Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,2,Mod(895,1792)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1792.895");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.e (of order \(2\), degree \(1\), 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: | \(14.3091920422\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 895.3 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.895 |
Dual form | 1792.2.e.c.895.1 |
$q$-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 \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.00000i | 1.15470i | 0.816497 | + | 0.577350i | \(0.195913\pi\) | ||||
−0.816497 | + | 0.577350i | \(0.804087\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.46410 | −1.54919 | −0.774597 | − | 0.632456i | \(-0.782047\pi\) | ||||
−0.774597 | + | 0.632456i | \(0.782047\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | − | 1.73205i | 0.755929 | − | 0.654654i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.46410 | 1.04447 | 0.522233 | − | 0.852803i | \(-0.325099\pi\) | ||||
0.522233 | + | 0.852803i | \(0.325099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.46410 | −0.960769 | −0.480384 | − | 0.877058i | \(-0.659503\pi\) | ||||
−0.480384 | + | 0.877058i | \(0.659503\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 6.92820i | − | 1.78885i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000i | 0.458831i | 0.973329 | + | 0.229416i | \(0.0736815\pi\) | ||||
−0.973329 | + | 0.229416i | \(0.926318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.46410 | + | 4.00000i | 0.755929 | + | 0.872872i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.46410i | 0.722315i | 0.932505 | + | 0.361158i | \(0.117618\pi\) | ||||
−0.932505 | + | 0.361158i | \(0.882382\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.00000 | 1.40000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000i | 0.769800i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00000i | 1.11417i | 0.830455 | + | 0.557086i | \(0.188081\pi\) | ||||
−0.830455 | + | 0.557086i | \(0.811919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.00000 | −1.43684 | −0.718421 | − | 0.695608i | \(-0.755135\pi\) | ||||
−0.718421 | + | 0.695608i | \(0.755135\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.92820i | 1.20605i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.92820 | + | 6.00000i | −1.17108 | + | 1.01419i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000i | 0.328798i | 0.986394 | + | 0.164399i | \(0.0525685\pi\) | ||||
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 6.92820i | − | 1.10940i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.92820i | 1.08200i | 0.841021 | + | 0.541002i | \(0.181955\pi\) | ||||
−0.841021 | + | 0.541002i | \(0.818045\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.3923 | −1.58481 | −0.792406 | − | 0.609994i | \(-0.791172\pi\) | ||||
−0.792406 | + | 0.609994i | \(0.791172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.46410 | 0.516398 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | − | 6.92820i | 0.142857 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 6.00000i | − | 0.824163i | −0.911147 | − | 0.412082i | \(-0.864802\pi\) | ||
0.911147 | − | 0.412082i | \(-0.135198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12.0000 | −1.61808 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.00000 | −0.529813 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 6.00000i | − | 0.781133i | −0.920575 | − | 0.390567i | \(-0.872279\pi\) | ||
0.920575 | − | 0.390567i | \(-0.127721\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.46410 | −0.443533 | −0.221766 | − | 0.975100i | \(-0.571182\pi\) | ||||
−0.221766 | + | 0.975100i | \(0.571182\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.00000 | + | 1.73205i | −0.251976 | + | 0.218218i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.0000 | 1.48842 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.46410 | −0.423207 | −0.211604 | − | 0.977356i | \(-0.567869\pi\) | ||||
−0.211604 | + | 0.977356i | \(0.567869\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.92820 | −0.834058 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.46410i | − | 0.411113i | −0.978645 | − | 0.205557i | \(-0.934100\pi\) | ||
0.978645 | − | 0.205557i | \(-0.0659005\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.92820i | − | 0.810885i | −0.914121 | − | 0.405442i | \(-0.867117\pi\) | ||
0.914121 | − | 0.405442i | \(-0.132883\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 14.0000i | 1.61658i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.92820 | − | 6.00000i | 0.789542 | − | 0.683763i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.46410i | 0.389742i | 0.980829 | + | 0.194871i | \(0.0624288\pi\) | ||||
−0.980829 | + | 0.194871i | \(0.937571\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 6.00000i | − | 0.658586i | −0.944228 | − | 0.329293i | \(-0.893190\pi\) | ||
0.944228 | − | 0.329293i | \(-0.106810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −12.0000 | −1.28654 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.92820i | 0.734388i | 0.930144 | + | 0.367194i | \(0.119682\pi\) | ||||
−0.930144 | + | 0.367194i | \(0.880318\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.92820 | + | 6.00000i | −0.726273 | + | 0.628971i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 16.0000i | − | 1.65912i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 6.92820i | − | 0.710819i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.8564i | 1.40690i | 0.710742 | + | 0.703452i | \(0.248359\pi\) | ||||
−0.710742 | + | 0.703452i | \(0.751641\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.46410 | −0.348155 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.3923 | 1.03407 | 0.517036 | − | 0.855963i | \(-0.327035\pi\) | ||||
0.517036 | + | 0.855963i | \(0.327035\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00000 | −0.394132 | −0.197066 | − | 0.980390i | \(-0.563141\pi\) | ||||
−0.197066 | + | 0.980390i | \(0.563141\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −12.0000 | − | 13.8564i | −1.17108 | − | 1.35225i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.3923 | −1.00466 | −0.502331 | − | 0.864675i | \(-0.667524\pi\) | ||||
