Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,2,Mod(373,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("882.373");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.e (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: | \(7.04280545828\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 373.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.373 |
Dual form | 882.2.e.e.655.1 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.50000 | + | 0.866025i | 0.866025 | + | 0.500000i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | + | 1.73205i | 0.447214 | + | 0.774597i | 0.998203 | − | 0.0599153i | \(-0.0190830\pi\) |
−0.550990 | + | 0.834512i | \(0.685750\pi\) | |||||||
\(6\) | −1.50000 | − | 0.866025i | −0.612372 | − | 0.353553i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.50000 | + | 2.59808i | 0.500000 | + | 0.866025i | ||||
\(10\) | −1.00000 | − | 1.73205i | −0.316228 | − | 0.547723i | ||||
\(11\) | −0.500000 | + | 0.866025i | −0.150756 | + | 0.261116i | −0.931505 | − | 0.363727i | \(-0.881504\pi\) |
0.780750 | + | 0.624844i | \(0.214837\pi\) | |||||||
\(12\) | 1.50000 | + | 0.866025i | 0.433013 | + | 0.250000i | ||||
\(13\) | −3.00000 | + | 5.19615i | −0.832050 | + | 1.44115i | 0.0643593 | + | 0.997927i | \(0.479500\pi\) |
−0.896410 | + | 0.443227i | \(0.853834\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.46410i | 0.894427i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.50000 | − | 4.33013i | −0.606339 | − | 1.05021i | −0.991838 | − | 0.127502i | \(-0.959304\pi\) |
0.385499 | − | 0.922708i | \(-0.374029\pi\) | |||||||
\(18\) | −1.50000 | − | 2.59808i | −0.353553 | − | 0.612372i | ||||
\(19\) | −3.50000 | + | 6.06218i | −0.802955 | + | 1.39076i | 0.114708 | + | 0.993399i | \(0.463407\pi\) |
−0.917663 | + | 0.397360i | \(0.869927\pi\) | |||||||
\(20\) | 1.00000 | + | 1.73205i | 0.223607 | + | 0.387298i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.500000 | − | 0.866025i | 0.106600 | − | 0.184637i | ||||
\(23\) | −2.00000 | − | 3.46410i | −0.417029 | − | 0.722315i | 0.578610 | − | 0.815604i | \(-0.303595\pi\) |
−0.995639 | + | 0.0932891i | \(0.970262\pi\) | |||||||
\(24\) | −1.50000 | − | 0.866025i | −0.306186 | − | 0.176777i | ||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | 3.00000 | − | 5.19615i | 0.588348 | − | 1.01905i | ||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | + | 3.46410i | 0.371391 | + | 0.643268i | 0.989780 | − | 0.142605i | \(-0.0455477\pi\) |
−0.618389 | + | 0.785872i | \(0.712214\pi\) | |||||||
\(30\) | − | 3.46410i | − | 0.632456i | ||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.50000 | + | 0.866025i | −0.261116 | + | 0.150756i | ||||
\(34\) | 2.50000 | + | 4.33013i | 0.428746 | + | 0.742611i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.50000 | + | 2.59808i | 0.250000 | + | 0.433013i | ||||
\(37\) | −1.00000 | + | 1.73205i | −0.164399 | + | 0.284747i | −0.936442 | − | 0.350823i | \(-0.885902\pi\) |
0.772043 | + | 0.635571i | \(0.219235\pi\) | |||||||
\(38\) | 3.50000 | − | 6.06218i | 0.567775 | − | 0.983415i | ||||
\(39\) | −9.00000 | + | 5.19615i | −1.44115 | + | 0.832050i | ||||
\(40\) | −1.00000 | − | 1.73205i | −0.158114 | − | 0.273861i | ||||
\(41\) | 1.50000 | − | 2.59808i | 0.234261 | − | 0.405751i | −0.724797 | − | 0.688963i | \(-0.758066\pi\) |
0.959058 | + | 0.283211i | \(0.0913998\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.500000 | + | 0.866025i | 0.0762493 | + | 0.132068i | 0.901629 | − | 0.432511i | \(-0.142372\pi\) |
−0.825380 | + | 0.564578i | \(0.809039\pi\) | |||||||
\(44\) | −0.500000 | + | 0.866025i | −0.0753778 | + | 0.130558i | ||||
\(45\) | −3.00000 | + | 5.19615i | −0.447214 | + | 0.774597i | ||||
\(46\) | 2.00000 | + | 3.46410i | 0.294884 | + | 0.510754i | ||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 1.50000 | + | 0.866025i | 0.216506 | + | 0.125000i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.500000 | + | 0.866025i | −0.0707107 | + | 0.122474i | ||||
\(51\) | − | 8.66025i | − | 1.21268i | ||||||
\(52\) | −3.00000 | + | 5.19615i | −0.416025 | + | 0.720577i | ||||
\(53\) | −6.00000 | − | 10.3923i | −0.824163 | − | 1.42749i | −0.902557 | − | 0.430570i | \(-0.858312\pi\) |
0.0783936 | − | 0.996922i | \(-0.475021\pi\) | |||||||
\(54\) | − | 5.19615i | − | 0.707107i | ||||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.5000 | + | 6.06218i | −1.39076 | + | 0.802955i | ||||
\(58\) | −2.00000 | − | 3.46410i | −0.262613 | − | 0.454859i | ||||
\(59\) | 7.00000 | 0.911322 | 0.455661 | − | 0.890153i | \(-0.349403\pi\) | ||||
0.455661 | + | 0.890153i | \(0.349403\pi\) | |||||||
\(60\) | 3.46410i | 0.447214i | ||||||||
\(61\) | 12.0000 | 1.53644 | 0.768221 | − | 0.640184i | \(-0.221142\pi\) | ||||
0.768221 | + | 0.640184i | \(0.221142\pi\) | |||||||
\(62\) | −6.00000 | −0.762001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −12.0000 | −1.48842 | ||||||||
\(66\) | 1.50000 | − | 0.866025i | 0.184637 | − | 0.106600i | ||||
\(67\) | 13.0000 | 1.58820 | 0.794101 | − | 0.607785i | \(-0.207942\pi\) | ||||
0.794101 | + | 0.607785i | \(0.207942\pi\) | |||||||
\(68\) | −2.50000 | − | 4.33013i | −0.303170 | − | 0.525105i | ||||
\(69\) | − | 6.92820i | − | 0.834058i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | −1.50000 | − | 2.59808i | −0.176777 | − | 0.306186i | ||||
\(73\) | 0.500000 | + | 0.866025i | 0.0585206 | + | 0.101361i | 0.893801 | − | 0.448463i | \(-0.148028\pi\) |
−0.835281 | + | 0.549823i | \(0.814695\pi\) | |||||||
\(74\) | 1.00000 | − | 1.73205i | 0.116248 | − | 0.201347i | ||||
\(75\) | 1.50000 | − | 0.866025i | 0.173205 | − | 0.100000i | ||||
\(76\) | −3.50000 | + | 6.06218i | −0.401478 | + | 0.695379i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 9.00000 | − | 5.19615i | 1.01905 | − | 0.588348i | ||||
\(79\) | −6.00000 | −0.675053 | −0.337526 | − | 0.941316i | \(-0.609590\pi\) | ||||
−0.337526 | + | 0.941316i | \(0.609590\pi\) | |||||||
\(80\) | 1.00000 | + | 1.73205i | 0.111803 | + | 0.193649i | ||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | −1.50000 | + | 2.59808i | −0.165647 | + | 0.286910i | ||||
\(83\) | 8.00000 | + | 13.8564i | 0.878114 | + | 1.52094i | 0.853408 | + | 0.521243i | \(0.174532\pi\) |
0.0247060 | + | 0.999695i | \(0.492135\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.00000 | − | 8.66025i | 0.542326 | − | 0.939336i | ||||
\(86\) | −0.500000 | − | 0.866025i | −0.0539164 | − | 0.0933859i | ||||
\(87\) | 6.92820i | 0.742781i | ||||||||
\(88\) | 0.500000 | − | 0.866025i | 0.0533002 | − | 0.0923186i | ||||
\(89\) | −3.00000 | + | 5.19615i | −0.317999 | + | 0.550791i | −0.980071 | − | 0.198650i | \(-0.936344\pi\) |
0.662071 | + | 0.749441i | \(0.269678\pi\) | |||||||
\(90\) | 3.00000 | − | 5.19615i | 0.316228 | − | 0.547723i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.00000 | − | 3.46410i | −0.208514 | − | 0.361158i | ||||
\(93\) | 9.00000 | + | 5.19615i | 0.933257 | + | 0.538816i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −14.0000 | −1.43637 | ||||||||
\(96\) | −1.50000 | − | 0.866025i | −0.153093 | − | 0.0883883i | ||||
\(97\) | −2.50000 | − | 4.33013i | −0.253837 | − | 0.439658i | 0.710742 | − | 0.703452i | \(-0.248359\pi\) |
−0.964579 | + | 0.263795i | \(0.915026\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.00000 | −0.301511 | ||||||||
\(100\) | 0.500000 | − | 0.866025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | −2.00000 | + | 3.46410i | −0.199007 | + | 0.344691i | −0.948207 | − | 0.317653i | \(-0.897105\pi\) |
0.749199 | + | 0.662344i | \(0.230438\pi\) | |||||||
\(102\) | 8.66025i | 0.857493i | ||||||||
\(103\) | 7.00000 | + | 12.1244i | 0.689730 | + | 1.19465i | 0.971925 | + | 0.235291i | \(0.0756043\pi\) |
−0.282194 | + | 0.959357i | \(0.591062\pi\) | |||||||
\(104\) | 3.00000 | − | 5.19615i | 0.294174 | − | 0.509525i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | + | 10.3923i | 0.582772 | + | 1.00939i | ||||
\(107\) | −1.50000 | + | 2.59808i | −0.145010 | + | 0.251166i | −0.929377 | − | 0.369132i | \(-0.879655\pi\) |
0.784366 | + | 0.620298i | \(0.212988\pi\) | |||||||
\(108\) | 5.19615i | 0.500000i | ||||||||
\(109\) | 1.00000 | + | 1.73205i | 0.0957826 | + | 0.165900i | 0.909935 | − | 0.414751i | \(-0.136131\pi\) |
−0.814152 | + | 0.580651i | \(0.802798\pi\) | |||||||
\(110\) | 2.00000 | 0.190693 | ||||||||
\(111\) | −3.00000 | + | 1.73205i | −0.284747 | + | 0.164399i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.00000 | − | 8.66025i | 0.470360 | − | 0.814688i | −0.529065 | − | 0.848581i | \(-0.677457\pi\) |
0.999425 | + | 0.0338931i | \(0.0107906\pi\) | |||||||
\(114\) | 10.5000 | − | 6.06218i | 0.983415 | − | 0.567775i | ||||
