Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3240,2,Mod(1081,3240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3240, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3240.1081");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3240.q (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: | \(25.8715302549\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2161.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3240.2161 |
Dual form | 3240.2.q.q.1081.1 |
$q$-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 \(\left(\mathbb{Z}/3240\mathbb{Z}\right)^\times\).
\(n\) | \(1297\) | \(1621\) | \(2431\) | \(3161\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | + | 3.46410i | −0.603023 | + | 1.04447i | 0.389338 | + | 0.921095i | \(0.372704\pi\) |
−0.992361 | + | 0.123371i | \(0.960630\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.00000 | − | 5.19615i | −0.832050 | − | 1.44115i | −0.896410 | − | 0.443227i | \(-0.853834\pi\) |
0.0643593 | − | 0.997927i | \(-0.479500\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.00000 | 1.45521 | 0.727607 | − | 0.685994i | \(-0.240633\pi\) | ||||
0.727607 | + | 0.685994i | \(0.240633\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.00000 | −0.917663 | −0.458831 | − | 0.888523i | \(-0.651732\pi\) | ||||
−0.458831 | + | 0.888523i | \(0.651732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | + | 1.73205i | −0.185695 | + | 0.321634i | −0.943811 | − | 0.330487i | \(-0.892787\pi\) |
0.758115 | + | 0.652121i | \(0.226120\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | + | 6.92820i | 0.718421 | + | 1.24434i | 0.961625 | + | 0.274367i | \(0.0884683\pi\) |
−0.243204 | + | 0.969975i | \(0.578198\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.00000 | − | 5.19615i | −0.468521 | − | 0.811503i | 0.530831 | − | 0.847477i | \(-0.321880\pi\) |
−0.999353 | + | 0.0359748i | \(0.988546\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.00000 | + | 10.3923i | −0.914991 | + | 1.58481i | −0.108078 | + | 0.994142i | \(0.534469\pi\) |
−0.806914 | + | 0.590669i | \(0.798864\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.00000 | − | 6.92820i | 0.583460 | − | 1.01058i | −0.411606 | − | 0.911362i | \(-0.635032\pi\) |
0.995066 | − | 0.0992202i | \(-0.0316348\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.50000 | + | 6.06218i | 0.500000 | + | 0.866025i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.00000 | −0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.00000 | + | 10.3923i | 0.781133 | + | 1.35296i | 0.931282 | + | 0.364299i | \(0.118692\pi\) |
−0.150148 | + | 0.988663i | \(0.547975\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.00000 | + | 12.1244i | −0.896258 | + | 1.55236i | −0.0640184 | + | 0.997949i | \(0.520392\pi\) |
−0.832240 | + | 0.554416i | \(0.812942\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.00000 | − | 5.19615i | 0.372104 | − | 0.644503i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.00000 | − | 3.46410i | −0.244339 | − | 0.423207i | 0.717607 | − | 0.696449i | \(-0.245238\pi\) |
−0.961946 | + | 0.273241i | \(0.911904\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00000 | −0.702247 | −0.351123 | − | 0.936329i | \(-0.614200\pi\) | ||||
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000 | − | 6.92820i | 0.450035 | − | 0.779484i | −0.548352 | − | 0.836247i | \(-0.684745\pi\) |
0.998388 | + | 0.0567635i | \(0.0180781\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.00000 | + | 10.3923i | −0.658586 | + | 1.14070i | 0.322396 | + | 0.946605i | \(0.395512\pi\) |
−0.980982 | + | 0.194099i | \(0.937822\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.00000 | + | 5.19615i | 0.325396 | + | 0.563602i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.0000 | −1.06000 | −0.529999 | − | 0.847998i | \(-0.677808\pi\) | ||||
−0.529999 | + | 0.847998i | \(0.677808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.00000 | − | 3.46410i | −0.205196 | − | 0.355409i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.00000 | + | 1.73205i | −0.101535 | + | 0.175863i | −0.912317 | − | 0.409484i | \(-0.865709\pi\) |
0.810782 | + | 0.585348i | \(0.199042\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.00000 | − | 5.19615i | 0.298511 | − | 0.517036i | −0.677284 | − | 0.735721i | \(-0.736843\pi\) |
