Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [980,2,Mod(569,980)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(980, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("980.569");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 980.q (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: | \(7.82533939809\) |
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: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 140) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 949.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 980.949 |
Dual form | 980.2.q.d.569.2 |
$q$-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 \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.23205 | − | 1.86603i | 0.550990 | − | 0.834512i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.50000 | − | 2.59808i | −0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.00000i | − | 1.10940i | −0.832050 | − | 0.554700i | \(-0.812833\pi\) | ||
0.832050 | − | 0.554700i | \(-0.187167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.46410 | − | 2.00000i | −0.840168 | − | 0.485071i | 0.0171533 | − | 0.999853i | \(-0.494540\pi\) |
−0.857321 | + | 0.514782i | \(0.827873\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | + | 3.46410i | 0.458831 | + | 0.794719i | 0.998899 | − | 0.0469020i | \(-0.0149348\pi\) |
−0.540068 | + | 0.841621i | \(0.681602\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.92820 | + | 4.00000i | −1.44463 | + | 0.834058i | −0.998154 | − | 0.0607377i | \(-0.980655\pi\) |
−0.446476 | + | 0.894795i | \(0.647321\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.96410 | − | 4.59808i | −0.392820 | − | 0.919615i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | − | 6.92820i | 0.718421 | − | 1.24434i | −0.243204 | − | 0.969975i | \(-0.578198\pi\) |
0.961625 | − | 0.274367i | \(-0.0884683\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.92820 | + | 4.00000i | −1.13899 | + | 0.657596i | −0.946180 | − | 0.323640i | \(-0.895093\pi\) |
−0.192809 | + | 0.981236i | \(0.561760\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.00000i | − | 1.21999i | −0.792406 | − | 0.609994i | \(-0.791172\pi\) | ||
0.792406 | − | 0.609994i | \(-0.208828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.69615 | − | 0.401924i | −0.998203 | − | 0.0599153i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.92820 | − | 4.00000i | 1.01058 | − | 0.583460i | 0.0992202 | − | 0.995066i | \(-0.468365\pi\) |
0.911362 | + | 0.411606i | \(0.135032\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.00000 | + | 3.46410i | −0.260378 | + | 0.450988i | −0.966342 | − | 0.257260i | \(-0.917180\pi\) |
0.705965 | + | 0.708247i | \(0.250514\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.00000 | + | 5.19615i | 0.384111 | + | 0.665299i | 0.991645 | − | 0.128994i | \(-0.0411748\pi\) |
−0.607535 | + | 0.794293i | \(0.707841\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.46410 | − | 4.92820i | −0.925808 | − | 0.611268i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.92820 | − | 4.00000i | −0.846415 | − | 0.488678i | 0.0130248 | − | 0.999915i | \(-0.495854\pi\) |
−0.859440 | + | 0.511237i | \(0.829187\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 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 | ||||||||
\(73\) | −3.46410 | − | 2.00000i | −0.405442 | − | 0.234082i | 0.283387 | − | 0.959006i | \(-0.408542\pi\) |
−0.688830 | + | 0.724923i | \(0.741875\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 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 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.00000 | + | 4.00000i | −0.867722 | + | 0.433861i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.00000 | − | 8.66025i | −0.529999 | − | 0.917985i | −0.999388 | − | 0.0349934i | \(-0.988859\pi\) |
0.469389 | − | 0.882992i | \(-0.344474\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.92820 | + | 0.535898i | 0.916014 | + | 0.0549820i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 12.0000i | − | 1.21842i | −0.793011 | − | 0.609208i | \(-0.791488\pi\) | ||
0.793011 | − | 0.609208i | \(-0.208512\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.00000 | − | 15.5885i | 0.895533 | − | 1.55111i | 0.0623905 | − | 0.998052i | \(-0.480128\pi\) |
0.833143 | − | 0.553058i | \(-0.186539\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.92820 | − | 4.00000i | 0.682656 | − | 0.394132i | −0.118199 | − | 0.992990i | \(-0.537712\pi\) |
0.800855 | + | 0.598858i | \(0.204379\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.92820 | − | 4.00000i | 0.669775 | − | 0.386695i | −0.126217 | − | 0.992003i | \(-0.540283\pi\) |
0.795991 | + | 0.605308i | \(0.206950\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.00000 | − | 12.1244i | 0.670478 | − | 1.16130i | −0.307290 | − | 0.951616i | \(-0.599422\pi\) |
0.977769 | − | 0.209687i | \(-0.0672444\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.0000i | 1.50515i | 0.658505 | + | 0.752577i | \(0.271189\pi\) | ||||
