Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1024,2,Mod(257,1024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1024, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1024.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1024 = 2^{10} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1024.e (of order \(4\), 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: | \(8.17668116698\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
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: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 128) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 257.1 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.257 |
Dual form | 1024.2.e.i.769.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(1023\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.41421 | − | 1.41421i | −0.816497 | − | 0.816497i | 0.169102 | − | 0.985599i | \(-0.445913\pi\) |
−0.985599 | + | 0.169102i | \(0.945913\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.41421 | − | 1.41421i | 0.632456 | − | 0.632456i | −0.316228 | − | 0.948683i | \(-0.602416\pi\) |
0.948683 | + | 0.316228i | \(0.102416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.00000i | 1.51186i | 0.654654 | + | 0.755929i | \(0.272814\pi\) | ||||
−0.654654 | + | 0.755929i | \(0.727186\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.41421 | − | 1.41421i | 0.426401 | − | 0.426401i | −0.460999 | − | 0.887401i | \(-0.652509\pi\) |
0.887401 | + | 0.460999i | \(0.152509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.41421 | + | 1.41421i | 0.392232 | + | 0.392232i | 0.875482 | − | 0.483250i | \(-0.160544\pi\) |
−0.483250 | + | 0.875482i | \(0.660544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.00000 | −1.03280 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.41421 | + | 1.41421i | 0.324443 | + | 0.324443i | 0.850469 | − | 0.526026i | \(-0.176318\pi\) |
−0.526026 | + | 0.850469i | \(0.676318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.65685 | − | 5.65685i | 1.23443 | − | 1.23443i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000i | 0.834058i | 0.908893 | + | 0.417029i | \(0.136929\pi\) | ||||
−0.908893 | + | 0.417029i | \(0.863071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.82843 | + | 2.82843i | −0.544331 | + | 0.544331i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.24264 | + | 4.24264i | 0.787839 | + | 0.787839i | 0.981140 | − | 0.193301i | \(-0.0619194\pi\) |
−0.193301 | + | 0.981140i | \(0.561919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.00000 | −0.696311 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.65685 | + | 5.65685i | 0.956183 | + | 0.956183i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.07107 | − | 7.07107i | 1.16248 | − | 1.16248i | 0.178545 | − | 0.983932i | \(-0.442861\pi\) |
0.983932 | − | 0.178545i | \(-0.0571389\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 4.00000i | − | 0.640513i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.00000i | − | 0.937043i | −0.883452 | − | 0.468521i | \(-0.844787\pi\) | ||
0.883452 | − | 0.468521i | \(-0.155213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.24264 | + | 4.24264i | −0.646997 | + | 0.646997i | −0.952266 | − | 0.305269i | \(-0.901253\pi\) |
0.305269 | + | 0.952266i | \(0.401253\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.41421 | + | 1.41421i | 0.210819 | + | 0.210819i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.00000 | 1.16692 | 0.583460 | − | 0.812142i | \(-0.301699\pi\) | ||||
0.583460 | + | 0.812142i | \(0.301699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.00000 | −1.28571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.82843 | − | 2.82843i | −0.396059 | − | 0.396059i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.24264 | − | 4.24264i | 0.582772 | − | 0.582772i | −0.352892 | − | 0.935664i | \(-0.614802\pi\) |
0.935664 | + | 0.352892i | \(0.114802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.00000i | − | 0.539360i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 4.00000i | − | 0.529813i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.89949 | − | 9.89949i | 1.28880 | − | 1.28880i | 0.353291 | − | 0.935513i | \(-0.385063\pi\) |
0.935513 | − | 0.353291i | \(-0.114937\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.41421 | − | 1.41421i | −0.181071 | − | 0.181071i | 0.610751 | − | 0.791823i | \(-0.290868\pi\) |
−0.791823 | + | 0.610751i | \(0.790868\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.00000 | −0.503953 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.00000 | 0.496139 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.07107 | − | 7.07107i | −0.863868 | − | 0.863868i | 0.127917 | − | 0.991785i | \(-0.459171\pi\) |
−0.991785 | + | 0.127917i | \(0.959171\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.65685 | − | 5.65685i | 0.681005 | − | 0.681005i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12.0000i | − | 1.42414i | −0.702109 | − | 0.712069i | \(-0.747758\pi\) | ||
0.702109 | − | 0.712069i | \(-0.252242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.0000i | 1.63858i | 0.573382 | + | 0.819288i | \(0.305631\pi\) | ||||
−0.573382 | + | 0.819288i | \(0.694369\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.41421 | − | 1.41421i | 0.163299 | − | 0.163299i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.65685 | + | 5.65685i | 0.644658 | + | 0.644658i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 11.0000 | 1.22222 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.24264 | − | 4.24264i | −0.465690 | − | 0.465690i | 0.434825 | − | 0.900515i | \(-0.356810\pi\) |
−0.900515 | + | 0.434825i | \(0.856810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.82843 | − | 2.82843i | 0.306786 | − | 0.306786i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 12.0000i | − | 1.28654i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.00000i | 0.212000i | 0.994366 | + | 0.106000i | \(0.0338043\pi\) | ||||
−0.994366 | + | 0.106000i | \(0.966196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.65685 | + | 5.65685i | −0.592999 | + | 0.592999i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.00000 | 0.410391 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.00000 | −0.203069 | −0.101535 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101535 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.41421 | + | 1.41421i | 0.142134 | + | 0.142134i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.24264 | + | 4.24264i | −0.422159 | + | 0.422159i | −0.885946 | − | 0.463788i | \(-0.846490\pi\) |
0.463788 | + | 0.885946i | \(0.346490\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.00000i | 0.394132i | 0.980390 | + | 0.197066i | \(0.0631413\pi\) | ||||
−0.980390 | + | 0.197066i | \(0.936859\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 16.0000i | − | 1.56144i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.41421 | − | 1.41421i | 0.136717 | − | 0.136717i | −0.635436 | − | 0.772153i | \(-0.719180\pi\) |
