Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(199,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.199");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.f (of order \(2\), degree \(1\), 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: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 12) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.4 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.199 |
Dual form | 900.3.f.c.199.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.73205 | + | 1.00000i | 0.866025 | + | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.92820 | −0.989743 | −0.494872 | − | 0.868966i | \(-0.664785\pi\) | ||||
−0.494872 | + | 0.868966i | \(0.664785\pi\) | |||||||
\(8\) | 8.00000i | 1.00000i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.92820i | 0.629837i | 0.949119 | + | 0.314918i | \(0.101977\pi\) | ||||
−0.949119 | + | 0.314918i | \(0.898023\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.00000i | − | 0.153846i | −0.997037 | − | 0.0769231i | \(-0.975490\pi\) | ||
0.997037 | − | 0.0769231i | \(-0.0245096\pi\) | |||||||
\(14\) | −12.0000 | − | 6.92820i | −0.857143 | − | 0.494872i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(17\) | − | 10.0000i | − | 0.588235i | −0.955769 | − | 0.294118i | \(-0.904974\pi\) | ||
0.955769 | − | 0.294118i | \(-0.0950258\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 20.7846i | 1.09393i | 0.837157 | + | 0.546963i | \(0.184216\pi\) | ||||
−0.837157 | + | 0.546963i | \(0.815784\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.92820 | + | 12.0000i | −0.314918 | + | 0.545455i | ||||
\(23\) | −27.7128 | −1.20490 | −0.602452 | − | 0.798155i | \(-0.705810\pi\) | ||||
−0.602452 | + | 0.798155i | \(0.705810\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.00000 | − | 3.46410i | 0.0769231 | − | 0.133235i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −13.8564 | − | 24.0000i | −0.494872 | − | 0.857143i | ||||
\(29\) | −26.0000 | −0.896552 | −0.448276 | − | 0.893895i | \(-0.647962\pi\) | ||||
−0.448276 | + | 0.893895i | \(0.647962\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.92820i | − | 0.223490i | −0.993737 | − | 0.111745i | \(-0.964356\pi\) | ||
0.993737 | − | 0.111745i | \(-0.0356441\pi\) | |||||||
\(32\) | −27.7128 | + | 16.0000i | −0.866025 | + | 0.500000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 10.0000 | − | 17.3205i | 0.294118 | − | 0.509427i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 26.0000i | 0.702703i | 0.936244 | + | 0.351351i | \(0.114278\pi\) | ||||
−0.936244 | + | 0.351351i | \(0.885722\pi\) | |||||||
\(38\) | −20.7846 | + | 36.0000i | −0.546963 | + | 0.947368i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −58.0000 | −1.41463 | −0.707317 | − | 0.706896i | \(-0.750095\pi\) | ||||
−0.707317 | + | 0.706896i | \(0.750095\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 48.4974 | 1.12785 | 0.563924 | − | 0.825827i | \(-0.309291\pi\) | ||||
0.563924 | + | 0.825827i | \(0.309291\pi\) | |||||||
\(44\) | −24.0000 | + | 13.8564i | −0.545455 | + | 0.314918i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −48.0000 | − | 27.7128i | −1.04348 | − | 0.602452i | ||||
\(47\) | −69.2820 | −1.47409 | −0.737043 | − | 0.675846i | \(-0.763778\pi\) | ||||
−0.737043 | + | 0.675846i | \(0.763778\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.0204082 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.92820 | − | 4.00000i | 0.133235 | − | 0.0769231i | ||||
\(53\) | − | 74.0000i | − | 1.39623i | −0.715987 | − | 0.698113i | \(-0.754023\pi\) | ||
0.715987 | − | 0.698113i | \(-0.245977\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 55.4256i | − | 0.989743i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −45.0333 | − | 26.0000i | −0.776437 | − | 0.448276i | ||||
\(59\) | 90.0666i | 1.52655i | 0.646072 | + | 0.763277i | \(0.276411\pi\) | ||||
−0.646072 | + | 0.763277i | \(0.723589\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 26.0000 | 0.426230 | 0.213115 | − | 0.977027i | \(-0.431639\pi\) | ||||
0.213115 | + | 0.977027i | \(0.431639\pi\) | |||||||
\(62\) | 6.92820 | − | 12.0000i | 0.111745 | − | 0.193548i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −64.0000 | −1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.92820 | 0.103406 | 0.0517030 | − | 0.998663i | \(-0.483535\pi\) | ||||
0.0517030 | + | 0.998663i | \(0.483535\pi\) | |||||||
\(68\) | 34.6410 | − | 20.0000i | 0.509427 | − | 0.294118i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 46.0000i | 0.630137i | 0.949069 | + | 0.315068i | \(0.102027\pi\) | ||||
−0.949069 | + | 0.315068i | \(0.897973\pi\) | |||||||
\(74\) | −26.0000 | + | 45.0333i | −0.351351 | + | 0.608558i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −72.0000 | + | 41.5692i | −0.947368 | + | 0.546963i | ||||
\(77\) | − | 48.0000i | − | 0.623377i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 117.779i | 1.49088i | 0.666573 | + | 0.745440i | \(0.267760\pi\) | ||||
−0.666573 | + | 0.745440i | \(0.732240\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −100.459 | − | 58.0000i | −1.22511 | − | 0.707317i | ||||
\(83\) | 48.4974 | 0.584306 | 0.292153 | − | 0.956372i | \(-0.405628\pi\) | ||||
0.292153 | + | 0.956372i | \(0.405628\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 84.0000 | + | 48.4974i | 0.976744 | + | 0.563924i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −55.4256 | −0.629837 | ||||||||
\(89\) | 82.0000 | 0.921348 | 0.460674 | − | 0.887569i | \(-0.347608\pi\) | ||||
0.460674 | + | 0.887569i | \(0.347608\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.8564i | 0.152268i | ||||||||
\(92\) | −55.4256 | − | 96.0000i | −0.602452 | − | 1.04348i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −120.000 | − | 69.2820i | −1.27660 | − | 0.737043i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.00000i | 0.0206186i | 0.999947 | + | 0.0103093i | \(0.00328160\pi\) | ||||
−0.999947 | + | 0.0103093i | \(0.996718\pi\) | |||||||
\(98\) | −1.73205 | − | 1.00000i | −0.0176740 | − | 0.0102041i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 74.0000 | 0.732673 | 0.366337 | − | 0.930482i | \(-0.380612\pi\) | ||||
0.366337 | + | 0.930482i | \(0.380612\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 76.2102 | 0.739905 | 0.369953 | − | 0.929051i | \(-0.379374\pi\) | ||||
0.369953 | + | 0.929051i | \(0.379374\pi\) | |||||||
\(104\) | 16.0000 | 0.153846 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 74.0000 | − | 128.172i | 0.698113 | − | 1.20917i | ||||
\(107\) | −20.7846 | −0.194249 | −0.0971243 | − | 0.995272i | \(-0.530964\pi\) | ||||
−0.0971243 | + | 0.995272i | \(0.530964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 46.0000 | 0.422018 | 0.211009 | − | 0.977484i | \(-0.432325\pi\) | ||||
