Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,2,Mod(199,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1350.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.j (of order \(6\), 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: | \(10.7798042729\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 18) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 199.1 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.199 |
Dual form | 1350.2.j.a.1099.1 |
$q$-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 \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.73205 | − | 1.00000i | 0.654654 | − | 0.377964i | −0.135583 | − | 0.990766i | \(-0.543291\pi\) |
0.790237 | + | 0.612801i | \(0.209957\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | − | 2.59808i | −0.452267 | − | 0.783349i | 0.546259 | − | 0.837616i | \(-0.316051\pi\) |
−0.998526 | + | 0.0542666i | \(0.982718\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.73205 | + | 1.00000i | 0.480384 | + | 0.277350i | 0.720577 | − | 0.693375i | \(-0.243877\pi\) |
−0.240192 | + | 0.970725i | \(0.577210\pi\) | |||||||
\(14\) | −1.00000 | + | 1.73205i | −0.267261 | + | 0.462910i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 3.00000i | 0.727607i | 0.931476 | + | 0.363803i | \(0.118522\pi\) | ||||
−0.931476 | + | 0.363803i | \(0.881478\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | 0.114708 | − | 0.993399i | \(-0.463407\pi\) | ||||
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.59808 | + | 1.50000i | 0.553912 | + | 0.319801i | ||||
\(23\) | 5.19615 | + | 3.00000i | 1.08347 | + | 0.625543i | 0.931831 | − | 0.362892i | \(-0.118211\pi\) |
0.151642 | + | 0.988436i | \(0.451544\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.00000 | −0.392232 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 2.00000i | − | 0.377964i | ||||||
\(29\) | −3.00000 | − | 5.19615i | −0.557086 | − | 0.964901i | −0.997738 | − | 0.0672232i | \(-0.978586\pi\) |
0.440652 | − | 0.897678i | \(-0.354747\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | − | 3.46410i | 0.359211 | − | 0.622171i | −0.628619 | − | 0.777714i | \(-0.716379\pi\) |
0.987829 | + | 0.155543i | \(0.0497126\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.50000 | − | 2.59808i | −0.257248 | − | 0.445566i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.00000i | − | 0.657596i | −0.944400 | − | 0.328798i | \(-0.893356\pi\) | ||
0.944400 | − | 0.328798i | \(-0.106644\pi\) | |||||||
\(38\) | −0.866025 | + | 0.500000i | −0.140488 | + | 0.0811107i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.50000 | − | 7.79423i | 0.702782 | − | 1.21725i | −0.264704 | − | 0.964330i | \(-0.585274\pi\) |
0.967486 | − | 0.252924i | \(-0.0813924\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.866025 | − | 0.500000i | 0.132068 | − | 0.0762493i | −0.432511 | − | 0.901629i | \(-0.642372\pi\) |
0.564578 | + | 0.825380i | \(0.309039\pi\) | |||||||
\(44\) | −3.00000 | −0.452267 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.00000 | −0.884652 | ||||||||
\(47\) | 5.19615 | − | 3.00000i | 0.757937 | − | 0.437595i | −0.0706177 | − | 0.997503i | \(-0.522497\pi\) |
0.828554 | + | 0.559908i | \(0.189164\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.50000 | + | 2.59808i | −0.214286 | + | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.73205 | − | 1.00000i | 0.240192 | − | 0.138675i | ||||
\(53\) | 12.0000i | 1.64833i | 0.566352 | + | 0.824163i | \(0.308354\pi\) | ||||
−0.566352 | + | 0.824163i | \(0.691646\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | + | 1.73205i | 0.133631 | + | 0.231455i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.19615 | + | 3.00000i | 0.682288 | + | 0.393919i | ||||
\(59\) | −1.50000 | + | 2.59808i | −0.195283 | + | 0.338241i | −0.946993 | − | 0.321253i | \(-0.895896\pi\) |
0.751710 | + | 0.659494i | \(0.229229\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.00000 | − | 6.92820i | −0.512148 | − | 0.887066i | −0.999901 | − | 0.0140840i | \(-0.995517\pi\) |
0.487753 | − | 0.872982i | \(-0.337817\pi\) | |||||||
\(62\) | 4.00000i | 0.508001i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.33013 | − | 2.50000i | −0.529009 | − | 0.305424i | 0.211604 | − | 0.977356i | \(-0.432131\pi\) |
−0.740613 | + | 0.671932i | \(0.765465\pi\) | |||||||
\(68\) | 2.59808 | + | 1.50000i | 0.315063 | + | 0.181902i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000 | 1.42414 | 0.712069 | − | 0.702109i | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702109i | \(0.247758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 11.0000i | − | 1.28745i | −0.765256 | − | 0.643726i | \(-0.777388\pi\) | ||
0.765256 | − | 0.643726i | \(-0.222612\pi\) | |||||||
\(74\) | 2.00000 | + | 3.46410i | 0.232495 | + | 0.402694i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.500000 | − | 0.866025i | 0.0573539 | − | 0.0993399i | ||||
\(77\) | −5.19615 | − | 3.00000i | −0.592157 | − | 0.341882i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.00000 | − | 3.46410i | −0.225018 | − | 0.389742i | 0.731307 | − | 0.682048i | \(-0.238911\pi\) |
−0.956325 | + | 0.292306i | \(0.905577\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.00000i | 0.993884i | ||||||||
\(83\) | 10.3923 | − | 6.00000i | 1.14070 | − | 0.658586i | 0.194099 | − | 0.980982i | \(-0.437822\pi\) |
0.946605 | + | 0.322396i | \(0.104488\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.500000 | + | 0.866025i | −0.0539164 | + | 0.0933859i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.59808 | − | 1.50000i | 0.276956 | − | 0.159901i | ||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000 | 0.419314 | ||||||||
\(92\) | 5.19615 | − | 3.00000i | 0.541736 | − | 0.312772i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.00000 | + | 5.19615i | −0.309426 | + | 0.535942i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.33013 | − | 2.50000i | 0.439658 | − | 0.253837i | −0.263795 | − | 0.964579i | \(-0.584974\pi\) |
0.703452 | + | 0.710742i | \(0.251641\pi\) | |||||||
\(98\) | − | 3.00000i | − | 0.303046i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.1244 | + | 7.00000i | 1.19465 | + | 0.689730i | 0.959357 | − | 0.282194i | \(-0.0910623\pi\) |
0.235291 | + | 0.971925i | \(0.424396\pi\) | |||||||
\(104\) | −1.00000 | + | 1.73205i | −0.0980581 | + | 0.169842i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | − | 10.3923i | −0.582772 | − | 1.00939i | ||||
\(107\) | − | 3.00000i | − | 0.290021i | −0.989430 | − | 0.145010i | \(-0.953678\pi\) | ||
0.989430 | − | 0.145010i | \(-0.0463216\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.0000 | 1.53252 | 0.766261 | − | 0.642529i | \(-0.222115\pi\) | ||||
0.766261 | + | 0.642529i | \(0.222115\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.73205 | − | 1.00000i | −0.163663 | − | 0.0944911i | ||||
\(113\) | −5.19615 | − | 3.00000i | −0.488813 | − | 0.282216i | 0.235269 | − | 0.971930i | \(-0.424403\pi\) |