\(115\) | 4.00000 | − | 6.92820i | 0.373002 | − | 0.646058i | ||||
\(116\) | 2.00000 | + | 3.46410i | 0.185695 | + | 0.321634i | ||||
\(117\) | −18.0000 | −1.66410 | ||||||||
\(118\) | −7.00000 | −0.644402 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | − | 3.46410i | − | 0.316228i | ||||||
\(121\) | 5.00000 | + | 8.66025i | 0.454545 | + | 0.787296i | ||||
\(122\) | −12.0000 | −1.08643 | ||||||||
\(123\) | 4.50000 | − | 2.59808i | 0.405751 | − | 0.234261i | ||||
\(124\) | 6.00000 | 0.538816 | ||||||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.0000 | −1.06483 | −0.532414 | − | 0.846484i | \(-0.678715\pi\) | ||||
−0.532414 | + | 0.846484i | \(0.678715\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 1.73205i | 0.152499i | ||||||||
\(130\) | 12.0000 | 1.05247 | ||||||||
\(131\) | −2.00000 | − | 3.46410i | −0.174741 | − | 0.302660i | 0.765331 | − | 0.643637i | \(-0.222575\pi\) |
−0.940072 | + | 0.340977i | \(0.889242\pi\) | |||||||
\(132\) | −1.50000 | + | 0.866025i | −0.130558 | + | 0.0753778i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −13.0000 | −1.12303 | ||||||||
\(135\) | −9.00000 | + | 5.19615i | −0.774597 | + | 0.447214i | ||||
\(136\) | 2.50000 | + | 4.33013i | 0.214373 | + | 0.371305i | ||||
\(137\) | 9.50000 | − | 16.4545i | 0.811640 | − | 1.40580i | −0.100076 | − | 0.994980i | \(-0.531909\pi\) |
0.911716 | − | 0.410822i | \(-0.134758\pi\) | |||||||
\(138\) | 6.92820i | 0.589768i | ||||||||
\(139\) | −2.50000 | + | 4.33013i | −0.212047 | + | 0.367277i | −0.952355 | − | 0.304991i | \(-0.901346\pi\) |
0.740308 | + | 0.672268i | \(0.234680\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.00000 | 0.671345 | ||||||||
\(143\) | −3.00000 | − | 5.19615i | −0.250873 | − | 0.434524i | ||||
\(144\) | 1.50000 | + | 2.59808i | 0.125000 | + | 0.216506i | ||||
\(145\) | −4.00000 | + | 6.92820i | −0.332182 | + | 0.575356i | ||||
\(146\) | −0.500000 | − | 0.866025i | −0.0413803 | − | 0.0716728i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.00000 | + | 1.73205i | −0.0821995 | + | 0.142374i | ||||
\(149\) | 12.0000 | + | 20.7846i | 0.983078 | + | 1.70274i | 0.650183 | + | 0.759778i | \(0.274692\pi\) |
0.332896 | + | 0.942964i | \(0.391974\pi\) | |||||||
\(150\) | −1.50000 | + | 0.866025i | −0.122474 | + | 0.0707107i | ||||
\(151\) | −5.00000 | + | 8.66025i | −0.406894 | + | 0.704761i | −0.994540 | − | 0.104357i | \(-0.966722\pi\) |
0.587646 | + | 0.809118i | \(0.300055\pi\) | |||||||
\(152\) | 3.50000 | − | 6.06218i | 0.283887 | − | 0.491708i | ||||
\(153\) | 7.50000 | − | 12.9904i | 0.606339 | − | 1.05021i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.00000 | + | 10.3923i | 0.481932 | + | 0.834730i | ||||
\(156\) | −9.00000 | + | 5.19615i | −0.720577 | + | 0.416025i | ||||
\(157\) | −2.00000 | −0.159617 | −0.0798087 | − | 0.996810i | \(-0.525431\pi\) | ||||
−0.0798087 | + | 0.996810i | \(0.525431\pi\) | |||||||
\(158\) | 6.00000 | 0.477334 | ||||||||
\(159\) | − | 20.7846i | − | 1.64833i | ||||||
\(160\) | −1.00000 | − | 1.73205i | −0.0790569 | − | 0.136931i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 4.50000 | − | 7.79423i | 0.353553 | − | 0.612372i | ||||
\(163\) | 2.00000 | − | 3.46410i | 0.156652 | − | 0.271329i | −0.777007 | − | 0.629492i | \(-0.783263\pi\) |
0.933659 | + | 0.358162i | \(0.116597\pi\) | |||||||
\(164\) | 1.50000 | − | 2.59808i | 0.117130 | − | 0.202876i | ||||
\(165\) | −3.00000 | − | 1.73205i | −0.233550 | − | 0.134840i | ||||
\(166\) | −8.00000 | − | 13.8564i | −0.620920 | − | 1.07547i | ||||
\(167\) | 10.0000 | − | 17.3205i | 0.773823 | − | 1.34030i | −0.161630 | − | 0.986851i | \(-0.551675\pi\) |
0.935454 | − | 0.353450i | \(-0.114991\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.5000 | − | 19.9186i | −0.884615 | − | 1.53220i | ||||
\(170\) | −5.00000 | + | 8.66025i | −0.383482 | + | 0.664211i | ||||
\(171\) | −21.0000 | −1.60591 | ||||||||
\(172\) | 0.500000 | + | 0.866025i | 0.0381246 | + | 0.0660338i | ||||
\(173\) | −2.00000 | −0.152057 | −0.0760286 | − | 0.997106i | \(-0.524224\pi\) | ||||
−0.0760286 | + | 0.997106i | \(0.524224\pi\) | |||||||
\(174\) | − | 6.92820i | − | 0.525226i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.500000 | + | 0.866025i | −0.0376889 | + | 0.0652791i | ||||
\(177\) | 10.5000 | + | 6.06218i | 0.789228 | + | 0.455661i | ||||
\(178\) | 3.00000 | − | 5.19615i | 0.224860 | − | 0.389468i | ||||
\(179\) | −12.0000 | − | 20.7846i | −0.896922 | − | 1.55351i | −0.831408 | − | 0.555663i | \(-0.812464\pi\) |
−0.0655145 | − | 0.997852i | \(-0.520869\pi\) | |||||||
\(180\) | −3.00000 | + | 5.19615i | −0.223607 | + | 0.387298i | ||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 18.0000 | + | 10.3923i | 1.33060 | + | 0.768221i | ||||
\(184\) | 2.00000 | + | 3.46410i | 0.147442 | + | 0.255377i | ||||
\(185\) | −4.00000 | −0.294086 | ||||||||
\(186\) | −9.00000 | − | 5.19615i | −0.659912 | − | 0.381000i | ||||
\(187\) | 5.00000 | 0.365636 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 14.0000 | 1.01567 | ||||||||
\(191\) | 12.0000 | 0.868290 | 0.434145 | − | 0.900843i | \(-0.357051\pi\) | ||||
0.434145 | + | 0.900843i | \(0.357051\pi\) | |||||||
\(192\) | 1.50000 | + | 0.866025i | 0.108253 | + | 0.0625000i | ||||
\(193\) | 17.0000 | 1.22369 | 0.611843 | − | 0.790979i | \(-0.290428\pi\) | ||||
0.611843 | + | 0.790979i | \(0.290428\pi\) | |||||||
\(194\) | 2.50000 | + | 4.33013i | 0.179490 | + | 0.310885i | ||||
\(195\) | −18.0000 | − | 10.3923i | −1.28901 | − | 0.744208i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.0000 | 0.712470 | 0.356235 | − | 0.934396i | \(-0.384060\pi\) | ||||
0.356235 | + | 0.934396i | \(0.384060\pi\) | |||||||
\(198\) | 3.00000 | 0.213201 | ||||||||
\(199\) | 7.00000 | + | 12.1244i | 0.496217 | + | 0.859473i | 0.999990 | − | 0.00436292i | \(-0.00138876\pi\) |
−0.503774 | + | 0.863836i | \(0.668055\pi\) | |||||||
\(200\) | −0.500000 | + | 0.866025i | −0.0353553 | + | 0.0612372i | ||||
\(201\) | 19.5000 | + | 11.2583i | 1.37542 | + | 0.794101i | ||||
\(202\) | 2.00000 | − | 3.46410i | 0.140720 | − | 0.243733i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | − | 8.66025i | − | 0.606339i | ||||||
\(205\) | 6.00000 | 0.419058 | ||||||||
\(206\) | −7.00000 | − | 12.1244i | −0.487713 | − | 0.844744i | ||||
\(207\) | 6.00000 | − | 10.3923i | 0.417029 | − | 0.722315i | ||||
\(208\) | −3.00000 | + | 5.19615i | −0.208013 | + | 0.360288i | ||||
\(209\) | −3.50000 | − | 6.06218i | −0.242100 | − | 0.419330i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.00000 | − | 13.8564i | 0.550743 | − | 0.953914i | −0.447478 | − | 0.894295i | \(-0.647678\pi\) |
0.998221 | − | 0.0596196i | \(-0.0189888\pi\) | |||||||
\(212\) | −6.00000 | − | 10.3923i | −0.412082 | − | 0.713746i | ||||
\(213\) | −12.0000 | − | 6.92820i | −0.822226 | − | 0.474713i | ||||
\(214\) | 1.50000 | − | 2.59808i | 0.102538 | − | 0.177601i | ||||
\(215\) | −1.00000 | + | 1.73205i | −0.0681994 | + | 0.118125i | ||||
\(216\) | − | 5.19615i | − | 0.353553i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.00000 | − | 1.73205i | −0.0677285 | − | 0.117309i | ||||
\(219\) | 1.73205i | 0.117041i | ||||||||
\(220\) | −2.00000 | −0.134840 | ||||||||
\(221\) | 30.0000 | 2.01802 | ||||||||
\(222\) | 3.00000 | − | 1.73205i | 0.201347 | − | 0.116248i | ||||
\(223\) | −2.00000 | − | 3.46410i | −0.133930 | − | 0.231973i | 0.791258 | − | 0.611482i | \(-0.209426\pi\) |
−0.925188 | + | 0.379509i | \(0.876093\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00000 | 0.200000 | ||||||||
\(226\) | −5.00000 | + | 8.66025i | −0.332595 | + | 0.576072i | ||||
\(227\) | 1.50000 | − | 2.59808i | 0.0995585 | − | 0.172440i | −0.811943 | − | 0.583736i | \(-0.801590\pi\) |
0.911502 | + | 0.411296i | \(0.134924\pi\) | |||||||
\(228\) | −10.5000 | + | 6.06218i | −0.695379 | + | 0.401478i | ||||
\(229\) | −13.0000 | − | 22.5167i | −0.859064 | − | 1.48794i | −0.872823 | − | 0.488037i | \(-0.837713\pi\) |
0.0137585 | − | 0.999905i | \(-0.495620\pi\) | |||||||
\(230\) | −4.00000 | + | 6.92820i | −0.263752 | + | 0.456832i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.00000 | − | 3.46410i | −0.131306 | − | 0.227429i | ||||
\(233\) | 14.5000 | − | 25.1147i | 0.949927 | − | 1.64532i | 0.204354 | − | 0.978897i | \(-0.434491\pi\) |
0.745573 | − | 0.666424i | \(-0.232176\pi\) | |||||||
\(234\) | 18.0000 | 1.17670 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.00000 | 0.455661 | ||||||||
\(237\) | −9.00000 | − | 5.19615i | −0.584613 | − | 0.337526i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.00000 | + | 5.19615i | −0.194054 | + | 0.336111i | −0.946590 | − | 0.322440i | \(-0.895497\pi\) |
0.752536 | + | 0.658551i | \(0.228830\pi\) | |||||||
\(240\) | 3.46410i | 0.223607i | ||||||||