0.772153 | + | 0.635436i | \(0.219180\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.24264 | − | 4.24264i | −0.406371 | − | 0.406371i | 0.474100 | − | 0.880471i | \(-0.342774\pi\) |
−0.880471 | + | 0.474100i | \(0.842774\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −20.0000 | −1.89832 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.00000 | −0.188144 | −0.0940721 | − | 0.995565i | \(-0.529988\pi\) | ||||
−0.0940721 | + | 0.995565i | \(0.529988\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.65685 | + | 5.65685i | 0.527504 | + | 0.527504i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.41421 | + | 1.41421i | −0.130744 | + | 0.130744i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.00000i | 0.733359i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000i | 0.636364i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.48528 | + | 8.48528i | −0.765092 | + | 0.765092i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.48528 | + | 8.48528i | 0.758947 | + | 0.758947i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.0000 | 1.41977 | 0.709885 | − | 0.704317i | \(-0.248747\pi\) | ||||
0.709885 | + | 0.704317i | \(0.248747\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.0000 | 1.05654 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.24264 | + | 4.24264i | 0.370681 | + | 0.370681i | 0.867725 | − | 0.497044i | \(-0.165581\pi\) |
−0.497044 | + | 0.867725i | \(0.665581\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.65685 | + | 5.65685i | −0.490511 | + | 0.490511i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.00000i | 0.688530i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.0000i | 0.854358i | 0.904167 | + | 0.427179i | \(0.140493\pi\) | ||||
−0.904167 | + | 0.427179i | \(0.859507\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.07107 | − | 7.07107i | 0.599760 | − | 0.599760i | −0.340489 | − | 0.940249i | \(-0.610592\pi\) |
0.940249 | + | 0.340489i | \(0.110592\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.3137 | − | 11.3137i | −0.952786 | − | 0.952786i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.00000 | 0.334497 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.0000 | 0.996546 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.7279 | + | 12.7279i | 1.04978 | + | 1.04978i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.7279 | + | 12.7279i | −1.04271 | + | 1.04271i | −0.0436658 | + | 0.999046i | \(0.513904\pi\) |
−0.999046 | + | 0.0436658i | \(0.986096\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000i | 0.325515i | 0.986666 | + | 0.162758i | \(0.0520389\pi\) | ||||
−0.986666 | + | 0.162758i | \(0.947961\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.00000i | 0.161690i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.7279 | − | 12.7279i | −1.01580 | − | 1.01580i | −0.999873 | − | 0.0159256i | \(-0.994931\pi\) |
−0.0159256 | − | 0.999873i | \(-0.505069\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.0000 | −0.951662 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.0000 | −1.26098 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.41421 | − | 1.41421i | −0.110770 | − | 0.110770i | 0.649550 | − | 0.760319i | \(-0.274958\pi\) |
−0.760319 | + | 0.649550i | \(0.774958\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.65685 | + | 5.65685i | −0.440386 | + | 0.440386i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.0000i | 1.54765i | 0.633402 | + | 0.773823i | \(0.281658\pi\) | ||||
−0.633402 | + | 0.773823i | \(0.718342\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 9.00000i | − | 0.692308i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.41421 | + | 1.41421i | −0.108148 | + | 0.108148i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.7279 | + | 12.7279i | 0.967686 | + | 0.967686i | 0.999494 | − | 0.0318080i | \(-0.0101265\pi\) |
−0.0318080 | + | 0.999494i | \(0.510127\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.00000 | −0.302372 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −28.0000 | −2.10461 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.24264 | − | 4.24264i | −0.317110 | − | 0.317110i | 0.530546 | − | 0.847656i | \(-0.321987\pi\) |
−0.847656 | + | 0.530546i | \(0.821987\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.41421 | + | 1.41421i | −0.105118 | + | 0.105118i | −0.757710 | − | 0.652592i | \(-0.773682\pi\) |
0.652592 | + | 0.757710i | \(0.273682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.00000i | 0.295689i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 20.0000i | − | 1.47043i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.82843 | − | 2.82843i | 0.206835 | − | 0.206835i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11.3137 | − | 11.3137i | −0.822951 | − | 0.822951i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.0000 | −1.15772 | −0.578860 | − | 0.815427i | \(-0.696502\pi\) | ||||
−0.578860 | + | 0.815427i | \(0.696502\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.00000 | −0.143963 | −0.0719816 | − | 0.997406i | \(-0.522932\pi\) | ||||
−0.0719816 | + | 0.997406i | \(0.522932\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.65685 | − | 5.65685i | −0.405096 | − | 0.405096i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.89949 | + | 9.89949i | −0.705310 | + | 0.705310i | −0.965545 | − | 0.260235i | \(-0.916200\pi\) |
0.260235 | + | 0.965545i | \(0.416200\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.00000i | 0.283552i | 0.989899 | + | 0.141776i | \(0.0452813\pi\) | ||||
−0.989899 | + | 0.141776i | \(0.954719\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 20.0000i | 1.41069i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.9706 | + | 16.9706i | −1.19110 | + | 1.19110i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.48528 | − | 8.48528i | −0.592638 | − | 0.592638i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.00000 | −0.278019 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.5563 | − | 15.5563i | −1.07094 | − | 1.07094i | −0.997283 | − | 0.0736598i | \(-0.976532\pi\) |
−0.0736598 | − | 0.997283i | \(-0.523468\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −16.9706 | + | 16.9706i | −1.16280 | + | 1.16280i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.0000i | 0.818393i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 19.7990 | − | 19.7990i | 1.33789 | − | 1.33789i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.82843 | + | 2.82843i | 0.190261 | + | 0.190261i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.7279 | − | 12.7279i | −0.844782 | − | 0.844782i | 0.144695 | − | 0.989476i | \(-0.453780\pi\) |
−0.989476 | + | 0.144695i | \(0.953780\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.89949 | + | 9.89949i | −0.654177 | + | 0.654177i | −0.953996 | − | 0.299819i | \(-0.903074\pi\) |
0.299819 | + | 0.953996i | \(0.403074\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 16.0000i | − | 1.05272i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 18.0000i | − | 1.17922i | −0.807688 | − | 0.589610i | \(-0.799282\pi\) | ||