−0.724082 | + | 0.689714i | \(0.757736\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.00000 | −0.557086 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 3.00000i | − | 0.276172i | ||||||
\(119\) | 3.00000 | + | 5.19615i | 0.275010 | + | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | 6.92820 | + | 4.00000i | 0.627250 | + | 0.362143i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.00000 | − | 3.46410i | −0.179605 | − | 0.311086i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.00000i | 0.177471i | 0.996055 | + | 0.0887357i | \(0.0282826\pi\) | ||||
−0.996055 | + | 0.0887357i | \(0.971717\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.73205 | − | 1.00000i | 0.150188 | − | 0.0867110i | ||||
\(134\) | 5.00000 | 0.431934 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.00000 | −0.257248 | ||||||||
\(137\) | 2.59808 | − | 1.50000i | 0.221969 | − | 0.128154i | −0.384893 | − | 0.922961i | \(-0.625762\pi\) |
0.606861 | + | 0.794808i | \(0.292428\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.50000 | + | 16.4545i | −0.805779 | + | 1.39565i | 0.109984 | + | 0.993933i | \(0.464920\pi\) |
−0.915764 | + | 0.401718i | \(0.868413\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.3923 | + | 6.00000i | −0.872103 | + | 0.503509i | ||||
\(143\) | − | 6.00000i | − | 0.501745i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 5.50000 | + | 9.52628i | 0.455183 | + | 0.788400i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.46410 | − | 2.00000i | −0.284747 | − | 0.164399i | ||||
\(149\) | 3.00000 | − | 5.19615i | 0.245770 | − | 0.425685i | −0.716578 | − | 0.697507i | \(-0.754293\pi\) |
0.962348 | + | 0.271821i | \(0.0876260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.00000 | + | 8.66025i | 0.406894 | + | 0.704761i | 0.994540 | − | 0.104357i | \(-0.0332784\pi\) |
−0.587646 | + | 0.809118i | \(0.699945\pi\) | |||||||
\(152\) | 1.00000i | 0.0811107i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.00000 | 0.483494 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.46410 | + | 2.00000i | 0.276465 | + | 0.159617i | 0.631822 | − | 0.775113i | \(-0.282307\pi\) |
−0.355357 | + | 0.934731i | \(0.615641\pi\) | |||||||
\(158\) | 3.46410 | + | 2.00000i | 0.275589 | + | 0.159111i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.0000 | 0.945732 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.00000i | 0.313304i | 0.987654 | + | 0.156652i | \(0.0500701\pi\) | ||||
−0.987654 | + | 0.156652i | \(0.949930\pi\) | |||||||
\(164\) | −4.50000 | − | 7.79423i | −0.351391 | − | 0.608627i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.00000 | + | 10.3923i | −0.465690 | + | 0.806599i | ||||
\(167\) | −10.3923 | − | 6.00000i | −0.804181 | − | 0.464294i | 0.0407502 | − | 0.999169i | \(-0.487025\pi\) |
−0.844931 | + | 0.534875i | \(0.820359\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.50000 | − | 7.79423i | −0.346154 | − | 0.599556i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 1.00000i | − | 0.0762493i | ||||||
\(173\) | −5.19615 | + | 3.00000i | −0.395056 | + | 0.228086i | −0.684349 | − | 0.729155i | \(-0.739913\pi\) |
0.289292 | + | 0.957241i | \(0.406580\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.50000 | + | 2.59808i | −0.113067 | + | 0.195837i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.19615 | + | 3.00000i | −0.389468 | + | 0.224860i | ||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.0000 | 1.04061 | 0.520306 | − | 0.853980i | \(-0.325818\pi\) | ||||
0.520306 | + | 0.853980i | \(0.325818\pi\) | |||||||
\(182\) | −3.46410 | + | 2.00000i | −0.256776 | + | 0.148250i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.00000 | + | 5.19615i | −0.221163 | + | 0.383065i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.79423 | − | 4.50000i | 0.569970 | − | 0.329073i | ||||
\(188\) | − | 6.00000i | − | 0.437595i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.00000 | − | 15.5885i | −0.651217 | − | 1.12794i | −0.982828 | − | 0.184525i | \(-0.940925\pi\) |
0.331611 | − | 0.943416i | \(-0.392408\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.33013 | + | 2.50000i | 0.311689 | + | 0.179954i | 0.647682 | − | 0.761911i | \(-0.275738\pi\) |
−0.335993 | + | 0.941865i | \(0.609072\pi\) | |||||||
\(194\) | −2.50000 | + | 4.33013i | −0.179490 | + | 0.310885i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.50000 | + | 2.59808i | 0.107143 | + | 0.185577i | ||||
\(197\) | 12.0000i | 0.854965i | 0.904024 | + | 0.427482i | \(0.140599\pi\) | ||||
−0.904024 | + | 0.427482i | \(0.859401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.0000 | 0.708881 | 0.354441 | − | 0.935079i | \(-0.384671\pi\) | ||||
0.354441 | + | 0.935079i | \(0.384671\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.3923 | − | 6.00000i | −0.729397 | − | 0.421117i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −14.0000 | −0.975426 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 2.00000i | − | 0.138675i | ||||||
\(209\) | −1.50000 | − | 2.59808i | −0.103757 | − | 0.179713i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.0000 | + | 17.3205i | −0.688428 | + | 1.19239i | 0.283918 | + | 0.958849i | \(0.408366\pi\) |
−0.972346 | + | 0.233544i | \(0.924968\pi\) | |||||||
\(212\) | 10.3923 | + | 6.00000i | 0.713746 | + | 0.412082i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.50000 | + | 2.59808i | 0.102538 | + | 0.177601i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 8.00000i | − | 0.543075i | ||||||
\(218\) | −13.8564 | + | 8.00000i | −0.938474 | + | 0.541828i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.00000 | + | 5.19615i | −0.201802 | + | 0.349531i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.5167 | + | 13.0000i | −1.50783 | + | 0.870544i | −0.507869 | + | 0.861435i | \(0.669566\pi\) |
−0.999959 | + | 0.00910984i | \(0.997100\pi\) | |||||||
\(224\) | 2.00000 | 0.133631 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.00000 | 0.399114 | ||||||||
\(227\) | −18.1865 | + | 10.5000i | −1.20708 | + | 0.696909i | −0.962121 | − | 0.272623i | \(-0.912109\pi\) |
−0.244962 | + | 0.969533i | \(0.578775\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.00000 | − | 12.1244i | 0.462573 | − | 0.801200i | −0.536515 | − | 0.843891i | \(-0.680260\pi\) |
0.999088 | + | 0.0426906i | \(0.0135930\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.19615 | − | 3.00000i | 0.341144 | − | 0.196960i | ||||
\(233\) | 3.00000i | 0.196537i | 0.995160 | + | 0.0982683i | \(0.0313303\pi\) | ||||
−0.995160 | + | 0.0982683i | \(0.968670\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.50000 | + | 2.59808i | 0.0976417 | + | 0.169120i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.19615 | − | 3.00000i | −0.336817 | − | 0.194461i | ||||
\(239\) | −3.00000 | + | 5.19615i | −0.194054 | + | 0.336111i | −0.946590 | − | 0.322440i | \(-0.895497\pi\) |