0.975796 | + | 0.218685i | \(0.0701767\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.00000 | 0.386695 | 0.193347 | − | 0.981130i | \(-0.438066\pi\) | ||||
0.193347 | + | 0.981130i | \(0.438066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.0000 | −1.72409 | −0.862044 | − | 0.506834i | \(-0.830816\pi\) | ||||
−0.862044 | + | 0.506834i | \(0.830816\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.00000 | − | 5.19615i | −0.282216 | − | 0.488813i | 0.689714 | − | 0.724082i | \(-0.257736\pi\) |
−0.971930 | + | 0.235269i | \(0.924403\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.50000 | − | 4.33013i | −0.227273 | − | 0.393648i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.00000 | −0.709885 | −0.354943 | − | 0.934888i | \(-0.615500\pi\) | ||||
−0.354943 | + | 0.934888i | \(0.615500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.00000 | + | 3.46410i | 0.174741 | + | 0.302660i | 0.940072 | − | 0.340977i | \(-0.110758\pi\) |
−0.765331 | + | 0.643637i | \(0.777425\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.00000 | − | 1.73205i | 0.0854358 | − | 0.147979i | −0.820141 | − | 0.572161i | \(-0.806105\pi\) |
0.905577 | + | 0.424182i | \(0.139438\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.00000 | − | 3.46410i | −0.169638 | − | 0.293821i | 0.768655 | − | 0.639664i | \(-0.220926\pi\) |
−0.938293 | + | 0.345843i | \(0.887593\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 24.0000 | 2.00698 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.00000 | −0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.00000 | − | 8.66025i | −0.409616 | − | 0.709476i | 0.585231 | − | 0.810867i | \(-0.301004\pi\) |
−0.994847 | + | 0.101391i | \(0.967671\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | + | 13.8564i | −0.651031 | + | 1.12762i | 0.331842 | + | 0.943335i | \(0.392330\pi\) |
−0.982873 | + | 0.184284i | \(0.941004\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.00000 | + | 6.92820i | −0.321288 | + | 0.556487i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.00000 | − | 5.19615i | −0.239426 | − | 0.414698i | 0.721124 | − | 0.692806i | \(-0.243626\pi\) |
−0.960550 | + | 0.278108i | \(0.910293\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.00000 | 0.313304 | 0.156652 | − | 0.987654i | \(-0.449930\pi\) | ||||
0.156652 | + | 0.987654i | \(0.449930\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.00000 | + | 13.8564i | 0.619059 | + | 1.07224i | 0.989658 | + | 0.143448i | \(0.0458190\pi\) |
−0.370599 | + | 0.928793i | \(0.620848\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.5000 | + | 19.9186i | −0.884615 | + | 1.53220i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.00000 | − | 12.1244i | 0.532200 | − | 0.921798i | −0.467093 | − | 0.884208i | \(-0.654699\pi\) |
0.999293 | − | 0.0375896i | \(-0.0119679\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.00000 | − | 1.73205i | −0.0735215 | − | 0.127343i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.0000 | + | 20.7846i | −0.877527 | + | 1.51992i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.00000 | + | 12.1244i | 0.503871 | + | 0.872730i | 0.999990 | + | 0.00447566i | \(0.00142465\pi\) |
−0.496119 | + | 0.868255i | \(0.665242\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.0000 | 0.712470 | 0.356235 | − | 0.934396i | \(-0.384060\pi\) | ||||
0.356235 | + | 0.934396i | \(0.384060\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.00000 | − | 5.19615i | 0.209529 | − | 0.362915i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.00000 | − | 13.8564i | 0.553372 | − | 0.958468i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.00000 | − | 10.3923i | −0.413057 | − | 0.715436i | 0.582165 | − | 0.813070i | \(-0.302206\pi\) |
−0.995222 | + | 0.0976347i | \(0.968872\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.0000 | −0.818393 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.0000 | − | 31.1769i | −1.21081 | − | 2.09719i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.00000 | + | 6.92820i | −0.267860 | + | 0.463947i | −0.968309 | − | 0.249756i | \(-0.919650\pi\) |
0.700449 | + | 0.713702i | \(0.252983\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.0000 | + | 24.2487i | −0.929213 | + | 1.60944i | −0.144571 | + | 0.989494i | \(0.546180\pi\) |
