Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,2,Mod(541,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1620.541");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.9357651274\) |
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 540) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1081.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.1081 |
Dual form | 1620.2.i.i.541.1 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | − | 1.73205i | −0.377964 | − | 0.654654i | 0.612801 | − | 0.790237i | \(-0.290043\pi\) |
−0.990766 | + | 0.135583i | \(0.956709\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | + | 1.73205i | −0.277350 | + | 0.480384i | −0.970725 | − | 0.240192i | \(-0.922790\pi\) |
0.693375 | + | 0.720577i | \(0.256123\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.00000 | 0.727607 | 0.363803 | − | 0.931476i | \(-0.381478\pi\) | ||||
0.363803 | + | 0.931476i | \(0.381478\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.00000 | 1.14708 | 0.573539 | − | 0.819178i | \(-0.305570\pi\) | ||||
0.573539 | + | 0.819178i | \(0.305570\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.50000 | − | 2.59808i | 0.312772 | − | 0.541736i | −0.666190 | − | 0.745782i | \(-0.732076\pi\) |
0.978961 | + | 0.204046i | \(0.0654092\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −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 | ||||||||
\(31\) | −2.50000 | + | 4.33013i | −0.449013 | + | 0.777714i | −0.998322 | − | 0.0579057i | \(-0.981558\pi\) |
0.549309 | + | 0.835619i | \(0.314891\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00000 | −0.338062 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | − | 10.3923i | 0.937043 | − | 1.62301i | 0.166092 | − | 0.986110i | \(-0.446885\pi\) |
0.770950 | − | 0.636895i | \(-0.219782\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | − | 6.92820i | −0.609994 | − | 1.05654i | −0.991241 | − | 0.132068i | \(-0.957838\pi\) |
0.381246 | − | 0.924473i | \(-0.375495\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.00000 | − | 10.3923i | −0.875190 | − | 1.51587i | −0.856560 | − | 0.516047i | \(-0.827403\pi\) |
−0.0186297 | − | 0.999826i | \(-0.505930\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.50000 | − | 2.59808i | 0.214286 | − | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.00000 | 0.412082 | 0.206041 | − | 0.978543i | \(-0.433942\pi\) | ||||
0.206041 | + | 0.978543i | \(0.433942\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.00000 | − | 5.19615i | 0.390567 | − | 0.676481i | −0.601958 | − | 0.798528i | \(-0.705612\pi\) |
0.992524 | + | 0.122047i | \(0.0389457\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.50000 | + | 6.06218i | 0.448129 | + | 0.776182i | 0.998264 | − | 0.0588933i | \(-0.0187572\pi\) |
−0.550135 | + | 0.835076i | \(0.685424\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00000 | + | 1.73205i | 0.124035 | + | 0.214834i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | + | 1.73205i | −0.122169 | + | 0.211604i | −0.920623 | − | 0.390453i | \(-0.872318\pi\) |
0.798454 | + | 0.602056i | \(0.205652\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.0000 | −1.42414 | −0.712069 | − | 0.702109i | \(-0.752242\pi\) | ||||
−0.712069 | + | 0.702109i | \(0.752242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −16.0000 | −1.87266 | −0.936329 | − | 0.351123i | \(-0.885800\pi\) | ||||
−0.936329 | + | 0.351123i | \(0.885800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.500000 | + | 0.866025i | 0.0562544 | + | 0.0974355i | 0.892781 | − | 0.450490i | \(-0.148751\pi\) |
−0.836527 | + | 0.547926i | \(0.815418\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.50000 | − | 12.9904i | −0.823232 | − | 1.42588i | −0.903263 | − | 0.429087i | \(-0.858835\pi\) |
0.0800311 | − | 0.996792i | \(-0.474498\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.50000 | − | 2.59808i | 0.162698 | − | 0.281801i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.0000 | 1.27200 | 0.635999 | − | 0.771690i | \(-0.280588\pi\) | ||||
