Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(251,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("1050.251");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.38429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 251.3 | ||
Root | \(-1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.251 |
Dual form | 1050.2.b.b.251.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −1.22474 | − | 1.22474i | −0.707107 | − | 0.707107i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.22474 | − | 1.22474i | 0.500000 | − | 0.500000i | ||||
\(7\) | 1.00000 | + | 2.44949i | 0.377964 | + | 0.925820i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 3.00000i | 1.00000i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | 1.22474 | + | 1.22474i | 0.353553 | + | 0.353553i | ||||
\(13\) | − | 2.44949i | − | 0.679366i | −0.940540 | − | 0.339683i | \(-0.889680\pi\) | ||
0.940540 | − | 0.339683i | \(-0.110320\pi\) | |||||||
\(14\) | −2.44949 | + | 1.00000i | −0.654654 | + | 0.267261i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.89898 | −1.18818 | −0.594089 | − | 0.804400i | \(-0.702487\pi\) | ||||
−0.594089 | + | 0.804400i | \(0.702487\pi\) | |||||||
\(18\) | −3.00000 | −0.707107 | ||||||||
\(19\) | − | 2.44949i | − | 0.561951i | −0.959715 | − | 0.280976i | \(-0.909342\pi\) | ||
0.959715 | − | 0.280976i | \(-0.0906580\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.77526 | − | 4.22474i | 0.387392 | − | 0.921915i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.00000i | 1.25109i | 0.780189 | + | 0.625543i | \(0.215123\pi\) | ||||
−0.780189 | + | 0.625543i | \(0.784877\pi\) | |||||||
\(24\) | −1.22474 | + | 1.22474i | −0.250000 | + | 0.250000i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.44949 | 0.480384 | ||||||||
\(27\) | 3.67423 | − | 3.67423i | 0.707107 | − | 0.707107i | ||||
\(28\) | −1.00000 | − | 2.44949i | −0.188982 | − | 0.462910i | ||||
\(29\) | 6.00000i | 1.11417i | 0.830455 | + | 0.557086i | \(0.188081\pi\) | ||||
−0.830455 | + | 0.557086i | \(0.811919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 4.89898i | − | 0.840168i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | − | 3.00000i | − | 0.500000i | ||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 2.44949 | 0.397360 | ||||||||
\(39\) | −3.00000 | + | 3.00000i | −0.480384 | + | 0.480384i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.89898 | −0.765092 | −0.382546 | − | 0.923936i | \(-0.624953\pi\) | ||||
−0.382546 | + | 0.923936i | \(0.624953\pi\) | |||||||
\(42\) | 4.22474 | + | 1.77526i | 0.651892 | + | 0.273928i | ||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.00000 | −0.884652 | ||||||||
\(47\) | −4.89898 | −0.714590 | −0.357295 | − | 0.933992i | \(-0.616301\pi\) | ||||
−0.357295 | + | 0.933992i | \(0.616301\pi\) | |||||||
\(48\) | −1.22474 | − | 1.22474i | −0.176777 | − | 0.176777i | ||||
\(49\) | −5.00000 | + | 4.89898i | −0.714286 | + | 0.699854i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.00000 | + | 6.00000i | 0.840168 | + | 0.840168i | ||||
\(52\) | 2.44949i | 0.339683i | ||||||||
\(53\) | 6.00000i | 0.824163i | 0.911147 | + | 0.412082i | \(0.135198\pi\) | ||||
−0.911147 | + | 0.412082i | \(0.864802\pi\) | |||||||
\(54\) | 3.67423 | + | 3.67423i | 0.500000 | + | 0.500000i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.44949 | − | 1.00000i | 0.327327 | − | 0.133631i | ||||
\(57\) | −3.00000 | + | 3.00000i | −0.397360 | + | 0.397360i | ||||
\(58\) | −6.00000 | −0.787839 | ||||||||
\(59\) | −12.2474 | −1.59448 | −0.797241 | − | 0.603661i | \(-0.793708\pi\) | ||||
−0.797241 | + | 0.603661i | \(0.793708\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.2474i | 1.56813i | 0.620682 | + | 0.784063i | \(0.286856\pi\) | ||||
−0.620682 | + | 0.784063i | \(0.713144\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.34847 | + | 3.00000i | −0.925820 | + | 0.377964i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.00000 | −0.977356 | −0.488678 | − | 0.872464i | \(-0.662521\pi\) | ||||
−0.488678 | + | 0.872464i | \(0.662521\pi\) | |||||||
\(68\) | 4.89898 | 0.594089 | ||||||||
\(69\) | 7.34847 | − | 7.34847i | 0.884652 | − | 0.884652i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 3.00000 | 0.353553 | ||||||||
\(73\) | 9.79796i | 1.14676i | 0.819288 | + | 0.573382i | \(0.194369\pi\) | ||||
−0.819288 | + | 0.573382i | \(0.805631\pi\) | |||||||
\(74\) | 2.00000i | 0.232495i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.44949i | 0.280976i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.00000 | − | 3.00000i | −0.339683 | − | 0.339683i | ||||
\(79\) | −10.0000 | −1.12509 | −0.562544 | − | 0.826767i | \(-0.690177\pi\) | ||||
−0.562544 | + | 0.826767i | \(0.690177\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | − | 4.89898i | − | 0.541002i | ||||||
\(83\) | −2.44949 | −0.268866 | −0.134433 | − | 0.990923i | \(-0.542921\pi\) | ||||
−0.134433 | + | 0.990923i | \(0.542921\pi\) | |||||||
\(84\) | −1.77526 | + | 4.22474i | −0.193696 | + | 0.460957i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 4.00000i | − | 0.431331i | ||||||
\(87\) | 7.34847 | − | 7.34847i | 0.787839 | − | 0.787839i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.00000 | − | 2.44949i | 0.628971 | − | 0.256776i | ||||
\(92\) | − | 6.00000i | − | 0.625543i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 4.89898i | − | 0.505291i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.22474 | − | 1.22474i | 0.125000 | − | 0.125000i | ||||
\(97\) | 4.89898i | 0.497416i | 0.968579 | + | 0.248708i | \(0.0800060\pi\) | ||||
−0.968579 | + | 0.248708i | \(0.919994\pi\) | |||||||
\(98\) | −4.89898 | − | 5.00000i | −0.494872 | − | 0.505076i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.34847 | 0.731200 | 0.365600 | − | 0.930772i | \(-0.380864\pi\) | ||||
0.365600 | + | 0.930772i | \(0.380864\pi\) | |||||||
\(102\) | −6.00000 | + | 6.00000i | −0.594089 | + | 0.594089i | ||||
\(103\) | 9.79796i | 0.965422i | 0.875780 | + | 0.482711i | \(0.160348\pi\) | ||||
−0.875780 | + | 0.482711i | \(0.839652\pi\) | |||||||
\(104\) | −2.44949 | −0.240192 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | − | 12.0000i | − | 1.16008i | −0.814587 | − | 0.580042i | \(-0.803036\pi\) | ||
0.814587 | − | 0.580042i | \(-0.196964\pi\) | |||||||
\(108\) | −3.67423 | + | 3.67423i | −0.353553 | + | 0.353553i | ||||
\(109\) | 10.0000 | 0.957826 | 0.478913 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.44949 | − | 2.44949i | −0.232495 | − | 0.232495i | ||||
\(112\) | 1.00000 | + | 2.44949i | 0.0944911 | + | 0.231455i | ||||
\(113\) | 6.00000i | 0.564433i | 0.959351 | + | 0.282216i | \(0.0910696\pi\) | ||||
−0.959351 | + | 0.282216i | \(0.908930\pi\) | |||||||
\(114\) | −3.00000 | − | 3.00000i | −0.280976 | − | 0.280976i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 6.00000i | − | 0.557086i | ||||||
\(117\) | 7.34847 | 0.679366 | ||||||||
\(118\) | − | 12.2474i | − | 1.12747i | ||||||
\(119\) | −4.89898 | − | 12.0000i | −0.449089 | − | 1.10004i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.0000 | 1.00000 | ||||||||
\(122\) | −12.2474 | −1.10883 | ||||||||