−0.658505 | + | 0.752577i | \(0.728811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.07180 | + | 17.8564i | −0.0999456 | + | 1.66512i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.3923 | + | 6.00000i | −0.960769 | + | 0.554700i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.50000 | + | 9.52628i | 0.500000 | + | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.0000 | − | 2.00000i | −0.983870 | − | 0.178885i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 8.00000i | − | 0.709885i | −0.934888 | − | 0.354943i | \(-0.884500\pi\) | ||
0.934888 | − | 0.354943i | \(-0.115500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.00000 | + | 3.46410i | 0.174741 | + | 0.302660i | 0.940072 | − | 0.340977i | \(-0.110758\pi\) |
−0.765331 | + | 0.643637i | \(0.777425\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.92820 | + | 4.00000i | 0.591916 | + | 0.341743i | 0.765855 | − | 0.643013i | \(-0.222316\pi\) |
−0.173939 | + | 0.984757i | \(0.555649\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.46410 | + | 3.73205i | −0.204633 | + | 0.309930i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.00000 | + | 5.19615i | 0.245770 | + | 0.425685i | 0.962348 | − | 0.271821i | \(-0.0876260\pi\) |
−0.716578 | + | 0.697507i | \(0.754293\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.00000 | + | 10.3923i | −0.488273 | + | 0.845714i | −0.999909 | − | 0.0134886i | \(-0.995706\pi\) |
0.511636 | + | 0.859202i | \(0.329040\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.0000i | 0.970143i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.00000 | − | 16.0000i | −0.642575 | − | 1.28515i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.3923 | + | 6.00000i | 0.829396 | + | 0.478852i | 0.853646 | − | 0.520854i | \(-0.174386\pi\) |
−0.0242497 | + | 0.999706i | \(0.507720\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.7846 | − | 12.0000i | 1.62798 | − | 0.939913i | 0.643280 | − | 0.765631i | \(-0.277573\pi\) |
0.984696 | − | 0.174282i | \(-0.0557604\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 24.0000i | 1.85718i | 0.371113 | + | 0.928588i | \(0.378976\pi\) | ||||
−0.371113 | + | 0.928588i | \(0.621024\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.00000 | −0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.00000 | − | 10.3923i | 0.458831 | − | 0.794719i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.3923 | + | 6.00000i | −0.790112 | + | 0.456172i | −0.840002 | − | 0.542583i | \(-0.817446\pi\) |
0.0498898 | + | 0.998755i | \(0.484113\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.00000 | + | 6.92820i | −0.298974 | + | 0.517838i | −0.975901 | − | 0.218212i | \(-0.929978\pi\) |
0.676927 | + | 0.736050i | \(0.263311\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.0000 | 1.04061 | 0.520306 | − | 0.853980i | \(-0.325818\pi\) | ||||
0.520306 | + | 0.853980i | \(0.325818\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.07180 | + | 17.8564i | −0.0788001 | + | 1.31283i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.0000 | + | 17.3205i | 0.723575 | + | 1.25327i | 0.959558 | + | 0.281511i | \(0.0908356\pi\) |
−0.235983 | + | 0.971757i | \(0.575831\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.8564 | − | 8.00000i | −0.997406 | − | 0.575853i | −0.0899262 | − | 0.995948i | \(-0.528663\pi\) |
−0.907480 | + | 0.420096i | \(0.861996\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.0000i | 1.13995i | 0.821661 | + | 0.569976i | \(0.193048\pi\) | ||||
−0.821661 | + | 0.569976i | \(0.806952\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.0000 | + | 20.7846i | −0.850657 | + | 1.47338i | 0.0299585 | + | 0.999551i | \(0.490462\pi\) |
−0.880616 | + | 0.473831i | \(0.842871\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.39230 | − | 11.1962i | 0.516301 | − | 0.781973i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 20.7846 | + | 12.0000i | 1.44463 | + | 0.834058i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.0000 | 1.65223 | 0.826114 | − | 0.563503i | \(-0.190547\pi\) | ||||
0.826114 | + | 0.563503i | \(0.190547\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.9282 | − | 9.85641i | −1.01810 | − | 0.672201i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.00000 | + | 13.8564i | −0.538138 | + | 0.932083i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.00000i | 0.535720i | 0.963458 | + | 0.267860i | \(0.0863164\pi\) | ||||
−0.963458 | + | 0.267860i | \(0.913684\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.00000 | + | 12.0000i | −0.600000 | + | 0.800000i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.00000 | − | 12.1244i | −0.462573 | − | 0.801200i | 0.536515 | − | 0.843891i | \(-0.319740\pi\) |
−0.999088 | + | 0.0426906i | \(0.986407\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.92820 | − | 4.00000i | 0.453882 | − | 0.262049i | −0.255586 | − | 0.966786i | \(-0.582269\pi\) |
