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 | 1351.3 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3042.1351 |
Dual form | 3042.2.b.l.1351.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3042\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 | ||||||||
\(7\) | − 1.26795i | − 0.479240i | −0.970867 | − | 0.239620i | \(-0.922977\pi\) | ||||
0.970867 | − | 0.239620i | \(-0.0770228\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.73205 | 0.547723 | ||||||||
\(11\) | 1.26795i | 0.382301i | 0.981561 | + | 0.191151i | \(0.0612219\pi\) | ||||
−0.981561 | + | 0.191151i | \(0.938778\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.26795 | 0.338874 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.19615 | 1.26025 | 0.630126 | − | 0.776493i | \(-0.283003\pi\) | ||||
0.630126 | + | 0.776493i | \(0.283003\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.73205i | 1.08561i | 0.839860 | + | 0.542803i | \(0.182637\pi\) | ||||
−0.839860 | + | 0.542803i | \(0.817363\pi\) | |||||||
\(20\) | 1.73205i | 0.387298i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.26795 | −0.270328 | ||||||||
\(23\) | −8.19615 | −1.70902 | −0.854508 | − | 0.519438i | \(-0.826141\pi\) | ||||
−0.854508 | + | 0.519438i | \(0.826141\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | 0.400000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.26795i | 0.239620i | ||||||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.46410i | 1.69980i | 0.526942 | + | 0.849901i | \(0.323339\pi\) | ||||
−0.526942 | + | 0.849901i | \(0.676661\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.19615i | 0.891133i | ||||||||
\(35\) | −2.19615 | −0.371218 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 3.00000i | − 0.493197i | −0.969118 | − | 0.246598i | \(-0.920687\pi\) | ||||
0.969118 | − | 0.246598i | \(-0.0793129\pi\) | |||||||
\(38\) | −4.73205 | −0.767640 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.73205 | −0.273861 | ||||||||
\(41\) | − 6.46410i | − 1.00952i | −0.863259 | − | 0.504762i | \(-0.831580\pi\) | ||||
0.863259 | − | 0.504762i | \(-0.168420\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.19615 | 0.639907 | 0.319954 | − | 0.947433i | \(-0.396333\pi\) | ||||
0.319954 | + | 0.947433i | \(0.396333\pi\) | |||||||
\(44\) | − 1.26795i | − 0.191151i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − 8.19615i | − 1.20846i | ||||||||
\(47\) | − 4.73205i | − 0.690241i | −0.938558 | − | 0.345120i | \(-0.887838\pi\) | ||||
0.938558 | − | 0.345120i | \(-0.112162\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.39230 | 0.770329 | ||||||||
\(50\) | 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 | ||||||||
\(55\) | 2.19615 | 0.296129 | ||||||||
\(56\) | −1.26795 | −0.169437 | ||||||||
\(57\) | 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 | ||||||||
\(61\) | 15.1962 | 1.94567 | 0.972834 | − | 0.231504i | \(-0.0743646\pi\) | ||||
0.972834 | + | 0.231504i | \(0.0743646\pi\) | |||||||
\(62\) | −9.46410 | −1.20194 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.26795i | 0.887921i | 0.896046 | + | 0.443961i | \(0.146427\pi\) | ||||
−0.896046 | + | 0.443961i | \(0.853573\pi\) | |||||||
\(68\) | −5.19615 | −0.630126 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − 2.19615i | − 0.262490i | ||||||||
\(71\) | 2.19615i | 0.260635i | 0.991472 | + | 0.130318i | \(0.0415997\pi\) | ||||
−0.991472 | + | 0.130318i | \(0.958400\pi\) | |||||||
\(72\) | 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 | ||||||||
\(76\) | − 4.73205i | − 0.542803i | ||||||||
\(77\) | 1.60770 | 0.183214 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.39230 | 0.944208 | 0.472104 | − | 0.881543i | \(-0.343495\pi\) | ||||
0.472104 | + | 0.881543i | \(0.343495\pi\) | |||||||
\(80\) | − 1.73205i | − 0.193649i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.46410 | 0.713841 | ||||||||
\(83\) | − 5.66025i | − 0.621294i | −0.950525 | − | 0.310647i | \(-0.899454\pi\) | ||||
0.950525 | − | 0.310647i | \(-0.100546\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 9.00000i | − 0.976187i | ||||||||
\(86\) | 4.19615i | 0.452483i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.26795 | 0.135164 | ||||||||
\(89\) | 9.46410i | 1.00319i | 0.865102 | + | 0.501596i | \(0.167254\pi\) | ||||
−0.865102 | + | 0.501596i | \(0.832746\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.19615 | 0.854508 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.73205 | 0.488074 | ||||||||
\(95\) | 8.19615 | 0.840907 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.00000i | 0.609208i | 0.952479 | + | 0.304604i | \(0.0985241\pi\) | ||||
−0.952479 | + | 0.304604i | \(0.901476\pi\) | |||||||
\(98\) | 5.39230i | 0.544705i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.00000 | −0.200000 | ||||||||
\(101\) | 19.3923 | 1.92961 | 0.964803 | − | 0.262973i | \(-0.0847030\pi\) | ||||
0.964803 | + | 0.262973i | \(0.0847030\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.19615 | −0.610525 | −0.305263 | − | 0.952268i | \(-0.598744\pi\) | ||||
−0.305263 | + | 0.952268i | \(0.598744\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − 3.00000i | − 0.291386i | ||||||||
\(107\) | 2.19615 | 0.212310 | 0.106155 | − | 0.994350i | \(-0.466146\pi\) | ||||
0.106155 | + | 0.994350i | \(0.466146\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 4.39230i | − 0.420707i | −0.977625 | − | 0.210353i | \(-0.932539\pi\) | ||||
0.977625 | − | 0.210353i | \(-0.0674614\pi\) | |||||||
\(110\) | 2.19615i | 0.209395i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 1.26795i | − 0.119810i | ||||||||
\(113\) | −0.803848 | −0.0756196 | −0.0378098 | − | 0.999285i | \(-0.512038\pi\) | ||||
−0.0378098 | + | 0.999285i | \(0.512038\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.1962i | 1.32380i | ||||||||
\(116\) | −3.00000 | −0.278543 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 13.8564 | 1.27559 | ||||||||
\(119\) | − 6.58846i | − 0.603963i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.39230 | 0.853846 | ||||||||