0.752536 | + | 0.658551i | \(0.228830\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.50000 | + | 6.06218i | 0.225455 | + | 0.390499i | 0.956456 | − | 0.291877i | \(-0.0942799\pi\) |
−0.731001 | + | 0.682376i | \(0.760947\pi\) | |||||||
\(242\) | 2.00000i | 0.128565i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.00000 | −0.512148 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.73205 | + | 1.00000i | 0.110208 | + | 0.0636285i | ||||
\(248\) | 3.46410 | + | 2.00000i | 0.219971 | + | 0.127000i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.0000 | −1.32551 | −0.662754 | − | 0.748837i | \(-0.730613\pi\) | ||||
−0.662754 | + | 0.748837i | \(0.730613\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 18.0000i | − | 1.13165i | ||||||
\(254\) | −1.00000 | − | 1.73205i | −0.0627456 | − | 0.108679i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −18.1865 | − | 10.5000i | −1.13444 | − | 0.654972i | −0.189396 | − | 0.981901i | \(-0.560653\pi\) |
−0.945049 | + | 0.326929i | \(0.893986\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.00000 | − | 6.92820i | −0.248548 | − | 0.430498i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.5885 | − | 9.00000i | 0.961225 | − | 0.554964i | 0.0646755 | − | 0.997906i | \(-0.479399\pi\) |
0.896550 | + | 0.442943i | \(0.146065\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.00000 | + | 1.73205i | −0.0613139 | + | 0.106199i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.33013 | + | 2.50000i | −0.264505 | + | 0.152712i | ||||
\(269\) | −24.0000 | −1.46331 | −0.731653 | − | 0.681677i | \(-0.761251\pi\) | ||||
−0.731653 | + | 0.681677i | \(0.761251\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.0000 | 1.21491 | 0.607457 | − | 0.794353i | \(-0.292190\pi\) | ||||
0.607457 | + | 0.794353i | \(0.292190\pi\) | |||||||
\(272\) | 2.59808 | − | 1.50000i | 0.157532 | − | 0.0909509i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.50000 | + | 2.59808i | −0.0906183 | + | 0.156956i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.66025 | + | 5.00000i | −0.520344 | + | 0.300421i | −0.737075 | − | 0.675810i | \(-0.763794\pi\) |
0.216731 | + | 0.976231i | \(0.430460\pi\) | |||||||
\(278\) | − | 19.0000i | − | 1.13954i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.00000 | + | 5.19615i | 0.178965 | + | 0.309976i | 0.941526 | − | 0.336939i | \(-0.109392\pi\) |
−0.762561 | + | 0.646916i | \(0.776058\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.46410 | − | 2.00000i | −0.205919 | − | 0.118888i | 0.393494 | − | 0.919327i | \(-0.371266\pi\) |
−0.599414 | + | 0.800439i | \(0.704600\pi\) | |||||||
\(284\) | 6.00000 | − | 10.3923i | 0.356034 | − | 0.616670i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.00000 | + | 5.19615i | 0.177394 | + | 0.307255i | ||||
\(287\) | − | 18.0000i | − | 1.06251i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.00000 | 0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.52628 | − | 5.50000i | −0.557483 | − | 0.321863i | ||||
\(293\) | −25.9808 | − | 15.0000i | −1.51781 | − | 0.876309i | −0.999781 | − | 0.0209480i | \(-0.993332\pi\) |
−0.518032 | − | 0.855361i | \(-0.673335\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.00000 | 0.232495 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.00000i | 0.347571i | ||||||||
\(299\) | 6.00000 | + | 10.3923i | 0.346989 | + | 0.601003i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.00000 | − | 1.73205i | 0.0576390 | − | 0.0998337i | ||||
\(302\) | −8.66025 | − | 5.00000i | −0.498342 | − | 0.287718i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.500000 | − | 0.866025i | −0.0286770 | − | 0.0496700i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 7.00000i | − | 0.399511i | −0.979846 | − | 0.199756i | \(-0.935985\pi\) | ||
0.979846 | − | 0.199756i | \(-0.0640148\pi\) | |||||||
\(308\) | −5.19615 | + | 3.00000i | −0.296078 | + | 0.170941i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.00000 | + | 15.5885i | −0.510343 | + | 0.883940i | 0.489585 | + | 0.871956i | \(0.337148\pi\) |
−0.999928 | + | 0.0119847i | \(0.996185\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.1147 | + | 14.5000i | −1.41957 | + | 0.819588i | −0.996261 | − | 0.0863973i | \(-0.972465\pi\) |
−0.423308 | + | 0.905986i | \(0.639131\pi\) | |||||||
\(314\) | −4.00000 | −0.225733 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.00000 | −0.225018 | ||||||||
\(317\) | 15.5885 | − | 9.00000i | 0.875535 | − | 0.505490i | 0.00635137 | − | 0.999980i | \(-0.497978\pi\) |
0.869184 | + | 0.494489i | \(0.164645\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.00000 | + | 15.5885i | −0.503903 | + | 0.872786i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −10.3923 | + | 6.00000i | −0.579141 | + | 0.334367i | ||||
\(323\) | 3.00000i | 0.166924i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.00000 | − | 3.46410i | −0.110770 | − | 0.191859i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.79423 | + | 4.50000i | 0.430364 | + | 0.248471i | ||||
\(329\) | 6.00000 | − | 10.3923i | 0.330791 | − | 0.572946i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.00000 | + | 3.46410i | 0.109930 | + | 0.190404i | 0.915742 | − | 0.401768i | \(-0.131604\pi\) |
−0.805812 | + | 0.592172i | \(0.798271\pi\) | |||||||
\(332\) | − | 12.0000i | − | 0.658586i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.0000 | 0.656611 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.866025 | + | 0.500000i | 0.0471754 | + | 0.0272367i | 0.523402 | − | 0.852086i | \(-0.324663\pi\) |
−0.476227 | + | 0.879322i | \(0.657996\pi\) | |||||||
\(338\) | 7.79423 | + | 4.50000i | 0.423950 | + | 0.244768i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.0000 | −0.649836 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0000i | 1.07990i | ||||||||
\(344\) | 0.500000 | + | 0.866025i | 0.0269582 | + | 0.0466930i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.00000 | − | 5.19615i | 0.161281 | − | 0.279347i | ||||
\(347\) | 28.5788 | + | 16.5000i | 1.53419 | + | 0.885766i | 0.999162 | + | 0.0409337i | \(0.0130332\pi\) |
0.535031 | + | 0.844833i | \(0.320300\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.00000 | − | 13.8564i | −0.428230 | − | 0.741716i | 0.568486 | − | 0.822693i | \(-0.307529\pi\) |
−0.996716 | + | 0.0809766i | \(0.974196\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 3.00000i | − | 0.159901i | ||||||
\(353\) | −18.1865 | + | 10.5000i | −0.967972 | + | 0.558859i | −0.898617 | − | 0.438733i | \(-0.855427\pi\) |
−0.0693543 | + | 0.997592i | \(0.522094\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.00000 | − | 5.19615i | 0.159000 | − | 0.275396i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.3923 | + | 6.00000i | −0.549250 | + | 0.317110i | ||||
\(359\) | −18.0000 | −0.950004 | −0.475002 | − | 0.879985i | \(-0.657553\pi\) | ||||
−0.475002 | + | 0.879985i | \(0.657553\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0000 | −0.947368 | ||||||||
