Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3042,2,Mod(1351,3042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3042, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3042.1351");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3042 = 2 \cdot 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3042.b (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: | \(24.2904922949\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 78) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1351.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3042.1351 |
Dual form | 3042.2.b.l.1351.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3042\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − 1.73205i | − 0.774597i | −0.921954 | − | 0.387298i | \(-0.873408\pi\) | ||||
0.921954 | − | 0.387298i | \(-0.126592\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.73205i | 1.78855i | 0.447521 | + | 0.894274i | \(0.352307\pi\) | ||||
−0.447521 | + | 0.894274i | \(0.647693\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.73205 | −0.547723 | ||||||||
\(11\) | − 4.73205i | − 1.42677i | −0.700774 | − | 0.713384i | \(-0.747162\pi\) | ||||
0.700774 | − | 0.713384i | \(-0.252838\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 4.73205 | 1.26469 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.19615 | −1.26025 | −0.630126 | − | 0.776493i | \(-0.716997\pi\) | ||||
−0.630126 | + | 0.776493i | \(0.716997\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 1.26795i | − 0.290887i | −0.989367 | − | 0.145444i | \(-0.953539\pi\) | ||||
0.989367 | − | 0.145444i | \(-0.0464610\pi\) | |||||||
\(20\) | 1.73205i | 0.387298i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.73205 | −1.00888 | ||||||||
\(23\) | 2.19615 | 0.457929 | 0.228965 | − | 0.973435i | \(-0.426466\pi\) | ||||
0.228965 | + | 0.973435i | \(0.426466\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | 0.400000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 4.73205i | − 0.894274i | ||||||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 2.53590i | − 0.455461i | −0.973724 | − | 0.227730i | \(-0.926870\pi\) | ||||
0.973724 | − | 0.227730i | \(-0.0731305\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.19615i | 0.891133i | ||||||||
\(35\) | 8.19615 | 1.38540 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00000i | 0.493197i | 0.969118 | + | 0.246598i | \(0.0793129\pi\) | ||||
−0.969118 | + | 0.246598i | \(0.920687\pi\) | |||||||
\(38\) | −1.26795 | −0.205689 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.73205 | 0.273861 | ||||||||
\(41\) | − 0.464102i | − 0.0724805i | −0.999343 | − | 0.0362402i | \(-0.988462\pi\) | ||||
0.999343 | − | 0.0362402i | \(-0.0115382\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.19615 | −0.944904 | −0.472452 | − | 0.881356i | \(-0.656631\pi\) | ||||
−0.472452 | + | 0.881356i | \(0.656631\pi\) | |||||||
\(44\) | 4.73205i | 0.713384i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − 2.19615i | − 0.323805i | ||||||||
\(47\) | 1.26795i | 0.184949i | 0.995715 | + | 0.0924747i | \(0.0294777\pi\) | ||||
−0.995715 | + | 0.0924747i | \(0.970522\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15.3923 | −2.19890 | ||||||||
\(50\) | − 2.00000i | − 0.282843i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.00000 | −0.412082 | −0.206041 | − | 0.978543i | \(-0.566058\pi\) | ||||
−0.206041 | + | 0.978543i | \(0.566058\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.19615 | −1.10517 | ||||||||
\(56\) | −4.73205 | −0.632347 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 3.00000i | − 0.393919i | ||||||||
\(59\) | − 13.8564i | − 1.80395i | −0.431788 | − | 0.901975i | \(-0.642117\pi\) | ||||
0.431788 | − | 0.901975i | \(-0.357883\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.80385 | 0.615070 | 0.307535 | − | 0.951537i | \(-0.400496\pi\) | ||||
0.307535 | + | 0.951537i | \(0.400496\pi\) | |||||||
\(62\) | −2.53590 | −0.322059 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 10.7321i | − 1.31113i | −0.755139 | − | 0.655564i | \(-0.772431\pi\) | ||||
0.755139 | − | 0.655564i | \(-0.227569\pi\) | |||||||
\(68\) | 5.19615 | 0.630126 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − 8.19615i | − 0.979628i | ||||||||
\(71\) | 8.19615i | 0.972704i | 0.873763 | + | 0.486352i | \(0.161673\pi\) | ||||
−0.873763 | + | 0.486352i | \(0.838327\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 12.1244i | − 1.41905i | −0.704681 | − | 0.709524i | \(-0.748910\pi\) | ||||
0.704681 | − | 0.709524i | \(-0.251090\pi\) | |||||||
\(74\) | 3.00000 | 0.348743 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.26795i | 0.145444i | ||||||||
\(77\) | 22.3923 | 2.55184 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.3923 | −1.39424 | −0.697122 | − | 0.716953i | \(-0.745536\pi\) | ||||
−0.697122 | + | 0.716953i | \(0.745536\pi\) | |||||||
\(80\) | − 1.73205i | − 0.193649i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.464102 | −0.0512514 | ||||||||
\(83\) | − 11.6603i | − 1.27988i | −0.768425 | − | 0.639940i | \(-0.778959\pi\) | ||||
0.768425 | − | 0.639940i | \(-0.221041\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.00000i | 0.976187i | ||||||||
\(86\) | 6.19615i | 0.668148i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.73205 | 0.504438 | ||||||||
\(89\) | − 2.53590i | − 0.268805i | −0.990927 | − | 0.134402i | \(-0.957089\pi\) | ||||
0.990927 | − | 0.134402i | \(-0.0429115\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.19615 | −0.228965 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.26795 | 0.130779 | ||||||||
\(95\) | −2.19615 | −0.225320 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 6.00000i | − 0.609208i | −0.952479 | − | 0.304604i | \(-0.901476\pi\) | ||||
0.952479 | − | 0.304604i | \(-0.0985241\pi\) | |||||||
\(98\) | 15.3923i | 1.55486i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.00000 | −0.200000 | ||||||||
\(101\) | −1.39230 | −0.138540 | −0.0692698 | − | 0.997598i | \(-0.522067\pi\) | ||||
−0.0692698 | + | 0.997598i | \(0.522067\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.19615 | 0.413459 | 0.206730 | − | 0.978398i | \(-0.433718\pi\) | ||||
0.206730 | + | 0.978398i | \(0.433718\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.00000i | 0.291386i | ||||||||
\(107\) | −8.19615 | −0.792352 | −0.396176 | − | 0.918175i | \(-0.629663\pi\) | ||||