0.635999 | + | 0.771690i | \(0.280588\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000 | 0.419314 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.50000 | − | 4.33013i | 0.256495 | − | 0.444262i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.00000 | + | 13.8564i | 0.812277 | + | 1.40690i | 0.911267 | + | 0.411816i | \(0.135106\pi\) |
−0.0989899 | + | 0.995088i | \(0.531561\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | + | 10.3923i | 0.597022 | + | 1.03407i | 0.993258 | + | 0.115924i | \(0.0369830\pi\) |
−0.396236 | + | 0.918149i | \(0.629684\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.00000 | − | 3.46410i | 0.197066 | − | 0.341328i | −0.750510 | − | 0.660859i | \(-0.770192\pi\) |
0.947576 | + | 0.319531i | \(0.103525\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.0000 | 1.16008 | 0.580042 | − | 0.814587i | \(-0.303036\pi\) | ||||
0.580042 | + | 0.814587i | \(0.303036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.00000 | −0.670478 | −0.335239 | − | 0.942133i | \(-0.608817\pi\) | ||||
−0.335239 | + | 0.942133i | \(0.608817\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.00000 | − | 5.19615i | 0.282216 | − | 0.488813i | −0.689714 | − | 0.724082i | \(-0.742264\pi\) |
0.971930 | + | 0.235269i | \(0.0755971\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.50000 | − | 2.59808i | −0.139876 | − | 0.242272i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.00000 | − | 5.19615i | −0.275010 | − | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.50000 | − | 9.52628i | 0.500000 | − | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.00000 | 0.177471 | 0.0887357 | − | 0.996055i | \(-0.471717\pi\) | ||||
0.0887357 | + | 0.996055i | \(0.471717\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.00000 | − | 15.5885i | 0.786334 | − | 1.36197i | −0.141865 | − | 0.989886i | \(-0.545310\pi\) |
0.928199 | − | 0.372084i | \(-0.121357\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.00000 | − | 8.66025i | −0.433555 | − | 0.750939i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.50000 | − | 7.79423i | −0.384461 | − | 0.665906i | 0.607233 | − | 0.794524i | \(-0.292279\pi\) |
−0.991694 | + | 0.128618i | \(0.958946\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.00000 | − | 3.46410i | 0.169638 | − | 0.293821i | −0.768655 | − | 0.639664i | \(-0.779074\pi\) |
0.938293 | + | 0.345843i | \(0.112407\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.00000 | −0.498273 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.00000 | + | 10.3923i | −0.491539 | + | 0.851371i | −0.999953 | − | 0.00974235i | \(-0.996899\pi\) |
0.508413 | + | 0.861113i | \(0.330232\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | + | 13.8564i | 0.651031 | + | 1.12762i | 0.982873 | + | 0.184284i | \(0.0589965\pi\) |
−0.331842 | + | 0.943335i | \(0.607670\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.50000 | + | 4.33013i | 0.200805 | + | 0.347804i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.00000 | − | 3.46410i | 0.159617 | − | 0.276465i | −0.775113 | − | 0.631822i | \(-0.782307\pi\) |
0.934731 | + | 0.355357i | \(0.115641\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.00000 | −0.472866 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.0000 | −0.783260 | −0.391630 | − | 0.920123i | \(-0.628089\pi\) | ||||
−0.391630 | + | 0.920123i | \(0.628089\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.50000 | + | 7.79423i | −0.348220 | + | 0.603136i | −0.985933 | − | 0.167139i | \(-0.946547\pi\) |
0.637713 | + | 0.770274i | \(0.279881\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.50000 | + | 7.79423i | 0.346154 | + | 0.599556i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.50000 | + | 12.9904i | 0.570214 | + | 0.987640i | 0.996544 | + | 0.0830722i | \(0.0264732\pi\) |
−0.426329 | + | 0.904568i | \(0.640193\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | + | 1.73205i | −0.0755929 | + | 0.130931i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.0000 | 1.26360 | 0.631800 | − | 0.775131i | \(-0.282316\pi\) | ||||