\(362\) | −12.1244 | + | 7.00000i | −0.637242 | + | 0.367912i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.00000 | − | 3.46410i | 0.104828 | − | 0.181568i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.2487 | + | 14.0000i | −1.26577 | + | 0.730794i | −0.974185 | − | 0.225750i | \(-0.927517\pi\) |
−0.291587 | + | 0.956544i | \(0.594183\pi\) | |||||||
\(368\) | − | 6.00000i | − | 0.312772i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.0000 | + | 20.7846i | 0.623009 | + | 1.07908i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −29.4449 | − | 17.0000i | −1.52460 | − | 0.880227i | −0.999575 | − | 0.0291379i | \(-0.990724\pi\) |
−0.525022 | − | 0.851089i | \(-0.675943\pi\) | |||||||
\(374\) | −4.50000 | + | 7.79423i | −0.232689 | + | 0.403030i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.00000 | + | 5.19615i | 0.154713 | + | 0.267971i | ||||
\(377\) | − | 12.0000i | − | 0.618031i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.0000 | −1.18143 | −0.590715 | − | 0.806880i | \(-0.701154\pi\) | ||||
−0.590715 | + | 0.806880i | \(0.701154\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 15.5885 | + | 9.00000i | 0.797575 | + | 0.460480i | ||||
\(383\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.00000 | −0.254493 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 5.00000i | − | 0.253837i | ||||||
\(389\) | −9.00000 | − | 15.5885i | −0.456318 | − | 0.790366i | 0.542445 | − | 0.840091i | \(-0.317499\pi\) |
−0.998763 | + | 0.0497253i | \(0.984165\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.00000 | + | 15.5885i | −0.455150 | + | 0.788342i | ||||
\(392\) | −2.59808 | − | 1.50000i | −0.131223 | − | 0.0757614i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.00000 | − | 10.3923i | −0.302276 | − | 0.523557i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.0000i | 1.00377i | 0.864934 | + | 0.501886i | \(0.167360\pi\) | ||||
−0.864934 | + | 0.501886i | \(0.832640\pi\) | |||||||
\(398\) | −8.66025 | + | 5.00000i | −0.434099 | + | 0.250627i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.5000 | + | 23.3827i | −0.674158 | + | 1.16768i | 0.302556 | + | 0.953131i | \(0.402160\pi\) |
−0.976714 | + | 0.214544i | \(0.931173\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.92820 | − | 4.00000i | 0.345118 | − | 0.199254i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12.0000 | 0.595550 | ||||||||
\(407\) | −10.3923 | + | 6.00000i | −0.515127 | + | 0.297409i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.50000 | − | 14.7224i | 0.420298 | − | 0.727977i | −0.575670 | − | 0.817682i | \(-0.695259\pi\) |
0.995968 | + | 0.0897044i | \(0.0285922\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.1244 | − | 7.00000i | 0.597324 | − | 0.344865i | ||||
\(413\) | 6.00000i | 0.295241i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.00000 | + | 1.73205i | 0.0490290 | + | 0.0849208i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.59808 | + | 1.50000i | 0.127076 | + | 0.0733674i | ||||
\(419\) | 6.00000 | − | 10.3923i | 0.293119 | − | 0.507697i | −0.681426 | − | 0.731887i | \(-0.738640\pi\) |
0.974546 | + | 0.224189i | \(0.0719734\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | − | 17.3205i | −0.487370 | − | 0.844150i | 0.512524 | − | 0.858673i | \(-0.328710\pi\) |
−0.999895 | + | 0.0145228i | \(0.995377\pi\) | |||||||
\(422\) | − | 20.0000i | − | 0.973585i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12.0000 | −0.582772 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.8564 | − | 8.00000i | −0.670559 | − | 0.387147i | ||||
\(428\) | −2.59808 | − | 1.50000i | −0.125583 | − | 0.0725052i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.0000 | 1.44505 | 0.722525 | − | 0.691345i | \(-0.242982\pi\) | ||||
0.722525 | + | 0.691345i | \(0.242982\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.00000i | 0.336399i | 0.985753 | + | 0.168199i | \(0.0537952\pi\) | ||||
−0.985753 | + | 0.168199i | \(0.946205\pi\) | |||||||
\(434\) | 4.00000 | + | 6.92820i | 0.192006 | + | 0.332564i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.00000 | − | 13.8564i | 0.383131 | − | 0.663602i | ||||
\(437\) | 5.19615 | + | 3.00000i | 0.248566 | + | 0.143509i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.00000 | + | 6.92820i | 0.190910 | + | 0.330665i | 0.945552 | − | 0.325471i | \(-0.105523\pi\) |
−0.754642 | + | 0.656136i | \(0.772190\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 6.00000i | − | 0.285391i | ||||||
\(443\) | 2.59808 | − | 1.50000i | 0.123438 | − | 0.0712672i | −0.437009 | − | 0.899457i | \(-0.643962\pi\) |
0.560448 | + | 0.828190i | \(0.310629\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 13.0000 | − | 22.5167i | 0.615568 | − | 1.06619i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.73205 | + | 1.00000i | −0.0818317 | + | 0.0472456i | ||||
\(449\) | 9.00000 | 0.424736 | 0.212368 | − | 0.977190i | \(-0.431882\pi\) | ||||
0.212368 | + | 0.977190i | \(0.431882\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −27.0000 | −1.27138 | ||||||||
\(452\) | −5.19615 | + | 3.00000i | −0.244406 | + | 0.141108i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10.5000 | − | 18.1865i | 0.492789 | − | 0.853536i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.7224 | − | 8.50000i | 0.688686 | − | 0.397613i | −0.114433 | − | 0.993431i | \(-0.536505\pi\) |
0.803120 | + | 0.595818i | \(0.203172\pi\) | |||||||
\(458\) | 14.0000i | 0.654177i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.0000 | − | 25.9808i | −0.698620 | − | 1.21004i | −0.968945 | − | 0.247276i | \(-0.920465\pi\) |
0.270326 | − | 0.962769i | \(-0.412869\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.3205 | + | 10.0000i | 0.804952 | + | 0.464739i | 0.845200 | − | 0.534450i | \(-0.179481\pi\) |
−0.0402476 | + | 0.999190i | \(0.512815\pi\) | |||||||
\(464\) | −3.00000 | + | 5.19615i | −0.139272 | + | 0.241225i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.50000 | − | 2.59808i | −0.0694862 | − | 0.120354i | ||||
\(467\) | 15.0000i | 0.694117i | 0.937843 | + | 0.347059i | \(0.112820\pi\) | ||||
−0.937843 | + | 0.347059i | \(0.887180\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.0000 | −0.461757 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.59808 | − | 1.50000i | −0.119586 | − | 0.0690431i | ||||
\(473\) | −2.59808 | − | 1.50000i | −0.119460 | − | 0.0689701i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.00000 | 0.275010 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 6.00000i | − | 0.274434i | ||||||
\(479\) | 21.0000 | + | 36.3731i | 0.959514 | + | 1.66193i | 0.723681 | + | 0.690134i | \(0.242449\pi\) |
0.235833 | + | 0.971794i | \(0.424218\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.00000 | − | 6.92820i | 0.182384 | − | 0.315899i | ||||
\(482\) | −6.06218 | − | 3.50000i | −0.276125 | − | 0.159421i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.00000 | − | 1.73205i | −0.0454545 | − | 0.0787296i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.0000i | 1.17817i | 0.808070 | + | 0.589086i | \(0.200512\pi\) | ||||
