Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [420,2,Mod(239,420)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(420, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("420.239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 420.l (of order \(2\), degree \(1\), 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: | \(3.35371688489\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 239.2 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 420.239 |
Dual form | 420.2.l.a.239.4 |
$q$-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 \(\left(\mathbb{Z}/420\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(241\) | \(281\) | \(337\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 1.00000i | ||||||
\(3\) | −1.00000 | + | 1.41421i | −0.577350 | + | 0.816497i | ||||
\(4\) | −2.00000 | −1.00000 | ||||||||
\(5\) | 2.12132 | + | 0.707107i | 0.948683 | + | 0.316228i | ||||
\(6\) | 2.00000 | + | 1.41421i | 0.816497 | + | 0.577350i | ||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.82843i | 1.00000i | ||||||||
\(9\) | −1.00000 | − | 2.82843i | −0.333333 | − | 0.942809i | ||||
\(10\) | 1.00000 | − | 3.00000i | 0.316228 | − | 0.948683i | ||||
\(11\) | −4.24264 | −1.27920 | −0.639602 | − | 0.768706i | \(-0.720901\pi\) | ||||
−0.639602 | + | 0.768706i | \(0.720901\pi\) | |||||||
\(12\) | 2.00000 | − | 2.82843i | 0.577350 | − | 0.816497i | ||||
\(13\) | 6.00000i | 1.66410i | 0.554700 | + | 0.832050i | \(0.312833\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | − | 1.41421i | − | 0.377964i | ||||||
\(15\) | −3.12132 | + | 2.29289i | −0.805921 | + | 0.592022i | ||||
\(16\) | 4.00000 | 1.00000 | ||||||||
\(17\) | 4.24264 | 1.02899 | 0.514496 | − | 0.857493i | \(-0.327979\pi\) | ||||
0.514496 | + | 0.857493i | \(0.327979\pi\) | |||||||
\(18\) | −4.00000 | + | 1.41421i | −0.942809 | + | 0.333333i | ||||
\(19\) | 6.00000i | 1.37649i | 0.725476 | + | 0.688247i | \(0.241620\pi\) | ||||
−0.725476 | + | 0.688247i | \(0.758380\pi\) | |||||||
\(20\) | −4.24264 | − | 1.41421i | −0.948683 | − | 0.316228i | ||||
\(21\) | −1.00000 | + | 1.41421i | −0.218218 | + | 0.308607i | ||||
\(22\) | 6.00000i | 1.27920i | ||||||||
\(23\) | 1.41421i | 0.294884i | 0.989071 | + | 0.147442i | \(0.0471040\pi\) | ||||
−0.989071 | + | 0.147442i | \(0.952896\pi\) | |||||||
\(24\) | −4.00000 | − | 2.82843i | −0.816497 | − | 0.577350i | ||||
\(25\) | 4.00000 | + | 3.00000i | 0.800000 | + | 0.600000i | ||||
\(26\) | 8.48528 | 1.66410 | ||||||||
\(27\) | 5.00000 | + | 1.41421i | 0.962250 | + | 0.272166i | ||||
\(28\) | −2.00000 | −0.377964 | ||||||||
\(29\) | − | 2.82843i | − | 0.525226i | −0.964901 | − | 0.262613i | \(-0.915416\pi\) | ||
0.964901 | − | 0.262613i | \(-0.0845842\pi\) | |||||||
\(30\) | 3.24264 | + | 4.41421i | 0.592022 | + | 0.805921i | ||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | − | 5.65685i | − | 1.00000i | ||||||
\(33\) | 4.24264 | − | 6.00000i | 0.738549 | − | 1.04447i | ||||
\(34\) | − | 6.00000i | − | 1.02899i | ||||||
\(35\) | 2.12132 | + | 0.707107i | 0.358569 | + | 0.119523i | ||||
\(36\) | 2.00000 | + | 5.65685i | 0.333333 | + | 0.942809i | ||||
\(37\) | 6.00000i | 0.986394i | 0.869918 | + | 0.493197i | \(0.164172\pi\) | ||||
−0.869918 | + | 0.493197i | \(0.835828\pi\) | |||||||
\(38\) | 8.48528 | 1.37649 | ||||||||
\(39\) | −8.48528 | − | 6.00000i | −1.35873 | − | 0.960769i | ||||
\(40\) | −2.00000 | + | 6.00000i | −0.316228 | + | 0.948683i | ||||
\(41\) | 1.41421i | 0.220863i | 0.993884 | + | 0.110432i | \(0.0352233\pi\) | ||||
−0.993884 | + | 0.110432i | \(0.964777\pi\) | |||||||
\(42\) | 2.00000 | + | 1.41421i | 0.308607 | + | 0.218218i | ||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 8.48528 | 1.27920 | ||||||||
\(45\) | −0.121320 | − | 6.70711i | −0.0180854 | − | 0.999836i | ||||
\(46\) | 2.00000 | 0.294884 | ||||||||
\(47\) | − | 2.82843i | − | 0.412568i | −0.978492 | − | 0.206284i | \(-0.933863\pi\) | ||
0.978492 | − | 0.206284i | \(-0.0661372\pi\) | |||||||
\(48\) | −4.00000 | + | 5.65685i | −0.577350 | + | 0.816497i | ||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 4.24264 | − | 5.65685i | 0.600000 | − | 0.800000i | ||||
\(51\) | −4.24264 | + | 6.00000i | −0.594089 | + | 0.840168i | ||||
\(52\) | − | 12.0000i | − | 1.66410i | ||||||
\(53\) | −8.48528 | −1.16554 | −0.582772 | − | 0.812636i | \(-0.698032\pi\) | ||||
−0.582772 | + | 0.812636i | \(0.698032\pi\) | |||||||
\(54\) | 2.00000 | − | 7.07107i | 0.272166 | − | 0.962250i | ||||
\(55\) | −9.00000 | − | 3.00000i | −1.21356 | − | 0.404520i | ||||
\(56\) | 2.82843i | 0.377964i | ||||||||
\(57\) | −8.48528 | − | 6.00000i | −1.12390 | − | 0.794719i | ||||
\(58\) | −4.00000 | −0.525226 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 6.24264 | − | 4.58579i | 0.805921 | − | 0.592022i | ||||
\(61\) | −10.0000 | −1.28037 | −0.640184 | − | 0.768221i | \(-0.721142\pi\) | ||||
−0.640184 | + | 0.768221i | \(0.721142\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | − | 2.82843i | −0.125988 | − | 0.356348i | ||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | −4.24264 | + | 12.7279i | −0.526235 | + | 1.57870i | ||||
\(66\) | −8.48528 | − | 6.00000i | −1.04447 | − | 0.738549i | ||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | −8.48528 | −1.02899 | ||||||||
\(69\) | −2.00000 | − | 1.41421i | −0.240772 | − | 0.170251i | ||||
\(70\) | 1.00000 | − | 3.00000i | 0.119523 | − | 0.358569i | ||||
\(71\) | 12.7279 | 1.51053 | 0.755263 | − | 0.655422i | \(-0.227509\pi\) | ||||
0.755263 | + | 0.655422i | \(0.227509\pi\) | |||||||
\(72\) | 8.00000 | − | 2.82843i | 0.942809 | − | 0.333333i | ||||
\(73\) | − | 6.00000i | − | 0.702247i | −0.936329 | − | 0.351123i | \(-0.885800\pi\) | ||
0.936329 | − | 0.351123i | \(-0.114200\pi\) | |||||||
\(74\) | 8.48528 | 0.986394 | ||||||||
\(75\) | −8.24264 | + | 2.65685i | −0.951778 | + | 0.306787i | ||||
\(76\) | − | 12.0000i | − | 1.37649i | ||||||
\(77\) | −4.24264 | −0.483494 | ||||||||
\(78\) | −8.48528 | + | 12.0000i | −0.960769 | + | 1.35873i | ||||
\(79\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(80\) | 8.48528 | + | 2.82843i | 0.948683 | + | 0.316228i | ||||
\(81\) | −7.00000 | + | 5.65685i | −0.777778 | + | 0.628539i | ||||
\(82\) | 2.00000 | 0.220863 | ||||||||
\(83\) | − | 2.82843i | − | 0.310460i | −0.987878 | − | 0.155230i | \(-0.950388\pi\) | ||
0.987878 | − | 0.155230i | \(-0.0496119\pi\) | |||||||
\(84\) | 2.00000 | − | 2.82843i | 0.218218 | − | 0.308607i | ||||
\(85\) | 9.00000 | + | 3.00000i | 0.976187 | + | 0.325396i | ||||
\(86\) | − | 11.3137i | − | 1.21999i | ||||||
\(87\) | 4.00000 | + | 2.82843i | 0.428845 | + | 0.303239i | ||||
\(88\) | − | 12.0000i | − | 1.27920i | ||||||
\(89\) | − | 7.07107i | − | 0.749532i | −0.927119 | − | 0.374766i | \(-0.877723\pi\) | ||
0.927119 | − | 0.374766i | \(-0.122277\pi\) | |||||||
\(90\) | −9.48528 | + | 0.171573i | −0.999836 | + | 0.0180854i | ||||
\(91\) | 6.00000i | 0.628971i | ||||||||
\(92\) | − | 2.82843i | − | 0.294884i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.00000 | −0.412568 | ||||||||
\(95\) | −4.24264 | + | 12.7279i | −0.435286 | + | 1.30586i | ||||
\(96\) | 8.00000 | + | 5.65685i | 0.816497 | + | 0.577350i | ||||
\(97\) | − | 6.00000i | − | 0.609208i | −0.952479 | − | 0.304604i | \(-0.901476\pi\) | ||
0.952479 | − | 0.304604i | \(-0.0985241\pi\) | |||||||
\(98\) | − | 1.41421i | − | 0.142857i | ||||||
\(99\) | 4.24264 | + | 12.0000i | 0.426401 | + | 1.20605i | ||||
\(100\) | −8.00000 | − | 6.00000i | −0.800000 | − | 0.600000i | ||||
\(101\) | − | 15.5563i | − | 1.54791i | −0.633238 | − | 0.773957i | \(-0.718274\pi\) | ||
0.633238 | − | 0.773957i | \(-0.281726\pi\) | |||||||
\(102\) | 8.48528 | + | 6.00000i | 0.840168 | + | 0.594089i | ||||
\(103\) | 14.0000 | 1.37946 | 0.689730 | − | 0.724066i | \(-0.257729\pi\) | ||||
0.689730 | + | 0.724066i | \(0.257729\pi\) | |||||||
\(104\) | −16.9706 | −1.66410 | ||||||||
\(105\) | −3.12132 | + | 2.29289i | −0.304610 | + | 0.223763i | ||||
\(106\) | 12.0000i | 1.16554i | ||||||||
\(107\) | − | 7.07107i | − | 0.683586i | −0.939775 | − | 0.341793i | \(-0.888966\pi\) | ||
0.939775 | − | 0.341793i | \(-0.111034\pi\) | |||||||
\(108\) | −10.0000 | − | 2.82843i | −0.962250 | − | 0.272166i | ||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | −4.24264 | + | 12.7279i | −0.404520 | + | 1.21356i | ||||
\(111\) | −8.48528 | − | 6.00000i | −0.805387 | − | 0.569495i | ||||
\(112\) | 4.00000 | 0.377964 | ||||||||
\(113\) | 8.48528 | 0.798228 | 0.399114 | − | 0.916901i | \(-0.369318\pi\) | ||||
0.399114 | + | 0.916901i | \(0.369318\pi\) | |||||||