0.807688 | − | 0.589610i | \(-0.200718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.3137 | − | 11.3137i | 0.738025 | − | 0.738025i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.3137 | − | 11.3137i | −0.734904 | − | 0.734904i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.0000 | 1.55243 | 0.776215 | − | 0.630468i | \(-0.217137\pi\) | ||||
0.776215 | + | 0.630468i | \(0.217137\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.00000 | 0.128831 | 0.0644157 | − | 0.997923i | \(-0.479482\pi\) | ||||
0.0644157 | + | 0.997923i | \(0.479482\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.07107 | − | 7.07107i | −0.453609 | − | 0.453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.7279 | + | 12.7279i | −0.813157 | + | 0.813157i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.00000i | 0.254514i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.0000i | 0.760469i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.7279 | + | 12.7279i | −0.803379 | + | 0.803379i | −0.983622 | − | 0.180243i | \(-0.942312\pi\) |
0.180243 | + | 0.983622i | \(0.442312\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.65685 | + | 5.65685i | 0.355643 | + | 0.355643i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.00000 | −0.500979 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.0000 | 1.12281 | 0.561405 | − | 0.827541i | \(-0.310261\pi\) | ||||
0.561405 | + | 0.827541i | \(0.310261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 28.2843 | + | 28.2843i | 1.75750 | + | 1.75750i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.24264 | + | 4.24264i | −0.262613 | + | 0.262613i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 12.0000i | − | 0.739952i | −0.929041 | − | 0.369976i | \(-0.879366\pi\) | ||
0.929041 | − | 0.369976i | \(-0.120634\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 12.0000i | − | 0.737154i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.82843 | − | 2.82843i | 0.173097 | − | 0.173097i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.07107 | + | 7.07107i | 0.431131 | + | 0.431131i | 0.889013 | − | 0.457882i | \(-0.151392\pi\) |
−0.457882 | + | 0.889013i | \(0.651392\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | −0.485965 | −0.242983 | − | 0.970031i | \(-0.578126\pi\) | ||||
−0.242983 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 16.0000 | 0.968364 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.41421 | + | 1.41421i | 0.0852803 | + | 0.0852803i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.24264 | − | 4.24264i | 0.254916 | − | 0.254916i | −0.568067 | − | 0.822982i | \(-0.692309\pi\) |
0.822982 | + | 0.568067i | \(0.192309\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.0000i | 1.07379i | 0.843649 | + | 0.536895i | \(0.180403\pi\) | ||||
−0.843649 | + | 0.536895i | \(0.819597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.24264 | − | 4.24264i | 0.252199 | − | 0.252199i | −0.569673 | − | 0.821872i | \(-0.692930\pi\) |
0.821872 | + | 0.569673i | \(0.192930\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.65685 | − | 5.65685i | −0.335083 | − | 0.335083i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 24.0000 | 1.41668 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.82843 | + | 2.82843i | 0.165805 | + | 0.165805i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.89949 | + | 9.89949i | −0.578335 | + | 0.578335i | −0.934444 | − | 0.356110i | \(-0.884103\pi\) |
0.356110 | + | 0.934444i | \(0.384103\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 28.0000i | − | 1.63022i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.00000i | 0.464207i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.65685 | + | 5.65685i | −0.327144 | + | 0.327144i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.9706 | − | 16.9706i | −0.978167 | − | 0.978167i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.0000 | 0.689382 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.00000 | −0.229039 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.7279 | + | 12.7279i | 0.726421 | + | 0.726421i | 0.969905 | − | 0.243484i | \(-0.0782903\pi\) |
−0.243484 | + | 0.969905i | \(0.578290\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.65685 | − | 5.65685i | 0.321807 | − | 0.321807i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 28.0000i | − | 1.58773i | −0.608091 | − | 0.793867i | \(-0.708065\pi\) | ||
0.608091 | − | 0.793867i | \(-0.291935\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 10.0000i | − | 0.565233i | −0.959233 | − | 0.282617i | \(-0.908798\pi\) | ||
0.959233 | − | 0.282617i | \(-0.0912024\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.65685 | + | 5.65685i | −0.318728 | + | 0.318728i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.24264 | + | 4.24264i | 0.238290 | + | 0.238290i | 0.816142 | − | 0.577851i | \(-0.196109\pi\) |
−0.577851 | + | 0.816142i | \(0.696109\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.0000 | 0.671871 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.82843 | + | 2.82843i | 0.157378 | + | 0.157378i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.41421 | + | 1.41421i | −0.0784465 | + | 0.0784465i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.0000i | 0.663602i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 32.0000i | 1.76422i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.89949 | + | 9.89949i | −0.544125 | + | 0.544125i | −0.924736 | − | 0.380610i | \(-0.875714\pi\) |
0.380610 | + | 0.924736i | \(0.375714\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.07107 | + | 7.07107i | 0.387492 | + | 0.387492i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −20.0000 | −1.09272 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0000 | 0.762629 | 0.381314 | − | 0.924445i | \(-0.375472\pi\) | ||||
0.381314 | + | 0.924445i | \(0.375472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.82843 | + | 2.82843i | 0.153619 | + | 0.153619i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 8.00000i | − | 0.431959i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 16.0000i | − | 0.861411i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.7279 | + | 12.7279i | −0.683271 | + | 0.683271i | −0.960736 | − | 0.277465i | \(-0.910506\pi\) |
0.277465 | + | 0.960736i | \(0.410506\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.07107 | − | 7.07107i | −0.378506 | − | 0.378506i | 0.492057 | − | 0.870563i | \(-0.336245\pi\) |
−0.870563 | + | 0.492057i | \(0.836245\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.00000 | −0.427008 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.0000 | 0.958043 | 0.479022 | − | 0.877803i | \(-0.340992\pi\) | ||||
0.479022 | + | 0.877803i | \(0.340992\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.9706 | − | 16.9706i | −0.900704 | − | 0.900704i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11.3137 | − | 11.3137i | 0.598785 | − | 0.598785i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.00000i | 0.211112i | 0.994413 | + | 0.105556i | \(0.0336622\pi\) | ||||