0.631800 | + | 0.775131i | \(0.282316\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.00000 | − | 1.73205i | 0.0735215 | − | 0.127343i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.00000 | − | 5.19615i | −0.217072 | − | 0.375980i | 0.736839 | − | 0.676068i | \(-0.236317\pi\) |
−0.953912 | + | 0.300088i | \(0.902984\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.00000 | − | 8.66025i | 0.359908 | − | 0.623379i | −0.628037 | − | 0.778183i | \(-0.716141\pi\) |
0.987945 | + | 0.154805i | \(0.0494748\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.00000 | 0.641223 | 0.320612 | − | 0.947211i | \(-0.396112\pi\) | ||||
0.320612 | + | 0.947211i | \(0.396112\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000 | 0.567105 | 0.283552 | − | 0.958957i | \(-0.408487\pi\) | ||||
0.283552 | + | 0.958957i | \(0.408487\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.00000 | + | 10.3923i | −0.421117 | + | 0.729397i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.00000 | − | 10.3923i | −0.419058 | − | 0.725830i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.50000 | + | 9.52628i | −0.378636 | + | 0.655816i | −0.990864 | − | 0.134865i | \(-0.956940\pi\) |
0.612228 | + | 0.790681i | \(0.290273\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.00000 | −0.545595 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.0000 | 0.678844 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.00000 | + | 5.19615i | −0.201802 | + | 0.349531i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.0000 | − | 22.5167i | −0.870544 | − | 1.50783i | −0.861435 | − | 0.507869i | \(-0.830434\pi\) |
−0.00910984 | − | 0.999959i | \(-0.502900\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.50000 | − | 2.59808i | −0.0995585 | − | 0.172440i | 0.811943 | − | 0.583736i | \(-0.198410\pi\) |
−0.911502 | + | 0.411296i | \(0.865076\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.5000 | + | 19.9186i | −0.759941 | + | 1.31626i | 0.182939 | + | 0.983124i | \(0.441439\pi\) |
−0.942880 | + | 0.333133i | \(0.891894\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.00000 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.0000 | −0.782794 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.00000 | − | 5.19615i | 0.194054 | − | 0.336111i | −0.752536 | − | 0.658551i | \(-0.771170\pi\) |
0.946590 | + | 0.322440i | \(0.104503\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.50000 | + | 11.2583i | 0.418702 | + | 0.725213i | 0.995809 | − | 0.0914555i | \(-0.0291519\pi\) |
−0.577107 | + | 0.816668i | \(0.695819\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.50000 | − | 2.59808i | −0.0958315 | − | 0.165985i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.00000 | + | 8.66025i | −0.318142 | + | 0.551039i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.5000 | + | 18.1865i | −0.654972 | + | 1.13444i | 0.326929 | + | 0.945049i | \(0.393986\pi\) |
−0.981901 | + | 0.189396i | \(0.939347\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.00000 | − | 3.46410i | −0.124274 | − | 0.215249i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.50000 | − | 2.59808i | 0.0921443 | − | 0.159599i | ||||
\(266\) | 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 | ||||||||
\(271\) | 29.0000 | 1.76162 | 0.880812 | − | 0.473466i | \(-0.156997\pi\) | ||||
0.880812 | + | 0.473466i | \(0.156997\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.00000 | − | 6.92820i | −0.240337 | − | 0.416275i | 0.720473 | − | 0.693482i | \(-0.243925\pi\) |
−0.960810 | + | 0.277207i | \(0.910591\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.0000 | + | 25.9808i | 0.894825 | + | 1.54988i | 0.834021 | + | 0.551733i | \(0.186033\pi\) |
0.0608039 | + | 0.998150i | \(0.480634\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.00000 | − | 3.46410i | 0.118888 | − | 0.205919i | −0.800439 | − | 0.599414i | \(-0.795400\pi\) |
0.919327 | + | 0.393494i | \(0.128734\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −24.0000 | −1.41668 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.50000 | − | 2.59808i | 0.0876309 | − | 0.151781i | −0.818878 | − | 0.573967i | \(-0.805404\pi\) |