−0.502331 | + | 0.864675i | \(0.667524\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.0000i | 1.34096i | 0.741929 | + | 0.670478i | \(0.233911\pi\) | ||||
−0.741929 | + | 0.670478i | \(0.766089\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.00000 | −0.379663 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.0000 | −1.69330 | −0.846649 | − | 0.532152i | \(-0.821383\pi\) | ||||
−0.846649 | + | 0.532152i | \(0.821383\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 12.0000i | − | 1.11901i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.46410 | 0.320256 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −13.8564 | −1.24939 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.92820 | −0.619677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.3923i | 0.922168i | 0.887357 | + | 0.461084i | \(0.152539\pi\) | ||||
−0.887357 | + | 0.461084i | \(0.847461\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 20.7846i | − | 1.82998i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.0000i | 1.57267i | 0.617802 | + | 0.786334i | \(0.288023\pi\) | ||||
−0.617802 | + | 0.786334i | \(0.711977\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.46410 | + | 4.00000i | 0.300376 | + | 0.346844i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 13.8564i | − | 1.19257i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.00000 | 0.512615 | 0.256307 | − | 0.966595i | \(-0.417494\pi\) | ||||
0.256307 | + | 0.966595i | \(0.417494\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.00000i | 0.169638i | 0.996396 | + | 0.0848189i | \(0.0270312\pi\) | ||||
−0.996396 | + | 0.0848189i | \(0.972969\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.0000 | −1.00349 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 20.7846i | − | 1.72607i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 13.8564 | + | 2.00000i | 1.14286 | + | 0.164957i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 6.00000i | − | 0.491539i | −0.969328 | − | 0.245770i | \(-0.920959\pi\) | ||
0.969328 | − | 0.245770i | \(-0.0790407\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.46410i | 0.281905i | 0.990016 | + | 0.140952i | \(0.0450164\pi\) | ||||
−0.990016 | + | 0.140952i | \(0.954984\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 27.7128 | 2.22595 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.3923 | 0.829396 | 0.414698 | − | 0.909959i | \(-0.363887\pi\) | ||||
0.414698 | + | 0.909959i | \(0.363887\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.0000 | 0.951662 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.00000 | + | 6.92820i | 0.472866 | + | 0.546019i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.3205 | −1.35665 | −0.678323 | − | 0.734763i | \(-0.737293\pi\) | ||||
−0.678323 | + | 0.734763i | \(0.737293\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 24.0000i | − | 1.86840i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.0000 | 0.928588 | 0.464294 | − | 0.885681i | \(-0.346308\pi\) | ||||
0.464294 | + | 0.885681i | \(0.346308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 2.00000i | − | 0.152944i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.46410 | −0.263371 | −0.131685 | − | 0.991292i | \(-0.542039\pi\) | ||||
−0.131685 | + | 0.991292i | \(0.542039\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.0000 | − | 12.1244i | 1.05830 | − | 0.916515i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.0000 | 0.901975 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.3923 | 0.776757 | 0.388379 | − | 0.921500i | \(-0.373035\pi\) | ||||
0.388379 | + | 0.921500i | \(0.373035\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.3205 | −1.28742 | −0.643712 | − | 0.765268i | \(-0.722606\pi\) | ||||
−0.643712 | + | 0.765268i | \(0.722606\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 6.92820i | − | 0.512148i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 6.92820i | − | 0.509372i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.92820 | + | 8.00000i | 0.503953 | + | 0.581914i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 24.2487i | − | 1.75458i | −0.479965 | − | 0.877288i | \(-0.659351\pi\) | ||
0.479965 | − | 0.877288i | \(-0.340649\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.00000 | −0.143963 | −0.0719816 | − | 0.997406i | \(-0.522932\pi\) | ||||
−0.0719816 | + | 0.997406i | \(0.522932\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 24.0000i | 1.71868i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0000i | 1.28245i | 0.767354 | + | 0.641223i | \(0.221573\pi\) | ||||
−0.767354 | + | 0.641223i | \(0.778427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.0000 | −1.41776 | −0.708881 | − | 0.705328i | \(-0.750800\pi\) | ||||
−0.708881 | + | 0.705328i | \(0.750800\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 6.92820i | − | 0.488678i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.3923 | + | 12.0000i | 0.729397 | + | 0.842235i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 24.0000i | − | 1.67623i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 3.46410i | − | 0.240772i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.92820i | 0.479234i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.46410 | −0.238479 | −0.119239 | − | 0.992866i | \(-0.538046\pi\) | ||||
−0.119239 | + | 0.992866i | \(0.538046\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.92820 | 0.474713 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 36.0000 | 2.45518 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.0000 | + | 13.8564i | −1.08615 | + | 0.940634i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.8564 | 0.936329 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.0000 | −1.07144 | −0.535720 | − | 0.844396i | \(-0.679960\pi\) | ||||
−0.535720 | + | 0.844396i | \(0.679960\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.00000 | −0.466667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 6.00000i | − | 0.398234i | −0.979976 | − | 0.199117i | \(-0.936193\pi\) | ||
0.979976 | − | 0.199117i | \(-0.0638074\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.3923 | 0.686743 | 0.343371 | − | 0.939200i | \(-0.388431\pi\) | ||||
0.343371 | + | 0.939200i | \(0.388431\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.0000 | + | 13.8564i | 0.789542 | + | 0.911685i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.00000 | 0.393073 | 0.196537 | − | 0.980497i | \(-0.437031\pi\) | ||||
