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 | 655.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.655 |
Dual form | 882.2.e.a.373.1 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −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 | \(-0.980917\pi\) |
0.550990 | + | 0.834512i | \(0.314250\pi\) | |||||||
\(6\) | 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 | 0.780750 | − | 0.624844i | \(-0.214837\pi\) |
−0.931505 | + | 0.363727i | \(0.881504\pi\) | |||||||
\(12\) | −1.50000 | + | 0.866025i | −0.433013 | + | 0.250000i | ||||
\(13\) | 3.00000 | + | 5.19615i | 0.832050 | + | 1.44115i | 0.896410 | + | 0.443227i | \(0.146166\pi\) |
−0.0643593 | + | 0.997927i | \(0.520500\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 3.46410i | − | 0.894427i | ||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.50000 | − | 4.33013i | 0.606339 | − | 1.05021i | −0.385499 | − | 0.922708i | \(-0.625971\pi\) |
0.991838 | − | 0.127502i | \(-0.0406959\pi\) | |||||||
\(18\) | −1.50000 | + | 2.59808i | −0.353553 | + | 0.612372i | ||||
\(19\) | 3.50000 | + | 6.06218i | 0.802955 | + | 1.39076i | 0.917663 | + | 0.397360i | \(0.130073\pi\) |
−0.114708 | + | 0.993399i | \(0.536593\pi\) | |||||||
\(20\) | −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 | −0.995639 | − | 0.0932891i | \(-0.970262\pi\) |
0.578610 | + | 0.815604i | \(0.303595\pi\) | |||||||
\(24\) | 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 | −0.618389 | − | 0.785872i | \(-0.712214\pi\) |
0.989780 | + | 0.142605i | \(0.0455477\pi\) | |||||||
\(30\) | 3.46410i | 0.632456i | ||||||||
\(31\) | −6.00000 | −1.07763 | −0.538816 | − | 0.842424i | \(-0.681128\pi\) | ||||
−0.538816 | + | 0.842424i | \(0.681128\pi\) | |||||||
\(32\) | −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 | 0.772043 | − | 0.635571i | \(-0.219235\pi\) |
−0.936442 | + | 0.350823i | \(0.885902\pi\) | |||||||
\(38\) | −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 | \(-0.241934\pi\) |
−0.959058 | + | 0.283211i | \(0.908600\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.500000 | − | 0.866025i | 0.0762493 | − | 0.132068i | −0.825380 | − | 0.564578i | \(-0.809039\pi\) |
0.901629 | + | 0.432511i | \(0.142372\pi\) | |||||||
\(44\) | −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 | 0.0783936 | + | 0.996922i | \(0.475021\pi\) |
−0.902557 | + | 0.430570i | \(0.858312\pi\) | |||||||
\(54\) | − | 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 | \(-0.650597\pi\) | ||||
−0.455661 | + | 0.890153i | \(0.650597\pi\) | |||||||
\(60\) | − | 3.46410i | − | 0.447214i | ||||||
\(61\) | −12.0000 | −1.53644 | −0.768221 | − | 0.640184i | \(-0.778858\pi\) | ||||
−0.768221 | + | 0.640184i | \(0.778858\pi\) | |||||||
\(62\) | 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 | \(-0.851972\pi\) |
0.835281 | + | 0.549823i | \(0.185305\pi\) | |||||||
\(74\) | 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 | −0.0247060 | + | 0.999695i | \(0.507865\pi\) |
−0.853408 | + | 0.521243i | \(0.825468\pi\) | |||||||
\(84\) | 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 | \(-0.0636557\pi\) |
−0.662071 | + | 0.749441i | \(0.730322\pi\) | |||||||
\(90\) | −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 | \(-0.751641\pi\) |
0.964579 | + | 0.263795i | \(0.0849741\pi\) | |||||||
\(98\) | 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 | \(-0.102895\pi\) |
−0.749199 | + | 0.662344i | \(0.769562\pi\) | |||||||
\(102\) | − | 8.66025i | − | 0.857493i | ||||||
\(103\) | −7.00000 | + | 12.1244i | −0.689730 | + | 1.19465i | 0.282194 | + | 0.959357i | \(0.408938\pi\) |
−0.971925 | + | 0.235291i | \(0.924396\pi\) | |||||||
\(104\) | −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 | 0.784366 | − | 0.620298i | \(-0.212988\pi\) |
−0.929377 | + | 0.369132i | \(0.879655\pi\) | |||||||