\(241\) | 11.5000 | − | 19.9186i | 0.740780 | − | 1.28307i | −0.211360 | − | 0.977408i | \(-0.567789\pi\) |
0.952141 | − | 0.305661i | \(-0.0988773\pi\) | |||||||
\(242\) | −5.00000 | − | 8.66025i | −0.321412 | − | 0.556702i | ||||
\(243\) | −13.5000 | + | 7.79423i | −0.866025 | + | 0.500000i | ||||
\(244\) | 12.0000 | 0.768221 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.50000 | + | 2.59808i | −0.286910 | + | 0.165647i | ||||
\(247\) | −21.0000 | − | 36.3731i | −1.33620 | − | 2.31436i | ||||
\(248\) | −6.00000 | −0.381000 | ||||||||
\(249\) | 27.7128i | 1.75623i | ||||||||
\(250\) | −12.0000 | −0.758947 | ||||||||
\(251\) | −3.00000 | −0.189358 | −0.0946792 | − | 0.995508i | \(-0.530183\pi\) | ||||
−0.0946792 | + | 0.995508i | \(0.530183\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.00000 | 0.251478 | ||||||||
\(254\) | 12.0000 | 0.752947 | ||||||||
\(255\) | 15.0000 | − | 8.66025i | 0.939336 | − | 0.542326i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −7.50000 | − | 12.9904i | −0.467837 | − | 0.810318i | 0.531487 | − | 0.847066i | \(-0.321633\pi\) |
−0.999325 | + | 0.0367485i | \(0.988300\pi\) | |||||||
\(258\) | − | 1.73205i | − | 0.107833i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −12.0000 | −0.744208 | ||||||||
\(261\) | −6.00000 | + | 10.3923i | −0.371391 | + | 0.643268i | ||||
\(262\) | 2.00000 | + | 3.46410i | 0.123560 | + | 0.214013i | ||||
\(263\) | −9.00000 | + | 15.5885i | −0.554964 | + | 0.961225i | 0.442943 | + | 0.896550i | \(0.353935\pi\) |
−0.997906 | + | 0.0646755i | \(0.979399\pi\) | |||||||
\(264\) | 1.50000 | − | 0.866025i | 0.0923186 | − | 0.0533002i | ||||
\(265\) | 12.0000 | − | 20.7846i | 0.737154 | − | 1.27679i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.00000 | + | 5.19615i | −0.550791 | + | 0.317999i | ||||
\(268\) | 13.0000 | 0.794101 | ||||||||
\(269\) | 10.0000 | + | 17.3205i | 0.609711 | + | 1.05605i | 0.991288 | + | 0.131713i | \(0.0420477\pi\) |
−0.381577 | + | 0.924337i | \(0.624619\pi\) | |||||||
\(270\) | 9.00000 | − | 5.19615i | 0.547723 | − | 0.316228i | ||||
\(271\) | −3.00000 | + | 5.19615i | −0.182237 | + | 0.315644i | −0.942642 | − | 0.333805i | \(-0.891667\pi\) |
0.760405 | + | 0.649449i | \(0.225000\pi\) | |||||||
\(272\) | −2.50000 | − | 4.33013i | −0.151585 | − | 0.262553i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.50000 | + | 16.4545i | −0.573916 | + | 0.994052i | ||||
\(275\) | 0.500000 | + | 0.866025i | 0.0301511 | + | 0.0522233i | ||||
\(276\) | − | 6.92820i | − | 0.417029i | ||||||
\(277\) | −1.00000 | + | 1.73205i | −0.0600842 | + | 0.104069i | −0.894503 | − | 0.447062i | \(-0.852470\pi\) |
0.834419 | + | 0.551131i | \(0.185804\pi\) | |||||||
\(278\) | 2.50000 | − | 4.33013i | 0.149940 | − | 0.259704i | ||||
\(279\) | 9.00000 | + | 15.5885i | 0.538816 | + | 0.933257i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.0000 | − | 19.0526i | −0.656205 | − | 1.13658i | −0.981590 | − | 0.190999i | \(-0.938827\pi\) |
0.325385 | − | 0.945582i | \(-0.394506\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.00000 | −0.237775 | −0.118888 | − | 0.992908i | \(-0.537933\pi\) | ||||
−0.118888 | + | 0.992908i | \(0.537933\pi\) | |||||||
\(284\) | −8.00000 | −0.474713 | ||||||||
\(285\) | −21.0000 | − | 12.1244i | −1.24393 | − | 0.718185i | ||||
\(286\) | 3.00000 | + | 5.19615i | 0.177394 | + | 0.307255i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.50000 | − | 2.59808i | −0.0883883 | − | 0.153093i | ||||
\(289\) | −4.00000 | + | 6.92820i | −0.235294 | + | 0.407541i | ||||
\(290\) | 4.00000 | − | 6.92820i | 0.234888 | − | 0.406838i | ||||
\(291\) | − | 8.66025i | − | 0.507673i | ||||||
\(292\) | 0.500000 | + | 0.866025i | 0.0292603 | + | 0.0506803i | ||||
\(293\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.00000 | + | 12.1244i | 0.407556 | + | 0.705907i | ||||
\(296\) | 1.00000 | − | 1.73205i | 0.0581238 | − | 0.100673i | ||||
\(297\) | −4.50000 | − | 2.59808i | −0.261116 | − | 0.150756i | ||||
\(298\) | −12.0000 | − | 20.7846i | −0.695141 | − | 1.20402i | ||||
\(299\) | 24.0000 | 1.38796 | ||||||||
\(300\) | 1.50000 | − | 0.866025i | 0.0866025 | − | 0.0500000i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 5.00000 | − | 8.66025i | 0.287718 | − | 0.498342i | ||||
\(303\) | −6.00000 | + | 3.46410i | −0.344691 | + | 0.199007i | ||||
\(304\) | −3.50000 | + | 6.06218i | −0.200739 | + | 0.347690i | ||||
\(305\) | 12.0000 | + | 20.7846i | 0.687118 | + | 1.19012i | ||||
\(306\) | −7.50000 | + | 12.9904i | −0.428746 | + | 0.742611i | ||||
\(307\) | −7.00000 | −0.399511 | −0.199756 | − | 0.979846i | \(-0.564015\pi\) | ||||
−0.199756 | + | 0.979846i | \(0.564015\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 24.2487i | 1.37946i | ||||||||
\(310\) | −6.00000 | − | 10.3923i | −0.340777 | − | 0.590243i | ||||
\(311\) | −2.00000 | −0.113410 | −0.0567048 | − | 0.998391i | \(-0.518059\pi\) | ||||
−0.0567048 | + | 0.998391i | \(0.518059\pi\) | |||||||
\(312\) | 9.00000 | − | 5.19615i | 0.509525 | − | 0.294174i | ||||
\(313\) | 17.0000 | 0.960897 | 0.480448 | − | 0.877023i | \(-0.340474\pi\) | ||||
0.480448 | + | 0.877023i | \(0.340474\pi\) | |||||||
\(314\) | 2.00000 | 0.112867 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.00000 | −0.337526 | ||||||||
\(317\) | −6.00000 | −0.336994 | −0.168497 | − | 0.985702i | \(-0.553891\pi\) | ||||
−0.168497 | + | 0.985702i | \(0.553891\pi\) | |||||||
\(318\) | 20.7846i | 1.16554i | ||||||||
\(319\) | −4.00000 | −0.223957 | ||||||||
\(320\) | 1.00000 | + | 1.73205i | 0.0559017 | + | 0.0968246i | ||||
\(321\) | −4.50000 | + | 2.59808i | −0.251166 | + | 0.145010i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 35.0000 | 1.94745 | ||||||||
\(324\) | −4.50000 | + | 7.79423i | −0.250000 | + | 0.433013i | ||||
\(325\) | 3.00000 | + | 5.19615i | 0.166410 | + | 0.288231i | ||||
\(326\) | −2.00000 | + | 3.46410i | −0.110770 | + | 0.191859i | ||||
\(327\) | 3.46410i | 0.191565i | ||||||||
\(328\) | −1.50000 | + | 2.59808i | −0.0828236 | + | 0.143455i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 3.00000 | + | 1.73205i | 0.165145 | + | 0.0953463i | ||||
\(331\) | 8.00000 | 0.439720 | 0.219860 | − | 0.975531i | \(-0.429440\pi\) | ||||
0.219860 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(332\) | 8.00000 | + | 13.8564i | 0.439057 | + | 0.760469i | ||||
\(333\) | −6.00000 | −0.328798 | ||||||||
\(334\) | −10.0000 | + | 17.3205i | −0.547176 | + | 0.947736i | ||||
\(335\) | 13.0000 | + | 22.5167i | 0.710266 | + | 1.23022i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.50000 | − | 7.79423i | 0.245131 | − | 0.424579i | −0.717038 | − | 0.697034i | \(-0.754502\pi\) |
0.962168 | + | 0.272456i | \(0.0878358\pi\) | |||||||
\(338\) | 11.5000 | + | 19.9186i | 0.625518 | + | 1.08343i | ||||
\(339\) | 15.0000 | − | 8.66025i | 0.814688 | − | 0.470360i | ||||
\(340\) | 5.00000 | − | 8.66025i | 0.271163 | − | 0.469668i | ||||
\(341\) | −3.00000 | + | 5.19615i | −0.162459 | + | 0.281387i | ||||
\(342\) | 21.0000 | 1.13555 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.500000 | − | 0.866025i | −0.0269582 | − | 0.0466930i | ||||
\(345\) | 12.0000 | − | 6.92820i | 0.646058 | − | 0.373002i | ||||
\(346\) | 2.00000 | 0.107521 | ||||||||
\(347\) | −3.00000 | −0.161048 | −0.0805242 | − | 0.996753i | \(-0.525659\pi\) | ||||
−0.0805242 | + | 0.996753i | \(0.525659\pi\) | |||||||
\(348\) | 6.92820i | 0.371391i | ||||||||
\(349\) | −7.00000 | − | 12.1244i | −0.374701 | − | 0.649002i | 0.615581 | − | 0.788074i | \(-0.288921\pi\) |
−0.990282 | + | 0.139072i | \(0.955588\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −27.0000 | − | 15.5885i | −1.44115 | − | 0.832050i | ||||
\(352\) | 0.500000 | − | 0.866025i | 0.0266501 | − | 0.0461593i | ||||
\(353\) | −7.50000 | + | 12.9904i | −0.399185 | + | 0.691408i | −0.993626 | − | 0.112731i | \(-0.964040\pi\) |
0.594441 | + | 0.804139i | \(0.297373\pi\) | |||||||
\(354\) | −10.5000 | − | 6.06218i | −0.558069 | − | 0.322201i | ||||
\(355\) | −8.00000 | − | 13.8564i | −0.424596 | − | 0.735422i | ||||
\(356\) | −3.00000 | + | 5.19615i | −0.159000 | + | 0.275396i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.0000 | + | 20.7846i | 0.634220 | + | 1.09850i | ||||
\(359\) | −1.00000 | + | 1.73205i | −0.0527780 | + | 0.0914141i | −0.891207 | − | 0.453596i | \(-0.850141\pi\) |
0.838429 | + | 0.545010i | \(0.183474\pi\) | |||||||
\(360\) | 3.00000 | − | 5.19615i | 0.158114 | − | 0.273861i | ||||
\(361\) | −15.0000 | − | 25.9808i | −0.789474 | − | 1.36741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 17.3205i | 0.909091i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.00000 | + | 1.73205i | −0.0523424 | + | 0.0906597i | ||||