0.196537 | + | 0.980497i | \(0.437031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.92820 | −0.450035 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.3923i | 0.672222i | 0.941822 | + | 0.336111i | \(0.109112\pi\) | ||||
−0.941822 | + | 0.336111i | \(0.890888\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.7128i | 1.78514i | 0.450910 | + | 0.892570i | \(0.351100\pi\) | ||||
−0.450910 | + | 0.892570i | \(0.648900\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 10.0000i | − | 0.641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.46410 | + | 24.0000i | −0.221313 | + | 1.53330i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 6.92820i | − | 0.440831i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.0000 | 0.760469 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 30.0000i | − | 1.89358i | −0.321847 | − | 0.946792i | \(-0.604304\pi\) | ||
0.321847 | − | 0.946792i | \(-0.395696\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.0000i | 0.754434i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 27.7128i | 1.72868i | 0.502910 | + | 0.864339i | \(0.332263\pi\) | ||||
−0.502910 | + | 0.864339i | \(0.667737\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.46410 | + | 4.00000i | 0.215249 | + | 0.248548i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 6.00000i | − | 0.371391i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.2487i | 1.49524i | 0.664127 | + | 0.747620i | \(0.268803\pi\) | ||||
−0.664127 | + | 0.747620i | \(0.731197\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.7846i | 1.27679i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.8564 | −0.847998 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.46410 | −0.211210 | −0.105605 | − | 0.994408i | \(-0.533678\pi\) | ||||
−0.105605 | + | 0.994408i | \(0.533678\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | −0.485965 | −0.242983 | − | 0.970031i | \(-0.578126\pi\) | ||||
−0.242983 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −12.0000 | − | 13.8564i | −0.726273 | − | 0.838628i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 24.2487 | 1.46225 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.00000i | 0.120168i | 0.998193 | + | 0.0600842i | \(0.0191369\pi\) | ||||
−0.998193 | + | 0.0600842i | \(0.980863\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.00000 | 0.478947 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 14.0000i | − | 0.832214i | −0.909316 | − | 0.416107i | \(-0.863394\pi\) | ||
0.909316 | − | 0.416107i | \(-0.136606\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 13.8564 | 0.820783 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.0000 | + | 13.8564i | 0.708338 | + | 0.817918i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.0000 | 1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −27.7128 | −1.62455 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.3923 | 0.607125 | 0.303562 | − | 0.952812i | \(-0.401824\pi\) | ||||
0.303562 | + | 0.952812i | \(0.401824\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.7846i | 1.21013i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.8564i | 0.804030i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 12.0000i | − | 0.693978i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.7846 | + | 18.0000i | −1.19800 | + | 1.03750i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 20.7846i | 1.19404i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.0000 | 0.687118 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 22.0000i | − | 1.25561i | −0.778372 | − | 0.627803i | \(-0.783954\pi\) | ||
0.778372 | − | 0.627803i | \(-0.216046\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 8.00000i | − | 0.455104i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0000 | 0.680458 | 0.340229 | − | 0.940343i | \(-0.389495\pi\) | ||||
0.340229 | + | 0.940343i | \(0.389495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 6.92820i | − | 0.391605i | −0.980643 | − | 0.195803i | \(-0.937269\pi\) | ||
0.980643 | − | 0.195803i | \(-0.0627312\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.92820 | − | 6.00000i | 0.390360 | − | 0.338062i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.00000i | 0.336994i | 0.985702 | + | 0.168497i | \(0.0538913\pi\) | ||||
−0.985702 | + | 0.168497i | \(0.946109\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.7846i | 1.16371i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 20.7846i | − | 1.16008i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −24.2487 | −1.34508 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −28.0000 | −1.54840 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.46410 | 0.190404 | 0.0952021 | − | 0.995458i | \(-0.469650\pi\) | ||||
0.0952021 | + | 0.995458i | \(0.469650\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 2.00000i | − | 0.109599i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.0000 | 0.655630 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0000 | 0.762629 | 0.381314 | − | 0.924445i | \(-0.375472\pi\) | ||||
0.381314 | + | 0.924445i | \(0.375472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 36.0000i | − | 1.95525i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −27.7128 | −1.50073 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 24.0000 | 1.29212 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.3205 | 0.929814 | 0.464907 | − | 0.885360i | \(-0.346088\pi\) | ||||
0.464907 | + | 0.885360i | \(0.346088\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.46410 | −0.185429 | −0.0927146 | − | 0.995693i | \(-0.529554\pi\) | ||||
−0.0927146 | + | 0.995693i | \(0.529554\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 13.8564i | − | 0.739600i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 27.7128i | − | 1.47500i | −0.675345 | − | 0.737502i | \(-0.736005\pi\) | ||
0.675345 | − | 0.737502i | \(-0.263995\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.0000i | 0.636894i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 31.1769i | 1.64545i | 0.568436 | + | 0.822727i | \(0.307549\pi\) | ||||