0.709468 | + | 0.704737i | \(0.248935\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.07180 | − | 17.8564i | 0.0699163 | − | 1.16482i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.0000 | −1.29369 | −0.646846 | − | 0.762620i | \(-0.723912\pi\) | ||||
−0.646846 | + | 0.762620i | \(0.723912\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.00000 | − | 15.5885i | 0.579741 | − | 1.00414i | −0.415768 | − | 0.909471i | \(-0.636487\pi\) |
0.995509 | − | 0.0946700i | \(-0.0301796\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.8564 | − | 8.00000i | 0.881662 | − | 0.509028i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.00000 | −0.252478 | −0.126239 | − | 0.992000i | \(-0.540291\pi\) | ||||
−0.126239 | + | 0.992000i | \(0.540291\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.3923 | + | 6.00000i | −0.648254 | + | 0.374270i | −0.787787 | − | 0.615948i | \(-0.788773\pi\) |
0.139533 | + | 0.990217i | \(0.455440\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.00000 | + | 5.19615i | 0.185695 | + | 0.321634i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.7846 | + | 12.0000i | 1.28163 | + | 0.739952i | 0.977147 | − | 0.212565i | \(-0.0681817\pi\) |
0.304487 | + | 0.952517i | \(0.401515\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.00000 | + | 8.66025i | −0.304855 | + | 0.528025i | −0.977229 | − | 0.212187i | \(-0.931941\pi\) |
0.672374 | + | 0.740212i | \(0.265275\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.8564 | − | 8.00000i | −0.832551 | − | 0.480673i | 0.0221745 | − | 0.999754i | \(-0.492941\pi\) |
−0.854725 | + | 0.519081i | \(0.826274\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −24.0000 | −1.43684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.7128 | + | 16.0000i | 1.64736 | + | 0.951101i | 0.978117 | + | 0.208053i | \(0.0667128\pi\) |
0.669238 | + | 0.743048i | \(0.266621\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.500000 | − | 0.866025i | −0.0294118 | − | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 12.0000i | − | 0.701047i | −0.936554 | − | 0.350524i | \(-0.886004\pi\) | ||
0.936554 | − | 0.350524i | \(-0.113996\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.00000 | + | 8.00000i | 0.232889 | + | 0.465778i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.0000 | + | 27.7128i | 0.925304 | + | 1.60267i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.3923 | + | 0.803848i | 0.766841 | + | 0.0460282i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 16.0000i | − | 0.913168i | −0.889680 | − | 0.456584i | \(-0.849073\pi\) | ||
0.889680 | − | 0.456584i | \(-0.150927\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0000 | − | 20.7846i | 0.680458 | − | 1.17859i | −0.294384 | − | 0.955687i | \(-0.595114\pi\) |
0.974841 | − | 0.222900i | \(-0.0715523\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.46410 | − | 2.00000i | 0.195803 | − | 0.113047i | −0.398894 | − | 0.916997i | \(-0.630606\pi\) |
0.594696 | + | 0.803951i | \(0.297272\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.8564 | − | 8.00000i | 0.778253 | − | 0.449325i | −0.0575576 | − | 0.998342i | \(-0.518331\pi\) |
0.835811 | + | 0.549017i | \(0.184998\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 16.0000i | − | 0.890264i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −18.3923 | + | 7.85641i | −1.02022 | + | 0.435795i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.00000 | + | 13.8564i | 0.439720 | + | 0.761617i | 0.997668 | − | 0.0682590i | \(-0.0217444\pi\) |
−0.557948 | + | 0.829876i | \(0.688411\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 20.7846 | + | 12.0000i | 1.13899 | + | 0.657596i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −16.0000 | + | 8.00000i | −0.874173 | + | 0.437087i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 8.00000i | − | 0.435788i | −0.975972 | − | 0.217894i | \(-0.930081\pi\) | ||
0.975972 | − | 0.217894i | \(-0.0699187\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.7846 | − | 12.0000i | −1.11578 | − | 0.644194i | −0.175457 | − | 0.984487i | \(-0.556140\pi\) |
−0.940319 | + | 0.340293i | \(0.889474\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.00000 | 0.321173 | 0.160586 | − | 0.987022i | \(-0.448662\pi\) | ||||
0.160586 | + | 0.987022i | \(0.448662\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.3923 | − | 6.00000i | −0.553127 | − | 0.319348i | 0.197256 | − | 0.980352i | \(-0.436797\pi\) |
−0.750382 | + | 0.661004i | \(0.770130\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.7846 | − | 22.3923i | 0.784686 | − | 1.18846i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.0000 | − | 17.3205i | −0.527780 | − | 0.914141i | −0.999476 | − | 0.0323801i | \(-0.989691\pi\) |
0.471696 | − | 0.881761i | \(-0.343642\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.50000 | − | 2.59808i | 0.0789474 | − | 0.136741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.00000 | + | 4.00000i | −0.418739 | + | 0.209370i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.92820 | + | 4.00000i | 0.361649 | + | 0.208798i | 0.669804 | − | 0.742538i | \(-0.266378\pi\) |