0.211009 | + | 0.977484i | \(0.432325\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 55.4256 | − | 96.0000i | 0.494872 | − | 0.857143i | ||||
\(113\) | − | 110.000i | − | 0.973451i | −0.873555 | − | 0.486726i | \(-0.838191\pi\) | ||
0.873555 | − | 0.486726i | \(-0.161809\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −52.0000 | − | 90.0666i | −0.448276 | − | 0.776437i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −90.0666 | + | 156.000i | −0.763277 | + | 1.32203i | ||||
\(119\) | 69.2820i | 0.582202i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 73.0000 | 0.603306 | ||||||||
\(122\) | 45.0333 | + | 26.0000i | 0.369126 | + | 0.213115i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 24.0000 | − | 13.8564i | 0.193548 | − | 0.111745i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −145.492 | −1.14561 | −0.572804 | − | 0.819692i | \(-0.694144\pi\) | ||||
−0.572804 | + | 0.819692i | \(0.694144\pi\) | |||||||
\(128\) | −110.851 | − | 64.0000i | −0.866025 | − | 0.500000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 117.779i | 0.899080i | 0.893260 | + | 0.449540i | \(0.148412\pi\) | ||||
−0.893260 | + | 0.449540i | \(0.851588\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 144.000i | − | 1.08271i | ||||||
\(134\) | 12.0000 | + | 6.92820i | 0.0895522 | + | 0.0517030i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 80.0000 | 0.588235 | ||||||||
\(137\) | − | 10.0000i | − | 0.0729927i | −0.999334 | − | 0.0364964i | \(-0.988380\pi\) | ||
0.999334 | − | 0.0364964i | \(-0.0116197\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 48.4974i | 0.348902i | 0.984666 | + | 0.174451i | \(0.0558151\pi\) | ||||
−0.984666 | + | 0.174451i | \(0.944185\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.8564 | 0.0968979 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −46.0000 | + | 79.6743i | −0.315068 | + | 0.545715i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −90.0666 | + | 52.0000i | −0.608558 | + | 0.351351i | ||||
\(149\) | −2.00000 | −0.0134228 | −0.00671141 | − | 0.999977i | \(-0.502136\pi\) | ||||
−0.00671141 | + | 0.999977i | \(0.502136\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 90.0666i | 0.596468i | 0.954493 | + | 0.298234i | \(0.0963975\pi\) | ||||
−0.954493 | + | 0.298234i | \(0.903602\pi\) | |||||||
\(152\) | −166.277 | −1.09393 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 48.0000 | − | 83.1384i | 0.311688 | − | 0.539860i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 214.000i | − | 1.36306i | −0.731791 | − | 0.681529i | \(-0.761315\pi\) | ||
0.731791 | − | 0.681529i | \(-0.238685\pi\) | |||||||
\(158\) | −117.779 | + | 204.000i | −0.745440 | + | 1.29114i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 192.000 | 1.19255 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.7846 | −0.127513 | −0.0637565 | − | 0.997965i | \(-0.520308\pi\) | ||||
−0.0637565 | + | 0.997965i | \(0.520308\pi\) | |||||||
\(164\) | −116.000 | − | 200.918i | −0.707317 | − | 1.22511i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 84.0000 | + | 48.4974i | 0.506024 | + | 0.292153i | ||||
\(167\) | −96.9948 | −0.580807 | −0.290404 | − | 0.956904i | \(-0.593790\pi\) | ||||
−0.290404 | + | 0.956904i | \(0.593790\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 165.000 | 0.976331 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 96.9948 | + | 168.000i | 0.563924 | + | 0.976744i | ||||
\(173\) | 334.000i | 1.93064i | 0.261077 | + | 0.965318i | \(0.415922\pi\) | ||||
−0.261077 | + | 0.965318i | \(0.584078\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −96.0000 | − | 55.4256i | −0.545455 | − | 0.314918i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 142.028 | + | 82.0000i | 0.797911 | + | 0.460674i | ||||
\(179\) | 187.061i | 1.04504i | 0.852628 | + | 0.522518i | \(0.175007\pi\) | ||||
−0.852628 | + | 0.522518i | \(0.824993\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.0110497 | 0.00552486 | − | 0.999985i | \(-0.498241\pi\) | ||||
0.00552486 | + | 0.999985i | \(0.498241\pi\) | |||||||
\(182\) | −13.8564 | + | 24.0000i | −0.0761341 | + | 0.131868i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 221.703i | − | 1.20490i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 69.2820 | 0.370492 | ||||||||
\(188\) | −138.564 | − | 240.000i | −0.737043 | − | 1.27660i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 221.703i | − | 1.16075i | −0.814351 | − | 0.580373i | \(-0.802907\pi\) | ||
0.814351 | − | 0.580373i | \(-0.197093\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 290.000i | − | 1.50259i | −0.659966 | − | 0.751295i | \(-0.729429\pi\) | ||
0.659966 | − | 0.751295i | \(-0.270571\pi\) | |||||||
\(194\) | −2.00000 | + | 3.46410i | −0.0103093 | + | 0.0178562i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.00000 | − | 3.46410i | −0.0102041 | − | 0.0176740i | ||||
\(197\) | 26.0000i | 0.131980i | 0.997820 | + | 0.0659898i | \(0.0210205\pi\) | ||||
−0.997820 | + | 0.0659898i | \(0.978980\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 394.908i | 1.98446i | 0.124416 | + | 0.992230i | \(0.460294\pi\) | ||||
−0.124416 | + | 0.992230i | \(0.539706\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 128.172 | + | 74.0000i | 0.634514 | + | 0.366337i | ||||
\(203\) | 180.133 | 0.887356 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 132.000 | + | 76.2102i | 0.640777 | + | 0.369953i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 27.7128 | + | 16.0000i | 0.133235 | + | 0.0769231i | ||||
\(209\) | −144.000 | −0.688995 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 242.487i | 1.14923i | 0.818425 | + | 0.574614i | \(0.194848\pi\) | ||||
−0.818425 | + | 0.574614i | \(0.805152\pi\) | |||||||
\(212\) | 256.344 | − | 148.000i | 1.20917 | − | 0.698113i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −36.0000 | − | 20.7846i | −0.168224 | − | 0.0971243i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 48.0000i | 0.221198i | ||||||||
\(218\) | 79.6743 | + | 46.0000i | 0.365479 | + | 0.211009i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.0000 | −0.0904977 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 339.482 | 1.52234 | 0.761170 | − | 0.648552i | \(-0.224625\pi\) | ||||
0.761170 | + | 0.648552i | \(0.224625\pi\) | |||||||
\(224\) | 192.000 | − | 110.851i | 0.857143 | − | 0.494872i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 110.000 | − | 190.526i | 0.486726 | − | 0.843034i | ||||
\(227\) | 284.056 | 1.25135 | 0.625675 | − | 0.780084i | \(-0.284824\pi\) | ||||
0.625675 | + | 0.780084i | \(0.284824\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 142.000 | 0.620087 | 0.310044 | − | 0.950722i | \(-0.399656\pi\) | ||||
0.310044 | + | 0.950722i | \(0.399656\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 208.000i | − | 0.896552i | ||||||
\(233\) | 82.0000i | 0.351931i | 0.984396 | + | 0.175966i | \(0.0563048\pi\) | ||||