\(114\) | −8.48528 | + | 12.0000i | −0.794719 | + | 1.12390i | ||||
\(115\) | −1.00000 | + | 3.00000i | −0.0932505 | + | 0.279751i | ||||
\(116\) | 5.65685i | 0.525226i | ||||||||
\(117\) | 16.9706 | − | 6.00000i | 1.56893 | − | 0.554700i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.24264 | 0.388922 | ||||||||
\(120\) | −6.48528 | − | 8.82843i | −0.592022 | − | 0.805921i | ||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 14.1421i | 1.28037i | ||||||||
\(123\) | −2.00000 | − | 1.41421i | −0.180334 | − | 0.127515i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.36396 | + | 9.19239i | 0.569210 | + | 0.822192i | ||||
\(126\) | −4.00000 | + | 1.41421i | −0.356348 | + | 0.125988i | ||||
\(127\) | −16.0000 | −1.41977 | −0.709885 | − | 0.704317i | \(-0.751253\pi\) | ||||
−0.709885 | + | 0.704317i | \(0.751253\pi\) | |||||||
\(128\) | 11.3137i | 1.00000i | ||||||||
\(129\) | −8.00000 | + | 11.3137i | −0.704361 | + | 0.996116i | ||||
\(130\) | 18.0000 | + | 6.00000i | 1.57870 | + | 0.526235i | ||||
\(131\) | −8.48528 | −0.741362 | −0.370681 | − | 0.928760i | \(-0.620876\pi\) | ||||
−0.370681 | + | 0.928760i | \(0.620876\pi\) | |||||||
\(132\) | −8.48528 | + | 12.0000i | −0.738549 | + | 1.04447i | ||||
\(133\) | 6.00000i | 0.520266i | ||||||||
\(134\) | 5.65685i | 0.488678i | ||||||||
\(135\) | 9.60660 | + | 6.53553i | 0.826805 | + | 0.562489i | ||||
\(136\) | 12.0000i | 1.02899i | ||||||||
\(137\) | −16.9706 | −1.44989 | −0.724947 | − | 0.688805i | \(-0.758136\pi\) | ||||
−0.724947 | + | 0.688805i | \(0.758136\pi\) | |||||||
\(138\) | −2.00000 | + | 2.82843i | −0.170251 | + | 0.240772i | ||||
\(139\) | − | 12.0000i | − | 1.01783i | −0.860818 | − | 0.508913i | \(-0.830047\pi\) | ||
0.860818 | − | 0.508913i | \(-0.169953\pi\) | |||||||
\(140\) | −4.24264 | − | 1.41421i | −0.358569 | − | 0.119523i | ||||
\(141\) | 4.00000 | + | 2.82843i | 0.336861 | + | 0.238197i | ||||
\(142\) | − | 18.0000i | − | 1.51053i | ||||||
\(143\) | − | 25.4558i | − | 2.12872i | ||||||
\(144\) | −4.00000 | − | 11.3137i | −0.333333 | − | 0.942809i | ||||
\(145\) | 2.00000 | − | 6.00000i | 0.166091 | − | 0.498273i | ||||
\(146\) | −8.48528 | −0.702247 | ||||||||
\(147\) | −1.00000 | + | 1.41421i | −0.0824786 | + | 0.116642i | ||||
\(148\) | − | 12.0000i | − | 0.986394i | ||||||
\(149\) | − | 11.3137i | − | 0.926855i | −0.886135 | − | 0.463428i | \(-0.846619\pi\) | ||
0.886135 | − | 0.463428i | \(-0.153381\pi\) | |||||||
\(150\) | 3.75736 | + | 11.6569i | 0.306787 | + | 0.951778i | ||||
\(151\) | − | 12.0000i | − | 0.976546i | −0.872691 | − | 0.488273i | \(-0.837627\pi\) | ||
0.872691 | − | 0.488273i | \(-0.162373\pi\) | |||||||
\(152\) | −16.9706 | −1.37649 | ||||||||
\(153\) | −4.24264 | − | 12.0000i | −0.342997 | − | 0.970143i | ||||
\(154\) | 6.00000i | 0.483494i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 16.9706 | + | 12.0000i | 1.35873 | + | 0.960769i | ||||
\(157\) | 18.0000i | 1.43656i | 0.695756 | + | 0.718278i | \(0.255069\pi\) | ||||
−0.695756 | + | 0.718278i | \(0.744931\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.48528 | − | 12.0000i | 0.672927 | − | 0.951662i | ||||
\(160\) | 4.00000 | − | 12.0000i | 0.316228 | − | 0.948683i | ||||
\(161\) | 1.41421i | 0.111456i | ||||||||
\(162\) | 8.00000 | + | 9.89949i | 0.628539 | + | 0.777778i | ||||
\(163\) | 20.0000 | 1.56652 | 0.783260 | − | 0.621694i | \(-0.213555\pi\) | ||||
0.783260 | + | 0.621694i | \(0.213555\pi\) | |||||||
\(164\) | − | 2.82843i | − | 0.220863i | ||||||
\(165\) | 13.2426 | − | 9.72792i | 1.03094 | − | 0.757318i | ||||
\(166\) | −4.00000 | −0.310460 | ||||||||
\(167\) | 14.1421i | 1.09435i | 0.837018 | + | 0.547176i | \(0.184297\pi\) | ||||
−0.837018 | + | 0.547176i | \(0.815703\pi\) | |||||||
\(168\) | −4.00000 | − | 2.82843i | −0.308607 | − | 0.218218i | ||||
\(169\) | −23.0000 | −1.76923 | ||||||||
\(170\) | 4.24264 | − | 12.7279i | 0.325396 | − | 0.976187i | ||||
\(171\) | 16.9706 | − | 6.00000i | 1.29777 | − | 0.458831i | ||||
\(172\) | −16.0000 | −1.21999 | ||||||||
\(173\) | 12.7279 | 0.967686 | 0.483843 | − | 0.875155i | \(-0.339241\pi\) | ||||
0.483843 | + | 0.875155i | \(0.339241\pi\) | |||||||
\(174\) | 4.00000 | − | 5.65685i | 0.303239 | − | 0.428845i | ||||
\(175\) | 4.00000 | + | 3.00000i | 0.302372 | + | 0.226779i | ||||
\(176\) | −16.9706 | −1.27920 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −10.0000 | −0.749532 | ||||||||
\(179\) | 4.24264 | 0.317110 | 0.158555 | − | 0.987350i | \(-0.449317\pi\) | ||||
0.158555 | + | 0.987350i | \(0.449317\pi\) | |||||||
\(180\) | 0.242641 | + | 13.4142i | 0.0180854 | + | 0.999836i | ||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 8.48528 | 0.628971 | ||||||||
\(183\) | 10.0000 | − | 14.1421i | 0.739221 | − | 1.04542i | ||||
\(184\) | −4.00000 | −0.294884 | ||||||||
\(185\) | −4.24264 | + | 12.7279i | −0.311925 | + | 0.935775i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.0000 | −1.31629 | ||||||||
\(188\) | 5.65685i | 0.412568i | ||||||||
\(189\) | 5.00000 | + | 1.41421i | 0.363696 | + | 0.102869i | ||||
\(190\) | 18.0000 | + | 6.00000i | 1.30586 | + | 0.435286i | ||||
\(191\) | 12.7279 | 0.920960 | 0.460480 | − | 0.887670i | \(-0.347677\pi\) | ||||
0.460480 | + | 0.887670i | \(0.347677\pi\) | |||||||
\(192\) | 8.00000 | − | 11.3137i | 0.577350 | − | 0.816497i | ||||
\(193\) | 18.0000i | 1.29567i | 0.761781 | + | 0.647834i | \(0.224325\pi\) | ||||
−0.761781 | + | 0.647834i | \(0.775675\pi\) | |||||||
\(194\) | −8.48528 | −0.609208 | ||||||||
\(195\) | −13.7574 | − | 18.7279i | −0.985185 | − | 1.34113i | ||||
\(196\) | −2.00000 | −0.142857 | ||||||||
\(197\) | 25.4558 | 1.81365 | 0.906827 | − | 0.421503i | \(-0.138497\pi\) | ||||
0.906827 | + | 0.421503i | \(0.138497\pi\) | |||||||
\(198\) | 16.9706 | − | 6.00000i | 1.20605 | − | 0.426401i | ||||
\(199\) | − | 6.00000i | − | 0.425329i | −0.977125 | − | 0.212664i | \(-0.931786\pi\) | ||
0.977125 | − | 0.212664i | \(-0.0682141\pi\) | |||||||
\(200\) | −8.48528 | + | 11.3137i | −0.600000 | + | 0.800000i | ||||
\(201\) | 4.00000 | − | 5.65685i | 0.282138 | − | 0.399004i | ||||
\(202\) | −22.0000 | −1.54791 | ||||||||
\(203\) | − | 2.82843i | − | 0.198517i | ||||||
\(204\) | 8.48528 | − | 12.0000i | 0.594089 | − | 0.840168i | ||||
\(205\) | −1.00000 | + | 3.00000i | −0.0698430 | + | 0.209529i | ||||
\(206\) | − | 19.7990i | − | 1.37946i | ||||||
\(207\) | 4.00000 | − | 1.41421i | 0.278019 | − | 0.0982946i | ||||
\(208\) | 24.0000i | 1.66410i | ||||||||
\(209\) | − | 25.4558i | − | 1.76082i | ||||||
\(210\) | 3.24264 | + | 4.41421i | 0.223763 | + | 0.304610i | ||||
\(211\) | − | 12.0000i | − | 0.826114i | −0.910705 | − | 0.413057i | \(-0.864461\pi\) | ||
0.910705 | − | 0.413057i | \(-0.135539\pi\) | |||||||
\(212\) | 16.9706 | 1.16554 | ||||||||
\(213\) | −12.7279 | + | 18.0000i | −0.872103 | + | 1.23334i | ||||
\(214\) | −10.0000 | −0.683586 | ||||||||
\(215\) | 16.9706 | + | 5.65685i | 1.15738 | + | 0.385794i | ||||
\(216\) | −4.00000 | + | 14.1421i | −0.272166 | + | 0.962250i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 2.82843i | − | 0.191565i | ||||||
\(219\) | 8.48528 | + | 6.00000i | 0.573382 | + | 0.405442i | ||||
\(220\) | 18.0000 | + | 6.00000i | 1.21356 | + | 0.404520i | ||||
\(221\) | 25.4558i | 1.71235i | ||||||||
\(222\) | −8.48528 | + | 12.0000i | −0.569495 | + | 0.805387i | ||||
\(223\) | 8.00000 | 0.535720 | 0.267860 | − | 0.963458i | \(-0.413684\pi\) | ||||
0.267860 | + | 0.963458i | \(0.413684\pi\) | |||||||
\(224\) | − | 5.65685i | − | 0.377964i | ||||||
\(225\) | 4.48528 | − | 14.3137i | 0.299019 | − | 0.954247i | ||||
\(226\) | − | 12.0000i | − | 0.798228i | ||||||
\(227\) | 22.6274i | 1.50183i | 0.660396 | + | 0.750917i | \(0.270388\pi\) | ||||
−0.660396 | + | 0.750917i | \(0.729612\pi\) | |||||||
\(228\) | 16.9706 | + | 12.0000i | 1.12390 | + | 0.794719i | ||||
\(229\) | 14.0000 | 0.925146 | 0.462573 | − | 0.886581i | \(-0.346926\pi\) | ||||
0.462573 | + | 0.886581i | \(0.346926\pi\) | |||||||
\(230\) | 4.24264 | + | 1.41421i | 0.279751 | + | 0.0932505i | ||||
\(231\) | 4.24264 | − | 6.00000i | 0.279145 | − | 0.394771i | ||||
\(232\) | 8.00000 | 0.525226 | ||||||||
\(233\) | −16.9706 | −1.11178 | −0.555889 | − | 0.831256i | \(-0.687622\pi\) | ||||
−0.555889 | + | 0.831256i | \(0.687622\pi\) | |||||||
\(234\) | −8.48528 | − | 24.0000i | −0.554700 | − | 1.56893i | ||||
\(235\) | 2.00000 | − | 6.00000i | 0.130466 | − | 0.391397i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 6.00000i | − | 0.388922i | ||||||
\(239\) | −4.24264 | −0.274434 | −0.137217 | − | 0.990541i | \(-0.543816\pi\) | ||||
−0.137217 | + | 0.990541i | \(0.543816\pi\) | |||||||