−0.808070 | + | 0.589086i | \(0.799488\pi\) | |||||||
\(488\) | 6.92820 | − | 4.00000i | 0.313625 | − | 0.181071i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.50000 | + | 12.9904i | −0.338470 | + | 0.586248i | −0.984145 | − | 0.177365i | \(-0.943243\pi\) |
0.645675 | + | 0.763612i | \(0.276576\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.5885 | − | 9.00000i | 0.702069 | − | 0.405340i | ||||
\(494\) | −2.00000 | −0.0899843 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | 20.7846 | − | 12.0000i | 0.932317 | − | 0.538274i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.50000 | + | 11.2583i | −0.290980 | + | 0.503992i | −0.974042 | − | 0.226369i | \(-0.927315\pi\) |
0.683062 | + | 0.730361i | \(0.260648\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 18.1865 | − | 10.5000i | 0.811705 | − | 0.468638i | ||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 9.00000 | + | 15.5885i | 0.400099 | + | 0.692991i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.73205 | + | 1.00000i | 0.0768473 | + | 0.0443678i | ||||
\(509\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.0000 | − | 19.0526i | −0.486611 | − | 0.842836i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 21.0000 | 0.926270 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.5885 | − | 9.00000i | −0.685580 | − | 0.395820i | ||||
\(518\) | 6.92820 | + | 4.00000i | 0.304408 | + | 0.175750i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.00000 | 0.131432 | 0.0657162 | − | 0.997838i | \(-0.479067\pi\) | ||||
0.0657162 | + | 0.997838i | \(0.479067\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 20.0000i | − | 0.874539i | −0.899331 | − | 0.437269i | \(-0.855946\pi\) | ||
0.899331 | − | 0.437269i | \(-0.144054\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.00000 | + | 15.5885i | −0.392419 | + | 0.679689i | ||||
\(527\) | 10.3923 | + | 6.00000i | 0.452696 | + | 0.261364i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.50000 | + | 11.2583i | 0.282609 | + | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 2.00000i | − | 0.0867110i | ||||||
\(533\) | 15.5885 | − | 9.00000i | 0.675211 | − | 0.389833i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.50000 | − | 4.33013i | 0.107984 | − | 0.187033i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 20.7846 | − | 12.0000i | 0.896088 | − | 0.517357i | ||||
\(539\) | 9.00000 | 0.387657 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.00000 | −0.171973 | −0.0859867 | − | 0.996296i | \(-0.527404\pi\) | ||||
−0.0859867 | + | 0.996296i | \(0.527404\pi\) | |||||||
\(542\) | −17.3205 | + | 10.0000i | −0.743980 | + | 0.429537i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.50000 | + | 2.59808i | −0.0643120 | + | 0.111392i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.866025 | + | 0.500000i | −0.0370286 | + | 0.0213785i | −0.518400 | − | 0.855138i | \(-0.673472\pi\) |
0.481371 | + | 0.876517i | \(0.340139\pi\) | |||||||
\(548\) | − | 3.00000i | − | 0.128154i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.00000 | − | 5.19615i | −0.127804 | − | 0.221364i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.92820 | − | 4.00000i | −0.294617 | − | 0.170097i | ||||
\(554\) | 5.00000 | − | 8.66025i | 0.212430 | − | 0.367939i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.50000 | + | 16.4545i | 0.402890 | + | 0.697826i | ||||
\(557\) | 30.0000i | 1.27114i | 0.772043 | + | 0.635570i | \(0.219235\pi\) | ||||
−0.772043 | + | 0.635570i | \(0.780765\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.00000 | 0.0845910 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.19615 | − | 3.00000i | −0.219186 | − | 0.126547i | ||||
\(563\) | 33.7750 | + | 19.5000i | 1.42345 | + | 0.821827i | 0.996592 | − | 0.0824933i | \(-0.0262883\pi\) |
0.426855 | + | 0.904320i | \(0.359622\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4.00000 | 0.168133 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.0000i | 0.503509i | ||||||||
\(569\) | −22.5000 | − | 38.9711i | −0.943249 | − | 1.63376i | −0.759220 | − | 0.650835i | \(-0.774419\pi\) |
−0.184030 | − | 0.982921i | \(-0.558914\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.5000 | − | 32.0429i | 0.774201 | − | 1.34096i | −0.161042 | − | 0.986948i | \(-0.551485\pi\) |
0.935243 | − | 0.354008i | \(-0.115181\pi\) | |||||||
\(572\) | −5.19615 | − | 3.00000i | −0.217262 | − | 0.125436i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9.00000 | + | 15.5885i | 0.375653 | + | 0.650650i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.0000i | 0.457936i | 0.973434 | + | 0.228968i | \(0.0735351\pi\) | ||||
−0.973434 | + | 0.228968i | \(0.926465\pi\) | |||||||
\(578\) | −6.92820 | + | 4.00000i | −0.288175 | + | 0.166378i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.0000 | − | 20.7846i | 0.497844 | − | 0.862291i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 31.1769 | − | 18.0000i | 1.29122 | − | 0.745484i | ||||
\(584\) | 11.0000 | 0.455183 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 30.0000 | 1.23929 | ||||||||
\(587\) | 7.79423 | − | 4.50000i | 0.321702 | − | 0.185735i | −0.330449 | − | 0.943824i | \(-0.607200\pi\) |
0.652151 | + | 0.758089i | \(0.273867\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.00000 | − | 3.46410i | 0.0824086 | − | 0.142736i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.46410 | + | 2.00000i | −0.142374 | + | 0.0821995i | ||||
\(593\) | 6.00000i | 0.246390i | 0.992382 | + | 0.123195i | \(0.0393141\pi\) | ||||
−0.992382 | + | 0.123195i | \(0.960686\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.00000 | − | 5.19615i | −0.122885 | − | 0.212843i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −10.3923 | − | 6.00000i | −0.424973 | − | 0.245358i | ||||
\(599\) | −6.00000 | + | 10.3923i | −0.245153 | + | 0.424618i | −0.962175 | − | 0.272433i | \(-0.912172\pi\) |
0.717021 | + | 0.697051i | \(0.245505\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.5000 | + | 32.0429i | 0.754631 | + | 1.30706i | 0.945558 | + | 0.325455i | \(0.105517\pi\) |
−0.190927 | + | 0.981604i | \(0.561149\pi\) | |||||||
\(602\) | 2.00000i | 0.0815139i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.0000 | 0.406894 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.2487 | + | 14.0000i | 0.984225 | + | 0.568242i | 0.903543 | − | 0.428497i | \(-0.140957\pi\) |
0.0806818 | + | 0.996740i | \(0.474290\pi\) | |||||||
\(608\) | 0.866025 | + | 0.500000i | 0.0351220 | + | 0.0202777i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.0000 | 0.485468 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.0000i | 0.646234i | 0.946359 | + | 0.323117i | \(0.104731\pi\) | ||||
−0.946359 | + | 0.323117i | \(0.895269\pi\) | |||||||
\(614\) | 3.50000 | + | 6.06218i | 0.141249 | + | 0.244650i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.00000 | − | 5.19615i | 0.120873 | − | 0.209359i | ||||