−0.568436 | + | 0.822727i | \(0.692451\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | 0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.00000i | 0.104973i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 24.0000i | 1.25622i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.00000 | 0.417597 | 0.208798 | − | 0.977959i | \(-0.433045\pi\) | ||||
0.208798 | + | 0.977959i | \(0.433045\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 6.92820i | − | 0.360668i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.3923 | − | 12.0000i | −0.539542 | − | 0.623009i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 14.0000i | − | 0.724893i | −0.932005 | − | 0.362446i | \(-0.881942\pi\) | ||
0.932005 | − | 0.362446i | \(-0.118058\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 13.8564i | − | 0.715542i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 20.7846i | − | 1.07046i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.2487 | −1.24557 | −0.622786 | − | 0.782392i | \(-0.713999\pi\) | ||||
−0.622786 | + | 0.782392i | \(0.713999\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −20.7846 | −1.06483 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.0000 | 1.22634 | 0.613171 | − | 0.789950i | \(-0.289894\pi\) | ||||
0.613171 | + | 0.789950i | \(0.289894\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −24.0000 | + | 20.7846i | −1.22315 | + | 1.05928i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.3923 | 0.528271 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.0000i | 0.912636i | 0.889817 | + | 0.456318i | \(0.150832\pi\) | ||||
−0.889817 | + | 0.456318i | \(0.849168\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −36.0000 | −1.81596 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 12.0000i | − | 0.603786i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.3923 | 0.521575 | 0.260787 | − | 0.965396i | \(-0.416018\pi\) | ||||
0.260787 | + | 0.965396i | \(0.416018\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.00000 | + | 6.92820i | −0.400501 | + | 0.346844i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.0000 | 1.49813 | 0.749064 | − | 0.662497i | \(-0.230503\pi\) | ||||
0.749064 | + | 0.662497i | \(0.230503\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 27.7128 | 1.38047 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 38.1051 | 1.89346 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.92820i | 0.343418i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 6.92820i | − | 0.342578i | −0.985221 | − | 0.171289i | \(-0.945207\pi\) | ||
0.985221 | − | 0.171289i | \(-0.0547931\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.0000i | 0.591916i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.3923 | − | 12.0000i | −0.511372 | − | 0.590481i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.7846i | 1.02028i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.00000 | −0.195881 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 30.0000i | − | 1.46560i | −0.680446 | − | 0.732798i | \(-0.738214\pi\) | ||
0.680446 | − | 0.732798i | \(-0.261786\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.0000i | 1.26716i | 0.773676 | + | 0.633581i | \(0.218416\pi\) | ||||
−0.773676 | + | 0.633581i | \(0.781584\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.92820 | + | 6.00000i | −0.335279 | + | 0.290360i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 24.0000i | − | 1.15873i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 38.1051i | 1.83546i | 0.397206 | + | 0.917729i | \(0.369980\pi\) | ||||
−0.397206 | + | 0.917729i | \(0.630020\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 41.5692 | 1.99309 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.92820 | −0.331421 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.0000 | 1.33637 | 0.668184 | − | 0.743996i | \(-0.267072\pi\) | ||||
0.668184 | + | 0.743996i | \(0.267072\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00000 | + | 6.92820i | −0.0476190 | + | 0.329914i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.46410 | 0.164584 | 0.0822922 | − | 0.996608i | \(-0.473776\pi\) | ||||
0.0822922 | + | 0.996608i | \(0.473776\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 24.0000i | − | 1.13771i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.0000 | 0.567581 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −30.0000 | −1.41579 | −0.707894 | − | 0.706319i | \(-0.750354\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.0000i | 1.13012i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.92820 | −0.325515 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 24.0000 | − | 20.7846i | 1.12514 | − | 0.974398i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.0000 | 1.59045 | 0.795226 | − | 0.606313i | \(-0.207352\pi\) | ||||
0.795226 | + | 0.606313i | \(0.207352\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 38.1051 | 1.77473 | 0.887366 | − | 0.461065i | \(-0.152533\pi\) | ||||
0.887366 | + | 0.461065i | \(0.152533\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 24.2487i | − | 1.12693i | −0.826139 | − | 0.563467i | \(-0.809467\pi\) | ||
0.826139 | − | 0.563467i | \(-0.190533\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 55.4256i | 2.57030i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 30.0000i | − | 1.38823i | −0.719862 | − | 0.694117i | \(-0.755795\pi\) | ||
0.719862 | − | 0.694117i | \(-0.244205\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.92820 | + | 6.00000i | −0.319915 | + | 0.277054i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 20.7846i | 0.957704i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −36.0000 | −1.65528 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.0000i | 0.642364i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.00000i | 0.274721i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.0000 | 1.09659 | 0.548294 | − | 0.836286i | \(-0.315277\pi\) | ||||
0.548294 | + | 0.836286i | \(0.315277\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 6.92820i | − | 0.315899i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −13.8564 | + | 12.0000i | −0.630488 | + | 0.546019i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 48.0000i | − | 2.17957i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 24.2487i | − | 1.09881i | −0.835555 | − | 0.549407i | \(-0.814854\pi\) | ||