−0.396176 | + | 0.918175i | \(0.629663\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 16.3923i | − 1.57010i | −0.619434 | − | 0.785049i | \(-0.712638\pi\) | ||||
0.619434 | − | 0.785049i | \(-0.287362\pi\) | |||||||
\(110\) | 8.19615i | 0.781472i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.73205i | 0.447137i | ||||||||
\(113\) | −11.1962 | −1.05325 | −0.526623 | − | 0.850099i | \(-0.676542\pi\) | ||||
−0.526623 | + | 0.850099i | \(0.676542\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 3.80385i | − 0.354711i | ||||||||
\(116\) | −3.00000 | −0.278543 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −13.8564 | −1.27559 | ||||||||
\(119\) | − 24.5885i | − 2.25402i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.3923 | −1.03566 | ||||||||
\(122\) | − 4.80385i | − 0.434920i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.53590i | 0.227730i | ||||||||
\(125\) | − 12.1244i | − 1.08444i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.00000 | 0.354943 | 0.177471 | − | 0.984126i | \(-0.443208\pi\) | ||||
0.177471 | + | 0.984126i | \(0.443208\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.3923 | −1.43220 | −0.716101 | − | 0.697997i | \(-0.754075\pi\) | ||||
−0.716101 | + | 0.697997i | \(0.754075\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.00000 | 0.520266 | ||||||||
\(134\) | −10.7321 | −0.927108 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − 5.19615i | − 0.445566i | ||||||||
\(137\) | 9.00000i | 0.768922i | 0.923141 | + | 0.384461i | \(0.125613\pi\) | ||||
−0.923141 | + | 0.384461i | \(0.874387\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | −8.19615 | −0.692701 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.19615 | 0.687806 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 5.19615i | − 0.431517i | ||||||||
\(146\) | −12.1244 | −1.00342 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 3.00000i | − 0.246598i | ||||||||
\(149\) | − 18.1244i | − 1.48481i | −0.669954 | − | 0.742403i | \(-0.733686\pi\) | ||||
0.669954 | − | 0.742403i | \(-0.266314\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.26795i | 0.591457i | 0.955272 | + | 0.295729i | \(0.0955624\pi\) | ||||
−0.955272 | + | 0.295729i | \(0.904438\pi\) | |||||||
\(152\) | 1.26795 | 0.102844 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − 22.3923i | − 1.80442i | ||||||||
\(155\) | −4.39230 | −0.352798 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.19615 | −0.255081 | −0.127540 | − | 0.991833i | \(-0.540708\pi\) | ||||
−0.127540 | + | 0.991833i | \(0.540708\pi\) | |||||||
\(158\) | 12.3923i | 0.985879i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.73205 | −0.136931 | ||||||||
\(161\) | 10.3923i | 0.819028i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.46410i | 0.741286i | 0.928775 | + | 0.370643i | \(0.120863\pi\) | ||||
−0.928775 | + | 0.370643i | \(0.879137\pi\) | |||||||
\(164\) | 0.464102i | 0.0362402i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.6603 | −0.905011 | ||||||||
\(167\) | 2.53590i | 0.196234i | 0.995175 | + | 0.0981169i | \(0.0312819\pi\) | ||||
−0.995175 | + | 0.0981169i | \(0.968718\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 9.00000 | 0.690268 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.19615 | 0.472452 | ||||||||
\(173\) | 16.3923 | 1.24628 | 0.623142 | − | 0.782109i | \(-0.285856\pi\) | ||||
0.623142 | + | 0.782109i | \(0.285856\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.46410i | 0.715419i | ||||||||
\(176\) | − 4.73205i | − 0.356692i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.53590 | −0.190074 | ||||||||
\(179\) | −8.19615 | −0.612609 | −0.306305 | − | 0.951934i | \(-0.599093\pi\) | ||||
−0.306305 | + | 0.951934i | \(0.599093\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.5885 | 0.861363 | 0.430682 | − | 0.902504i | \(-0.358273\pi\) | ||||
0.430682 | + | 0.902504i | \(0.358273\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.19615i | 0.161903i | ||||||||
\(185\) | 5.19615 | 0.382029 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24.5885i | 1.79809i | ||||||||
\(188\) | − 1.26795i | − 0.0924747i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.19615i | 0.159326i | ||||||||
\(191\) | −20.7846 | −1.50392 | −0.751961 | − | 0.659208i | \(-0.770892\pi\) | ||||
−0.751961 | + | 0.659208i | \(0.770892\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 12.8038i | − 0.921641i | −0.887493 | − | 0.460821i | \(-0.847555\pi\) | ||||
0.887493 | − | 0.460821i | \(-0.152445\pi\) | |||||||
\(194\) | −6.00000 | −0.430775 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 15.3923 | 1.09945 | ||||||||
\(197\) | 6.92820i | 0.493614i | 0.969065 | + | 0.246807i | \(0.0793814\pi\) | ||||
−0.969065 | + | 0.246807i | \(0.920619\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.58846 | −0.608820 | −0.304410 | − | 0.952541i | \(-0.598459\pi\) | ||||
−0.304410 | + | 0.952541i | \(0.598459\pi\) | |||||||
\(200\) | 2.00000i | 0.141421i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.39230i | 0.0979622i | ||||||||
\(203\) | 14.1962i | 0.996375i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.803848 | −0.0561432 | ||||||||
\(206\) | − 4.19615i | − 0.292360i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.00000 | −0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.60770 | −0.248364 | −0.124182 | − | 0.992259i | \(-0.539631\pi\) | ||||
−0.124182 | + | 0.992259i | \(0.539631\pi\) | |||||||
\(212\) | 3.00000 | 0.206041 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.19615i | 0.560277i | ||||||||
\(215\) | 10.7321i | 0.731920i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.0000 | 0.814613 | ||||||||
\(218\) | −16.3923 | −1.11023 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 8.19615 | 0.552584 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.9282i | 1.26753i | 0.773527 | + | 0.633763i | \(0.218491\pi\) | ||||
−0.773527 | + | 0.633763i | \(0.781509\pi\) | |||||||
\(224\) | 4.73205 | 0.316173 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.1962i | 0.744757i | ||||||||
\(227\) | − 9.80385i | − 0.650704i | −0.945593 | − | 0.325352i | \(-0.894517\pi\) | ||||
0.945593 | − | 0.325352i | \(-0.105483\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.8564i | 1.31215i | 0.754696 | + | 0.656074i | \(0.227784\pi\) | ||||
−0.754696 | + | 0.656074i | \(0.772216\pi\) | |||||||
\(230\) | −3.80385 | −0.250818 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.00000i | 0.196960i | ||||||||