−0.994413 | + | 0.105556i | \(0.966338\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 15.0000i | − | 0.789474i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.89949 | − | 9.89949i | 0.519589 | − | 0.519589i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.7990 | + | 19.7990i | 1.03633 | + | 1.03633i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.00000 | 0.417597 | 0.208798 | − | 0.977959i | \(-0.433045\pi\) | ||||
0.208798 | + | 0.977959i | \(0.433045\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.00000 | 0.312348 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.9706 | + | 16.9706i | 0.881068 | + | 0.881068i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.07107 | + | 7.07107i | −0.366126 | + | 0.366126i | −0.866062 | − | 0.499936i | \(-0.833357\pi\) |
0.499936 | + | 0.866062i | \(0.333357\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 24.0000i | − | 1.23935i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0000i | 0.618031i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.41421 | + | 1.41421i | −0.0726433 | + | 0.0726433i | −0.742495 | − | 0.669852i | \(-0.766358\pi\) |
0.669852 | + | 0.742495i | \(0.266358\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −22.6274 | − | 22.6274i | −1.15924 | − | 1.15924i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.0000 | 0.815436 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.24264 | − | 4.24264i | −0.215666 | − | 0.215666i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.07107 | − | 7.07107i | 0.358517 | − | 0.358517i | −0.504749 | − | 0.863266i | \(-0.668415\pi\) |
0.863266 | + | 0.504749i | \(0.168415\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.00000i | 0.404577i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 12.0000i | − | 0.605320i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.3137 | − | 11.3137i | 0.569254 | − | 0.569254i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.24264 | − | 4.24264i | −0.212932 | − | 0.212932i | 0.592580 | − | 0.805512i | \(-0.298110\pi\) |
−0.805512 | + | 0.592580i | \(0.798110\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 16.0000 | 0.801002 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.0000 | −1.49813 | −0.749064 | − | 0.662497i | \(-0.769497\pi\) | ||||
−0.749064 | + | 0.662497i | \(0.769497\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 15.5563 | − | 15.5563i | 0.773001 | − | 0.773001i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 20.0000i | − | 0.991363i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 10.0000i | − | 0.494468i | −0.968956 | − | 0.247234i | \(-0.920478\pi\) | ||
0.968956 | − | 0.247234i | \(-0.0795217\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.1421 | − | 14.1421i | 0.697580 | − | 0.697580i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 39.5980 | + | 39.5980i | 1.94849 | + | 1.94849i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.0000 | −0.589057 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −20.0000 | −0.979404 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.3848 | − | 18.3848i | −0.898155 | − | 0.898155i | 0.0971178 | − | 0.995273i | \(-0.469038\pi\) |
−0.995273 | + | 0.0971178i | \(0.969038\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.0416 | − | 24.0416i | 1.17172 | − | 1.17172i | 0.189917 | − | 0.981800i | \(-0.439178\pi\) |
0.981800 | − | 0.189917i | \(-0.0608220\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.00000i | 0.388973i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.00000i | 0.0970143i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.65685 | − | 5.65685i | 0.273754 | − | 0.273754i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.65685 | − | 5.65685i | −0.273115 | − | 0.273115i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −40.0000 | −1.92673 | −0.963366 | − | 0.268190i | \(-0.913575\pi\) | ||||
−0.963366 | + | 0.268190i | \(0.913575\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.0000 | −1.44171 | −0.720854 | − | 0.693087i | \(-0.756250\pi\) | ||||
−0.720854 | + | 0.693087i | \(0.756250\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −16.9706 | − | 16.9706i | −0.813676 | − | 0.813676i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.65685 | + | 5.65685i | −0.270604 | + | 0.270604i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 36.0000i | 1.71819i | 0.511819 | + | 0.859093i | \(0.328972\pi\) | ||||
−0.511819 | + | 0.859093i | \(0.671028\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 9.00000i | − | 0.428571i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.24264 | − | 4.24264i | 0.201574 | − | 0.201574i | −0.599100 | − | 0.800674i | \(-0.704475\pi\) |
0.800674 | + | 0.599100i | \(0.204475\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.82843 | + | 2.82843i | 0.134080 | + | 0.134080i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 36.0000 | 1.70274 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.0000 | −1.60456 | −0.802280 | − | 0.596948i | \(-0.796380\pi\) | ||||
−0.802280 | + | 0.596948i | \(0.796380\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.48528 | − | 8.48528i | −0.399556 | − | 0.399556i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.65685 | − | 5.65685i | 0.265782 | − | 0.265782i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 16.0000i | 0.750092i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 6.00000i | − | 0.280668i | −0.990104 | − | 0.140334i | \(-0.955182\pi\) | ||
0.990104 | − | 0.140334i | \(-0.0448177\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.65685 | + | 5.65685i | −0.264039 | + | 0.264039i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.07107 | + | 7.07107i | 0.329332 | + | 0.329332i | 0.852333 | − | 0.523000i | \(-0.175187\pi\) |
−0.523000 | + | 0.852333i | \(0.675187\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.00000 | 0.371792 | 0.185896 | − | 0.982569i | \(-0.440481\pi\) | ||||
0.185896 | + | 0.982569i | \(0.440481\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.89949 | − | 9.89949i | −0.458094 | − | 0.458094i | 0.439935 | − | 0.898029i | \(-0.355001\pi\) |
−0.898029 | + | 0.439935i | \(0.855001\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 28.2843 | − | 28.2843i | 1.30605 | − | 1.30605i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 36.0000i | 1.65879i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.0000i | 0.551761i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.41421 | + | 1.41421i | −0.0648886 | + | 0.0648886i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.24264 | + | 4.24264i | 0.194257 | + | 0.194257i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.0000 | 0.911922 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 22.6274 | + | 22.6274i | 1.02958 | + | 1.02958i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.82843 | + | 2.82843i | −0.128432 | + | 0.128432i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.0000i | 0.906287i | 0.891438 | + | 0.453143i | \(0.149697\pi\) | ||||
−0.891438 | + | 0.453143i | \(0.850303\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.00000i | 0.180886i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.07107 | − | 7.07107i | 0.319113 | − | 0.319113i | −0.529313 | − | 0.848426i | \(-0.677550\pi\) |