\(240\) | −12.4853 | + | 9.17157i | −0.805921 | + | 0.592022i | ||||
\(241\) | 26.0000 | 1.67481 | 0.837404 | − | 0.546585i | \(-0.184072\pi\) | ||||
0.837404 | + | 0.546585i | \(0.184072\pi\) | |||||||
\(242\) | − | 9.89949i | − | 0.636364i | ||||||
\(243\) | −1.00000 | − | 15.5563i | −0.0641500 | − | 0.997940i | ||||
\(244\) | 20.0000 | 1.28037 | ||||||||
\(245\) | 2.12132 | + | 0.707107i | 0.135526 | + | 0.0451754i | ||||
\(246\) | −2.00000 | + | 2.82843i | −0.127515 | + | 0.180334i | ||||
\(247\) | −36.0000 | −2.29063 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.00000 | + | 2.82843i | 0.253490 | + | 0.179244i | ||||
\(250\) | 13.0000 | − | 9.00000i | 0.822192 | − | 0.569210i | ||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 2.00000 | + | 5.65685i | 0.125988 | + | 0.356348i | ||||
\(253\) | − | 6.00000i | − | 0.377217i | ||||||
\(254\) | 22.6274i | 1.41977i | ||||||||
\(255\) | −13.2426 | + | 9.72792i | −0.829286 | + | 0.609186i | ||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 4.24264 | 0.264649 | 0.132324 | − | 0.991206i | \(-0.457756\pi\) | ||||
0.132324 | + | 0.991206i | \(0.457756\pi\) | |||||||
\(258\) | 16.0000 | + | 11.3137i | 0.996116 | + | 0.704361i | ||||
\(259\) | 6.00000i | 0.372822i | ||||||||
\(260\) | 8.48528 | − | 25.4558i | 0.526235 | − | 1.57870i | ||||
\(261\) | −8.00000 | + | 2.82843i | −0.495188 | + | 0.175075i | ||||
\(262\) | 12.0000i | 0.741362i | ||||||||
\(263\) | − | 15.5563i | − | 0.959246i | −0.877475 | − | 0.479623i | \(-0.840774\pi\) | ||
0.877475 | − | 0.479623i | \(-0.159226\pi\) | |||||||
\(264\) | 16.9706 | + | 12.0000i | 1.04447 | + | 0.738549i | ||||
\(265\) | −18.0000 | − | 6.00000i | −1.10573 | − | 0.368577i | ||||
\(266\) | 8.48528 | 0.520266 | ||||||||
\(267\) | 10.0000 | + | 7.07107i | 0.611990 | + | 0.432742i | ||||
\(268\) | 8.00000 | 0.488678 | ||||||||
\(269\) | 18.3848i | 1.12094i | 0.828175 | + | 0.560470i | \(0.189379\pi\) | ||||
−0.828175 | + | 0.560470i | \(0.810621\pi\) | |||||||
\(270\) | 9.24264 | − | 13.5858i | 0.562489 | − | 0.826805i | ||||
\(271\) | 24.0000i | 1.45790i | 0.684569 | + | 0.728948i | \(0.259990\pi\) | ||||
−0.684569 | + | 0.728948i | \(0.740010\pi\) | |||||||
\(272\) | 16.9706 | 1.02899 | ||||||||
\(273\) | −8.48528 | − | 6.00000i | −0.513553 | − | 0.363137i | ||||
\(274\) | 24.0000i | 1.44989i | ||||||||
\(275\) | −16.9706 | − | 12.7279i | −1.02336 | − | 0.767523i | ||||
\(276\) | 4.00000 | + | 2.82843i | 0.240772 | + | 0.170251i | ||||
\(277\) | 6.00000i | 0.360505i | 0.983620 | + | 0.180253i | \(0.0576915\pi\) | ||||
−0.983620 | + | 0.180253i | \(0.942309\pi\) | |||||||
\(278\) | −16.9706 | −1.01783 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.00000 | + | 6.00000i | −0.119523 | + | 0.358569i | ||||
\(281\) | − | 2.82843i | − | 0.168730i | −0.996435 | − | 0.0843649i | \(-0.973114\pi\) | ||
0.996435 | − | 0.0843649i | \(-0.0268861\pi\) | |||||||
\(282\) | 4.00000 | − | 5.65685i | 0.238197 | − | 0.336861i | ||||
\(283\) | −4.00000 | −0.237775 | −0.118888 | − | 0.992908i | \(-0.537933\pi\) | ||||
−0.118888 | + | 0.992908i | \(0.537933\pi\) | |||||||
\(284\) | −25.4558 | −1.51053 | ||||||||
\(285\) | −13.7574 | − | 18.7279i | −0.814916 | − | 1.10935i | ||||
\(286\) | −36.0000 | −2.12872 | ||||||||
\(287\) | 1.41421i | 0.0834784i | ||||||||
\(288\) | −16.0000 | + | 5.65685i | −0.942809 | + | 0.333333i | ||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −8.48528 | − | 2.82843i | −0.498273 | − | 0.166091i | ||||
\(291\) | 8.48528 | + | 6.00000i | 0.497416 | + | 0.351726i | ||||
\(292\) | 12.0000i | 0.702247i | ||||||||
\(293\) | 21.2132 | 1.23929 | 0.619644 | − | 0.784883i | \(-0.287277\pi\) | ||||
0.619644 | + | 0.784883i | \(0.287277\pi\) | |||||||
\(294\) | 2.00000 | + | 1.41421i | 0.116642 | + | 0.0824786i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −16.9706 | −0.986394 | ||||||||
\(297\) | −21.2132 | − | 6.00000i | −1.23091 | − | 0.348155i | ||||
\(298\) | −16.0000 | −0.926855 | ||||||||
\(299\) | −8.48528 | −0.490716 | ||||||||
\(300\) | 16.4853 | − | 5.31371i | 0.951778 | − | 0.306787i | ||||
\(301\) | 8.00000 | 0.461112 | ||||||||
\(302\) | −16.9706 | −0.976546 | ||||||||
\(303\) | 22.0000 | + | 15.5563i | 1.26387 | + | 0.893689i | ||||
\(304\) | 24.0000i | 1.37649i | ||||||||
\(305\) | −21.2132 | − | 7.07107i | −1.21466 | − | 0.404888i | ||||
\(306\) | −16.9706 | + | 6.00000i | −0.970143 | + | 0.342997i | ||||
\(307\) | 20.0000 | 1.14146 | 0.570730 | − | 0.821138i | \(-0.306660\pi\) | ||||
0.570730 | + | 0.821138i | \(0.306660\pi\) | |||||||
\(308\) | 8.48528 | 0.483494 | ||||||||
\(309\) | −14.0000 | + | 19.7990i | −0.796432 | + | 1.12633i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −25.4558 | −1.44347 | −0.721734 | − | 0.692170i | \(-0.756655\pi\) | ||||
−0.721734 | + | 0.692170i | \(0.756655\pi\) | |||||||
\(312\) | 16.9706 | − | 24.0000i | 0.960769 | − | 1.35873i | ||||
\(313\) | − | 18.0000i | − | 1.01742i | −0.860938 | − | 0.508710i | \(-0.830123\pi\) | ||
0.860938 | − | 0.508710i | \(-0.169877\pi\) | |||||||
\(314\) | 25.4558 | 1.43656 | ||||||||
\(315\) | −0.121320 | − | 6.70711i | −0.00683563 | − | 0.377903i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25.4558 | −1.42974 | −0.714871 | − | 0.699256i | \(-0.753515\pi\) | ||||
−0.714871 | + | 0.699256i | \(0.753515\pi\) | |||||||
\(318\) | −16.9706 | − | 12.0000i | −0.951662 | − | 0.672927i | ||||
\(319\) | 12.0000i | 0.671871i | ||||||||
\(320\) | −16.9706 | − | 5.65685i | −0.948683 | − | 0.316228i | ||||
\(321\) | 10.0000 | + | 7.07107i | 0.558146 | + | 0.394669i | ||||
\(322\) | 2.00000 | 0.111456 | ||||||||
\(323\) | 25.4558i | 1.41640i | ||||||||
\(324\) | 14.0000 | − | 11.3137i | 0.777778 | − | 0.628539i | ||||
\(325\) | −18.0000 | + | 24.0000i | −0.998460 | + | 1.33128i | ||||
\(326\) | − | 28.2843i | − | 1.56652i | ||||||
\(327\) | −2.00000 | + | 2.82843i | −0.110600 | + | 0.156412i | ||||
\(328\) | −4.00000 | −0.220863 | ||||||||
\(329\) | − | 2.82843i | − | 0.155936i | ||||||
\(330\) | −13.7574 | − | 18.7279i | −0.757318 | − | 1.03094i | ||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | 5.65685i | 0.310460i | ||||||||
\(333\) | 16.9706 | − | 6.00000i | 0.929981 | − | 0.328798i | ||||
\(334\) | 20.0000 | 1.09435 | ||||||||
\(335\) | −8.48528 | − | 2.82843i | −0.463600 | − | 0.154533i | ||||
\(336\) | −4.00000 | + | 5.65685i | −0.218218 | + | 0.308607i | ||||
\(337\) | − | 12.0000i | − | 0.653682i | −0.945079 | − | 0.326841i | \(-0.894016\pi\) | ||
0.945079 | − | 0.326841i | \(-0.105984\pi\) | |||||||
\(338\) | 32.5269i | 1.76923i | ||||||||
\(339\) | −8.48528 | + | 12.0000i | −0.460857 | + | 0.651751i | ||||
\(340\) | −18.0000 | − | 6.00000i | −0.976187 | − | 0.325396i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −8.48528 | − | 24.0000i | −0.458831 | − | 1.29777i | ||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 22.6274i | 1.21999i | ||||||||
\(345\) | −3.24264 | − | 4.41421i | −0.174578 | − | 0.237653i | ||||
\(346\) | − | 18.0000i | − | 0.967686i | ||||||
\(347\) | 1.41421i | 0.0759190i | 0.999279 | + | 0.0379595i | \(0.0120858\pi\) | ||||
−0.999279 | + | 0.0379595i | \(0.987914\pi\) | |||||||
\(348\) | −8.00000 | − | 5.65685i | −0.428845 | − | 0.303239i | ||||
\(349\) | 26.0000 | 1.39175 | 0.695874 | − | 0.718164i | \(-0.255017\pi\) | ||||
0.695874 | + | 0.718164i | \(0.255017\pi\) | |||||||
\(350\) | 4.24264 | − | 5.65685i | 0.226779 | − | 0.302372i | ||||
\(351\) | −8.48528 | + | 30.0000i | −0.452911 | + | 1.60128i | ||||
\(352\) | 24.0000i | 1.27920i | ||||||||
\(353\) | −4.24264 | −0.225813 | −0.112906 | − | 0.993606i | \(-0.536016\pi\) | ||||
−0.112906 | + | 0.993606i | \(0.536016\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 27.0000 | + | 9.00000i | 1.43301 | + | 0.477670i | ||||
\(356\) | 14.1421i | 0.749532i | ||||||||
\(357\) | −4.24264 | + | 6.00000i | −0.224544 | + | 0.317554i | ||||
\(358\) | − | 6.00000i | − | 0.317110i | ||||||
\(359\) | −4.24264 | −0.223918 | −0.111959 | − | 0.993713i | \(-0.535713\pi\) | ||||
−0.111959 | + | 0.993713i | \(0.535713\pi\) | |||||||
\(360\) | 18.9706 | − | 0.343146i | 0.999836 | − | 0.0180854i | ||||
\(361\) | −17.0000 | −0.894737 | ||||||||
\(362\) | − | 2.82843i | − | 0.148659i | ||||||
\(363\) | −7.00000 | + | 9.89949i | −0.367405 | + | 0.519589i | ||||
\(364\) | − | 12.0000i | − | 0.628971i | ||||||
\(365\) | 4.24264 | − | 12.7279i | 0.222070 | − | 0.666210i | ||||
\(366\) | −20.0000 | − | 14.1421i | −1.04542 | − | 0.739221i | ||||
\(367\) | 8.00000 | 0.417597 | 0.208798 | − | 0.977959i | \(-0.433045\pi\) | ||||
0.208798 | + | 0.977959i | \(0.433045\pi\) | |||||||