\(108\) | 5.19615i | 0.500000i | ||||||||
\(109\) | 1.00000 | − | 1.73205i | 0.0957826 | − | 0.165900i | −0.814152 | − | 0.580651i | \(-0.802798\pi\) |
0.909935 | + | 0.414751i | \(0.136131\pi\) | |||||||
\(110\) | −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 | 0.999425 | − | 0.0338931i | \(-0.0107906\pi\) |
−0.529065 | + | 0.848581i | \(0.677457\pi\) | |||||||
\(114\) | 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 | \(-0.777425\pi\) |
0.940072 | + | 0.340977i | \(0.110758\pi\) | |||||||
\(132\) | 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 | 0.911716 | + | 0.410822i | \(0.134758\pi\) |
−0.100076 | + | 0.994980i | \(0.531909\pi\) | |||||||
\(138\) | 6.92820i | 0.589768i | ||||||||
\(139\) | 2.50000 | + | 4.33013i | 0.212047 | + | 0.367277i | 0.952355 | − | 0.304991i | \(-0.0986536\pi\) |
−0.740308 | + | 0.672268i | \(0.765320\pi\) | |||||||
\(140\) | 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 | 0.332896 | − | 0.942964i | \(-0.391974\pi\) |
0.650183 | − | 0.759778i | \(-0.274692\pi\) | |||||||
\(150\) | 1.50000 | + | 0.866025i | 0.122474 | + | 0.0707107i | ||||
\(151\) | −5.00000 | − | 8.66025i | −0.406894 | − | 0.704761i | 0.587646 | − | 0.809118i | \(-0.300055\pi\) |
−0.994540 | + | 0.104357i | \(0.966722\pi\) | |||||||
\(152\) | −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 | \(-0.474569\pi\) | ||||
0.0798087 | + | 0.996810i | \(0.474569\pi\) | |||||||
\(158\) | 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 | 0.933659 | − | 0.358162i | \(-0.116597\pi\) |
−0.777007 | + | 0.629492i | \(0.783263\pi\) | |||||||
\(164\) | −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 | −0.935454 | − | 0.353450i | \(-0.885009\pi\) |
0.161630 | − | 0.986851i | \(-0.448325\pi\) | |||||||
\(168\) | 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 | \(-0.475776\pi\) | ||||
0.0760286 | + | 0.997106i | \(0.475776\pi\) | |||||||
\(174\) | − | 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 | −0.0655145 | + | 0.997852i | \(0.520869\pi\) |
−0.831408 | + | 0.555663i | \(0.812464\pi\) | |||||||
\(180\) | 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 | \(-0.998611\pi\) |
0.503774 | + | 0.863836i | \(0.331945\pi\) | |||||||
\(200\) | −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 | 0.998221 | + | 0.0596196i | \(0.0189888\pi\) |
−0.447478 | + | 0.894295i | \(0.647678\pi\) | |||||||
\(212\) | −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 | \(-0.790574\pi\) |
0.925188 | + | 0.379509i | \(0.123907\pi\) | |||||||
\(224\) | 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 | \(-0.198410\pi\) |
−0.911502 | + | 0.411296i | \(0.865076\pi\) | |||||||
\(228\) | −10.5000 | − | 6.06218i | −0.695379 | − | 0.401478i | ||||
\(229\) | 13.0000 | − | 22.5167i | 0.859064 | − | 1.48794i | −0.0137585 | − | 0.999905i | \(-0.504380\pi\) |
0.872823 | − | 0.488037i | \(-0.162287\pi\) | |||||||
\(230\) | 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 | 0.745573 | + | 0.666424i | \(0.232176\pi\) |
0.204354 | + | 0.978897i | \(0.434491\pi\) | |||||||
\(234\) | −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 | 0.752536 | − | 0.658551i | \(-0.228830\pi\) |
−0.946590 | + | 0.322440i | \(0.895497\pi\) | |||||||
\(240\) | − | 3.46410i | − | 0.223607i | ||||||
\(241\) | −11.5000 | − | 19.9186i | −0.740780 | − | 1.28307i | −0.952141 | − | 0.305661i | \(-0.901123\pi\) |
0.211360 | − | 0.977408i | \(-0.432211\pi\) | |||||||
\(242\) | −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 | \(-0.469817\pi\) | ||||
0.0946792 | + | 0.995508i | \(0.469817\pi\) | |||||||
\(252\) | 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 | \(-0.678367\pi\) |
0.999325 | + | 0.0367485i | \(0.0117000\pi\) | |||||||
\(258\) | − | 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 | −0.997906 | − | 0.0646755i | \(-0.979399\pi\) |