0.848426 | + | 0.529313i | \(0.177550\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.48528 | + | 8.48528i | 0.382158 | + | 0.382158i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.00000 | 0.179787 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 48.0000 | 2.15309 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.5563 | − | 15.5563i | −0.696398 | − | 0.696398i | 0.267234 | − | 0.963632i | \(-0.413890\pi\) |
−0.963632 | + | 0.267234i | \(0.913890\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 28.2843 | − | 28.2843i | 1.26365 | − | 1.26365i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.0000i | 0.891756i | 0.895094 | + | 0.445878i | \(0.147108\pi\) | ||||
−0.895094 | + | 0.445878i | \(0.852892\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.0000i | 0.533993i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.7279 | + | 12.7279i | −0.565267 | + | 0.565267i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.89949 | + | 9.89949i | 0.438787 | + | 0.438787i | 0.891604 | − | 0.452816i | \(-0.149581\pi\) |
−0.452816 | + | 0.891604i | \(0.649581\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −56.0000 | −2.47729 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.00000 | −0.353209 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.65685 | + | 5.65685i | 0.249271 | + | 0.249271i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.3137 | − | 11.3137i | 0.497576 | − | 0.497576i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 36.0000i | − | 1.58022i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 22.0000i | − | 0.963837i | −0.876216 | − | 0.481919i | \(-0.839940\pi\) | ||
0.876216 | − | 0.481919i | \(-0.160060\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.89949 | + | 9.89949i | −0.432875 | + | 0.432875i | −0.889605 | − | 0.456730i | \(-0.849020\pi\) |
0.456730 | + | 0.889605i | \(0.349020\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.65685 | + | 5.65685i | 0.246885 | + | 0.246885i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.89949 | + | 9.89949i | 0.429601 | + | 0.429601i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.48528 | − | 8.48528i | 0.367538 | − | 0.367538i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 4.00000i | − | 0.172935i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.0000i | 0.517838i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12.7279 | + | 12.7279i | −0.548230 | + | 0.548230i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.0416 | − | 24.0416i | −1.03363 | − | 1.03363i | −0.999414 | − | 0.0342160i | \(-0.989107\pi\) |
−0.0342160 | − | 0.999414i | \(-0.510893\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.00000 | 0.171656 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.0000 | −0.514024 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.8701 | + | 26.8701i | 1.14888 | + | 1.14888i | 0.986773 | + | 0.162108i | \(0.0518292\pi\) |
0.162108 | + | 0.986773i | \(0.448171\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.41421 | − | 1.41421i | 0.0603572 | − | 0.0603572i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.0000i | 0.511217i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 32.0000i | 1.36078i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −28.2843 | + | 28.2843i | −1.20060 | + | 1.20060i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.41421 | + | 1.41421i | 0.0599222 | + | 0.0599222i | 0.736433 | − | 0.676511i | \(-0.236509\pi\) |
−0.676511 | + | 0.736433i | \(0.736509\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.0000 | −0.507546 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.00000 | −0.337760 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.7279 | + | 12.7279i | 0.536418 | + | 0.536418i | 0.922475 | − | 0.386057i | \(-0.126163\pi\) |
−0.386057 | + | 0.922475i | \(0.626163\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.82843 | + | 2.82843i | −0.118993 | + | 0.118993i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 44.0000i | 1.84783i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 26.0000i | − | 1.08998i | −0.838444 | − | 0.544988i | \(-0.816534\pi\) | ||
0.838444 | − | 0.544988i | \(-0.183466\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.8701 | − | 26.8701i | 1.12448 | − | 1.12448i | 0.133417 | − | 0.991060i | \(-0.457405\pi\) |
0.991060 | − | 0.133417i | \(-0.0425949\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.6274 | + | 22.6274i | 0.945274 | + | 0.945274i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.00000 | −0.166812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.00000 | 0.0832611 | 0.0416305 | − | 0.999133i | \(-0.486745\pi\) | ||||
0.0416305 | + | 0.999133i | \(0.486745\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.82843 | + | 2.82843i | 0.117545 | + | 0.117545i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.9706 | − | 16.9706i | 0.704058 | − | 0.704058i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 12.0000i | − | 0.496989i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.00000i | 0.165380i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.0416 | − | 24.0416i | 0.992304 | − | 0.992304i | −0.00766632 | − | 0.999971i | \(-0.502440\pi\) |
0.999971 | + | 0.00766632i | \(0.00244029\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 28.0000 | 1.15177 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.0000 | −0.739171 | −0.369586 | − | 0.929197i | \(-0.620500\pi\) | ||||
−0.369586 | + | 0.929197i | \(0.620500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.3137 | + | 11.3137i | 0.463817 | + | 0.463817i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.65685 | − | 5.65685i | 0.231520 | − | 0.231520i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 12.0000i | − | 0.490307i | −0.969484 | − | 0.245153i | \(-0.921162\pi\) | ||
0.969484 | − | 0.245153i | \(-0.0788383\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 30.0000i | − | 1.22373i | −0.790964 | − | 0.611863i | \(-0.790420\pi\) | ||
0.790964 | − | 0.611863i | \(-0.209580\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.07107 | − | 7.07107i | 0.287956 | − | 0.287956i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.89949 | + | 9.89949i | 0.402472 | + | 0.402472i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.0000 | −0.649420 | −0.324710 | − | 0.945814i | \(-0.605267\pi\) | ||||
−0.324710 | + | 0.945814i | \(0.605267\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 48.0000 | 1.94506 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.3137 | + | 11.3137i | 0.457704 | + | 0.457704i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.0416 | − | 24.0416i | 0.971032 | − | 0.971032i | −0.0285598 | − | 0.999592i | \(-0.509092\pi\) |
0.999592 | + | 0.0285598i | \(0.00909209\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 24.0000i | 0.967773i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 2.00000i | − | 0.0805170i | −0.999189 | − | 0.0402585i | \(-0.987182\pi\) | ||