\(123\) | 6.00000 | + | 6.00000i | 0.541002 | + | 0.541002i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3.00000 | − | 7.34847i | −0.267261 | − | 0.654654i | ||||
\(127\) | −8.00000 | −0.709885 | −0.354943 | − | 0.934888i | \(-0.615500\pi\) | ||||
−0.354943 | + | 0.934888i | \(0.615500\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 4.89898 | + | 4.89898i | 0.431331 | + | 0.431331i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.34847 | 0.642039 | 0.321019 | − | 0.947073i | \(-0.395975\pi\) | ||||
0.321019 | + | 0.947073i | \(0.395975\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.00000 | − | 2.44949i | 0.520266 | − | 0.212398i | ||||
\(134\) | − | 8.00000i | − | 0.691095i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.89898i | 0.420084i | ||||||||
\(137\) | − | 12.0000i | − | 1.02523i | −0.858619 | − | 0.512615i | \(-0.828677\pi\) | ||
0.858619 | − | 0.512615i | \(-0.171323\pi\) | |||||||
\(138\) | 7.34847 | + | 7.34847i | 0.625543 | + | 0.625543i | ||||
\(139\) | − | 2.44949i | − | 0.207763i | −0.994590 | − | 0.103882i | \(-0.966874\pi\) | ||
0.994590 | − | 0.103882i | \(-0.0331263\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | + | 6.00000i | 0.505291 | + | 0.505291i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.00000i | 0.250000i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −9.79796 | −0.810885 | ||||||||
\(147\) | 12.1237 | + | 0.123724i | 0.999948 | + | 0.0102046i | ||||
\(148\) | −2.00000 | −0.164399 | ||||||||
\(149\) | 6.00000i | 0.491539i | 0.969328 | + | 0.245770i | \(0.0790407\pi\) | ||||
−0.969328 | + | 0.245770i | \(0.920959\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | −2.44949 | −0.198680 | ||||||||
\(153\) | − | 14.6969i | − | 1.18818i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.00000 | − | 3.00000i | 0.240192 | − | 0.240192i | ||||
\(157\) | − | 7.34847i | − | 0.586472i | −0.956040 | − | 0.293236i | \(-0.905268\pi\) | ||
0.956040 | − | 0.293236i | \(-0.0947321\pi\) | |||||||
\(158\) | − | 10.0000i | − | 0.795557i | ||||||
\(159\) | 7.34847 | − | 7.34847i | 0.582772 | − | 0.582772i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.6969 | + | 6.00000i | −1.15828 | + | 0.472866i | ||||
\(162\) | − | 9.00000i | − | 0.707107i | ||||||
\(163\) | 16.0000 | 1.25322 | 0.626608 | − | 0.779334i | \(-0.284443\pi\) | ||||
0.626608 | + | 0.779334i | \(0.284443\pi\) | |||||||
\(164\) | 4.89898 | 0.382546 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 2.44949i | − | 0.190117i | ||||||
\(167\) | −4.89898 | −0.379094 | −0.189547 | − | 0.981872i | \(-0.560702\pi\) | ||||
−0.189547 | + | 0.981872i | \(0.560702\pi\) | |||||||
\(168\) | −4.22474 | − | 1.77526i | −0.325946 | − | 0.136964i | ||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.34847 | 0.561951 | ||||||||
\(172\) | 4.00000 | 0.304997 | ||||||||
\(173\) | 22.0454 | 1.67608 | 0.838041 | − | 0.545608i | \(-0.183701\pi\) | ||||
0.838041 | + | 0.545608i | \(0.183701\pi\) | |||||||
\(174\) | 7.34847 | + | 7.34847i | 0.557086 | + | 0.557086i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 15.0000 | + | 15.0000i | 1.12747 | + | 1.12747i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 24.0000i | − | 1.79384i | −0.442189 | − | 0.896922i | \(-0.645798\pi\) | ||
0.442189 | − | 0.896922i | \(-0.354202\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 12.2474i | − | 0.910346i | −0.890403 | − | 0.455173i | \(-0.849577\pi\) | ||
0.890403 | − | 0.455173i | \(-0.150423\pi\) | |||||||
\(182\) | 2.44949 | + | 6.00000i | 0.181568 | + | 0.444750i | ||||
\(183\) | 15.0000 | − | 15.0000i | 1.10883 | − | 1.10883i | ||||
\(184\) | 6.00000 | 0.442326 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 4.89898 | 0.357295 | ||||||||
\(189\) | 12.6742 | + | 5.32577i | 0.921915 | + | 0.387392i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(192\) | 1.22474 | + | 1.22474i | 0.0883883 | + | 0.0883883i | ||||
\(193\) | −4.00000 | −0.287926 | −0.143963 | − | 0.989583i | \(-0.545985\pi\) | ||||
−0.143963 | + | 0.989583i | \(0.545985\pi\) | |||||||
\(194\) | −4.89898 | −0.351726 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.00000 | − | 4.89898i | 0.357143 | − | 0.349927i | ||||
\(197\) | 18.0000i | 1.28245i | 0.767354 | + | 0.641223i | \(0.221573\pi\) | ||||
−0.767354 | + | 0.641223i | \(0.778427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.79796i | 0.694559i | 0.937762 | + | 0.347279i | \(0.112894\pi\) | ||||
−0.937762 | + | 0.347279i | \(0.887106\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.79796 | + | 9.79796i | 0.691095 | + | 0.691095i | ||||
\(202\) | 7.34847i | 0.517036i | ||||||||
\(203\) | −14.6969 | + | 6.00000i | −1.03152 | + | 0.421117i | ||||
\(204\) | −6.00000 | − | 6.00000i | −0.420084 | − | 0.420084i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −9.79796 | −0.682656 | ||||||||
\(207\) | −18.0000 | −1.25109 | ||||||||
\(208\) | − | 2.44949i | − | 0.169842i | ||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.00000 | −0.550743 | −0.275371 | − | 0.961338i | \(-0.588801\pi\) | ||||
−0.275371 | + | 0.961338i | \(0.588801\pi\) | |||||||
\(212\) | − | 6.00000i | − | 0.412082i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 12.0000 | 0.820303 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.67423 | − | 3.67423i | −0.250000 | − | 0.250000i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 10.0000i | 0.677285i | ||||||||
\(219\) | 12.0000 | − | 12.0000i | 0.810885 | − | 0.810885i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000i | 0.807207i | ||||||||
\(222\) | 2.44949 | − | 2.44949i | 0.164399 | − | 0.164399i | ||||
\(223\) | − | 14.6969i | − | 0.984180i | −0.870544 | − | 0.492090i | \(-0.836233\pi\) | ||
0.870544 | − | 0.492090i | \(-0.163767\pi\) | |||||||
\(224\) | −2.44949 | + | 1.00000i | −0.163663 | + | 0.0668153i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | −0.399114 | ||||||||
\(227\) | 7.34847 | 0.487735 | 0.243868 | − | 0.969809i | \(-0.421584\pi\) | ||||
0.243868 | + | 0.969809i | \(0.421584\pi\) | |||||||
\(228\) | 3.00000 | − | 3.00000i | 0.198680 | − | 0.198680i | ||||
\(229\) | 22.0454i | 1.45680i | 0.685151 | + | 0.728401i | \(0.259736\pi\) | ||||
−0.685151 | + | 0.728401i | \(0.740264\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.00000 | 0.393919 | ||||||||
\(233\) | − | 24.0000i | − | 1.57229i | −0.618041 | − | 0.786146i | \(-0.712073\pi\) | ||
0.618041 | − | 0.786146i | \(-0.287927\pi\) | |||||||
\(234\) | 7.34847i | 0.480384i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 12.2474 | 0.797241 | ||||||||
\(237\) | 12.2474 | + | 12.2474i | 0.795557 | + | 0.795557i | ||||
\(238\) | 12.0000 | − | 4.89898i | 0.777844 | − | 0.317554i | ||||
\(239\) | 6.00000i | 0.388108i | 0.980991 | + | 0.194054i | \(0.0621637\pi\) | ||||
−0.980991 | + | 0.194054i | \(0.937836\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 24.4949i | − | 1.57786i | −0.614486 | − | 0.788928i | \(-0.710637\pi\) | ||
0.614486 | − | 0.788928i | \(-0.289363\pi\) | |||||||
\(242\) | 11.0000i | 0.707107i | ||||||||
\(243\) | 11.0227 | + | 11.0227i | 0.707107 | + | 0.707107i | ||||
\(244\) | − | 12.2474i | − | 0.784063i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.00000 | + | 6.00000i | −0.382546 | + | 0.382546i | ||||