\(122\) | 15.1962i | 1.37579i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − 9.46410i | − 0.849901i | ||||||||
\(125\) | − 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 | ||||||||
\(131\) | 4.39230 | 0.383757 | 0.191879 | − | 0.981419i | \(-0.438542\pi\) | ||||
0.191879 | + | 0.981419i | \(0.438542\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.00000 | 0.520266 | ||||||||
\(134\) | −7.26795 | −0.627855 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − 5.19615i | − 0.445566i | ||||||||
\(137\) | − 9.00000i | − 0.768922i | −0.923141 | − | 0.384461i | \(-0.874387\pi\) | ||||
0.923141 | − | 0.384461i | \(-0.125613\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 2.19615 | 0.185609 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.19615 | −0.184297 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 5.19615i | − 0.431517i | ||||||||
\(146\) | 12.1244 | 1.00342 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.00000i | 0.246598i | ||||||||
\(149\) | − 6.12436i | − 0.501727i | −0.968023 | − | 0.250863i | \(-0.919286\pi\) | ||||
0.968023 | − | 0.250863i | \(-0.0807145\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 10.7321i | − 0.873362i | −0.899616 | − | 0.436681i | \(-0.856154\pi\) | ||||
0.899616 | − | 0.436681i | \(-0.143846\pi\) | |||||||
\(152\) | 4.73205 | 0.383820 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.60770i | 0.129552i | ||||||||
\(155\) | 16.3923 | 1.31666 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.19615 | 0.574315 | 0.287158 | − | 0.957883i | \(-0.407290\pi\) | ||||
0.287158 | + | 0.957883i | \(0.407290\pi\) | |||||||
\(158\) | 8.39230i | 0.667656i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.73205 | 0.136931 | ||||||||
\(161\) | 10.3923i | 0.819028i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 2.53590i | − 0.198627i | −0.995056 | − | 0.0993134i | \(-0.968335\pi\) | ||||
0.995056 | − | 0.0993134i | \(-0.0316646\pi\) | |||||||
\(164\) | 6.46410i | 0.504762i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.66025 | 0.439321 | ||||||||
\(167\) | − 9.46410i | − 0.732354i | −0.930545 | − | 0.366177i | \(-0.880666\pi\) | ||||
0.930545 | − | 0.366177i | \(-0.119334\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 9.00000 | 0.690268 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.19615 | −0.319954 | ||||||||
\(173\) | −4.39230 | −0.333941 | −0.166970 | − | 0.985962i | \(-0.553398\pi\) | ||||
−0.166970 | + | 0.985962i | \(0.553398\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 2.53590i | − 0.191696i | ||||||||
\(176\) | 1.26795i | 0.0955753i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −9.46410 | −0.709364 | ||||||||
\(179\) | 2.19615 | 0.164148 | 0.0820741 | − | 0.996626i | \(-0.473846\pi\) | ||||
0.0820741 | + | 0.996626i | \(0.473846\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.5885 | −1.45600 | −0.727999 | − | 0.685578i | \(-0.759550\pi\) | ||||
−0.727999 | + | 0.685578i | \(0.759550\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.19615i | 0.604228i | ||||||||
\(185\) | −5.19615 | −0.382029 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.58846i | 0.481796i | ||||||||
\(188\) | 4.73205i | 0.345120i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.19615i | 0.594611i | ||||||||
\(191\) | 20.7846 | 1.50392 | 0.751961 | − | 0.659208i | \(-0.229108\pi\) | ||||
0.751961 | + | 0.659208i | \(0.229108\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.1962i | 1.66970i | 0.550481 | + | 0.834848i | \(0.314444\pi\) | ||||
−0.550481 | + | 0.834848i | \(0.685556\pi\) | |||||||
\(194\) | −6.00000 | −0.430775 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.39230 | −0.385165 | ||||||||
\(197\) | 6.92820i | 0.493614i | 0.969065 | + | 0.246807i | \(0.0793814\pi\) | ||||
−0.969065 | + | 0.246807i | \(0.920619\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.5885 | 1.60125 | 0.800627 | − | 0.599164i | \(-0.204500\pi\) | ||||
0.800627 | + | 0.599164i | \(0.204500\pi\) | |||||||
\(200\) | − 2.00000i | − 0.141421i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 19.3923i | 1.36444i | ||||||||
\(203\) | − 3.80385i | − 0.266978i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.1962 | −0.781973 | ||||||||
\(206\) | − 6.19615i | − 0.431706i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.00000 | −0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.3923 | −1.67924 | −0.839618 | − | 0.543178i | \(-0.817221\pi\) | ||||
−0.839618 | + | 0.543178i | \(0.817221\pi\) | |||||||
\(212\) | 3.00000 | 0.206041 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.19615i | 0.150126i | ||||||||
\(215\) | − 7.26795i | − 0.495670i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.0000 | 0.814613 | ||||||||
\(218\) | 4.39230 | 0.297484 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.19615 | −0.148065 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 5.07180i | − 0.339633i | −0.985476 | − | 0.169816i | \(-0.945683\pi\) | ||||
0.985476 | − | 0.169816i | \(-0.0543174\pi\) | |||||||
\(224\) | 1.26795 | 0.0847184 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − 0.803848i | − 0.0534711i | ||||||||
\(227\) | 20.1962i | 1.34047i | 0.742151 | + | 0.670233i | \(0.233806\pi\) | ||||
−0.742151 | + | 0.670233i | \(0.766194\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.85641i | 0.519166i | 0.965721 | + | 0.259583i | \(0.0835851\pi\) | ||||
−0.965721 | + | 0.259583i | \(0.916415\pi\) | |||||||
\(230\) | −14.1962 | −0.936067 | ||||||||
\(231\) | 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 | ||||||||
\(235\) | −8.19615 | −0.534658 | ||||||||
\(236\) | 13.8564i | 0.901975i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.58846 | 0.427066 | ||||||||
\(239\) | − 6.58846i | − 0.426172i | −0.977033 | − | 0.213086i | \(-0.931649\pi\) | ||||
0.977033 | − | 0.213086i | \(-0.0683514\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 11.1962i | − 0.721208i | −0.932719 | − | 0.360604i | \(-0.882571\pi\) | ||||
0.932719 | − | 0.360604i | \(-0.117429\pi\) | |||||||
\(242\) | 9.39230i | 0.603760i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −15.1962 | −0.972834 | ||||||||