−0.784642 | + | 0.619949i | \(0.787153\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.00000 | + | 8.66025i | 0.330409 | + | 0.572286i | 0.982592 | − | 0.185776i | \(-0.0594799\pi\) |
−0.652183 | + | 0.758062i | \(0.726147\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.00000 | −0.131024 | −0.0655122 | − | 0.997852i | \(-0.520868\pi\) | ||||
−0.0655122 | + | 0.997852i | \(0.520868\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.00000 | 0.521862 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.00000 | − | 12.1244i | 0.450910 | − | 0.780998i | −0.547533 | − | 0.836784i | \(-0.684433\pi\) |
0.998443 | + | 0.0557856i | \(0.0177663\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.50000 | + | 6.06218i | −0.223607 | + | 0.387298i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.0000 | + | 20.7846i | 0.763542 | + | 1.32249i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −28.0000 | −1.76734 | −0.883672 | − | 0.468106i | \(-0.844936\pi\) | ||||
−0.883672 | + | 0.468106i | \(0.844936\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.00000 | + | 8.66025i | 0.311891 | + | 0.540212i | 0.978772 | − | 0.204953i | \(-0.0657041\pi\) |
−0.666880 | + | 0.745165i | \(0.732371\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.00000 | − | 5.19615i | −0.184289 | − | 0.319197i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.0000 | 1.09748 | 0.548740 | − | 0.835993i | \(-0.315108\pi\) | ||||
0.548740 | + | 0.835993i | \(0.315108\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.0000 | −1.45790 | −0.728948 | − | 0.684569i | \(-0.759990\pi\) | ||||
−0.728948 | + | 0.684569i | \(0.759990\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.00000 | − | 3.46410i | −0.120605 | − | 0.208893i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.00000 | − | 1.73205i | 0.0600842 | − | 0.104069i | −0.834419 | − | 0.551131i | \(-0.814196\pi\) |
0.894503 | + | 0.447062i | \(0.147530\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 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 | ||||||||
\(283\) | 2.00000 | + | 3.46410i | 0.118888 | + | 0.205919i | 0.919327 | − | 0.393494i | \(-0.128734\pi\) |
−0.800439 | + | 0.599414i | \(0.795400\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.0000 | + | 19.0526i | 0.642627 | + | 1.11306i | 0.984844 | + | 0.173442i | \(0.0554888\pi\) |
−0.342217 | + | 0.939621i | \(0.611178\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.00000 | + | 10.3923i | −0.349334 | + | 0.605063i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.0000 | −0.801638 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.0000 | −1.59804 | −0.799022 | − | 0.601302i | \(-0.794649\pi\) | ||||
−0.799022 | + | 0.601302i | \(0.794649\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.00000 | + | 6.92820i | 0.226819 | + | 0.392862i | 0.956864 | − | 0.290537i | \(-0.0938340\pi\) |
−0.730044 | + | 0.683400i | \(0.760501\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.00000 | + | 8.66025i | −0.282617 | + | 0.489506i | −0.972028 | − | 0.234863i | \(-0.924536\pi\) |
0.689412 | + | 0.724370i | \(0.257869\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.00000 | − | 12.1244i | 0.393159 | − | 0.680972i | −0.599705 | − | 0.800221i | \(-0.704715\pi\) |
0.992864 | + | 0.119249i | \(0.0380488\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.00000 | − | 6.92820i | −0.223957 | − | 0.387905i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −24.0000 | −1.33540 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.00000 | 0.332820 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.0000 | − | 24.2487i | 0.769510 | − | 1.33283i | −0.168320 | − | 0.985732i | \(-0.553834\pi\) |
0.937829 | − | 0.347097i | \(-0.112833\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.00000 | − | 3.46410i | 0.109272 | − | 0.189264i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.00000 | − | 1.73205i | −0.0544735 | − | 0.0943508i | 0.837503 | − | 0.546433i | \(-0.184015\pi\) |
−0.891976 | + | 0.452082i | \(0.850681\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −32.0000 | −1.73290 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.00000 | + | 10.3923i | 0.322097 | + | 0.557888i | 0.980921 | − | 0.194409i | \(-0.0622790\pi\) |
−0.658824 | + | 0.752297i | \(0.728946\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.00000 | + | 12.1244i | −0.374701 | + | 0.649002i | −0.990282 | − | 0.139072i | \(-0.955588\pi\) |