\(366\) | −18.0000 | − | 10.3923i | −0.940875 | − | 0.543214i | ||||
\(367\) | −11.0000 | + | 19.0526i | −0.574195 | + | 0.994535i | 0.421933 | + | 0.906627i | \(0.361352\pi\) |
−0.996129 | + | 0.0879086i | \(0.971982\pi\) | |||||||
\(368\) | −2.00000 | − | 3.46410i | −0.104257 | − | 0.180579i | ||||
\(369\) | 9.00000 | 0.468521 | ||||||||
\(370\) | 4.00000 | 0.207950 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 9.00000 | + | 5.19615i | 0.466628 | + | 0.269408i | ||||
\(373\) | −11.0000 | − | 19.0526i | −0.569558 | − | 0.986504i | −0.996610 | − | 0.0822766i | \(-0.973781\pi\) |
0.427051 | − | 0.904227i | \(-0.359552\pi\) | |||||||
\(374\) | −5.00000 | −0.258544 | ||||||||
\(375\) | 18.0000 | + | 10.3923i | 0.929516 | + | 0.536656i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −24.0000 | −1.23606 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.0000 | −0.873231 | −0.436616 | − | 0.899648i | \(-0.643823\pi\) | ||||
−0.436616 | + | 0.899648i | \(0.643823\pi\) | |||||||
\(380\) | −14.0000 | −0.718185 | ||||||||
\(381\) | −18.0000 | − | 10.3923i | −0.922168 | − | 0.532414i | ||||
\(382\) | −12.0000 | −0.613973 | ||||||||
\(383\) | 2.00000 | + | 3.46410i | 0.102195 | + | 0.177007i | 0.912589 | − | 0.408879i | \(-0.134080\pi\) |
−0.810394 | + | 0.585886i | \(0.800747\pi\) | |||||||
\(384\) | −1.50000 | − | 0.866025i | −0.0765466 | − | 0.0441942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −17.0000 | −0.865277 | ||||||||
\(387\) | −1.50000 | + | 2.59808i | −0.0762493 | + | 0.132068i | ||||
\(388\) | −2.50000 | − | 4.33013i | −0.126918 | − | 0.219829i | ||||
\(389\) | −4.00000 | + | 6.92820i | −0.202808 | + | 0.351274i | −0.949432 | − | 0.313972i | \(-0.898340\pi\) |
0.746624 | + | 0.665246i | \(0.231673\pi\) | |||||||
\(390\) | 18.0000 | + | 10.3923i | 0.911465 | + | 0.526235i | ||||
\(391\) | −10.0000 | + | 17.3205i | −0.505722 | + | 0.875936i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 6.92820i | − | 0.349482i | ||||||
\(394\) | −10.0000 | −0.503793 | ||||||||
\(395\) | −6.00000 | − | 10.3923i | −0.301893 | − | 0.522894i | ||||
\(396\) | −3.00000 | −0.150756 | ||||||||
\(397\) | 9.00000 | − | 15.5885i | 0.451697 | − | 0.782362i | −0.546795 | − | 0.837267i | \(-0.684152\pi\) |
0.998492 | + | 0.0549046i | \(0.0174855\pi\) | |||||||
\(398\) | −7.00000 | − | 12.1244i | −0.350878 | − | 0.607739i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.500000 | − | 0.866025i | 0.0250000 | − | 0.0433013i | ||||
\(401\) | −4.50000 | − | 7.79423i | −0.224719 | − | 0.389225i | 0.731516 | − | 0.681824i | \(-0.238813\pi\) |
−0.956235 | + | 0.292599i | \(0.905480\pi\) | |||||||
\(402\) | −19.5000 | − | 11.2583i | −0.972572 | − | 0.561514i | ||||
\(403\) | −18.0000 | + | 31.1769i | −0.896644 | + | 1.55303i | ||||
\(404\) | −2.00000 | + | 3.46410i | −0.0995037 | + | 0.172345i | ||||
\(405\) | −18.0000 | −0.894427 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.00000 | − | 1.73205i | −0.0495682 | − | 0.0858546i | ||||
\(408\) | 8.66025i | 0.428746i | ||||||||
\(409\) | −11.0000 | −0.543915 | −0.271957 | − | 0.962309i | \(-0.587671\pi\) | ||||
−0.271957 | + | 0.962309i | \(0.587671\pi\) | |||||||
\(410\) | −6.00000 | −0.296319 | ||||||||
\(411\) | 28.5000 | − | 16.4545i | 1.40580 | − | 0.811640i | ||||
\(412\) | 7.00000 | + | 12.1244i | 0.344865 | + | 0.597324i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −6.00000 | + | 10.3923i | −0.294884 | + | 0.510754i | ||||
\(415\) | −16.0000 | + | 27.7128i | −0.785409 | + | 1.36037i | ||||
\(416\) | 3.00000 | − | 5.19615i | 0.147087 | − | 0.254762i | ||||
\(417\) | −7.50000 | + | 4.33013i | −0.367277 | + | 0.212047i | ||||
\(418\) | 3.50000 | + | 6.06218i | 0.171191 | + | 0.296511i | ||||
\(419\) | −6.00000 | + | 10.3923i | −0.293119 | + | 0.507697i | −0.974546 | − | 0.224189i | \(-0.928027\pi\) |
0.681426 | + | 0.731887i | \(0.261360\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.00000 | + | 10.3923i | 0.292422 | + | 0.506490i | 0.974382 | − | 0.224900i | \(-0.0722054\pi\) |
−0.681960 | + | 0.731390i | \(0.738872\pi\) | |||||||
\(422\) | −8.00000 | + | 13.8564i | −0.389434 | + | 0.674519i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.00000 | + | 10.3923i | 0.291386 | + | 0.504695i | ||||
\(425\) | −5.00000 | −0.242536 | ||||||||
\(426\) | 12.0000 | + | 6.92820i | 0.581402 | + | 0.335673i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.50000 | + | 2.59808i | −0.0725052 | + | 0.125583i | ||||
\(429\) | − | 10.3923i | − | 0.501745i | ||||||
\(430\) | 1.00000 | − | 1.73205i | 0.0482243 | − | 0.0835269i | ||||
\(431\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(432\) | 5.19615i | 0.250000i | ||||||||
\(433\) | 25.0000 | 1.20142 | 0.600712 | − | 0.799466i | \(-0.294884\pi\) | ||||
0.600712 | + | 0.799466i | \(0.294884\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.0000 | + | 6.92820i | −0.575356 | + | 0.332182i | ||||
\(436\) | 1.00000 | + | 1.73205i | 0.0478913 | + | 0.0829502i | ||||
\(437\) | 28.0000 | 1.33942 | ||||||||
\(438\) | − | 1.73205i | − | 0.0827606i | ||||||
\(439\) | 24.0000 | 1.14546 | 0.572729 | − | 0.819745i | \(-0.305885\pi\) | ||||
0.572729 | + | 0.819745i | \(0.305885\pi\) | |||||||
\(440\) | 2.00000 | 0.0953463 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −30.0000 | −1.42695 | ||||||||
\(443\) | 7.00000 | 0.332580 | 0.166290 | − | 0.986077i | \(-0.446821\pi\) | ||||
0.166290 | + | 0.986077i | \(0.446821\pi\) | |||||||
\(444\) | −3.00000 | + | 1.73205i | −0.142374 | + | 0.0821995i | ||||
\(445\) | −12.0000 | −0.568855 | ||||||||
\(446\) | 2.00000 | + | 3.46410i | 0.0947027 | + | 0.164030i | ||||
\(447\) | 41.5692i | 1.96616i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.0000 | 0.802280 | 0.401140 | − | 0.916017i | \(-0.368614\pi\) | ||||
0.401140 | + | 0.916017i | \(0.368614\pi\) | |||||||
\(450\) | −3.00000 | −0.141421 | ||||||||
\(451\) | 1.50000 | + | 2.59808i | 0.0706322 | + | 0.122339i | ||||
\(452\) | 5.00000 | − | 8.66025i | 0.235180 | − | 0.407344i | ||||
\(453\) | −15.0000 | + | 8.66025i | −0.704761 | + | 0.406894i | ||||
\(454\) | −1.50000 | + | 2.59808i | −0.0703985 | + | 0.121934i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 10.5000 | − | 6.06218i | 0.491708 | − | 0.283887i | ||||
\(457\) | 1.00000 | 0.0467780 | 0.0233890 | − | 0.999726i | \(-0.492554\pi\) | ||||
0.0233890 | + | 0.999726i | \(0.492554\pi\) | |||||||
\(458\) | 13.0000 | + | 22.5167i | 0.607450 | + | 1.05213i | ||||
\(459\) | 22.5000 | − | 12.9904i | 1.05021 | − | 0.606339i | ||||
\(460\) | 4.00000 | − | 6.92820i | 0.186501 | − | 0.323029i | ||||
\(461\) | 7.00000 | + | 12.1244i | 0.326023 | + | 0.564688i | 0.981719 | − | 0.190337i | \(-0.0609581\pi\) |
−0.655696 | + | 0.755025i | \(0.727625\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.00000 | − | 6.92820i | 0.185896 | − | 0.321981i | −0.757982 | − | 0.652275i | \(-0.773815\pi\) |
0.943878 | + | 0.330294i | \(0.107148\pi\) | |||||||
\(464\) | 2.00000 | + | 3.46410i | 0.0928477 | + | 0.160817i | ||||
\(465\) | 20.7846i | 0.963863i | ||||||||
\(466\) | −14.5000 | + | 25.1147i | −0.671700 | + | 1.16342i | ||||
\(467\) | −6.50000 | + | 11.2583i | −0.300784 | + | 0.520973i | −0.976314 | − | 0.216359i | \(-0.930582\pi\) |
0.675530 | + | 0.737333i | \(0.263915\pi\) | |||||||
\(468\) | −18.0000 | −0.832050 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.00000 | − | 1.73205i | −0.138233 | − | 0.0798087i | ||||
\(472\) | −7.00000 | −0.322201 | ||||||||
\(473\) | −1.00000 | −0.0459800 | ||||||||
\(474\) | 9.00000 | + | 5.19615i | 0.413384 | + | 0.238667i | ||||
\(475\) | 3.50000 | + | 6.06218i | 0.160591 | + | 0.278152i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.0000 | − | 31.1769i | 0.824163 | − | 1.42749i | ||||
\(478\) | 3.00000 | − | 5.19615i | 0.137217 | − | 0.237666i | ||||
\(479\) | −10.0000 | + | 17.3205i | −0.456912 | + | 0.791394i | −0.998796 | − | 0.0490589i | \(-0.984378\pi\) |
0.541884 | + | 0.840453i | \(0.317711\pi\) | |||||||
\(480\) | − | 3.46410i | − | 0.158114i | ||||||
\(481\) | −6.00000 | − | 10.3923i | −0.273576 | − | 0.473848i | ||||
\(482\) | −11.5000 | + | 19.9186i | −0.523811 | + | 0.907267i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.00000 | + | 8.66025i | 0.227273 | + | 0.393648i | ||||
\(485\) | 5.00000 | − | 8.66025i | 0.227038 | − | 0.393242i | ||||
\(486\) | 13.5000 | − | 7.79423i | 0.612372 | − | 0.353553i | ||||
\(487\) | 5.00000 | + | 8.66025i | 0.226572 | + | 0.392434i | 0.956790 | − | 0.290780i | \(-0.0939149\pi\) |
−0.730218 | + | 0.683214i | \(0.760582\pi\) | |||||||
\(488\) | −12.0000 | −0.543214 | ||||||||