−0.984396 | + | 0.175966i | \(0.943695\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −312.000 | + | 180.133i | −1.32203 | + | 0.763277i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −69.2820 | + | 120.000i | −0.291101 | + | 0.504202i | ||||
\(239\) | − | 387.979i | − | 1.62334i | −0.584113 | − | 0.811672i | \(-0.698558\pi\) | ||
0.584113 | − | 0.811672i | \(-0.301442\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −46.0000 | −0.190871 | −0.0954357 | − | 0.995436i | \(-0.530424\pi\) | ||||
−0.0954357 | + | 0.995436i | \(0.530424\pi\) | |||||||
\(242\) | 126.440 | + | 73.0000i | 0.522478 | + | 0.301653i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 52.0000 | + | 90.0666i | 0.213115 | + | 0.369126i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 41.5692 | 0.168296 | ||||||||
\(248\) | 55.4256 | 0.223490 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 145.492i | 0.579650i | 0.957080 | + | 0.289825i | \(0.0935972\pi\) | ||||
−0.957080 | + | 0.289825i | \(0.906403\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 192.000i | − | 0.758893i | ||||||
\(254\) | −252.000 | − | 145.492i | −0.992126 | − | 0.572804i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.500000 | − | 0.866025i | ||||
\(257\) | 254.000i | 0.988327i | 0.869369 | + | 0.494163i | \(0.164526\pi\) | ||||
−0.869369 | + | 0.494163i | \(0.835474\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 180.133i | − | 0.695495i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −117.779 | + | 204.000i | −0.449540 | + | 0.778626i | ||||
\(263\) | 152.420 | 0.579546 | 0.289773 | − | 0.957095i | \(-0.406420\pi\) | ||||
0.289773 | + | 0.957095i | \(0.406420\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 144.000 | − | 249.415i | 0.541353 | − | 0.937652i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 13.8564 | + | 24.0000i | 0.0517030 | + | 0.0895522i | ||||
\(269\) | 262.000 | 0.973978 | 0.486989 | − | 0.873408i | \(-0.338095\pi\) | ||||
0.486989 | + | 0.873408i | \(0.338095\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 20.7846i | − | 0.0766960i | −0.999264 | − | 0.0383480i | \(-0.987790\pi\) | ||
0.999264 | − | 0.0383480i | \(-0.0122095\pi\) | |||||||
\(272\) | 138.564 | + | 80.0000i | 0.509427 | + | 0.294118i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.0000 | − | 17.3205i | 0.0364964 | − | 0.0632135i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 290.000i | 1.04693i | 0.852047 | + | 0.523466i | \(0.175361\pi\) | ||||
−0.852047 | + | 0.523466i | \(0.824639\pi\) | |||||||
\(278\) | −48.4974 | + | 84.0000i | −0.174451 | + | 0.302158i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −226.000 | −0.804270 | −0.402135 | − | 0.915580i | \(-0.631732\pi\) | ||||
−0.402135 | + | 0.915580i | \(0.631732\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −297.913 | −1.05270 | −0.526348 | − | 0.850269i | \(-0.676439\pi\) | ||||
−0.526348 | + | 0.850269i | \(0.676439\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 24.0000 | + | 13.8564i | 0.0839161 | + | 0.0484490i | ||||
\(287\) | 401.836 | 1.40012 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 189.000 | 0.653979 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −159.349 | + | 92.0000i | −0.545715 | + | 0.315068i | ||||
\(293\) | − | 362.000i | − | 1.23549i | −0.786377 | − | 0.617747i | \(-0.788045\pi\) | ||
0.786377 | − | 0.617747i | \(-0.211955\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −208.000 | −0.702703 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.46410 | − | 2.00000i | −0.0116245 | − | 0.00671141i | ||||
\(299\) | 55.4256i | 0.185370i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −336.000 | −1.11628 | ||||||||
\(302\) | −90.0666 | + | 156.000i | −0.298234 | + | 0.516556i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −288.000 | − | 166.277i | −0.947368 | − | 0.546963i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 145.492 | 0.473916 | 0.236958 | − | 0.971520i | \(-0.423850\pi\) | ||||
0.236958 | + | 0.971520i | \(0.423850\pi\) | |||||||
\(308\) | 166.277 | − | 96.0000i | 0.539860 | − | 0.311688i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 235.559i | − | 0.757424i | −0.925515 | − | 0.378712i | \(-0.876367\pi\) | ||
0.925515 | − | 0.378712i | \(-0.123633\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 478.000i | 1.52716i | 0.645715 | + | 0.763578i | \(0.276559\pi\) | ||||
−0.645715 | + | 0.763578i | \(0.723441\pi\) | |||||||
\(314\) | 214.000 | − | 370.659i | 0.681529 | − | 1.18044i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −408.000 | + | 235.559i | −1.29114 | + | 0.745440i | ||||
\(317\) | 170.000i | 0.536278i | 0.963380 | + | 0.268139i | \(0.0864086\pi\) | ||||
−0.963380 | + | 0.268139i | \(0.913591\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 180.133i | − | 0.564681i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 332.554 | + | 192.000i | 1.03278 | + | 0.596273i | ||||
\(323\) | 207.846 | 0.643486 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −36.0000 | − | 20.7846i | −0.110429 | − | 0.0637565i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 464.000i | − | 1.41463i | ||||||
\(329\) | 480.000 | 1.45897 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 408.764i | − | 1.23494i | −0.786596 | − | 0.617468i | \(-0.788158\pi\) | ||
0.786596 | − | 0.617468i | \(-0.211842\pi\) | |||||||
\(332\) | 96.9948 | + | 168.000i | 0.292153 | + | 0.506024i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −168.000 | − | 96.9948i | −0.502994 | − | 0.290404i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 338.000i | 1.00297i | 0.865167 | + | 0.501484i | \(0.167212\pi\) | ||||
−0.865167 | + | 0.501484i | \(0.832788\pi\) | |||||||
\(338\) | 285.788 | + | 165.000i | 0.845528 | + | 0.488166i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 48.0000 | 0.140762 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 346.410 | 1.00994 | ||||||||
\(344\) | 387.979i | 1.12785i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −334.000 | + | 578.505i | −0.965318 | + | 1.67198i | ||||
\(347\) | −200.918 | −0.579014 | −0.289507 | − | 0.957176i | \(-0.593491\pi\) | ||||
−0.289507 | + | 0.957176i | \(0.593491\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −506.000 | −1.44986 | −0.724928 | − | 0.688824i | \(-0.758127\pi\) | ||||
−0.724928 | + | 0.688824i | \(0.758127\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −110.851 | − | 192.000i | −0.314918 | − | 0.545455i | ||||
\(353\) | 178.000i | 0.504249i | 0.967695 | + | 0.252125i | \(0.0811293\pi\) | ||||
−0.967695 | + | 0.252125i | \(0.918871\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 164.000 | + | 284.056i | 0.460674 | + | 0.797911i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −187.061 | + | 324.000i | −0.522518 | + | 0.905028i | ||||
\(359\) | − | 166.277i | − | 0.463167i | −0.972815 | − | 0.231583i | \(-0.925609\pi\) | ||