0.906509 | + | 0.422186i | \(0.138737\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.00000 | − | 5.19615i | −0.174667 | − | 0.302532i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.00000 | + | 5.19615i | 0.173494 | + | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.00000 | + | 13.8564i | −0.461112 | + | 0.798670i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.00000 | 0.400819 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.00000 | 0.114146 | 0.0570730 | − | 0.998370i | \(-0.481823\pi\) | ||||
0.0570730 | + | 0.998370i | \(0.481823\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.0000 | + | 25.9808i | −0.850572 | + | 1.47323i | 0.0301210 | + | 0.999546i | \(0.490411\pi\) |
−0.880693 | + | 0.473688i | \(0.842923\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.0000 | − | 27.7128i | −0.904373 | − | 1.56642i | −0.821756 | − | 0.569839i | \(-0.807005\pi\) |
−0.0826174 | − | 0.996581i | \(-0.526328\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.5000 | + | 28.5788i | 0.926732 | + | 1.60515i | 0.788751 | + | 0.614713i | \(0.210728\pi\) |
0.137981 | + | 0.990435i | \(0.455939\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.0000 | 0.834622 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.00000 | 0.110940 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.0000 | + | 20.7846i | −0.661581 | + | 1.14589i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.0000 | + | 24.2487i | 0.769510 | + | 1.33283i | 0.937829 | + | 0.347097i | \(0.112833\pi\) |
−0.168320 | + | 0.985732i | \(0.553834\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.00000 | + | 1.73205i | 0.0546358 | + | 0.0946320i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.00000 | + | 1.73205i | −0.0544735 | + | 0.0943508i | −0.891976 | − | 0.452082i | \(-0.850681\pi\) |
0.837503 | + | 0.546433i | \(0.184015\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.00000 | − | 10.3923i | 0.322097 | − | 0.557888i | −0.658824 | − | 0.752297i | \(-0.728946\pi\) |
0.980921 | + | 0.194409i | \(0.0622790\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.50000 | − | 14.7224i | −0.454995 | − | 0.788074i | 0.543693 | − | 0.839284i | \(-0.317025\pi\) |
−0.998688 | + | 0.0512103i | \(0.983692\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.00000 | + | 15.5885i | 0.479022 | + | 0.829690i | 0.999711 | − | 0.0240566i | \(-0.00765819\pi\) |
−0.520689 | + | 0.853746i | \(0.674325\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.00000 | + | 10.3923i | −0.318447 | + | 0.551566i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.0000 | −1.58334 | −0.791670 | − | 0.610949i | \(-0.790788\pi\) | ||||
−0.791670 | + | 0.610949i | \(0.790788\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.00000 | 0.315789 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.00000 | + | 13.8564i | −0.418739 | + | 0.725277i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.0000 | + | 19.0526i | 0.574195 | + | 0.994535i | 0.996129 | + | 0.0879086i | \(0.0280183\pi\) |
−0.421933 | + | 0.906627i | \(0.638648\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.00000 | − | 5.19615i | −0.155752 | − | 0.269771i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.00000 | + | 6.92820i | −0.207112 | + | 0.358729i | −0.950804 | − | 0.309794i | \(-0.899740\pi\) |
0.743691 | + | 0.668523i | \(0.233073\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0000 | 0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.00000 | −0.0513665 | −0.0256833 | − | 0.999670i | \(-0.508176\pi\) | ||||
−0.0256833 | + | 0.999670i | \(0.508176\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.5000 | + | 28.5788i | −0.843111 | + | 1.46031i | 0.0441413 | + | 0.999025i | \(0.485945\pi\) |
−0.887252 | + | 0.461285i | \(0.847389\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.0000 | + | 20.7846i | 0.608424 | + | 1.05382i | 0.991500 | + | 0.130105i | \(0.0415314\pi\) |