\(617\) | 23.3827 | + | 13.5000i | 0.941351 | + | 0.543490i | 0.890384 | − | 0.455211i | \(-0.150436\pi\) |
0.0509678 | + | 0.998700i | \(0.483769\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.5000 | + | 30.3109i | 0.703384 | + | 1.21830i | 0.967271 | + | 0.253744i | \(0.0816620\pi\) |
−0.263887 | + | 0.964554i | \(0.585005\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 18.0000i | − | 0.721734i | ||||||
\(623\) | 10.3923 | − | 6.00000i | 0.416359 | − | 0.240385i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 14.5000 | − | 25.1147i | 0.579537 | − | 1.00379i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.46410 | − | 2.00000i | 0.138233 | − | 0.0798087i | ||||
\(629\) | 12.0000 | 0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.0000 | −1.59237 | −0.796187 | − | 0.605050i | \(-0.793153\pi\) | ||||
−0.796187 | + | 0.605050i | \(0.793153\pi\) | |||||||
\(632\) | 3.46410 | − | 2.00000i | 0.137795 | − | 0.0795557i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9.00000 | + | 15.5885i | −0.357436 | + | 0.619097i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.19615 | + | 3.00000i | −0.205879 | + | 0.118864i | ||||
\(638\) | − | 18.0000i | − | 0.712627i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.50000 | − | 2.59808i | −0.0592464 | − | 0.102618i | 0.834881 | − | 0.550431i | \(-0.185536\pi\) |
−0.894127 | + | 0.447813i | \(0.852203\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.9186 | + | 11.5000i | 0.785512 | + | 0.453516i | 0.838380 | − | 0.545086i | \(-0.183503\pi\) |
−0.0528680 | + | 0.998602i | \(0.516836\pi\) | |||||||
\(644\) | 6.00000 | − | 10.3923i | 0.236433 | − | 0.409514i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.50000 | − | 2.59808i | −0.0590167 | − | 0.102220i | ||||
\(647\) | − | 18.0000i | − | 0.707653i | −0.935311 | − | 0.353827i | \(-0.884880\pi\) | ||
0.935311 | − | 0.353827i | \(-0.115120\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.00000 | 0.353281 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.46410 | + | 2.00000i | 0.135665 | + | 0.0783260i | ||||
\(653\) | 5.19615 | + | 3.00000i | 0.203341 | + | 0.117399i | 0.598213 | − | 0.801337i | \(-0.295878\pi\) |
−0.394872 | + | 0.918736i | \(0.629211\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −9.00000 | −0.351391 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 12.0000i | 0.467809i | ||||||||
\(659\) | 18.0000 | + | 31.1769i | 0.701180 | + | 1.21448i | 0.968052 | + | 0.250748i | \(0.0806766\pi\) |
−0.266872 | + | 0.963732i | \(0.585990\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.00000 | − | 3.46410i | 0.0777910 | − | 0.134738i | −0.824506 | − | 0.565854i | \(-0.808547\pi\) |
0.902297 | + | 0.431116i | \(0.141880\pi\) | |||||||
\(662\) | −3.46410 | − | 2.00000i | −0.134636 | − | 0.0777322i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.00000 | + | 10.3923i | 0.232845 | + | 0.403300i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 36.0000i | − | 1.39393i | ||||||
\(668\) | −10.3923 | + | 6.00000i | −0.402090 | + | 0.232147i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.0000 | + | 20.7846i | −0.463255 | + | 0.802381i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.0526 | − | 11.0000i | 0.734422 | − | 0.424019i | −0.0856156 | − | 0.996328i | \(-0.527286\pi\) |
0.820038 | + | 0.572309i | \(0.193952\pi\) | |||||||
\(674\) | −1.00000 | −0.0385186 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | −31.1769 | + | 18.0000i | −1.19823 | + | 0.691796i | −0.960159 | − | 0.279453i | \(-0.909847\pi\) |
−0.238067 | + | 0.971249i | \(0.576514\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.00000 | − | 8.66025i | 0.191882 | − | 0.332350i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 10.3923 | − | 6.00000i | 0.397942 | − | 0.229752i | ||||
\(683\) | − | 9.00000i | − | 0.344375i | −0.985064 | − | 0.172188i | \(-0.944916\pi\) | ||
0.985064 | − | 0.172188i | \(-0.0550836\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −10.0000 | − | 17.3205i | −0.381802 | − | 0.661300i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.866025 | − | 0.500000i | −0.0330169 | − | 0.0190623i | ||||
\(689\) | −12.0000 | + | 20.7846i | −0.457164 | + | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.00000 | − | 6.92820i | −0.152167 | − | 0.263561i | 0.779857 | − | 0.625958i | \(-0.215292\pi\) |
−0.932024 | + | 0.362397i | \(0.881959\pi\) | |||||||
\(692\) | 6.00000i | 0.228086i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −33.0000 | −1.25266 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.3827 | + | 13.5000i | 0.885682 | + | 0.511349i | ||||
\(698\) | 13.8564 | + | 8.00000i | 0.524473 | + | 0.302804i | ||||
\(699\) | 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 | ||||||||
\(703\) | − | 4.00000i | − | 0.150863i | ||||||
\(704\) | 1.50000 | + | 2.59808i | 0.0565334 | + | 0.0979187i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.5000 | − | 18.1865i | 0.395173 | − | 0.684459i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.00000 | − | 3.46410i | −0.0751116 | − | 0.130097i | 0.826023 | − | 0.563636i | \(-0.190598\pi\) |
−0.901135 | + | 0.433539i | \(0.857265\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.00000i | 0.224860i | ||||||||
\(713\) | 20.7846 | − | 12.0000i | 0.778390 | − | 0.449404i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.00000 | − | 10.3923i | 0.224231 | − | 0.388379i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 15.5885 | − | 9.00000i | 0.581756 | − | 0.335877i | ||||
\(719\) | −36.0000 | −1.34257 | −0.671287 | − | 0.741198i | \(-0.734258\pi\) | ||||
−0.671287 | + | 0.741198i | \(0.734258\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28.0000 | 1.04277 | ||||||||
\(722\) | 15.5885 | − | 9.00000i | 0.580142 | − | 0.334945i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.00000 | − | 12.1244i | 0.260153 | − | 0.450598i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.5167 | − | 13.0000i | 0.835097 | − | 0.482143i | −0.0204978 | − | 0.999790i | \(-0.506525\pi\) |
0.855595 | + | 0.517647i | \(0.173192\pi\) | |||||||
\(728\) | 4.00000i | 0.148250i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.50000 | + | 2.59808i | 0.0554795 | + | 0.0960933i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.1244 | + | 7.00000i | 0.447823 | + | 0.258551i | 0.706910 | − | 0.707303i | \(-0.250088\pi\) |
−0.259087 | + | 0.965854i | \(0.583422\pi\) | |||||||
\(734\) | 14.0000 | − | 24.2487i | 0.516749 | − | 0.895036i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.00000 | + | 5.19615i | 0.110581 | + | 0.191533i | ||||
\(737\) | 15.0000i | 0.552532i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −47.0000 | −1.72892 | −0.864461 | − | 0.502699i | \(-0.832340\pi\) | ||||
−0.864461 | + | 0.502699i | \(0.832340\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −20.7846 | − | 12.0000i | −0.763027 | − | 0.440534i | ||||