0.972815 | − | 0.231583i | \(-0.0743906\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −71.0000 | −0.196676 | ||||||||
\(362\) | 3.46410 | + | 2.00000i | 0.00956934 | + | 0.00552486i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −48.0000 | + | 27.7128i | −0.131868 | + | 0.0761341i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 200.918 | 0.547460 | 0.273730 | − | 0.961807i | \(-0.411742\pi\) | ||||
0.273730 | + | 0.961807i | \(0.411742\pi\) | |||||||
\(368\) | 221.703 | − | 384.000i | 0.602452 | − | 1.04348i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 512.687i | 1.38191i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 310.000i | 0.831099i | 0.909571 | + | 0.415550i | \(0.136411\pi\) | ||||
−0.909571 | + | 0.415550i | \(0.863589\pi\) | |||||||
\(374\) | 120.000 | + | 69.2820i | 0.320856 | + | 0.185246i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 554.256i | − | 1.47409i | ||||||
\(377\) | 52.0000i | 0.137931i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 436.477i | − | 1.15165i | −0.817572 | − | 0.575827i | \(-0.804680\pi\) | ||
0.817572 | − | 0.575827i | \(-0.195320\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 221.703 | − | 384.000i | 0.580373 | − | 1.00524i | ||||
\(383\) | −609.682 | −1.59186 | −0.795929 | − | 0.605390i | \(-0.793017\pi\) | ||||
−0.795929 | + | 0.605390i | \(0.793017\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 290.000 | − | 502.295i | 0.751295 | − | 1.30128i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6.92820 | + | 4.00000i | −0.0178562 | + | 0.0103093i | ||||
\(389\) | −578.000 | −1.48586 | −0.742931 | − | 0.669368i | \(-0.766565\pi\) | ||||
−0.742931 | + | 0.669368i | \(0.766565\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 277.128i | 0.708768i | ||||||||
\(392\) | − | 8.00000i | − | 0.0204082i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −26.0000 | + | 45.0333i | −0.0659898 | + | 0.114298i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.0000i | 0.0654912i | 0.999464 | + | 0.0327456i | \(0.0104251\pi\) | ||||
−0.999464 | + | 0.0327456i | \(0.989575\pi\) | |||||||
\(398\) | −394.908 | + | 684.000i | −0.992230 | + | 1.71859i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −250.000 | −0.623441 | −0.311721 | − | 0.950174i | \(-0.600905\pi\) | ||||
−0.311721 | + | 0.950174i | \(0.600905\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.8564 | −0.0343831 | ||||||||
\(404\) | 148.000 | + | 256.344i | 0.366337 | + | 0.634514i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 312.000 | + | 180.133i | 0.768473 | + | 0.443678i | ||||
\(407\) | −180.133 | −0.442588 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −290.000 | −0.709046 | −0.354523 | − | 0.935047i | \(-0.615357\pi\) | ||||
−0.354523 | + | 0.935047i | \(0.615357\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 152.420 | + | 264.000i | 0.369953 | + | 0.640777i | ||||
\(413\) | − | 624.000i | − | 1.51090i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 32.0000 | + | 55.4256i | 0.0769231 | + | 0.133235i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −249.415 | − | 144.000i | −0.596687 | − | 0.344498i | ||||
\(419\) | 339.482i | 0.810219i | 0.914268 | + | 0.405110i | \(0.132767\pi\) | ||||
−0.914268 | + | 0.405110i | \(0.867233\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 674.000 | 1.60095 | 0.800475 | − | 0.599366i | \(-0.204581\pi\) | ||||
0.800475 | + | 0.599366i | \(0.204581\pi\) | |||||||
\(422\) | −242.487 | + | 420.000i | −0.574614 | + | 0.995261i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 592.000 | 1.39623 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −180.133 | −0.421858 | ||||||||
\(428\) | −41.5692 | − | 72.0000i | −0.0971243 | − | 0.168224i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 540.400i | 1.25383i | 0.779088 | + | 0.626914i | \(0.215682\pi\) | ||||
−0.779088 | + | 0.626914i | \(0.784318\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 334.000i | 0.771363i | 0.922632 | + | 0.385681i | \(0.126034\pi\) | ||||
−0.922632 | + | 0.385681i | \(0.873966\pi\) | |||||||
\(434\) | −48.0000 | + | 83.1384i | −0.110599 | + | 0.191563i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 92.0000 | + | 159.349i | 0.211009 | + | 0.365479i | ||||
\(437\) | − | 576.000i | − | 1.31808i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 117.779i | 0.268290i | 0.990962 | + | 0.134145i | \(0.0428288\pi\) | ||||
−0.990962 | + | 0.134145i | \(0.957171\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −34.6410 | − | 20.0000i | −0.0783733 | − | 0.0452489i | ||||
\(443\) | −76.2102 | −0.172032 | −0.0860161 | − | 0.996294i | \(-0.527414\pi\) | ||||
−0.0860161 | + | 0.996294i | \(0.527414\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 588.000 | + | 339.482i | 1.31839 | + | 0.761170i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 443.405 | 0.989743 | ||||||||
\(449\) | 394.000 | 0.877506 | 0.438753 | − | 0.898608i | \(-0.355420\pi\) | ||||
0.438753 | + | 0.898608i | \(0.355420\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 401.836i | − | 0.890988i | ||||||
\(452\) | 381.051 | − | 220.000i | 0.843034 | − | 0.486726i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 492.000 | + | 284.056i | 1.08370 | + | 0.625675i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 478.000i | − | 1.04595i | −0.852347 | − | 0.522976i | \(-0.824822\pi\) | ||
0.852347 | − | 0.522976i | \(-0.175178\pi\) | |||||||
\(458\) | 245.951 | + | 142.000i | 0.537011 | + | 0.310044i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −142.000 | −0.308026 | −0.154013 | − | 0.988069i | \(-0.549220\pi\) | ||||
−0.154013 | + | 0.988069i | \(0.549220\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −630.466 | −1.36170 | −0.680849 | − | 0.732423i | \(-0.738389\pi\) | ||||
−0.680849 | + | 0.732423i | \(0.738389\pi\) | |||||||
\(464\) | 208.000 | − | 360.267i | 0.448276 | − | 0.776437i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −82.0000 | + | 142.028i | −0.175966 | + | 0.304781i | ||||
\(467\) | −20.7846 | −0.0445067 | −0.0222533 | − | 0.999752i | \(-0.507084\pi\) | ||||
−0.0222533 | + | 0.999752i | \(0.507084\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −48.0000 | −0.102345 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −720.533 | −1.52655 | ||||||||
\(473\) | 336.000i | 0.710359i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −240.000 | + | 138.564i | −0.504202 | + | 0.291101i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 387.979 | − | 672.000i | 0.811672 | − | 1.40586i | ||||
\(479\) | − | 734.390i | − | 1.53317i | −0.642141 | − | 0.766586i | \(-0.721954\pi\) | ||
0.642141 | − | 0.766586i | \(-0.278046\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 52.0000 | 0.108108 | ||||||||