−0.383076 | + | 0.923717i | \(0.625135\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.50000 | − | 7.79423i | 0.227575 | − | 0.394171i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.00000 | 0.0503155 | ||||||||
\(396\) | 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 | ||||||||
\(401\) | −3.00000 | + | 5.19615i | −0.149813 | + | 0.259483i | −0.931158 | − | 0.364615i | \(-0.881200\pi\) |
0.781345 | + | 0.624099i | \(0.214534\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.00000 | − | 8.66025i | −0.249068 | − | 0.431398i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.50000 | − | 6.06218i | 0.173064 | − | 0.299755i | −0.766426 | − | 0.642333i | \(-0.777967\pi\) |
0.939490 | + | 0.342578i | \(0.111300\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.0000 | −0.590481 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.0000 | −0.736321 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.500000 | + | 0.866025i | 0.0243685 | + | 0.0422075i | 0.877952 | − | 0.478748i | \(-0.158909\pi\) |
−0.853584 | + | 0.520955i | \(0.825576\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.50000 | − | 2.59808i | −0.0727607 | − | 0.126025i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.00000 | − | 12.1244i | 0.338754 | − | 0.586739i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.0000 | 0.867029 | 0.433515 | − | 0.901146i | \(-0.357273\pi\) | ||||
0.433515 | + | 0.901146i | \(0.357273\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.0000 | −1.63394 | −0.816968 | − | 0.576683i | \(-0.804347\pi\) | ||||
−0.816968 | + | 0.576683i | \(0.804347\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.50000 | − | 12.9904i | 0.358774 | − | 0.621414i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.50000 | + | 16.4545i | 0.453410 | + | 0.785330i | 0.998595 | − | 0.0529862i | \(-0.0168739\pi\) |
−0.545185 | + | 0.838316i | \(0.683541\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.50000 | − | 12.9904i | −0.356336 | − | 0.617192i | 0.631010 | − | 0.775775i | \(-0.282641\pi\) |
−0.987346 | + | 0.158583i | \(0.949307\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.00000 | − | 10.3923i | 0.284427 | − | 0.492642i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.00000 | 0.283158 | 0.141579 | − | 0.989927i | \(-0.454782\pi\) | ||||
0.141579 | + | 0.989927i | \(0.454782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.00000 | − | 3.46410i | 0.0937614 | − | 0.162400i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.0000 | + | 24.2487i | 0.654892 | + | 1.13431i | 0.981921 | + | 0.189292i | \(0.0606194\pi\) |
−0.327028 | + | 0.945015i | \(0.606047\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 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 | ||||||||
\(463\) | 11.0000 | − | 19.0526i | 0.511213 | − | 0.885448i | −0.488702 | − | 0.872451i | \(-0.662530\pi\) |
0.999916 | − | 0.0129968i | \(-0.00413714\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.0000 | −0.971764 | −0.485882 | − | 0.874024i | \(-0.661502\pi\) | ||||
−0.485882 | + | 0.874024i | \(0.661502\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.00000 | 0.184703 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.50000 | − | 4.33013i | −0.114708 | − | 0.198680i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.0000 | + | 20.7846i | 0.548294 | + | 0.949673i | 0.998392 | + | 0.0566937i | \(0.0180558\pi\) |
−0.450098 | + | 0.892979i | \(0.648611\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.00000 | + | 3.46410i | −0.0911922 | + | 0.157949i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.0000 | 0.726523 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −28.0000 | −1.26880 | −0.634401 | − | 0.773004i | \(-0.718753\pi\) | ||||
−0.634401 | + | 0.773004i | \(0.718753\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.00000 | + | 15.5885i | −0.406164 | + | 0.703497i | −0.994456 | − | 0.105151i | \(-0.966467\pi\) |