0.835555 | − | 0.549407i | \(-0.185146\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 34.6410i | − | 1.56652i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.3205 | 0.781664 | 0.390832 | − | 0.920462i | \(-0.372187\pi\) | ||||
0.390832 | + | 0.920462i | \(0.372187\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12.0000 | 0.539360 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.00000 | − | 6.92820i | −0.269137 | − | 0.310772i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.3923 | 0.465223 | 0.232612 | − | 0.972570i | \(-0.425273\pi\) | ||||
0.232612 | + | 0.972570i | \(0.425273\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.0000i | 1.07224i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −36.0000 | −1.60516 | −0.802580 | − | 0.596544i | \(-0.796540\pi\) | ||||
−0.802580 | + | 0.596544i | \(0.796540\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −36.0000 | −1.60198 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 2.00000i | − | 0.0888231i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −31.1769 | −1.38189 | −0.690946 | − | 0.722906i | \(-0.742806\pi\) | ||||
−0.690946 | + | 0.722906i | \(0.742806\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.0000 | − | 13.8564i | −0.530849 | − | 0.612971i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.00000 | −0.353209 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.8564 | 0.610586 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 6.92820i | − | 0.304114i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.6410i | 1.51765i | 0.651294 | + | 0.758825i | \(0.274226\pi\) | ||||
−0.651294 | + | 0.758825i | \(0.725774\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.00000i | 0.0874539i | 0.999044 | + | 0.0437269i | \(0.0139232\pi\) | ||||
−0.999044 | + | 0.0437269i | \(0.986077\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 24.2487 | + | 28.0000i | 1.05830 | + | 1.22202i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000 | 0.478261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.00000i | 0.260378i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 24.0000i | − | 1.03956i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 36.0000 | 1.55642 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.7846i | 0.896922i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.46410 | − | 24.0000i | 0.149209 | − | 1.03375i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 2.00000i | − | 0.0859867i | −0.999075 | − | 0.0429934i | \(-0.986311\pi\) | ||
0.999075 | − | 0.0429934i | \(-0.0136894\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 34.6410i | − | 1.48659i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 48.4974i | − | 2.07740i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.3205 | −0.740571 | −0.370286 | − | 0.928918i | \(-0.620740\pi\) | ||||
−0.370286 | + | 0.928918i | \(0.620740\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.46410 | 0.147844 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.0000 | −0.511217 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.00000 | + | 6.92820i | 0.255146 | + | 0.294617i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 13.8564 | 0.588172 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 18.0000i | − | 0.762684i | −0.924434 | − | 0.381342i | \(-0.875462\pi\) | ||
0.924434 | − | 0.381342i | \(-0.124538\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 36.0000 | 1.52264 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.0000i | 0.758610i | 0.925272 | + | 0.379305i | \(0.123837\pi\) | ||||
−0.925272 | + | 0.379305i | \(0.876163\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 62.3538 | 2.62325 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −22.0000 | + | 19.0526i | −0.923913 | + | 0.800132i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.0000 | 0.754599 | 0.377300 | − | 0.926091i | \(-0.376853\pi\) | ||||
0.377300 | + | 0.926091i | \(0.376853\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 45.0333 | 1.88459 | 0.942293 | − | 0.334790i | \(-0.108665\pi\) | ||||
0.942293 | + | 0.334790i | \(0.108665\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 48.4974 | 2.02601 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.2487i | 1.01124i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 27.7128i | − | 1.15370i | −0.816850 | − | 0.576850i | \(-0.804282\pi\) | ||
0.816850 | − | 0.576850i | \(-0.195718\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 4.00000i | − | 0.166234i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.3923 | − | 12.0000i | −0.431145 | − | 0.497844i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 20.7846i | − | 0.860811i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −12.0000 | −0.496139 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.0000i | 0.742940i | 0.928445 | + | 0.371470i | \(0.121146\pi\) | ||||
−0.928445 | + | 0.371470i | \(0.878854\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 16.0000i | − | 0.659269i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −36.0000 | −1.48084 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 13.8564i | − | 0.569014i | −0.958674 | − | 0.284507i | \(-0.908170\pi\) | ||
0.958674 | − | 0.284507i | \(-0.0918300\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 40.0000i | − | 1.63709i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.2487i | 0.990775i | 0.868672 | + | 0.495388i | \(0.164974\pi\) | ||||
−0.868672 | + | 0.495388i | \(0.835026\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 20.7846i | − | 0.847822i | −0.905704 | − | 0.423911i | \(-0.860657\pi\) | ||
0.905704 | − | 0.423911i | \(-0.139343\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.46410 | 0.141069 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.46410 | −0.140836 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.0000 | −0.649420 | −0.324710 | − | 0.945814i | \(-0.605267\pi\) | ||||
−0.324710 | + | 0.945814i | \(0.605267\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −24.0000 | + | 20.7846i | −0.972529 | + | 0.842235i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 38.0000i | − | 1.53481i | −0.641165 | − | 0.767403i | \(-0.721549\pi\) | ||