\(482\) | −79.6743 | − | 46.0000i | −0.165299 | − | 0.0954357i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 146.000 | + | 252.879i | 0.301653 | + | 0.522478i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 103.923 | 0.213394 | 0.106697 | − | 0.994292i | \(-0.465972\pi\) | ||||
0.106697 | + | 0.994292i | \(0.465972\pi\) | |||||||
\(488\) | 208.000i | 0.426230i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 921.451i | − | 1.87668i | −0.345711 | − | 0.938341i | \(-0.612362\pi\) | ||
0.345711 | − | 0.938341i | \(-0.387638\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 260.000i | 0.527383i | ||||||||
\(494\) | 72.0000 | + | 41.5692i | 0.145749 | + | 0.0841482i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 96.0000 | + | 55.4256i | 0.193548 | + | 0.111745i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 76.2102i | − | 0.152726i | −0.997080 | − | 0.0763630i | \(-0.975669\pi\) | ||
0.997080 | − | 0.0763630i | \(-0.0243308\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −145.492 | + | 252.000i | −0.289825 | + | 0.501992i | ||||
\(503\) | −581.969 | −1.15700 | −0.578498 | − | 0.815684i | \(-0.696361\pi\) | ||||
−0.578498 | + | 0.815684i | \(0.696361\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 192.000 | − | 332.554i | 0.379447 | − | 0.657221i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −290.985 | − | 504.000i | −0.572804 | − | 0.992126i | ||||
\(509\) | −842.000 | −1.65422 | −0.827112 | − | 0.562037i | \(-0.810018\pi\) | ||||
−0.827112 | + | 0.562037i | \(0.810018\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 318.697i | − | 0.623674i | ||||||
\(512\) | − | 512.000i | − | 1.00000i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −254.000 | + | 439.941i | −0.494163 | + | 0.855916i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 480.000i | − | 0.928433i | ||||||
\(518\) | 180.133 | − | 312.000i | 0.347748 | − | 0.602317i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 326.000 | 0.625720 | 0.312860 | − | 0.949799i | \(-0.398713\pi\) | ||||
0.312860 | + | 0.949799i | \(0.398713\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −311.769 | −0.596117 | −0.298058 | − | 0.954548i | \(-0.596339\pi\) | ||||
−0.298058 | + | 0.954548i | \(0.596339\pi\) | |||||||
\(524\) | −408.000 | + | 235.559i | −0.778626 | + | 0.449540i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 264.000 | + | 152.420i | 0.501901 | + | 0.289773i | ||||
\(527\) | −69.2820 | −0.131465 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 239.000 | 0.451796 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 498.831 | − | 288.000i | 0.937652 | − | 0.541353i | ||||
\(533\) | 116.000i | 0.217636i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 55.4256i | 0.103406i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 453.797 | + | 262.000i | 0.843489 | + | 0.486989i | ||||
\(539\) | − | 6.92820i | − | 0.0128538i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 530.000 | 0.979667 | 0.489834 | − | 0.871816i | \(-0.337058\pi\) | ||||
0.489834 | + | 0.871816i | \(0.337058\pi\) | |||||||
\(542\) | 20.7846 | − | 36.0000i | 0.0383480 | − | 0.0664207i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 160.000 | + | 277.128i | 0.294118 | + | 0.509427i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −339.482 | −0.620625 | −0.310313 | − | 0.950635i | \(-0.600434\pi\) | ||||
−0.310313 | + | 0.950635i | \(0.600434\pi\) | |||||||
\(548\) | 34.6410 | − | 20.0000i | 0.0632135 | − | 0.0364964i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 540.400i | − | 0.980762i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 816.000i | − | 1.47559i | ||||||
\(554\) | −290.000 | + | 502.295i | −0.523466 | + | 0.906669i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −168.000 | + | 96.9948i | −0.302158 | + | 0.174451i | ||||
\(557\) | − | 766.000i | − | 1.37522i | −0.726078 | − | 0.687612i | \(-0.758659\pi\) | ||
0.726078 | − | 0.687612i | \(-0.241341\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 96.9948i | − | 0.173515i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −391.443 | − | 226.000i | −0.696519 | − | 0.402135i | ||||
\(563\) | 491.902 | 0.873717 | 0.436858 | − | 0.899530i | \(-0.356091\pi\) | ||||
0.436858 | + | 0.899530i | \(0.356091\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −516.000 | − | 297.913i | −0.911661 | − | 0.526348i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −422.000 | −0.741652 | −0.370826 | − | 0.928702i | \(-0.620925\pi\) | ||||
−0.370826 | + | 0.928702i | \(0.620925\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 284.056i | 0.497472i | 0.968571 | + | 0.248736i | \(0.0800151\pi\) | ||||
−0.968571 | + | 0.248736i | \(0.919985\pi\) | |||||||
\(572\) | 27.7128 | + | 48.0000i | 0.0484490 | + | 0.0839161i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 696.000 | + | 401.836i | 1.21254 | + | 0.700062i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 46.0000i | − | 0.0797227i | −0.999205 | − | 0.0398614i | \(-0.987308\pi\) | ||
0.999205 | − | 0.0398614i | \(-0.0126916\pi\) | |||||||
\(578\) | 327.358 | + | 189.000i | 0.566363 | + | 0.326990i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −336.000 | −0.578313 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 512.687 | 0.879395 | ||||||||
\(584\) | −368.000 | −0.630137 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 362.000 | − | 627.002i | 0.617747 | − | 1.06997i | ||||
\(587\) | −630.466 | −1.07405 | −0.537024 | − | 0.843567i | \(-0.680452\pi\) | ||||
−0.537024 | + | 0.843567i | \(0.680452\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 144.000 | 0.244482 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −360.267 | − | 208.000i | −0.608558 | − | 0.351351i | ||||
\(593\) | 82.0000i | 0.138280i | 0.997607 | + | 0.0691400i | \(0.0220255\pi\) | ||||
−0.997607 | + | 0.0691400i | \(0.977974\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.00000 | − | 6.92820i | −0.00671141 | − | 0.0116245i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −55.4256 | + | 96.0000i | −0.0926850 | + | 0.160535i | ||||
\(599\) | − | 55.4256i | − | 0.0925303i | −0.998929 | − | 0.0462651i | \(-0.985268\pi\) | ||
0.998929 | − | 0.0462651i | \(-0.0147319\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −334.000 | −0.555740 | −0.277870 | − | 0.960619i | \(-0.589629\pi\) | ||||
−0.277870 | + | 0.960619i | \(0.589629\pi\) | |||||||
\(602\) | −581.969 | − | 336.000i | −0.966726 | − | 0.558140i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −312.000 | + | 180.133i | −0.516556 | + | 0.298234i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −367.195 | −0.604934 | −0.302467 | − | 0.953160i | \(-0.597810\pi\) | ||||
−0.302467 | + | 0.953160i | \(0.597810\pi\) | |||||||
\(608\) | −332.554 | − | 576.000i | −0.546963 | − | 0.947368i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 138.564i | 0.226782i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 214.000i | 0.349103i | 0.984648 | + | 0.174551i | \(0.0558475\pi\) | ||||