\(233\) | −18.0000 | −1.17922 | −0.589610 | − | 0.807688i | \(-0.700718\pi\) | ||||
−0.589610 | + | 0.807688i | \(0.700718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.19615 | 0.143261 | ||||||||
\(236\) | 13.8564i | 0.901975i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −24.5885 | −1.59383 | ||||||||
\(239\) | − 24.5885i | − 1.59050i | −0.606285 | − | 0.795248i | \(-0.707341\pi\) | ||||
0.606285 | − | 0.795248i | \(-0.292659\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.803848i | 0.0517804i | 0.999665 | + | 0.0258902i | \(0.00824202\pi\) | ||||
−0.999665 | + | 0.0258902i | \(0.991758\pi\) | |||||||
\(242\) | 11.3923i | 0.732325i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.80385 | −0.307535 | ||||||||
\(245\) | 26.6603i | 1.70326i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2.53590 | 0.161030 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −12.1244 | −0.766812 | ||||||||
\(251\) | −4.39230 | −0.277240 | −0.138620 | − | 0.990346i | \(-0.544267\pi\) | ||||
−0.138620 | + | 0.990346i | \(0.544267\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 10.3923i | − 0.653359i | ||||||||
\(254\) | − 4.00000i | − 0.250982i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.8038 | 0.798682 | 0.399341 | − | 0.916802i | \(-0.369239\pi\) | ||||
0.399341 | + | 0.916802i | \(0.369239\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.1962 | −0.882106 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 16.3923i | 1.01272i | ||||||||
\(263\) | 2.19615 | 0.135421 | 0.0677103 | − | 0.997705i | \(-0.478431\pi\) | ||||
0.0677103 | + | 0.997705i | \(0.478431\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.19615i | 0.319197i | ||||||||
\(266\) | − 6.00000i | − 0.367884i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10.7321i | 0.655564i | ||||||||
\(269\) | 28.3923 | 1.73111 | 0.865555 | − | 0.500814i | \(-0.166966\pi\) | ||||
0.865555 | + | 0.500814i | \(0.166966\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | −5.19615 | −0.315063 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.00000 | 0.543710 | ||||||||
\(275\) | − 9.46410i | − 0.570707i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.1962 | −0.913048 | −0.456524 | − | 0.889711i | \(-0.650906\pi\) | ||||
−0.456524 | + | 0.889711i | \(0.650906\pi\) | |||||||
\(278\) | 4.00000i | 0.239904i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8.19615i | 0.489814i | ||||||||
\(281\) | − 24.4641i | − 1.45941i | −0.683764 | − | 0.729703i | \(-0.739658\pi\) | ||||
0.683764 | − | 0.729703i | \(-0.260342\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.1962 | 1.79497 | 0.897487 | − | 0.441040i | \(-0.145390\pi\) | ||||
0.897487 | + | 0.441040i | \(0.145390\pi\) | |||||||
\(284\) | − 8.19615i | − 0.486352i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.19615 | 0.129635 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.0000 | 0.588235 | ||||||||
\(290\) | −5.19615 | −0.305129 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 12.1244i | 0.709524i | ||||||||
\(293\) | 14.6603i | 0.856461i | 0.903669 | + | 0.428231i | \(0.140863\pi\) | ||||
−0.903669 | + | 0.428231i | \(0.859137\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24.0000 | −1.39733 | ||||||||
\(296\) | −3.00000 | −0.174371 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −18.1244 | −1.04992 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 29.3205i | − 1.69001i | ||||||||
\(302\) | 7.26795 | 0.418223 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − 1.26795i | − 0.0727219i | ||||||||
\(305\) | − 8.32051i | − 0.476431i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.7321i | 0.612510i | 0.951949 | + | 0.306255i | \(0.0990761\pi\) | ||||
−0.951949 | + | 0.306255i | \(0.900924\pi\) | |||||||
\(308\) | −22.3923 | −1.27592 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.39230i | 0.249466i | ||||||||
\(311\) | 2.19615 | 0.124532 | 0.0622662 | − | 0.998060i | \(-0.480167\pi\) | ||||
0.0622662 | + | 0.998060i | \(0.480167\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.3923 | −1.37873 | −0.689367 | − | 0.724412i | \(-0.742111\pi\) | ||||
−0.689367 | + | 0.724412i | \(0.742111\pi\) | |||||||
\(314\) | 3.19615i | 0.180369i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.3923 | 0.697122 | ||||||||
\(317\) | 6.12436i | 0.343978i | 0.985099 | + | 0.171989i | \(0.0550194\pi\) | ||||
−0.985099 | + | 0.171989i | \(0.944981\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 14.1962i | − 0.794832i | ||||||||
\(320\) | 1.73205i | 0.0968246i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 10.3923 | 0.579141 | ||||||||
\(323\) | 6.58846i | 0.366592i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9.46410 | 0.524168 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.464102 | 0.0256257 | ||||||||
\(329\) | −6.00000 | −0.330791 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 12.0000i | − 0.659580i | −0.944054 | − | 0.329790i | \(-0.893022\pi\) | ||||
0.944054 | − | 0.329790i | \(-0.106978\pi\) | |||||||
\(332\) | 11.6603i | 0.639940i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.53590 | 0.138758 | ||||||||
\(335\) | −18.5885 | −1.01560 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 31.0000 | 1.68868 | 0.844339 | − | 0.535810i | \(-0.179994\pi\) | ||||
0.844339 | + | 0.535810i | \(0.179994\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − 9.00000i | − 0.488094i | ||||||||
\(341\) | −12.0000 | −0.649836 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 39.7128i | − 2.14429i | ||||||||
\(344\) | − 6.19615i | − 0.334074i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 16.3923i | − 0.881256i | ||||||||
\(347\) | 12.5885 | 0.675784 | 0.337892 | − | 0.941185i | \(-0.390286\pi\) | ||||
0.337892 | + | 0.941185i | \(0.390286\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.53590i | 0.135744i | 0.997694 | + | 0.0678718i | \(0.0216209\pi\) | ||||
−0.997694 | + | 0.0678718i | \(0.978379\pi\) | |||||||
\(350\) | 9.46410 | 0.505878 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.73205 | −0.252219 | ||||||||
\(353\) | 5.78461i | 0.307884i | 0.988080 | + | 0.153942i | \(0.0491968\pi\) | ||||
−0.988080 | + | 0.153942i | \(0.950803\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.1962 | 0.753454 | ||||||||
\(356\) | 2.53590i | 0.134402i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.19615i | 0.433180i | ||||||||