\(368\) | 5.65685i | 0.294884i | ||||||||
\(369\) | 4.00000 | − | 1.41421i | 0.208232 | − | 0.0736210i | ||||
\(370\) | 18.0000 | + | 6.00000i | 0.935775 | + | 0.311925i | ||||
\(371\) | −8.48528 | −0.440534 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.0000i | 0.621336i | 0.950518 | + | 0.310668i | \(0.100553\pi\) | ||||
−0.950518 | + | 0.310668i | \(0.899447\pi\) | |||||||
\(374\) | 25.4558i | 1.31629i | ||||||||
\(375\) | −19.3640 | − | 0.192388i | −0.999951 | − | 0.00993488i | ||||
\(376\) | 8.00000 | 0.412568 | ||||||||
\(377\) | 16.9706 | 0.874028 | ||||||||
\(378\) | 2.00000 | − | 7.07107i | 0.102869 | − | 0.363696i | ||||
\(379\) | − | 36.0000i | − | 1.84920i | −0.380945 | − | 0.924598i | \(-0.624401\pi\) | ||
0.380945 | − | 0.924598i | \(-0.375599\pi\) | |||||||
\(380\) | 8.48528 | − | 25.4558i | 0.435286 | − | 1.30586i | ||||
\(381\) | 16.0000 | − | 22.6274i | 0.819705 | − | 1.15924i | ||||
\(382\) | − | 18.0000i | − | 0.920960i | ||||||
\(383\) | − | 11.3137i | − | 0.578103i | −0.957313 | − | 0.289052i | \(-0.906660\pi\) | ||
0.957313 | − | 0.289052i | \(-0.0933400\pi\) | |||||||
\(384\) | −16.0000 | − | 11.3137i | −0.816497 | − | 0.577350i | ||||
\(385\) | −9.00000 | − | 3.00000i | −0.458682 | − | 0.152894i | ||||
\(386\) | 25.4558 | 1.29567 | ||||||||
\(387\) | −8.00000 | − | 22.6274i | −0.406663 | − | 1.15022i | ||||
\(388\) | 12.0000i | 0.609208i | ||||||||
\(389\) | − | 2.82843i | − | 0.143407i | −0.997426 | − | 0.0717035i | \(-0.977156\pi\) | ||
0.997426 | − | 0.0717035i | \(-0.0228435\pi\) | |||||||
\(390\) | −26.4853 | + | 19.4558i | −1.34113 | + | 0.985185i | ||||
\(391\) | 6.00000i | 0.303433i | ||||||||
\(392\) | 2.82843i | 0.142857i | ||||||||
\(393\) | 8.48528 | − | 12.0000i | 0.428026 | − | 0.605320i | ||||
\(394\) | − | 36.0000i | − | 1.81365i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −8.48528 | − | 24.0000i | −0.426401 | − | 1.20605i | ||||
\(397\) | − | 30.0000i | − | 1.50566i | −0.658217 | − | 0.752828i | \(-0.728689\pi\) | ||
0.658217 | − | 0.752828i | \(-0.271311\pi\) | |||||||
\(398\) | −8.48528 | −0.425329 | ||||||||
\(399\) | −8.48528 | − | 6.00000i | −0.424795 | − | 0.300376i | ||||
\(400\) | 16.0000 | + | 12.0000i | 0.800000 | + | 0.600000i | ||||
\(401\) | 14.1421i | 0.706225i | 0.935581 | + | 0.353112i | \(0.114877\pi\) | ||||
−0.935581 | + | 0.353112i | \(0.885123\pi\) | |||||||
\(402\) | −8.00000 | − | 5.65685i | −0.399004 | − | 0.282138i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 31.1127i | 1.54791i | ||||||||
\(405\) | −18.8492 | + | 7.05025i | −0.936626 | + | 0.350330i | ||||
\(406\) | −4.00000 | −0.198517 | ||||||||
\(407\) | − | 25.4558i | − | 1.26180i | ||||||
\(408\) | −16.9706 | − | 12.0000i | −0.840168 | − | 0.594089i | ||||
\(409\) | −22.0000 | −1.08783 | −0.543915 | − | 0.839140i | \(-0.683059\pi\) | ||||
−0.543915 | + | 0.839140i | \(0.683059\pi\) | |||||||
\(410\) | 4.24264 | + | 1.41421i | 0.209529 | + | 0.0698430i | ||||
\(411\) | 16.9706 | − | 24.0000i | 0.837096 | − | 1.18383i | ||||
\(412\) | −28.0000 | −1.37946 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.00000 | − | 5.65685i | −0.0982946 | − | 0.278019i | ||||
\(415\) | 2.00000 | − | 6.00000i | 0.0981761 | − | 0.294528i | ||||
\(416\) | 33.9411 | 1.66410 | ||||||||
\(417\) | 16.9706 | + | 12.0000i | 0.831052 | + | 0.587643i | ||||
\(418\) | −36.0000 | −1.76082 | ||||||||
\(419\) | −16.9706 | −0.829066 | −0.414533 | − | 0.910034i | \(-0.636055\pi\) | ||||
−0.414533 | + | 0.910034i | \(0.636055\pi\) | |||||||
\(420\) | 6.24264 | − | 4.58579i | 0.304610 | − | 0.223763i | ||||
\(421\) | 8.00000 | 0.389896 | 0.194948 | − | 0.980814i | \(-0.437546\pi\) | ||||
0.194948 | + | 0.980814i | \(0.437546\pi\) | |||||||
\(422\) | −16.9706 | −0.826114 | ||||||||
\(423\) | −8.00000 | + | 2.82843i | −0.388973 | + | 0.137523i | ||||
\(424\) | − | 24.0000i | − | 1.16554i | ||||||
\(425\) | 16.9706 | + | 12.7279i | 0.823193 | + | 0.617395i | ||||
\(426\) | 25.4558 | + | 18.0000i | 1.23334 | + | 0.872103i | ||||
\(427\) | −10.0000 | −0.483934 | ||||||||
\(428\) | 14.1421i | 0.683586i | ||||||||
\(429\) | 36.0000 | + | 25.4558i | 1.73810 | + | 1.22902i | ||||
\(430\) | 8.00000 | − | 24.0000i | 0.385794 | − | 1.15738i | ||||
\(431\) | 4.24264 | 0.204361 | 0.102180 | − | 0.994766i | \(-0.467418\pi\) | ||||
0.102180 | + | 0.994766i | \(0.467418\pi\) | |||||||
\(432\) | 20.0000 | + | 5.65685i | 0.962250 | + | 0.272166i | ||||
\(433\) | − | 18.0000i | − | 0.865025i | −0.901628 | − | 0.432512i | \(-0.857627\pi\) | ||
0.901628 | − | 0.432512i | \(-0.142373\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.48528 | + | 8.82843i | 0.310945 | + | 0.423291i | ||||
\(436\) | −4.00000 | −0.191565 | ||||||||
\(437\) | −8.48528 | −0.405906 | ||||||||
\(438\) | 8.48528 | − | 12.0000i | 0.405442 | − | 0.573382i | ||||
\(439\) | 18.0000i | 0.859093i | 0.903045 | + | 0.429547i | \(0.141327\pi\) | ||||
−0.903045 | + | 0.429547i | \(0.858673\pi\) | |||||||
\(440\) | 8.48528 | − | 25.4558i | 0.404520 | − | 1.21356i | ||||
\(441\) | −1.00000 | − | 2.82843i | −0.0476190 | − | 0.134687i | ||||
\(442\) | 36.0000 | 1.71235 | ||||||||
\(443\) | 35.3553i | 1.67978i | 0.542754 | + | 0.839891i | \(0.317381\pi\) | ||||
−0.542754 | + | 0.839891i | \(0.682619\pi\) | |||||||
\(444\) | 16.9706 | + | 12.0000i | 0.805387 | + | 0.569495i | ||||
\(445\) | 5.00000 | − | 15.0000i | 0.237023 | − | 0.711068i | ||||
\(446\) | − | 11.3137i | − | 0.535720i | ||||||
\(447\) | 16.0000 | + | 11.3137i | 0.756774 | + | 0.535120i | ||||
\(448\) | −8.00000 | −0.377964 | ||||||||
\(449\) | 5.65685i | 0.266963i | 0.991051 | + | 0.133482i | \(0.0426157\pi\) | ||||
−0.991051 | + | 0.133482i | \(0.957384\pi\) | |||||||
\(450\) | −20.2426 | − | 6.34315i | −0.954247 | − | 0.299019i | ||||
\(451\) | − | 6.00000i | − | 0.282529i | ||||||
\(452\) | −16.9706 | −0.798228 | ||||||||
\(453\) | 16.9706 | + | 12.0000i | 0.797347 | + | 0.563809i | ||||
\(454\) | 32.0000 | 1.50183 | ||||||||
\(455\) | −4.24264 | + | 12.7279i | −0.198898 | + | 0.596694i | ||||
\(456\) | 16.9706 | − | 24.0000i | 0.794719 | − | 1.12390i | ||||
\(457\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(458\) | − | 19.7990i | − | 0.925146i | ||||||
\(459\) | 21.2132 | + | 6.00000i | 0.990148 | + | 0.280056i | ||||
\(460\) | 2.00000 | − | 6.00000i | 0.0932505 | − | 0.279751i | ||||
\(461\) | − | 15.5563i | − | 0.724531i | −0.932075 | − | 0.362266i | \(-0.882003\pi\) | ||
0.932075 | − | 0.362266i | \(-0.117997\pi\) | |||||||
\(462\) | −8.48528 | − | 6.00000i | −0.394771 | − | 0.279145i | ||||
\(463\) | −4.00000 | −0.185896 | −0.0929479 | − | 0.995671i | \(-0.529629\pi\) | ||||
−0.0929479 | + | 0.995671i | \(0.529629\pi\) | |||||||
\(464\) | − | 11.3137i | − | 0.525226i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 24.0000i | 1.11178i | ||||||||
\(467\) | 5.65685i | 0.261768i | 0.991398 | + | 0.130884i | \(0.0417815\pi\) | ||||
−0.991398 | + | 0.130884i | \(0.958218\pi\) | |||||||
\(468\) | −33.9411 | + | 12.0000i | −1.56893 | + | 0.554700i | ||||
\(469\) | −4.00000 | −0.184703 | ||||||||
\(470\) | −8.48528 | − | 2.82843i | −0.391397 | − | 0.130466i | ||||
\(471\) | −25.4558 | − | 18.0000i | −1.17294 | − | 0.829396i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −33.9411 | −1.56061 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.0000 | + | 24.0000i | −0.825897 | + | 1.10120i | ||||
\(476\) | −8.48528 | −0.388922 | ||||||||
\(477\) | 8.48528 | + | 24.0000i | 0.388514 | + | 1.09888i | ||||
\(478\) | 6.00000i | 0.274434i | ||||||||
\(479\) | 8.48528 | 0.387702 | 0.193851 | − | 0.981031i | \(-0.437902\pi\) | ||||
0.193851 | + | 0.981031i | \(0.437902\pi\) | |||||||
\(480\) | 12.9706 | + | 17.6569i | 0.592022 | + | 0.805921i | ||||
\(481\) | −36.0000 | −1.64146 | ||||||||
\(482\) | − | 36.7696i | − | 1.67481i | ||||||
\(483\) | −2.00000 | − | 1.41421i | −0.0910032 | − | 0.0643489i | ||||
\(484\) | −14.0000 | −0.636364 | ||||||||
\(485\) | 4.24264 | − | 12.7279i | 0.192648 | − | 0.577945i | ||||
\(486\) | −22.0000 | + | 1.41421i | −0.997940 | + | 0.0641500i | ||||
\(487\) | 20.0000 | 0.906287 | 0.453143 | − | 0.891438i | \(-0.350303\pi\) | ||||
0.453143 | + | 0.891438i | \(0.350303\pi\) | |||||||
\(488\) | − | 28.2843i | − | 1.28037i | ||||||
\(489\) | −20.0000 | + | 28.2843i | −0.904431 | + | 1.27906i | ||||
\(490\) | 1.00000 | − | 3.00000i | 0.0451754 | − | 0.135526i | ||||
\(491\) | −29.6985 | −1.34027 | −0.670137 | − | 0.742237i | \(-0.733765\pi\) | ||||
−0.670137 | + | 0.742237i | \(0.733765\pi\) | |||||||
\(492\) | 4.00000 | + | 2.82843i | 0.180334 | + | 0.127515i | ||||