0.588292 | + | 0.808649i | \(0.299801\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.00000 | − | 15.5885i | −0.405340 | − | 0.702069i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.0000 | + | 20.7846i | 0.538274 | + | 0.932317i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.5000 | − | 26.8468i | 0.693875 | − | 1.20183i | −0.276683 | − | 0.960961i | \(-0.589235\pi\) |
0.970558 | − | 0.240866i | \(-0.0774314\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.0000 | −1.20387 | −0.601935 | − | 0.798545i | \(-0.705603\pi\) | ||||
−0.601935 | + | 0.798545i | \(0.705603\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.0000 | 0.533993 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.00000 | − | 10.3923i | 0.265945 | − | 0.460631i | −0.701866 | − | 0.712309i | \(-0.747649\pi\) |
0.967811 | + | 0.251679i | \(0.0809826\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.0000 | + | 27.7128i | 0.707798 | + | 1.22594i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.00000 | − | 3.46410i | −0.0881305 | − | 0.152647i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.0000 | 0.525730 | 0.262865 | − | 0.964833i | \(-0.415333\pi\) | ||||
0.262865 | + | 0.964833i | \(0.415333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.0000 | −0.961993 | −0.480996 | − | 0.876723i | \(-0.659725\pi\) | ||||
−0.480996 | + | 0.876723i | \(0.659725\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.50000 | + | 12.9904i | −0.326705 | + | 0.565870i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | + | 12.1244i | 0.304348 | + | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.0000 | + | 20.7846i | 0.519778 | + | 0.900281i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.00000 | − | 10.3923i | 0.259403 | − | 0.449299i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.0000 | 0.601907 | 0.300954 | − | 0.953639i | \(-0.402695\pi\) | ||||
0.300954 | + | 0.953639i | \(0.402695\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.50000 | + | 6.06218i | −0.149924 | + | 0.259675i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.00000 | − | 6.92820i | −0.171028 | − | 0.296229i | 0.767752 | − | 0.640747i | \(-0.221375\pi\) |
−0.938779 | + | 0.344519i | \(0.888042\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.0000 | − | 25.9808i | −0.639021 | − | 1.10682i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.00000 | − | 1.73205i | 0.0425243 | − | 0.0736543i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −30.0000 | −1.27114 | −0.635570 | − | 0.772043i | \(-0.719235\pi\) | ||||
−0.635570 | + | 0.772043i | \(0.719235\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.0000 | 0.676728 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.0000 | − | 31.1769i | 0.758610 | − | 1.31395i | −0.184950 | − | 0.982748i | \(-0.559212\pi\) |
0.943560 | − | 0.331202i | \(-0.107454\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.00000 | − | 5.19615i | −0.126211 | − | 0.218604i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.0000 | − | 25.9808i | −0.628833 | − | 1.08917i | −0.987786 | − | 0.155815i | \(-0.950200\pi\) |
0.358954 | − | 0.933355i | \(-0.383134\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.50000 | − | 16.4545i | 0.397563 | − | 0.688599i | −0.595862 | − | 0.803087i | \(-0.703189\pi\) |
0.993425 | + | 0.114488i | \(0.0365228\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.00000 | −0.125109 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.00000 | −0.166522 | −0.0832611 | − | 0.996528i | \(-0.526534\pi\) | ||||
−0.0832611 | + | 0.996528i | \(0.526534\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.0000 | + | 25.9808i | −0.622305 | + | 1.07786i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.50000 | + | 12.9904i | 0.309558 | + | 0.536170i | 0.978266 | − | 0.207355i | \(-0.0664855\pi\) |
−0.668708 | + | 0.743525i | \(0.733152\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.5000 | + | 21.6506i | −0.515054 | + | 0.892099i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.00000 | 0.369586 | 0.184793 | − | 0.982777i | \(-0.440839\pi\) | ||||