\(247\) | −6.00000 | −0.381771 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.00000 | + | 3.00000i | 0.190117 | + | 0.190117i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.1464 | −1.08227 | −0.541136 | − | 0.840935i | \(-0.682006\pi\) | ||||
−0.541136 | + | 0.840935i | \(0.682006\pi\) | |||||||
\(252\) | 7.34847 | − | 3.00000i | 0.462910 | − | 0.188982i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − | 8.00000i | − | 0.501965i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −29.3939 | −1.83354 | −0.916770 | − | 0.399416i | \(-0.869213\pi\) | ||||
−0.916770 | + | 0.399416i | \(0.869213\pi\) | |||||||
\(258\) | −4.89898 | + | 4.89898i | −0.304997 | + | 0.304997i | ||||
\(259\) | 2.00000 | + | 4.89898i | 0.124274 | + | 0.304408i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −18.0000 | −1.11417 | ||||||||
\(262\) | 7.34847i | 0.453990i | ||||||||
\(263\) | − | 24.0000i | − | 1.47990i | −0.672660 | − | 0.739952i | \(-0.734848\pi\) | ||
0.672660 | − | 0.739952i | \(-0.265152\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.44949 | + | 6.00000i | 0.150188 | + | 0.367884i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.00000 | 0.488678 | ||||||||
\(269\) | −12.2474 | −0.746740 | −0.373370 | − | 0.927682i | \(-0.621798\pi\) | ||||
−0.373370 | + | 0.927682i | \(0.621798\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.4949i | 1.48796i | 0.668202 | + | 0.743980i | \(0.267064\pi\) | ||||
−0.668202 | + | 0.743980i | \(0.732936\pi\) | |||||||
\(272\) | −4.89898 | −0.297044 | ||||||||
\(273\) | −10.3485 | − | 4.34847i | −0.626318 | − | 0.263181i | ||||
\(274\) | 12.0000 | 0.724947 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −7.34847 | + | 7.34847i | −0.442326 | + | 0.442326i | ||||
\(277\) | 22.0000 | 1.32185 | 0.660926 | − | 0.750451i | \(-0.270164\pi\) | ||||
0.660926 | + | 0.750451i | \(0.270164\pi\) | |||||||
\(278\) | 2.44949 | 0.146911 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | −6.00000 | + | 6.00000i | −0.357295 | + | 0.357295i | ||||
\(283\) | 22.0454i | 1.31046i | 0.755428 | + | 0.655232i | \(0.227429\pi\) | ||||
−0.755428 | + | 0.655232i | \(0.772571\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.89898 | − | 12.0000i | −0.289178 | − | 0.708338i | ||||
\(288\) | −3.00000 | −0.176777 | ||||||||
\(289\) | 7.00000 | 0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.00000 | − | 6.00000i | 0.351726 | − | 0.351726i | ||||
\(292\) | − | 9.79796i | − | 0.573382i | ||||||
\(293\) | −2.44949 | −0.143101 | −0.0715504 | − | 0.997437i | \(-0.522795\pi\) | ||||
−0.0715504 | + | 0.997437i | \(0.522795\pi\) | |||||||
\(294\) | −0.123724 | + | 12.1237i | −0.00721575 | + | 0.707070i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 2.00000i | − | 0.116248i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.00000 | −0.347571 | ||||||||
\(299\) | 14.6969 | 0.849946 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.00000 | − | 9.79796i | −0.230556 | − | 0.564745i | ||||
\(302\) | − | 8.00000i | − | 0.460348i | ||||||
\(303\) | −9.00000 | − | 9.00000i | −0.517036 | − | 0.517036i | ||||
\(304\) | − | 2.44949i | − | 0.140488i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 14.6969 | 0.840168 | ||||||||
\(307\) | − | 7.34847i | − | 0.419399i | −0.977766 | − | 0.209700i | \(-0.932751\pi\) | ||
0.977766 | − | 0.209700i | \(-0.0672486\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.0000 | − | 12.0000i | 0.682656 | − | 0.682656i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.5959 | 1.11118 | 0.555591 | − | 0.831456i | \(-0.312492\pi\) | ||||
0.555591 | + | 0.831456i | \(0.312492\pi\) | |||||||
\(312\) | 3.00000 | + | 3.00000i | 0.169842 | + | 0.169842i | ||||
\(313\) | 34.2929i | 1.93835i | 0.246380 | + | 0.969173i | \(0.420759\pi\) | ||||
−0.246380 | + | 0.969173i | \(0.579241\pi\) | |||||||
\(314\) | 7.34847 | 0.414698 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.0000 | 0.562544 | ||||||||
\(317\) | 18.0000i | 1.01098i | 0.862832 | + | 0.505490i | \(0.168688\pi\) | ||||
−0.862832 | + | 0.505490i | \(0.831312\pi\) | |||||||
\(318\) | 7.34847 | + | 7.34847i | 0.412082 | + | 0.412082i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.6969 | + | 14.6969i | −0.820303 | + | 0.820303i | ||||
\(322\) | −6.00000 | − | 14.6969i | −0.334367 | − | 0.819028i | ||||
\(323\) | 12.0000i | 0.667698i | ||||||||
\(324\) | 9.00000 | 0.500000 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 16.0000i | 0.886158i | ||||||||
\(327\) | −12.2474 | − | 12.2474i | −0.677285 | − | 0.677285i | ||||
\(328\) | 4.89898i | 0.270501i | ||||||||
\(329\) | −4.89898 | − | 12.0000i | −0.270089 | − | 0.661581i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.00000 | −0.439720 | −0.219860 | − | 0.975531i | \(-0.570560\pi\) | ||||
−0.219860 | + | 0.975531i | \(0.570560\pi\) | |||||||
\(332\) | 2.44949 | 0.134433 | ||||||||
\(333\) | 6.00000i | 0.328798i | ||||||||
\(334\) | − | 4.89898i | − | 0.268060i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.77526 | − | 4.22474i | 0.0968481 | − | 0.230479i | ||||
\(337\) | 32.0000 | 1.74315 | 0.871576 | − | 0.490261i | \(-0.163099\pi\) | ||||
0.871576 | + | 0.490261i | \(0.163099\pi\) | |||||||
\(338\) | 7.00000i | 0.380750i | ||||||||
\(339\) | 7.34847 | − | 7.34847i | 0.399114 | − | 0.399114i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 7.34847i | 0.397360i | ||||||||
\(343\) | −17.0000 | − | 7.34847i | −0.917914 | − | 0.396780i | ||||
\(344\) | 4.00000i | 0.215666i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 22.0454i | 1.18517i | ||||||||
\(347\) | − | 12.0000i | − | 0.644194i | −0.946707 | − | 0.322097i | \(-0.895612\pi\) | ||
0.946707 | − | 0.322097i | \(-0.104388\pi\) | |||||||
\(348\) | −7.34847 | + | 7.34847i | −0.393919 | + | 0.393919i | ||||
\(349\) | − | 2.44949i | − | 0.131118i | −0.997849 | − | 0.0655591i | \(-0.979117\pi\) | ||
0.997849 | − | 0.0655591i | \(-0.0208831\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.00000 | − | 9.00000i | −0.480384 | − | 0.480384i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.79796 | 0.521493 | 0.260746 | − | 0.965407i | \(-0.416031\pi\) | ||||
0.260746 | + | 0.965407i | \(0.416031\pi\) | |||||||
\(354\) | −15.0000 | + | 15.0000i | −0.797241 | + | 0.797241i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.69694 | + | 20.6969i | −0.460291 | + | 1.09540i | ||||
\(358\) | 24.0000 | 1.26844 | ||||||||
\(359\) | 6.00000i | 0.316668i | 0.987386 | + | 0.158334i | \(0.0506123\pi\) | ||||
−0.987386 | + | 0.158334i | \(0.949388\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | 0.684211 | ||||||||
\(362\) | 12.2474 | 0.643712 | ||||||||
\(363\) | −13.4722 | − | 13.4722i | −0.707107 | − | 0.707107i | ||||
\(364\) | −6.00000 | + | 2.44949i | −0.314485 | + | 0.128388i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 15.0000 | + | 15.0000i | 0.784063 | + | 0.784063i | ||||
\(367\) | 4.89898i | 0.255725i | 0.991792 | + | 0.127862i | \(0.0408116\pi\) | ||||
−0.991792 | + | 0.127862i | \(0.959188\pi\) | |||||||
\(368\) | 6.00000i | 0.312772i | ||||||||
\(369\) | − | 14.6969i | − | 0.765092i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.6969 | + | 6.00000i | −0.763027 | + | 0.311504i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.0000 | −0.724893 | −0.362446 | − | 0.932005i | \(-0.618058\pi\) | ||||