−0.308155 | + | 0.951336i | \(0.599711\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.00000 | − | 15.5885i | −0.468521 | − | 0.811503i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.7128 | + | 16.0000i | −1.43492 | + | 0.828449i | −0.997490 | − | 0.0708063i | \(-0.977443\pi\) |
−0.437425 | + | 0.899255i | \(0.644109\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.00000i | 0.412021i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.00000 | 0.410932 | 0.205466 | − | 0.978664i | \(-0.434129\pi\) | ||||
0.205466 | + | 0.978664i | \(0.434129\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.7846 | + | 12.0000i | −1.06204 | + | 0.613171i | −0.925997 | − | 0.377531i | \(-0.876773\pi\) |
−0.136047 | + | 0.990702i | \(0.543440\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −20.7846 | + | 12.0000i | −1.05654 | + | 0.609994i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.00000 | − | 5.19615i | 0.152106 | − | 0.263455i | −0.779895 | − | 0.625910i | \(-0.784728\pi\) |
0.932002 | + | 0.362454i | \(0.118061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 32.0000 | 1.61831 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.92820 | − | 0.535898i | −0.449227 | − | 0.0269640i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.2487 | − | 14.0000i | 1.21701 | − | 0.702640i | 0.252731 | − | 0.967537i | \(-0.418671\pi\) |
0.964277 | + | 0.264897i | \(0.0853379\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.00000 | − | 15.5885i | −0.449439 | − | 0.778450i | 0.548911 | − | 0.835881i | \(-0.315043\pi\) |
−0.998350 | + | 0.0574304i | \(0.981709\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −27.7128 | − | 16.0000i | −1.38047 | − | 0.797017i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.00000 | + | 18.0000i | 0.447214 | + | 0.894427i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.00000 | − | 8.66025i | 0.247234 | − | 0.428222i | −0.715523 | − | 0.698589i | \(-0.753812\pi\) |
0.962757 | + | 0.270367i | \(0.0871450\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.0000 | 1.36789 | 0.683945 | − | 0.729534i | \(-0.260263\pi\) | ||||
0.683945 | + | 0.729534i | \(0.260263\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.0000 | 0.487370 | 0.243685 | − | 0.969854i | \(-0.421644\pi\) | ||||
0.243685 | + | 0.969854i | \(0.421644\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −20.7846 | − | 12.0000i | −1.01058 | − | 0.583460i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.39230 | + | 19.8564i | −0.116044 | + | 0.963177i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.0000 | + | 17.3205i | −0.481683 | + | 0.834300i | −0.999779 | − | 0.0210230i | \(-0.993308\pi\) |
0.518096 | + | 0.855323i | \(0.326641\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 28.0000i | − | 1.34559i | −0.739827 | − | 0.672797i | \(-0.765093\pi\) | ||
0.739827 | − | 0.672797i | \(-0.234907\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −27.7128 | − | 16.0000i | −1.32568 | − | 0.765384i | ||||
\(438\) | 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 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.7846 | + | 12.0000i | −0.987507 | + | 0.570137i | −0.904528 | − | 0.426414i | \(-0.859777\pi\) |
−0.0829786 | + | 0.996551i | \(0.526443\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −22.3205 | − | 1.33975i | −1.05809 | − | 0.0635100i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.00000 | −0.0943858 | −0.0471929 | − | 0.998886i | \(-0.515028\pi\) | ||||
−0.0471929 | + | 0.998886i | \(0.515028\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.8564 | + | 8.00000i | −0.648175 | + | 0.374224i | −0.787757 | − | 0.615986i | \(-0.788758\pi\) |
0.139581 | + | 0.990211i | \(0.455424\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.0000 | −1.21094 | −0.605470 | − | 0.795868i | \(-0.707015\pi\) | ||||
−0.605470 | + | 0.795868i | \(0.707015\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.00000i | 0.371792i | 0.982569 | + | 0.185896i | \(0.0595187\pi\) | ||||
−0.982569 | + | 0.185896i | \(0.940481\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.8564 | − | 8.00000i | 0.641198 | − | 0.370196i | −0.143878 | − | 0.989595i | \(-0.545957\pi\) |
0.785076 | + | 0.619400i | \(0.212624\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.0000 | − | 16.0000i | 0.550598 | − | 0.734130i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.0000 | + | 27.7128i | 0.729537 | + | 1.26360i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −22.3923 | − | 14.7846i | −1.01678 | − | 0.671335i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.92820 | + | 4.00000i | 0.313947 | + | 0.181257i | 0.648691 | − | 0.761052i | \(-0.275317\pi\) |
−0.334744 | + | 0.942309i | \(0.608650\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.92820 | + | 4.00000i | 0.312031 | + | 0.180151i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.00000 | − | 6.92820i | −0.179065 | − | 0.310149i | 0.762496 | − | 0.646993i | \(-0.223974\pi\) |