\(359\) | − 22.0526i | − 1.16389i | −0.813228 | − | 0.581945i | \(-0.802292\pi\) | ||||
0.813228 | − | 0.581945i | \(-0.197708\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.3923 | 0.915384 | ||||||||
\(362\) | − 11.5885i | − 0.609076i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −21.0000 | −1.09919 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.1962 | −1.26303 | −0.631514 | − | 0.775364i | \(-0.717566\pi\) | ||||
−0.631514 | + | 0.775364i | \(0.717566\pi\) | |||||||
\(368\) | 2.19615 | 0.114482 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − 5.19615i | − 0.270135i | ||||||||
\(371\) | − 14.1962i | − 0.737028i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.9808 | 1.24168 | 0.620838 | − | 0.783939i | \(-0.286792\pi\) | ||||
0.620838 | + | 0.783939i | \(0.286792\pi\) | |||||||
\(374\) | 24.5885 | 1.27144 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.26795 | −0.0653895 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.2487i | 0.937373i | 0.883364 | + | 0.468687i | \(0.155273\pi\) | ||||
−0.883364 | + | 0.468687i | \(0.844727\pi\) | |||||||
\(380\) | 2.19615 | 0.112660 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 20.7846i | 1.06343i | ||||||||
\(383\) | 11.3205i | 0.578451i | 0.957261 | + | 0.289225i | \(0.0933977\pi\) | ||||
−0.957261 | + | 0.289225i | \(0.906602\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − 38.7846i | − 1.97665i | ||||||||
\(386\) | −12.8038 | −0.651699 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.00000i | 0.304604i | ||||||||
\(389\) | −13.3923 | −0.679017 | −0.339508 | − | 0.940603i | \(-0.610261\pi\) | ||||
−0.339508 | + | 0.940603i | \(0.610261\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.4115 | −0.577107 | ||||||||
\(392\) | − 15.3923i | − 0.777429i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.92820 | 0.349038 | ||||||||
\(395\) | 21.4641i | 1.07998i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 16.3923i | − 0.822706i | −0.911476 | − | 0.411353i | \(-0.865056\pi\) | ||||
0.911476 | − | 0.411353i | \(-0.134944\pi\) | |||||||
\(398\) | 8.58846i | 0.430500i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.00000 | 0.100000 | ||||||||
\(401\) | − 21.0000i | − 1.04869i | −0.851506 | − | 0.524345i | \(-0.824310\pi\) | ||||
0.851506 | − | 0.524345i | \(-0.175690\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 1.39230 | 0.0692698 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 14.1962 | 0.704543 | ||||||||
\(407\) | 14.1962 | 0.703677 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.33975i | 0.165140i | 0.996585 | + | 0.0825699i | \(0.0263128\pi\) | ||||
−0.996585 | + | 0.0825699i | \(0.973687\pi\) | |||||||
\(410\) | 0.803848i | 0.0396992i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.19615 | −0.206730 | ||||||||
\(413\) | 65.5692 | 3.22645 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −20.1962 | −0.991390 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.00000i | 0.293470i | ||||||||
\(419\) | −16.3923 | −0.800816 | −0.400408 | − | 0.916337i | \(-0.631132\pi\) | ||||
−0.400408 | + | 0.916337i | \(0.631132\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 0.464102i | − 0.0226189i | −0.999936 | − | 0.0113095i | \(-0.996400\pi\) | ||||
0.999936 | − | 0.0113095i | \(-0.00359999\pi\) | |||||||
\(422\) | 3.60770i | 0.175620i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − 3.00000i | − 0.145693i | ||||||||
\(425\) | −10.3923 | −0.504101 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 22.7321i | 1.10008i | ||||||||
\(428\) | 8.19615 | 0.396176 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.7321 | 0.517545 | ||||||||
\(431\) | 27.8038i | 1.33926i | 0.742693 | + | 0.669632i | \(0.233548\pi\) | ||||
−0.742693 | + | 0.669632i | \(0.766452\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.7846 | 1.62358 | 0.811792 | − | 0.583946i | \(-0.198492\pi\) | ||||
0.811792 | + | 0.583946i | \(0.198492\pi\) | |||||||
\(434\) | − 12.0000i | − 0.576018i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 16.3923i | 0.785049i | ||||||||
\(437\) | − 2.78461i | − 0.133206i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.5885 | −0.791724 | −0.395862 | − | 0.918310i | \(-0.629554\pi\) | ||||
−0.395862 | + | 0.918310i | \(0.629554\pi\) | |||||||
\(440\) | − 8.19615i | − 0.390736i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.39230 | 0.208685 | 0.104342 | − | 0.994541i | \(-0.466726\pi\) | ||||
0.104342 | + | 0.994541i | \(0.466726\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.39230 | −0.208215 | ||||||||
\(446\) | 18.9282 | 0.896276 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 4.73205i | − 0.223568i | ||||||||
\(449\) | − 33.4641i | − 1.57927i | −0.613578 | − | 0.789634i | \(-0.710270\pi\) | ||||
0.613578 | − | 0.789634i | \(-0.289730\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.19615 | −0.103413 | ||||||||
\(452\) | 11.1962 | 0.526623 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9.80385 | −0.460117 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 19.9808i | − 0.934661i | −0.884083 | − | 0.467330i | \(-0.845216\pi\) | ||||
0.884083 | − | 0.467330i | \(-0.154784\pi\) | |||||||
\(458\) | 19.8564 | 0.927829 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.80385i | 0.177355i | ||||||||
\(461\) | − 19.9808i | − 0.930597i | −0.885154 | − | 0.465298i | \(-0.845947\pi\) | ||||
0.885154 | − | 0.465298i | \(-0.154053\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 26.1962i | − 1.21744i | −0.793386 | − | 0.608719i | \(-0.791684\pi\) | ||||
0.793386 | − | 0.608719i | \(-0.208316\pi\) | |||||||
\(464\) | 3.00000 | 0.139272 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.0000i | 0.833834i | ||||||||
\(467\) | 36.5885 | 1.69311 | 0.846556 | − | 0.532300i | \(-0.178672\pi\) | ||||
0.846556 | + | 0.532300i | \(0.178672\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 50.7846 | 2.34502 | ||||||||
\(470\) | − 2.19615i | − 0.101301i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 13.8564 | 0.637793 | ||||||||
\(473\) | 29.3205i | 1.34816i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 2.53590i | − 0.116355i | ||||||||
\(476\) | 24.5885i | 1.12701i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −24.5885 | −1.12465 | ||||||||
\(479\) | 35.3205i | 1.61384i | 0.590664 | + | 0.806918i | \(0.298866\pi\) | ||||