−0.362446 | + | 0.932005i | \(0.618058\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.89898i | 0.252646i | ||||||||
\(377\) | 14.6969 | 0.756931 | ||||||||
\(378\) | −5.32577 | + | 12.6742i | −0.273928 | + | 0.651892i | ||||
\(379\) | −20.0000 | −1.02733 | −0.513665 | − | 0.857991i | \(-0.671713\pi\) | ||||
−0.513665 | + | 0.857991i | \(0.671713\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.79796 | + | 9.79796i | 0.501965 | + | 0.501965i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 34.2929 | 1.75228 | 0.876142 | − | 0.482054i | \(-0.160109\pi\) | ||||
0.876142 | + | 0.482054i | \(0.160109\pi\) | |||||||
\(384\) | −1.22474 | + | 1.22474i | −0.0625000 | + | 0.0625000i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 4.00000i | − | 0.203595i | ||||||
\(387\) | − | 12.0000i | − | 0.609994i | ||||||
\(388\) | − | 4.89898i | − | 0.248708i | ||||||
\(389\) | 6.00000i | 0.304212i | 0.988364 | + | 0.152106i | \(0.0486055\pi\) | ||||
−0.988364 | + | 0.152106i | \(0.951394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 29.3939i | − | 1.48651i | ||||||
\(392\) | 4.89898 | + | 5.00000i | 0.247436 | + | 0.252538i | ||||
\(393\) | −9.00000 | − | 9.00000i | −0.453990 | − | 0.453990i | ||||
\(394\) | −18.0000 | −0.906827 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 7.34847i | − | 0.368809i | −0.982850 | − | 0.184405i | \(-0.940964\pi\) | ||
0.982850 | − | 0.184405i | \(-0.0590357\pi\) | |||||||
\(398\) | −9.79796 | −0.491127 | ||||||||
\(399\) | −10.3485 | − | 4.34847i | −0.518071 | − | 0.217696i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 30.0000i | − | 1.49813i | −0.662497 | − | 0.749064i | \(-0.730503\pi\) | ||
0.662497 | − | 0.749064i | \(-0.269497\pi\) | |||||||
\(402\) | −9.79796 | + | 9.79796i | −0.488678 | + | 0.488678i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −7.34847 | −0.365600 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.00000 | − | 14.6969i | −0.297775 | − | 0.729397i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 6.00000 | − | 6.00000i | 0.297044 | − | 0.297044i | ||||
\(409\) | 34.2929i | 1.69567i | 0.530258 | + | 0.847836i | \(0.322095\pi\) | ||||
−0.530258 | + | 0.847836i | \(0.677905\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.6969 | + | 14.6969i | −0.724947 | + | 0.724947i | ||||
\(412\) | − | 9.79796i | − | 0.482711i | ||||||
\(413\) | −12.2474 | − | 30.0000i | −0.602658 | − | 1.47620i | ||||
\(414\) | − | 18.0000i | − | 0.884652i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.44949 | 0.120096 | ||||||||
\(417\) | −3.00000 | + | 3.00000i | −0.146911 | + | 0.146911i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.2474 | 0.598327 | 0.299164 | − | 0.954202i | \(-0.403292\pi\) | ||||
0.299164 | + | 0.954202i | \(0.403292\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.00000 | 0.0974740 | 0.0487370 | − | 0.998812i | \(-0.484480\pi\) | ||||
0.0487370 | + | 0.998812i | \(0.484480\pi\) | |||||||
\(422\) | − | 8.00000i | − | 0.389434i | ||||||
\(423\) | − | 14.6969i | − | 0.714590i | ||||||
\(424\) | 6.00000 | 0.291386 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −30.0000 | + | 12.2474i | −1.45180 | + | 0.592696i | ||||
\(428\) | 12.0000i | 0.580042i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 30.0000i | − | 1.44505i | −0.691345 | − | 0.722525i | \(-0.742982\pi\) | ||
0.691345 | − | 0.722525i | \(-0.257018\pi\) | |||||||
\(432\) | 3.67423 | − | 3.67423i | 0.176777 | − | 0.176777i | ||||
\(433\) | − | 14.6969i | − | 0.706290i | −0.935569 | − | 0.353145i | \(-0.885112\pi\) | ||
0.935569 | − | 0.353145i | \(-0.114888\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.0000 | −0.478913 | ||||||||
\(437\) | 14.6969 | 0.703050 | ||||||||
\(438\) | 12.0000 | + | 12.0000i | 0.573382 | + | 0.573382i | ||||
\(439\) | − | 14.6969i | − | 0.701447i | −0.936479 | − | 0.350723i | \(-0.885936\pi\) | ||
0.936479 | − | 0.350723i | \(-0.114064\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.6969 | − | 15.0000i | −0.699854 | − | 0.714286i | ||||
\(442\) | −12.0000 | −0.570782 | ||||||||
\(443\) | 36.0000i | 1.71041i | 0.518289 | + | 0.855206i | \(0.326569\pi\) | ||||
−0.518289 | + | 0.855206i | \(0.673431\pi\) | |||||||
\(444\) | 2.44949 | + | 2.44949i | 0.116248 | + | 0.116248i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 14.6969 | 0.695920 | ||||||||
\(447\) | 7.34847 | − | 7.34847i | 0.347571 | − | 0.347571i | ||||
\(448\) | −1.00000 | − | 2.44949i | −0.0472456 | − | 0.115728i | ||||
\(449\) | 36.0000i | 1.69895i | 0.527633 | + | 0.849473i | \(0.323080\pi\) | ||||
−0.527633 | + | 0.849473i | \(0.676920\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 6.00000i | − | 0.282216i | ||||||
\(453\) | 9.79796 | + | 9.79796i | 0.460348 | + | 0.460348i | ||||
\(454\) | 7.34847i | 0.344881i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.00000 | + | 3.00000i | 0.140488 | + | 0.140488i | ||||
\(457\) | −28.0000 | −1.30978 | −0.654892 | − | 0.755722i | \(-0.727286\pi\) | ||||
−0.654892 | + | 0.755722i | \(0.727286\pi\) | |||||||
\(458\) | −22.0454 | −1.03011 | ||||||||
\(459\) | −18.0000 | + | 18.0000i | −0.840168 | + | 0.840168i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.8434 | 1.48309 | 0.741547 | − | 0.670901i | \(-0.234093\pi\) | ||||
0.741547 | + | 0.670901i | \(0.234093\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.0000 | −0.650635 | −0.325318 | − | 0.945605i | \(-0.605471\pi\) | ||||
−0.325318 | + | 0.945605i | \(0.605471\pi\) | |||||||
\(464\) | 6.00000i | 0.278543i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 24.0000 | 1.11178 | ||||||||
\(467\) | 7.34847 | 0.340047 | 0.170023 | − | 0.985440i | \(-0.445616\pi\) | ||||
0.170023 | + | 0.985440i | \(0.445616\pi\) | |||||||
\(468\) | −7.34847 | −0.339683 | ||||||||
\(469\) | −8.00000 | − | 19.5959i | −0.369406 | − | 0.904855i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.00000 | + | 9.00000i | −0.414698 | + | 0.414698i | ||||
\(472\) | 12.2474i | 0.563735i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −12.2474 | + | 12.2474i | −0.562544 | + | 0.562544i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.89898 | + | 12.0000i | 0.224544 | + | 0.550019i | ||||
\(477\) | −18.0000 | −0.824163 | ||||||||
\(478\) | −6.00000 | −0.274434 | ||||||||
\(479\) | 24.4949 | 1.11920 | 0.559600 | − | 0.828763i | \(-0.310955\pi\) | ||||
0.559600 | + | 0.828763i | \(0.310955\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 4.89898i | − | 0.223374i | ||||||
\(482\) | 24.4949 | 1.11571 | ||||||||
\(483\) | 25.3485 | + | 10.6515i | 1.15340 | + | 0.484661i | ||||
\(484\) | −11.0000 | −0.500000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −11.0227 | + | 11.0227i | −0.500000 | + | 0.500000i | ||||
\(487\) | 32.0000 | 1.45006 | 0.725029 | − | 0.688718i | \(-0.241826\pi\) | ||||
0.725029 | + | 0.688718i | \(0.241826\pi\) | |||||||
\(488\) | 12.2474 | 0.554416 | ||||||||
\(489\) | −19.5959 | − | 19.5959i | −0.886158 | − | 0.886158i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | −6.00000 | − | 6.00000i | −0.270501 | − | 0.270501i | ||||
\(493\) | − | 29.3939i | − | 1.32383i | ||||||