−0.984648 | + | 0.174551i | \(0.944152\pi\) | |||||||
\(614\) | 252.000 | + | 145.492i | 0.410423 | + | 0.236958i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 384.000 | 0.623377 | ||||||||
\(617\) | 1118.00i | 1.81199i | 0.423285 | + | 0.905997i | \(0.360877\pi\) | ||||
−0.423285 | + | 0.905997i | \(0.639123\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 672.036i | − | 1.08568i | −0.839836 | − | 0.542840i | \(-0.817349\pi\) | ||
0.839836 | − | 0.542840i | \(-0.182651\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 235.559 | − | 408.000i | 0.378712 | − | 0.655949i | ||||
\(623\) | −568.113 | −0.911898 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −478.000 | + | 827.920i | −0.763578 | + | 1.32256i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 741.318 | − | 428.000i | 1.18044 | − | 0.681529i | ||||
\(629\) | 260.000 | 0.413355 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 145.492i | 0.230574i | 0.993332 | + | 0.115287i | \(0.0367788\pi\) | ||||
−0.993332 | + | 0.115287i | \(0.963221\pi\) | |||||||
\(632\) | −942.236 | −1.49088 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −170.000 | + | 294.449i | −0.268139 | + | 0.464430i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.00000i | 0.00313972i | ||||||||
\(638\) | 180.133 | − | 312.000i | 0.282341 | − | 0.489028i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.0000 | −0.0156006 | −0.00780031 | − | 0.999970i | \(-0.502483\pi\) | ||||
−0.00780031 | + | 0.999970i | \(0.502483\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1212.44 | −1.88559 | −0.942796 | − | 0.333370i | \(-0.891814\pi\) | ||||
−0.942796 | + | 0.333370i | \(0.891814\pi\) | |||||||
\(644\) | 384.000 | + | 665.108i | 0.596273 | + | 1.03278i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 360.000 | + | 207.846i | 0.557276 | + | 0.321743i | ||||
\(647\) | 332.554 | 0.513993 | 0.256997 | − | 0.966412i | \(-0.417267\pi\) | ||||
0.256997 | + | 0.966412i | \(0.417267\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −624.000 | −0.961479 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −41.5692 | − | 72.0000i | −0.0637565 | − | 0.110429i | ||||
\(653\) | 670.000i | 1.02603i | 0.858379 | + | 0.513017i | \(0.171472\pi\) | ||||
−0.858379 | + | 0.513017i | \(0.828528\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 464.000 | − | 803.672i | 0.707317 | − | 1.22511i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 831.384 | + | 480.000i | 1.26350 | + | 0.729483i | ||||
\(659\) | 824.456i | 1.25107i | 0.780195 | + | 0.625536i | \(0.215120\pi\) | ||||
−0.780195 | + | 0.625536i | \(0.784880\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1222.00 | −1.84871 | −0.924357 | − | 0.381529i | \(-0.875398\pi\) | ||||
−0.924357 | + | 0.381529i | \(0.875398\pi\) | |||||||
\(662\) | 408.764 | − | 708.000i | 0.617468 | − | 1.06949i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 387.979i | 0.584306i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 720.533 | 1.08026 | ||||||||
\(668\) | −193.990 | − | 336.000i | −0.290404 | − | 0.502994i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 180.133i | 0.268455i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 334.000i | 0.496285i | 0.968724 | + | 0.248143i | \(0.0798202\pi\) | ||||
−0.968724 | + | 0.248143i | \(0.920180\pi\) | |||||||
\(674\) | −338.000 | + | 585.433i | −0.501484 | + | 0.868595i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 330.000 | + | 571.577i | 0.488166 | + | 0.845528i | ||||
\(677\) | − | 1006.00i | − | 1.48597i | −0.669309 | − | 0.742984i | \(-0.733410\pi\) | ||
0.669309 | − | 0.742984i | \(-0.266590\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 13.8564i | − | 0.0204071i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 83.1384 | + | 48.0000i | 0.121904 | + | 0.0703812i | ||||
\(683\) | −187.061 | −0.273882 | −0.136941 | − | 0.990579i | \(-0.543727\pi\) | ||||
−0.136941 | + | 0.990579i | \(0.543727\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 600.000 | + | 346.410i | 0.874636 | + | 0.504971i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −387.979 | + | 672.000i | −0.563924 | + | 0.976744i | ||||
\(689\) | −148.000 | −0.214804 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 990.733i | − | 1.43377i | −0.697193 | − | 0.716884i | \(-0.745568\pi\) | ||
0.697193 | − | 0.716884i | \(-0.254432\pi\) | |||||||
\(692\) | −1157.01 | + | 668.000i | −1.67198 | + | 0.965318i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −348.000 | − | 200.918i | −0.501441 | − | 0.289507i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 580.000i | 0.832138i | ||||||||
\(698\) | −876.418 | − | 506.000i | −1.25561 | − | 0.724928i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1034.00 | 1.47504 | 0.737518 | − | 0.675328i | \(-0.235998\pi\) | ||||
0.737518 | + | 0.675328i | \(0.235998\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −540.400 | −0.768705 | ||||||||
\(704\) | − | 443.405i | − | 0.629837i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −178.000 | + | 308.305i | −0.252125 | + | 0.436693i | ||||
\(707\) | −512.687 | −0.725158 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −530.000 | −0.747532 | −0.373766 | − | 0.927523i | \(-0.621934\pi\) | ||||
−0.373766 | + | 0.927523i | \(0.621934\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 656.000i | 0.921348i | ||||||||
\(713\) | 192.000i | 0.269285i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −648.000 | + | 374.123i | −0.905028 | + | 0.522518i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 166.277 | − | 288.000i | 0.231583 | − | 0.401114i | ||||
\(719\) | 706.677i | 0.982861i | 0.870917 | + | 0.491430i | \(0.163526\pi\) | ||||
−0.870917 | + | 0.491430i | \(0.836474\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −528.000 | −0.732316 | ||||||||
\(722\) | −122.976 | − | 71.0000i | −0.170326 | − | 0.0983380i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.00000 | + | 6.92820i | 0.00552486 | + | 0.00956934i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 242.487 | 0.333545 | 0.166772 | − | 0.985995i | \(-0.446665\pi\) | ||||
0.166772 | + | 0.985995i | \(0.446665\pi\) | |||||||
\(728\) | −110.851 | −0.152268 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 484.974i | − | 0.663439i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 194.000i | − | 0.264666i | −0.991205 | − | 0.132333i | \(-0.957753\pi\) | ||
0.991205 | − | 0.132333i | \(-0.0422468\pi\) | |||||||
\(734\) | 348.000 | + | 200.918i | 0.474114 | + | 0.273730i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 768.000 | − | 443.405i | 1.04348 | − | 0.602452i | ||||
\(737\) | 48.0000i | 0.0651289i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1351.00i | − | 1.82815i | −0.405550 | − | 0.914073i | \(-0.632920\pi\) | ||
