967686 | − | 0.252159i | \(-0.0811407\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.993579 | + | 1.72093i | 0.0328827 | + | 0.0569545i | ||||
\(914\) | 7.88827 | + | 13.6629i | 0.260921 | + | 0.451928i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.49524 | − | 3.17268i | −0.181568 | − | 0.104828i | ||||
\(917\) | 24.4988i | 0.809021i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42.7987 | −1.41180 | −0.705899 | − | 0.708313i | \(-0.749457\pi\) | ||||
−0.705899 | + | 0.708313i | \(0.749457\pi\) | |||||||
\(920\) | 12.2186 | − | 21.1633i | 0.402836 | − | 0.697733i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −10.8068 | − | 18.7179i | −0.355903 | − | 0.616441i | ||||
\(923\) | −9.52734 | − | 0.933432i | −0.313596 | − | 0.0307243i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.149090 | − | 0.0860769i | −0.00490203 | − | 0.00283019i | ||||
\(926\) | −9.54253 | −0.313587 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 13.1667i | 0.432218i | ||||||||
\(929\) | −10.2242 | − | 5.90296i | −0.335446 | − | 0.193670i | 0.322810 | − | 0.946464i | \(-0.395372\pi\) |
−0.658257 | + | 0.752794i | \(0.728706\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.7046 | + | 10.2218i | −0.580245 | + | 0.335004i | ||||
\(932\) | 11.8575 | + | 20.5378i | 0.388405 | + | 0.672738i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.59511 | + | 3.80769i | 0.215799 | + | 0.124591i | ||||
\(935\) | 34.9177 | 1.14193 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.7925 | 0.809935 | 0.404967 | − | 0.914331i | \(-0.367283\pi\) | ||||
0.404967 | + | 0.914331i | \(0.367283\pi\) | |||||||
\(938\) | −36.4079 | − | 21.0201i | −1.18876 | − | 0.686331i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7.33531 | + | 12.7051i | 0.239251 | + | 0.414395i | ||||
\(941\) | −20.6367 | + | 11.9146i | −0.672737 | + | 0.388405i | −0.797113 | − | 0.603830i | \(-0.793640\pi\) |
0.124376 | + | 0.992235i | \(0.460307\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −25.9563 | − | 14.9859i | −0.845253 | − | 0.488007i | ||||
\(944\) | 1.27285i | 0.0414278i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.01462 | 0.0980138 | ||||||||
\(947\) | −42.4532 | − | 24.5104i | −1.37954 | − | 0.796480i | −0.387440 | − | 0.921895i | \(-0.626641\pi\) |
−0.992104 | + | 0.125415i | \(0.959974\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.5832 | − | 1.91865i | −0.635698 | − | 0.0622819i | ||||
\(950\) | 0.0602850 | + | 0.104417i | 0.00195590 | + | 0.00338773i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −20.8349 | + | 36.0870i | −0.675262 | + | 1.16959i | ||||
\(953\) | −7.78372 | −0.252140 | −0.126070 | − | 0.992021i | \(-0.540236\pi\) | ||||
−0.126070 | + | 0.992021i | \(0.540236\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 36.2055i | 1.17158i | ||||||||
\(956\) | 14.4697 | + | 8.35406i | 0.467982 | + | 0.270190i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.11200 | + | 12.3183i | 0.229778 | + | 0.397987i | ||||
\(959\) | 7.76661 | + | 13.4522i | 0.250797 | + | 0.434393i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.5651 | − | 20.0314i | 0.373069 | − | 0.646174i | ||||
\(962\) | −14.6009 | − | 10.4515i | −0.470752 | − | 0.336971i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 35.7011i | − | 1.14985i | ||||||
\(965\) | 3.67777 | − | 6.37008i | 0.118392 | − | 0.205060i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.5591 | + | 18.7980i | −1.04703 | + | 0.604502i | −0.921816 | − | 0.387627i | \(-0.873295\pi\) |