−0.590664 | + | 0.806918i | \(0.701134\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0.803848 | 0.0366143 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.3923 | 0.517832 | ||||||||
\(485\) | −10.3923 | −0.471890 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 9.12436i | − 0.413464i | −0.978398 | − | 0.206732i | \(-0.933717\pi\) | ||||
0.978398 | − | 0.206732i | \(-0.0662828\pi\) | |||||||
\(488\) | 4.80385i | 0.217460i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 26.6603 | 1.20439 | ||||||||
\(491\) | 0.588457 | 0.0265567 | 0.0132784 | − | 0.999912i | \(-0.495773\pi\) | ||||
0.0132784 | + | 0.999912i | \(0.495773\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.5885 | −0.702069 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − 2.53590i | − 0.113865i | ||||||||
\(497\) | −38.7846 | −1.73973 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(500\) | 12.1244i | 0.542218i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.39230i | 0.196038i | ||||||||
\(503\) | 18.5885 | 0.828818 | 0.414409 | − | 0.910091i | \(-0.363988\pi\) | ||||
0.414409 | + | 0.910091i | \(0.363988\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.41154i | 0.107312i | ||||||||
\(506\) | −10.3923 | −0.461994 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.00000 | −0.177471 | ||||||||
\(509\) | 9.33975i | 0.413977i | 0.978343 | + | 0.206988i | \(0.0663663\pi\) | ||||
−0.978343 | + | 0.206988i | \(0.933634\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 57.3731 | 2.53804 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 12.8038i | − 0.564754i | ||||||||
\(515\) | − 7.26795i | − 0.320264i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.00000 | 0.263880 | ||||||||
\(518\) | 14.1962i | 0.623743i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.8038 | 0.823812 | 0.411906 | − | 0.911226i | \(-0.364863\pi\) | ||||
0.411906 | + | 0.911226i | \(0.364863\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.41154 | 0.0617225 | 0.0308612 | − | 0.999524i | \(-0.490175\pi\) | ||||
0.0308612 | + | 0.999524i | \(0.490175\pi\) | |||||||
\(524\) | 16.3923 | 0.716101 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − 2.19615i | − 0.0957568i | ||||||||
\(527\) | 13.1769i | 0.573995i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.1769 | −0.790301 | ||||||||
\(530\) | 5.19615 | 0.225706 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.00000 | −0.260133 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.1962i | 0.613753i | ||||||||
\(536\) | 10.7321 | 0.463554 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 28.3923i | − 1.22408i | ||||||||
\(539\) | 72.8372i | 3.13732i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.8564i | 0.724714i | 0.932039 | + | 0.362357i | \(0.118028\pi\) | ||||
−0.932039 | + | 0.362357i | \(0.881972\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.19615i | 0.222783i | ||||||||
\(545\) | −28.3923 | −1.21619 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.19615 | −0.264928 | −0.132464 | − | 0.991188i | \(-0.542289\pi\) | ||||
−0.132464 | + | 0.991188i | \(0.542289\pi\) | |||||||
\(548\) | − 9.00000i | − 0.384461i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −9.46410 | −0.403551 | ||||||||
\(551\) | − 3.80385i | − 0.162049i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 58.6410i | − 2.49367i | ||||||||
\(554\) | 15.1962i | 0.645623i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.00000 | 0.169638 | ||||||||
\(557\) | − 22.2679i | − 0.943523i | −0.881726 | − | 0.471762i | \(-0.843618\pi\) | ||||
0.881726 | − | 0.471762i | \(-0.156382\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 8.19615 | 0.346351 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −24.4641 | −1.03196 | ||||||||
\(563\) | 8.78461 | 0.370227 | 0.185114 | − | 0.982717i | \(-0.440735\pi\) | ||||
0.185114 | + | 0.982717i | \(0.440735\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.3923i | 0.815840i | ||||||||
\(566\) | − 30.1962i | − 1.26924i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.19615 | −0.343903 | ||||||||
\(569\) | −32.7846 | −1.37440 | −0.687201 | − | 0.726467i | \(-0.741161\pi\) | ||||
−0.687201 | + | 0.726467i | \(0.741161\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.8038 | 0.577673 | 0.288837 | − | 0.957378i | \(-0.406732\pi\) | ||||
0.288837 | + | 0.957378i | \(0.406732\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − 2.19615i | − 0.0916656i | ||||||||
\(575\) | 4.39230 | 0.183172 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.2679i | 0.677244i | 0.940923 | + | 0.338622i | \(0.109961\pi\) | ||||
−0.940923 | + | 0.338622i | \(0.890039\pi\) | |||||||
\(578\) | − 10.0000i | − 0.415945i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.19615i | 0.215758i | ||||||||
\(581\) | 55.1769 | 2.28912 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.1962i | 0.587945i | ||||||||
\(584\) | 12.1244 | 0.501709 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.6603 | 0.605610 | ||||||||
\(587\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.21539 | −0.132488 | ||||||||
\(590\) | 24.0000i | 0.988064i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.00000i | 0.123299i | ||||||||
\(593\) | 46.8564i | 1.92416i | 0.272764 | + | 0.962081i | \(0.412062\pi\) | ||||
−0.272764 | + | 0.962081i | \(0.587938\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −42.5885 | −1.74596 | ||||||||
\(596\) | 18.1244i | 0.742403i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.39230 | 0.179465 | 0.0897324 | − | 0.995966i | \(-0.471399\pi\) | ||||
0.0897324 | + | 0.995966i | \(0.471399\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.7846 | 0.888613 | 0.444306 | − | 0.895875i | \(-0.353450\pi\) | ||||
0.444306 | + | 0.895875i | \(0.353450\pi\) | |||||||
\(602\) | −29.3205 | −1.19501 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − 7.26795i | − 0.295729i | ||||||||
\(605\) | 19.7321i | 0.802222i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −48.7846 | −1.98011 | −0.990053 | − | 0.140694i | \(-0.955067\pi\) | ||||
−0.990053 | + | 0.140694i | \(0.955067\pi\) | |||||||
\(608\) | −1.26795 | −0.0514221 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.32051 | −0.336888 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 40.8564i | 1.65017i | 0.565005 | + | 0.825087i | \(0.308874\pi\) | ||||
−0.565005 | + | 0.825087i | \(0.691126\pi\) | |||||||