\(494\) | − | 6.00000i | − | 0.269953i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −3.00000 | + | 3.00000i | −0.134433 | + | 0.134433i | ||||
\(499\) | −20.0000 | −0.895323 | −0.447661 | − | 0.894203i | \(-0.647743\pi\) | ||||
−0.447661 | + | 0.894203i | \(0.647743\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.00000 | + | 6.00000i | 0.268060 | + | 0.268060i | ||||
\(502\) | − | 17.1464i | − | 0.765283i | ||||||
\(503\) | −39.1918 | −1.74748 | −0.873739 | − | 0.486395i | \(-0.838311\pi\) | ||||
−0.873739 | + | 0.486395i | \(0.838311\pi\) | |||||||
\(504\) | 3.00000 | + | 7.34847i | 0.133631 | + | 0.327327i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.57321 | − | 8.57321i | −0.380750 | − | 0.380750i | ||||
\(508\) | 8.00000 | 0.354943 | ||||||||
\(509\) | −12.2474 | −0.542859 | −0.271429 | − | 0.962458i | \(-0.587496\pi\) | ||||
−0.271429 | + | 0.962458i | \(0.587496\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.0000 | + | 9.79796i | −1.06170 | + | 0.433436i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −9.00000 | − | 9.00000i | −0.397360 | − | 0.397360i | ||||
\(514\) | − | 29.3939i | − | 1.29651i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.89898 | − | 4.89898i | −0.215666 | − | 0.215666i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −4.89898 | + | 2.00000i | −0.215249 | + | 0.0878750i | ||||
\(519\) | −27.0000 | − | 27.0000i | −1.18517 | − | 1.18517i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.89898 | −0.214628 | −0.107314 | − | 0.994225i | \(-0.534225\pi\) | ||||
−0.107314 | + | 0.994225i | \(0.534225\pi\) | |||||||
\(522\) | − | 18.0000i | − | 0.787839i | ||||||
\(523\) | − | 2.44949i | − | 0.107109i | −0.998565 | − | 0.0535544i | \(-0.982945\pi\) | ||
0.998565 | − | 0.0535544i | \(-0.0170550\pi\) | |||||||
\(524\) | −7.34847 | −0.321019 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.0000 | 1.04645 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.0000 | −0.565217 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 36.7423i | − | 1.59448i | ||||||
\(532\) | −6.00000 | + | 2.44949i | −0.260133 | + | 0.106199i | ||||
\(533\) | 12.0000i | 0.519778i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8.00000i | 0.345547i | ||||||||
\(537\) | −29.3939 | + | 29.3939i | −1.26844 | + | 1.26844i | ||||
\(538\) | − | 12.2474i | − | 0.528025i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.00000 | 0.0859867 | 0.0429934 | − | 0.999075i | \(-0.486311\pi\) | ||||
0.0429934 | + | 0.999075i | \(0.486311\pi\) | |||||||
\(542\) | −24.4949 | −1.05215 | ||||||||
\(543\) | −15.0000 | + | 15.0000i | −0.643712 | + | 0.643712i | ||||
\(544\) | − | 4.89898i | − | 0.210042i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 4.34847 | − | 10.3485i | 0.186097 | − | 0.442874i | ||||
\(547\) | −8.00000 | −0.342055 | −0.171028 | − | 0.985266i | \(-0.554709\pi\) | ||||
−0.171028 | + | 0.985266i | \(0.554709\pi\) | |||||||
\(548\) | 12.0000i | 0.512615i | ||||||||
\(549\) | −36.7423 | −1.56813 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.6969 | 0.626111 | ||||||||
\(552\) | −7.34847 | − | 7.34847i | −0.312772 | − | 0.312772i | ||||
\(553\) | −10.0000 | − | 24.4949i | −0.425243 | − | 1.04163i | ||||
\(554\) | 22.0000i | 0.934690i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.44949i | 0.103882i | ||||||||
\(557\) | 18.0000i | 0.762684i | 0.924434 | + | 0.381342i | \(0.124538\pi\) | ||||
−0.924434 | + | 0.381342i | \(0.875462\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.79796i | 0.414410i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.0454 | 0.929103 | 0.464552 | − | 0.885546i | \(-0.346216\pi\) | ||||
0.464552 | + | 0.885546i | \(0.346216\pi\) | |||||||
\(564\) | −6.00000 | − | 6.00000i | −0.252646 | − | 0.252646i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −22.0454 | −0.926638 | ||||||||
\(567\) | −9.00000 | − | 22.0454i | −0.377964 | − | 0.925820i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.00000i | 0.251533i | 0.992060 | + | 0.125767i | \(0.0401390\pi\) | ||||
−0.992060 | + | 0.125767i | \(0.959861\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.0000 | 1.33916 | 0.669579 | − | 0.742741i | \(-0.266474\pi\) | ||||
0.669579 | + | 0.742741i | \(0.266474\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 12.0000 | − | 4.89898i | 0.500870 | − | 0.204479i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | − | 3.00000i | − | 0.125000i | ||||||
\(577\) | − | 19.5959i | − | 0.815789i | −0.913029 | − | 0.407894i | \(-0.866263\pi\) | ||
0.913029 | − | 0.407894i | \(-0.133737\pi\) | |||||||
\(578\) | 7.00000i | 0.291162i | ||||||||
\(579\) | 4.89898 | + | 4.89898i | 0.203595 | + | 0.203595i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.44949 | − | 6.00000i | −0.101622 | − | 0.248922i | ||||
\(582\) | 6.00000 | + | 6.00000i | 0.248708 | + | 0.248708i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 9.79796 | 0.405442 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 2.44949i | − | 0.101187i | ||||||
\(587\) | 7.34847 | 0.303304 | 0.151652 | − | 0.988434i | \(-0.451541\pi\) | ||||
0.151652 | + | 0.988434i | \(0.451541\pi\) | |||||||
\(588\) | −12.1237 | − | 0.123724i | −0.499974 | − | 0.00510231i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.0454 | − | 22.0454i | 0.906827 | − | 0.906827i | ||||
\(592\) | 2.00000 | 0.0821995 | ||||||||
\(593\) | −39.1918 | −1.60942 | −0.804708 | − | 0.593671i | \(-0.797678\pi\) | ||||
−0.804708 | + | 0.593671i | \(0.797678\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 6.00000i | − | 0.245770i | ||||||
\(597\) | 12.0000 | − | 12.0000i | 0.491127 | − | 0.491127i | ||||
\(598\) | 14.6969i | 0.601003i | ||||||||
\(599\) | − | 24.0000i | − | 0.980613i | −0.871550 | − | 0.490307i | \(-0.836885\pi\) | ||
0.871550 | − | 0.490307i | \(-0.163115\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 9.79796 | − | 4.00000i | 0.399335 | − | 0.163028i | ||||
\(603\) | − | 24.0000i | − | 0.977356i | ||||||
\(604\) | 8.00000 | 0.325515 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 9.00000 | − | 9.00000i | 0.365600 | − | 0.365600i | ||||
\(607\) | 4.89898i | 0.198843i | 0.995045 | + | 0.0994217i | \(0.0316993\pi\) | ||||
−0.995045 | + | 0.0994217i | \(0.968301\pi\) | |||||||
\(608\) | 2.44949 | 0.0993399 | ||||||||
\(609\) | 25.3485 | + | 10.6515i | 1.02717 | + | 0.431622i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.0000i | 0.485468i | ||||||||
\(612\) | 14.6969i | 0.594089i | ||||||||
\(613\) | −14.0000 | −0.565455 | −0.282727 | − | 0.959200i | \(-0.591239\pi\) | ||||
−0.282727 | + | 0.959200i | \(0.591239\pi\) | |||||||
\(614\) | 7.34847 | 0.296560 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.0000i | 0.724653i | 0.932051 | + | 0.362326i | \(0.118017\pi\) | ||||
−0.932051 | + | 0.362326i | \(0.881983\pi\) | |||||||
\(618\) | 12.0000 | + | 12.0000i | 0.482711 | + | 0.482711i | ||||
\(619\) | − | 26.9444i | − | 1.08299i | −0.840705 | − | 0.541493i | \(-0.817859\pi\) | ||
0.840705 | − | 0.541493i | \(-0.182141\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 22.0454 | + | 22.0454i | 0.884652 | + | 0.884652i | ||||