−0.941560 | + | 0.336844i | \(0.890640\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.00000i | 0.356702i | 0.983967 | + | 0.178351i | \(0.0570763\pi\) | ||||
−0.983967 | + | 0.178351i | \(0.942924\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.0000 | − | 36.0000i | −0.800989 | − | 1.60198i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.0000 | − | 19.0526i | −0.487566 | − | 0.844490i | 0.512331 | − | 0.858788i | \(-0.328782\pi\) |
−0.999898 | + | 0.0142980i | \(0.995449\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.07180 | − | 17.8564i | 0.0472290 | − | 0.786847i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.00000 | − | 5.19615i | 0.131432 | − | 0.227648i | −0.792797 | − | 0.609486i | \(-0.791376\pi\) |
0.924229 | + | 0.381839i | \(0.124709\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.7128 | − | 16.0000i | 1.21180 | − | 0.699631i | 0.248646 | − | 0.968594i | \(-0.420014\pi\) |
0.963150 | + | 0.268963i | \(0.0866810\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −27.7128 | + | 16.0000i | −1.20719 | + | 0.696971i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.5000 | − | 35.5070i | 0.891304 | − | 1.54378i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.0000 | 0.520756 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 24.0000i | − | 1.03956i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.07180 | − | 17.8564i | 0.0463378 | − | 0.772000i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.00000 | − | 12.1244i | −0.300954 | − | 0.521267i | 0.675399 | − | 0.737453i | \(-0.263972\pi\) |
−0.976352 | + | 0.216186i | \(0.930638\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.0000 | − | 28.0000i | −0.599694 | − | 1.19939i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 8.00000i | − | 0.342055i | −0.985266 | − | 0.171028i | \(-0.945291\pi\) | ||
0.985266 | − | 0.171028i | \(-0.0547087\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.00000 | − | 15.5885i | 0.384111 | − | 0.665299i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.00000 | − | 6.92820i | −0.170406 | − | 0.295151i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.8564 | + | 8.00000i | 0.587115 | + | 0.338971i | 0.763956 | − | 0.645269i | \(-0.223255\pi\) |
−0.176841 | + | 0.984239i | \(0.556588\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −32.0000 | −1.35346 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.8564 | − | 8.00000i | −0.583978 | − | 0.337160i | 0.178735 | − | 0.983897i | \(-0.442800\pi\) |
−0.762713 | + | 0.646737i | \(0.776133\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 29.8564 | + | 19.7128i | 1.25607 | + | 0.829324i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.0000 | + | 36.3731i | 0.880366 | + | 1.52484i | 0.850935 | + | 0.525271i | \(0.176036\pi\) |
0.0294311 | + | 0.999567i | \(0.490630\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.0000 | − | 34.6410i | 0.836974 | − | 1.44968i | −0.0554391 | − | 0.998462i | \(-0.517656\pi\) |
0.892413 | − | 0.451219i | \(-0.149011\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 32.0000 | + | 24.0000i | 1.33449 | + | 1.00087i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.46410 | + | 2.00000i | 0.144212 | + | 0.0832611i | 0.570370 | − | 0.821388i | \(-0.306800\pi\) |
−0.426158 | + | 0.904649i | \(0.640133\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.60770 | + | 26.7846i | −0.0664700 | + | 1.10741i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 32.0000i | − | 1.32078i | −0.750922 | − | 0.660391i | \(-0.770391\pi\) | ||
0.750922 | − | 0.660391i | \(-0.229609\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 32.0000 | 1.31854 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 31.1769 | − | 18.0000i | 1.28028 | − | 0.739171i | 0.303383 | − | 0.952869i | \(-0.401884\pi\) |
0.976900 | + | 0.213697i | \(0.0685507\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.0000 | + | 31.1769i | −0.735460 | + | 1.27385i | 0.219061 | + | 0.975711i | \(0.429701\pi\) |
−0.954521 | + | 0.298143i | \(0.903633\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.0000 | −0.407909 | −0.203954 | − | 0.978980i | \(-0.565379\pi\) | ||||
−0.203954 | + | 0.978980i | \(0.565379\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 24.0000i | 0.977356i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24.5526 | + | 1.47372i | 0.998203 | + | 0.0599153i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −34.6410 | + | 20.0000i | −1.40604 | + | 0.811775i | −0.995003 | − | 0.0998457i | \(-0.968165\pi\) |
−0.411033 | + | 0.911621i | \(0.634832\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.0000 | − | 27.7128i | −0.647291 | − | 1.12114i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.7846 | − | 12.0000i | −0.839482 | − | 0.484675i | 0.0176058 | − | 0.999845i | \(-0.494396\pi\) |
−0.857088 | + | 0.515170i | \(0.827729\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.00000i | 0.322068i | 0.986949 | + | 0.161034i | \(0.0514829\pi\) | ||||