0.184793 | + | 0.982777i | \(0.440839\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.00000 | −0.245976 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.00000 | − | 15.5885i | 0.367730 | − | 0.636927i | −0.621480 | − | 0.783430i | \(-0.713468\pi\) |
0.989210 | + | 0.146503i | \(0.0468017\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.50000 | + | 16.4545i | 0.387513 | + | 0.671192i | 0.992114 | − | 0.125336i | \(-0.0400009\pi\) |
−0.604601 | + | 0.796528i | \(0.706668\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.50000 | − | 9.52628i | −0.223607 | − | 0.387298i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.0000 | + | 27.7128i | −0.649420 | + | 1.12483i | 0.333842 | + | 0.942629i | \(0.391655\pi\) |
−0.983262 | + | 0.182199i | \(0.941678\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.0000 | 0.970936 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.0000 | −0.646234 | −0.323117 | − | 0.946359i | \(-0.604731\pi\) | ||||
−0.323117 | + | 0.946359i | \(0.604731\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.5000 | − | 28.5788i | 0.664265 | − | 1.15054i | −0.315219 | − | 0.949019i | \(-0.602078\pi\) |
0.979484 | − | 0.201522i | \(-0.0645887\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.00000 | + | 13.8564i | 0.321547 | + | 0.556936i | 0.980807 | − | 0.194979i | \(-0.0624638\pi\) |
−0.659260 | + | 0.751915i | \(0.729130\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.0000 | − | 20.7846i | −0.480770 | − | 0.832718i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.00000 | 0.239236 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.00000 | −0.0398094 | −0.0199047 | − | 0.999802i | \(-0.506336\pi\) | ||||
−0.0199047 | + | 0.999802i | \(0.506336\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.00000 | − | 1.73205i | 0.0396838 | − | 0.0687343i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.00000 | + | 5.19615i | 0.118864 | + | 0.205879i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.00000 | + | 12.1244i | −0.276053 | + | 0.478138i | −0.970400 | − | 0.241502i | \(-0.922360\pi\) |
0.694347 | + | 0.719640i | \(0.255693\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.00000 | −0.117942 | −0.0589711 | − | 0.998260i | \(-0.518782\pi\) | ||||
−0.0589711 | + | 0.998260i | \(0.518782\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.5000 | − | 18.1865i | 0.410897 | − | 0.711694i | −0.584091 | − | 0.811688i | \(-0.698549\pi\) |
0.994988 | + | 0.0999939i | \(0.0318823\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.00000 | − | 15.5885i | −0.351659 | − | 0.609091i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.00000 | + | 15.5885i | 0.350590 | + | 0.607240i | 0.986353 | − | 0.164644i | \(-0.0526477\pi\) |
−0.635763 | + | 0.771885i | \(0.719314\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.00000 | + | 12.1244i | −0.272268 | + | 0.471583i | −0.969442 | − | 0.245319i | \(-0.921107\pi\) |
0.697174 | + | 0.716902i | \(0.254441\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.0000 | −0.387783 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.0000 | −0.696963 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.0000 | − | 22.5167i | −0.501113 | − | 0.867953i | −0.999999 | − | 0.00128586i | \(-0.999591\pi\) |
0.498886 | − | 0.866668i | \(-0.333743\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.00000 | − | 15.5885i | −0.345898 | − | 0.599113i | 0.639618 | − | 0.768693i | \(-0.279092\pi\) |
−0.985517 | + | 0.169580i | \(0.945759\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.0000 | − | 27.7128i | 0.614024 | − | 1.06352i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 39.0000 | 1.49229 | 0.746147 | − | 0.665782i | \(-0.231902\pi\) | ||||
0.746147 | + | 0.665782i | \(0.231902\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.00000 | −0.343872 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.00000 | + | 5.19615i | −0.114291 | + | 0.197958i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.5000 | − | 30.3109i | −0.665731 | − | 1.15308i | −0.979086 | − | 0.203445i | \(-0.934786\pi\) |
0.313355 | − | 0.949636i | \(-0.398547\pi\) | |||||||