\(245\) | − 9.33975i | − 0.596694i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 9.46410 | 0.600971 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 12.1244 | 0.766812 | ||||||||
\(251\) | 16.3923 | 1.03467 | 0.517337 | − | 0.855782i | \(-0.326924\pi\) | ||||
0.517337 | + | 0.855782i | \(0.326924\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 10.3923i | − 0.653359i | ||||||||
\(254\) | 4.00000i | 0.250982i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 23.1962 | 1.44694 | 0.723468 | − | 0.690358i | \(-0.242547\pi\) | ||||
0.723468 | + | 0.690358i | \(0.242547\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.80385 | −0.236360 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.39230i | 0.271357i | ||||||||
\(263\) | −8.19615 | −0.505396 | −0.252698 | − | 0.967545i | \(-0.581318\pi\) | ||||
−0.252698 | + | 0.967545i | \(0.581318\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.19615i | 0.319197i | ||||||||
\(266\) | 6.00000i | 0.367884i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 7.26795i | − 0.443961i | ||||||||
\(269\) | 7.60770 | 0.463849 | 0.231925 | − | 0.972734i | \(-0.425498\pi\) | ||||
0.231925 | + | 0.972734i | \(0.425498\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 5.19615 | 0.315063 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.00000 | 0.543710 | ||||||||
\(275\) | 2.53590i | 0.152920i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.80385 | −0.288635 | −0.144318 | − | 0.989531i | \(-0.546099\pi\) | ||||
−0.144318 | + | 0.989531i | \(0.546099\pi\) | |||||||
\(278\) | − 4.00000i | − 0.239904i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.19615i | 0.131245i | ||||||||
\(281\) | 17.5359i | 1.04610i | 0.852301 | + | 0.523052i | \(0.175207\pi\) | ||||
−0.852301 | + | 0.523052i | \(0.824793\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.8038 | 1.17722 | 0.588608 | − | 0.808418i | \(-0.299676\pi\) | ||||
0.588608 | + | 0.808418i | \(0.299676\pi\) | |||||||
\(284\) | − 2.19615i | − 0.130318i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.19615 | −0.483804 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.0000 | 0.588235 | ||||||||
\(290\) | 5.19615 | 0.305129 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 12.1244i | 0.709524i | ||||||||
\(293\) | 2.66025i | 0.155414i | 0.996976 | + | 0.0777069i | \(0.0247598\pi\) | ||||
−0.996976 | + | 0.0777069i | \(0.975240\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24.0000 | −1.39733 | ||||||||
\(296\) | −3.00000 | −0.174371 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.12436 | 0.354774 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 5.32051i | − 0.306669i | ||||||||
\(302\) | 10.7321 | 0.617560 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.73205i | 0.271402i | ||||||||
\(305\) | − 26.3205i | − 1.50711i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 7.26795i | − 0.414804i | −0.978256 | − | 0.207402i | \(-0.933499\pi\) | ||||
0.978256 | − | 0.207402i | \(-0.0665008\pi\) | |||||||
\(308\) | −1.60770 | −0.0916069 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 16.3923i | 0.931020i | ||||||||
\(311\) | −8.19615 | −0.464761 | −0.232381 | − | 0.972625i | \(-0.574651\pi\) | ||||
−0.232381 | + | 0.972625i | \(0.574651\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.60770 | −0.203919 | −0.101959 | − | 0.994789i | \(-0.532511\pi\) | ||||
−0.101959 | + | 0.994789i | \(0.532511\pi\) | |||||||
\(314\) | 7.19615i | 0.406102i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.39230 | −0.472104 | ||||||||
\(317\) | 18.1244i | 1.01797i | 0.860777 | + | 0.508983i | \(0.169978\pi\) | ||||
−0.860777 | + | 0.508983i | \(0.830022\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.80385i | 0.212975i | ||||||||
\(320\) | 1.73205i | 0.0968246i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −10.3923 | −0.579141 | ||||||||
\(323\) | 24.5885i | 1.36814i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.53590 | 0.140450 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.46410 | −0.356920 | ||||||||
\(329\) | −6.00000 | −0.330791 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.0000i | 0.659580i | 0.944054 | + | 0.329790i | \(0.106978\pi\) | ||||
−0.944054 | + | 0.329790i | \(0.893022\pi\) | |||||||
\(332\) | 5.66025i | 0.310647i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.46410 | 0.517853 | ||||||||
\(335\) | 12.5885 | 0.687781 | ||||||||
\(336\) | 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 | ||||||||
\(343\) | − 15.7128i | − 0.848412i | ||||||||
\(344\) | − 4.19615i | − 0.226241i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 4.39230i | − 0.236132i | ||||||||
\(347\) | −18.5885 | −0.997881 | −0.498940 | − | 0.866636i | \(-0.666277\pi\) | ||||
−0.498940 | + | 0.866636i | \(0.666277\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 9.46410i | − 0.506602i | −0.967388 | − | 0.253301i | \(-0.918484\pi\) | ||||
0.967388 | − | 0.253301i | \(-0.0815163\pi\) | |||||||
\(350\) | 2.53590 | 0.135549 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.26795 | −0.0675819 | ||||||||
\(353\) | 35.7846i | 1.90462i | 0.305128 | + | 0.952311i | \(0.401301\pi\) | ||||
−0.305128 | + | 0.952311i | \(0.598699\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.80385 | 0.201887 | ||||||||
\(356\) | − 9.46410i | − 0.501596i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.19615i | 0.116070i | ||||||||
\(359\) | − 16.0526i | − 0.847222i | −0.905844 | − | 0.423611i | \(-0.860762\pi\) | ||||
0.905844 | − | 0.423611i | \(-0.139238\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.39230 | −0.178542 | ||||||||
\(362\) | − 19.5885i | − 1.02955i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −21.0000 | −1.09919 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.8038 | −0.720555 | −0.360277 | − | 0.932845i | \(-0.617318\pi\) | ||||
−0.360277 | + | 0.932845i | \(0.617318\pi\) | |||||||
\(368\) | −8.19615 | −0.427254 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − 5.19615i | − 0.270135i | ||||||||
\(371\) | 3.80385i | 0.197486i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.9808 | −1.44879 | −0.724394 | − | 0.689386i | \(-0.757881\pi\) | ||||
