Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5292,2,Mod(1549,5292)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5292, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5292.1549");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5292.i (of order \(3\), 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: | \(42.2568327497\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1549.1 | ||
Root | \(0.500000 - 2.05195i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5292.1549 |
Dual form | 5292.2.i.e.2125.1 |
$q$-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 \(\left(\mathbb{Z}/5292\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) | \(2647\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.23025 | − | 2.13086i | −0.550186 | − | 0.952949i | −0.998261 | − | 0.0589535i | \(-0.981224\pi\) |
0.448075 | − | 0.893996i | \(-0.352110\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.32383 | − | 4.02499i | 0.700662 | − | 1.21358i | −0.267573 | − | 0.963538i | \(-0.586222\pi\) |
0.968234 | − | 0.250044i | \(-0.0804451\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.55408 | − | 6.15585i | 0.985726 | − | 1.70733i | 0.347059 | − | 0.937843i | \(-0.387180\pi\) |
0.638667 | − | 0.769484i | \(-0.279486\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.25729 | + | 3.90975i | 0.547474 | + | 0.948253i | 0.998447 | + | 0.0557155i | \(0.0177440\pi\) |
−0.450972 | + | 0.892538i | \(0.648923\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.16372 | − | 3.74766i | 0.496390 | − | 0.859773i | −0.503601 | − | 0.863936i | \(-0.667992\pi\) |
0.999991 | + | 0.00416311i | \(0.00132516\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.93346 | + | 5.08091i | 0.611669 | + | 1.05944i | 0.990959 | + | 0.134164i | \(0.0428350\pi\) |
−0.379290 | + | 0.925278i | \(0.623832\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.527042 | + | 0.912864i | −0.105408 | + | 0.182573i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.48755 | − | 6.04061i | −0.647621 | − | 1.12171i | −0.983689 | − | 0.179875i | \(-0.942431\pi\) |
0.336068 | − | 0.941838i | \(-0.390903\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.38151 | 1.32576 | 0.662880 | − | 0.748726i | \(-0.269334\pi\) | ||||
0.662880 | + | 0.748726i | \(0.269334\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.363327 | − | 0.629301i | 0.0597306 | − | 0.103456i | −0.834614 | − | 0.550835i | \(-0.814309\pi\) |
0.894344 | + | 0.447379i | \(0.147643\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.136673 | + | 0.236725i | −0.0213448 | + | 0.0369702i | −0.876500 | − | 0.481401i | \(-0.840128\pi\) |
0.855156 | + | 0.518371i | \(0.173461\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.41741 | + | 4.18708i | 0.368652 | + | 0.638524i | 0.989355 | − | 0.145522i | \(-0.0464862\pi\) |
−0.620703 | + | 0.784046i | \(0.713153\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.67257 | 0.535699 | 0.267850 | − | 0.963461i | \(-0.413687\pi\) | ||||
0.267850 | + | 0.963461i | \(0.413687\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.52704 | + | 4.37697i | 0.347116 | + | 0.601222i | 0.985736 | − | 0.168300i | \(-0.0538277\pi\) |
−0.638620 | + | 0.769522i | \(0.720494\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.4356 | −1.54198 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.13307 | 1.18903 | 0.594513 | − | 0.804086i | \(-0.297345\pi\) | ||||
0.594513 | + | 0.804086i | \(0.297345\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.8171 | 1.76910 | 0.884550 | − | 0.466445i | \(-0.154466\pi\) | ||||
0.884550 | + | 0.466445i | \(0.154466\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −17.4897 | −2.16933 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.32743 | −0.162171 | −0.0810857 | − | 0.996707i | \(-0.525839\pi\) | ||||
−0.0810857 | + | 0.996707i | \(0.525839\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.5218 | −1.60474 | −0.802370 | − | 0.596826i | \(-0.796428\pi\) | ||||
−0.802370 | + | 0.596826i | \(0.796428\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.16372 | − | 3.74766i | −0.253244 | − | 0.438631i | 0.711173 | − | 0.703017i | \(-0.248164\pi\) |
−0.964417 | + | 0.264386i | \(0.914831\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.43560 | 0.724061 | 0.362031 | − | 0.932166i | \(-0.382084\pi\) | ||||
0.362031 | + | 0.932166i | \(0.382084\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.742705 | − | 1.28640i | −0.0815225 | − | 0.141201i | 0.822382 | − | 0.568936i | \(-0.192645\pi\) |
−0.903904 | + | 0.427735i | \(0.859312\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.55408 | − | 9.61996i | 0.602425 | − | 1.04343i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.91741 | + | 8.51721i | −0.521245 | + | 0.902822i | 0.478450 | + | 0.878115i | \(0.341199\pi\) |
−0.999695 | + | 0.0247073i | \(0.992135\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.6477 | −1.09243 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.246304 | − | 0.426611i | −0.0250084 | − | 0.0433158i | 0.853250 | − | 0.521502i | \(-0.174628\pi\) |
−0.878259 | + | 0.478186i | \(0.841295\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.70321 | + | 2.95005i | −0.169476 | + | 0.293541i | −0.938236 | − | 0.345997i | \(-0.887541\pi\) |