0.999189 | − | 0.0402585i | \(-0.0128181\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.5269 | + | 32.5269i | −1.30737 | + | 1.30737i | −0.384058 | + | 0.923309i | \(0.625474\pi\) |
−0.923309 | + | 0.384058i | \(0.874526\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.3137 | − | 11.3137i | −0.454003 | − | 0.454003i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.00000 | −0.320513 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.0000 | 0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.65685 | − | 5.65685i | −0.225913 | − | 0.225913i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.1421 | − | 14.1421i | 0.563884 | − | 0.563884i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 44.0000i | − | 1.75161i | −0.482663 | − | 0.875806i | \(-0.660330\pi\) | ||
0.482663 | − | 0.875806i | \(-0.339670\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 44.0000i | 1.74884i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 22.6274 | − | 22.6274i | 0.897942 | − | 0.897942i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.7279 | − | 12.7279i | −0.504299 | − | 0.504299i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.0000 | 0.474713 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.0000 | 1.18493 | 0.592464 | − | 0.805597i | \(-0.298155\pi\) | ||||
0.592464 | + | 0.805597i | \(0.298155\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.6985 | − | 29.6985i | −1.17119 | − | 1.17119i | −0.981925 | − | 0.189269i | \(-0.939388\pi\) |
−0.189269 | − | 0.981925i | \(-0.560612\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 16.9706 | − | 16.9706i | 0.668215 | − | 0.668215i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 12.0000i | − | 0.471769i | −0.971781 | − | 0.235884i | \(-0.924201\pi\) | ||
0.971781 | − | 0.235884i | \(-0.0757987\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 28.0000i | − | 1.09910i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29.6985 | + | 29.6985i | 1.16219 | + | 1.16219i | 0.983995 | + | 0.178197i | \(0.0570263\pi\) |
0.178197 | + | 0.983995i | \(0.442974\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.0000 | 0.468879 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.0000 | −0.546192 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.24264 | − | 4.24264i | −0.165270 | − | 0.165270i | 0.619627 | − | 0.784897i | \(-0.287284\pi\) |
−0.784897 | + | 0.619627i | \(0.787284\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.0416 | + | 24.0416i | −0.935111 | + | 0.935111i | −0.998019 | − | 0.0629083i | \(-0.979962\pi\) |
0.0629083 | + | 0.998019i | \(0.479962\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 8.00000i | − | 0.310694i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 16.0000i | 0.620453i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16.9706 | + | 16.9706i | −0.657103 | + | 0.657103i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.00000 | −0.154418 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.00000 | −0.0770943 | −0.0385472 | − | 0.999257i | \(-0.512273\pi\) | ||||
−0.0385472 | + | 0.999257i | \(0.512273\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.82843 | − | 2.82843i | −0.108866 | − | 0.108866i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.5563 | + | 15.5563i | −0.597879 | + | 0.597879i | −0.939748 | − | 0.341869i | \(-0.888940\pi\) |
0.341869 | + | 0.939748i | \(0.388940\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 8.00000i | − | 0.307012i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 36.0000i | 1.37952i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.6985 | − | 29.6985i | 1.13638 | − | 1.13638i | 0.147287 | − | 0.989094i | \(-0.452946\pi\) |
0.989094 | − | 0.147287i | \(-0.0470541\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.1421 | + | 14.1421i | 0.540343 | + | 0.540343i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 28.0000 | 1.06827 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.0000 | 0.457164 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.24264 | − | 4.24264i | −0.161398 | − | 0.161398i | 0.621788 | − | 0.783186i | \(-0.286407\pi\) |
−0.783186 | + | 0.621788i | \(0.786407\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.65685 | + | 5.65685i | −0.214886 | + | 0.214886i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 20.0000i | − | 0.758643i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 12.0000i | − | 0.454532i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −25.4558 | + | 25.4558i | −0.962828 | + | 0.962828i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.41421 | − | 1.41421i | −0.0534141 | − | 0.0534141i | 0.679895 | − | 0.733309i | \(-0.262025\pi\) |
−0.733309 | + | 0.679895i | \(0.762025\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.0000 | 0.754314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −32.0000 | −1.20519 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16.9706 | − | 16.9706i | −0.638244 | − | 0.638244i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.5563 | + | 15.5563i | −0.584231 | + | 0.584231i | −0.936063 | − | 0.351832i | \(-0.885559\pi\) |
0.351832 | + | 0.936063i | \(0.385559\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.00000i | 0.300023i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.65685 | − | 5.65685i | 0.211554 | − | 0.211554i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −33.9411 | − | 33.9411i | −1.26755 | − | 1.26755i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.0000 | −0.895049 | −0.447524 | − | 0.894272i | \(-0.647694\pi\) | ||||
−0.447524 | + | 0.894272i | \(0.647694\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.0000 | −0.595871 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.82843 | − | 2.82843i | −0.105190 | − | 0.105190i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.24264 | + | 4.24264i | −0.157568 | + | 0.157568i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 12.0000i | − | 0.445055i | −0.974926 | − | 0.222528i | \(-0.928569\pi\) | ||
0.974926 | − | 0.222528i | \(-0.0714308\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 13.0000i | − | 0.481481i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.48528 | + | 8.48528i | −0.313839 | + | 0.313839i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.24264 | + | 4.24264i | 0.156706 | + | 0.156706i | 0.781105 | − | 0.624400i | \(-0.214656\pi\) |
−0.624400 | + | 0.781105i | \(0.714656\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 36.0000 | 1.32788 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −20.0000 | −0.736709 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.7279 | − | 12.7279i | −0.468204 | − | 0.468204i | 0.433128 | − | 0.901332i | \(-0.357410\pi\) |
−0.901332 | + | 0.433128i | \(0.857410\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.65685 | − | 5.65685i | 0.207810 | − | 0.207810i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 44.0000i | − | 1.61420i | −0.590412 | − | 0.807102i | \(-0.701035\pi\) | ||