\(622\) | 19.5959i | 0.785725i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.00000 | + | 3.00000i | −0.120096 | + | 0.120096i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −34.2929 | −1.37062 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.34847i | 0.293236i | ||||||||
\(629\) | −9.79796 | −0.390670 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.00000 | 0.0796187 | 0.0398094 | − | 0.999207i | \(-0.487325\pi\) | ||||
0.0398094 | + | 0.999207i | \(0.487325\pi\) | |||||||
\(632\) | 10.0000i | 0.397779i | ||||||||
\(633\) | 9.79796 | + | 9.79796i | 0.389434 | + | 0.389434i | ||||
\(634\) | −18.0000 | −0.714871 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −7.34847 | + | 7.34847i | −0.291386 | + | 0.291386i | ||||
\(637\) | 12.0000 | + | 12.2474i | 0.475457 | + | 0.485262i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.0000i | 1.18493i | 0.805597 | + | 0.592464i | \(0.201845\pi\) | ||||
−0.805597 | + | 0.592464i | \(0.798155\pi\) | |||||||
\(642\) | −14.6969 | − | 14.6969i | −0.580042 | − | 0.580042i | ||||
\(643\) | 22.0454i | 0.869386i | 0.900579 | + | 0.434693i | \(0.143143\pi\) | ||||
−0.900579 | + | 0.434693i | \(0.856857\pi\) | |||||||
\(644\) | 14.6969 | − | 6.00000i | 0.579141 | − | 0.236433i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.0000 | −0.472134 | ||||||||
\(647\) | 44.0908 | 1.73339 | 0.866694 | − | 0.498839i | \(-0.166240\pi\) | ||||
0.866694 | + | 0.498839i | \(0.166240\pi\) | |||||||
\(648\) | 9.00000i | 0.353553i | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −16.0000 | −0.626608 | ||||||||
\(653\) | 6.00000i | 0.234798i | 0.993085 | + | 0.117399i | \(0.0374557\pi\) | ||||
−0.993085 | + | 0.117399i | \(0.962544\pi\) | |||||||
\(654\) | 12.2474 | − | 12.2474i | 0.478913 | − | 0.478913i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.89898 | −0.191273 | ||||||||
\(657\) | −29.3939 | −1.14676 | ||||||||
\(658\) | 12.0000 | − | 4.89898i | 0.467809 | − | 0.190982i | ||||
\(659\) | 36.0000i | 1.40236i | 0.712984 | + | 0.701180i | \(0.247343\pi\) | ||||
−0.712984 | + | 0.701180i | \(0.752657\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 12.2474i | − | 0.476371i | −0.971220 | − | 0.238185i | \(-0.923447\pi\) | ||
0.971220 | − | 0.238185i | \(-0.0765525\pi\) | |||||||
\(662\) | − | 8.00000i | − | 0.310929i | ||||||
\(663\) | 14.6969 | − | 14.6969i | 0.570782 | − | 0.570782i | ||||
\(664\) | 2.44949i | 0.0950586i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.00000 | −0.232495 | ||||||||
\(667\) | −36.0000 | −1.39393 | ||||||||
\(668\) | 4.89898 | 0.189547 | ||||||||
\(669\) | −18.0000 | + | 18.0000i | −0.695920 | + | 0.695920i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 4.22474 | + | 1.77526i | 0.162973 | + | 0.0684820i | ||||
\(673\) | −34.0000 | −1.31060 | −0.655302 | − | 0.755367i | \(-0.727459\pi\) | ||||
−0.655302 | + | 0.755367i | \(0.727459\pi\) | |||||||
\(674\) | 32.0000i | 1.23259i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.00000 | −0.269231 | ||||||||
\(677\) | 7.34847 | 0.282425 | 0.141212 | − | 0.989979i | \(-0.454900\pi\) | ||||
0.141212 | + | 0.989979i | \(0.454900\pi\) | |||||||
\(678\) | 7.34847 | + | 7.34847i | 0.282216 | + | 0.282216i | ||||
\(679\) | −12.0000 | + | 4.89898i | −0.460518 | + | 0.188006i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.00000 | − | 9.00000i | −0.344881 | − | 0.344881i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 24.0000i | − | 0.918334i | −0.888350 | − | 0.459167i | \(-0.848148\pi\) | ||
0.888350 | − | 0.459167i | \(-0.151852\pi\) | |||||||
\(684\) | −7.34847 | −0.280976 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 7.34847 | − | 17.0000i | 0.280566 | − | 0.649063i | ||||
\(687\) | 27.0000 | − | 27.0000i | 1.03011 | − | 1.03011i | ||||
\(688\) | −4.00000 | −0.152499 | ||||||||
\(689\) | 14.6969 | 0.559909 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.7423i | 1.39774i | 0.715246 | + | 0.698872i | \(0.246314\pi\) | ||||
−0.715246 | + | 0.698872i | \(0.753686\pi\) | |||||||
\(692\) | −22.0454 | −0.838041 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.0000 | 0.455514 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7.34847 | − | 7.34847i | −0.278543 | − | 0.278543i | ||||
\(697\) | 24.0000 | 0.909065 | ||||||||
\(698\) | 2.44949 | 0.0927146 | ||||||||
\(699\) | −29.3939 | + | 29.3939i | −1.11178 | + | 1.11178i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 30.0000i | − | 1.13308i | −0.824033 | − | 0.566542i | \(-0.808281\pi\) | ||
0.824033 | − | 0.566542i | \(-0.191719\pi\) | |||||||
\(702\) | 9.00000 | − | 9.00000i | 0.339683 | − | 0.339683i | ||||
\(703\) | − | 4.89898i | − | 0.184769i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.79796i | 0.368751i | ||||||||
\(707\) | 7.34847 | + | 18.0000i | 0.276368 | + | 0.676960i | ||||
\(708\) | −15.0000 | − | 15.0000i | −0.563735 | − | 0.563735i | ||||
\(709\) | 10.0000 | 0.375558 | 0.187779 | − | 0.982211i | \(-0.439871\pi\) | ||||
0.187779 | + | 0.982211i | \(0.439871\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 30.0000i | − | 1.12509i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −20.6969 | − | 8.69694i | −0.774563 | − | 0.325475i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 24.0000i | 0.896922i | ||||||||
\(717\) | 7.34847 | − | 7.34847i | 0.274434 | − | 0.274434i | ||||
\(718\) | −6.00000 | −0.223918 | ||||||||
\(719\) | 24.4949 | 0.913506 | 0.456753 | − | 0.889594i | \(-0.349012\pi\) | ||||
0.456753 | + | 0.889594i | \(0.349012\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.0000 | + | 9.79796i | −0.893807 | + | 0.364895i | ||||
\(722\) | 13.0000i | 0.483810i | ||||||||
\(723\) | −30.0000 | + | 30.0000i | −1.11571 | + | 1.11571i | ||||
\(724\) | 12.2474i | 0.455173i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 13.4722 | − | 13.4722i | 0.500000 | − | 0.500000i | ||||
\(727\) | 29.3939i | 1.09016i | 0.838385 | + | 0.545079i | \(0.183500\pi\) | ||||
−0.838385 | + | 0.545079i | \(0.816500\pi\) | |||||||
\(728\) | −2.44949 | − | 6.00000i | −0.0907841 | − | 0.222375i | ||||
\(729\) | − | 27.0000i | − | 1.00000i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19.5959 | 0.724781 | ||||||||
\(732\) | −15.0000 | + | 15.0000i | −0.554416 | + | 0.554416i | ||||
\(733\) | 22.0454i | 0.814266i | 0.913369 | + | 0.407133i | \(0.133471\pi\) | ||||
−0.913369 | + | 0.407133i | \(0.866529\pi\) | |||||||
\(734\) | −4.89898 | −0.180825 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.00000 | −0.221163 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 14.6969 | 0.541002 | ||||||||
\(739\) | 20.0000 | 0.735712 | 0.367856 | − | 0.929883i | \(-0.380092\pi\) | ||||
0.367856 | + | 0.929883i | \(0.380092\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.34847 | + | 7.34847i | 0.269953 | + | 0.269953i | ||||
\(742\) | −6.00000 | − | 14.6969i | −0.220267 | − | 0.539542i | ||||
\(743\) | 6.00000i | 0.220119i | 0.993925 | + | 0.110059i | \(0.0351041\pi\) | ||||
−0.993925 | + | 0.110059i | \(0.964896\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 14.0000i | − | 0.512576i | ||||||
\(747\) | − | 7.34847i | − | 0.268866i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 29.3939 | − | 12.0000i | 1.07403 | − | 0.438470i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.00000 | −0.291924 | −0.145962 | − | 0.989290i | \(-0.546628\pi\) | ||||