−0.986949 | + | 0.161034i | \(0.948517\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.00000 | − | 3.46410i | 0.0803868 | − | 0.139234i | −0.823029 | − | 0.567999i | \(-0.807718\pi\) |
0.903416 | + | 0.428765i | \(0.141051\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.2846 | + | 18.0622i | −0.691384 | + | 0.722487i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 32.0000 | 1.27592 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.0000 | −1.43314 | −0.716569 | − | 0.697517i | \(-0.754288\pi\) | ||||
−0.716569 | + | 0.697517i | \(0.754288\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.9282 | − | 9.85641i | −0.592408 | − | 0.391140i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −18.0000 | − | 31.1769i | −0.712069 | − | 1.23334i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.00000 | − | 1.73205i | 0.0394976 | − | 0.0684119i | −0.845601 | − | 0.533816i | \(-0.820758\pi\) |
0.885098 | + | 0.465404i | \(0.154091\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 16.0000i | − | 0.630978i | −0.948929 | − | 0.315489i | \(-0.897831\pi\) | ||
0.948929 | − | 0.315489i | \(-0.102169\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.7846 | − | 12.0000i | −0.817127 | − | 0.471769i | 0.0322975 | − | 0.999478i | \(-0.489718\pi\) |
−0.849425 | + | 0.527710i | \(0.823051\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.7846 | − | 12.0000i | 0.813365 | − | 0.469596i | −0.0347583 | − | 0.999396i | \(-0.511066\pi\) |
0.848123 | + | 0.529799i | \(0.177733\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.92820 | + | 0.535898i | 0.348854 | + | 0.0209393i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.0000i | 0.468165i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.0000 | −0.934907 | −0.467454 | − | 0.884018i | \(-0.654829\pi\) | ||||
−0.467454 | + | 0.884018i | \(0.654829\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.0000 | + | 29.4449i | −0.661223 | + | 1.14527i | 0.319071 | + | 0.947731i | \(0.396629\pi\) |
−0.980294 | + | 0.197542i | \(0.936704\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.8564 | − | 8.00000i | 0.536522 | − | 0.309761i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 8.00000i | − | 0.308377i | −0.988041 | − | 0.154189i | \(-0.950724\pi\) | ||
0.988041 | − | 0.154189i | \(-0.0492764\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.46410 | − | 2.00000i | 0.133136 | − | 0.0768662i | −0.431953 | − | 0.901896i | \(-0.642175\pi\) |
0.565089 | + | 0.825030i | \(0.308842\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.92820 | − | 4.00000i | −0.265100 | − | 0.153056i | 0.361559 | − | 0.932349i | \(-0.382245\pi\) |
−0.626659 | + | 0.779294i | \(0.715578\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.0000 | − | 8.00000i | 0.611329 | − | 0.305664i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.0000 | − | 24.2487i | −0.532585 | − | 0.922464i | −0.999276 | − | 0.0380440i | \(-0.987887\pi\) |
0.466691 | − | 0.884420i | \(-0.345446\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.92820 | + | 7.46410i | −0.186937 | + | 0.283130i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.7846 | − | 12.0000i | −0.787273 | − | 0.454532i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.00000 | 0.0755390 | 0.0377695 | − | 0.999286i | \(-0.487975\pi\) | ||||
0.0377695 | + | 0.999286i | \(0.487975\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −27.7128 | − | 16.0000i | −1.04521 | − | 0.603451i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.00000 | − | 5.19615i | −0.112667 | − | 0.195146i | 0.804178 | − | 0.594389i | \(-0.202606\pi\) |
−0.916845 | + | 0.399244i | \(0.869273\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.00000 | + | 10.3923i | −0.225018 | + | 0.389742i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 64.0000i | 2.39682i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.0000 | + | 27.7128i | 0.596699 | + | 1.03351i | 0.993305 | + | 0.115524i | \(0.0368548\pi\) |
−0.396605 | + | 0.917989i | \(0.629812\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.92820 | + | 9.19615i | 0.145890 | + | 0.341537i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 8.00000i | − | 0.296704i | −0.988935 | − | 0.148352i | \(-0.952603\pi\) | ||
0.988935 | − | 0.148352i | \(-0.0473968\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16.0000 | + | 27.7128i | −0.591781 | + | 1.02500i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.3205 | + | 10.0000i | −0.639748 | + | 0.369358i | −0.784517 | − | 0.620107i | \(-0.787089\pi\) |
0.144770 | + | 0.989465i | \(0.453756\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.00000 | + | 6.92820i | −0.147142 | + | 0.254858i | −0.930170 | − | 0.367129i | \(-0.880341\pi\) |
0.783028 | + | 0.621987i | \(0.213674\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.0000i | 0.880475i | 0.897881 | + | 0.440237i | \(0.145106\pi\) | ||||