\(489\) | 6.00000 | − | 3.46410i | 0.271329 | − | 0.156652i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.5000 | + | 28.5788i | −0.744635 | + | 1.28974i | 0.205731 | + | 0.978609i | \(0.434043\pi\) |
−0.950365 | + | 0.311136i | \(0.899290\pi\) | |||||||
\(492\) | 4.50000 | − | 2.59808i | 0.202876 | − | 0.117130i | ||||
\(493\) | 10.0000 | − | 17.3205i | 0.450377 | − | 0.780076i | ||||
\(494\) | 21.0000 | + | 36.3731i | 0.944835 | + | 1.63650i | ||||
\(495\) | −3.00000 | − | 5.19615i | −0.134840 | − | 0.233550i | ||||
\(496\) | 6.00000 | 0.269408 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | − | 27.7128i | − | 1.24184i | ||||||
\(499\) | 14.5000 | + | 25.1147i | 0.649109 | + | 1.12429i | 0.983336 | + | 0.181797i | \(0.0581915\pi\) |
−0.334227 | + | 0.942493i | \(0.608475\pi\) | |||||||
\(500\) | 12.0000 | 0.536656 | ||||||||
\(501\) | 30.0000 | − | 17.3205i | 1.34030 | − | 0.773823i | ||||
\(502\) | 3.00000 | 0.133897 | ||||||||
\(503\) | −6.00000 | −0.267527 | −0.133763 | − | 0.991013i | \(-0.542706\pi\) | ||||
−0.133763 | + | 0.991013i | \(0.542706\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.00000 | −0.355995 | ||||||||
\(506\) | −4.00000 | −0.177822 | ||||||||
\(507\) | − | 39.8372i | − | 1.76923i | ||||||
\(508\) | −12.0000 | −0.532414 | ||||||||
\(509\) | 15.0000 | + | 25.9808i | 0.664863 | + | 1.15158i | 0.979322 | + | 0.202306i | \(0.0648436\pi\) |
−0.314459 | + | 0.949271i | \(0.601823\pi\) | |||||||
\(510\) | −15.0000 | + | 8.66025i | −0.664211 | + | 0.383482i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −31.5000 | − | 18.1865i | −1.39076 | − | 0.802955i | ||||
\(514\) | 7.50000 | + | 12.9904i | 0.330811 | + | 0.572981i | ||||
\(515\) | −14.0000 | + | 24.2487i | −0.616914 | + | 1.06853i | ||||
\(516\) | 1.73205i | 0.0762493i | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.00000 | − | 1.73205i | −0.131685 | − | 0.0760286i | ||||
\(520\) | 12.0000 | 0.526235 | ||||||||
\(521\) | −4.50000 | − | 7.79423i | −0.197149 | − | 0.341471i | 0.750454 | − | 0.660922i | \(-0.229835\pi\) |
−0.947603 | + | 0.319451i | \(0.896501\pi\) | |||||||
\(522\) | 6.00000 | − | 10.3923i | 0.262613 | − | 0.454859i | ||||
\(523\) | −14.0000 | + | 24.2487i | −0.612177 | + | 1.06032i | 0.378695 | + | 0.925521i | \(0.376373\pi\) |
−0.990873 | + | 0.134801i | \(0.956961\pi\) | |||||||
\(524\) | −2.00000 | − | 3.46410i | −0.0873704 | − | 0.151330i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.00000 | − | 15.5885i | 0.392419 | − | 0.679689i | ||||
\(527\) | −15.0000 | − | 25.9808i | −0.653410 | − | 1.13174i | ||||
\(528\) | −1.50000 | + | 0.866025i | −0.0652791 | + | 0.0376889i | ||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | −12.0000 | + | 20.7846i | −0.521247 | + | 0.902826i | ||||
\(531\) | 10.5000 | + | 18.1865i | 0.455661 | + | 0.789228i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.00000 | + | 15.5885i | 0.389833 | + | 0.675211i | ||||
\(534\) | 9.00000 | − | 5.19615i | 0.389468 | − | 0.224860i | ||||
\(535\) | −6.00000 | −0.259403 | ||||||||
\(536\) | −13.0000 | −0.561514 | ||||||||
\(537\) | − | 41.5692i | − | 1.79384i | ||||||
\(538\) | −10.0000 | − | 17.3205i | −0.431131 | − | 0.746740i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −9.00000 | + | 5.19615i | −0.387298 | + | 0.223607i | ||||
\(541\) | 12.0000 | − | 20.7846i | 0.515920 | − | 0.893600i | −0.483909 | − | 0.875118i | \(-0.660783\pi\) |
0.999829 | − | 0.0184818i | \(-0.00588327\pi\) | |||||||
\(542\) | 3.00000 | − | 5.19615i | 0.128861 | − | 0.223194i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.50000 | + | 4.33013i | 0.107187 | + | 0.185653i | ||||
\(545\) | −2.00000 | + | 3.46410i | −0.0856706 | + | 0.148386i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.5000 | + | 18.1865i | 0.448948 | + | 0.777600i | 0.998318 | − | 0.0579790i | \(-0.0184657\pi\) |
−0.549370 | + | 0.835579i | \(0.685132\pi\) | |||||||
\(548\) | 9.50000 | − | 16.4545i | 0.405820 | − | 0.702901i | ||||
\(549\) | 18.0000 | + | 31.1769i | 0.768221 | + | 1.33060i | ||||
\(550\) | −0.500000 | − | 0.866025i | −0.0213201 | − | 0.0369274i | ||||
\(551\) | −28.0000 | −1.19284 | ||||||||
\(552\) | 6.92820i | 0.294884i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.00000 | − | 1.73205i | 0.0424859 | − | 0.0735878i | ||||
\(555\) | −6.00000 | − | 3.46410i | −0.254686 | − | 0.147043i | ||||
\(556\) | −2.50000 | + | 4.33013i | −0.106024 | + | 0.183638i | ||||
\(557\) | 14.0000 | + | 24.2487i | 0.593199 | + | 1.02745i | 0.993798 | + | 0.111198i | \(0.0354686\pi\) |
−0.400599 | + | 0.916253i | \(0.631198\pi\) | |||||||
\(558\) | −9.00000 | − | 15.5885i | −0.381000 | − | 0.659912i | ||||
\(559\) | −6.00000 | −0.253773 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.50000 | + | 4.33013i | 0.316650 | + | 0.182818i | ||||
\(562\) | 11.0000 | + | 19.0526i | 0.464007 | + | 0.803684i | ||||
\(563\) | −31.0000 | −1.30649 | −0.653247 | − | 0.757145i | \(-0.726594\pi\) | ||||
−0.653247 | + | 0.757145i | \(0.726594\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.0000 | 0.841406 | ||||||||
\(566\) | 4.00000 | 0.168133 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.00000 | 0.335673 | ||||||||
\(569\) | −15.0000 | −0.628833 | −0.314416 | − | 0.949285i | \(-0.601809\pi\) | ||||
−0.314416 | + | 0.949285i | \(0.601809\pi\) | |||||||
\(570\) | 21.0000 | + | 12.1244i | 0.879593 | + | 0.507833i | ||||
\(571\) | −33.0000 | −1.38101 | −0.690504 | − | 0.723329i | \(-0.742611\pi\) | ||||
−0.690504 | + | 0.723329i | \(0.742611\pi\) | |||||||
\(572\) | −3.00000 | − | 5.19615i | −0.125436 | − | 0.217262i | ||||
\(573\) | 18.0000 | + | 10.3923i | 0.751961 | + | 0.434145i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.00000 | −0.166812 | ||||||||
\(576\) | 1.50000 | + | 2.59808i | 0.0625000 | + | 0.108253i | ||||
\(577\) | −17.5000 | − | 30.3109i | −0.728535 | − | 1.26186i | −0.957503 | − | 0.288425i | \(-0.906868\pi\) |
0.228968 | − | 0.973434i | \(-0.426465\pi\) | |||||||
\(578\) | 4.00000 | − | 6.92820i | 0.166378 | − | 0.288175i | ||||
\(579\) | 25.5000 | + | 14.7224i | 1.05974 | + | 0.611843i | ||||
\(580\) | −4.00000 | + | 6.92820i | −0.166091 | + | 0.287678i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 8.66025i | 0.358979i | ||||||||
\(583\) | 12.0000 | 0.496989 | ||||||||
\(584\) | −0.500000 | − | 0.866025i | −0.0206901 | − | 0.0358364i | ||||
\(585\) | −18.0000 | − | 31.1769i | −0.744208 | − | 1.28901i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23.5000 | − | 40.7032i | −0.969949 | − | 1.68000i | −0.695686 | − | 0.718346i | \(-0.744900\pi\) |
−0.274263 | − | 0.961655i | \(-0.588434\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.0000 | + | 36.3731i | −0.865290 | + | 1.49873i | ||||
\(590\) | −7.00000 | − | 12.1244i | −0.288185 | − | 0.499152i | ||||
\(591\) | 15.0000 | + | 8.66025i | 0.617018 | + | 0.356235i | ||||
\(592\) | −1.00000 | + | 1.73205i | −0.0410997 | + | 0.0711868i | ||||
\(593\) | −3.00000 | + | 5.19615i | −0.123195 | + | 0.213380i | −0.921026 | − | 0.389501i | \(-0.872647\pi\) |
0.797831 | + | 0.602881i | \(0.205981\pi\) | |||||||
\(594\) | 4.50000 | + | 2.59808i | 0.184637 | + | 0.106600i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.0000 | + | 20.7846i | 0.491539 | + | 0.851371i | ||||
\(597\) | 24.2487i | 0.992434i | ||||||||
\(598\) | −24.0000 | −0.981433 | ||||||||
\(599\) | 24.0000 | 0.980613 | 0.490307 | − | 0.871550i | \(-0.336885\pi\) | ||||
0.490307 | + | 0.871550i | \(0.336885\pi\) | |||||||
\(600\) | −1.50000 | + | 0.866025i | −0.0612372 | + | 0.0353553i | ||||
\(601\) | −9.50000 | − | 16.4545i | −0.387513 | − | 0.671192i | 0.604601 | − | 0.796528i | \(-0.293332\pi\) |
−0.992114 | + | 0.125336i | \(0.959999\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 19.5000 | + | 33.7750i | 0.794101 | + | 1.37542i | ||||
\(604\) | −5.00000 | + | 8.66025i | −0.203447 | + | 0.352381i | ||||
\(605\) | −10.0000 | + | 17.3205i | −0.406558 | + | 0.704179i | ||||
\(606\) | 6.00000 | − | 3.46410i | 0.243733 | − | 0.140720i | ||||
\(607\) | −12.0000 | − | 20.7846i | −0.487065 | − | 0.843621i | 0.512824 | − | 0.858494i | \(-0.328599\pi\) |
−0.999889 | + | 0.0148722i | \(0.995266\pi\) | |||||||
\(608\) | 3.50000 | − | 6.06218i | 0.141944 | − | 0.245854i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.0000 | − | 20.7846i | −0.485866 | − | 0.841544i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 7.50000 | − | 12.9904i | 0.303170 | − | 0.525105i | ||||
\(613\) | −21.0000 | − | 36.3731i | −0.848182 | − | 1.46909i | −0.882829 | − | 0.469695i | \(-0.844364\pi\) |
0.0346469 | − | 0.999400i | \(-0.488969\pi\) | |||||||
\(614\) | 7.00000 | 0.282497 | ||||||||
\(615\) | 9.00000 | + | 5.19615i | 0.362915 | + | 0.209529i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.50000 | − | 14.7224i | 0.342197 | − | 0.592703i | −0.642643 | − | 0.766165i | \(-0.722162\pi\) |