0.768760 | + | 0.639537i | \(0.220874\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.58113 | + | 4.47064i | 0.254326 | + | 0.440505i | 0.964712 | − | 0.263307i | \(-0.0848131\pi\) |
−0.710386 | + | 0.703812i | \(0.751480\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.88151 | + | 4.99093i | −0.278567 | + | 0.482491i | −0.971029 | − | 0.238963i | \(-0.923193\pi\) |
0.692462 | + | 0.721454i | \(0.256526\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.49115 | + | 7.77889i | 0.430174 | + | 0.745083i | 0.996888 | − | 0.0788317i | \(-0.0251190\pi\) |
−0.566714 | + | 0.823914i | \(0.691786\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.679767 | + | 1.17739i | −0.0639471 | + | 0.110760i | −0.896226 | − | 0.443597i | \(-0.853702\pi\) |
0.832279 | + | 0.554356i | \(0.187036\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.21780 | − | 12.5016i | 0.673063 | − | 1.16578i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.30039 | − | 9.18054i | −0.481853 | − | 0.834595i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.70895 | −0.868394 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.820039 | −0.0727667 | −0.0363833 | − | 0.999338i | \(-0.511584\pi\) | ||||
−0.0363833 | + | 0.999338i | \(0.511584\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.89397 | − | 6.74455i | −0.340218 | − | 0.589274i | 0.644255 | − | 0.764810i | \(-0.277167\pi\) |
−0.984473 | + | 0.175536i | \(0.943834\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.49640 | + | 2.59184i | −0.127846 | + | 0.221436i | −0.922842 | − | 0.385179i | \(-0.874140\pi\) |
0.794996 | + | 0.606615i | \(0.207473\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.16372 | − | 5.47972i | 0.268343 | − | 0.464783i | −0.700091 | − | 0.714053i | \(-0.746857\pi\) |
0.968434 | + | 0.249270i | \(0.0801907\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −16.5182 | − | 28.6103i | −1.38132 | − | 2.39252i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.58113 | + | 14.8629i | −0.712624 | + | 1.23430i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.19076 | − | 3.79450i | −0.179474 | − | 0.310858i | 0.762227 | − | 0.647310i | \(-0.224106\pi\) |
−0.941700 | + | 0.336452i | \(0.890773\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.30039 | + | 5.71644i | −0.268582 | + | 0.465197i | −0.968496 | − | 0.249030i | \(-0.919888\pi\) |
0.699914 | + | 0.714227i | \(0.253222\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.08113 | − | 15.7290i | −0.729414 | − | 1.26338i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.78074 | 0.461353 | 0.230677 | − | 0.973030i | \(-0.425906\pi\) | ||||
0.230677 | + | 0.973030i | \(0.425906\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.66372 | + | 6.34574i | −0.286964 | + | 0.497037i | −0.973084 | − | 0.230452i | \(-0.925979\pi\) |
0.686119 | + | 0.727489i | \(0.259313\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.01459 | − | 10.4176i | 0.465423 | − | 0.806136i | −0.533798 | − | 0.845612i | \(-0.679236\pi\) |
0.999221 | + | 0.0394762i | \(0.0125689\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −18.7630 | − | 32.4985i | −1.44331 | − | 2.49989i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.89903 | 0.372466 | 0.186233 | − | 0.982506i | \(-0.440372\pi\) | ||||
0.186233 | + | 0.982506i | \(0.440372\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.890369 | − | 1.54216i | −0.0665493 | − | 0.115267i | 0.830831 | − | 0.556525i | \(-0.187866\pi\) |
−0.897380 | + | 0.441258i | \(0.854532\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.9430 | 1.25936 | 0.629681 | − | 0.776854i | \(-0.283185\pi\) | ||||
0.629681 | + | 0.776854i | \(0.283185\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.78794 | −0.131452 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.9823 | 1.53438 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.48968 | 0.397220 | 0.198610 | − | 0.980079i | \(-0.436357\pi\) | ||||
0.198610 | + | 0.980079i | \(0.436357\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.50739 | −0.396431 | −0.198215 | − | 0.980158i | \(-0.563515\pi\) | ||||
−0.198215 | + | 0.980158i | \(0.563515\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.6300 | −0.828600 | −0.414300 | − | 0.910140i | \(-0.635974\pi\) | ||||
−0.414300 | + | 0.910140i | \(0.635974\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.07373 | − | 3.59181i | −0.147003 | − | 0.254617i | 0.783115 | − | 0.621876i | \(-0.213629\pi\) |
−0.930118 | + | 0.367260i | \(0.880296\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.672570 | 0.0469743 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.0562 | − | 17.4179i | −0.695603 | − | 1.20482i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.6082 | − | 23.5700i | 0.936825 | − | 1.62263i | 0.165478 | − | 0.986213i | \(-0.447083\pi\) |
0.771347 | − | 0.636415i | \(-0.219583\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.94805 | − | 10.3023i | 0.405654 | − | 0.702613i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 32.0905 | 2.15864 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.60817 | − | 2.78543i | −0.107691 | − | 0.186526i | 0.807144 | − | 0.590355i | \(-0.201012\pi\) |