−0.145962 | + | 0.989290i | \(0.546628\pi\) | |||||||
\(752\) | −4.89898 | −0.178647 | ||||||||
\(753\) | 21.0000 | + | 21.0000i | 0.765283 | + | 0.765283i | ||||
\(754\) | 14.6969i | 0.535231i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −12.6742 | − | 5.32577i | −0.460957 | − | 0.193696i | ||||
\(757\) | 2.00000 | 0.0726912 | 0.0363456 | − | 0.999339i | \(-0.488428\pi\) | ||||
0.0363456 | + | 0.999339i | \(0.488428\pi\) | |||||||
\(758\) | − | 20.0000i | − | 0.726433i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.89898 | −0.177588 | −0.0887939 | − | 0.996050i | \(-0.528301\pi\) | ||||
−0.0887939 | + | 0.996050i | \(0.528301\pi\) | |||||||
\(762\) | −9.79796 | + | 9.79796i | −0.354943 | + | 0.354943i | ||||
\(763\) | 10.0000 | + | 24.4949i | 0.362024 | + | 0.886775i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 34.2929i | 1.23905i | ||||||||
\(767\) | 30.0000i | 1.08324i | ||||||||
\(768\) | −1.22474 | − | 1.22474i | −0.0441942 | − | 0.0441942i | ||||
\(769\) | 34.2929i | 1.23663i | 0.785930 | + | 0.618316i | \(0.212185\pi\) | ||||
−0.785930 | + | 0.618316i | \(0.787815\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 36.0000 | + | 36.0000i | 1.29651 | + | 1.29651i | ||||
\(772\) | 4.00000 | 0.143963 | ||||||||
\(773\) | −26.9444 | −0.969122 | −0.484561 | − | 0.874757i | \(-0.661021\pi\) | ||||
−0.484561 | + | 0.874757i | \(0.661021\pi\) | |||||||
\(774\) | 12.0000 | 0.431331 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.89898 | 0.175863 | ||||||||
\(777\) | 3.55051 | − | 8.44949i | 0.127374 | − | 0.303124i | ||||
\(778\) | −6.00000 | −0.215110 | ||||||||
\(779\) | 12.0000i | 0.429945i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 29.3939 | 1.05112 | ||||||||
\(783\) | 22.0454 | + | 22.0454i | 0.787839 | + | 0.787839i | ||||
\(784\) | −5.00000 | + | 4.89898i | −0.178571 | + | 0.174964i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 9.00000 | − | 9.00000i | 0.321019 | − | 0.321019i | ||||
\(787\) | − | 31.8434i | − | 1.13509i | −0.823341 | − | 0.567547i | \(-0.807893\pi\) | ||
0.823341 | − | 0.567547i | \(-0.192107\pi\) | |||||||
\(788\) | − | 18.0000i | − | 0.641223i | ||||||
\(789\) | −29.3939 | + | 29.3939i | −1.04645 | + | 1.04645i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.6969 | + | 6.00000i | −0.522563 | + | 0.213335i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 30.0000 | 1.06533 | ||||||||
\(794\) | 7.34847 | 0.260787 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 9.79796i | − | 0.347279i | ||||||
\(797\) | 7.34847 | 0.260296 | 0.130148 | − | 0.991495i | \(-0.458455\pi\) | ||||
0.130148 | + | 0.991495i | \(0.458455\pi\) | |||||||
\(798\) | 4.34847 | − | 10.3485i | 0.153934 | − | 0.366332i | ||||
\(799\) | 24.0000 | 0.849059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 30.0000 | 1.05934 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −9.79796 | − | 9.79796i | −0.345547 | − | 0.345547i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.0000 | + | 15.0000i | 0.528025 | + | 0.528025i | ||||
\(808\) | − | 7.34847i | − | 0.258518i | ||||||
\(809\) | 6.00000i | 0.210949i | 0.994422 | + | 0.105474i | \(0.0336361\pi\) | ||||
−0.994422 | + | 0.105474i | \(0.966364\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.7423i | 1.29020i | 0.764099 | + | 0.645099i | \(0.223184\pi\) | ||||
−0.764099 | + | 0.645099i | \(0.776816\pi\) | |||||||
\(812\) | 14.6969 | − | 6.00000i | 0.515761 | − | 0.210559i | ||||
\(813\) | 30.0000 | − | 30.0000i | 1.05215 | − | 1.05215i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 6.00000 | + | 6.00000i | 0.210042 | + | 0.210042i | ||||
\(817\) | 9.79796i | 0.342787i | ||||||||
\(818\) | −34.2929 | −1.19902 | ||||||||
\(819\) | 7.34847 | + | 18.0000i | 0.256776 | + | 0.628971i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.0000i | 1.04701i | 0.852023 | + | 0.523504i | \(0.175375\pi\) | ||||
−0.852023 | + | 0.523504i | \(0.824625\pi\) | |||||||
\(822\) | −14.6969 | − | 14.6969i | −0.512615 | − | 0.512615i | ||||
\(823\) | −14.0000 | −0.488009 | −0.244005 | − | 0.969774i | \(-0.578461\pi\) | ||||
−0.244005 | + | 0.969774i | \(0.578461\pi\) | |||||||
\(824\) | 9.79796 | 0.341328 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 30.0000 | − | 12.2474i | 1.04383 | − | 0.426143i | ||||
\(827\) | − | 12.0000i | − | 0.417281i | −0.977992 | − | 0.208640i | \(-0.933096\pi\) | ||
0.977992 | − | 0.208640i | \(-0.0669038\pi\) | |||||||
\(828\) | 18.0000 | 0.625543 | ||||||||
\(829\) | − | 26.9444i | − | 0.935817i | −0.883777 | − | 0.467909i | \(-0.845008\pi\) | ||
0.883777 | − | 0.467909i | \(-0.154992\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26.9444 | − | 26.9444i | −0.934690 | − | 0.934690i | ||||
\(832\) | 2.44949i | 0.0849208i | ||||||||
\(833\) | 24.4949 | − | 24.0000i | 0.848698 | − | 0.831551i | ||||
\(834\) | −3.00000 | − | 3.00000i | −0.103882 | − | 0.103882i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 12.2474i | 0.423081i | ||||||||
\(839\) | −24.4949 | −0.845658 | −0.422829 | − | 0.906210i | \(-0.638963\pi\) | ||||
−0.422829 | + | 0.906210i | \(0.638963\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.00000 | −0.241379 | ||||||||
\(842\) | 2.00000i | 0.0689246i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.00000 | 0.275371 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 14.6969 | 0.505291 | ||||||||
\(847\) | 11.0000 | + | 26.9444i | 0.377964 | + | 0.925820i | ||||
\(848\) | 6.00000i | 0.206041i | ||||||||
\(849\) | 27.0000 | − | 27.0000i | 0.926638 | − | 0.926638i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.0000i | 0.411355i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 2.44949i | − | 0.0838689i | −0.999120 | − | 0.0419345i | \(-0.986648\pi\) | ||
0.999120 | − | 0.0419345i | \(-0.0133521\pi\) | |||||||
\(854\) | −12.2474 | − | 30.0000i | −0.419099 | − | 1.02658i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.0000 | −0.410152 | ||||||||
\(857\) | −4.89898 | −0.167346 | −0.0836730 | − | 0.996493i | \(-0.526665\pi\) | ||||
−0.0836730 | + | 0.996493i | \(0.526665\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 26.9444i | − | 0.919331i | −0.888092 | − | 0.459665i | \(-0.847969\pi\) | ||
0.888092 | − | 0.459665i | \(-0.152031\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.69694 | + | 20.6969i | −0.296391 | + | 0.705350i | ||||
\(862\) | 30.0000 | 1.02180 | ||||||||
\(863\) | − | 24.0000i | − | 0.816970i | −0.912765 | − | 0.408485i | \(-0.866057\pi\) | ||
0.912765 | − | 0.408485i | \(-0.133943\pi\) | |||||||
\(864\) | 3.67423 | + | 3.67423i | 0.125000 | + | 0.125000i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 14.6969 | 0.499422 | ||||||||
\(867\) | −8.57321 | − | 8.57321i | −0.291162 | − | 0.291162i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.5959i | 0.663982i | ||||||||
\(872\) | − | 10.0000i | − | 0.338643i | ||||||
\(873\) | −14.6969 | −0.497416 | ||||||||
\(874\) | 14.6969i | 0.497131i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12.0000 | + | 12.0000i | −0.405442 | + | 0.405442i | ||||
\(877\) | 22.0000 | 0.742887 | 0.371444 | − | 0.928456i | \(-0.378863\pi\) | ||||