0.641165 | − | 0.767403i | \(-0.278451\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 48.0000 | 1.93555 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.0000 | 0.724653 | 0.362326 | − | 0.932051i | \(-0.381983\pi\) | ||||
0.362326 | + | 0.932051i | \(0.381983\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.0000i | 1.04503i | 0.852631 | + | 0.522514i | \(0.175006\pi\) | ||||
−0.852631 | + | 0.522514i | \(0.824994\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13.8564 | −0.556038 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.0000 | + | 13.8564i | 0.480770 | + | 0.555145i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −13.8564 | −0.553372 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 3.46410i | − | 0.137904i | −0.997620 | − | 0.0689519i | \(-0.978035\pi\) | ||
0.997620 | − | 0.0689519i | \(-0.0219655\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 6.92820i | − | 0.275371i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 36.0000i | − | 1.42862i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.46410 | + | 24.0000i | −0.137253 | + | 0.950915i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.46410i | 0.137038i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.0000 | 1.18493 | 0.592464 | − | 0.805597i | \(-0.298155\pi\) | ||||
0.592464 | + | 0.805597i | \(0.298155\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.0000i | 1.02534i | 0.858586 | + | 0.512670i | \(0.171344\pi\) | ||||
−0.858586 | + | 0.512670i | \(0.828656\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 72.0000i | 2.83500i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.0000 | 0.471769 | 0.235884 | − | 0.971781i | \(-0.424201\pi\) | ||||
0.235884 | + | 0.971781i | \(0.424201\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 20.7846i | − | 0.815867i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −27.7128 | − | 32.0000i | −1.08615 | − | 1.25418i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 18.0000i | − | 0.704394i | −0.935926 | − | 0.352197i | \(-0.885435\pi\) | ||
0.935926 | − | 0.352197i | \(-0.114565\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 62.3538i | − | 2.43637i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.92820i | 0.270295i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.46410 | −0.134942 | −0.0674711 | − | 0.997721i | \(-0.521493\pi\) | ||||
−0.0674711 | + | 0.997721i | \(0.521493\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.46410 | −0.134738 | −0.0673690 | − | 0.997728i | \(-0.521460\pi\) | ||||
−0.0673690 | + | 0.997728i | \(0.521460\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.0000 | − | 13.8564i | −0.465340 | − | 0.537328i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.7846 | −0.804783 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 32.0000i | − | 1.23719i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.0000 | −0.463255 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.0000 | −0.539660 | −0.269830 | − | 0.962908i | \(-0.586968\pi\) | ||||
−0.269830 | + | 0.962908i | \(0.586968\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 28.0000i | 1.07772i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.46410 | −0.133136 | −0.0665681 | − | 0.997782i | \(-0.521205\pi\) | ||||
−0.0665681 | + | 0.997782i | \(0.521205\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.0000 | + | 27.7128i | 0.921035 | + | 1.06352i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.0000 | 0.459841 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −38.1051 | −1.45805 | −0.729026 | − | 0.684486i | \(-0.760027\pi\) | ||||
−0.729026 | + | 0.684486i | \(0.760027\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.7846 | −0.794139 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.7846i | 0.792982i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20.7846i | 0.791831i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.0000i | 0.380418i | 0.981744 | + | 0.190209i | \(0.0609166\pi\) | ||||
−0.981744 | + | 0.190209i | \(0.939083\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.92820 | + | 6.00000i | −0.263181 | + | 0.227921i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 6.92820i | − | 0.262802i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.0000i | 0.453882i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.0000i | 1.13308i | 0.824033 | + | 0.566542i | \(0.191719\pi\) | ||||
−0.824033 | + | 0.566542i | \(0.808281\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.00000 | −0.150863 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 20.7846 | − | 18.0000i | 0.781686 | − | 0.676960i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.0000i | 0.375558i | 0.982211 | + | 0.187779i | \(0.0601289\pi\) | ||||
−0.982211 | + | 0.187779i | \(0.939871\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 3.46410i | − | 0.129914i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 27.7128i | − | 1.03785i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 41.5692 | 1.55460 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −20.7846 | −0.776215 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −48.0000 | −1.79010 | −0.895049 | − | 0.445968i | \(-0.852860\pi\) | ||||
−0.895049 | + | 0.445968i | \(0.852860\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.00000 | + | 6.92820i | −0.297936 | + | 0.258020i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −55.4256 | −2.06130 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 42.0000i | 1.55984i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.0000 | −1.03846 | −0.519231 | − | 0.854634i | \(-0.673782\pi\) | ||||
−0.519231 | + | 0.854634i | \(0.673782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 51.9615 | 1.91924 | 0.959621 | − | 0.281295i | \(-0.0907639\pi\) | ||||
0.959621 | + | 0.281295i | \(0.0907639\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −48.0000 | − | 6.92820i | −1.77051 | − | 0.255551i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.0000 | −0.442026 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.3923 | 0.382287 | 0.191144 | − | 0.981562i | \(-0.438780\pi\) | ||||
0.191144 | + | 0.981562i | \(0.438780\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.8564 | 0.509028 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 24.2487i | − | 0.889599i | −0.895630 | − | 0.444799i | \(-0.853275\pi\) | ||