−0.724394 | + | 0.689386i | \(0.757881\pi\) | |||||||
\(374\) | −6.58846 | −0.340681 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.73205 | −0.244037 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.2487i | 1.55377i | 0.629641 | + | 0.776886i | \(0.283202\pi\) | ||||
−0.629641 | + | 0.776886i | \(0.716798\pi\) | |||||||
\(380\) | −8.19615 | −0.420454 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 20.7846i | 1.06343i | ||||||||
\(383\) | 23.3205i | 1.19162i | 0.803125 | + | 0.595811i | \(0.203169\pi\) | ||||
−0.803125 | + | 0.595811i | \(0.796831\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − 2.78461i | − 0.141917i | ||||||||
\(386\) | −23.1962 | −1.18065 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 6.00000i | − 0.304604i | ||||||||
\(389\) | 7.39230 | 0.374805 | 0.187402 | − | 0.982283i | \(-0.439993\pi\) | ||||
0.187402 | + | 0.982283i | \(0.439993\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −42.5885 | −2.15379 | ||||||||
\(392\) | − 5.39230i | − 0.272353i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.92820 | −0.349038 | ||||||||
\(395\) | − 14.5359i | − 0.731380i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 4.39230i | − 0.220443i | −0.993907 | − | 0.110222i | \(-0.964844\pi\) | ||||
0.993907 | − | 0.110222i | \(-0.0351561\pi\) | |||||||
\(398\) | 22.5885i | 1.13226i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.00000 | 0.100000 | ||||||||
\(401\) | 21.0000i | 1.04869i | 0.851506 | + | 0.524345i | \(0.175690\pi\) | ||||
−0.851506 | + | 0.524345i | \(0.824310\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −19.3923 | −0.964803 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.80385 | 0.188782 | ||||||||
\(407\) | 3.80385 | 0.188550 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 20.6603i | − 1.02158i | −0.859704 | − | 0.510792i | \(-0.829352\pi\) | ||||
0.859704 | − | 0.510792i | \(-0.170648\pi\) | |||||||
\(410\) | − 11.1962i | − 0.552939i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.19615 | 0.305263 | ||||||||
\(413\) | −17.5692 | −0.864525 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.80385 | −0.481252 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 6.00000i | − 0.293470i | ||||||||
\(419\) | 4.39230 | 0.214578 | 0.107289 | − | 0.994228i | \(-0.465783\pi\) | ||||
0.107289 | + | 0.994228i | \(0.465783\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 6.46410i | − 0.315041i | −0.987516 | − | 0.157521i | \(-0.949650\pi\) | ||||
0.987516 | − | 0.157521i | \(-0.0503500\pi\) | |||||||
\(422\) | − 24.3923i | − 1.18740i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.00000i | 0.145693i | ||||||||
\(425\) | 10.3923 | 0.504101 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 19.2679i | − 0.932441i | ||||||||
\(428\) | −2.19615 | −0.106155 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.26795 | 0.350492 | ||||||||
\(431\) | − 38.1962i | − 1.83984i | −0.392101 | − | 0.919922i | \(-0.628252\pi\) | ||||
0.392101 | − | 0.919922i | \(-0.371748\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.78461 | −0.374104 | −0.187052 | − | 0.982350i | \(-0.559893\pi\) | ||||
−0.187052 | + | 0.982350i | \(0.559893\pi\) | |||||||
\(434\) | 12.0000i | 0.576018i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.39230i | 0.210353i | ||||||||
\(437\) | − 38.7846i | − 1.85532i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.5885 | 0.696269 | 0.348135 | − | 0.937445i | \(-0.386815\pi\) | ||||
0.348135 | + | 0.937445i | \(0.386815\pi\) | |||||||
\(440\) | − 2.19615i | − 0.104697i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.3923 | −0.778822 | −0.389411 | − | 0.921064i | \(-0.627321\pi\) | ||||
−0.389411 | + | 0.921064i | \(0.627321\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.3923 | 0.777070 | ||||||||
\(446\) | 5.07180 | 0.240157 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.26795i | 0.0599050i | ||||||||
\(449\) | 26.5359i | 1.25231i | 0.779700 | + | 0.626153i | \(0.215372\pi\) | ||||
−0.779700 | + | 0.626153i | \(0.784628\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.19615 | 0.385942 | ||||||||
\(452\) | 0.803848 | 0.0378098 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −20.1962 | −0.947852 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 31.9808i | − 1.49600i | −0.663700 | − | 0.747998i | \(-0.731015\pi\) | ||||
0.663700 | − | 0.747998i | \(-0.268985\pi\) | |||||||
\(458\) | −7.85641 | −0.367106 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − 14.1962i | − 0.661899i | ||||||||
\(461\) | − 31.9808i | − 1.48949i | −0.667348 | − | 0.744746i | \(-0.732570\pi\) | ||||
0.667348 | − | 0.744746i | \(-0.267430\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.8038i | 0.734467i | 0.930129 | + | 0.367234i | \(0.119695\pi\) | ||||
−0.930129 | + | 0.367234i | \(0.880305\pi\) | |||||||
\(464\) | 3.00000 | 0.139272 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − 18.0000i | − 0.833834i | ||||||||
\(467\) | 5.41154 | 0.250416 | 0.125208 | − | 0.992130i | \(-0.460040\pi\) | ||||
0.125208 | + | 0.992130i | \(0.460040\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.21539 | 0.425527 | ||||||||
\(470\) | − 8.19615i | − 0.378060i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −13.8564 | −0.637793 | ||||||||
\(473\) | 5.32051i | 0.244637i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.46410i | 0.434243i | ||||||||
\(476\) | 6.58846i | 0.301981i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.58846 | 0.301349 | ||||||||
\(479\) | − 0.679492i | − 0.0310468i | −0.999880 | − | 0.0155234i | \(-0.995059\pi\) | ||||
0.999880 | − | 0.0155234i | \(-0.00494145\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 11.1962 | 0.509971 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.39230 | −0.426923 | ||||||||
\(485\) | 10.3923 | 0.471890 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 15.1244i | − 0.685350i | −0.939454 | − | 0.342675i | \(-0.888667\pi\) | ||||
0.939454 | − | 0.342675i | \(-0.111333\pi\) | |||||||