−0.914834 | + | 0.403829i | \(0.867679\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.97296 | + | 13.8096i | −0.529184 | + | 0.916573i | 0.470237 | + | 0.882540i | \(0.344168\pi\) |
−0.999421 | + | 0.0340330i | \(0.989165\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.608168 | − | 1.05338i | −0.0401889 | − | 0.0696092i | 0.845231 | − | 0.534401i | \(-0.179463\pi\) |
−0.885420 | + | 0.464791i | \(0.846129\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.98608 | − | 17.2964i | 0.654210 | − | 1.13313i | −0.327881 | − | 0.944719i | \(-0.606335\pi\) |
0.982091 | − | 0.188406i | \(-0.0603321\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.51819 | − | 7.82573i | −0.294734 | − | 0.510494i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.00739 | − | 5.20896i | 0.194532 | − | 0.336939i | −0.752215 | − | 0.658918i | \(-0.771015\pi\) |
0.946747 | + | 0.321978i | \(0.104348\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.30778 | + | 16.1215i | −0.599567 | + | 1.03848i | 0.393318 | + | 0.919402i | \(0.371327\pi\) |
−0.992885 | + | 0.119078i | \(0.962006\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.3801 | − | 26.6390i | −0.978609 | − | 1.69500i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.99707 | 0.441651 | 0.220826 | − | 0.975313i | \(-0.429125\pi\) | ||||
0.220826 | + | 0.975313i | \(0.429125\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 27.2675 | 1.71429 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.88891 | + | 15.3960i | 0.554475 | + | 0.960378i | 0.997944 | + | 0.0640889i | \(0.0204141\pi\) |
−0.443469 | + | 0.896289i | \(0.646253\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.5993 | + | 23.5547i | −0.838570 | + | 1.45245i | 0.0525210 | + | 0.998620i | \(0.483274\pi\) |
−0.891091 | + | 0.453825i | \(0.850059\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.21780 | − | 10.7695i | 0.381956 | − | 0.661568i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.9481 | − | 20.6946i | −0.728486 | − | 1.26177i | −0.957523 | − | 0.288356i | \(-0.906891\pi\) |
0.229038 | − | 0.973418i | \(-0.426442\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.13667 | − | 10.6290i | 0.372776 | − | 0.645668i | −0.617215 | − | 0.786794i | \(-0.711739\pi\) |
0.989992 | + | 0.141127i | \(0.0450725\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.44951 | + | 4.24268i | 0.147711 | + | 0.255843i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.39037 | + | 11.0684i | −0.383960 | + | 0.665038i | −0.991624 | − | 0.129156i | \(-0.958773\pi\) |
0.607664 | + | 0.794194i | \(0.292107\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.2573 | − | 24.6944i | −0.850519 | − | 1.47314i | −0.880741 | − | 0.473599i | \(-0.842955\pi\) |
0.0302219 | − | 0.999543i | \(-0.490379\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.726654 | −0.0431951 | −0.0215975 | − | 0.999767i | \(-0.506875\pi\) | ||||
−0.0215975 | + | 0.999767i | \(0.506875\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.69076 | + | 2.92848i | −0.0994563 | + | 0.172263i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.7901 | + | 22.1531i | −0.747204 | + | 1.29420i | 0.201954 | + | 0.979395i | \(0.435271\pi\) |
−0.949158 | + | 0.314800i | \(0.898062\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.2360 | − | 19.4613i | −0.654184 | − | 1.13308i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 41.7031 | 2.41175 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −16.9985 | − | 29.4423i | −0.973333 | − | 1.68586i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.23405 | 0.355796 | 0.177898 | − | 0.984049i | \(-0.443070\pi\) | ||||
0.177898 | + | 0.984049i | \(0.443070\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 29.2383 | 1.65795 | 0.828976 | − | 0.559284i | \(-0.188924\pi\) | ||||
0.828976 | + | 0.559284i | \(0.188924\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.4868 | −1.61017 | −0.805083 | − | 0.593162i | \(-0.797879\pi\) | ||||
−0.805083 | + | 0.593162i | \(0.797879\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.61849 | −0.0909032 | −0.0454516 | − | 0.998967i | \(-0.514473\pi\) | ||||
−0.0454516 | + | 0.998967i | \(0.514473\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −32.4179 | −1.81505 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.5366 | 1.08704 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.74630 | + | 6.48879i | 0.207808 | + | 0.359933i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.9823 | −0.768536 | −0.384268 | − | 0.923222i | \(-0.625546\pi\) | ||||
−0.384268 | + | 0.923222i | \(0.625546\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.63307 | + | 2.82857i | 0.0892244 | + | 0.154541i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.8619 | + | 24.0095i | −0.755104 | + | 1.30788i | 0.190219 | + | 0.981742i | \(0.439080\pi\) |
−0.945323 | + | 0.326137i | \(0.894253\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.1534 | − | 29.7106i | 0.928909 | − | 1.60892i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.52898 | −0.404177 | −0.202089 | − | 0.979367i | \(-0.564773\pi\) | ||||
−0.202089 | + | 0.979367i | \(0.564773\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.0541 | − | 26.0744i | −0.805827 | − | 1.39573i | −0.915732 | − | 0.401791i | \(-0.868388\pi\) |