0.895630 | − | 0.444799i | \(-0.146725\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.7846i | 0.761489i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.00000i | 0.219529i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20.7846 | + | 18.0000i | −0.759453 | + | 0.657706i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 45.0333i | − | 1.64329i | −0.570000 | − | 0.821645i | \(-0.693057\pi\) | ||
0.570000 | − | 0.821645i | \(-0.306943\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 60.0000 | 2.18652 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 12.0000i | − | 0.436725i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.0000i | 0.363456i | 0.983349 | + | 0.181728i | \(0.0581691\pi\) | ||||
−0.983349 | + | 0.181728i | \(0.941831\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −24.0000 | −0.871145 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.7846i | 0.753442i | 0.926327 | + | 0.376721i | \(0.122948\pi\) | ||||
−0.926327 | + | 0.376721i | \(0.877052\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 24.2487 | + | 28.0000i | 0.877862 | + | 1.01367i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20.7846i | 0.750489i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.8564i | 0.499675i | 0.968288 | + | 0.249837i | \(0.0803772\pi\) | ||||
−0.968288 | + | 0.249837i | \(0.919623\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −55.4256 | −1.99611 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.46410 | −0.124595 | −0.0622975 | − | 0.998058i | \(-0.519843\pi\) | ||||
−0.0622975 | + | 0.998058i | \(0.519843\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −56.0000 | −2.01158 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.00000 | + | 6.92820i | −0.286998 | + | 0.248548i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13.8564 | −0.496457 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 12.0000i | − | 0.429394i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −24.0000 | −0.857690 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −36.0000 | −1.28490 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.0000i | 1.21197i | 0.795476 | + | 0.605985i | \(0.207221\pi\) | ||||
−0.795476 | + | 0.605985i | \(0.792779\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −48.4974 | −1.72655 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −36.0000 | + | 31.1769i | −1.28001 | + | 1.10852i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.0000 | 0.426132 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −41.5692 | −1.47431 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.3205 | −0.613524 | −0.306762 | − | 0.951786i | \(-0.599246\pi\) | ||||
−0.306762 | + | 0.951786i | \(0.599246\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 6.92820i | − | 0.244796i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 24.0000i | − | 0.846942i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20.7846 | − | 24.0000i | −0.732561 | − | 0.845889i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 6.92820i | − | 0.243884i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30.0000 | −1.05474 | −0.527372 | − | 0.849635i | \(-0.676823\pi\) | ||||
−0.527372 | + | 0.849635i | \(0.676823\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 22.0000i | − | 0.772524i | −0.922389 | − | 0.386262i | \(-0.873766\pi\) | ||
0.922389 | − | 0.386262i | \(-0.126234\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 16.0000i | − | 0.561144i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 60.0000 | 2.10171 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 20.7846i | − | 0.727161i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.92820 | − | 6.00000i | 0.242091 | − | 0.209657i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 30.0000i | − | 1.04701i | −0.852023 | − | 0.523504i | \(-0.824625\pi\) | ||
0.852023 | − | 0.523504i | \(-0.175375\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 3.46410i | − | 0.120751i | −0.998176 | − | 0.0603755i | \(-0.980770\pi\) | ||
0.998176 | − | 0.0603755i | \(-0.0192298\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 48.4974i | 1.68846i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.2487 | −0.843210 | −0.421605 | − | 0.906780i | \(-0.638533\pi\) | ||||
−0.421605 | + | 0.906780i | \(0.638533\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.46410 | −0.120313 | −0.0601566 | − | 0.998189i | \(-0.519160\pi\) | ||||
−0.0601566 | + | 0.998189i | \(0.519160\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.00000 | −0.138758 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −41.5692 | −1.43856 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 32.0000i | − | 1.10608i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.0000 | 0.414286 | 0.207143 | − | 0.978311i | \(-0.433583\pi\) | ||||
0.207143 | + | 0.978311i | \(0.433583\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.00000 | −0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.0000i | 0.413302i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.46410 | 0.119169 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.00000 | − | 1.73205i | 0.0687208 | − | 0.0595140i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 28.0000 | 0.960958 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.92820 | −0.237496 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.46410 | −0.118609 | −0.0593043 | − | 0.998240i | \(-0.518888\pi\) | ||||
−0.0593043 | + | 0.998240i | \(0.518888\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.92820i | 0.236940i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 34.6410i | − | 1.18331i | −0.806190 | − | 0.591657i | \(-0.798474\pi\) | ||
0.806190 | − | 0.591657i | \(-0.201526\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 14.0000i | − | 0.477674i | −0.971060 | − | 0.238837i | \(-0.923234\pi\) | ||
0.971060 | − | 0.238837i | \(-0.0767661\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −27.7128 | + | 24.0000i | −0.944450 | + | 0.817918i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31.1769i | 1.06127i | 0.847599 | + | 0.530637i | \(0.178047\pi\) | ||||