0.615581 | + | 0.788074i | \(0.288921\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.0000 | − | 22.5167i | 0.691920 | − | 1.19844i | −0.279288 | − | 0.960207i | \(-0.590098\pi\) |
0.971208 | − | 0.238233i | \(-0.0765683\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.00000 | − | 6.92820i | −0.212298 | − | 0.367711i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.0000 | 1.26667 | 0.633336 | − | 0.773877i | \(-0.281685\pi\) | ||||
0.633336 | + | 0.773877i | \(0.281685\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.00000 | − | 5.19615i | −0.157027 | − | 0.271979i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.00000 | − | 6.92820i | 0.208798 | − | 0.361649i | −0.742538 | − | 0.669804i | \(-0.766378\pi\) |
0.951336 | + | 0.308155i | \(0.0997115\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.00000 | + | 1.73205i | 0.0517780 | + | 0.0896822i | 0.890753 | − | 0.454488i | \(-0.150178\pi\) |
−0.838975 | + | 0.544170i | \(0.816844\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0000 | 0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.00000 | 0.205466 | 0.102733 | − | 0.994709i | \(-0.467241\pi\) | ||||
0.102733 | + | 0.994709i | \(0.467241\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.0000 | + | 20.7846i | 0.613171 | + | 1.06204i | 0.990702 | + | 0.136047i | \(0.0434398\pi\) |
−0.377531 | + | 0.925997i | \(0.623227\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.00000 | − | 5.19615i | 0.152106 | − | 0.263455i | −0.779895 | − | 0.625910i | \(-0.784728\pi\) |
0.932002 | + | 0.362454i | \(0.118061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.00000 | 0.402524 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 38.0000 | 1.90717 | 0.953583 | − | 0.301131i | \(-0.0973643\pi\) | ||||
0.953583 | + | 0.301131i | \(0.0973643\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.00000 | − | 12.1244i | −0.349563 | − | 0.605461i | 0.636609 | − | 0.771187i | \(-0.280337\pi\) |
−0.986172 | + | 0.165726i | \(0.947003\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 24.0000 | − | 41.5692i | 1.19553 | − | 2.07071i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.00000 | − | 6.92820i | 0.198273 | − | 0.343418i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.0000 | − | 22.5167i | −0.642809 | − | 1.11338i | −0.984803 | − | 0.173675i | \(-0.944436\pi\) |
0.341994 | − | 0.939702i | \(-0.388898\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.0000 | −0.589057 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.0000 | + | 31.1769i | 0.879358 | + | 1.52309i | 0.852047 | + | 0.523465i | \(0.175361\pi\) |
0.0273103 | + | 0.999627i | \(0.491306\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.00000 | − | 8.66025i | 0.243685 | − | 0.422075i | −0.718076 | − | 0.695965i | \(-0.754977\pi\) |
0.961761 | + | 0.273890i | \(0.0883103\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.00000 | + | 5.19615i | −0.145521 | + | 0.252050i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.0000 | 0.770693 | 0.385346 | − | 0.922772i | \(-0.374082\pi\) | ||||
0.385346 | + | 0.922772i | \(0.374082\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.0000 | −1.44171 | −0.720854 | − | 0.693087i | \(-0.756250\pi\) | ||||
−0.720854 | + | 0.693087i | \(0.756250\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.00000 | + | 13.8564i | −0.381819 | + | 0.661330i | −0.991322 | − | 0.131453i | \(-0.958036\pi\) |
0.609503 | + | 0.792784i | \(0.291369\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.00000 | + | 3.46410i | −0.0950229 | + | 0.164584i | −0.909618 | − | 0.415445i | \(-0.863626\pi\) |
0.814595 | + | 0.580030i | \(0.196959\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.00000 | − | 8.66025i | −0.237023 | − | 0.410535i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.0000 | 1.41579 | 0.707894 | − | 0.706319i | \(-0.249646\pi\) | ||||
0.707894 | + | 0.706319i | \(0.249646\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.0000 | 1.13012 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.0000 | − | 19.0526i | 0.514558 | − | 0.891241i | −0.485299 | − | 0.874348i | \(-0.661289\pi\) |
0.999857 | − | 0.0168929i | \(-0.00537742\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.00000 | − | 12.1244i | 0.326023 | − | 0.564688i | −0.655696 | − | 0.755025i | \(-0.727625\pi\) |