0.109905 | − | 0.993942i | \(-0.464945\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.1819 | − | 17.6356i | 0.541928 | − | 0.938647i | −0.456865 | − | 0.889536i | \(-0.651028\pi\) |
0.998793 | − | 0.0491110i | \(-0.0156388\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.6352 | + | 28.8130i | 0.882905 | + | 1.52924i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.01313 | + | 13.8791i | −0.422917 | + | 0.732513i | −0.996223 | − | 0.0868277i | \(-0.972327\pi\) |
0.573307 | + | 0.819341i | \(0.305660\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.136673 | + | 0.236725i | 0.00719332 | + | 0.0124592i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.32383 | + | 9.22115i | −0.278662 | + | 0.482657i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.79893 | + | 11.7761i | −0.354901 | + | 0.614707i | −0.987101 | − | 0.160099i | \(-0.948819\pi\) |
0.632200 | + | 0.774805i | \(0.282152\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.9641 | + | 18.9904i | 0.567700 | + | 0.983285i | 0.996793 | + | 0.0800246i | \(0.0254999\pi\) |
−0.429093 | + | 0.903260i | \(0.641167\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −49.5801 | −2.55351 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.7965 | −1.53054 | −0.765271 | − | 0.643708i | \(-0.777395\pi\) | ||||
−0.765271 | + | 0.643708i | \(0.777395\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.0109905 | + | 0.0190361i | 0.000561587 | + | 0.000972697i | 0.866306 | − | 0.499514i | \(-0.166488\pi\) |
−0.865744 | + | 0.500486i | \(0.833155\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.6783 | + | 30.6197i | −0.896326 | + | 1.55248i | −0.0641702 | + | 0.997939i | \(0.520440\pi\) |
−0.832155 | + | 0.554543i | \(0.812893\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.2434 | + | 22.9382i | −0.669746 | + | 1.16003i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.91741 | − | 13.7134i | −0.398368 | − | 0.689994i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.47150 | + | 14.6731i | −0.425172 | + | 0.736420i | −0.996436 | − | 0.0843464i | \(-0.973120\pi\) |
0.571264 | + | 0.820766i | \(0.306453\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.48181 | − | 2.56657i | −0.0739982 | − | 0.128169i | 0.826652 | − | 0.562713i | \(-0.190243\pi\) |
−0.900650 | + | 0.434545i | \(0.856909\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 26.2345 | − | 45.4395i | 1.30683 | − | 2.26350i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.68862 | − | 2.92478i | −0.0837018 | − | 0.144976i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.6549 | 0.724636 | 0.362318 | − | 0.932054i | \(-0.381985\pi\) | ||||
0.362318 | + | 0.932054i | \(0.381985\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.82743 | + | 3.16520i | −0.0897050 | + | 0.155374i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.6352 | − | 21.8848i | 0.617270 | − | 1.06914i | −0.372711 | − | 0.927947i | \(-0.621572\pi\) |
0.989982 | − | 0.141196i | \(-0.0450949\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.99854 | + | 13.8539i | 0.389825 | + | 0.675196i | 0.992426 | − | 0.122846i | \(-0.0392022\pi\) |
−0.602601 | + | 0.798043i | \(0.705869\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.75876 | −0.230834 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.51673 | + | 11.2873i | 0.313900 | + | 0.543690i | 0.979203 | − | 0.202883i | \(-0.0650311\pi\) |
−0.665303 | + | 0.746573i | \(0.731698\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.5467 | −1.13158 | −0.565791 | − | 0.824549i | \(-0.691429\pi\) | ||||
−0.565791 | + | 0.824549i | \(0.691429\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 25.3887 | 1.21451 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.70895 | −0.320200 | −0.160100 | − | 0.987101i | \(-0.551182\pi\) | ||||
−0.160100 | + | 0.987101i | \(0.551182\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −35.2455 | −1.67456 | −0.837282 | − | 0.546771i | \(-0.815857\pi\) | ||||
−0.837282 | + | 0.546771i | \(0.815857\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 24.1986 | 1.14712 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.9387 | 0.610616 | 0.305308 | − | 0.952254i | \(-0.401241\pi\) | ||||
0.305308 | + | 0.952254i | \(0.401241\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.635211 | + | 1.10022i | 0.0299109 | + | 0.0518072i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.1986 | −1.36585 | −0.682927 | − | 0.730487i | \(-0.739293\pi\) | ||||
−0.682927 | + | 0.730487i | \(0.739293\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.34348 | + | 16.1834i | 0.435169 | + | 0.753735i | 0.997309 | − | 0.0733066i | \(-0.0233552\pi\) |
−0.562140 | + | 0.827042i | \(0.690022\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.1249 | − | 33.1253i | 0.888809 | − | 1.53946i | 0.0475247 | − | 0.998870i | \(-0.484867\pi\) |
0.841285 | − | 0.540593i | \(-0.181800\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.64387 | − | 13.2396i | 0.353716 | − | 0.612654i | −0.633181 | − | 0.774004i | \(-0.718251\pi\) |