\(614\) | 10.7321 | 0.433110 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 22.3923i | 0.902212i | ||||||||
\(617\) | 10.6077i | 0.427050i | 0.976938 | + | 0.213525i | \(0.0684944\pi\) | ||||
−0.976938 | + | 0.213525i | \(0.931506\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 7.60770i | − 0.305779i | −0.988243 | − | 0.152890i | \(-0.951142\pi\) | ||||
0.988243 | − | 0.152890i | \(-0.0488579\pi\) | |||||||
\(620\) | 4.39230 | 0.176399 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 2.19615i | − 0.0880577i | ||||||||
\(623\) | 12.0000 | 0.480770 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 24.3923i | 0.974913i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.19615 | 0.127540 | ||||||||
\(629\) | − 15.5885i | − 0.621552i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.8564i | 1.02933i | 0.857392 | + | 0.514664i | \(0.172083\pi\) | ||||
−0.857392 | + | 0.514664i | \(0.827917\pi\) | |||||||
\(632\) | − 12.3923i | − 0.492939i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.12436 | 0.243229 | ||||||||
\(635\) | − 6.92820i | − 0.274937i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −14.1962 | −0.562031 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.73205 | 0.0684653 | ||||||||
\(641\) | −30.8038 | −1.21668 | −0.608339 | − | 0.793677i | \(-0.708164\pi\) | ||||
−0.608339 | + | 0.793677i | \(0.708164\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.7128i | 1.09289i | 0.837496 | + | 0.546443i | \(0.184019\pi\) | ||||
−0.837496 | + | 0.546443i | \(0.815981\pi\) | |||||||
\(644\) | − 10.3923i | − 0.409514i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.58846 | 0.259219 | ||||||||
\(647\) | 13.1769 | 0.518038 | 0.259019 | − | 0.965872i | \(-0.416601\pi\) | ||||
0.259019 | + | 0.965872i | \(0.416601\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −65.5692 | −2.57382 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 9.46410i | − 0.370643i | ||||||||
\(653\) | 49.1769 | 1.92444 | 0.962221 | − | 0.272271i | \(-0.0877746\pi\) | ||||
0.962221 | + | 0.272271i | \(0.0877746\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 28.3923i | 1.10938i | ||||||||
\(656\) | − 0.464102i | − 0.0181201i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.00000i | 0.233904i | ||||||||
\(659\) | −25.1769 | −0.980753 | −0.490377 | − | 0.871511i | \(-0.663141\pi\) | ||||
−0.490377 | + | 0.871511i | \(0.663141\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.00000i | 0.350059i | 0.984563 | + | 0.175030i | \(0.0560022\pi\) | ||||
−0.984563 | + | 0.175030i | \(0.943998\pi\) | |||||||
\(662\) | −12.0000 | −0.466393 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11.6603 | 0.452506 | ||||||||
\(665\) | − 10.3923i | − 0.402996i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.58846 | 0.255106 | ||||||||
\(668\) | − 2.53590i | − 0.0981169i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 18.5885i | 0.718135i | ||||||||
\(671\) | − 22.7321i | − 0.877561i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.00000 | −0.0385472 | −0.0192736 | − | 0.999814i | \(-0.506135\pi\) | ||||
−0.0192736 | + | 0.999814i | \(0.506135\pi\) | |||||||
\(674\) | − 31.0000i | − 1.19408i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.39230 | −0.168810 | −0.0844050 | − | 0.996432i | \(-0.526899\pi\) | ||||
−0.0844050 | + | 0.996432i | \(0.526899\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 28.3923 | 1.08960 | ||||||||
\(680\) | −9.00000 | −0.345134 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 12.0000i | 0.459504i | ||||||||
\(683\) | − 27.7128i | − 1.06040i | −0.847872 | − | 0.530201i | \(-0.822117\pi\) | ||||
0.847872 | − | 0.530201i | \(-0.177883\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.5885 | 0.595604 | ||||||||
\(686\) | −39.7128 | −1.51624 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.19615 | −0.236226 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.5167i | 0.742449i | 0.928543 | + | 0.371224i | \(0.121062\pi\) | ||||
−0.928543 | + | 0.371224i | \(0.878938\pi\) | |||||||
\(692\) | −16.3923 | −0.623142 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − 12.5885i | − 0.477851i | ||||||||
\(695\) | 6.92820i | 0.262802i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.41154i | 0.0913437i | ||||||||
\(698\) | 2.53590 | 0.0959852 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | − 9.46410i | − 0.357709i | ||||||||
\(701\) | 4.39230 | 0.165895 | 0.0829475 | − | 0.996554i | \(-0.473567\pi\) | ||||
0.0829475 | + | 0.996554i | \(0.473567\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.80385 | 0.143465 | ||||||||
\(704\) | 4.73205i | 0.178346i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.78461 | 0.217707 | ||||||||
\(707\) | − 6.58846i | − 0.247784i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.24871i | 0.122008i | 0.998138 | + | 0.0610040i | \(0.0194302\pi\) | ||||
−0.998138 | + | 0.0610040i | \(0.980570\pi\) | |||||||
\(710\) | − 14.1962i | − 0.532772i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.53590 | 0.0950368 | ||||||||
\(713\) | − 5.56922i | − 0.208569i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.19615 | 0.306305 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −22.0526 | −0.822994 | ||||||||
\(719\) | 52.3923 | 1.95390 | 0.976952 | − | 0.213461i | \(-0.0684736\pi\) | ||||
0.976952 | + | 0.213461i | \(0.0684736\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.8564i | 0.739491i | ||||||||
\(722\) | − 17.3923i | − 0.647275i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −11.5885 | −0.430682 | ||||||||
\(725\) | 6.00000 | 0.222834 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.1962 | 0.897386 | 0.448693 | − | 0.893686i | \(-0.351890\pi\) | ||||
0.448693 | + | 0.893686i | \(0.351890\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 21.0000i | 0.777245i | ||||||||
\(731\) | 32.1962 | 1.19082 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.3205i | 0.528940i | 0.964394 | + | 0.264470i | \(0.0851970\pi\) | ||||
−0.964394 | + | 0.264470i | \(0.914803\pi\) | |||||||
\(734\) | 24.1962i | 0.893096i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − 2.19615i | − 0.0809513i | ||||||||
\(737\) | −50.7846 | −1.87068 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 18.9282i | − 0.696285i | −0.937442 | − | 0.348143i | \(-0.886812\pi\) | ||||
0.937442 | − | 0.348143i | \(-0.113188\pi\) | |||||||
\(740\) | −5.19615 | −0.191014 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −14.1962 | −0.521157 | ||||||||