−0.125213 | + | 0.992130i | \(0.539961\pi\) | |||||||
\(968\) | 6.64538 | − | 3.83671i | 0.213590 | − | 0.123317i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 11.9357 | + | 6.89105i | 0.383231 | + | 0.221258i | ||||
\(971\) | 9.16512 | 0.294123 | 0.147061 | − | 0.989127i | \(-0.453019\pi\) | ||||
0.147061 | + | 0.989127i | \(0.453019\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 48.4833i | 1.55430i | ||||||||
\(974\) | 17.1587 | − | 29.7197i | 0.549800 | − | 0.952281i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.61463 | − | 2.79662i | −0.0516831 | − | 0.0895177i | ||||
\(977\) | 41.0043 | − | 23.6739i | 1.31184 | − | 0.757394i | 0.329443 | − | 0.944176i | \(-0.393139\pi\) |
0.982401 | + | 0.186782i | \(0.0598058\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.6318 | + | 18.4149i | −0.339795 | + | 0.588542i | ||||
\(980\) | 12.7217i | 0.406380i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 3.40553i | − | 0.108675i | ||||||
\(983\) | −14.0634 | − | 8.11949i | −0.448552 | − | 0.258972i | 0.258666 | − | 0.965967i | \(-0.416717\pi\) |
−0.707219 | + | 0.706995i | \(0.750050\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.97686 | − | 13.8163i | −0.254164 | − | 0.440225i | ||||
\(986\) | 7.85686 | − | 4.53616i | 0.250213 | − | 0.144461i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.47552 | − | 16.4764i | −0.237828 | − | 0.524183i | ||||
\(989\) | 3.40693 | 0.108334 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.7634 | −1.19959 | −0.599797 | − | 0.800152i | \(-0.704752\pi\) | ||||
−0.599797 | + | 0.800152i | \(0.704752\pi\) | |||||||
\(992\) | 20.3605 | − | 35.2655i | 0.646447 | − | 1.11968i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7.15496 | + | 4.13092i | −0.226942 | + | 0.131025i | ||||
\(995\) | 26.8943 | − | 15.5274i | 0.852606 | − | 0.492252i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −23.8283 | + | 41.2718i | −0.754649 | + | 1.30709i | 0.190899 | + | 0.981610i | \(0.438860\pi\) |
−0.945549 | + | 0.325481i | \(0.894474\pi\) | |||||||
\(998\) | −7.48156 | −0.236824 | ||||||||
\(999\) | 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 | 351.2.t.c.181.6 | 20 | ||
3.2 | odd | 2 | 117.2.t.c.25.5 | ✓ | 20 | ||
9.2 | odd | 6 | 1053.2.b.j.649.6 | 10 | |||
9.4 | even | 3 | inner | 351.2.t.c.64.5 | 20 | ||
9.5 | odd | 6 | 117.2.t.c.103.6 | yes | 20 | ||
9.7 | even | 3 | 1053.2.b.i.649.5 | 10 | |||
13.12 | even | 2 | inner | 351.2.t.c.181.5 | 20 | ||
39.38 | odd | 2 | 117.2.t.c.25.6 | yes | 20 | ||
117.25 | even | 6 | 1053.2.b.i.649.6 | 10 | |||
117.38 | odd | 6 | 1053.2.b.j.649.5 | 10 | |||
117.77 | odd | 6 | 117.2.t.c.103.5 | yes | 20 | ||
117.103 | even | 6 | inner | 351.2.t.c.64.6 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
117.2.t.c.25.5 | ✓ | 20 | 3.2 | odd | 2 | ||
117.2.t.c.25.6 | yes | 20 | 39.38 | odd | 2 | ||
117.2.t.c.103.5 | yes | 20 | 117.77 | odd | 6 | ||
117.2.t.c.103.6 | yes | 20 | 9.5 | odd | 6 | ||
351.2.t.c.64.5 | 20 | 9.4 | even | 3 | inner | ||
351.2.t.c.64.6 | 20 | 117.103 | even | 6 | inner | ||
351.2.t.c.181.5 | 20 | 13.12 | even | 2 | inner | ||
351.2.t.c.181.6 | 20 | 1.1 | even | 1 | trivial | ||
1053.2.b.i.649.5 | 10 | 9.7 | even | 3 | |||
1053.2.b.i.649.6 | 10 | 117.25 | even | 6 | |||
1053.2.b.j.649.5 | 10 | 117.38 | odd | 6 | |||
1053.2.b.j.649.6 | 10 | 9.2 | odd | 6 |