0.986897 | + | 0.161349i | \(0.0515846\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22.4706 | 1.03320 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.28074 | + | 3.95035i | 0.104647 | + | 0.181255i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.51605 | + | 9.55408i | −0.252035 | + | 0.436537i | −0.964086 | − | 0.265591i | \(-0.914433\pi\) |
0.712051 | + | 0.702128i | \(0.247766\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.58259 | − | 4.47318i | −0.117756 | − | 0.203959i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.606032 | + | 1.04968i | −0.0275185 | + | 0.0476635i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.30039 | − | 14.3767i | −0.376126 | − | 0.651470i | 0.614368 | − | 0.789019i | \(-0.289411\pi\) |
−0.990495 | + | 0.137549i | \(0.956078\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.3633 | + | 23.1460i | −0.603079 | + | 1.04456i | 0.389273 | + | 0.921122i | \(0.372726\pi\) |
−0.992352 | + | 0.123440i | \(0.960607\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.7448 | − | 27.2709i | 0.709112 | − | 1.22822i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.618485 | − | 1.07125i | −0.0276872 | − | 0.0479557i | 0.851850 | − | 0.523786i | \(-0.175481\pi\) |
−0.879537 | + | 0.475830i | \(0.842148\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.07179 | −0.0477889 | −0.0238944 | − | 0.999714i | \(-0.507607\pi\) | ||||
−0.0238944 | + | 0.999714i | \(0.507607\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.38151 | 0.372973 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.0344 | − | 17.3801i | −0.444768 | − | 0.770362i | 0.553268 | − | 0.833004i | \(-0.313381\pi\) |
−0.998036 | + | 0.0626420i | \(0.980047\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.35087 | − | 11.0000i | 0.279853 | − | 0.484720i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.53443 | − | 14.7821i | 0.375344 | − | 0.650115i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.4430 | + | 26.7480i | 0.676570 | + | 1.17185i | 0.976007 | + | 0.217737i | \(0.0698676\pi\) |
−0.299438 | + | 0.954116i | \(0.596799\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.69961 | + | 6.40792i | −0.161773 | + | 0.280199i | −0.935505 | − | 0.353315i | \(-0.885054\pi\) |
0.773732 | + | 0.633513i | \(0.218388\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.6623 | + | 28.8599i | 0.725819 | + | 1.25716i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.71041 | + | 9.89072i | −0.248279 | + | 0.430031i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.971495 | + | 1.68268i | 0.0420801 | + | 0.0728849i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.1800 | 0.613053 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.3348 | + | 19.6325i | −0.487322 | + | 0.844067i | −0.999894 | − | 0.0145779i | \(-0.995360\pi\) |
0.512572 | + | 0.858644i | \(0.328693\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.0505 | − | 19.1400i | 0.473351 | − | 0.819868i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.07373 | + | 5.32386i | 0.131423 | + | 0.227632i | 0.924225 | − | 0.381847i | \(-0.124712\pi\) |
−0.792802 | + | 0.609479i | \(0.791379\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −30.1842 | −1.28589 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.8370 | + | 25.6984i | 0.628662 | + | 1.08887i | 0.987820 | + | 0.155598i | \(0.0497305\pi\) |
−0.359158 | + | 0.933277i | \(0.616936\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.3667 | 1.45356 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.3111 | −1.23531 | −0.617657 | − | 0.786447i | \(-0.711918\pi\) | ||||
−0.617657 | + | 0.786447i | \(0.711918\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.34514 | 0.140731 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 36.8860 | 1.54634 | 0.773170 | − | 0.634198i | \(-0.218670\pi\) | ||||
0.773170 | + | 0.634198i | \(0.218670\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.3786 | 1.35500 | 0.677501 | − | 0.735522i | \(-0.263063\pi\) | ||||
0.677501 | + | 0.735522i | \(0.263063\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.18423 | −0.257900 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.5093 | + | 19.9348i | 0.479140 | + | 0.829895i | 0.999714 | − | 0.0239220i | \(-0.00761535\pi\) |
−0.520574 | + | 0.853817i | \(0.674282\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.4897 | 0.972843 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.87052 | − | 4.97189i | −0.118479 | − | 0.205212i | 0.800686 | − | 0.599084i | \(-0.204469\pi\) |
−0.919165 | + | 0.393872i | \(0.871135\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.9715 | − | 27.6634i | 0.658094 | − | 1.13985i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.8727 | + | 24.0282i | −0.569682 | + | 0.986718i | 0.426915 | + | 0.904292i | \(0.359600\pi\) |
−0.996597 | + | 0.0824263i | \(0.973733\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.10817 | −0.167855 | −0.0839276 | − | 0.996472i | \(-0.526746\pi\) | ||||
−0.0839276 | + | 0.996472i | \(0.526746\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.80924 | + | 13.5260i | 0.318546 | + | 0.551737i | 0.980185 | − | 0.198085i | \(-0.0634723\pi\) |
−0.661639 | + | 0.749822i | \(0.730139\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13.0416 | + | 22.5888i | −0.530218 | + | 0.918364i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.280738 | − | 0.486253i | −0.0113948 | − | 0.0197364i | 0.860272 | − | 0.509836i | \(-0.170294\pi\) |