0.371444 | + | 0.928456i | \(0.378863\pi\) | |||||||
\(878\) | 14.6969 | 0.495998 | ||||||||
\(879\) | 3.00000 | + | 3.00000i | 0.101187 | + | 0.101187i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.3939 | −0.990305 | −0.495152 | − | 0.868806i | \(-0.664888\pi\) | ||||
−0.495152 | + | 0.868806i | \(0.664888\pi\) | |||||||
\(882\) | 15.0000 | − | 14.6969i | 0.505076 | − | 0.494872i | ||||
\(883\) | 56.0000 | 1.88455 | 0.942275 | − | 0.334840i | \(-0.108682\pi\) | ||||
0.942275 | + | 0.334840i | \(0.108682\pi\) | |||||||
\(884\) | − | 12.0000i | − | 0.403604i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −36.0000 | −1.20944 | ||||||||
\(887\) | −4.89898 | −0.164492 | −0.0822458 | − | 0.996612i | \(-0.526209\pi\) | ||||
−0.0822458 | + | 0.996612i | \(0.526209\pi\) | |||||||
\(888\) | −2.44949 | + | 2.44949i | −0.0821995 | + | 0.0821995i | ||||
\(889\) | −8.00000 | − | 19.5959i | −0.268311 | − | 0.657226i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 14.6969i | 0.492090i | ||||||||
\(893\) | 12.0000i | 0.401565i | ||||||||
\(894\) | 7.34847 | + | 7.34847i | 0.245770 | + | 0.245770i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.44949 | − | 1.00000i | 0.0818317 | − | 0.0334077i | ||||
\(897\) | −18.0000 | − | 18.0000i | −0.601003 | − | 0.601003i | ||||
\(898\) | −36.0000 | −1.20134 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 29.3939i | − | 0.979252i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.10102 | + | 16.8990i | −0.236307 | + | 0.562363i | ||||
\(904\) | 6.00000 | 0.199557 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −9.79796 | + | 9.79796i | −0.325515 | + | 0.325515i | ||||
\(907\) | −28.0000 | −0.929725 | −0.464862 | − | 0.885383i | \(-0.653896\pi\) | ||||
−0.464862 | + | 0.885383i | \(0.653896\pi\) | |||||||
\(908\) | −7.34847 | −0.243868 | ||||||||
\(909\) | 22.0454i | 0.731200i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 30.0000i | − | 0.993944i | −0.867766 | − | 0.496972i | \(-0.834445\pi\) | ||
0.867766 | − | 0.496972i | \(-0.165555\pi\) | |||||||
\(912\) | −3.00000 | + | 3.00000i | −0.0993399 | + | 0.0993399i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − | 28.0000i | − | 0.926158i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 22.0454i | − | 0.728401i | ||||||
\(917\) | 7.34847 | + | 18.0000i | 0.242668 | + | 0.594412i | ||||
\(918\) | −18.0000 | − | 18.0000i | −0.594089 | − | 0.594089i | ||||
\(919\) | 10.0000 | 0.329870 | 0.164935 | − | 0.986304i | \(-0.447259\pi\) | ||||
0.164935 | + | 0.986304i | \(0.447259\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.00000 | + | 9.00000i | −0.296560 | + | 0.296560i | ||||
\(922\) | 31.8434i | 1.04871i | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 14.0000i | − | 0.460069i | ||||||
\(927\) | −29.3939 | −0.965422 | ||||||||
\(928\) | −6.00000 | −0.196960 | ||||||||
\(929\) | −24.4949 | −0.803652 | −0.401826 | − | 0.915716i | \(-0.631624\pi\) | ||||
−0.401826 | + | 0.915716i | \(0.631624\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.0000 | + | 12.2474i | 0.393284 | + | 0.401394i | ||||
\(932\) | 24.0000i | 0.786146i | ||||||||
\(933\) | −24.0000 | − | 24.0000i | −0.785725 | − | 0.785725i | ||||
\(934\) | 7.34847i | 0.240449i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − | 7.34847i | − | 0.240192i | ||||||
\(937\) | − | 19.5959i | − | 0.640171i | −0.947389 | − | 0.320085i | \(-0.896288\pi\) | ||
0.947389 | − | 0.320085i | \(-0.103712\pi\) | |||||||
\(938\) | 19.5959 | − | 8.00000i | 0.639829 | − | 0.261209i | ||||
\(939\) | 42.0000 | − | 42.0000i | 1.37062 | − | 1.37062i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.8434 | 1.03806 | 0.519032 | − | 0.854755i | \(-0.326293\pi\) | ||||
0.519032 | + | 0.854755i | \(0.326293\pi\) | |||||||
\(942\) | −9.00000 | − | 9.00000i | −0.293236 | − | 0.293236i | ||||
\(943\) | − | 29.3939i | − | 0.957196i | ||||||
\(944\) | −12.2474 | −0.398621 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 12.0000i | − | 0.389948i | −0.980808 | − | 0.194974i | \(-0.937538\pi\) | ||
0.980808 | − | 0.194974i | \(-0.0624622\pi\) | |||||||
\(948\) | −12.2474 | − | 12.2474i | −0.397779 | − | 0.397779i | ||||
\(949\) | 24.0000 | 0.779073 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.0454 | − | 22.0454i | 0.714871 | − | 0.714871i | ||||
\(952\) | −12.0000 | + | 4.89898i | −0.388922 | + | 0.158777i | ||||
\(953\) | 36.0000i | 1.16615i | 0.812417 | + | 0.583077i | \(0.198151\pi\) | ||||
−0.812417 | + | 0.583077i | \(0.801849\pi\) | |||||||
\(954\) | − | 18.0000i | − | 0.582772i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 6.00000i | − | 0.194054i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 24.4949i | 0.791394i | ||||||||
\(959\) | 29.3939 | − | 12.0000i | 0.949178 | − | 0.387500i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.0000 | 1.00000 | ||||||||
\(962\) | 4.89898 | 0.157949 | ||||||||
\(963\) | 36.0000 | 1.16008 | ||||||||
\(964\) | 24.4949i | 0.788928i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −10.6515 | + | 25.3485i | −0.342707 | + | 0.815574i | ||||
\(967\) | −8.00000 | −0.257263 | −0.128631 | − | 0.991692i | \(-0.541058\pi\) | ||||
−0.128631 | + | 0.991692i | \(0.541058\pi\) | |||||||
\(968\) | − | 11.0000i | − | 0.353553i | ||||||
\(969\) | 14.6969 | − | 14.6969i | 0.472134 | − | 0.472134i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41.6413 | −1.33633 | −0.668167 | − | 0.744011i | \(-0.732921\pi\) | ||||
−0.668167 | + | 0.744011i | \(0.732921\pi\) | |||||||
\(972\) | −11.0227 | − | 11.0227i | −0.353553 | − | 0.353553i | ||||
\(973\) | 6.00000 | − | 2.44949i | 0.192351 | − | 0.0785270i | ||||
\(974\) | 32.0000i | 1.02535i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.2474i | 0.392031i | ||||||||
\(977\) | − | 12.0000i | − | 0.383914i | −0.981403 | − | 0.191957i | \(-0.938517\pi\) | ||
0.981403 | − | 0.191957i | \(-0.0614834\pi\) | |||||||
\(978\) | 19.5959 | − | 19.5959i | 0.626608 | − | 0.626608i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 30.0000i | 0.957826i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 34.2929 | 1.09377 | 0.546886 | − | 0.837207i | \(-0.315813\pi\) | ||||
0.546886 | + | 0.837207i | \(0.315813\pi\) | |||||||
\(984\) | 6.00000 | − | 6.00000i | 0.191273 | − | 0.191273i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 29.3939 | 0.936092 | ||||||||
\(987\) | −8.69694 | + | 20.6969i | −0.276827 | + | 0.658791i | ||||
\(988\) | 6.00000 | 0.190885 | ||||||||
\(989\) | − | 24.0000i | − | 0.763156i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.0000 | −1.20711 | −0.603555 | − | 0.797321i | \(-0.706250\pi\) | ||||
−0.603555 | + | 0.797321i | \(0.706250\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.79796 | + | 9.79796i | 0.310929 | + | 0.310929i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.00000 | − | 3.00000i | −0.0950586 | − | 0.0950586i | ||||
\(997\) | − | 7.34847i | − | 0.232728i | −0.993207 | − | 0.116364i | \(-0.962876\pi\) | ||
0.993207 | − | 0.116364i | \(-0.0371240\pi\) | |||||||
\(998\) | − | 20.0000i | − | 0.633089i | ||||||
\(999\) | 7.34847 | − | 7.34847i | 0.232495 | − | 0.232495i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))