−0.897881 | + | 0.440237i | \(0.854894\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.3923 | + | 0.803848i | 0.490656 | + | 0.0294507i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.0000 | + | 17.3205i | 0.364905 | + | 0.632034i | 0.988761 | − | 0.149505i | \(-0.0477681\pi\) |
−0.623856 | + | 0.781540i | \(0.714435\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.0000 | + | 24.0000i | 0.436725 | + | 0.873449i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 24.0000i | − | 0.872295i | −0.899875 | − | 0.436147i | \(-0.856343\pi\) | ||
0.899875 | − | 0.436147i | \(-0.143657\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.00000 | − | 8.66025i | −0.181250 | − | 0.313934i | 0.761057 | − | 0.648686i | \(-0.224681\pi\) |
−0.942306 | + | 0.334752i | \(0.891348\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 22.3923 | + | 14.7846i | 0.809595 | + | 0.534539i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.8564 | + | 8.00000i | 0.500326 | + | 0.288863i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.00000 | 0.0721218 | 0.0360609 | − | 0.999350i | \(-0.488519\pi\) | ||||
0.0360609 | + | 0.999350i | \(0.488519\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.1769 | + | 18.0000i | 1.12136 | + | 0.647415i | 0.941747 | − | 0.336323i | \(-0.109183\pi\) |
0.179609 | + | 0.983738i | \(0.442517\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −39.7128 | − | 4.78461i | −1.42653 | − | 0.171868i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.0000 | + | 20.7846i | 0.429945 | + | 0.744686i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 24.0000 | − | 12.0000i | 0.856597 | − | 0.428298i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.5692 | + | 24.0000i | 1.48178 | + | 0.855508i | 0.999786 | − | 0.0206657i | \(-0.00657856\pi\) |
0.481996 | + | 0.876173i | \(0.339912\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.7846 | − | 12.0000i | 0.738083 | − | 0.426132i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.0000i | 0.991811i | 0.868377 | + | 0.495905i | \(0.165164\pi\) | ||||
−0.868377 | + | 0.495905i | \(0.834836\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.0000 | −1.13208 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.0000 | + | 25.9808i | −0.529999 | + | 0.917985i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.0000 | + | 22.5167i | −0.457056 | + | 0.791644i | −0.998804 | − | 0.0488972i | \(-0.984429\pi\) |
0.541748 | + | 0.840541i | \(0.317763\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.0000 | −1.26413 | −0.632065 | − | 0.774915i | \(-0.717793\pi\) | ||||
−0.632065 | + | 0.774915i | \(0.717793\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.21539 | − | 53.5692i | 0.112630 | − | 1.87645i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.7128 | − | 16.0000i | 0.969549 | − | 0.559769i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.00000 | + | 5.19615i | 0.104701 | + | 0.181347i | 0.913616 | − | 0.406578i | \(-0.133278\pi\) |
−0.808915 | + | 0.587925i | \(0.799945\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.7846 | + | 12.0000i | 0.724506 | + | 0.418294i | 0.816409 | − | 0.577474i | \(-0.195962\pi\) |
−0.0919029 | + | 0.995768i | \(0.529295\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.00000i | 0.278187i | 0.990279 | + | 0.139094i | \(0.0444189\pi\) | ||||
−0.990279 | + | 0.139094i | \(0.955581\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.0000 | − | 19.0526i | 0.382046 | − | 0.661723i | −0.609309 | − | 0.792933i | \(-0.708553\pi\) |
0.991355 | + | 0.131210i | \(0.0418863\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 44.7846 | + | 29.5692i | 1.54984 | + | 1.02329i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.0000 | 0.552381 | 0.276191 | − | 0.961103i | \(-0.410928\pi\) | ||||
0.276191 | + | 0.961103i | \(0.410928\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.69615 | + | 5.59808i | −0.127152 | + | 0.192580i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 32.0000 | − | 55.4256i | 1.09695 | − | 1.89997i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.00000i | 0.136957i | 0.997653 | + | 0.0684787i | \(0.0218145\pi\) | ||||
−0.997653 | + | 0.0684787i | \(0.978185\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.0000 | − | 24.0000i | −0.410391 | − | 0.820783i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 45.0333 | + | 26.0000i | 1.53831 | + | 0.888143i | 0.998938 | + | 0.0460748i | \(0.0146713\pi\) |
0.539371 | + | 0.842068i | \(0.318662\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.0000 | + | 31.1769i | 0.614152 | + | 1.06374i | 0.990533 | + | 0.137277i | \(0.0438352\pi\) |
−0.376381 | + | 0.926465i | \(0.622831\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.92820 | − | 4.00000i | 0.235839 | − | 0.136162i | −0.377424 | − | 0.926041i | \(-0.623190\pi\) |
0.613263 | + | 0.789879i | \(0.289857\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.60770 | + | 26.7846i | −0.0546633 | + | 0.910704i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.0000 | + | 27.7128i | −0.542139 | + | 0.939013i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −31.1769 | + | 18.0000i | −1.05518 | + | 0.609208i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.6410 | − | 20.0000i | 1.16974 | − | 0.675352i | 0.216124 | − | 0.976366i | \(-0.430658\pi\) |