−0.871667 | + | 0.490099i | \(0.836960\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.0526 | − | 22.6078i | 0.528053 | − | 0.914614i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.1008 | + | 17.4951i | 0.407967 | + | 0.706619i | 0.994662 | − | 0.103189i | \(-0.0329047\pi\) |
−0.586695 | + | 0.809808i | \(0.699571\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.4569 | + | 19.8439i | −0.461238 | + | 0.798887i | −0.999023 | − | 0.0441948i | \(-0.985928\pi\) |
0.537785 | + | 0.843082i | \(0.319261\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.8515 | − | 34.3839i | 0.797901 | − | 1.38201i | −0.123080 | − | 0.992397i | \(-0.539277\pi\) |
0.920981 | − | 0.389608i | \(-0.127390\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5797 | + | 25.2527i | 0.583187 | + | 1.01011i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.28054 | 0.130804 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.0364 | −1.23554 | −0.617769 | − | 0.786359i | \(-0.711963\pi\) | ||||
−0.617769 | + | 0.786359i | \(0.711963\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.00885 | + | 1.74739i | 0.0400352 | + | 0.0693429i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.7932 | + | 25.6226i | −0.584296 | + | 1.01203i | 0.410667 | + | 0.911785i | \(0.365296\pi\) |
−0.994963 | + | 0.100245i | \(0.968037\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.8442 | − | 22.2467i | 0.506524 | − | 0.877325i | −0.493447 | − | 0.869776i | \(-0.664263\pi\) |
0.999972 | − | 0.00754978i | \(-0.00240319\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.50885 | − | 14.7378i | −0.334518 | − | 0.579401i | 0.648874 | − | 0.760895i | \(-0.275240\pi\) |
−0.983392 | + | 0.181494i | \(0.941907\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21.2237 | − | 36.7606i | 0.833104 | − | 1.44298i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.735508 | + | 1.27394i | 0.0287827 | + | 0.0498530i | 0.880058 | − | 0.474866i | \(-0.157504\pi\) |
−0.851275 | + | 0.524719i | \(0.824170\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.58113 | + | 16.5950i | −0.374366 | + | 0.648420i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.7003 | − | 35.8539i | −0.806369 | − | 1.39667i | −0.915363 | − | 0.402629i | \(-0.868096\pi\) |
0.108995 | − | 0.994042i | \(-0.465237\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −38.2704 | −1.48855 | −0.744273 | − | 0.667875i | \(-0.767204\pi\) | ||||
−0.744273 | + | 0.667875i | \(0.767204\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.4612 | − | 35.4398i | 0.792260 | − | 1.37223i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 32.1086 | − | 55.6138i | 1.23954 | − | 2.14695i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.2448 | + | 26.4048i | 0.587645 | + | 1.01783i | 0.994540 | + | 0.104357i | \(0.0332783\pi\) |
−0.406894 | + | 0.913475i | \(0.633388\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 44.9253 | 1.72662 | 0.863309 | − | 0.504675i | \(-0.168388\pi\) | ||||
0.863309 | + | 0.504675i | \(0.168388\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.1986 | − | 41.9133i | −0.925935 | − | 1.60377i | −0.790051 | − | 0.613041i | \(-0.789946\pi\) |
−0.135884 | − | 0.990725i | \(-0.543387\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.36381 | 0.281357 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 35.9253 | 1.36864 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.3815 | −0.699266 | −0.349633 | − | 0.936887i | \(-0.613694\pi\) | ||||
−0.349633 | + | 0.936887i | \(0.613694\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.5687 | −0.590553 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.23405 | −0.0467428 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.0292 | 1.02088 | 0.510439 | − | 0.859914i | \(-0.329483\pi\) | ||||
0.510439 | + | 0.859914i | \(0.329483\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.57227 | − | 2.72325i | −0.0592994 | − | 0.102710i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.98522 | 0.187224 | 0.0936119 | − | 0.995609i | \(-0.470159\pi\) | ||||
0.0936119 | + | 0.995609i | \(0.470159\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21.6534 | + | 37.5048i | 0.810926 | + | 1.40457i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −40.6431 | + | 70.3959i | −1.51997 | + | 2.63266i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.84708 | + | 13.5915i | −0.292647 | + | 0.506879i | −0.974435 | − | 0.224671i | \(-0.927869\pi\) |
0.681788 | + | 0.731550i | \(0.261203\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.35234 | 0.273059 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.9071 | + | 18.8916i | 0.404522 | + | 0.700652i | 0.994266 | − | 0.106938i | \(-0.0341047\pi\) |
−0.589744 | + | 0.807590i | \(0.700771\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.9136 | + | 18.9029i | −0.403655 | + | 0.699151i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.0074 | − | 20.7974i | −0.443503 | − | 0.768170i | 0.554443 | − | 0.832221i | \(-0.312931\pi\) |