\(493\) | − | 12.0000i | − | 0.540453i | ||||||
\(494\) | 50.9117i | 2.29063i | ||||||||
\(495\) | 0.514719 | + | 28.4558i | 0.0231349 | + | 1.27900i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.7279 | 0.570925 | ||||||||
\(498\) | 4.00000 | − | 5.65685i | 0.179244 | − | 0.253490i | ||||
\(499\) | 12.0000i | 0.537194i | 0.963253 | + | 0.268597i | \(0.0865599\pi\) | ||||
−0.963253 | + | 0.268597i | \(0.913440\pi\) | |||||||
\(500\) | −12.7279 | − | 18.3848i | −0.569210 | − | 0.822192i | ||||
\(501\) | −20.0000 | − | 14.1421i | −0.893534 | − | 0.631824i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.65685i | 0.252227i | 0.992016 | + | 0.126113i | \(0.0402503\pi\) | ||||
−0.992016 | + | 0.126113i | \(0.959750\pi\) | |||||||
\(504\) | 8.00000 | − | 2.82843i | 0.356348 | − | 0.125988i | ||||
\(505\) | 11.0000 | − | 33.0000i | 0.489494 | − | 1.46848i | ||||
\(506\) | −8.48528 | −0.377217 | ||||||||
\(507\) | 23.0000 | − | 32.5269i | 1.02147 | − | 1.44457i | ||||
\(508\) | 32.0000 | 1.41977 | ||||||||
\(509\) | − | 24.0416i | − | 1.06563i | −0.846233 | − | 0.532813i | \(-0.821135\pi\) | ||
0.846233 | − | 0.532813i | \(-0.178865\pi\) | |||||||
\(510\) | 13.7574 | + | 18.7279i | 0.609186 | + | 0.829286i | ||||
\(511\) | − | 6.00000i | − | 0.265424i | ||||||
\(512\) | − | 22.6274i | − | 1.00000i | ||||||
\(513\) | −8.48528 | + | 30.0000i | −0.374634 | + | 1.32453i | ||||
\(514\) | − | 6.00000i | − | 0.264649i | ||||||
\(515\) | 29.6985 | + | 9.89949i | 1.30867 | + | 0.436224i | ||||
\(516\) | 16.0000 | − | 22.6274i | 0.704361 | − | 0.996116i | ||||
\(517\) | 12.0000i | 0.527759i | ||||||||
\(518\) | 8.48528 | 0.372822 | ||||||||
\(519\) | −12.7279 | + | 18.0000i | −0.558694 | + | 0.790112i | ||||
\(520\) | −36.0000 | − | 12.0000i | −1.57870 | − | 0.526235i | ||||
\(521\) | − | 7.07107i | − | 0.309789i | −0.987931 | − | 0.154895i | \(-0.950496\pi\) | ||
0.987931 | − | 0.154895i | \(-0.0495038\pi\) | |||||||
\(522\) | 4.00000 | + | 11.3137i | 0.175075 | + | 0.495188i | ||||
\(523\) | −34.0000 | −1.48672 | −0.743358 | − | 0.668894i | \(-0.766768\pi\) | ||||
−0.743358 | + | 0.668894i | \(0.766768\pi\) | |||||||
\(524\) | 16.9706 | 0.741362 | ||||||||
\(525\) | −8.24264 | + | 2.65685i | −0.359738 | + | 0.115955i | ||||
\(526\) | −22.0000 | −0.959246 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 16.9706 | − | 24.0000i | 0.738549 | − | 1.04447i | ||||
\(529\) | 21.0000 | 0.913043 | ||||||||
\(530\) | −8.48528 | + | 25.4558i | −0.368577 | + | 1.10573i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 12.0000i | − | 0.520266i | ||||||
\(533\) | −8.48528 | −0.367538 | ||||||||
\(534\) | 10.0000 | − | 14.1421i | 0.432742 | − | 0.611990i | ||||
\(535\) | 5.00000 | − | 15.0000i | 0.216169 | − | 0.648507i | ||||
\(536\) | − | 11.3137i | − | 0.488678i | ||||||
\(537\) | −4.24264 | + | 6.00000i | −0.183083 | + | 0.258919i | ||||
\(538\) | 26.0000 | 1.12094 | ||||||||
\(539\) | −4.24264 | −0.182743 | ||||||||
\(540\) | −19.2132 | − | 13.0711i | −0.826805 | − | 0.562489i | ||||
\(541\) | −16.0000 | −0.687894 | −0.343947 | − | 0.938989i | \(-0.611764\pi\) | ||||
−0.343947 | + | 0.938989i | \(0.611764\pi\) | |||||||
\(542\) | 33.9411 | 1.45790 | ||||||||
\(543\) | −2.00000 | + | 2.82843i | −0.0858282 | + | 0.121379i | ||||
\(544\) | − | 24.0000i | − | 1.02899i | ||||||
\(545\) | 4.24264 | + | 1.41421i | 0.181735 | + | 0.0605783i | ||||
\(546\) | −8.48528 | + | 12.0000i | −0.363137 | + | 0.513553i | ||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | 33.9411 | 1.44989 | ||||||||
\(549\) | 10.0000 | + | 28.2843i | 0.426790 | + | 1.20714i | ||||
\(550\) | −18.0000 | + | 24.0000i | −0.767523 | + | 1.02336i | ||||
\(551\) | 16.9706 | 0.722970 | ||||||||
\(552\) | 4.00000 | − | 5.65685i | 0.170251 | − | 0.240772i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 8.48528 | 0.360505 | ||||||||
\(555\) | −13.7574 | − | 18.7279i | −0.583967 | − | 0.794956i | ||||
\(556\) | 24.0000i | 1.01783i | ||||||||
\(557\) | −8.48528 | −0.359533 | −0.179766 | − | 0.983709i | \(-0.557534\pi\) | ||||
−0.179766 | + | 0.983709i | \(0.557534\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 48.0000i | 2.03018i | ||||||||
\(560\) | 8.48528 | + | 2.82843i | 0.358569 | + | 0.119523i | ||||
\(561\) | 18.0000 | − | 25.4558i | 0.759961 | − | 1.07475i | ||||
\(562\) | −4.00000 | −0.168730 | ||||||||
\(563\) | − | 11.3137i | − | 0.476816i | −0.971165 | − | 0.238408i | \(-0.923374\pi\) | ||
0.971165 | − | 0.238408i | \(-0.0766255\pi\) | |||||||
\(564\) | −8.00000 | − | 5.65685i | −0.336861 | − | 0.238197i | ||||
\(565\) | 18.0000 | + | 6.00000i | 0.757266 | + | 0.252422i | ||||
\(566\) | 5.65685i | 0.237775i | ||||||||
\(567\) | −7.00000 | + | 5.65685i | −0.293972 | + | 0.237566i | ||||
\(568\) | 36.0000i | 1.51053i | ||||||||
\(569\) | − | 2.82843i | − | 0.118574i | −0.998241 | − | 0.0592869i | \(-0.981117\pi\) | ||
0.998241 | − | 0.0592869i | \(-0.0188827\pi\) | |||||||
\(570\) | −26.4853 | + | 19.4558i | −1.10935 | + | 0.814916i | ||||
\(571\) | 36.0000i | 1.50655i | 0.657704 | + | 0.753277i | \(0.271528\pi\) | ||||
−0.657704 | + | 0.753277i | \(0.728472\pi\) | |||||||
\(572\) | 50.9117i | 2.12872i | ||||||||
\(573\) | −12.7279 | + | 18.0000i | −0.531717 | + | 0.751961i | ||||
\(574\) | 2.00000 | 0.0834784 | ||||||||
\(575\) | −4.24264 | + | 5.65685i | −0.176930 | + | 0.235907i | ||||
\(576\) | 8.00000 | + | 22.6274i | 0.333333 | + | 0.942809i | ||||
\(577\) | − | 42.0000i | − | 1.74848i | −0.485491 | − | 0.874241i | \(-0.661359\pi\) | ||
0.485491 | − | 0.874241i | \(-0.338641\pi\) | |||||||
\(578\) | − | 1.41421i | − | 0.0588235i | ||||||
\(579\) | −25.4558 | − | 18.0000i | −1.05791 | − | 0.748054i | ||||
\(580\) | −4.00000 | + | 12.0000i | −0.166091 | + | 0.498273i | ||||
\(581\) | − | 2.82843i | − | 0.117343i | ||||||
\(582\) | 8.48528 | − | 12.0000i | 0.351726 | − | 0.497416i | ||||
\(583\) | 36.0000 | 1.49097 | ||||||||
\(584\) | 16.9706 | 0.702247 | ||||||||
\(585\) | 40.2426 | − | 0.727922i | 1.66383 | − | 0.0300959i | ||||
\(586\) | − | 30.0000i | − | 1.23929i | ||||||
\(587\) | − | 28.2843i | − | 1.16742i | −0.811963 | − | 0.583708i | \(-0.801601\pi\) | ||
0.811963 | − | 0.583708i | \(-0.198399\pi\) | |||||||
\(588\) | 2.00000 | − | 2.82843i | 0.0824786 | − | 0.116642i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −25.4558 | + | 36.0000i | −1.04711 | + | 1.48084i | ||||
\(592\) | 24.0000i | 0.986394i | ||||||||
\(593\) | −4.24264 | −0.174224 | −0.0871122 | − | 0.996199i | \(-0.527764\pi\) | ||||
−0.0871122 | + | 0.996199i | \(0.527764\pi\) | |||||||
\(594\) | −8.48528 | + | 30.0000i | −0.348155 | + | 1.23091i | ||||
\(595\) | 9.00000 | + | 3.00000i | 0.368964 | + | 0.122988i | ||||
\(596\) | 22.6274i | 0.926855i | ||||||||
\(597\) | 8.48528 | + | 6.00000i | 0.347279 | + | 0.245564i | ||||
\(598\) | 12.0000i | 0.490716i | ||||||||
\(599\) | 12.7279 | 0.520049 | 0.260024 | − | 0.965602i | \(-0.416269\pi\) | ||||
0.260024 | + | 0.965602i | \(0.416269\pi\) | |||||||
\(600\) | −7.51472 | − | 23.3137i | −0.306787 | − | 0.951778i | ||||
\(601\) | −10.0000 | −0.407909 | −0.203954 | − | 0.978980i | \(-0.565379\pi\) | ||||
−0.203954 | + | 0.978980i | \(0.565379\pi\) | |||||||
\(602\) | − | 11.3137i | − | 0.461112i | ||||||
\(603\) | 4.00000 | + | 11.3137i | 0.162893 | + | 0.460730i | ||||
\(604\) | 24.0000i | 0.976546i | ||||||||
\(605\) | 14.8492 | + | 4.94975i | 0.603708 | + | 0.201236i | ||||
\(606\) | 22.0000 | − | 31.1127i | 0.893689 | − | 1.26387i | ||||
\(607\) | 32.0000 | 1.29884 | 0.649420 | − | 0.760430i | \(-0.275012\pi\) | ||||
0.649420 | + | 0.760430i | \(0.275012\pi\) | |||||||
\(608\) | 33.9411 | 1.37649 | ||||||||
\(609\) | 4.00000 | + | 2.82843i | 0.162088 | + | 0.114614i | ||||
\(610\) | −10.0000 | + | 30.0000i | −0.404888 | + | 1.21466i | ||||
\(611\) | 16.9706 | 0.686555 | ||||||||
\(612\) | 8.48528 | + | 24.0000i | 0.342997 | + | 0.970143i | ||||
\(613\) | − | 24.0000i | − | 0.969351i | −0.874694 | − | 0.484675i | \(-0.838938\pi\) | ||
0.874694 | − | 0.484675i | \(-0.161062\pi\) | |||||||
\(614\) | − | 28.2843i | − | 1.14146i | ||||||
\(615\) | −3.24264 | − | 4.41421i | −0.130756 | − | 0.177998i | ||||
\(616\) | − | 12.0000i | − | 0.483494i | ||||||
\(617\) | −16.9706 | −0.683209 | −0.341605 | − | 0.939844i | \(-0.610970\pi\) | ||||
−0.341605 | + | 0.939844i | \(0.610970\pi\) | |||||||
\(618\) | 28.0000 | + | 19.7990i | 1.12633 | + | 0.796432i | ||||
\(619\) | − | 12.0000i | − | 0.482321i | −0.970485 | − | 0.241160i | \(-0.922472\pi\) | ||
0.970485 | − | 0.241160i | \(-0.0775280\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.00000 | + | 7.07107i | −0.0802572 | + | 0.283752i | ||||