0.953620 | + | 0.301014i | \(0.0973250\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.0000 | −0.606435 | −0.303218 | − | 0.952921i | \(-0.598061\pi\) | ||||
−0.303218 | + | 0.952921i | \(0.598061\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.00000i | 0.269221i | 0.990899 | + | 0.134611i | \(0.0429784\pi\) | ||||
−0.990899 | + | 0.134611i | \(0.957022\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.7846 | + | 12.0000i | −0.697879 | + | 0.402921i | −0.806557 | − | 0.591156i | \(-0.798672\pi\) |
0.108678 | + | 0.994077i | \(0.465338\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27.7128 | + | 16.0000i | 0.927374 | + | 0.535420i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.00000 | + | 16.0000i | 0.267411 | + | 0.534821i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.00000 | + | 13.8564i | −0.266815 | + | 0.462137i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17.2487 | − | 26.1244i | 0.573367 | − | 0.868403i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.92820 | − | 4.00000i | −0.230047 | − | 0.132818i | 0.380547 | − | 0.924762i | \(-0.375736\pi\) |
−0.610594 | + | 0.791944i | \(0.709069\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −54.0000 | −1.79107 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.0000 | −0.927681 | −0.463841 | − | 0.885919i | \(-0.653529\pi\) | ||||
−0.463841 | + | 0.885919i | \(0.653529\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.00000 | − | 3.46410i | −0.0659739 | − | 0.114270i | 0.831152 | − | 0.556046i | \(-0.187682\pi\) |
−0.897126 | + | 0.441776i | \(0.854349\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 48.0000i | − | 1.57994i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32.0000 | + | 24.0000i | 1.05215 | + | 0.789115i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −20.7846 | − | 12.0000i | −0.682656 | − | 0.394132i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.0000 | − | 25.9808i | −0.492134 | − | 0.852401i | 0.507825 | − | 0.861460i | \(-0.330450\pi\) |
−0.999959 | + | 0.00905914i | \(0.997116\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.00000i | 0.130674i | 0.997863 | + | 0.0653372i | \(0.0208123\pi\) | ||||
−0.997863 | + | 0.0653372i | \(0.979188\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.0000 | + | 32.9090i | −0.619382 | + | 1.07280i | 0.370216 | + | 0.928946i | \(0.379284\pi\) |
−0.989599 | + | 0.143856i | \(0.954050\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −41.5692 | + | 24.0000i | −1.35368 | + | 0.781548i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.7846 | − | 12.0000i | 0.675409 | − | 0.389948i | −0.122714 | − | 0.992442i | \(-0.539160\pi\) |
0.798123 | + | 0.602494i | \(0.205826\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.00000 | + | 13.8564i | −0.259691 | + | 0.449798i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 44.6410 | + | 2.67949i | 1.44455 | + | 0.0867063i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.5000 | − | 28.5788i | −0.532258 | − | 0.921898i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −20.7846 | − | 12.0000i | −0.669775 | − | 0.386695i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −32.0000 | + | 16.0000i | −1.03012 | + | 0.515058i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 56.0000i | 1.80084i | 0.435023 | + | 0.900419i | \(0.356740\pi\) | ||||
−0.435023 | + | 0.900419i | \(0.643260\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.0000 | − | 51.9615i | −0.962746 | − | 1.66752i | −0.715553 | − | 0.698558i | \(-0.753825\pi\) |
−0.247193 | − | 0.968966i | \(-0.579508\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.7846 | + | 12.0000i | 0.664959 | + | 0.383914i | 0.794164 | − | 0.607704i | \(-0.207909\pi\) |
−0.129205 | + | 0.991618i | \(0.541243\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −42.0000 | −1.34096 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 34.6410 | + | 20.0000i | 1.10488 | + | 0.637901i | 0.937498 | − | 0.347992i | \(-0.113136\pi\) |
0.167379 | + | 0.985893i | \(0.446470\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 29.8564 | + | 19.7128i | 0.951304 | + | 0.628102i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.0000 | + | 55.4256i | 1.01754 | + | 1.76243i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.00000 | + | 3.46410i | −0.0635321 | + | 0.110041i | −0.896042 | − | 0.443969i | \(-0.853570\pi\) |
0.832510 | + | 0.554010i | \(0.186903\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.0000 | + | 48.0000i | 0.760851 | + | 1.52170i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.2487 | − | 14.0000i | −0.767964 | − | 0.443384i | 0.0641836 | − | 0.997938i | \(-0.479556\pi\) |
−0.832148 | + | 0.554554i | \(0.812889\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))