0.442943 | − | 0.896550i | \(-0.353935\pi\) | |||||||
\(264\) | −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 | 0.381577 | + | 0.924337i | \(0.375381\pi\) |
−0.991288 | + | 0.131713i | \(0.957952\pi\) | |||||||
\(270\) | 9.00000 | + | 5.19615i | 0.547723 | + | 0.316228i | ||||
\(271\) | 3.00000 | + | 5.19615i | 0.182237 | + | 0.315644i | 0.942642 | − | 0.333805i | \(-0.108333\pi\) |
−0.760405 | + | 0.649449i | \(0.775000\pi\) | |||||||
\(272\) | 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 | 0.834419 | − | 0.551131i | \(-0.185804\pi\) |
−0.894503 | + | 0.447062i | \(0.852470\pi\) | |||||||
\(278\) | −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 | 0.325385 | + | 0.945582i | \(0.394506\pi\) |
−0.981590 | + | 0.190999i | \(0.938827\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.00000 | 0.237775 | 0.118888 | − | 0.992908i | \(-0.462067\pi\) | ||||
0.118888 | + | 0.992908i | \(0.462067\pi\) | |||||||
\(284\) | −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 | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(294\) | 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 | \(-0.435985\pi\) | ||||
0.199756 | + | 0.979846i | \(0.435985\pi\) | |||||||
\(308\) | 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 | \(-0.481941\pi\) | ||||
0.0567048 | + | 0.998391i | \(0.481941\pi\) | |||||||
\(312\) | 9.00000 | + | 5.19615i | 0.509525 | + | 0.294174i | ||||
\(313\) | −17.0000 | −0.960897 | −0.480448 | − | 0.877023i | \(-0.659526\pi\) | ||||
−0.480448 | + | 0.877023i | \(0.659526\pi\) | |||||||
\(314\) | −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 | 0.962168 | − | 0.272456i | \(-0.0878358\pi\) |
−0.717038 | + | 0.697034i | \(0.754502\pi\) | |||||||
\(338\) | 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 | \(-0.711079\pi\) |
0.990282 | + | 0.139072i | \(0.0444119\pi\) | |||||||
\(350\) | 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 | \(-0.0359599\pi\) |
−0.594441 | + | 0.804139i | \(0.702627\pi\) | |||||||
\(354\) | −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 | 0.838429 | − | 0.545010i | \(-0.183474\pi\) |
−0.891207 | + | 0.453596i | \(0.850141\pi\) | |||||||
\(360\) | −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 | 0.996129 | + | 0.0879086i | \(0.0280183\pi\) |
−0.421933 | + | 0.906627i | \(0.638648\pi\) | |||||||
\(368\) | −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 | 0.427051 | + | 0.904227i | \(0.359552\pi\) |
−0.996610 | + | 0.0822766i | \(0.973781\pi\) | |||||||
\(374\) | 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 | \(-0.865920\pi\) |
0.810394 | + | 0.585886i | \(0.199253\pi\) | |||||||
\(384\) | 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 | 0.746624 | − | 0.665246i | \(-0.231673\pi\) |
−0.949432 | + | 0.313972i | \(0.898340\pi\) | |||||||
\(390\) | −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 | \(-0.315848\pi\) |
−0.998492 | + | 0.0549046i | \(0.982515\pi\) | |||||||
\(398\) | 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 | −0.956235 | − | 0.292599i | \(-0.905480\pi\) |
0.731516 | + | 0.681824i | \(0.238813\pi\) | |||||||
\(402\) | 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 | \(-0.412329\pi\) | ||||
0.271957 | + | 0.962309i | \(0.412329\pi\) | |||||||
\(410\) | −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 | \(-0.0719734\pi\) |
−0.681426 | + | 0.731887i | \(0.738640\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.00000 | − | 10.3923i | 0.292422 | − | 0.506490i | −0.681960 | − | 0.731390i | \(-0.738872\pi\) |
0.974382 | + | 0.224900i | \(0.0722054\pi\) | |||||||
\(422\) | −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 | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(432\) | 5.19615i | 0.250000i | ||||||||