0.405550 | − | 0.914073i | \(-0.367080\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −512.687 | + | 888.000i | −0.690953 | + | 1.19677i | ||||
\(743\) | 678.964 | 0.913814 | 0.456907 | − | 0.889514i | \(-0.348957\pi\) | ||||
0.456907 | + | 0.889514i | \(0.348957\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −310.000 | + | 536.936i | −0.415550 | + | 0.719753i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 138.564 | + | 240.000i | 0.185246 | + | 0.320856i | ||||
\(749\) | 144.000 | 0.192256 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 658.179i | 0.876404i | 0.898877 | + | 0.438202i | \(0.144385\pi\) | ||||
−0.898877 | + | 0.438202i | \(0.855615\pi\) | |||||||
\(752\) | 554.256 | − | 960.000i | 0.737043 | − | 1.27660i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −52.0000 | + | 90.0666i | −0.0689655 | + | 0.119452i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1006.00i | − | 1.32893i | −0.747319 | − | 0.664465i | \(-0.768659\pi\) | ||
0.747319 | − | 0.664465i | \(-0.231341\pi\) | |||||||
\(758\) | 436.477 | − | 756.000i | 0.575827 | − | 0.997361i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 758.000 | 0.996058 | 0.498029 | − | 0.867160i | \(-0.334057\pi\) | ||||
0.498029 | + | 0.867160i | \(0.334057\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −318.697 | −0.417690 | ||||||||
\(764\) | 768.000 | − | 443.405i | 1.00524 | − | 0.580373i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1056.00 | − | 609.682i | −1.37859 | − | 0.795929i | ||||
\(767\) | 180.133 | 0.234854 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.00000 | −0.00260078 | −0.00130039 | − | 0.999999i | \(-0.500414\pi\) | ||||
−0.00130039 | + | 0.999999i | \(0.500414\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1004.59 | − | 580.000i | 1.30128 | − | 0.751295i | ||||
\(773\) | 262.000i | 0.338939i | 0.985535 | + | 0.169470i | \(0.0542055\pi\) | ||||
−0.985535 | + | 0.169470i | \(0.945795\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −16.0000 | −0.0206186 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1001.13 | − | 578.000i | −1.28679 | − | 0.742931i | ||||
\(779\) | − | 1205.51i | − | 1.54751i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −277.128 | + | 480.000i | −0.354384 | + | 0.613811i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 8.00000 | − | 13.8564i | 0.0102041 | − | 0.0176740i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1447.99 | −1.83989 | −0.919946 | − | 0.392046i | \(-0.871767\pi\) | ||||
−0.919946 | + | 0.392046i | \(0.871767\pi\) | |||||||
\(788\) | −90.0666 | + | 52.0000i | −0.114298 | + | 0.0659898i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 762.102i | 0.963467i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 52.0000i | − | 0.0655738i | ||||||
\(794\) | −26.0000 | + | 45.0333i | −0.0327456 | + | 0.0567170i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1368.00 | + | 789.815i | −1.71859 | + | 0.992230i | ||||
\(797\) | 866.000i | 1.08657i | 0.839547 | + | 0.543287i | \(0.182821\pi\) | ||||
−0.839547 | + | 0.543287i | \(0.817179\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 692.820i | 0.867109i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −433.013 | − | 250.000i | −0.539916 | − | 0.311721i | ||||
\(803\) | −318.697 | −0.396883 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −24.0000 | − | 13.8564i | −0.0297767 | − | 0.0171916i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 592.000i | 0.732673i | ||||||||
\(809\) | 10.0000 | 0.0123609 | 0.00618047 | − | 0.999981i | \(-0.498033\pi\) | ||||
0.00618047 | + | 0.999981i | \(0.498033\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 436.477i | 0.538196i | 0.963113 | + | 0.269098i | \(0.0867255\pi\) | ||||
−0.963113 | + | 0.269098i | \(0.913274\pi\) | |||||||
\(812\) | 360.267 | + | 624.000i | 0.443678 | + | 0.768473i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −312.000 | − | 180.133i | −0.383292 | − | 0.221294i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1008.00i | 1.23378i | ||||||||
\(818\) | −502.295 | − | 290.000i | −0.614052 | − | 0.354523i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −838.000 | −1.02071 | −0.510353 | − | 0.859965i | \(-0.670485\pi\) | ||||
−0.510353 | + | 0.859965i | \(0.670485\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −879.882 | −1.06912 | −0.534558 | − | 0.845132i | \(-0.679522\pi\) | ||||
−0.534558 | + | 0.845132i | \(0.679522\pi\) | |||||||
\(824\) | 609.682i | 0.739905i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 624.000 | − | 1080.80i | 0.755448 | − | 1.30847i | ||||
\(827\) | 727.461 | 0.879639 | 0.439819 | − | 0.898086i | \(-0.355042\pi\) | ||||
0.439819 | + | 0.898086i | \(0.355042\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1298.00 | −1.56574 | −0.782871 | − | 0.622184i | \(-0.786246\pi\) | ||||
−0.782871 | + | 0.622184i | \(0.786246\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 128.000i | 0.153846i | ||||||||
\(833\) | 10.0000i | 0.0120048i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −288.000 | − | 498.831i | −0.344498 | − | 0.596687i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −339.482 | + | 588.000i | −0.405110 | + | 0.701671i | ||||
\(839\) | − | 193.990i | − | 0.231215i | −0.993295 | − | 0.115608i | \(-0.963118\pi\) | ||
0.993295 | − | 0.115608i | \(-0.0368815\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −165.000 | −0.196195 | ||||||||
\(842\) | 1167.40 | + | 674.000i | 1.38646 | + | 0.800475i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −840.000 | + | 484.974i | −0.995261 | + | 0.574614i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −505.759 | −0.597118 | ||||||||
\(848\) | 1025.37 | + | 592.000i | 1.20917 | + | 0.698113i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 720.533i | − | 0.846690i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 506.000i | − | 0.593200i | −0.955002 | − | 0.296600i | \(-0.904147\pi\) | ||
0.955002 | − | 0.296600i | \(-0.0958529\pi\) | |||||||
\(854\) | −312.000 | − | 180.133i | −0.365340 | − | 0.210929i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 166.277i | − | 0.194249i | ||||||
\(857\) | 998.000i | 1.16453i | 0.813000 | + | 0.582264i | \(0.197833\pi\) | ||||
−0.813000 | + | 0.582264i | \(0.802167\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 505.759i | 0.588776i | 0.955686 | + | 0.294388i | \(0.0951158\pi\) | ||||
−0.955686 | + | 0.294388i | \(0.904884\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −540.400 | + | 936.000i | −0.626914 | + | 1.08585i | ||||
\(863\) | 166.277 | 0.192673 | 0.0963365 | − | 0.995349i | \(-0.469287\pi\) | ||||
0.0963365 | + | 0.995349i | \(0.469287\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −334.000 | + | 578.505i | −0.385681 | + | 0.668020i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −166.277 | + | 96.0000i | −0.191563 | + | 0.110599i | ||||
