Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,2,Mod(257,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([10, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.p (of order \(12\), degree \(4\), 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: | \(3.59326809096\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 293.2 | ||
Root | \(-0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.293 |
Dual form | 450.2.p.g.407.2 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.258819 | − | 0.965926i | 0.183013 | − | 0.683013i | ||||
\(3\) | 1.22474 | + | 1.22474i | 0.707107 | + | 0.707107i | ||||
\(4\) | −0.866025 | − | 0.500000i | −0.433013 | − | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.50000 | − | 0.866025i | 0.612372 | − | 0.353553i | ||||
\(7\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 3.00000i | 1.00000i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.00000 | − | 1.73205i | 0.904534 | − | 0.522233i | 0.0258656 | − | 0.999665i | \(-0.491766\pi\) |
0.878668 | + | 0.477432i | \(0.158432\pi\) | |||||||
\(12\) | −0.448288 | − | 1.67303i | −0.129410 | − | 0.482963i | ||||
\(13\) | 3.34607 | − | 0.896575i | 0.928032 | − | 0.248665i | 0.237016 | − | 0.971506i | \(-0.423830\pi\) |
0.691015 | + | 0.722840i | \(0.257164\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | 4.24264 | + | 4.24264i | 1.02899 | + | 1.02899i | 0.999567 | + | 0.0294245i | \(0.00936746\pi\) |
0.0294245 | + | 0.999567i | \(0.490633\pi\) | |||||||
\(18\) | 2.89778 | + | 0.776457i | 0.683013 | + | 0.183013i | ||||
\(19\) | − | 5.00000i | − | 1.14708i | −0.819178 | − | 0.573539i | \(-0.805570\pi\) | ||
0.819178 | − | 0.573539i | \(-0.194430\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.896575 | − | 3.34607i | −0.191151 | − | 0.713384i | ||||
\(23\) | 1.55291 | + | 5.79555i | 0.323805 | + | 1.20846i | 0.915508 | + | 0.402300i | \(0.131789\pi\) |
−0.591703 | + | 0.806156i | \(0.701544\pi\) | |||||||
\(24\) | −1.73205 | −0.353553 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 3.46410i | − | 0.679366i | ||||||
\(27\) | −3.67423 | + | 3.67423i | −0.707107 | + | 0.707107i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.46410 | − | 6.00000i | −0.643268 | − | 1.11417i | −0.984699 | − | 0.174265i | \(-0.944245\pi\) |
0.341431 | − | 0.939907i | \(-0.389088\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | + | 3.46410i | −0.359211 | + | 0.622171i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) |
0.628619 | + | 0.777714i | \(0.283621\pi\) | |||||||
\(32\) | 0.965926 | − | 0.258819i | 0.170753 | − | 0.0457532i | ||||
\(33\) | 5.79555 | + | 1.55291i | 1.00888 | + | 0.270328i | ||||
\(34\) | 5.19615 | − | 3.00000i | 0.891133 | − | 0.514496i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.50000 | − | 2.59808i | 0.250000 | − | 0.433013i | ||||
\(37\) | −4.89898 | + | 4.89898i | −0.805387 | + | 0.805387i | −0.983932 | − | 0.178545i | \(-0.942861\pi\) |
0.178545 | + | 0.983932i | \(0.442861\pi\) | |||||||
\(38\) | −4.82963 | − | 1.29410i | −0.783469 | − | 0.209930i | ||||
\(39\) | 5.19615 | + | 3.00000i | 0.832050 | + | 0.480384i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.50000 | − | 0.866025i | −0.234261 | − | 0.135250i | 0.378275 | − | 0.925693i | \(-0.376517\pi\) |
−0.612536 | + | 0.790443i | \(0.709851\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.13801 | − | 11.7112i | 0.478543 | − | 1.78595i | −0.128984 | − | 0.991647i | \(-0.541172\pi\) |
0.607527 | − | 0.794299i | \(-0.292162\pi\) | |||||||
\(44\) | −3.46410 | −0.522233 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.00000 | 0.884652 | ||||||||
\(47\) | −1.55291 | + | 5.79555i | −0.226516 | + | 0.845369i | 0.755276 | + | 0.655407i | \(0.227503\pi\) |
−0.981792 | + | 0.189961i | \(0.939164\pi\) | |||||||
\(48\) | −0.448288 | + | 1.67303i | −0.0647048 | + | 0.241481i | ||||