0.590412 | − | 0.807102i | \(-0.298965\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 36.0000i | 1.31894i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.24264 | − | 4.24264i | 0.155230 | − | 0.155230i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.65685 | + | 5.65685i | 0.206697 | + | 0.206697i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.00000 | −0.291924 | −0.145962 | − | 0.989290i | \(-0.546628\pi\) | ||||
−0.145962 | + | 0.989290i | \(0.546628\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 36.0000 | 1.31191 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.65685 | + | 5.65685i | 0.205874 | + | 0.205874i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.5269 | − | 32.5269i | 1.18221 | − | 1.18221i | 0.203040 | − | 0.979170i | \(-0.434918\pi\) |
0.979170 | − | 0.203040i | \(-0.0650823\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 16.0000i | − | 0.580763i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 10.0000i | − | 0.362500i | −0.983437 | − | 0.181250i | \(-0.941986\pi\) | ||
0.983437 | − | 0.181250i | \(-0.0580143\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.9706 | − | 16.9706i | 0.614376 | − | 0.614376i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.82843 | + | 2.82843i | 0.102262 | + | 0.102262i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28.0000 | 1.01102 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.0000 | −1.22607 | −0.613036 | − | 0.790055i | \(-0.710052\pi\) | ||||
−0.613036 | + | 0.790055i | \(0.710052\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.4558 | − | 25.4558i | −0.916770 | − | 0.916770i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −38.1838 | + | 38.1838i | −1.37337 | + | 1.37337i | −0.517985 | + | 0.855390i | \(0.673318\pi\) |
−0.855390 | + | 0.517985i | \(0.826682\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 80.0000i | − | 2.86998i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.48528 | − | 8.48528i | 0.304017 | − | 0.304017i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.9706 | − | 16.9706i | −0.607254 | − | 0.607254i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −24.0000 | −0.857690 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −36.0000 | −1.28490 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.5563 | − | 15.5563i | −0.554524 | − | 0.554524i | 0.373219 | − | 0.927743i | \(-0.378254\pi\) |
−0.927743 | + | 0.373219i | \(0.878254\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16.9706 | + | 16.9706i | −0.604168 | + | 0.604168i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 8.00000i | − | 0.284447i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 4.00000i | − | 0.142044i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −16.9706 | + | 16.9706i | −0.601884 | + | 0.601884i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.7279 | − | 12.7279i | −0.450846 | − | 0.450846i | 0.444789 | − | 0.895635i | \(-0.353279\pi\) |
−0.895635 | + | 0.444789i | \(0.853279\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.0000 | 0.566039 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.00000 | −0.0706665 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.7990 | + | 19.7990i | 0.698691 | + | 0.698691i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −22.6274 | + | 22.6274i | −0.797512 | + | 0.797512i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 20.0000i | − | 0.704033i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 6.00000i | − | 0.210949i | −0.994422 | − | 0.105474i | \(-0.966364\pi\) | ||
0.994422 | − | 0.105474i | \(-0.0336361\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.7279 | − | 12.7279i | 0.446938 | − | 0.446938i | −0.447397 | − | 0.894335i | \(-0.647649\pi\) |
0.894335 | + | 0.447397i | \(0.147649\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.3137 | + | 11.3137i | 0.396789 | + | 0.396789i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.00000 | −0.140114 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.0000 | −0.419827 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.65685 | − | 5.65685i | −0.197666 | − | 0.197666i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.07107 | + | 7.07107i | −0.246782 | + | 0.246782i | −0.819649 | − | 0.572867i | \(-0.805831\pi\) |
0.572867 | + | 0.819649i | \(0.305831\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 28.0000i | − | 0.976019i | −0.872838 | − | 0.488009i | \(-0.837723\pi\) | ||
0.872838 | − | 0.488009i | \(-0.162277\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 4.00000i | − | 0.139262i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.5563 | − | 15.5563i | 0.540947 | − | 0.540947i | −0.382859 | − | 0.923807i | \(-0.625061\pi\) |
0.923807 | + | 0.382859i | \(0.125061\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.89949 | + | 9.89949i | 0.343824 | + | 0.343824i | 0.857803 | − | 0.513979i | \(-0.171829\pi\) |
−0.513979 | + | 0.857803i | \(0.671829\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.0000 | −0.416275 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.0000 | −0.623663 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 28.2843 | + | 28.2843i | 0.978818 | + | 0.978818i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 36.0000i | 1.24286i | 0.783470 | + | 0.621429i | \(0.213448\pi\) | ||||
−0.783470 | + | 0.621429i | \(0.786552\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000i | 0.241379i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 25.4558 | − | 25.4558i | 0.876746 | − | 0.876746i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.7279 | − | 12.7279i | −0.437854 | − | 0.437854i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −28.0000 | −0.962091 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.0000 | −0.411839 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 28.2843 | + | 28.2843i | 0.969572 | + | 0.969572i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.3848 | + | 18.3848i | −0.629483 | + | 0.629483i | −0.947938 | − | 0.318455i | \(-0.896836\pi\) |
0.318455 | + | 0.947938i | \(0.396836\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.00000i | 0.136797i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.00000i | 0.204956i | 0.994735 | + | 0.102478i | \(0.0326771\pi\) | ||||
−0.994735 | + | 0.102478i | \(0.967323\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.3553 | + | 35.3553i | −1.20631 | + | 1.20631i | −0.234095 | + | 0.972214i | \(0.575213\pi\) |
−0.972214 | + | 0.234095i | \(0.924787\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −33.9411 | − | 33.9411i | −1.15671 | − | 1.15671i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.0000 | −1.08929 | −0.544646 | − | 0.838666i | \(-0.683336\pi\) | ||||
−0.544646 | + | 0.838666i | \(0.683336\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36.0000 | 1.22404 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 18.3848 | + | 18.3848i | 0.624380 | + | 0.624380i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.3137 | − | 11.3137i | 0.383791 | − | 0.383791i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 20.0000i | − | 0.677674i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 2.00000i | − | 0.0676897i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −33.9411 | + | 33.9411i | −1.14742 | + | 1.14742i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.5563 | − | 15.5563i | −0.525301 | − | 0.525301i | 0.393867 | − | 0.919167i | \(-0.371137\pi\) |