\(488\) | − 15.1962i | − 0.687897i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 9.33975 | 0.421927 | ||||||||
\(491\) | −30.5885 | −1.38044 | −0.690219 | − | 0.723601i | \(-0.742486\pi\) | ||||
−0.690219 | + | 0.723601i | \(0.742486\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.5885 | 0.702069 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.46410i | 0.424951i | ||||||||
\(497\) | 2.78461 | 0.124907 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(500\) | 12.1244i | 0.542218i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 16.3923i | 0.731624i | ||||||||
\(503\) | −12.5885 | −0.561292 | −0.280646 | − | 0.959811i | \(-0.590549\pi\) | ||||
−0.280646 | + | 0.959811i | \(0.590549\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − 33.5885i | − 1.49467i | ||||||||
\(506\) | 10.3923 | 0.461994 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.00000 | −0.177471 | ||||||||
\(509\) | − 26.6603i | − 1.18169i | −0.806783 | − | 0.590847i | \(-0.798793\pi\) | ||||
0.806783 | − | 0.590847i | \(-0.201207\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.3731 | −0.680064 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 23.1962i | 1.02314i | ||||||||
\(515\) | 10.7321i | 0.472911i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.00000 | 0.263880 | ||||||||
\(518\) | − 3.80385i | − 0.167131i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.1962 | 1.27911 | 0.639553 | − | 0.768747i | \(-0.279119\pi\) | ||||
0.639553 | + | 0.768747i | \(0.279119\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.5885 | 1.42499 | 0.712497 | − | 0.701675i | \(-0.247564\pi\) | ||||
0.712497 | + | 0.701675i | \(0.247564\pi\) | |||||||
\(524\) | −4.39230 | −0.191879 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − 8.19615i | − 0.357369i | ||||||||
\(527\) | 49.1769i | 2.14218i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 44.1769 | 1.92074 | ||||||||
\(530\) | −5.19615 | −0.225706 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.00000 | −0.260133 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 3.80385i | − 0.164455i | ||||||||
\(536\) | 7.26795 | 0.313928 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7.60770i | 0.327991i | ||||||||
\(539\) | 6.83717i | 0.294498i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.8564i | 0.466753i | 0.972386 | + | 0.233377i | \(0.0749775\pi\) | ||||
−0.972386 | + | 0.233377i | \(0.925022\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.19615i | 0.222783i | ||||||||
\(545\) | −7.60770 | −0.325878 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.19615 | 0.179415 | 0.0897073 | − | 0.995968i | \(-0.471407\pi\) | ||||
0.0897073 | + | 0.995968i | \(0.471407\pi\) | |||||||
\(548\) | 9.00000i | 0.384461i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.53590 | −0.108131 | ||||||||
\(551\) | 14.1962i | 0.604776i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 10.6410i | − 0.452502i | ||||||||
\(554\) | − 4.80385i | − 0.204096i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.00000 | 0.169638 | ||||||||
\(557\) | 25.7321i | 1.09030i | 0.838338 | + | 0.545151i | \(0.183528\pi\) | ||||
−0.838338 | + | 0.545151i | \(0.816472\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2.19615 | −0.0928044 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −17.5359 | −0.739707 | ||||||||
\(563\) | −32.7846 | −1.38171 | −0.690853 | − | 0.722995i | \(-0.742765\pi\) | ||||
−0.690853 | + | 0.722995i | \(0.742765\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.39230i | 0.0585747i | ||||||||
\(566\) | 19.8038i | 0.832418i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.19615 | 0.0921485 | ||||||||
\(569\) | 8.78461 | 0.368270 | 0.184135 | − | 0.982901i | \(-0.441052\pi\) | ||||
0.184135 | + | 0.982901i | \(0.441052\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.1962 | 1.01258 | 0.506289 | − | 0.862364i | \(-0.331017\pi\) | ||||
0.506289 | + | 0.862364i | \(0.331017\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − 8.19615i | − 0.342101i | ||||||||
\(575\) | −16.3923 | −0.683606 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 19.7321i | − 0.821456i | −0.911758 | − | 0.410728i | \(-0.865275\pi\) | ||||
0.911758 | − | 0.410728i | \(-0.134725\pi\) | |||||||
\(578\) | 10.0000i | 0.415945i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.19615i | 0.215758i | ||||||||
\(581\) | −7.17691 | −0.297749 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 3.80385i | − 0.157539i | ||||||||
\(584\) | −12.1244 | −0.501709 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.66025 | −0.109894 | ||||||||
\(587\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −44.7846 | −1.84532 | ||||||||
\(590\) | − 24.0000i | − 0.988064i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 3.00000i | − 0.123299i | ||||||||
\(593\) | − 19.1436i | − 0.786133i | −0.919510 | − | 0.393067i | \(-0.871414\pi\) | ||||
0.919510 | − | 0.393067i | \(-0.128586\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.4115 | −0.467828 | ||||||||
\(596\) | 6.12436i | 0.250863i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.3923 | −0.669771 | −0.334886 | − | 0.942259i | \(-0.608698\pi\) | ||||
−0.334886 | + | 0.942259i | \(0.608698\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.7846 | −0.807031 | −0.403516 | − | 0.914973i | \(-0.632212\pi\) | ||||
−0.403516 | + | 0.914973i | \(0.632212\pi\) | |||||||
\(602\) | 5.32051 | 0.216848 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.7321i | 0.436681i | ||||||||
\(605\) | − 16.2679i | − 0.661386i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.21539 | −0.292864 | −0.146432 | − | 0.989221i | \(-0.546779\pi\) | ||||
−0.146432 | + | 0.989221i | \(0.546779\pi\) | |||||||
\(608\) | −4.73205 | −0.191910 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 26.3205 | 1.06569 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 13.1436i | − 0.530865i | −0.964129 | − | 0.265432i | \(-0.914485\pi\) | ||||
0.964129 | − | 0.265432i | \(-0.0855147\pi\) | |||||||
\(614\) | 7.26795 | 0.293311 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − 1.60770i | − 0.0647759i | ||||||||