\(49\) | −6.06218 | − | 3.50000i | −0.866025 | − | 0.500000i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.3923i | 1.45521i | ||||||||
\(52\) | −3.34607 | − | 0.896575i | −0.464016 | − | 0.124333i | ||||
\(53\) | −4.24264 | + | 4.24264i | −0.582772 | + | 0.582772i | −0.935664 | − | 0.352892i | \(-0.885198\pi\) |
0.352892 | + | 0.935664i | \(0.385198\pi\) | |||||||
\(54\) | 2.59808 | + | 4.50000i | 0.353553 | + | 0.612372i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.12372 | − | 6.12372i | 0.811107 | − | 0.811107i | ||||
\(58\) | −6.69213 | + | 1.79315i | −0.878720 | + | 0.235452i | ||||
\(59\) | 0.866025 | − | 1.50000i | 0.112747 | − | 0.195283i | −0.804130 | − | 0.594454i | \(-0.797368\pi\) |
0.916877 | + | 0.399170i | \(0.130702\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.00000 | − | 6.92820i | −0.512148 | − | 0.887066i | −0.999901 | − | 0.0140840i | \(-0.995517\pi\) |
0.487753 | − | 0.872982i | \(-0.337817\pi\) | |||||||
\(62\) | 2.82843 | + | 2.82843i | 0.359211 | + | 0.359211i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.00000 | − | 5.19615i | 0.369274 | − | 0.639602i | ||||
\(67\) | −2.24144 | − | 8.36516i | −0.273835 | − | 1.02197i | −0.956618 | − | 0.291346i | \(-0.905897\pi\) |
0.682783 | − | 0.730622i | \(-0.260770\pi\) | |||||||
\(68\) | −1.55291 | − | 5.79555i | −0.188319 | − | 0.702814i | ||||
\(69\) | −5.19615 | + | 9.00000i | −0.625543 | + | 1.08347i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.92820i | 0.822226i | 0.911584 | + | 0.411113i | \(0.134860\pi\) | ||||
−0.911584 | + | 0.411113i | \(0.865140\pi\) | |||||||
\(72\) | −2.12132 | − | 2.12132i | −0.250000 | − | 0.250000i | ||||
\(73\) | −8.57321 | − | 8.57321i | −1.00342 | − | 1.00342i | −0.999994 | − | 0.00342468i | \(-0.998910\pi\) |
−0.00342468 | − | 0.999994i | \(-0.501090\pi\) | |||||||
\(74\) | 3.46410 | + | 6.00000i | 0.402694 | + | 0.697486i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.50000 | + | 4.33013i | −0.286770 | + | 0.496700i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.24264 | − | 4.24264i | 0.480384 | − | 0.480384i | ||||
\(79\) | 12.1244 | − | 7.00000i | 1.36410 | − | 0.787562i | 0.373930 | − | 0.927457i | \(-0.378010\pi\) |
0.990166 | + | 0.139895i | \(0.0446766\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | −1.22474 | + | 1.22474i | −0.135250 | + | 0.135250i | ||||
\(83\) | −8.69333 | − | 2.32937i | −0.954217 | − | 0.255682i | −0.252066 | − | 0.967710i | \(-0.581110\pi\) |
−0.702151 | + | 0.712028i | \(0.747777\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −10.5000 | − | 6.06218i | −1.13224 | − | 0.653701i | ||||
\(87\) | 3.10583 | − | 11.5911i | 0.332980 | − | 1.24270i | ||||
\(88\) | −0.896575 | + | 3.34607i | −0.0955753 | + | 0.356692i | ||||
\(89\) | −12.1244 | −1.28518 | −0.642590 | − | 0.766211i | \(-0.722140\pi\) | ||||
−0.642590 | + | 0.766211i | \(0.722140\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.55291 | − | 5.79555i | 0.161903 | − | 0.604228i | ||||
\(93\) | −6.69213 | + | 1.79315i | −0.693942 | + | 0.185941i | ||||
\(94\) | 5.19615 | + | 3.00000i | 0.535942 | + | 0.309426i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.50000 | + | 0.866025i | 0.153093 | + | 0.0883883i | ||||
\(97\) | 5.01910 | + | 1.34486i | 0.509612 | + | 0.136550i | 0.504457 | − | 0.863437i | \(-0.331693\pi\) |
0.00515471 | + | 0.999987i | \(0.498359\pi\) | |||||||
\(98\) | −4.94975 | + | 4.94975i | −0.500000 | + | 0.500000i | ||||
\(99\) | 5.19615 | + | 9.00000i | 0.522233 | + | 0.904534i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.00000 | − | 1.73205i | 0.298511 | − | 0.172345i | −0.343263 | − | 0.939239i | \(-0.611532\pi\) |
0.641774 | + | 0.766894i | \(0.278199\pi\) | |||||||
\(102\) | 10.0382 | + | 2.68973i | 0.993929 | + | 0.266323i | ||||