0.984840 | + | 0.173463i | \(0.0554956\pi\) | |||||||
\(618\) | − | 24.2487i | − | 0.975426i | ||||||
\(619\) | 18.5000 | − | 32.0429i | 0.743578 | − | 1.28791i | −0.207279 | − | 0.978282i | \(-0.566461\pi\) |
0.950856 | − | 0.309633i | \(-0.100206\pi\) | |||||||
\(620\) | 6.00000 | + | 10.3923i | 0.240966 | + | 0.417365i | ||||
\(621\) | 18.0000 | − | 10.3923i | 0.722315 | − | 0.417029i | ||||
\(622\) | 2.00000 | 0.0801927 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −9.00000 | + | 5.19615i | −0.360288 | + | 0.208013i | ||||
\(625\) | 9.50000 | + | 16.4545i | 0.380000 | + | 0.658179i | ||||
\(626\) | −17.0000 | −0.679457 | ||||||||
\(627\) | − | 12.1244i | − | 0.484200i | ||||||
\(628\) | −2.00000 | −0.0798087 | ||||||||
\(629\) | 10.0000 | 0.398726 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.00000 | 0.318475 | 0.159237 | − | 0.987240i | \(-0.449096\pi\) | ||||
0.159237 | + | 0.987240i | \(0.449096\pi\) | |||||||
\(632\) | 6.00000 | 0.238667 | ||||||||
\(633\) | 24.0000 | − | 13.8564i | 0.953914 | − | 0.550743i | ||||
\(634\) | 6.00000 | 0.238290 | ||||||||
\(635\) | −12.0000 | − | 20.7846i | −0.476205 | − | 0.824812i | ||||
\(636\) | − | 20.7846i | − | 0.824163i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.00000 | 0.158362 | ||||||||
\(639\) | −12.0000 | − | 20.7846i | −0.474713 | − | 0.822226i | ||||
\(640\) | −1.00000 | − | 1.73205i | −0.0395285 | − | 0.0684653i | ||||
\(641\) | −0.500000 | + | 0.866025i | −0.0197488 | + | 0.0342059i | −0.875731 | − | 0.482800i | \(-0.839620\pi\) |
0.855982 | + | 0.517005i | \(0.172953\pi\) | |||||||
\(642\) | 4.50000 | − | 2.59808i | 0.177601 | − | 0.102538i | ||||
\(643\) | −3.50000 | + | 6.06218i | −0.138027 | + | 0.239069i | −0.926750 | − | 0.375680i | \(-0.877409\pi\) |
0.788723 | + | 0.614749i | \(0.210743\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.00000 | + | 1.73205i | −0.118125 | + | 0.0681994i | ||||
\(646\) | −35.0000 | −1.37706 | ||||||||
\(647\) | 6.00000 | + | 10.3923i | 0.235884 | + | 0.408564i | 0.959529 | − | 0.281609i | \(-0.0908680\pi\) |
−0.723645 | + | 0.690172i | \(0.757535\pi\) | |||||||
\(648\) | 4.50000 | − | 7.79423i | 0.176777 | − | 0.306186i | ||||
\(649\) | −3.50000 | + | 6.06218i | −0.137387 | + | 0.237961i | ||||
\(650\) | −3.00000 | − | 5.19615i | −0.117670 | − | 0.203810i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.00000 | − | 3.46410i | 0.0783260 | − | 0.135665i | ||||
\(653\) | 3.00000 | + | 5.19615i | 0.117399 | + | 0.203341i | 0.918736 | − | 0.394872i | \(-0.129211\pi\) |
−0.801337 | + | 0.598213i | \(0.795878\pi\) | |||||||
\(654\) | − | 3.46410i | − | 0.135457i | ||||||
\(655\) | 4.00000 | − | 6.92820i | 0.156293 | − | 0.270707i | ||||
\(656\) | 1.50000 | − | 2.59808i | 0.0585652 | − | 0.101438i | ||||
\(657\) | −1.50000 | + | 2.59808i | −0.0585206 | + | 0.101361i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.00000 | − | 13.8564i | −0.311636 | − | 0.539769i | 0.667081 | − | 0.744985i | \(-0.267544\pi\) |
−0.978717 | + | 0.205216i | \(0.934210\pi\) | |||||||
\(660\) | −3.00000 | − | 1.73205i | −0.116775 | − | 0.0674200i | ||||
\(661\) | −28.0000 | −1.08907 | −0.544537 | − | 0.838737i | \(-0.683295\pi\) | ||||
−0.544537 | + | 0.838737i | \(0.683295\pi\) | |||||||
\(662\) | −8.00000 | −0.310929 | ||||||||
\(663\) | 45.0000 | + | 25.9808i | 1.74766 | + | 1.00901i | ||||
\(664\) | −8.00000 | − | 13.8564i | −0.310460 | − | 0.537733i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.00000 | 0.232495 | ||||||||
\(667\) | 8.00000 | − | 13.8564i | 0.309761 | − | 0.536522i | ||||
\(668\) | 10.0000 | − | 17.3205i | 0.386912 | − | 0.670151i | ||||
\(669\) | − | 6.92820i | − | 0.267860i | ||||||
\(670\) | −13.0000 | − | 22.5167i | −0.502234 | − | 0.869894i | ||||
\(671\) | −6.00000 | + | 10.3923i | −0.231627 | + | 0.401190i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.00000 | − | 12.1244i | −0.269830 | − | 0.467360i | 0.698988 | − | 0.715134i | \(-0.253634\pi\) |
−0.968818 | + | 0.247774i | \(0.920301\pi\) | |||||||
\(674\) | −4.50000 | + | 7.79423i | −0.173334 | + | 0.300222i | ||||
\(675\) | 4.50000 | + | 2.59808i | 0.173205 | + | 0.100000i | ||||
\(676\) | −11.5000 | − | 19.9186i | −0.442308 | − | 0.766099i | ||||
\(677\) | −30.0000 | −1.15299 | −0.576497 | − | 0.817099i | \(-0.695581\pi\) | ||||
−0.576497 | + | 0.817099i | \(0.695581\pi\) | |||||||
\(678\) | −15.0000 | + | 8.66025i | −0.576072 | + | 0.332595i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −5.00000 | + | 8.66025i | −0.191741 | + | 0.332106i | ||||
\(681\) | 4.50000 | − | 2.59808i | 0.172440 | − | 0.0995585i | ||||
\(682\) | 3.00000 | − | 5.19615i | 0.114876 | − | 0.198971i | ||||
\(683\) | −19.5000 | − | 33.7750i | −0.746147 | − | 1.29236i | −0.949657 | − | 0.313291i | \(-0.898568\pi\) |
0.203510 | − | 0.979073i | \(-0.434765\pi\) | |||||||
\(684\) | −21.0000 | −0.802955 | ||||||||
\(685\) | 38.0000 | 1.45191 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 45.0333i | − | 1.71813i | ||||||
\(688\) | 0.500000 | + | 0.866025i | 0.0190623 | + | 0.0330169i | ||||
\(689\) | 72.0000 | 2.74298 | ||||||||
\(690\) | −12.0000 | + | 6.92820i | −0.456832 | + | 0.263752i | ||||
\(691\) | −32.0000 | −1.21734 | −0.608669 | − | 0.793424i | \(-0.708296\pi\) | ||||
−0.608669 | + | 0.793424i | \(0.708296\pi\) | |||||||
\(692\) | −2.00000 | −0.0760286 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.00000 | 0.113878 | ||||||||
\(695\) | −10.0000 | −0.379322 | ||||||||
\(696\) | − | 6.92820i | − | 0.262613i | ||||||
\(697\) | −15.0000 | −0.568166 | ||||||||
\(698\) | 7.00000 | + | 12.1244i | 0.264954 | + | 0.458914i | ||||
\(699\) | 43.5000 | − | 25.1147i | 1.64532 | − | 0.949927i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.00000 | 0.302156 | 0.151078 | − | 0.988522i | \(-0.451726\pi\) | ||||
0.151078 | + | 0.988522i | \(0.451726\pi\) | |||||||
\(702\) | 27.0000 | + | 15.5885i | 1.01905 | + | 0.588348i | ||||
\(703\) | −7.00000 | − | 12.1244i | −0.264010 | − | 0.457279i | ||||
\(704\) | −0.500000 | + | 0.866025i | −0.0188445 | + | 0.0326396i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.50000 | − | 12.9904i | 0.282266 | − | 0.488899i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 10.5000 | + | 6.06218i | 0.394614 | + | 0.227831i | ||||
\(709\) | −4.00000 | −0.150223 | −0.0751116 | − | 0.997175i | \(-0.523931\pi\) | ||||
−0.0751116 | + | 0.997175i | \(0.523931\pi\) | |||||||
\(710\) | 8.00000 | + | 13.8564i | 0.300235 | + | 0.520022i | ||||
\(711\) | −9.00000 | − | 15.5885i | −0.337526 | − | 0.584613i | ||||
\(712\) | 3.00000 | − | 5.19615i | 0.112430 | − | 0.194734i | ||||
\(713\) | −12.0000 | − | 20.7846i | −0.449404 | − | 0.778390i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.00000 | − | 10.3923i | 0.224387 | − | 0.388650i | ||||
\(716\) | −12.0000 | − | 20.7846i | −0.448461 | − | 0.776757i | ||||
\(717\) | −9.00000 | + | 5.19615i | −0.336111 | + | 0.194054i | ||||
\(718\) | 1.00000 | − | 1.73205i | 0.0373197 | − | 0.0646396i | ||||
\(719\) | 3.00000 | − | 5.19615i | 0.111881 | − | 0.193784i | −0.804648 | − | 0.593753i | \(-0.797646\pi\) |
0.916529 | + | 0.399969i | \(0.130979\pi\) | |||||||
\(720\) | −3.00000 | + | 5.19615i | −0.111803 | + | 0.193649i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 15.0000 | + | 25.9808i | 0.558242 | + | 0.966904i | ||||
\(723\) | 34.5000 | − | 19.9186i | 1.28307 | − | 0.740780i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.00000 | 0.148556 | ||||||||
\(726\) | − | 17.3205i | − | 0.642824i | ||||||
\(727\) | −7.00000 | − | 12.1244i | −0.259616 | − | 0.449667i | 0.706523 | − | 0.707690i | \(-0.250263\pi\) |
−0.966139 | + | 0.258022i | \(0.916929\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 1.00000 | − | 1.73205i | 0.0370117 | − | 0.0641061i | ||||
\(731\) | 2.50000 | − | 4.33013i | 0.0924658 | − | 0.160156i | ||||
\(732\) | 18.0000 | + | 10.3923i | 0.665299 | + | 0.384111i | ||||
\(733\) | −9.00000 | − | 15.5885i | −0.332423 | − | 0.575773i | 0.650564 | − | 0.759452i | \(-0.274533\pi\) |
−0.982986 | + | 0.183679i | \(0.941199\pi\) | |||||||
\(734\) | 11.0000 | − | 19.0526i | 0.406017 | − | 0.703243i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.00000 | + | 3.46410i | 0.0737210 | + | 0.127688i | ||||
\(737\) | −6.50000 | + | 11.2583i | −0.239431 | + | 0.414706i | ||||
\(738\) | −9.00000 | −0.331295 | ||||||||
\(739\) | 16.5000 | + | 28.5788i | 0.606962 | + | 1.05129i | 0.991738 | + | 0.128279i | \(0.0409454\pi\) |
−0.384776 | + | 0.923010i | \(0.625721\pi\) | |||||||
\(740\) | −4.00000 | −0.147043 | ||||||||