\(617\) | − 31.3923i | − 1.26381i | −0.775047 | − | 0.631903i | \(-0.782274\pi\) | ||||
0.775047 | − | 0.631903i | \(-0.217726\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.3923i | 1.14118i | 0.821234 | + | 0.570592i | \(0.193286\pi\) | ||||
−0.821234 | + | 0.570592i | \(0.806714\pi\) | |||||||
\(620\) | −16.3923 | −0.658331 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 8.19615i | − 0.328636i | ||||||||
\(623\) | 12.0000 | 0.480770 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | − 3.60770i | − 0.144192i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.19615 | −0.287158 | ||||||||
\(629\) | − 15.5885i | − 0.621552i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.85641i | 0.0739024i | 0.999317 | + | 0.0369512i | \(0.0117646\pi\) | ||||
−0.999317 | + | 0.0369512i | \(0.988235\pi\) | |||||||
\(632\) | − 8.39230i | − 0.333828i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −18.1244 | −0.719810 | ||||||||
\(635\) | − 6.92820i | − 0.274937i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −3.80385 | −0.150596 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.73205 | −0.0684653 | ||||||||
\(641\) | −41.1962 | −1.62715 | −0.813575 | − | 0.581460i | \(-0.802482\pi\) | ||||
−0.813575 | + | 0.581460i | \(0.802482\pi\) | |||||||
\(642\) | 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 | ||||||||
\(646\) | −24.5885 | −0.967420 | ||||||||
\(647\) | −49.1769 | −1.93334 | −0.966672 | − | 0.256018i | \(-0.917589\pi\) | ||||
−0.966672 | + | 0.256018i | \(0.917589\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.5692 | 0.689652 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.53590i | 0.0993134i | ||||||||
\(653\) | −13.1769 | −0.515653 | −0.257826 | − | 0.966191i | \(-0.583006\pi\) | ||||
−0.257826 | + | 0.966191i | \(0.583006\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 7.60770i | − 0.297257i | ||||||||
\(656\) | − 6.46410i | − 0.252381i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − 6.00000i | − 0.233904i | ||||||||
\(659\) | 37.1769 | 1.44821 | 0.724103 | − | 0.689691i | \(-0.242254\pi\) | ||||
0.724103 | + | 0.689691i | \(0.242254\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 9.00000i | − 0.350059i | −0.984563 | − | 0.175030i | \(-0.943998\pi\) | ||||
0.984563 | − | 0.175030i | \(-0.0560022\pi\) | |||||||
\(662\) | −12.0000 | −0.466393 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.66025 | −0.219660 | ||||||||
\(665\) | − 10.3923i | − 0.402996i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.5885 | −0.952069 | ||||||||
\(668\) | 9.46410i | 0.366177i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 12.5885i | 0.486335i | ||||||||
\(671\) | 19.2679i | 0.743831i | ||||||||
\(672\) | 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 | ||||||||
\(677\) | 16.3923 | 0.630007 | 0.315004 | − | 0.949090i | \(-0.397994\pi\) | ||||
0.315004 | + | 0.949090i | \(0.397994\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.60770 | 0.291957 | ||||||||
\(680\) | −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 | ||||||||
\(686\) | 15.7128 | 0.599918 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.19615 | 0.159977 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.5167i | 0.970700i | 0.874320 | + | 0.485350i | \(0.161308\pi\) | ||||
−0.874320 | + | 0.485350i | \(0.838692\pi\) | |||||||
\(692\) | 4.39230 | 0.166970 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − 18.5885i | − 0.705608i | ||||||||
\(695\) | 6.92820i | 0.262802i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 33.5885i | − 1.27225i | ||||||||
\(698\) | 9.46410 | 0.358222 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.53590i | 0.0958479i | ||||||||
\(701\) | −16.3923 | −0.619129 | −0.309564 | − | 0.950878i | \(-0.600183\pi\) | ||||
−0.309564 | + | 0.950878i | \(0.600183\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.1962 | 0.535418 | ||||||||
\(704\) | − 1.26795i | − 0.0477876i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −35.7846 | −1.34677 | ||||||||
\(707\) | − 24.5885i | − 0.924744i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 45.2487i | 1.69935i | 0.527306 | + | 0.849676i | \(0.323202\pi\) | ||||
−0.527306 | + | 0.849676i | \(0.676798\pi\) | |||||||
\(710\) | 3.80385i | 0.142756i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.46410 | 0.354682 | ||||||||
\(713\) | − 77.5692i | − 2.90499i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.19615 | −0.0820741 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 16.0526 | 0.599076 | ||||||||
\(719\) | 31.6077 | 1.17877 | 0.589384 | − | 0.807853i | \(-0.299370\pi\) | ||||
0.589384 | + | 0.807853i | \(0.299370\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.85641i | 0.292588i | ||||||||
\(722\) | − 3.39230i | − 0.126249i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 19.5885 | 0.727999 | ||||||||
\(725\) | 6.00000 | 0.222834 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.8038 | 0.511956 | 0.255978 | − | 0.966683i | \(-0.417602\pi\) | ||||
0.255978 | + | 0.966683i | \(0.417602\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | − 21.0000i | − 0.777245i | ||||||||
\(731\) | 21.8038 | 0.806444 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.3205i | 0.750555i | 0.926912 | + | 0.375278i | \(0.122453\pi\) | ||||
−0.926912 | + | 0.375278i | \(0.877547\pi\) | |||||||
\(734\) | − 13.8038i | − 0.509509i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − 8.19615i | − 0.302114i | ||||||||
\(737\) | −9.21539 | −0.339453 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.07180i | 0.186569i | 0.995639 | + | 0.0932845i | \(0.0297366\pi\) | ||||
−0.995639 | + | 0.0932845i | \(0.970263\pi\) | |||||||
\(740\) | 5.19615 | 0.191014 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.80385 | −0.139644 | ||||||||
\(743\) | 16.3923i | 0.601375i | 0.953723 | + | 0.300688i | \(0.0972162\pi\) | ||||
−0.953723 | + | 0.300688i | \(0.902784\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.6077 | −0.388636 | ||||||||
\(746\) | − 27.9808i | − 1.02445i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 6.58846i | − 0.240898i | ||||||||