\(743\) | 4.39230i | 0.161138i | 0.996749 | + | 0.0805690i | \(0.0256737\pi\) | ||||
−0.996749 | + | 0.0805690i | \(0.974326\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −31.3923 | −1.15013 | ||||||||
\(746\) | − 23.9808i | − 0.877998i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 24.5885i | − 0.899043i | ||||||||
\(749\) | − 38.7846i | − 1.41716i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.9808 | 0.911561 | 0.455780 | − | 0.890092i | \(-0.349360\pi\) | ||||
0.455780 | + | 0.890092i | \(0.349360\pi\) | |||||||
\(752\) | 1.26795i | 0.0462373i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.5885 | 0.458141 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.7846 | 0.682738 | 0.341369 | − | 0.939929i | \(-0.389109\pi\) | ||||
0.341369 | + | 0.939929i | \(0.389109\pi\) | |||||||
\(758\) | 18.2487 | 0.662823 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | − 2.19615i | − 0.0796628i | ||||||||
\(761\) | 4.39230i | 0.159221i | 0.996826 | + | 0.0796105i | \(0.0253676\pi\) | ||||
−0.996826 | + | 0.0796105i | \(0.974632\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 77.5692 | 2.80819 | ||||||||
\(764\) | 20.7846 | 0.751961 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11.3205 | 0.409027 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 33.7128i | − 1.21572i | −0.794046 | − | 0.607858i | \(-0.792029\pi\) | ||||
0.794046 | − | 0.607858i | \(-0.207971\pi\) | |||||||
\(770\) | −38.7846 | −1.39770 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 12.8038i | 0.460821i | ||||||||
\(773\) | − 50.7846i | − 1.82660i | −0.407293 | − | 0.913298i | \(-0.633527\pi\) | ||||
0.407293 | − | 0.913298i | \(-0.366473\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 5.07180i | − 0.182184i | ||||||||
\(776\) | 6.00000 | 0.215387 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.3923i | 0.480137i | ||||||||
\(779\) | −0.588457 | −0.0210837 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 38.7846 | 1.38782 | ||||||||
\(782\) | 11.4115i | 0.408076i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −15.3923 | −0.549725 | ||||||||
\(785\) | 5.53590i | 0.197585i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 14.5359i | − 0.518149i | −0.965857 | − | 0.259074i | \(-0.916583\pi\) | ||||
0.965857 | − | 0.259074i | \(-0.0834175\pi\) | |||||||
\(788\) | − 6.92820i | − 0.246807i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 21.4641 | 0.763658 | ||||||||
\(791\) | − 52.9808i | − 1.88378i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −16.3923 | −0.581741 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.58846 | 0.304410 | ||||||||
\(797\) | 6.00000 | 0.212531 | 0.106265 | − | 0.994338i | \(-0.466111\pi\) | ||||
0.106265 | + | 0.994338i | \(0.466111\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 6.58846i | − 0.233083i | ||||||||
\(800\) | − 2.00000i | − 0.0707107i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −21.0000 | −0.741536 | ||||||||
\(803\) | −57.3731 | −2.02465 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.0000 | 0.634417 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 1.39230i | − 0.0489811i | ||||||||
\(809\) | 47.1962 | 1.65933 | 0.829664 | − | 0.558263i | \(-0.188532\pi\) | ||||
0.829664 | + | 0.558263i | \(0.188532\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 4.39230i | − 0.154235i | −0.997022 | − | 0.0771173i | \(-0.975428\pi\) | ||||
0.997022 | − | 0.0771173i | \(-0.0245716\pi\) | |||||||
\(812\) | − 14.1962i | − 0.498187i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − 14.1962i | − 0.497575i | ||||||||
\(815\) | 16.3923 | 0.574197 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.85641i | 0.274861i | ||||||||
\(818\) | 3.33975 | 0.116771 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.803848 | 0.0280716 | ||||||||
\(821\) | − 40.6410i | − 1.41838i | −0.705017 | − | 0.709191i | \(-0.749061\pi\) | ||||
0.705017 | − | 0.709191i | \(-0.250939\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.0000 | 1.11545 | 0.557725 | − | 0.830026i | \(-0.311674\pi\) | ||||
0.557725 | + | 0.830026i | \(0.311674\pi\) | |||||||
\(824\) | 4.19615i | 0.146180i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | − 65.5692i | − 2.28144i | ||||||||
\(827\) | 32.1051i | 1.11640i | 0.829705 | + | 0.558202i | \(0.188509\pi\) | ||||
−0.829705 | + | 0.558202i | \(0.811491\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.9808 | 0.416109 | 0.208055 | − | 0.978117i | \(-0.433287\pi\) | ||||
0.208055 | + | 0.978117i | \(0.433287\pi\) | |||||||
\(830\) | 20.1962i | 0.701019i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 79.9808 | 2.77117 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.39230 | 0.152002 | ||||||||
\(836\) | 6.00000 | 0.207514 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 16.3923i | 0.566263i | ||||||||
\(839\) | 12.0000i | 0.414286i | 0.978311 | + | 0.207143i | \(0.0664165\pi\) | ||||
−0.978311 | + | 0.207143i | \(0.933583\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | −0.464102 | −0.0159940 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.60770 | 0.124182 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 53.9090i | − 1.85233i | ||||||||
\(848\) | −3.00000 | −0.103020 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 10.3923i | 0.356453i | ||||||||
\(851\) | 6.58846i | 0.225849i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.00000i | 0.308154i | 0.988059 | + | 0.154077i | \(0.0492404\pi\) | ||||
−0.988059 | + | 0.154077i | \(0.950760\pi\) | |||||||
\(854\) | 22.7321 | 0.777875 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − 8.19615i | − 0.280139i | ||||||||
\(857\) | −54.3731 | −1.85735 | −0.928674 | − | 0.370896i | \(-0.879051\pi\) | ||||
−0.928674 | + | 0.370896i | \(0.879051\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.5885 | 0.361273 | 0.180637 | − | 0.983550i | \(-0.442184\pi\) | ||||
0.180637 | + | 0.983550i | \(0.442184\pi\) | |||||||
\(860\) | − 10.7321i | − 0.365960i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27.8038 | 0.947003 | ||||||||
\(863\) | 4.48334i | 0.152615i | 0.997084 | + | 0.0763073i | \(0.0243130\pi\) | ||||
−0.997084 | + | 0.0763073i | \(0.975687\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − 28.3923i | − 0.965367i | ||||||||
\(866\) | − 33.7846i | − 1.14805i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −12.0000 | −0.407307 | ||||||||