\(622\) | 36.0000i | 1.44347i | ||||||||
\(623\) | − | 7.07107i | − | 0.283296i | ||||||
\(624\) | −33.9411 | − | 24.0000i | −1.35873 | − | 0.960769i | ||||
\(625\) | 7.00000 | + | 24.0000i | 0.280000 | + | 0.960000i | ||||
\(626\) | −25.4558 | −1.01742 | ||||||||
\(627\) | 36.0000 | + | 25.4558i | 1.43770 | + | 1.01661i | ||||
\(628\) | − | 36.0000i | − | 1.43656i | ||||||
\(629\) | 25.4558i | 1.01499i | ||||||||
\(630\) | −9.48528 | + | 0.171573i | −0.377903 | + | 0.00683563i | ||||
\(631\) | − | 36.0000i | − | 1.43314i | −0.697517 | − | 0.716569i | \(-0.745712\pi\) | ||
0.697517 | − | 0.716569i | \(-0.254288\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.9706 | + | 12.0000i | 0.674519 | + | 0.476957i | ||||
\(634\) | 36.0000i | 1.42974i | ||||||||
\(635\) | −33.9411 | − | 11.3137i | −1.34691 | − | 0.448971i | ||||
\(636\) | −16.9706 | + | 24.0000i | −0.672927 | + | 0.951662i | ||||
\(637\) | 6.00000i | 0.237729i | ||||||||
\(638\) | 16.9706 | 0.671871 | ||||||||
\(639\) | −12.7279 | − | 36.0000i | −0.503509 | − | 1.42414i | ||||
\(640\) | −8.00000 | + | 24.0000i | −0.316228 | + | 0.948683i | ||||
\(641\) | 48.0833i | 1.89917i | 0.313503 | + | 0.949587i | \(0.398498\pi\) | ||||
−0.313503 | + | 0.949587i | \(0.601502\pi\) | |||||||
\(642\) | 10.0000 | − | 14.1421i | 0.394669 | − | 0.558146i | ||||
\(643\) | −4.00000 | −0.157745 | −0.0788723 | − | 0.996885i | \(-0.525132\pi\) | ||||
−0.0788723 | + | 0.996885i | \(0.525132\pi\) | |||||||
\(644\) | − | 2.82843i | − | 0.111456i | ||||||
\(645\) | −24.9706 | + | 18.3431i | −0.983215 | + | 0.722261i | ||||
\(646\) | 36.0000 | 1.41640 | ||||||||
\(647\) | 31.1127i | 1.22317i | 0.791180 | + | 0.611583i | \(0.209467\pi\) | ||||
−0.791180 | + | 0.611583i | \(0.790533\pi\) | |||||||
\(648\) | −16.0000 | − | 19.7990i | −0.628539 | − | 0.777778i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 33.9411 | + | 25.4558i | 1.33128 | + | 0.998460i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −40.0000 | −1.56652 | ||||||||
\(653\) | 16.9706 | 0.664109 | 0.332055 | − | 0.943260i | \(-0.392258\pi\) | ||||
0.332055 | + | 0.943260i | \(0.392258\pi\) | |||||||
\(654\) | 4.00000 | + | 2.82843i | 0.156412 | + | 0.110600i | ||||
\(655\) | −18.0000 | − | 6.00000i | −0.703318 | − | 0.234439i | ||||
\(656\) | 5.65685i | 0.220863i | ||||||||
\(657\) | −16.9706 | + | 6.00000i | −0.662085 | + | 0.234082i | ||||
\(658\) | −4.00000 | −0.155936 | ||||||||
\(659\) | 4.24264 | 0.165270 | 0.0826349 | − | 0.996580i | \(-0.473666\pi\) | ||||
0.0826349 | + | 0.996580i | \(0.473666\pi\) | |||||||
\(660\) | −26.4853 | + | 19.4558i | −1.03094 | + | 0.757318i | ||||
\(661\) | 14.0000 | 0.544537 | 0.272268 | − | 0.962221i | \(-0.412226\pi\) | ||||
0.272268 | + | 0.962221i | \(0.412226\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −36.0000 | − | 25.4558i | −1.39812 | − | 0.988623i | ||||
\(664\) | 8.00000 | 0.310460 | ||||||||
\(665\) | −4.24264 | + | 12.7279i | −0.164523 | + | 0.493568i | ||||
\(666\) | −8.48528 | − | 24.0000i | −0.328798 | − | 0.929981i | ||||
\(667\) | 4.00000 | 0.154881 | ||||||||
\(668\) | − | 28.2843i | − | 1.09435i | ||||||
\(669\) | −8.00000 | + | 11.3137i | −0.309298 | + | 0.437413i | ||||
\(670\) | −4.00000 | + | 12.0000i | −0.154533 | + | 0.463600i | ||||
\(671\) | 42.4264 | 1.63785 | ||||||||
\(672\) | 8.00000 | + | 5.65685i | 0.308607 | + | 0.218218i | ||||
\(673\) | 30.0000i | 1.15642i | 0.815890 | + | 0.578208i | \(0.196248\pi\) | ||||
−0.815890 | + | 0.578208i | \(0.803752\pi\) | |||||||
\(674\) | −16.9706 | −0.653682 | ||||||||
\(675\) | 15.7574 | + | 20.6569i | 0.606501 | + | 0.795083i | ||||
\(676\) | 46.0000 | 1.76923 | ||||||||
\(677\) | 12.7279 | 0.489174 | 0.244587 | − | 0.969627i | \(-0.421348\pi\) | ||||
0.244587 | + | 0.969627i | \(0.421348\pi\) | |||||||
\(678\) | 16.9706 | + | 12.0000i | 0.651751 | + | 0.460857i | ||||
\(679\) | − | 6.00000i | − | 0.230259i | ||||||
\(680\) | −8.48528 | + | 25.4558i | −0.325396 | + | 0.976187i | ||||
\(681\) | −32.0000 | − | 22.6274i | −1.22624 | − | 0.867085i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 32.5269i | − | 1.24461i | −0.782776 | − | 0.622304i | \(-0.786197\pi\) | ||
0.782776 | − | 0.622304i | \(-0.213803\pi\) | |||||||
\(684\) | −33.9411 | + | 12.0000i | −1.29777 | + | 0.458831i | ||||
\(685\) | −36.0000 | − | 12.0000i | −1.37549 | − | 0.458496i | ||||
\(686\) | − | 1.41421i | − | 0.0539949i | ||||||
\(687\) | −14.0000 | + | 19.7990i | −0.534133 | + | 0.755379i | ||||
\(688\) | 32.0000 | 1.21999 | ||||||||
\(689\) | − | 50.9117i | − | 1.93958i | ||||||
\(690\) | −6.24264 | + | 4.58579i | −0.237653 | + | 0.174578i | ||||
\(691\) | − | 36.0000i | − | 1.36950i | −0.728776 | − | 0.684752i | \(-0.759910\pi\) | ||
0.728776 | − | 0.684752i | \(-0.240090\pi\) | |||||||
\(692\) | −25.4558 | −0.967686 | ||||||||
\(693\) | 4.24264 | + | 12.0000i | 0.161165 | + | 0.455842i | ||||
\(694\) | 2.00000 | 0.0759190 | ||||||||
\(695\) | 8.48528 | − | 25.4558i | 0.321865 | − | 0.965595i | ||||
\(696\) | −8.00000 | + | 11.3137i | −0.303239 | + | 0.428845i | ||||
\(697\) | 6.00000i | 0.227266i | ||||||||
\(698\) | − | 36.7696i | − | 1.39175i | ||||||
\(699\) | 16.9706 | − | 24.0000i | 0.641886 | − | 0.907763i | ||||
\(700\) | −8.00000 | − | 6.00000i | −0.302372 | − | 0.226779i | ||||
\(701\) | − | 19.7990i | − | 0.747798i | −0.927470 | − | 0.373899i | \(-0.878021\pi\) | ||
0.927470 | − | 0.373899i | \(-0.121979\pi\) | |||||||
\(702\) | 42.4264 | + | 12.0000i | 1.60128 | + | 0.452911i | ||||
\(703\) | −36.0000 | −1.35777 | ||||||||
\(704\) | 33.9411 | 1.27920 | ||||||||
\(705\) | 6.48528 | + | 8.82843i | 0.244250 | + | 0.332498i | ||||
\(706\) | 6.00000i | 0.225813i | ||||||||
\(707\) | − | 15.5563i | − | 0.585057i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.0000 | −0.375558 | −0.187779 | − | 0.982211i | \(-0.560129\pi\) | ||||
−0.187779 | + | 0.982211i | \(0.560129\pi\) | |||||||
\(710\) | 12.7279 | − | 38.1838i | 0.477670 | − | 1.43301i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 20.0000 | 0.749532 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 8.48528 | + | 6.00000i | 0.317554 | + | 0.224544i | ||||
\(715\) | 18.0000 | − | 54.0000i | 0.673162 | − | 2.01949i | ||||
\(716\) | −8.48528 | −0.317110 | ||||||||
\(717\) | 4.24264 | − | 6.00000i | 0.158444 | − | 0.224074i | ||||
\(718\) | 6.00000i | 0.223918i | ||||||||
\(719\) | 33.9411 | 1.26579 | 0.632895 | − | 0.774237i | \(-0.281866\pi\) | ||||
0.632895 | + | 0.774237i | \(0.281866\pi\) | |||||||
\(720\) | −0.485281 | − | 26.8284i | −0.0180854 | − | 0.999836i | ||||
\(721\) | 14.0000 | 0.521387 | ||||||||
\(722\) | 24.0416i | 0.894737i | ||||||||
\(723\) | −26.0000 | + | 36.7696i | −0.966950 | + | 1.36747i | ||||
\(724\) | −4.00000 | −0.148659 | ||||||||
\(725\) | 8.48528 | − | 11.3137i | 0.315135 | − | 0.420181i | ||||
\(726\) | 14.0000 | + | 9.89949i | 0.519589 | + | 0.367405i | ||||
\(727\) | 26.0000 | 0.964287 | 0.482143 | − | 0.876092i | \(-0.339858\pi\) | ||||
0.482143 | + | 0.876092i | \(0.339858\pi\) | |||||||
\(728\) | −16.9706 | −0.628971 | ||||||||
\(729\) | 23.0000 | + | 14.1421i | 0.851852 | + | 0.523783i | ||||
\(730\) | −18.0000 | − | 6.00000i | −0.666210 | − | 0.222070i | ||||
\(731\) | 33.9411 | 1.25536 | ||||||||
\(732\) | −20.0000 | + | 28.2843i | −0.739221 | + | 1.04542i | ||||
\(733\) | − | 6.00000i | − | 0.221615i | −0.993842 | − | 0.110808i | \(-0.964656\pi\) | ||
0.993842 | − | 0.110808i | \(-0.0353437\pi\) | |||||||
\(734\) | − | 11.3137i | − | 0.417597i | ||||||
\(735\) | −3.12132 | + | 2.29289i | −0.115132 | + | 0.0845746i | ||||
\(736\) | 8.00000 | 0.294884 | ||||||||
\(737\) | 16.9706 | 0.625119 | ||||||||
\(738\) | −2.00000 | − | 5.65685i | −0.0736210 | − | 0.208232i | ||||
\(739\) | − | 24.0000i | − | 0.882854i | −0.897297 | − | 0.441427i | \(-0.854472\pi\) | ||
0.897297 | − | 0.441427i | \(-0.145528\pi\) | |||||||
\(740\) | 8.48528 | − | 25.4558i | 0.311925 | − | 0.935775i | ||||
\(741\) | 36.0000 | − | 50.9117i | 1.32249 | − | 1.87029i | ||||
\(742\) | 12.0000i | 0.440534i | ||||||||
\(743\) | 1.41421i | 0.0518825i | 0.999663 | + | 0.0259412i | \(0.00825828\pi\) | ||||
−0.999663 | + | 0.0259412i | \(0.991742\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.00000 | − | 24.0000i | 0.293097 | − | 0.879292i | ||||
\(746\) | 16.9706 | 0.621336 | ||||||||
\(747\) | −8.00000 | + | 2.82843i | −0.292705 | + | 0.103487i | ||||
\(748\) | 36.0000 | 1.31629 | ||||||||
\(749\) | − | 7.07107i | − | 0.258371i | ||||||
\(750\) | −0.272078 | + | 27.3848i | −0.00993488 | + | 0.999951i | ||||