\(103\) | 3.34607 | − | 0.896575i | 0.329698 | − | 0.0883422i | −0.0901732 | − | 0.995926i | \(-0.528742\pi\) |
0.419871 | + | 0.907584i | \(0.362075\pi\) | |||||||
\(104\) | −1.73205 | + | 3.00000i | −0.169842 | + | 0.294174i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.00000 | + | 5.19615i | 0.291386 | + | 0.504695i | ||||
\(107\) | 2.12132 | + | 2.12132i | 0.205076 | + | 0.205076i | 0.802171 | − | 0.597095i | \(-0.203678\pi\) |
−0.597095 | + | 0.802171i | \(0.703678\pi\) | |||||||
\(108\) | 5.01910 | − | 1.34486i | 0.482963 | − | 0.129410i | ||||
\(109\) | 20.0000i | 1.91565i | 0.287348 | + | 0.957826i | \(0.407226\pi\) | ||||
−0.287348 | + | 0.957826i | \(0.592774\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.0000 | −1.13899 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.88229 | + | 14.4889i | 0.365215 | + | 1.36300i | 0.867129 | + | 0.498083i | \(0.165962\pi\) |
−0.501915 | + | 0.864917i | \(0.667371\pi\) | |||||||
\(114\) | −4.33013 | − | 7.50000i | −0.405554 | − | 0.702439i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.92820i | 0.643268i | ||||||||
\(117\) | 2.68973 | + | 10.0382i | 0.248665 | + | 0.928032i | ||||
\(118\) | −1.22474 | − | 1.22474i | −0.112747 | − | 0.112747i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.500000 | − | 0.866025i | 0.0454545 | − | 0.0787296i | ||||
\(122\) | −7.72741 | + | 2.07055i | −0.699607 | + | 0.187459i | ||||
\(123\) | −0.776457 | − | 2.89778i | −0.0700108 | − | 0.261284i | ||||
\(124\) | 3.46410 | − | 2.00000i | 0.311086 | − | 0.179605i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.34847 | + | 7.34847i | −0.652071 | + | 0.652071i | −0.953491 | − | 0.301420i | \(-0.902539\pi\) |
0.301420 | + | 0.953491i | \(0.402539\pi\) | |||||||
\(128\) | −0.965926 | − | 0.258819i | −0.0853766 | − | 0.0228766i | ||||
\(129\) | 18.1865 | − | 10.5000i | 1.60123 | − | 0.924473i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.00000 | + | 1.73205i | 0.262111 | + | 0.151330i | 0.625297 | − | 0.780387i | \(-0.284978\pi\) |
−0.363186 | + | 0.931717i | \(0.618311\pi\) | |||||||
\(132\) | −4.24264 | − | 4.24264i | −0.369274 | − | 0.369274i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −8.66025 | −0.748132 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.00000 | −0.514496 | ||||||||
\(137\) | 2.32937 | − | 8.69333i | 0.199012 | − | 0.742722i | −0.792180 | − | 0.610287i | \(-0.791054\pi\) |
0.991192 | − | 0.132434i | \(-0.0422793\pi\) | |||||||
\(138\) | 7.34847 | + | 7.34847i | 0.625543 | + | 0.625543i | ||||
\(139\) | −3.46410 | − | 2.00000i | −0.293821 | − | 0.169638i | 0.345843 | − | 0.938293i | \(-0.387593\pi\) |
−0.639664 | + | 0.768655i | \(0.720926\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.00000 | + | 5.19615i | −0.757937 | + | 0.437595i | ||||
\(142\) | 6.69213 | + | 1.79315i | 0.561591 | + | 0.150478i | ||||
\(143\) | 8.48528 | − | 8.48528i | 0.709575 | − | 0.709575i | ||||
\(144\) | −2.59808 | + | 1.50000i | −0.216506 | + | 0.125000i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −10.5000 | + | 6.06218i | −0.868986 | + | 0.501709i | ||||
\(147\) | −3.13801 | − | 11.7112i | −0.258819 | − | 0.965926i | ||||
\(148\) | 6.69213 | − | 1.79315i | 0.550090 | − | 0.147396i | ||||
\(149\) | −5.19615 | + | 9.00000i | −0.425685 | + | 0.737309i | −0.996484 | − | 0.0837813i | \(-0.973300\pi\) |
0.570799 | + | 0.821090i | \(0.306634\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | − | 13.8564i | −0.651031 | − | 1.12762i | −0.982873 | − | 0.184284i | \(-0.941004\pi\) |
0.331842 | − | 0.943335i | \(-0.392330\pi\) | |||||||
\(152\) | 3.53553 | + | 3.53553i | 0.286770 | + | 0.286770i | ||||
\(153\) | −12.7279 | + | 12.7279i | −1.02899 | + | 1.02899i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.00000 | − | 5.19615i | −0.240192 | − | 0.416025i | ||||