0.981719 | + | 0.190337i | \(0.0609581\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.00000 | − | 6.92820i | −0.185896 | − | 0.321981i | 0.757982 | − | 0.652275i | \(-0.226185\pi\) |
−0.943878 | + | 0.330294i | \(0.892852\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.0000 | 1.29569 | 0.647843 | − | 0.761774i | \(-0.275671\pi\) | ||||
0.647843 | + | 0.761774i | \(0.275671\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −24.0000 | − | 41.5692i | −1.10352 | − | 1.91135i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.00000 | − | 3.46410i | 0.0917663 | − | 0.158944i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.0000 | + | 27.7128i | −0.731059 | + | 1.26623i | 0.225372 | + | 0.974273i | \(0.427640\pi\) |
−0.956431 | + | 0.291958i | \(0.905693\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.00000 | + | 10.3923i | 0.273576 | + | 0.473848i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.00000 | −0.0908153 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.0000 | 0.725029 | 0.362515 | − | 0.931978i | \(-0.381918\pi\) | ||||
0.362515 | + | 0.931978i | \(0.381918\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.0000 | − | 31.1769i | −0.812329 | − | 1.40699i | −0.911230 | − | 0.411897i | \(-0.864866\pi\) |
0.0989017 | − | 0.995097i | \(-0.468467\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.00000 | + | 10.3923i | −0.270226 | + | 0.468046i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.0000 | + | 17.3205i | 0.447661 | + | 0.775372i | 0.998233 | − | 0.0594153i | \(-0.0189236\pi\) |
−0.550572 | + | 0.834788i | \(0.685590\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.0000 | 0.713405 | 0.356702 | − | 0.934218i | \(-0.383901\pi\) | ||||
0.356702 | + | 0.934218i | \(0.383901\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | 0.266996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.00000 | − | 1.73205i | −0.0443242 | − | 0.0767718i | 0.843012 | − | 0.537895i | \(-0.180780\pi\) |
−0.887336 | + | 0.461123i | \(0.847447\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.0000 | + | 27.7128i | 0.703679 | + | 1.21881i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −42.0000 | −1.84005 | −0.920027 | − | 0.391856i | \(-0.871833\pi\) | ||||
−0.920027 | + | 0.391856i | \(0.871833\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.00000 | −0.174908 | −0.0874539 | − | 0.996169i | \(-0.527873\pi\) | ||||
−0.0874539 | + | 0.996169i | \(0.527873\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 24.0000 | + | 41.5692i | 1.04546 | + | 1.81078i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.5000 | − | 19.9186i | 0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.0000 | + | 31.1769i | −0.779667 | + | 1.35042i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.00000 | + | 3.46410i | 0.0864675 | + | 0.149766i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −28.0000 | −1.20605 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.0000 | 1.28980 | 0.644900 | − | 0.764267i | \(-0.276899\pi\) | ||||
0.644900 | + | 0.764267i | \(0.276899\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.00000 | − | 15.5885i | −0.385518 | − | 0.667736i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.0000 | + | 31.1769i | −0.769624 | + | 1.33303i | 0.168142 | + | 0.985763i | \(0.446223\pi\) |
−0.937767 | + | 0.347266i | \(0.887110\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.00000 | − | 6.92820i | 0.170406 | − | 0.295151i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.0000 | 0.762684 | 0.381342 | − | 0.924434i | \(-0.375462\pi\) | ||||
0.381342 | + | 0.924434i | \(0.375462\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 72.0000 | 3.04528 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.00000 | + | 3.46410i | 0.0842900 | + | 0.145994i | 0.905088 | − | 0.425223i | \(-0.139804\pi\) |
−0.820798 | + | 0.571218i | \(0.806471\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.00000 | − | 5.19615i | 0.126211 | − | 0.218604i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.00000 | + | 5.19615i | −0.125767 | + | 0.217834i | −0.922032 | − | 0.387113i | \(-0.873472\pi\) |
0.796266 | + | 0.604947i | \(0.206806\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.00000 | + | 10.3923i | 0.251092 | + | 0.434904i | 0.963827 | − | 0.266529i | \(-0.0858769\pi\) |