−0.997947 | + | 0.0640514i | \(0.979598\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.08472 | + | 5.34290i | −0.113627 | + | 0.196808i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.35447 | − | 16.2024i | −0.344110 | − | 0.596016i | 0.641082 | − | 0.767473i | \(-0.278486\pi\) |
−0.985192 | + | 0.171457i | \(0.945153\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.1534 | + | 34.9067i | −0.739356 | + | 1.28060i | 0.213429 | + | 0.976959i | \(0.431537\pi\) |
−0.952785 | + | 0.303644i | \(0.901797\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.39037 | + | 9.33639i | −0.197488 | + | 0.342059i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.5629 | + | 18.2955i | 0.385447 | + | 0.667614i | 0.991831 | − | 0.127558i | \(-0.0407139\pi\) |
−0.606384 | + | 0.795172i | \(0.707381\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.2412 | 0.591079 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.85934 | 0.321998 | 0.160999 | − | 0.986955i | \(-0.448528\pi\) | ||||
0.160999 | + | 0.986955i | \(0.448528\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.694551 | − | 1.20300i | −0.0251774 | − | 0.0436086i | 0.853162 | − | 0.521646i | \(-0.174682\pi\) |
−0.878340 | + | 0.478037i | \(0.841348\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 32.4597 | − | 56.2219i | 1.17205 | − | 2.03005i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.9626 | + | 32.8443i | −0.683810 | + | 1.18439i | 0.289999 | + | 0.957027i | \(0.406345\pi\) |
−0.973809 | + | 0.227367i | \(0.926988\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.657981 | − | 1.13966i | −0.0236659 | − | 0.0409906i | 0.853950 | − | 0.520355i | \(-0.174200\pi\) |
−0.877616 | + | 0.479365i | \(0.840867\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.89037 | + | 6.73832i | −0.139746 | + | 0.242047i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.591443 | + | 1.02441i | 0.0211907 | + | 0.0367033i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31.4224 | + | 54.4251i | −1.12438 | + | 1.94748i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.11177 | − | 12.3179i | −0.253830 | − | 0.439646i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.2586 | −0.436971 | −0.218485 | − | 0.975840i | \(-0.570112\pi\) | ||||
−0.218485 | + | 0.975840i | \(0.570112\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 49.1072 | − | 85.0561i | 1.74385 | − | 3.02043i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.7178 | + | 18.5638i | −0.379644 | + | 0.657563i | −0.991010 | − | 0.133785i | \(-0.957287\pi\) |
0.611366 | + | 0.791348i | \(0.290620\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.29007 | + | 14.3588i | 0.293282 | + | 0.507979i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −20.1124 | −0.709753 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.3478 | + | 23.1190i | 0.469282 | + | 0.812820i | 0.999383 | − | 0.0351140i | \(-0.0111794\pi\) |
−0.530101 | + | 0.847934i | \(0.677846\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.2852 | −1.34438 | −0.672188 | − | 0.740381i | \(-0.734645\pi\) | ||||
−0.672188 | + | 0.740381i | \(0.734645\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18.0292 | 0.631535 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.9224 | 0.731981 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.4998 | 0.366446 | 0.183223 | − | 0.983071i | \(-0.441347\pi\) | ||||
0.183223 | + | 0.983071i | \(0.441347\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.0000 | 0.557725 | 0.278862 | − | 0.960331i | \(-0.410043\pi\) | ||||
0.278862 | + | 0.960331i | \(0.410043\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.7817 | 1.69631 | 0.848153 | − | 0.529752i | \(-0.177715\pi\) | ||||
0.848153 | + | 0.529752i | \(0.177715\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.10963 | − | 5.38604i | −0.108002 | − | 0.187065i | 0.806959 | − | 0.590608i | \(-0.201112\pi\) |
−0.914961 | + | 0.403543i | \(0.867779\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −29.5979 | −1.02428 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.0366 | + | 36.4364i | 0.726263 | + | 1.25792i | 0.958452 | + | 0.285254i | \(0.0920779\pi\) |
−0.232189 | + | 0.972671i | \(0.574589\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.82597 | + | 17.0191i | −0.338826 | + | 0.586865i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −46.1665 | + | 79.9628i | −1.58818 | + | 2.75080i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.26322 | 0.146141 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.72519 | − | 11.6484i | −0.230266 | − | 0.398833i | 0.727620 | − | 0.685980i | \(-0.240626\pi\) |
−0.957886 | + | 0.287147i | \(0.907293\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20.6893 | + | 35.8349i | −0.706733 | + | 1.22410i | 0.259330 | + | 0.965789i | \(0.416498\pi\) |
−0.966063 | + | 0.258308i | \(0.916835\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.8815 | − | 34.4358i | −0.678349 | − | 1.17493i | −0.975478 | − | 0.220097i | \(-0.929363\pi\) |
0.297129 | − | 0.954837i | \(-0.403971\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.6929 | − | 46.2334i | 0.908637 | − | 1.57380i | 0.0926768 | − | 0.995696i | \(-0.470458\pi\) |