\(433\) | −25.0000 | −1.20142 | −0.600712 | − | 0.799466i | \(-0.705116\pi\) | ||||
−0.600712 | + | 0.799466i | \(0.705116\pi\) | |||||||
\(434\) | 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 | \(-0.694115\pi\) | ||||
−0.572729 | + | 0.819745i | \(0.694115\pi\) | |||||||
\(440\) | −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 | \(-0.939042\pi\) |
0.655696 | + | 0.755025i | \(0.272375\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.00000 | + | 6.92820i | 0.185896 | + | 0.321981i | 0.943878 | − | 0.330294i | \(-0.107148\pi\) |
−0.757982 | + | 0.652275i | \(0.773815\pi\) | |||||||
\(464\) | 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 | \(-0.0694183\pi\) |
−0.675530 | + | 0.737333i | \(0.736085\pi\) | |||||||
\(468\) | 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 | \(-0.0156222\pi\) |
−0.541884 | + | 0.840453i | \(0.682289\pi\) | |||||||
\(480\) | 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 | −0.730218 | − | 0.683214i | \(-0.760582\pi\) |
0.956790 | + | 0.290780i | \(0.0939149\pi\) | |||||||
\(488\) | 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 | −0.950365 | − | 0.311136i | \(-0.899290\pi\) |
0.205731 | − | 0.978609i | \(-0.434043\pi\) | |||||||
\(492\) | 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 | −0.334227 | − | 0.942493i | \(-0.608475\pi\) |
0.983336 | − | 0.181797i | \(-0.0581915\pi\) | |||||||
\(500\) | −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 | \(-0.457294\pi\) | ||||
0.133763 | + | 0.991013i | \(0.457294\pi\) | |||||||
\(504\) | 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 | 0.314459 | + | 0.949271i | \(0.398177\pi\) |
−0.979322 | + | 0.202306i | \(0.935156\pi\) | |||||||
\(510\) | 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 | \(-0.770165\pi\) |
0.947603 | + | 0.319451i | \(0.103499\pi\) | |||||||
\(522\) | 6.00000 | + | 10.3923i | 0.262613 | + | 0.454859i | ||||
\(523\) | 14.0000 | + | 24.2487i | 0.612177 | + | 1.06032i | 0.990873 | + | 0.134801i | \(0.0430394\pi\) |
−0.378695 | + | 0.925521i | \(0.623627\pi\) | |||||||
\(524\) | 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 | 0.999829 | + | 0.0184818i | \(0.00588327\pi\) |
−0.483909 | + | 0.875118i | \(0.660783\pi\) | |||||||
\(542\) | −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 | −0.549370 | − | 0.835579i | \(-0.685132\pi\) |
0.998318 | + | 0.0579790i | \(0.0184657\pi\) | |||||||
\(548\) | 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 | −0.400599 | − | 0.916253i | \(-0.631198\pi\) |
0.993798 | − | 0.111198i | \(-0.0354686\pi\) | |||||||
\(558\) | 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 | \(-0.273406\pi\) | ||||
0.653247 | + | 0.757145i | \(0.273406\pi\) | |||||||
\(564\) | 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 | −0.228968 | − | 0.973434i | \(-0.573535\pi\) |
0.957503 | − | 0.288425i | \(-0.0931316\pi\) | |||||||
\(578\) | 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 | 0.274263 | − | 0.961655i | \(-0.411566\pi\) |
0.695686 | − | 0.718346i | \(-0.255100\pi\) | |||||||
\(588\) | 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 | \(-0.127353\pi\) |
−0.797831 | + | 0.602881i | \(0.794019\pi\) | |||||||
\(594\) | −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 | \(-0.706668\pi\) |
0.992114 | + | 0.125336i | \(0.0400009\pi\) | |||||||
\(602\) | 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 | \(-0.671401\pi\) |
0.999889 | + | 0.0148722i | \(0.00473415\pi\) | |||||||
\(608\) | −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 | 0.0346469 | + | 0.999400i | \(0.488969\pi\) |
−0.882829 | + | 0.469695i | \(0.844364\pi\) | |||||||
\(614\) | −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 | 0.984840 | − | 0.173463i | \(-0.0554956\pi\) |
−0.642643 | + | 0.766165i | \(0.722162\pi\) | |||||||
\(618\) | 24.2487i | 0.975426i | ||||||||