−0.712735 | + | 0.701434i | \(0.752544\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.00000 | 0.0832611 | 0.0416305 | − | 0.999133i | \(-0.486745\pi\) | ||||
0.0416305 | + | 0.999133i | \(0.486745\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.0000 | − | 20.7846i | 0.496989 | − | 0.860811i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.00000 | + | 3.46410i | −0.0825488 | + | 0.142979i | −0.904344 | − | 0.426804i | \(-0.859639\pi\) |
0.821795 | + | 0.569783i | \(0.192973\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.0000 | − | 27.7128i | −0.659269 | − | 1.14189i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.00000 | 0.246390 | 0.123195 | − | 0.992382i | \(-0.460686\pi\) | ||||
0.123195 | + | 0.992382i | \(0.460686\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.0000 | − | 34.6410i | −0.817178 | − | 1.41539i | −0.907754 | − | 0.419504i | \(-0.862204\pi\) |
0.0905757 | − | 0.995890i | \(-0.471129\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.0000 | + | 22.5167i | −0.530281 | + | 0.918474i | 0.469095 | + | 0.883148i | \(0.344580\pi\) |
−0.999376 | + | 0.0353259i | \(0.988753\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.50000 | − | 4.33013i | 0.101639 | − | 0.176045i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.0000 | − | 34.6410i | −0.811775 | − | 1.40604i | −0.911621 | − | 0.411033i | \(-0.865168\pi\) |
0.0998457 | − | 0.995003i | \(-0.468165\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −48.0000 | −1.94187 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.00000 | −0.0807792 | −0.0403896 | − | 0.999184i | \(-0.512860\pi\) | ||||
−0.0403896 | + | 0.999184i | \(0.512860\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.00000 | + | 1.73205i | 0.0402585 | + | 0.0697297i | 0.885453 | − | 0.464730i | \(-0.153849\pi\) |
−0.845194 | + | 0.534460i | \(0.820515\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.0000 | − | 24.2487i | 0.562708 | − | 0.974638i | −0.434551 | − | 0.900647i | \(-0.643093\pi\) |
0.997259 | − | 0.0739910i | \(-0.0235736\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.0000 | −0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.0000 | 1.27390 | 0.636950 | − | 0.770905i | \(-0.280196\pi\) | ||||
0.636950 | + | 0.770905i | \(0.280196\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.00000 | − | 6.92820i | −0.158735 | − | 0.274937i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.0000 | − | 36.3731i | 0.832050 | − | 1.44115i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.00000 | − | 15.5885i | 0.355479 | − | 0.615707i | −0.631721 | − | 0.775196i | \(-0.717651\pi\) |
0.987200 | + | 0.159489i | \(0.0509845\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.00000 | − | 3.46410i | −0.0788723 | − | 0.136611i | 0.823891 | − | 0.566748i | \(-0.191799\pi\) |
−0.902764 | + | 0.430137i | \(0.858465\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 48.0000 | 1.88707 | 0.943537 | − | 0.331266i | \(-0.107476\pi\) | ||||
0.943537 | + | 0.331266i | \(0.107476\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −48.0000 | −1.88416 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.00000 | + | 12.1244i | 0.273931 | + | 0.474463i | 0.969865 | − | 0.243643i | \(-0.0783426\pi\) |
−0.695934 | + | 0.718106i | \(0.745009\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.00000 | + | 3.46410i | −0.0781465 | + | 0.135354i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.00000 | − | 3.46410i | 0.0779089 | − | 0.134942i | −0.824439 | − | 0.565951i | \(-0.808509\pi\) |
0.902348 | + | 0.431009i | \(0.141842\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.00000 | − | 5.19615i | −0.116686 | − | 0.202107i | 0.801766 | − | 0.597638i | \(-0.203894\pi\) |
−0.918453 | + | 0.395531i | \(0.870561\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.0000 | − | 48.4974i | −1.08093 | − | 1.87222i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.00000 | − | 12.1244i | 0.269830 | − | 0.467360i | −0.698988 | − | 0.715134i | \(-0.746366\pi\) |
0.968818 | + | 0.247774i | \(0.0796991\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.0000 | − | 32.9090i | 0.730229 | − | 1.26479i | −0.226556 | − | 0.973998i | \(-0.572747\pi\) |
0.956785 | − | 0.290796i | \(-0.0939201\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −28.0000 | −1.07139 | −0.535695 | − | 0.844411i | \(-0.679950\pi\) | ||||