−0.919167 | + | 0.393867i | \(0.871137\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 28.0000 | 0.944417 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 46.0000 | 1.54978 | 0.774890 | − | 0.632096i | \(-0.217805\pi\) | ||||
0.774890 | + | 0.632096i | \(0.217805\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.0416 | + | 24.0416i | 0.809065 | + | 0.809065i | 0.984492 | − | 0.175427i | \(-0.0561306\pi\) |
−0.175427 | + | 0.984492i | \(0.556131\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −39.5980 | + | 39.5980i | −1.33107 | + | 1.33107i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36.0000i | 1.20876i | 0.796696 | + | 0.604381i | \(0.206579\pi\) | ||||
−0.796696 | + | 0.604381i | \(0.793421\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 64.0000i | 2.14649i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.5563 | − | 15.5563i | 0.521157 | − | 0.521157i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.3137 | + | 11.3137i | 0.378599 | + | 0.378599i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.0000 | −0.401116 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.0000 | 0.534224 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.48528 | − | 8.48528i | 0.282686 | − | 0.282686i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 48.0000i | 1.59734i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.00000i | 0.132964i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.8701 | + | 26.8701i | −0.892206 | + | 0.892206i | −0.994730 | − | 0.102525i | \(-0.967308\pi\) |
0.102525 | + | 0.994730i | \(0.467308\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.24264 | − | 4.24264i | −0.140720 | − | 0.140720i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.0000 | 0.795155 | 0.397578 | − | 0.917568i | \(-0.369851\pi\) | ||||
0.397578 | + | 0.917568i | \(0.369851\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.0000 | −0.397142 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.65685 | + | 5.65685i | 0.187010 | + | 0.187010i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16.9706 | + | 16.9706i | −0.560417 | + | 0.560417i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.0000i | 1.18753i | 0.804638 | + | 0.593765i | \(0.202359\pi\) | ||||
−0.804638 | + | 0.593765i | \(0.797641\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 36.0000i | − | 1.18624i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.9706 | − | 16.9706i | 0.558593 | − | 0.558593i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.07107 | + | 7.07107i | 0.232495 | + | 0.232495i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.00000 | −0.131377 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30.0000 | 0.984268 | 0.492134 | − | 0.870519i | \(-0.336217\pi\) | ||||
0.492134 | + | 0.870519i | \(0.336217\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.7279 | − | 12.7279i | −0.417141 | − | 0.417141i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −39.5980 | + | 39.5980i | −1.29638 | + | 1.29638i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 8.00000i | − | 0.261628i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.0000i | 1.50275i | 0.659873 | + | 0.751377i | \(0.270610\pi\) | ||||
−0.659873 | + | 0.751377i | \(0.729390\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.1421 | + | 14.1421i | −0.461511 | + | 0.461511i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.8701 | − | 26.8701i | −0.875939 | − | 0.875939i | 0.117173 | − | 0.993112i | \(-0.462617\pi\) |
−0.993112 | + | 0.117173i | \(0.962617\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.0000 | 0.781548 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −32.0000 | −1.04096 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.89949 | − | 9.89949i | −0.321690 | − | 0.321690i | 0.527725 | − | 0.849415i | \(-0.323045\pi\) |
−0.849415 | + | 0.527725i | \(0.823045\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.7990 | + | 19.7990i | −0.642702 | + | 0.642702i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 12.0000i | − | 0.389127i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 58.0000i | − | 1.87880i | −0.342817 | − | 0.939402i | \(-0.611381\pi\) | ||
0.342817 | − | 0.939402i | \(-0.388619\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22.6274 | + | 22.6274i | −0.732206 | + | 0.732206i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16.9706 | − | 16.9706i | −0.548580 | − | 0.548580i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −40.0000 | −1.29167 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.41421 | + | 1.41421i | 0.0455724 | + | 0.0455724i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.82843 | + | 2.82843i | −0.0910503 | + | 0.0910503i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 28.0000i | − | 0.900419i | −0.892923 | − | 0.450210i | \(-0.851349\pi\) | ||
0.892923 | − | 0.450210i | \(-0.148651\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 8.00000i | − | 0.256997i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.8701 | + | 26.8701i | −0.862301 | + | 0.862301i | −0.991605 | − | 0.129304i | \(-0.958726\pi\) |
0.129304 | + | 0.991605i | \(0.458726\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.2843 | + | 28.2843i | 0.906752 | + | 0.906752i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.00000 | 0.128103 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30.0000 | −0.959785 | −0.479893 | − | 0.877327i | \(-0.659324\pi\) | ||||
−0.479893 | + | 0.877327i | \(0.659324\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.82843 | + | 2.82843i | 0.0903969 | + | 0.0903969i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.24264 | − | 4.24264i | 0.135457 | − | 0.135457i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.0000i | 0.637901i | 0.947771 | + | 0.318950i | \(0.103330\pi\) | ||||
−0.947771 | + | 0.318950i | \(0.896670\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 28.0000i | 0.892154i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 45.2548 | − | 45.2548i | 1.44048 | − | 1.44048i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.9706 | − | 16.9706i | −0.539633 | − | 0.539633i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.0000 | 0.508257 | 0.254128 | − | 0.967170i | \(-0.418211\pi\) | ||||
0.254128 | + | 0.967170i | \(0.418211\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 28.0000 | 0.888553 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.65685 | + | 5.65685i | 0.179334 | + | 0.179334i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.1838 | + | 38.1838i | −1.20929 | + | 1.20929i | −0.238036 | + | 0.971256i | \(0.576503\pi\) |
−0.971256 | + | 0.238036i | \(0.923497\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 40.0000i | 1.26554i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))