\(751\) | 12.0000i | 0.437886i | 0.975738 | + | 0.218943i | \(0.0702609\pi\) | ||||
−0.975738 | + | 0.218943i | \(0.929739\pi\) | |||||||
\(752\) | − | 11.3137i | − | 0.412568i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 24.0000i | − | 0.874028i | ||||||
\(755\) | 8.48528 | − | 25.4558i | 0.308811 | − | 0.926433i | ||||
\(756\) | −10.0000 | − | 2.82843i | −0.363696 | − | 0.102869i | ||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | −50.9117 | −1.84920 | ||||||||
\(759\) | 8.48528 | + | 6.00000i | 0.307996 | + | 0.217786i | ||||
\(760\) | −36.0000 | − | 12.0000i | −1.30586 | − | 0.435286i | ||||
\(761\) | 52.3259i | 1.89681i | 0.317058 | + | 0.948406i | \(0.397305\pi\) | ||||
−0.317058 | + | 0.948406i | \(0.602695\pi\) | |||||||
\(762\) | −32.0000 | − | 22.6274i | −1.15924 | − | 0.819705i | ||||
\(763\) | 2.00000 | 0.0724049 | ||||||||
\(764\) | −25.4558 | −0.920960 | ||||||||
\(765\) | −0.514719 | − | 28.4558i | −0.0186097 | − | 1.02882i | ||||
\(766\) | −16.0000 | −0.578103 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −16.0000 | + | 22.6274i | −0.577350 | + | 0.816497i | ||||
\(769\) | 14.0000 | 0.504853 | 0.252426 | − | 0.967616i | \(-0.418771\pi\) | ||||
0.252426 | + | 0.967616i | \(0.418771\pi\) | |||||||
\(770\) | −4.24264 | + | 12.7279i | −0.152894 | + | 0.458682i | ||||
\(771\) | −4.24264 | + | 6.00000i | −0.152795 | + | 0.216085i | ||||
\(772\) | − | 36.0000i | − | 1.29567i | ||||||
\(773\) | 29.6985 | 1.06818 | 0.534090 | − | 0.845428i | \(-0.320654\pi\) | ||||
0.534090 | + | 0.845428i | \(0.320654\pi\) | |||||||
\(774\) | −32.0000 | + | 11.3137i | −1.15022 | + | 0.406663i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 16.9706 | 0.609208 | ||||||||
\(777\) | −8.48528 | − | 6.00000i | −0.304408 | − | 0.215249i | ||||
\(778\) | −4.00000 | −0.143407 | ||||||||
\(779\) | −8.48528 | −0.304017 | ||||||||
\(780\) | 27.5147 | + | 37.4558i | 0.985185 | + | 1.34113i | ||||
\(781\) | −54.0000 | −1.93227 | ||||||||
\(782\) | 8.48528 | 0.303433 | ||||||||
\(783\) | 4.00000 | − | 14.1421i | 0.142948 | − | 0.505399i | ||||
\(784\) | 4.00000 | 0.142857 | ||||||||
\(785\) | −12.7279 | + | 38.1838i | −0.454279 | + | 1.36284i | ||||
\(786\) | −16.9706 | − | 12.0000i | −0.605320 | − | 0.428026i | ||||
\(787\) | −22.0000 | −0.784215 | −0.392108 | − | 0.919919i | \(-0.628254\pi\) | ||||
−0.392108 | + | 0.919919i | \(0.628254\pi\) | |||||||
\(788\) | −50.9117 | −1.81365 | ||||||||
\(789\) | 22.0000 | + | 15.5563i | 0.783221 | + | 0.553821i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.48528 | 0.301702 | ||||||||
\(792\) | −33.9411 | + | 12.0000i | −1.20605 | + | 0.426401i | ||||
\(793\) | − | 60.0000i | − | 2.13066i | ||||||
\(794\) | −42.4264 | −1.50566 | ||||||||
\(795\) | 26.4853 | − | 19.4558i | 0.939336 | − | 0.690028i | ||||
\(796\) | 12.0000i | 0.425329i | ||||||||
\(797\) | −4.24264 | −0.150282 | −0.0751410 | − | 0.997173i | \(-0.523941\pi\) | ||||
−0.0751410 | + | 0.997173i | \(0.523941\pi\) | |||||||
\(798\) | −8.48528 | + | 12.0000i | −0.300376 | + | 0.424795i | ||||
\(799\) | − | 12.0000i | − | 0.424529i | ||||||
\(800\) | 16.9706 | − | 22.6274i | 0.600000 | − | 0.800000i | ||||
\(801\) | −20.0000 | + | 7.07107i | −0.706665 | + | 0.249844i | ||||
\(802\) | 20.0000 | 0.706225 | ||||||||
\(803\) | 25.4558i | 0.898317i | ||||||||
\(804\) | −8.00000 | + | 11.3137i | −0.282138 | + | 0.399004i | ||||
\(805\) | −1.00000 | + | 3.00000i | −0.0352454 | + | 0.105736i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −26.0000 | − | 18.3848i | −0.915243 | − | 0.647175i | ||||
\(808\) | 44.0000 | 1.54791 | ||||||||
\(809\) | − | 45.2548i | − | 1.59108i | −0.605904 | − | 0.795538i | \(-0.707189\pi\) | ||
0.605904 | − | 0.795538i | \(-0.292811\pi\) | |||||||
\(810\) | 9.97056 | + | 26.6569i | 0.350330 | + | 0.936626i | ||||
\(811\) | 36.0000i | 1.26413i | 0.774915 | + | 0.632065i | \(0.217793\pi\) | ||||
−0.774915 | + | 0.632065i | \(0.782207\pi\) | |||||||
\(812\) | 5.65685i | 0.198517i | ||||||||
\(813\) | −33.9411 | − | 24.0000i | −1.19037 | − | 0.841717i | ||||
\(814\) | −36.0000 | −1.26180 | ||||||||
\(815\) | 42.4264 | + | 14.1421i | 1.48613 | + | 0.495377i | ||||
\(816\) | −16.9706 | + | 24.0000i | −0.594089 | + | 0.840168i | ||||
\(817\) | 48.0000i | 1.67931i | ||||||||
\(818\) | 31.1127i | 1.08783i | ||||||||
\(819\) | 16.9706 | − | 6.00000i | 0.592999 | − | 0.209657i | ||||
\(820\) | 2.00000 | − | 6.00000i | 0.0698430 | − | 0.209529i | ||||
\(821\) | 22.6274i | 0.789702i | 0.918745 | + | 0.394851i | \(0.129204\pi\) | ||||
−0.918745 | + | 0.394851i | \(0.870796\pi\) | |||||||
\(822\) | −33.9411 | − | 24.0000i | −1.18383 | − | 0.837096i | ||||
\(823\) | −40.0000 | −1.39431 | −0.697156 | − | 0.716919i | \(-0.745552\pi\) | ||||
−0.697156 | + | 0.716919i | \(0.745552\pi\) | |||||||
\(824\) | 39.5980i | 1.37946i | ||||||||
\(825\) | 34.9706 | − | 11.2721i | 1.21752 | − | 0.392443i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 32.5269i | − | 1.13107i | −0.824724 | − | 0.565536i | \(-0.808669\pi\) | ||
0.824724 | − | 0.565536i | \(-0.191331\pi\) | |||||||
\(828\) | −8.00000 | + | 2.82843i | −0.278019 | + | 0.0982946i | ||||
\(829\) | 2.00000 | 0.0694629 | 0.0347314 | − | 0.999397i | \(-0.488942\pi\) | ||||
0.0347314 | + | 0.999397i | \(0.488942\pi\) | |||||||
\(830\) | −8.48528 | − | 2.82843i | −0.294528 | − | 0.0981761i | ||||
\(831\) | −8.48528 | − | 6.00000i | −0.294351 | − | 0.208138i | ||||
\(832\) | − | 48.0000i | − | 1.66410i | ||||||
\(833\) | 4.24264 | 0.146999 | ||||||||
\(834\) | 16.9706 | − | 24.0000i | 0.587643 | − | 0.831052i | ||||
\(835\) | −10.0000 | + | 30.0000i | −0.346064 | + | 1.03819i | ||||
\(836\) | 50.9117i | 1.76082i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 24.0000i | 0.829066i | ||||||||
\(839\) | 42.4264 | 1.46472 | 0.732361 | − | 0.680916i | \(-0.238418\pi\) | ||||
0.732361 | + | 0.680916i | \(0.238418\pi\) | |||||||
\(840\) | −6.48528 | − | 8.82843i | −0.223763 | − | 0.304610i | ||||
\(841\) | 21.0000 | 0.724138 | ||||||||
\(842\) | − | 11.3137i | − | 0.389896i | ||||||
\(843\) | 4.00000 | + | 2.82843i | 0.137767 | + | 0.0974162i | ||||
\(844\) | 24.0000i | 0.826114i | ||||||||
\(845\) | −48.7904 | − | 16.2635i | −1.67844 | − | 0.559480i | ||||
\(846\) | 4.00000 | + | 11.3137i | 0.137523 | + | 0.388973i | ||||
\(847\) | 7.00000 | 0.240523 | ||||||||
\(848\) | −33.9411 | −1.16554 | ||||||||
\(849\) | 4.00000 | − | 5.65685i | 0.137280 | − | 0.194143i | ||||
\(850\) | 18.0000 | − | 24.0000i | 0.617395 | − | 0.823193i | ||||
\(851\) | −8.48528 | −0.290872 | ||||||||
\(852\) | 25.4558 | − | 36.0000i | 0.872103 | − | 1.23334i | ||||
\(853\) | 30.0000i | 1.02718i | 0.858036 | + | 0.513590i | \(0.171685\pi\) | ||||
−0.858036 | + | 0.513590i | \(0.828315\pi\) | |||||||
\(854\) | 14.1421i | 0.483934i | ||||||||
\(855\) | 40.2426 | − | 0.727922i | 1.37627 | − | 0.0248944i | ||||
\(856\) | 20.0000 | 0.683586 | ||||||||
\(857\) | 21.2132 | 0.724629 | 0.362315 | − | 0.932056i | \(-0.381987\pi\) | ||||
0.362315 | + | 0.932056i | \(0.381987\pi\) | |||||||
\(858\) | 36.0000 | − | 50.9117i | 1.22902 | − | 1.73810i | ||||
\(859\) | − | 6.00000i | − | 0.204717i | −0.994748 | − | 0.102359i | \(-0.967361\pi\) | ||
0.994748 | − | 0.102359i | \(-0.0326389\pi\) | |||||||
\(860\) | −33.9411 | − | 11.3137i | −1.15738 | − | 0.385794i | ||||
\(861\) | −2.00000 | − | 1.41421i | −0.0681598 | − | 0.0481963i | ||||
\(862\) | − | 6.00000i | − | 0.204361i | ||||||
\(863\) | 18.3848i | 0.625825i | 0.949782 | + | 0.312913i | \(0.101305\pi\) | ||||
−0.949782 | + | 0.312913i | \(0.898695\pi\) | |||||||
\(864\) | 8.00000 | − | 28.2843i | 0.272166 | − | 0.962250i | ||||
\(865\) | 27.0000 | + | 9.00000i | 0.918028 | + | 0.306009i | ||||
\(866\) | −25.4558 | −0.865025 | ||||||||
\(867\) | −1.00000 | + | 1.41421i | −0.0339618 | + | 0.0480292i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 12.4853 | − | 9.17157i | 0.423291 | − | 0.310945i | ||||
\(871\) | − | 24.0000i | − | 0.813209i | ||||||
\(872\) | 5.65685i | 0.191565i | ||||||||
\(873\) | −16.9706 | + | 6.00000i | −0.574367 | + | 0.203069i | ||||
\(874\) | 12.0000i | 0.405906i | ||||||||
\(875\) | 6.36396 | + | 9.19239i | 0.215141 | + | 0.310759i | ||||
\(876\) | −16.9706 | − | 12.0000i | −0.573382 | − | 0.405442i | ||||
\(877\) | − | 24.0000i | − | 0.810422i | −0.914223 | − | 0.405211i | \(-0.867198\pi\) | ||
0.914223 | − | 0.405211i | \(-0.132802\pi\) | |||||||
\(878\) | 25.4558 | 0.859093 | ||||||||
\(879\) | −21.2132 | + | 30.0000i | −0.715504 | + | 1.01187i | ||||
\(880\) | −36.0000 | − | 12.0000i | −1.21356 | − | 0.404520i | ||||
\(881\) | − | 7.07107i | − | 0.238230i | −0.992880 | − | 0.119115i | \(-0.961994\pi\) | ||