\(869\) | 58.6410i | 1.98926i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 16.3923 | 0.555113 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.78461 | −0.0941908 | ||||||||
\(875\) | 57.3731 | 1.93956 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 43.3923i | − 1.46525i | −0.680630 | − | 0.732627i | \(-0.738294\pi\) | ||||
0.680630 | − | 0.732627i | \(-0.261706\pi\) | |||||||
\(878\) | 16.5885i | 0.559833i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8.19615 | −0.276292 | ||||||||
\(881\) | 37.9808 | 1.27960 | 0.639802 | − | 0.768540i | \(-0.279016\pi\) | ||||
0.639802 | + | 0.768540i | \(0.279016\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.7846 | 0.834069 | 0.417034 | − | 0.908891i | \(-0.363070\pi\) | ||||
0.417034 | + | 0.908891i | \(0.363070\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − 4.39230i | − 0.147562i | ||||||||
\(887\) | −48.0000 | −1.61168 | −0.805841 | − | 0.592132i | \(-0.798286\pi\) | ||||
−0.805841 | + | 0.592132i | \(0.798286\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.9282i | 0.634832i | ||||||||
\(890\) | 4.39230i | 0.147230i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 18.9282i | − 0.633763i | ||||||||
\(893\) | 1.60770 | 0.0537995 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.1962i | 0.474525i | ||||||||
\(896\) | −4.73205 | −0.158087 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −33.4641 | −1.11671 | ||||||||
\(899\) | − 7.60770i | − 0.253731i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.5885 | 0.519327 | ||||||||
\(902\) | 2.19615i | 0.0731239i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − 11.1962i | − 0.372378i | ||||||||
\(905\) | − 20.0718i | − 0.667209i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41.1769 | 1.36726 | 0.683629 | − | 0.729830i | \(-0.260401\pi\) | ||||
0.683629 | + | 0.729830i | \(0.260401\pi\) | |||||||
\(908\) | 9.80385i | 0.325352i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.1769 | −1.23173 | −0.615863 | − | 0.787853i | \(-0.711193\pi\) | ||||
−0.615863 | + | 0.787853i | \(0.711193\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −55.1769 | −1.82609 | ||||||||
\(914\) | −19.9808 | −0.660905 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − 19.8564i | − 0.656074i | ||||||||
\(917\) | − 77.5692i | − 2.56156i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.3923 | 1.06852 | 0.534262 | − | 0.845319i | \(-0.320590\pi\) | ||||
0.534262 | + | 0.845319i | \(0.320590\pi\) | |||||||
\(920\) | 3.80385 | 0.125409 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −19.9808 | −0.658031 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000i | 0.197279i | ||||||||
\(926\) | −26.1962 | −0.860859 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − 3.00000i | − 0.0984798i | ||||||||
\(929\) | − 34.6077i | − 1.13544i | −0.823221 | − | 0.567721i | \(-0.807825\pi\) | ||||
0.823221 | − | 0.567721i | \(-0.192175\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.5167i | 0.639633i | ||||||||
\(932\) | 18.0000 | 0.589610 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − 36.5885i | − 1.19721i | ||||||||
\(935\) | 42.5885 | 1.39279 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.39230 | 0.176159 | 0.0880795 | − | 0.996113i | \(-0.471927\pi\) | ||||
0.0880795 | + | 0.996113i | \(0.471927\pi\) | |||||||
\(938\) | − 50.7846i | − 1.65818i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.19615 | −0.0716306 | ||||||||
\(941\) | 2.78461i | 0.0907757i | 0.998969 | + | 0.0453878i | \(0.0144524\pi\) | ||||
−0.998969 | + | 0.0453878i | \(0.985548\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1.01924i | − 0.0331910i | ||||||||
\(944\) | − 13.8564i | − 0.450988i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 29.3205 | 0.953292 | ||||||||
\(947\) | 42.9282i | 1.39498i | 0.716595 | + | 0.697490i | \(0.245700\pi\) | ||||
−0.716595 | + | 0.697490i | \(0.754300\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −2.53590 | −0.0822754 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 24.5885 | 0.796916 | ||||||||
\(953\) | −24.0000 | −0.777436 | −0.388718 | − | 0.921357i | \(-0.627082\pi\) | ||||
−0.388718 | + | 0.921357i | \(0.627082\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 36.0000i | 1.16493i | ||||||||
\(956\) | 24.5885i | 0.795248i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 35.3205 | 1.14115 | ||||||||
\(959\) | −42.5885 | −1.37525 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.5692 | 0.792555 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − 0.803848i | − 0.0258902i | ||||||||
\(965\) | −22.1769 | −0.713900 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.8756i | 0.478368i | 0.970974 | + | 0.239184i | \(0.0768800\pi\) | ||||
−0.970974 | + | 0.239184i | \(0.923120\pi\) | |||||||
\(968\) | − 11.3923i | − 0.366163i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10.3923i | 0.333677i | ||||||||
\(971\) | 13.1769 | 0.422867 | 0.211434 | − | 0.977392i | \(-0.432187\pi\) | ||||
0.211434 | + | 0.977392i | \(0.432187\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 18.9282i | − 0.606810i | ||||||||
\(974\) | −9.12436 | −0.292363 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.80385 | 0.153767 | ||||||||
\(977\) | − 16.8564i | − 0.539284i | −0.962961 | − | 0.269642i | \(-0.913095\pi\) | ||||
0.962961 | − | 0.269642i | \(-0.0869054\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.0000 | −0.383522 | ||||||||
\(980\) | − 26.6603i | − 0.851631i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 0.588457i | − 0.0187784i | ||||||||
\(983\) | 20.7846i | 0.662926i | 0.943468 | + | 0.331463i | \(0.107542\pi\) | ||||
−0.943468 | + | 0.331463i | \(0.892458\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.0000 | 0.382352 | ||||||||
\(986\) | 15.5885i | 0.496438i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.6077 | −0.432700 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.3731 | 0.933066 | 0.466533 | − | 0.884504i | \(-0.345503\pi\) | ||||
0.466533 | + | 0.884504i | \(0.345503\pi\) | |||||||
\(992\) | −2.53590 | −0.0805149 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 38.7846i | 1.23017i | ||||||||
\(995\) | 14.8756i | 0.471590i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.1962 | 0.417926 | 0.208963 | − | 0.977924i | \(-0.432991\pi\) | ||||
0.208963 | + | 0.977924i | \(0.432991\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))