\(749\) | − 2.78461i | − 0.101747i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.9808 | −0.984542 | −0.492271 | − | 0.870442i | \(-0.663833\pi\) | ||||
−0.492271 | + | 0.870442i | \(0.663833\pi\) | |||||||
\(752\) | − 4.73205i | − 0.172560i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −18.5885 | −0.676503 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.7846 | −0.828121 | −0.414060 | − | 0.910249i | \(-0.635890\pi\) | ||||
−0.414060 | + | 0.910249i | \(0.635890\pi\) | |||||||
\(758\) | −30.2487 | −1.09868 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | − 8.19615i | − 0.297306i | ||||||||
\(761\) | 16.3923i | 0.594221i | 0.954843 | + | 0.297110i | \(0.0960229\pi\) | ||||
−0.954843 | + | 0.297110i | \(0.903977\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.56922 | −0.201619 | ||||||||
\(764\) | −20.7846 | −0.751961 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −23.3205 | −0.842604 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 21.7128i | − 0.782984i | −0.920181 | − | 0.391492i | \(-0.871959\pi\) | ||||
0.920181 | − | 0.391492i | \(-0.128041\pi\) | |||||||
\(770\) | 2.78461 | 0.100350 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 23.1962i | − 0.834848i | ||||||||
\(773\) | 9.21539i | 0.331455i | 0.986172 | + | 0.165727i | \(0.0529971\pi\) | ||||
−0.986172 | + | 0.165727i | \(0.947003\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18.9282i | 0.679921i | ||||||||
\(776\) | 6.00000 | 0.215387 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.39230i | 0.265027i | ||||||||
\(779\) | 30.5885 | 1.09595 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.78461 | −0.0996412 | ||||||||
\(782\) | − 42.5885i | − 1.52296i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.39230 | 0.192582 | ||||||||
\(785\) | − 12.4641i | − 0.444863i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.4641i | 0.765113i | 0.923932 | + | 0.382556i | \(0.124956\pi\) | ||||
−0.923932 | + | 0.382556i | \(0.875044\pi\) | |||||||
\(788\) | − 6.92820i | − 0.246807i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 14.5359 | 0.517164 | ||||||||
\(791\) | 1.01924i | 0.0362399i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 4.39230 | 0.155877 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −22.5885 | −0.800627 | ||||||||
\(797\) | 6.00000 | 0.212531 | 0.106265 | − | 0.994338i | \(-0.466111\pi\) | ||||
0.106265 | + | 0.994338i | \(0.466111\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 24.5885i | − 0.869877i | ||||||||
\(800\) | 2.00000i | 0.0707107i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −21.0000 | −0.741536 | ||||||||
\(803\) | 15.3731 | 0.542504 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.0000 | 0.634417 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 19.3923i | − 0.682219i | ||||||||
\(809\) | 36.8038 | 1.29395 | 0.646977 | − | 0.762509i | \(-0.276033\pi\) | ||||
0.646977 | + | 0.762509i | \(0.276033\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 16.3923i | − 0.575612i | −0.957689 | − | 0.287806i | \(-0.907074\pi\) | ||||
0.957689 | − | 0.287806i | \(-0.0929258\pi\) | |||||||
\(812\) | 3.80385i | 0.133489i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.80385i | 0.133325i | ||||||||
\(815\) | −4.39230 | −0.153856 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.8564i | 0.694688i | ||||||||
\(818\) | 20.6603 | 0.722369 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 11.1962 | 0.390987 | ||||||||
\(821\) | − 28.6410i | − 0.999578i | −0.866147 | − | 0.499789i | \(-0.833411\pi\) | ||||
0.866147 | − | 0.499789i | \(-0.166589\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.0000 | 1.11545 | 0.557725 | − | 0.830026i | \(-0.311674\pi\) | ||||
0.557725 | + | 0.830026i | \(0.311674\pi\) | |||||||
\(824\) | 6.19615i | 0.215853i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | − 17.5692i | − 0.611311i | ||||||||
\(827\) | 44.1051i | 1.53369i | 0.641835 | + | 0.766843i | \(0.278173\pi\) | ||||
−0.641835 | + | 0.766843i | \(0.721827\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −39.9808 | −1.38859 | −0.694295 | − | 0.719691i | \(-0.744284\pi\) | ||||
−0.694295 | + | 0.719691i | \(0.744284\pi\) | |||||||
\(830\) | − 9.80385i | − 0.340297i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 28.0192 | 0.970809 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.3923 | −0.567279 | ||||||||
\(836\) | 6.00000 | 0.207514 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.39230i | 0.151730i | ||||||||
\(839\) | − 12.0000i | − 0.414286i | −0.978311 | − | 0.207143i | \(-0.933583\pi\) | ||||
0.978311 | − | 0.207143i | \(-0.0664165\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 6.46410 | 0.222768 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 24.3923 | 0.839618 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 11.9090i | − 0.409197i | ||||||||
\(848\) | −3.00000 | −0.103020 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 10.3923i | 0.356453i | ||||||||
\(851\) | 24.5885i | 0.842881i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 9.00000i | − 0.308154i | −0.988059 | − | 0.154077i | \(-0.950760\pi\) | ||||
0.988059 | − | 0.154077i | \(-0.0492404\pi\) | |||||||
\(854\) | 19.2679 | 0.659336 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − 2.19615i | − 0.0750629i | ||||||||
\(857\) | 18.3731 | 0.627612 | 0.313806 | − | 0.949487i | \(-0.398396\pi\) | ||||
0.313806 | + | 0.949487i | \(0.398396\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.5885 | −0.702469 | −0.351235 | − | 0.936288i | \(-0.614238\pi\) | ||||
−0.351235 | + | 0.936288i | \(0.614238\pi\) | |||||||
\(860\) | 7.26795i | 0.247835i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 38.1962 | 1.30097 | ||||||||
\(863\) | − 49.5167i | − 1.68557i | −0.538253 | − | 0.842783i | \(-0.680915\pi\) | ||||
0.538253 | − | 0.842783i | \(-0.319085\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.60770i | 0.258669i | ||||||||
\(866\) | − 7.78461i | − 0.264532i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −12.0000 | −0.407307 | ||||||||