\(743\) | −5.19615 | − | 3.00000i | −0.190628 | − | 0.110059i | 0.401648 | − | 0.915794i | \(-0.368437\pi\) |
−0.592277 | + | 0.805735i | \(0.701771\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 34.0000 | 1.24483 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 9.00000i | − | 0.329073i | ||||||
\(749\) | −3.00000 | − | 5.19615i | −0.109618 | − | 0.189863i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.00000 | + | 6.92820i | −0.145962 | + | 0.252814i | −0.929731 | − | 0.368238i | \(-0.879961\pi\) |
0.783769 | + | 0.621052i | \(0.213294\pi\) | |||||||
\(752\) | −5.19615 | − | 3.00000i | −0.189484 | − | 0.109399i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.00000 | + | 10.3923i | 0.218507 | + | 0.378465i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.00000i | 0.0726912i | 0.999339 | + | 0.0363456i | \(0.0115717\pi\) | ||||
−0.999339 | + | 0.0363456i | \(0.988428\pi\) | |||||||
\(758\) | 19.9186 | − | 11.5000i | 0.723476 | − | 0.417699i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.0000 | − | 36.3731i | 0.761249 | − | 1.31852i | −0.180957 | − | 0.983491i | \(-0.557920\pi\) |
0.942207 | − | 0.335032i | \(-0.108747\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 27.7128 | − | 16.0000i | 1.00327 | − | 0.579239i | ||||
\(764\) | −18.0000 | −0.651217 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.19615 | + | 3.00000i | −0.187622 | + | 0.108324i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.00000 | − | 1.73205i | 0.0360609 | − | 0.0624593i | −0.847432 | − | 0.530904i | \(-0.821852\pi\) |
0.883493 | + | 0.468445i | \(0.155186\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.33013 | − | 2.50000i | 0.155845 | − | 0.0899770i | ||||
\(773\) | 18.0000i | 0.647415i | 0.946157 | + | 0.323708i | \(0.104929\pi\) | ||||
−0.946157 | + | 0.323708i | \(0.895071\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.50000 | + | 4.33013i | 0.0897448 | + | 0.155443i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15.5885 | + | 9.00000i | 0.558873 | + | 0.322666i | ||||
\(779\) | 4.50000 | − | 7.79423i | 0.161229 | − | 0.279257i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.0000 | − | 31.1769i | −0.644091 | − | 1.11560i | ||||
\(782\) | − | 18.0000i | − | 0.643679i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.00000 | 0.107143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.46410 | + | 2.00000i | 0.123482 | + | 0.0712923i | 0.560469 | − | 0.828176i | \(-0.310621\pi\) |
−0.436987 | + | 0.899468i | \(0.643954\pi\) | |||||||
\(788\) | 10.3923 | + | 6.00000i | 0.370211 | + | 0.213741i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.0000 | −0.426671 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 16.0000i | − | 0.568177i | ||||||
\(794\) | −10.0000 | − | 17.3205i | −0.354887 | − | 0.614682i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.00000 | − | 8.66025i | 0.177220 | − | 0.306955i | ||||
\(797\) | −10.3923 | − | 6.00000i | −0.368114 | − | 0.212531i | 0.304520 | − | 0.952506i | \(-0.401504\pi\) |
−0.672634 | + | 0.739975i | \(0.734837\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.00000 | + | 15.5885i | 0.318397 | + | 0.551480i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 27.0000i | − | 0.953403i | ||||||
\(803\) | −28.5788 | + | 16.5000i | −1.00853 | + | 0.582272i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.00000 | + | 6.92820i | −0.140894 | + | 0.244036i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 33.0000 | 1.16022 | 0.580109 | − | 0.814539i | \(-0.303010\pi\) | ||||
0.580109 | + | 0.814539i | \(0.303010\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.00000 | −0.245803 | −0.122902 | − | 0.992419i | \(-0.539220\pi\) | ||||
−0.122902 | + | 0.992419i | \(0.539220\pi\) | |||||||
\(812\) | −10.3923 | + | 6.00000i | −0.364698 | + | 0.210559i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.00000 | − | 10.3923i | 0.210300 | − | 0.364250i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.866025 | − | 0.500000i | 0.0302984 | − | 0.0174928i | ||||
\(818\) | 17.0000i | 0.594391i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.00000 | − | 15.5885i | −0.314102 | − | 0.544041i | 0.665144 | − | 0.746715i | \(-0.268370\pi\) |
−0.979246 | + | 0.202674i | \(0.935037\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.8564 | − | 8.00000i | −0.483004 | − | 0.278862i | 0.238664 | − | 0.971102i | \(-0.423291\pi\) |
−0.721668 | + | 0.692240i | \(0.756624\pi\) | |||||||
\(824\) | −7.00000 | + | 12.1244i | −0.243857 | + | 0.422372i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.00000 | − | 5.19615i | −0.104383 | − | 0.180797i | ||||
\(827\) | 12.0000i | 0.417281i | 0.977992 | + | 0.208640i | \(0.0669038\pi\) | ||||
−0.977992 | + | 0.208640i | \(0.933096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.0000 | 0.347314 | 0.173657 | − | 0.984806i | \(-0.444442\pi\) | ||||
0.173657 | + | 0.984806i | \(0.444442\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.73205 | − | 1.00000i | −0.0600481 | − | 0.0346688i | ||||
\(833\) | −7.79423 | − | 4.50000i | −0.270054 | − | 0.155916i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.00000 | −0.103757 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 12.0000i | 0.414533i | ||||||||
\(839\) | −6.00000 | − | 10.3923i | −0.207143 | − | 0.358782i | 0.743670 | − | 0.668546i | \(-0.233083\pi\) |
−0.950813 | + | 0.309764i | \(0.899750\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | + | 6.06218i | −0.120690 | + | 0.209041i | ||||
\(842\) | 17.3205 | + | 10.0000i | 0.596904 | + | 0.344623i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10.0000 | + | 17.3205i | 0.344214 | + | 0.596196i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 4.00000i | − | 0.137442i | ||||||
\(848\) | 10.3923 | − | 6.00000i | 0.356873 | − | 0.206041i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.0000 | − | 20.7846i | 0.411355 | − | 0.712487i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.5167 | + | 13.0000i | −0.770956 | + | 0.445112i | −0.833215 | − | 0.552948i | \(-0.813503\pi\) |
0.0622597 | + | 0.998060i | \(0.480169\pi\) | |||||||
\(854\) | 16.0000 | 0.547509 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.00000 | 0.102538 | ||||||||
\(857\) | 36.3731 | − | 21.0000i | 1.24248 | − | 0.717346i | 0.272882 | − | 0.962048i | \(-0.412023\pi\) |
0.969599 | + | 0.244701i | \(0.0786899\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.5000 | − | 30.3109i | 0.597092 | − | 1.03419i | −0.396156 | − | 0.918183i | \(-0.629656\pi\) |
0.993248 | − | 0.116011i | \(-0.0370107\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −25.9808 | + | 15.0000i | −0.884908 | + | 0.510902i | ||||
\(863\) | 24.0000i | 0.816970i | 0.912765 | + | 0.408485i | \(0.133943\pi\) | ||||
−0.912765 | + | 0.408485i | \(0.866057\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3.50000 | − | 6.06218i | −0.118935 | − | 0.206001i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.92820 | − | 4.00000i | −0.235159 | − | 0.135769i | ||||