−0.535695 | + | 0.844411i | \(0.679950\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.00000 | 0.0764161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.0000 | + | 31.1769i | 0.685745 | + | 1.18775i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.0000 | − | 17.3205i | 0.380418 | − | 0.658903i | −0.610704 | − | 0.791859i | \(-0.709113\pi\) |
0.991122 | + | 0.132956i | \(0.0424468\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.00000 | − | 3.46410i | 0.0758643 | − | 0.131401i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.0000 | − | 31.1769i | −0.681799 | − | 1.18091i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.0000 | −1.13308 | −0.566542 | − | 0.824033i | \(-0.691719\pi\) | ||||
−0.566542 | + | 0.824033i | \(0.691719\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.00000 | 0.301726 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.00000 | − | 8.66025i | 0.187779 | − | 0.325243i | −0.756730 | − | 0.653727i | \(-0.773204\pi\) |
0.944509 | + | 0.328484i | \(0.106538\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.0000 | + | 20.7846i | 0.448775 | + | 0.777300i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.00000 | − | 1.73205i | −0.0371391 | − | 0.0643268i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.0000 | − | 27.7128i | 0.593407 | − | 1.02781i | −0.400362 | − | 0.916357i | \(-0.631116\pi\) |
0.993770 | − | 0.111454i | \(-0.0355509\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −36.0000 | + | 62.3538i | −1.33151 | + | 2.30624i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.0000 | + | 22.5167i | 0.480166 | + | 0.831672i | 0.999741 | − | 0.0227529i | \(-0.00724310\pi\) |
−0.519575 | + | 0.854425i | \(0.673910\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.0000 | 0.589368 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.00000 | −0.147142 | −0.0735712 | − | 0.997290i | \(-0.523440\pi\) | ||||
−0.0735712 | + | 0.997290i | \(0.523440\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.00000 | − | 13.8564i | −0.293492 | − | 0.508342i | 0.681141 | − | 0.732152i | \(-0.261484\pi\) |
−0.974633 | + | 0.223810i | \(0.928151\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.00000 | − | 8.66025i | 0.183186 | − | 0.317287i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.00000 | − | 6.92820i | −0.145962 | − | 0.252814i | 0.783769 | − | 0.621052i | \(-0.213294\pi\) |
−0.929731 | + | 0.368238i | \(0.879961\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.0000 | −0.582300 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.00000 | −0.0726912 | −0.0363456 | − | 0.999339i | \(-0.511572\pi\) | ||||
−0.0363456 | + | 0.999339i | \(0.511572\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.0000 | + | 22.5167i | 0.471250 | + | 0.816228i | 0.999459 | − | 0.0328858i | \(-0.0104698\pi\) |
−0.528209 | + | 0.849114i | \(0.677136\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 36.0000 | − | 62.3538i | 1.29988 | − | 2.25147i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.0000 | + | 25.9808i | 0.540914 | + | 0.936890i | 0.998852 | + | 0.0479061i | \(0.0152548\pi\) |
−0.457938 | + | 0.888984i | \(0.651412\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 42.0000 | 1.51064 | 0.755318 | − | 0.655359i | \(-0.227483\pi\) | ||||
0.755318 | + | 0.655359i | \(0.227483\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.00000 | −0.287368 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.0000 | + | 20.7846i | 0.429945 | + | 0.744686i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.0000 | − | 27.7128i | 0.572525 | − | 0.991642i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.00000 | − | 5.19615i | 0.107075 | − | 0.185459i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.00000 | − | 3.46410i | −0.0712923 | − | 0.123482i | 0.828176 | − | 0.560469i | \(-0.189379\pi\) |
−0.899468 | + | 0.436987i | \(0.856046\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 84.0000 | 2.98293 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.00000 | − | 1.73205i | −0.0354218 | − | 0.0613524i | 0.847771 | − | 0.530362i | \(-0.177944\pi\) |
−0.883193 | + | 0.469010i | \(0.844611\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.0000 | − | 41.5692i | 0.849059 | − | 1.47061i | ||||
\(800\) | 0 |