\(692\) | 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 | ||||||||
\(701\) | 42.0000 | 1.58632 | 0.793159 | − | 0.609015i | \(-0.208435\pi\) | ||||
0.793159 | + | 0.609015i | \(0.208435\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.0000 | 0.377157 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.0000 | − | 20.7846i | 0.451306 | − | 0.781686i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.00000 | − | 1.73205i | −0.0375558 | − | 0.0650485i | 0.846637 | − | 0.532172i | \(-0.178624\pi\) |
−0.884192 | + | 0.467123i | \(0.845291\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.50000 | + | 12.9904i | 0.280877 | + | 0.486494i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −42.0000 | −1.56634 | −0.783168 | − | 0.621810i | \(-0.786397\pi\) | ||||
−0.783168 | + | 0.621810i | \(0.786397\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.00000 | −0.297936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.00000 | + | 5.19615i | −0.111417 | + | 0.192980i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.00000 | − | 6.92820i | −0.148352 | − | 0.256953i | 0.782267 | − | 0.622944i | \(-0.214063\pi\) |
−0.930618 | + | 0.365991i | \(0.880730\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.0000 | − | 20.7846i | −0.443836 | − | 0.768747i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.0000 | + | 27.7128i | −0.590973 | + | 1.02360i | 0.403128 | + | 0.915144i | \(0.367923\pi\) |
−0.994102 | + | 0.108453i | \(0.965410\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 47.0000 | 1.72892 | 0.864461 | − | 0.502699i | \(-0.167660\pi\) | ||||
0.864461 | + | 0.502699i | \(0.167660\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.0000 | + | 20.7846i | −0.440237 | + | 0.762513i | −0.997707 | − | 0.0676840i | \(-0.978439\pi\) |
0.557470 | + | 0.830197i | \(0.311772\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.00000 | + | 10.3923i | 0.219823 | + | 0.380745i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.0000 | − | 20.7846i | −0.438470 | − | 0.759453i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.5000 | + | 19.9186i | −0.419641 | + | 0.726839i | −0.995903 | − | 0.0904254i | \(-0.971177\pi\) |
0.576262 | + | 0.817265i | \(0.304511\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.0000 | 0.582300 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 50.0000 | 1.81728 | 0.908640 | − | 0.417579i | \(-0.137121\pi\) | ||||
0.908640 | + | 0.417579i | \(0.137121\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.0000 | − | 25.9808i | 0.543750 | − | 0.941802i | −0.454935 | − | 0.890525i | \(-0.650337\pi\) |
0.998684 | − | 0.0512772i | \(-0.0163292\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.00000 | + | 12.1244i | 0.253417 | + | 0.438931i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.00000 | + | 10.3923i | 0.216647 | + | 0.375244i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.5000 | + | 25.1147i | −0.522883 | + | 0.905661i | 0.476762 | + | 0.879032i | \(0.341810\pi\) |
−0.999645 | + | 0.0266282i | \(0.991523\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.0000 | −0.755318 | −0.377659 | − | 0.925945i | \(-0.623271\pi\) | ||||
−0.377659 | + | 0.925945i | \(0.623271\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.00000 | 0.179605 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 30.0000 | − | 51.9615i | 1.07486 | − | 1.86171i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.00000 | − | 3.46410i | −0.0713831 | − | 0.123639i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.0000 | + | 38.1051i | −0.784215 | + | 1.35830i | 0.145251 | + | 0.989395i | \(0.453601\pi\) |
−0.929467 | + | 0.368906i | \(0.879732\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.0000 | −0.426671 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.0000 | −0.497155 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19.5000 | − | 33.7750i | 0.690725 | − | 1.19637i | −0.280875 | − | 0.959744i | \(-0.590625\pi\) |
0.971601 | − | 0.236627i | \(-0.0760420\pi\) | |||||||
\(798\) | 0 |