\(869\) | −816.000 | −0.939010 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 13.8564i | − | 0.0159086i | ||||||
\(872\) | 368.000i | 0.422018i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 576.000 | − | 997.661i | 0.659039 | − | 1.14149i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 646.000i | − | 0.736602i | −0.929707 | − | 0.368301i | \(-0.879940\pi\) | ||
0.929707 | − | 0.368301i | \(-0.120060\pi\) | |||||||
\(878\) | −117.779 | + | 204.000i | −0.134145 | + | 0.232346i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −898.000 | −1.01930 | −0.509648 | − | 0.860383i | \(-0.670224\pi\) | ||||
−0.509648 | + | 0.860383i | \(0.670224\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 727.461 | 0.823852 | 0.411926 | − | 0.911217i | \(-0.364856\pi\) | ||||
0.411926 | + | 0.911217i | \(0.364856\pi\) | |||||||
\(884\) | −40.0000 | − | 69.2820i | −0.0452489 | − | 0.0783733i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −132.000 | − | 76.2102i | −0.148984 | − | 0.0860161i | ||||
\(887\) | −845.241 | −0.952921 | −0.476460 | − | 0.879196i | \(-0.658080\pi\) | ||||
−0.476460 | + | 0.879196i | \(0.658080\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1008.00 | 1.13386 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 678.964 | + | 1176.00i | 0.761170 | + | 1.31839i | ||||
\(893\) | − | 1440.00i | − | 1.61254i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 768.000 | + | 443.405i | 0.857143 | + | 0.494872i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 682.428 | + | 394.000i | 0.759942 | + | 0.438753i | ||||
\(899\) | 180.133i | 0.200371i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −740.000 | −0.821310 | ||||||||
\(902\) | 401.836 | − | 696.000i | 0.445494 | − | 0.771619i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 880.000 | 0.973451 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1364.86 | 1.50480 | 0.752401 | − | 0.658705i | \(-0.228895\pi\) | ||||
0.752401 | + | 0.658705i | \(0.228895\pi\) | |||||||
\(908\) | 568.113 | + | 984.000i | 0.625675 | + | 1.08370i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 387.979i | − | 0.425883i | −0.977065 | − | 0.212941i | \(-0.931696\pi\) | ||
0.977065 | − | 0.212941i | \(-0.0683044\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 336.000i | 0.368018i | ||||||||
\(914\) | 478.000 | − | 827.920i | 0.522976 | − | 0.905821i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 284.000 | + | 491.902i | 0.310044 | + | 0.537011i | ||||
\(917\) | − | 816.000i | − | 0.889858i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 602.754i | 0.655880i | 0.944699 | + | 0.327940i | \(0.106354\pi\) | ||||
−0.944699 | + | 0.327940i | \(0.893646\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −245.951 | − | 142.000i | −0.266758 | − | 0.154013i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1092.00 | − | 630.466i | −1.17927 | − | 0.680849i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 720.533 | − | 416.000i | 0.776437 | − | 0.448276i | ||||
\(929\) | 1594.00 | 1.71582 | 0.857912 | − | 0.513797i | \(-0.171762\pi\) | ||||
0.857912 | + | 0.513797i | \(0.171762\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 20.7846i | − | 0.0223250i | ||||||
\(932\) | −284.056 | + | 164.000i | −0.304781 | + | 0.175966i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −36.0000 | − | 20.7846i | −0.0385439 | − | 0.0222533i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 674.000i | 0.719317i | 0.933084 | + | 0.359658i | \(0.117107\pi\) | ||||
−0.933084 | + | 0.359658i | \(0.882893\pi\) | |||||||
\(938\) | −83.1384 | − | 48.0000i | −0.0886337 | − | 0.0511727i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −430.000 | −0.456961 | −0.228480 | − | 0.973549i | \(-0.573376\pi\) | ||||
−0.228480 | + | 0.973549i | \(0.573376\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1607.34 | 1.70450 | ||||||||
\(944\) | −1248.00 | − | 720.533i | −1.32203 | − | 0.763277i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −336.000 | + | 581.969i | −0.355180 | + | 0.615189i | ||||
\(947\) | 76.2102 | 0.0804754 | 0.0402377 | − | 0.999190i | \(-0.487188\pi\) | ||||
0.0402377 | + | 0.999190i | \(0.487188\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 92.0000 | 0.0969442 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −554.256 | −0.582202 | ||||||||
\(953\) | 730.000i | 0.766002i | 0.923748 | + | 0.383001i | \(0.125109\pi\) | ||||
−0.923748 | + | 0.383001i | \(0.874891\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1344.00 | − | 775.959i | 1.40586 | − | 0.811672i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 734.390 | − | 1272.00i | 0.766586 | − | 1.32777i | ||||
\(959\) | 69.2820i | 0.0722440i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 913.000 | 0.950052 | ||||||||
\(962\) | 90.0666 | + | 52.0000i | 0.0936244 | + | 0.0540541i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −92.0000 | − | 159.349i | −0.0954357 | − | 0.165299i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 921.451 | 0.952897 | 0.476448 | − | 0.879202i | \(-0.341924\pi\) | ||||
0.476448 | + | 0.879202i | \(0.341924\pi\) | |||||||
\(968\) | 584.000i | 0.603306i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1475.71i | 1.51978i | 0.650051 | + | 0.759890i | \(0.274747\pi\) | ||||
−0.650051 | + | 0.759890i | \(0.725253\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 336.000i | − | 0.345324i | ||||||
\(974\) | 180.000 | + | 103.923i | 0.184805 | + | 0.106697i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −208.000 | + | 360.267i | −0.213115 | + | 0.369126i | ||||
\(977\) | − | 346.000i | − | 0.354145i | −0.984198 | − | 0.177073i | \(-0.943337\pi\) | ||
0.984198 | − | 0.177073i | \(-0.0566628\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 568.113i | 0.580299i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 921.451 | − | 1596.00i | 0.938341 | − | 1.62525i | ||||
\(983\) | 734.390 | 0.747090 | 0.373545 | − | 0.927612i | \(-0.378142\pi\) | ||||
0.373545 | + | 0.927612i | \(0.378142\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −260.000 | + | 450.333i | −0.263692 | + | 0.456727i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 83.1384 | + | 144.000i | 0.0841482 | + | 0.145749i | ||||
\(989\) | −1344.00 | −1.35895 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 976.877i | − | 0.985748i | −0.870101 | − | 0.492874i | \(-0.835946\pi\) | ||
0.870101 | − | 0.492874i | \(-0.164054\pi\) | |||||||
\(992\) | 110.851 | + | 192.000i | 0.111745 | + | 0.193548i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 458.000i | 0.459378i | 0.973264 | + | 0.229689i | \(0.0737709\pi\) | ||||
−0.973264 | + | 0.229689i | \(0.926229\pi\) | |||||||
\(998\) | 76.2102 | − | 132.000i | 0.0763630 | − | 0.132265i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))