\(741\) | − | 72.7461i | − | 2.67240i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.00000 | − | 5.19615i | 0.110059 | − | 0.190628i | −0.805735 | − | 0.592277i | \(-0.798229\pi\) |
0.915794 | + | 0.401648i | \(0.131563\pi\) | |||||||
\(744\) | −9.00000 | − | 5.19615i | −0.329956 | − | 0.190500i | ||||
\(745\) | −24.0000 | + | 41.5692i | −0.879292 | + | 1.52298i | ||||
\(746\) | 11.0000 | + | 19.0526i | 0.402739 | + | 0.697564i | ||||
\(747\) | −24.0000 | + | 41.5692i | −0.878114 | + | 1.52094i | ||||
\(748\) | 5.00000 | 0.182818 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −18.0000 | − | 10.3923i | −0.657267 | − | 0.379473i | ||||
\(751\) | 9.00000 | + | 15.5885i | 0.328415 | + | 0.568831i | 0.982197 | − | 0.187851i | \(-0.0601523\pi\) |
−0.653783 | + | 0.756682i | \(0.726819\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.50000 | − | 2.59808i | −0.163989 | − | 0.0946792i | ||||
\(754\) | 24.0000 | 0.874028 | ||||||||
\(755\) | −20.0000 | −0.727875 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −48.0000 | −1.74459 | −0.872295 | − | 0.488980i | \(-0.837369\pi\) | ||||
−0.872295 | + | 0.488980i | \(0.837369\pi\) | |||||||
\(758\) | 17.0000 | 0.617468 | ||||||||
\(759\) | 6.00000 | + | 3.46410i | 0.217786 | + | 0.125739i | ||||
\(760\) | 14.0000 | 0.507833 | ||||||||
\(761\) | 5.00000 | + | 8.66025i | 0.181250 | + | 0.313934i | 0.942306 | − | 0.334752i | \(-0.108652\pi\) |
−0.761057 | + | 0.648686i | \(0.775319\pi\) | |||||||
\(762\) | 18.0000 | + | 10.3923i | 0.652071 | + | 0.376473i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 12.0000 | 0.434145 | ||||||||
\(765\) | 30.0000 | 1.08465 | ||||||||
\(766\) | −2.00000 | − | 3.46410i | −0.0722629 | − | 0.125163i | ||||
\(767\) | −21.0000 | + | 36.3731i | −0.758266 | + | 1.31336i | ||||
\(768\) | 1.50000 | + | 0.866025i | 0.0541266 | + | 0.0312500i | ||||
\(769\) | 11.0000 | − | 19.0526i | 0.396670 | − | 0.687053i | −0.596643 | − | 0.802507i | \(-0.703499\pi\) |
0.993313 | + | 0.115454i | \(0.0368323\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 25.9808i | − | 0.935674i | ||||||
\(772\) | 17.0000 | 0.611843 | ||||||||
\(773\) | −26.0000 | − | 45.0333i | −0.935155 | − | 1.61974i | −0.774357 | − | 0.632749i | \(-0.781927\pi\) |
−0.160798 | − | 0.986987i | \(-0.551407\pi\) | |||||||
\(774\) | 1.50000 | − | 2.59808i | 0.0539164 | − | 0.0933859i | ||||
\(775\) | 3.00000 | − | 5.19615i | 0.107763 | − | 0.186651i | ||||
\(776\) | 2.50000 | + | 4.33013i | 0.0897448 | + | 0.155443i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.00000 | − | 6.92820i | 0.143407 | − | 0.248388i | ||||
\(779\) | 10.5000 | + | 18.1865i | 0.376202 | + | 0.651600i | ||||
\(780\) | −18.0000 | − | 10.3923i | −0.644503 | − | 0.372104i | ||||
\(781\) | 4.00000 | − | 6.92820i | 0.143131 | − | 0.247911i | ||||
\(782\) | 10.0000 | − | 17.3205i | 0.357599 | − | 0.619380i | ||||
\(783\) | −18.0000 | + | 10.3923i | −0.643268 | + | 0.371391i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.00000 | − | 3.46410i | −0.0713831 | − | 0.123639i | ||||
\(786\) | 6.92820i | 0.247121i | ||||||||
\(787\) | 12.0000 | 0.427754 | 0.213877 | − | 0.976861i | \(-0.431391\pi\) | ||||
0.213877 | + | 0.976861i | \(0.431391\pi\) | |||||||
\(788\) | 10.0000 | 0.356235 | ||||||||
\(789\) | −27.0000 | + | 15.5885i | −0.961225 | + | 0.554964i | ||||
\(790\) | 6.00000 | + | 10.3923i | 0.213470 | + | 0.369742i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.00000 | 0.106600 | ||||||||
\(793\) | −36.0000 | + | 62.3538i | −1.27840 | + | 2.21425i | ||||
\(794\) | −9.00000 | + | 15.5885i | −0.319398 | + | 0.553214i | ||||
\(795\) | 36.0000 | − | 20.7846i | 1.27679 | − | 0.737154i | ||||
\(796\) | 7.00000 | + | 12.1244i | 0.248108 | + | 0.429736i | ||||
\(797\) | −6.00000 | + | 10.3923i | −0.212531 | + | 0.368114i | −0.952506 | − | 0.304520i | \(-0.901504\pi\) |
0.739975 | + | 0.672634i | \(0.234837\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.500000 | + | 0.866025i | −0.0176777 | + | 0.0306186i | ||||
\(801\) | −18.0000 | −0.635999 | ||||||||
\(802\) | 4.50000 | + | 7.79423i | 0.158901 | + | 0.275224i | ||||
\(803\) | −1.00000 | −0.0352892 | ||||||||
\(804\) | 19.5000 | + | 11.2583i | 0.687712 | + | 0.397051i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 18.0000 | − | 31.1769i | 0.634023 | − | 1.09816i | ||||
\(807\) | 34.6410i | 1.21942i | ||||||||
\(808\) | 2.00000 | − | 3.46410i | 0.0703598 | − | 0.121867i | ||||
\(809\) | 21.5000 | + | 37.2391i | 0.755900 | + | 1.30926i | 0.944926 | + | 0.327285i | \(0.106134\pi\) |
−0.189026 | + | 0.981972i | \(0.560533\pi\) | |||||||
\(810\) | 18.0000 | 0.632456 | ||||||||
\(811\) | −31.0000 | −1.08856 | −0.544279 | − | 0.838905i | \(-0.683197\pi\) | ||||
−0.544279 | + | 0.838905i | \(0.683197\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.00000 | + | 5.19615i | −0.315644 | + | 0.182237i | ||||
\(814\) | 1.00000 | + | 1.73205i | 0.0350500 | + | 0.0607083i | ||||
\(815\) | 8.00000 | 0.280228 | ||||||||
\(816\) | − | 8.66025i | − | 0.303170i | ||||||
\(817\) | −7.00000 | −0.244899 | ||||||||
\(818\) | 11.0000 | 0.384606 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.00000 | 0.209529 | ||||||||
\(821\) | 46.0000 | 1.60541 | 0.802706 | − | 0.596376i | \(-0.203393\pi\) | ||||
0.802706 | + | 0.596376i | \(0.203393\pi\) | |||||||
\(822\) | −28.5000 | + | 16.4545i | −0.994052 | + | 0.573916i | ||||
\(823\) | 34.0000 | 1.18517 | 0.592583 | − | 0.805510i | \(-0.298108\pi\) | ||||
0.592583 | + | 0.805510i | \(0.298108\pi\) | |||||||
\(824\) | −7.00000 | − | 12.1244i | −0.243857 | − | 0.422372i | ||||
\(825\) | 1.73205i | 0.0603023i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.0000 | 0.417281 | 0.208640 | − | 0.977992i | \(-0.433096\pi\) | ||||
0.208640 | + | 0.977992i | \(0.433096\pi\) | |||||||
\(828\) | 6.00000 | − | 10.3923i | 0.208514 | − | 0.361158i | ||||
\(829\) | 2.00000 | + | 3.46410i | 0.0694629 | + | 0.120313i | 0.898665 | − | 0.438636i | \(-0.144538\pi\) |
−0.829202 | + | 0.558949i | \(0.811205\pi\) | |||||||
\(830\) | 16.0000 | − | 27.7128i | 0.555368 | − | 0.961926i | ||||
\(831\) | −3.00000 | + | 1.73205i | −0.104069 | + | 0.0600842i | ||||
\(832\) | −3.00000 | + | 5.19615i | −0.104006 | + | 0.180144i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 7.50000 | − | 4.33013i | 0.259704 | − | 0.149940i | ||||
\(835\) | 40.0000 | 1.38426 | ||||||||
\(836\) | −3.50000 | − | 6.06218i | −0.121050 | − | 0.209665i | ||||
\(837\) | 31.1769i | 1.07763i | ||||||||
\(838\) | 6.00000 | − | 10.3923i | 0.207267 | − | 0.358996i | ||||
\(839\) | −10.0000 | − | 17.3205i | −0.345238 | − | 0.597970i | 0.640159 | − | 0.768243i | \(-0.278869\pi\) |
−0.985397 | + | 0.170272i | \(0.945535\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.50000 | − | 11.2583i | 0.224138 | − | 0.388218i | ||||
\(842\) | −6.00000 | − | 10.3923i | −0.206774 | − | 0.358142i | ||||
\(843\) | − | 38.1051i | − | 1.31241i | ||||||
\(844\) | 8.00000 | − | 13.8564i | 0.275371 | − | 0.476957i | ||||
\(845\) | 23.0000 | − | 39.8372i | 0.791224 | − | 1.37044i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.00000 | − | 10.3923i | −0.206041 | − | 0.356873i | ||||
\(849\) | −6.00000 | − | 3.46410i | −0.205919 | − | 0.118888i | ||||
\(850\) | 5.00000 | 0.171499 | ||||||||
\(851\) | 8.00000 | 0.274236 | ||||||||
\(852\) | −12.0000 | − | 6.92820i | −0.411113 | − | 0.237356i | ||||
\(853\) | 22.0000 | + | 38.1051i | 0.753266 | + | 1.30469i | 0.946232 | + | 0.323489i | \(0.104856\pi\) |
−0.192966 | + | 0.981205i | \(0.561811\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −21.0000 | − | 36.3731i | −0.718185 | − | 1.24393i | ||||
\(856\) | 1.50000 | − | 2.59808i | 0.0512689 | − | 0.0888004i | ||||
\(857\) | 15.0000 | − | 25.9808i | 0.512390 | − | 0.887486i | −0.487507 | − | 0.873119i | \(-0.662093\pi\) |
0.999897 | − | 0.0143666i | \(-0.00457319\pi\) | |||||||
\(858\) | 10.3923i | 0.354787i | ||||||||
\(859\) | 14.5000 | + | 25.1147i | 0.494734 | + | 0.856904i | 0.999982 | − | 0.00607046i | \(-0.00193230\pi\) |
−0.505248 | + | 0.862974i | \(0.668599\pi\) | |||||||
\(860\) | −1.00000 | + | 1.73205i | −0.0340997 | + | 0.0590624i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.0000 | + | 32.9090i | −0.646768 | + | 1.12023i | 0.337123 | + | 0.941461i | \(0.390546\pi\) |
−0.983890 | + | 0.178774i | \(0.942787\pi\) | |||||||
\(864\) | − | 5.19615i | − | 0.176777i | ||||||
\(865\) | −2.00000 | − | 3.46410i | −0.0680020 | − | 0.117783i | ||||
\(866\) | −25.0000 | −0.849535 | ||||||||
\(867\) | −12.0000 | + | 6.92820i | −0.407541 | + | 0.235294i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.00000 | − | 5.19615i | 0.101768 | − | 0.176267i | ||||
\(870\) | 12.0000 | − | 6.92820i | 0.406838 | − | 0.234888i | ||||