−0.847599 | + | 0.530637i | \(0.821953\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.0000 | 0.408012 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 34.0000i | 1.15470i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.0000i | 0.407072i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.0000 | 0.406604 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 13.8564i | − | 0.468968i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.8564 | + | 12.0000i | −0.468432 | + | 0.405674i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.0000i | 1.28317i | 0.767052 | + | 0.641584i | \(0.221723\pi\) | ||||
−0.767052 | + | 0.641584i | \(0.778277\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 20.7846i | 0.701047i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.8564i | 0.466834i | 0.972377 | + | 0.233417i | \(0.0749907\pi\) | ||||
−0.972377 | + | 0.233417i | \(0.925009\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.46410 | −0.116576 | −0.0582882 | − | 0.998300i | \(-0.518564\pi\) | ||||
−0.0582882 | + | 0.998300i | \(0.518564\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −41.5692 | −1.39733 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.0000 | −0.402921 | −0.201460 | − | 0.979497i | \(-0.564569\pi\) | ||||
−0.201460 | + | 0.979497i | \(0.564569\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.0000 | + | 20.7846i | 0.603701 | + | 0.697093i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −38.1051 | −1.27657 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −36.0000 | −1.20335 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 24.0000 | 0.801337 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 48.0000i | − | 1.60089i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −36.0000 | − | 41.5692i | −1.19800 | − | 1.38334i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 60.0000 | 1.99447 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.2487 | −0.805165 | −0.402583 | − | 0.915384i | \(-0.631887\pi\) | ||||
−0.402583 | + | 0.915384i | \(0.631887\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.3923 | −0.344691 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.3923i | 0.344312i | 0.985070 | + | 0.172156i | \(0.0550734\pi\) | ||||
−0.985070 | + | 0.172156i | \(0.944927\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 20.7846i | − | 0.687870i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 24.0000i | 0.793416i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 31.1769 | + | 36.0000i | 1.02955 | + | 1.18882i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 31.1769i | − | 1.02843i | −0.857661 | − | 0.514216i | \(-0.828083\pi\) | ||
0.857661 | − | 0.514216i | \(-0.171917\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 44.0000 | 1.44985 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.0000i | 0.394985i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.0000i | 0.460317i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.00000 | 0.131377 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 41.5692i | 1.36384i | 0.731426 | + | 0.681921i | \(0.238855\pi\) | ||||
−0.731426 | + | 0.681921i | \(0.761145\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.8564 | + | 2.00000i | 0.454125 | + | 0.0655474i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 24.0000i | 0.785725i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.4974i | 1.58434i | 0.610299 | + | 0.792171i | \(0.291049\pi\) | ||||
−0.610299 | + | 0.792171i | \(0.708951\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.8564 | 0.452187 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.2487 | 0.790485 | 0.395243 | − | 0.918577i | \(-0.370660\pi\) | ||||
0.395243 | + | 0.918577i | \(0.370660\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.0000 | −0.781548 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −24.0000 | − | 27.7128i | −0.780720 | − | 0.901498i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.2487 | 0.787977 | 0.393989 | − | 0.919115i | \(-0.371095\pi\) | ||||
0.393989 | + | 0.919115i | \(0.371095\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.0000i | 0.779073i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.0000 | −0.389127 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.00000 | 0.194359 | 0.0971795 | − | 0.995267i | \(-0.469018\pi\) | ||||
0.0971795 | + | 0.995267i | \(0.469018\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 84.0000i | 2.71818i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −41.5692 | −1.34374 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.0000 | − | 10.3923i | 0.387500 | − | 0.335585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.3923 | 0.334887 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.92820 | 0.223027 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 24.2487i | − | 0.779786i | −0.920860 | − | 0.389893i | \(-0.872512\pi\) | ||
0.920860 | − | 0.389893i | \(-0.127488\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.0000i | 0.577647i | 0.957382 | + | 0.288824i | \(0.0932642\pi\) | ||||
−0.957382 | + | 0.288824i | \(0.906736\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.46410 | + | 4.00000i | 0.111054 | + | 0.128234i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 48.4974i | − | 1.55316i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30.0000 | −0.959785 | −0.479893 | − | 0.877327i | \(-0.659324\pi\) | ||||
−0.479893 | + | 0.877327i | \(0.659324\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.0000i | 0.767043i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 14.0000i | − | 0.446986i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 36.0000 | 1.14822 | 0.574111 | − | 0.818778i | \(-0.305348\pi\) | ||||
0.574111 | + | 0.818778i | \(0.305348\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 62.3538i | − | 1.98676i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 36.0000i | − | 1.14473i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.46410i | 0.110041i | 0.998485 | + | 0.0550204i | \(0.0175224\pi\) | ||||
−0.998485 | + | 0.0550204i | \(0.982478\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.92820i | 0.219860i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 69.2820 | 2.19639 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 51.9615 | 1.64564 | 0.822819 | − | 0.568304i | \(-0.192400\pi\) | ||||
0.822819 | + | 0.568304i | \(0.192400\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.00000 | −0.253109 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))