\(619\) | −18.5000 | − | 32.0429i | −0.743578 | − | 1.28791i | −0.950856 | − | 0.309633i | \(-0.899794\pi\) |
0.207279 | − | 0.978282i | \(-0.433539\pi\) | |||||||
\(620\) | 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 | 0.855982 | − | 0.517005i | \(-0.172953\pi\) |
−0.875731 | + | 0.482800i | \(0.839620\pi\) | |||||||
\(642\) | −4.50000 | − | 2.59808i | −0.177601 | − | 0.102538i | ||||
\(643\) | 3.50000 | + | 6.06218i | 0.138027 | + | 0.239069i | 0.926750 | − | 0.375680i | \(-0.122591\pi\) |
−0.788723 | + | 0.614749i | \(0.789257\pi\) | |||||||
\(644\) | 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 | \(-0.909132\pi\) |
0.723645 | + | 0.690172i | \(0.242465\pi\) | |||||||
\(648\) | 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 | −0.801337 | − | 0.598213i | \(-0.795878\pi\) |
0.918736 | + | 0.394872i | \(0.129211\pi\) | |||||||
\(654\) | − | 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 | −0.978717 | − | 0.205216i | \(-0.934210\pi\) |
0.667081 | + | 0.744985i | \(0.267544\pi\) | |||||||
\(660\) | −3.00000 | + | 1.73205i | −0.116775 | + | 0.0674200i | ||||
\(661\) | 28.0000 | 1.08907 | 0.544537 | − | 0.838737i | \(-0.316705\pi\) | ||||
0.544537 | + | 0.838737i | \(0.316705\pi\) | |||||||
\(662\) | −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 | −0.968818 | − | 0.247774i | \(-0.920301\pi\) |
0.698988 | + | 0.715134i | \(0.253634\pi\) | |||||||
\(674\) | −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 | \(-0.304419\pi\) | ||||
0.576497 | + | 0.817099i | \(0.304419\pi\) | |||||||
\(678\) | 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 | 0.203510 | + | 0.979073i | \(0.434765\pi\) |
−0.949657 | + | 0.313291i | \(0.898568\pi\) | |||||||
\(684\) | 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 | \(-0.291704\pi\) | ||||
0.608669 | + | 0.793424i | \(0.291704\pi\) | |||||||
\(692\) | 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 | \(-0.202354\pi\) |
−0.916529 | + | 0.399969i | \(0.869021\pi\) | |||||||
\(720\) | 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 | \(-0.749737\pi\) |
0.966139 | + | 0.258022i | \(0.0830708\pi\) | |||||||
\(728\) | 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 | \(-0.725467\pi\) |
0.982986 | + | 0.183679i | \(0.0588007\pi\) | |||||||
\(734\) | −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 | −0.384776 | − | 0.923010i | \(-0.625721\pi\) |
0.991738 | − | 0.128279i | \(-0.0409454\pi\) | |||||||
\(740\) | 4.00000 | 0.147043 | ||||||||
\(741\) | − | 72.7461i | − | 2.67240i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.00000 | + | 5.19615i | 0.110059 | + | 0.190628i | 0.915794 | − | 0.401648i | \(-0.131563\pi\) |
−0.805735 | + | 0.592277i | \(0.798229\pi\) | |||||||
\(744\) | −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 | −0.653783 | − | 0.756682i | \(-0.726819\pi\) |
0.982197 | + | 0.187851i | \(0.0601523\pi\) | |||||||
\(752\) | 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 | \(-0.891348\pi\) |
0.761057 | + | 0.648686i | \(0.224681\pi\) | |||||||
\(762\) | −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 | \(-0.296501\pi\) |
−0.993313 | + | 0.115454i | \(0.963168\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 25.9808i | 0.935674i | ||||||||
\(772\) | 17.0000 | 0.611843 | ||||||||
\(773\) | 26.0000 | − | 45.0333i | 0.935155 | − | 1.61974i | 0.160798 | − | 0.986987i | \(-0.448593\pi\) |
0.774357 | − | 0.632749i | \(-0.218073\pi\) | |||||||
\(774\) | 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 | \(-0.568609\pi\) | ||||
−0.213877 | + | 0.976861i | \(0.568609\pi\) | |||||||
\(788\) | 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 | \(-0.0984960\pi\) |
−0.739975 | + | 0.672634i | \(0.765163\pi\) | |||||||
\(798\) | 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 | −0.189026 | − | 0.981972i | \(-0.560533\pi\) |