\(871\) | −39.0000 | + | 67.5500i | −1.32146 | + | 2.28884i | ||||
\(872\) | −1.00000 | − | 1.73205i | −0.0338643 | − | 0.0586546i | ||||
\(873\) | 7.50000 | − | 12.9904i | 0.253837 | − | 0.439658i | ||||
\(874\) | −28.0000 | −0.947114 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.73205i | 0.0585206i | ||||||||
\(877\) | −8.00000 | − | 13.8564i | −0.270141 | − | 0.467898i | 0.698757 | − | 0.715359i | \(-0.253737\pi\) |
−0.968898 | + | 0.247462i | \(0.920404\pi\) | |||||||
\(878\) | −24.0000 | −0.809961 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.00000 | −0.0674200 | ||||||||
\(881\) | −42.0000 | −1.41502 | −0.707508 | − | 0.706705i | \(-0.750181\pi\) | ||||
−0.707508 | + | 0.706705i | \(0.750181\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 53.0000 | 1.78359 | 0.891796 | − | 0.452438i | \(-0.149446\pi\) | ||||
0.891796 | + | 0.452438i | \(0.149446\pi\) | |||||||
\(884\) | 30.0000 | 1.00901 | ||||||||
\(885\) | 24.2487i | 0.815112i | ||||||||
\(886\) | −7.00000 | −0.235170 | ||||||||
\(887\) | −3.00000 | − | 5.19615i | −0.100730 | − | 0.174470i | 0.811256 | − | 0.584692i | \(-0.198785\pi\) |
−0.911986 | + | 0.410222i | \(0.865451\pi\) | |||||||
\(888\) | 3.00000 | − | 1.73205i | 0.100673 | − | 0.0581238i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 12.0000 | 0.402241 | ||||||||
\(891\) | −4.50000 | − | 7.79423i | −0.150756 | − | 0.261116i | ||||
\(892\) | −2.00000 | − | 3.46410i | −0.0669650 | − | 0.115987i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | − | 41.5692i | − | 1.39028i | ||||||
\(895\) | 24.0000 | − | 41.5692i | 0.802232 | − | 1.38951i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 36.0000 | + | 20.7846i | 1.20201 | + | 0.693978i | ||||
\(898\) | −17.0000 | −0.567297 | ||||||||
\(899\) | 12.0000 | + | 20.7846i | 0.400222 | + | 0.693206i | ||||
\(900\) | 3.00000 | 0.100000 | ||||||||
\(901\) | −30.0000 | + | 51.9615i | −0.999445 | + | 1.73109i | ||||
\(902\) | −1.50000 | − | 2.59808i | −0.0499445 | − | 0.0865065i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.00000 | + | 8.66025i | −0.166298 | + | 0.288036i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 15.0000 | − | 8.66025i | 0.498342 | − | 0.287718i | ||||
\(907\) | 13.5000 | − | 23.3827i | 0.448260 | − | 0.776409i | −0.550013 | − | 0.835156i | \(-0.685377\pi\) |
0.998273 | + | 0.0587469i | \(0.0187105\pi\) | |||||||
\(908\) | 1.50000 | − | 2.59808i | 0.0497792 | − | 0.0862202i | ||||
\(909\) | −12.0000 | −0.398015 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(912\) | −10.5000 | + | 6.06218i | −0.347690 | + | 0.200739i | ||||
\(913\) | −16.0000 | −0.529523 | ||||||||
\(914\) | −1.00000 | −0.0330771 | ||||||||
\(915\) | 41.5692i | 1.37424i | ||||||||
\(916\) | −13.0000 | − | 22.5167i | −0.429532 | − | 0.743971i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −22.5000 | + | 12.9904i | −0.742611 | + | 0.428746i | ||||
\(919\) | −8.00000 | + | 13.8564i | −0.263896 | + | 0.457081i | −0.967274 | − | 0.253735i | \(-0.918341\pi\) |
0.703378 | + | 0.710816i | \(0.251674\pi\) | |||||||
\(920\) | −4.00000 | + | 6.92820i | −0.131876 | + | 0.228416i | ||||
\(921\) | −10.5000 | − | 6.06218i | −0.345987 | − | 0.199756i | ||||
\(922\) | −7.00000 | − | 12.1244i | −0.230533 | − | 0.399294i | ||||
\(923\) | 24.0000 | − | 41.5692i | 0.789970 | − | 1.36827i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.00000 | + | 1.73205i | 0.0328798 | + | 0.0569495i | ||||
\(926\) | −4.00000 | + | 6.92820i | −0.131448 | + | 0.227675i | ||||
\(927\) | −21.0000 | + | 36.3731i | −0.689730 | + | 1.19465i | ||||
\(928\) | −2.00000 | − | 3.46410i | −0.0656532 | − | 0.113715i | ||||
\(929\) | 18.0000 | 0.590561 | 0.295280 | − | 0.955411i | \(-0.404587\pi\) | ||||
0.295280 | + | 0.955411i | \(0.404587\pi\) | |||||||
\(930\) | − | 20.7846i | − | 0.681554i | ||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 14.5000 | − | 25.1147i | 0.474963 | − | 0.822661i | ||||
\(933\) | −3.00000 | − | 1.73205i | −0.0982156 | − | 0.0567048i | ||||
\(934\) | 6.50000 | − | 11.2583i | 0.212686 | − | 0.368384i | ||||
\(935\) | 5.00000 | + | 8.66025i | 0.163517 | + | 0.283221i | ||||
\(936\) | 18.0000 | 0.588348 | ||||||||
\(937\) | −2.00000 | −0.0653372 | −0.0326686 | − | 0.999466i | \(-0.510401\pi\) | ||||
−0.0326686 | + | 0.999466i | \(0.510401\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25.5000 | + | 14.7224i | 0.832161 | + | 0.480448i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.0000 | −0.651981 | −0.325991 | − | 0.945373i | \(-0.605698\pi\) | ||||
−0.325991 | + | 0.945373i | \(0.605698\pi\) | |||||||
\(942\) | 3.00000 | + | 1.73205i | 0.0977453 | + | 0.0564333i | ||||
\(943\) | −12.0000 | −0.390774 | ||||||||
\(944\) | 7.00000 | 0.227831 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.00000 | 0.0325128 | ||||||||
\(947\) | −37.0000 | −1.20234 | −0.601169 | − | 0.799122i | \(-0.705298\pi\) | ||||
−0.601169 | + | 0.799122i | \(0.705298\pi\) | |||||||
\(948\) | −9.00000 | − | 5.19615i | −0.292306 | − | 0.168763i | ||||
\(949\) | −6.00000 | −0.194768 | ||||||||
\(950\) | −3.50000 | − | 6.06218i | −0.113555 | − | 0.196683i | ||||
\(951\) | −9.00000 | − | 5.19615i | −0.291845 | − | 0.168497i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.0000 | −1.13376 | −0.566881 | − | 0.823800i | \(-0.691850\pi\) | ||||
−0.566881 | + | 0.823800i | \(0.691850\pi\) | |||||||
\(954\) | −18.0000 | + | 31.1769i | −0.582772 | + | 1.00939i | ||||
\(955\) | 12.0000 | + | 20.7846i | 0.388311 | + | 0.672574i | ||||
\(956\) | −3.00000 | + | 5.19615i | −0.0970269 | + | 0.168056i | ||||
\(957\) | −6.00000 | − | 3.46410i | −0.193952 | − | 0.111979i | ||||
\(958\) | 10.0000 | − | 17.3205i | 0.323085 | − | 0.559600i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 3.46410i | 0.111803i | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 6.00000 | + | 10.3923i | 0.193448 | + | 0.335061i | ||||
\(963\) | −9.00000 | −0.290021 | ||||||||
\(964\) | 11.5000 | − | 19.9186i | 0.370390 | − | 0.641534i | ||||
\(965\) | 17.0000 | + | 29.4449i | 0.547249 | + | 0.947864i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.00000 | + | 12.1244i | −0.225105 | + | 0.389893i | −0.956351 | − | 0.292221i | \(-0.905606\pi\) |
0.731246 | + | 0.682114i | \(0.238939\pi\) | |||||||
\(968\) | −5.00000 | − | 8.66025i | −0.160706 | − | 0.278351i | ||||
\(969\) | 52.5000 | + | 30.3109i | 1.68654 | + | 0.973726i | ||||
\(970\) | −5.00000 | + | 8.66025i | −0.160540 | + | 0.278064i | ||||
\(971\) | −6.00000 | + | 10.3923i | −0.192549 | + | 0.333505i | −0.946094 | − | 0.323891i | \(-0.895009\pi\) |
0.753545 | + | 0.657396i | \(0.228342\pi\) | |||||||
\(972\) | −13.5000 | + | 7.79423i | −0.433013 | + | 0.250000i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −5.00000 | − | 8.66025i | −0.160210 | − | 0.277492i | ||||
\(975\) | 10.3923i | 0.332820i | ||||||||
\(976\) | 12.0000 | 0.384111 | ||||||||
\(977\) | −15.0000 | −0.479893 | −0.239946 | − | 0.970786i | \(-0.577130\pi\) | ||||
−0.239946 | + | 0.970786i | \(0.577130\pi\) | |||||||
\(978\) | −6.00000 | + | 3.46410i | −0.191859 | + | 0.110770i | ||||
\(979\) | −3.00000 | − | 5.19615i | −0.0958804 | − | 0.166070i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.00000 | + | 5.19615i | −0.0957826 | + | 0.165900i | ||||
\(982\) | 16.5000 | − | 28.5788i | 0.526536 | − | 0.911987i | ||||
\(983\) | −30.0000 | + | 51.9615i | −0.956851 | + | 1.65732i | −0.226778 | + | 0.973946i | \(0.572819\pi\) |
−0.730073 | + | 0.683369i | \(0.760514\pi\) | |||||||
\(984\) | −4.50000 | + | 2.59808i | −0.143455 | + | 0.0828236i | ||||
\(985\) | 10.0000 | + | 17.3205i | 0.318626 | + | 0.551877i | ||||
\(986\) | −10.0000 | + | 17.3205i | −0.318465 | + | 0.551597i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −21.0000 | − | 36.3731i | −0.668099 | − | 1.15718i | ||||
\(989\) | 2.00000 | − | 3.46410i | 0.0635963 | − | 0.110152i | ||||
\(990\) | 3.00000 | + | 5.19615i | 0.0953463 | + | 0.165145i | ||||
\(991\) | 14.0000 | + | 24.2487i | 0.444725 | + | 0.770286i | 0.998033 | − | 0.0626908i | \(-0.0199682\pi\) |
−0.553308 | + | 0.832977i | \(0.686635\pi\) | |||||||
\(992\) | −6.00000 | −0.190500 | ||||||||
\(993\) | 12.0000 | + | 6.92820i | 0.380808 | + | 0.219860i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.0000 | + | 24.2487i | −0.443830 | + | 0.768736i | ||||
\(996\) | 27.7128i | 0.878114i | ||||||||
\(997\) | 1.00000 | − | 1.73205i | 0.0316703 | − | 0.0548546i | −0.849756 | − | 0.527176i | \(-0.823251\pi\) |
0.881426 | + | 0.472322i | \(0.156584\pi\) | |||||||
\(998\) | −14.5000 | − | 25.1147i | −0.458989 | − | 0.794993i | ||||
\(999\) | −9.00000 | − | 5.19615i | −0.284747 | − | 0.164399i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))