\(869\) | 10.6410i | 0.360972i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −4.39230 | −0.148742 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 38.7846 | 1.31191 | ||||||||
\(875\) | −15.3731 | −0.519705 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.6077i | 0.763408i | 0.924285 | + | 0.381704i | \(0.124663\pi\) | ||||
−0.924285 | + | 0.381704i | \(0.875337\pi\) | |||||||
\(878\) | 14.5885i | 0.492337i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.19615 | 0.0740323 | ||||||||
\(881\) | −13.9808 | −0.471024 | −0.235512 | − | 0.971871i | \(-0.575677\pi\) | ||||
−0.235512 | + | 0.971871i | \(0.575677\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.7846 | −0.564847 | −0.282424 | − | 0.959290i | \(-0.591138\pi\) | ||||
−0.282424 | + | 0.959290i | \(0.591138\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − 16.3923i | − 0.550710i | ||||||||
\(887\) | −48.0000 | −1.61168 | −0.805841 | − | 0.592132i | \(-0.798286\pi\) | ||||
−0.805841 | + | 0.592132i | \(0.798286\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − 5.07180i | − 0.170103i | ||||||||
\(890\) | 16.3923i | 0.549471i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.07180i | 0.169816i | ||||||||
\(893\) | 22.3923 | 0.749330 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 3.80385i | − 0.127149i | ||||||||
\(896\) | −1.26795 | −0.0423592 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −26.5359 | −0.885514 | ||||||||
\(899\) | 28.3923i | 0.946936i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.5885 | −0.519327 | ||||||||
\(902\) | 8.19615i | 0.272902i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.803848i | 0.0267356i | ||||||||
\(905\) | 33.9282i | 1.12781i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.1769 | −0.703168 | −0.351584 | − | 0.936156i | \(-0.614357\pi\) | ||||
−0.351584 | + | 0.936156i | \(0.614357\pi\) | |||||||
\(908\) | − 20.1962i | − 0.670233i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.1769 | 0.834148 | 0.417074 | − | 0.908872i | \(-0.363056\pi\) | ||||
0.417074 | + | 0.908872i | \(0.363056\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.17691 | 0.237521 | ||||||||
\(914\) | 31.9808 | 1.05783 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − 7.85641i | − 0.259583i | ||||||||
\(917\) | − 5.56922i | − 0.183912i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.6077 | 0.382903 | 0.191451 | − | 0.981502i | \(-0.438681\pi\) | ||||
0.191451 | + | 0.981502i | \(0.438681\pi\) | |||||||
\(920\) | 14.1962 | 0.468033 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 31.9808 | 1.05323 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 6.00000i | − 0.197279i | ||||||||
\(926\) | −15.8038 | −0.519347 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.00000i | 0.0984798i | ||||||||
\(929\) | 55.3923i | 1.81736i | 0.417491 | + | 0.908681i | \(0.362910\pi\) | ||||
−0.417491 | + | 0.908681i | \(0.637090\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25.5167i | 0.836275i | ||||||||
\(932\) | 18.0000 | 0.589610 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.41154i | 0.177071i | ||||||||
\(935\) | 11.4115 | 0.373197 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.3923 | −0.502845 | −0.251422 | − | 0.967877i | \(-0.580898\pi\) | ||||
−0.251422 | + | 0.967877i | \(0.580898\pi\) | |||||||
\(938\) | 9.21539i | 0.300893i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8.19615 | 0.267329 | ||||||||
\(941\) | 38.7846i | 1.26434i | 0.774829 | + | 0.632171i | \(0.217836\pi\) | ||||
−0.774829 | + | 0.632171i | \(0.782164\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 52.9808i | 1.72529i | ||||||||
\(944\) | − 13.8564i | − 0.450988i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.32051 | −0.172985 | ||||||||
\(947\) | − 29.0718i | − 0.944706i | −0.881409 | − | 0.472353i | \(-0.843405\pi\) | ||||
0.881409 | − | 0.472353i | \(-0.156595\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −9.46410 | −0.307056 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.58846 | −0.213533 | ||||||||
\(953\) | −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 | ||||||||
\(956\) | 6.58846i | 0.213086i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.679492 | 0.0219534 | ||||||||
\(959\) | −11.4115 | −0.368498 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −58.5692 | −1.88933 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11.1962i | 0.360604i | ||||||||
\(965\) | 40.1769 | 1.29334 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 39.1244i | − 1.25815i | −0.777343 | − | 0.629077i | \(-0.783433\pi\) | ||||
0.777343 | − | 0.629077i | \(-0.216567\pi\) | |||||||
\(968\) | − 9.39230i | − 0.301880i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10.3923i | 0.333677i | ||||||||
\(971\) | −49.1769 | −1.57816 | −0.789081 | − | 0.614289i | \(-0.789443\pi\) | ||||
−0.789081 | + | 0.614289i | \(0.789443\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.07180i | 0.162594i | ||||||||
\(974\) | 15.1244 | 0.484616 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 15.1962 | 0.486417 | ||||||||
\(977\) | − 10.8564i | − 0.347327i | −0.984805 | − | 0.173664i | \(-0.944439\pi\) | ||||
0.984805 | − | 0.173664i | \(-0.0555605\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.0000 | −0.383522 | ||||||||
\(980\) | 9.33975i | 0.298347i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 30.5885i | − 0.976117i | ||||||||
\(983\) | 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 | ||||||||
\(989\) | −34.3923 | −1.09361 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43.3731 | −1.37779 | −0.688895 | − | 0.724861i | \(-0.741904\pi\) | ||||
−0.688895 | + | 0.724861i | \(0.741904\pi\) | |||||||
\(992\) | −9.46410 | −0.300486 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.78461i | 0.0883225i | ||||||||
\(995\) | − 39.1244i | − 1.24033i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.80385 | 0.0887987 | 0.0443994 | − | 0.999014i | \(-0.485863\pi\) | ||||
0.0443994 | + | 0.999014i | \(0.485863\pi\) | |||||||
\(998\) | 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 \(a_p\))