0.815960 | − | 0.578109i | \(-0.196209\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.02704 | − | 10.4391i | −0.204926 | − | 0.354942i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.9552 | − | 25.9033i | 0.507322 | − | 0.878708i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.71780 | + | 8.17147i | −0.159857 | + | 0.276880i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.42674 | + | 5.93530i | 0.115713 | + | 0.200421i | 0.918065 | − | 0.396431i | \(-0.129751\pi\) |
−0.802352 | + | 0.596852i | \(0.796418\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.5103 | −0.421483 | −0.210742 | − | 0.977542i | \(-0.567588\pi\) | ||||
−0.210742 | + | 0.977542i | \(0.567588\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.69124 | 0.225178 | 0.112589 | − | 0.993642i | \(-0.464086\pi\) | ||||
0.112589 | + | 0.993642i | \(0.464086\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.0708 | − | 27.8355i | −0.539605 | − | 0.934623i | −0.998925 | − | 0.0463524i | \(-0.985240\pi\) |
0.459320 | − | 0.888271i | \(-0.348093\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.94639 | − | 13.7636i | 0.265916 | − | 0.460580i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.19076 | + | 3.79450i | −0.0732289 | + | 0.126836i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −25.7434 | − | 44.5888i | −0.858590 | − | 1.48712i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.4086 | + | 19.7602i | −0.380074 | + | 0.658308i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.8442 | − | 36.1031i | −0.692883 | − | 1.20011i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.7016 | − | 27.1959i | 0.521362 | − | 0.903025i | −0.478330 | − | 0.878180i | \(-0.658758\pi\) |
0.999691 | − | 0.0248444i | \(-0.00790902\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.8982 | + | 39.6609i | 0.758653 | + | 1.31402i | 0.943538 | + | 0.331265i | \(0.107475\pi\) |
−0.184885 | + | 0.982760i | \(0.559191\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.90369 | −0.228479 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.5900 | + | 23.5385i | −0.448292 | + | 0.776465i | −0.998275 | − | 0.0587112i | \(-0.981301\pi\) |
0.549983 | + | 0.835176i | \(0.314634\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −48.0576 | + | 83.2381i | −1.58183 | + | 2.73982i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.382977 | + | 0.663336i | 0.0125922 | + | 0.0218104i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −40.6677 | −1.33426 | −0.667132 | − | 0.744940i | \(-0.732478\pi\) | ||||
−0.667132 | + | 0.744940i | \(0.732478\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −25.8135 | − | 44.7103i | −0.844192 | − | 1.46218i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.4150 | −0.536254 | −0.268127 | − | 0.963384i | \(-0.586405\pi\) | ||||
−0.268127 | + | 0.963384i | \(0.586405\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.33755 | 0.239197 | 0.119599 | − | 0.992822i | \(-0.461839\pi\) | ||||
0.119599 | + | 0.992822i | \(0.461839\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.60370 | −0.0522237 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −59.1124 | −1.92090 | −0.960448 | − | 0.278459i | \(-0.910176\pi\) | ||||
−0.960448 | + | 0.278459i | \(0.910176\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.7601 | −0.998515 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16.9354 | 0.548592 | 0.274296 | − | 0.961645i | \(-0.411555\pi\) | ||||
0.274296 | + | 0.961645i | \(0.411555\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.75370 | − | 11.6977i | −0.218544 | − | 0.378530i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.4868 | 0.757637 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.77548 | + | 11.7355i | 0.218110 | + | 0.377778i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.55555 | − | 6.15839i | 0.114339 | − | 0.198040i | −0.803177 | − | 0.595741i | \(-0.796858\pi\) |
0.917515 | + | 0.397701i | \(0.130192\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.735508 | − | 1.27394i | 0.0236036 | − | 0.0408826i | −0.853982 | − | 0.520302i | \(-0.825819\pi\) |
0.877586 | + | 0.479419i | \(0.159153\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.4327 | 0.621706 | 0.310853 | − | 0.950458i | \(-0.399385\pi\) | ||||
0.310853 | + | 0.950458i | \(0.399385\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.8545 | + | 39.5851i | 0.730432 | + | 1.26515i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.87218 | + | 6.70681i | −0.123503 | + | 0.213914i | −0.921147 | − | 0.389215i | \(-0.872746\pi\) |
0.797644 | + | 0.603129i | \(0.206080\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.3078 | + | 24.7818i | 0.455884 | + | 0.789614i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.1828 | + | 24.5653i | −0.450986 | + | 0.781130i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.23551 | + | 12.5323i | 0.229843 | + | 0.398101i | 0.957762 | − | 0.287563i | \(-0.0928452\pi\) |
−0.727918 | + | 0.685664i | \(0.759512\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.10243 | + | 8.83767i | −0.161758 | + | 0.280173i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −27.6549 | + | 47.8996i | −0.875838 | + | 1.51700i | −0.0199711 | + | 0.999801i | \(0.506357\pi\) |
−0.855867 | + | 0.517196i | \(0.826976\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))