0.944926 | − | 0.327285i | \(-0.106134\pi\) | |||||||
\(810\) | −18.0000 | −0.632456 | ||||||||
\(811\) | 31.0000 | 1.08856 | 0.544279 | − | 0.838905i | \(-0.316803\pi\) | ||||
0.544279 | + | 0.838905i | \(0.316803\pi\) | |||||||
\(812\) | 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 | \(-0.855462\pi\) |
0.829202 | + | 0.558949i | \(0.188795\pi\) | |||||||
\(830\) | 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 | \(-0.721131\pi\) |
0.985397 | + | 0.170272i | \(0.0544647\pi\) | |||||||
\(840\) | 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 | 0.192966 | + | 0.981205i | \(0.438189\pi\) |
−0.946232 | + | 0.323489i | \(0.895144\pi\) | |||||||
\(854\) | 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 | −0.999897 | − | 0.0143666i | \(-0.995427\pi\) |
0.487507 | − | 0.873119i | \(-0.337907\pi\) | |||||||
\(858\) | − | 10.3923i | − | 0.354787i | ||||||
\(859\) | −14.5000 | + | 25.1147i | −0.494734 | + | 0.856904i | −0.999982 | − | 0.00607046i | \(-0.998068\pi\) |
0.505248 | + | 0.862974i | \(0.331401\pi\) | |||||||
\(860\) | 1.00000 | + | 1.73205i | 0.0340997 | + | 0.0590624i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.0000 | − | 32.9090i | −0.646768 | − | 1.12023i | −0.983890 | − | 0.178774i | \(-0.942787\pi\) |
0.337123 | − | 0.941461i | \(-0.390546\pi\) | |||||||
\(864\) | − | 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 | −0.968898 | − | 0.247462i | \(-0.920404\pi\) |
0.698757 | + | 0.715359i | \(0.253737\pi\) | |||||||
\(878\) | 24.0000 | 0.809961 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.00000 | 0.0674200 | ||||||||
\(881\) | 42.0000 | 1.41502 | 0.707508 | − | 0.706705i | \(-0.249819\pi\) | ||||
0.707508 | + | 0.706705i | \(0.249819\pi\) | |||||||
\(882\) | 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 | \(-0.801215\pi\) |
0.911986 | + | 0.410222i | \(0.134549\pi\) | |||||||
\(888\) | −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 | 0.998273 | − | 0.0587469i | \(-0.0187105\pi\) |
−0.550013 | + | 0.835156i | \(0.685377\pi\) | |||||||
\(908\) | −1.50000 | − | 2.59808i | −0.0497792 | − | 0.0862202i | ||||
\(909\) | 12.0000 | 0.398015 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(912\) | −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 | 0.703378 | − | 0.710816i | \(-0.251674\pi\) |
−0.967274 | + | 0.253735i | \(0.918341\pi\) | |||||||
\(920\) | 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 | \(-0.595413\pi\) | ||||
−0.295280 | + | 0.955411i | \(0.595413\pi\) | |||||||
\(930\) | − | 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 | \(-0.489599\pi\) | ||||
0.0326686 | + | 0.999466i | \(0.489599\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25.5000 | − | 14.7224i | 0.832161 | − | 0.480448i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.0000 | 0.651981 | 0.325991 | − | 0.945373i | \(-0.394302\pi\) | ||||
0.325991 | + | 0.945373i | \(0.394302\pi\) | |||||||
\(942\) | 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 | 0.731246 | − | 0.682114i | \(-0.238939\pi\) |
−0.956351 | + | 0.292221i | \(0.905606\pi\) | |||||||
\(968\) | −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 | \(-0.104991\pi\) |
−0.753545 | + | 0.657396i | \(0.771658\pi\) | |||||||
\(972\) | 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 | 0.730073 | + | 0.683369i | \(0.239486\pi\) |
0.226778 | + | 0.973946i | \(0.427181\pi\) | |||||||
\(984\) | −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 | −0.553308 | − | 0.832977i | \(-0.686635\pi\) |
0.998033 | + | 0.0626908i | \(0.0199682\pi\) | |||||||
\(992\) | 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 | \(-0.176749\pi\) |
−0.881426 | + | 0.472322i | \(0.843416\pi\) | |||||||
\(998\) | −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 \(a_p\))