\(869\) | −6.00000 | + | 10.3923i | −0.203536 | + | 0.352535i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.00000 | − | 8.66025i | −0.169419 | − | 0.293442i | ||||
\(872\) | 16.0000i | 0.541828i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.00000 | −0.202953 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.92820 | − | 4.00000i | −0.233949 | − | 0.135070i | 0.378444 | − | 0.925624i | \(-0.376459\pi\) |
−0.612392 | + | 0.790554i | \(0.709793\pi\) | |||||||
\(878\) | −6.92820 | − | 4.00000i | −0.233816 | − | 0.134993i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.0000 | 1.41502 | 0.707508 | − | 0.706705i | \(-0.249819\pi\) | ||||
0.707508 | + | 0.706705i | \(0.249819\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.0000i | 0.639401i | 0.947519 | + | 0.319700i | \(0.103582\pi\) | ||||
−0.947519 | + | 0.319700i | \(0.896418\pi\) | |||||||
\(884\) | 3.00000 | + | 5.19615i | 0.100901 | + | 0.174766i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.50000 | + | 2.59808i | −0.0503935 | + | 0.0872841i | ||||
\(887\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.00000 | + | 3.46410i | 0.0670778 | + | 0.116182i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 26.0000i | 0.870544i | ||||||||
\(893\) | 5.19615 | − | 3.00000i | 0.173883 | − | 0.100391i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.00000 | − | 1.73205i | 0.0334077 | − | 0.0578638i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.79423 | + | 4.50000i | −0.260097 | + | 0.150167i | ||||
\(899\) | −24.0000 | −0.800445 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.0000 | −1.19933 | ||||||||
\(902\) | 23.3827 | − | 13.5000i | 0.778558 | − | 0.449501i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.00000 | − | 5.19615i | 0.0997785 | − | 0.172821i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.8468 | + | 15.5000i | −0.891433 | + | 0.514669i | −0.874411 | − | 0.485186i | \(-0.838752\pi\) |
−0.0170220 | + | 0.999855i | \(0.505419\pi\) | |||||||
\(908\) | 21.0000i | 0.696909i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.0000 | + | 41.5692i | 0.795155 | + | 1.37725i | 0.922740 | + | 0.385422i | \(0.125944\pi\) |
−0.127585 | + | 0.991828i | \(0.540723\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −31.1769 | − | 18.0000i | −1.03181 | − | 0.595713i | ||||
\(914\) | −8.50000 | + | 14.7224i | −0.281155 | + | 0.486975i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.00000 | − | 12.1244i | −0.231287 | − | 0.400600i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.0000 | −1.25350 | −0.626752 | − | 0.779219i | \(-0.715616\pi\) | ||||
−0.626752 | + | 0.779219i | \(0.715616\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 25.9808 | + | 15.0000i | 0.855631 | + | 0.493999i | ||||
\(923\) | 20.7846 | + | 12.0000i | 0.684134 | + | 0.394985i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −20.0000 | −0.657241 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 6.00000i | − | 0.196960i | ||||||
\(929\) | 3.00000 | + | 5.19615i | 0.0984268 | + | 0.170480i | 0.911034 | − | 0.412332i | \(-0.135286\pi\) |
−0.812607 | + | 0.582812i | \(0.801952\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.50000 | + | 2.59808i | −0.0491605 | + | 0.0851485i | ||||
\(932\) | 2.59808 | + | 1.50000i | 0.0851028 | + | 0.0491341i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.50000 | − | 12.9904i | −0.245407 | − | 0.425058i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.0000i | 0.457360i | 0.973502 | + | 0.228680i | \(0.0734410\pi\) | ||||
−0.973502 | + | 0.228680i | \(0.926559\pi\) | |||||||
\(938\) | 8.66025 | − | 5.00000i | 0.282767 | − | 0.163256i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.0000 | + | 51.9615i | −0.977972 | + | 1.69390i | −0.308215 | + | 0.951317i | \(0.599732\pi\) |
−0.669757 | + | 0.742581i | \(0.733602\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 46.7654 | − | 27.0000i | 1.52289 | − | 0.879241i | ||||
\(944\) | 3.00000 | 0.0976417 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.00000 | 0.0975384 | ||||||||
\(947\) | −2.59808 | + | 1.50000i | −0.0844261 | + | 0.0487435i | −0.541619 | − | 0.840624i | \(-0.682188\pi\) |
0.457193 | + | 0.889368i | \(0.348855\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.0000 | − | 19.0526i | 0.357075 | − | 0.618472i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.19615 | + | 3.00000i | −0.168408 | + | 0.0972306i | ||||
\(953\) | 9.00000i | 0.291539i | 0.989319 | + | 0.145769i | \(0.0465657\pi\) | ||||
−0.989319 | + | 0.145769i | \(0.953434\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.00000 | + | 5.19615i | 0.0970269 | + | 0.168056i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −36.3731 | − | 21.0000i | −1.17516 | − | 0.678479i | ||||
\(959\) | 3.00000 | − | 5.19615i | 0.0968751 | − | 0.167793i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | + | 12.9904i | 0.241935 | + | 0.419045i | ||||
\(962\) | 8.00000i | 0.257930i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 7.00000 | 0.225455 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.0526 | + | 11.0000i | 0.612689 | + | 0.353736i | 0.774017 | − | 0.633165i | \(-0.218244\pi\) |
−0.161328 | + | 0.986901i | \(0.551578\pi\) | |||||||
\(968\) | 1.73205 | + | 1.00000i | 0.0556702 | + | 0.0321412i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.0000 | 1.15529 | 0.577647 | − | 0.816286i | \(-0.303971\pi\) | ||||
0.577647 | + | 0.816286i | \(0.303971\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 38.0000i | 1.21822i | ||||||||
\(974\) | −13.0000 | − | 22.5167i | −0.416547 | − | 0.721480i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.00000 | + | 6.92820i | −0.128037 | + | 0.221766i | ||||
\(977\) | −44.1673 | − | 25.5000i | −1.41304 | − | 0.815817i | −0.417364 | − | 0.908740i | \(-0.637046\pi\) |
−0.995673 | + | 0.0929223i | \(0.970379\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.00000 | − | 15.5885i | −0.287641 | − | 0.498209i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 15.0000i | − | 0.478669i | ||||||
\(983\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −9.00000 | + | 15.5885i | −0.286618 | + | 0.496438i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.73205 | − | 1.00000i | 0.0551039 | − | 0.0318142i | ||||
\(989\) | 6.00000 | 0.190789 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.0000 | −0.508257 | −0.254128 | − | 0.967170i | \(-0.581789\pi\) | ||||
−0.254128 | + | 0.967170i | \(0.581789\pi\) | |||||||
\(992\) | 3.46410 | − | 2.00000i | 0.109985 | − | 0.0635001i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −12.0000 | + | 20.7846i | −0.380617 | + | 0.659248i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.2487 | + | 14.0000i | −0.767964 | + | 0.443384i | −0.832148 | − | 0.554554i | \(-0.812889\pi\) |
0.0641836 | + | 0.997938i | \(0.479556\pi\) | |||||||
\(998\) | − | 13.0000i | − | 0.411508i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))