0.992880 | − | 0.119115i | \(-0.0380058\pi\) | |||||||
\(882\) | −4.00000 | + | 1.41421i | −0.134687 | + | 0.0476190i | ||||
\(883\) | −16.0000 | −0.538443 | −0.269221 | − | 0.963078i | \(-0.586766\pi\) | ||||
−0.269221 | + | 0.963078i | \(0.586766\pi\) | |||||||
\(884\) | − | 50.9117i | − | 1.71235i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 50.0000 | 1.67978 | ||||||||
\(887\) | 14.1421i | 0.474846i | 0.971406 | + | 0.237423i | \(0.0763028\pi\) | ||||
−0.971406 | + | 0.237423i | \(0.923697\pi\) | |||||||
\(888\) | 16.9706 | − | 24.0000i | 0.569495 | − | 0.805387i | ||||
\(889\) | −16.0000 | −0.536623 | ||||||||
\(890\) | −21.2132 | − | 7.07107i | −0.711068 | − | 0.237023i | ||||
\(891\) | 29.6985 | − | 24.0000i | 0.994937 | − | 0.804030i | ||||
\(892\) | −16.0000 | −0.535720 | ||||||||
\(893\) | 16.9706 | 0.567898 | ||||||||
\(894\) | 16.0000 | − | 22.6274i | 0.535120 | − | 0.756774i | ||||
\(895\) | 9.00000 | + | 3.00000i | 0.300837 | + | 0.100279i | ||||
\(896\) | 11.3137i | 0.377964i | ||||||||
\(897\) | 8.48528 | − | 12.0000i | 0.283315 | − | 0.400668i | ||||
\(898\) | 8.00000 | 0.266963 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −8.97056 | + | 28.6274i | −0.299019 | + | 0.954247i | ||||
\(901\) | −36.0000 | −1.19933 | ||||||||
\(902\) | −8.48528 | −0.282529 | ||||||||
\(903\) | −8.00000 | + | 11.3137i | −0.266223 | + | 0.376497i | ||||
\(904\) | 24.0000i | 0.798228i | ||||||||
\(905\) | 4.24264 | + | 1.41421i | 0.141030 | + | 0.0470100i | ||||
\(906\) | 16.9706 | − | 24.0000i | 0.563809 | − | 0.797347i | ||||
\(907\) | 8.00000 | 0.265636 | 0.132818 | − | 0.991140i | \(-0.457597\pi\) | ||||
0.132818 | + | 0.991140i | \(0.457597\pi\) | |||||||
\(908\) | − | 45.2548i | − | 1.50183i | ||||||
\(909\) | −44.0000 | + | 15.5563i | −1.45939 | + | 0.515972i | ||||
\(910\) | 18.0000 | + | 6.00000i | 0.596694 | + | 0.198898i | ||||
\(911\) | 4.24264 | 0.140565 | 0.0702825 | − | 0.997527i | \(-0.477610\pi\) | ||||
0.0702825 | + | 0.997527i | \(0.477610\pi\) | |||||||
\(912\) | −33.9411 | − | 24.0000i | −1.12390 | − | 0.794719i | ||||
\(913\) | 12.0000i | 0.397142i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 31.2132 | − | 22.9289i | 1.03188 | − | 0.758007i | ||||
\(916\) | −28.0000 | −0.925146 | ||||||||
\(917\) | −8.48528 | −0.280209 | ||||||||
\(918\) | 8.48528 | − | 30.0000i | 0.280056 | − | 0.990148i | ||||
\(919\) | − | 12.0000i | − | 0.395843i | −0.980218 | − | 0.197922i | \(-0.936581\pi\) | ||
0.980218 | − | 0.197922i | \(-0.0634192\pi\) | |||||||
\(920\) | −8.48528 | − | 2.82843i | −0.279751 | − | 0.0932505i | ||||
\(921\) | −20.0000 | + | 28.2843i | −0.659022 | + | 0.931998i | ||||
\(922\) | −22.0000 | −0.724531 | ||||||||
\(923\) | 76.3675i | 2.51367i | ||||||||
\(924\) | −8.48528 | + | 12.0000i | −0.279145 | + | 0.394771i | ||||
\(925\) | −18.0000 | + | 24.0000i | −0.591836 | + | 0.789115i | ||||
\(926\) | 5.65685i | 0.185896i | ||||||||
\(927\) | −14.0000 | − | 39.5980i | −0.459820 | − | 1.30057i | ||||
\(928\) | −16.0000 | −0.525226 | ||||||||
\(929\) | − | 41.0122i | − | 1.34557i | −0.739840 | − | 0.672783i | \(-0.765099\pi\) | ||
0.739840 | − | 0.672783i | \(-0.234901\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.00000i | 0.196642i | ||||||||
\(932\) | 33.9411 | 1.11178 | ||||||||
\(933\) | 25.4558 | − | 36.0000i | 0.833387 | − | 1.17859i | ||||
\(934\) | 8.00000 | 0.261768 | ||||||||
\(935\) | −38.1838 | − | 12.7279i | −1.24874 | − | 0.416248i | ||||
\(936\) | 16.9706 | + | 48.0000i | 0.554700 | + | 1.56893i | ||||
\(937\) | − | 18.0000i | − | 0.588034i | −0.955800 | − | 0.294017i | \(-0.905008\pi\) | ||
0.955800 | − | 0.294017i | \(-0.0949923\pi\) | |||||||
\(938\) | 5.65685i | 0.184703i | ||||||||
\(939\) | 25.4558 | + | 18.0000i | 0.830720 | + | 0.587408i | ||||
\(940\) | −4.00000 | + | 12.0000i | −0.130466 | + | 0.391397i | ||||
\(941\) | 26.8701i | 0.875939i | 0.898990 | + | 0.437969i | \(0.144302\pi\) | ||||
−0.898990 | + | 0.437969i | \(0.855698\pi\) | |||||||
\(942\) | −25.4558 | + | 36.0000i | −0.829396 | + | 1.17294i | ||||
\(943\) | −2.00000 | −0.0651290 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.60660 | + | 6.53553i | 0.312503 | + | 0.212601i | ||||
\(946\) | 48.0000i | 1.56061i | ||||||||
\(947\) | 9.89949i | 0.321690i | 0.986980 | + | 0.160845i | \(0.0514220\pi\) | ||||
−0.986980 | + | 0.160845i | \(0.948578\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 36.0000 | 1.16861 | ||||||||
\(950\) | 33.9411 | + | 25.4558i | 1.10120 | + | 0.825897i | ||||
\(951\) | 25.4558 | − | 36.0000i | 0.825462 | − | 1.16738i | ||||
\(952\) | 12.0000i | 0.388922i | ||||||||
\(953\) | 25.4558 | 0.824596 | 0.412298 | − | 0.911049i | \(-0.364726\pi\) | ||||
0.412298 | + | 0.911049i | \(0.364726\pi\) | |||||||
\(954\) | 33.9411 | − | 12.0000i | 1.09888 | − | 0.388514i | ||||
\(955\) | 27.0000 | + | 9.00000i | 0.873699 | + | 0.291233i | ||||
\(956\) | 8.48528 | 0.274434 | ||||||||
\(957\) | −16.9706 | − | 12.0000i | −0.548580 | − | 0.387905i | ||||
\(958\) | − | 12.0000i | − | 0.387702i | ||||||
\(959\) | −16.9706 | −0.548008 | ||||||||
\(960\) | 24.9706 | − | 18.3431i | 0.805921 | − | 0.592022i | ||||
\(961\) | 31.0000 | 1.00000 | ||||||||
\(962\) | 50.9117i | 1.64146i | ||||||||
\(963\) | −20.0000 | + | 7.07107i | −0.644491 | + | 0.227862i | ||||
\(964\) | −52.0000 | −1.67481 | ||||||||
\(965\) | −12.7279 | + | 38.1838i | −0.409726 | + | 1.22918i | ||||
\(966\) | −2.00000 | + | 2.82843i | −0.0643489 | + | 0.0910032i | ||||
\(967\) | −4.00000 | −0.128631 | −0.0643157 | − | 0.997930i | \(-0.520486\pi\) | ||||
−0.0643157 | + | 0.997930i | \(0.520486\pi\) | |||||||
\(968\) | 19.7990i | 0.636364i | ||||||||
\(969\) | −36.0000 | − | 25.4558i | −1.15649 | − | 0.817760i | ||||
\(970\) | −18.0000 | − | 6.00000i | −0.577945 | − | 0.192648i | ||||
\(971\) | −42.4264 | −1.36153 | −0.680764 | − | 0.732503i | \(-0.738352\pi\) | ||||
−0.680764 | + | 0.732503i | \(0.738352\pi\) | |||||||
\(972\) | 2.00000 | + | 31.1127i | 0.0641500 | + | 0.997940i | ||||
\(973\) | − | 12.0000i | − | 0.384702i | ||||||
\(974\) | − | 28.2843i | − | 0.906287i | ||||||
\(975\) | −15.9411 | − | 49.4558i | −0.510525 | − | 1.58385i | ||||
\(976\) | −40.0000 | −1.28037 | ||||||||
\(977\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(978\) | 40.0000 | + | 28.2843i | 1.27906 | + | 0.904431i | ||||
\(979\) | 30.0000i | 0.958804i | ||||||||
\(980\) | −4.24264 | − | 1.41421i | −0.135526 | − | 0.0451754i | ||||
\(981\) | −2.00000 | − | 5.65685i | −0.0638551 | − | 0.180609i | ||||
\(982\) | 42.0000i | 1.34027i | ||||||||
\(983\) | − | 28.2843i | − | 0.902128i | −0.892492 | − | 0.451064i | \(-0.851045\pi\) | ||
0.892492 | − | 0.451064i | \(-0.148955\pi\) | |||||||
\(984\) | 4.00000 | − | 5.65685i | 0.127515 | − | 0.180334i | ||||
\(985\) | 54.0000 | + | 18.0000i | 1.72058 | + | 0.573528i | ||||
\(986\) | −16.9706 | −0.540453 | ||||||||
\(987\) | 4.00000 | + | 2.82843i | 0.127321 | + | 0.0900298i | ||||
\(988\) | 72.0000 | 2.29063 | ||||||||
\(989\) | 11.3137i | 0.359755i | ||||||||
\(990\) | 40.2426 | − | 0.727922i | 1.27900 | − | 0.0231349i | ||||
\(991\) | − | 60.0000i | − | 1.90596i | −0.303029 | − | 0.952981i | \(-0.597998\pi\) | ||
0.303029 | − | 0.952981i | \(-0.402002\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 18.0000i | − | 0.570925i | ||||||
\(995\) | 4.24264 | − | 12.7279i | 0.134501 | − | 0.403502i | ||||
\(996\) | −8.00000 | − | 5.65685i | −0.253490 | − | 0.179244i | ||||
\(997\) | 42.0000i | 1.33015i | 0.746775 | + | 0.665077i | \(0.231601\pi\) | ||||
−0.746775 | + | 0.665077i | \(0.768399\pi\) | |||||||
\(998\) | 16.9706 | 0.537194 | ||||||||
\(999\) | −8.48528 | + | 30.0000i | −0.268462 | + | 0.949158i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 420.2.l.a.239.2 | yes | 4 | |
3.2 | odd | 2 | inner | 420.2.l.a.239.3 | yes | 4 | |
4.3 | odd | 2 | 420.2.l.b.239.4 | yes | 4 | ||
5.4 | even | 2 | 420.2.l.b.239.3 | yes | 4 | ||
12.11 | even | 2 | 420.2.l.b.239.1 | yes | 4 | ||
15.14 | odd | 2 | 420.2.l.b.239.2 | yes | 4 | ||
20.19 | odd | 2 | inner | 420.2.l.a.239.1 | ✓ | 4 | |
60.59 | even | 2 | inner | 420.2.l.a.239.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.l.a.239.1 | ✓ | 4 | 20.19 | odd | 2 | inner | |
420.2.l.a.239.2 | yes | 4 | 1.1 | even | 1 | trivial | |
420.2.l.a.239.3 | yes | 4 | 3.2 | odd | 2 | inner | |
420.2.l.a.239.4 | yes | 4 | 60.59 | even | 2 | inner | |
420.2.l.b.239.1 | yes | 4 | 12.11 | even | 2 | ||
420.2.l.b.239.2 | yes | 4 | 15.14 | odd | 2 | ||
420.2.l.b.239.3 | yes | 4 | 5.4 | even | 2 | ||
420.2.l.b.239.4 | yes | 4 | 4.3 | odd | 2 |