\(157\) | 0.896575 | + | 3.34607i | 0.0715545 | + | 0.267045i | 0.992430 | − | 0.122812i | \(-0.0391911\pi\) |
−0.920875 | + | 0.389857i | \(0.872524\pi\) | |||||||
\(158\) | −3.62347 | − | 13.5230i | −0.288268 | − | 1.07583i | ||||
\(159\) | −10.3923 | −0.824163 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.32937 | + | 8.69333i | −0.183013 | + | 0.683013i | ||||
\(163\) | −1.22474 | − | 1.22474i | −0.0959294 | − | 0.0959294i | 0.657513 | − | 0.753443i | \(-0.271608\pi\) |
−0.753443 | + | 0.657513i | \(0.771608\pi\) | |||||||
\(164\) | 0.866025 | + | 1.50000i | 0.0676252 | + | 0.117130i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.50000 | + | 7.79423i | −0.349268 | + | 0.604949i | ||||
\(167\) | −11.5911 | + | 3.10583i | −0.896947 | + | 0.240336i | −0.677705 | − | 0.735334i | \(-0.737025\pi\) |
−0.219242 | + | 0.975670i | \(0.570359\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.866025 | + | 0.500000i | −0.0666173 | + | 0.0384615i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 15.0000 | 1.14708 | ||||||||
\(172\) | −8.57321 | + | 8.57321i | −0.653701 | + | 0.653701i | ||||
\(173\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(174\) | −10.3923 | − | 6.00000i | −0.787839 | − | 0.454859i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.00000 | + | 1.73205i | 0.226134 | + | 0.130558i | ||||
\(177\) | 2.89778 | − | 0.776457i | 0.217810 | − | 0.0583621i | ||||
\(178\) | −3.13801 | + | 11.7112i | −0.235204 | + | 0.877794i | ||||
\(179\) | 22.5167 | 1.68297 | 0.841487 | − | 0.540277i | \(-0.181681\pi\) | ||||
0.841487 | + | 0.540277i | \(0.181681\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.0000 | 1.18927 | 0.594635 | − | 0.803996i | \(-0.297296\pi\) | ||||
0.594635 | + | 0.803996i | \(0.297296\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.58630 | − | 13.3843i | 0.265107 | − | 0.989393i | ||||
\(184\) | −5.19615 | − | 3.00000i | −0.383065 | − | 0.221163i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 6.92820i | 0.508001i | ||||||||
\(187\) | 20.0764 | + | 5.37945i | 1.46813 | + | 0.393385i | ||||
\(188\) | 4.24264 | − | 4.24264i | 0.309426 | − | 0.309426i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.0000 | − | 12.1244i | 1.51951 | − | 0.877288i | 0.519771 | − | 0.854306i | \(-0.326017\pi\) |
0.999736 | − | 0.0229818i | \(-0.00731599\pi\) | |||||||
\(192\) | 1.22474 | − | 1.22474i | 0.0883883 | − | 0.0883883i | ||||
\(193\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(194\) | 2.59808 | − | 4.50000i | 0.186531 | − | 0.323081i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.50000 | + | 6.06218i | 0.250000 | + | 0.433013i | ||||
\(197\) | −16.9706 | − | 16.9706i | −1.20910 | − | 1.20910i | −0.971318 | − | 0.237785i | \(-0.923579\pi\) |
−0.237785 | − | 0.971318i | \(-0.576421\pi\) | |||||||
\(198\) | 10.0382 | − | 2.68973i | 0.713384 | − | 0.191151i | ||||
\(199\) | 8.00000i | 0.567105i | 0.958957 | + | 0.283552i | \(0.0915130\pi\) | ||||
−0.958957 | + | 0.283552i | \(0.908487\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.50000 | − | 12.9904i | 0.529009 | − | 0.916271i | ||||
\(202\) | −0.896575 | − | 3.34607i | −0.0630828 | − | 0.235428i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 5.19615 | − | 9.00000i | 0.363803 | − | 0.630126i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 3.46410i | − | 0.241355i | ||||||
\(207\) | −17.3867 | + | 4.65874i | −1.20846 | + | 0.323805i | ||||
\(208\) | 2.44949 | + | 2.44949i | 0.169842 | + | 0.169842i | ||||
\(209\) | −8.66025 | − | 15.0000i | −0.599042 | − | 1.03757i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.50000 | − | 11.2583i | 0.447478 | − | 0.775055i | −0.550743 | − | 0.834675i | \(-0.685655\pi\) |
0.998221 | + | 0.0596196i | \(0.0189888\pi\) | |||||||
\(212\) | 5.79555 | − | 1.55291i | 0.398040 | − | 0.106655i | ||||
\(213\) | −8.48528 | + | 8.48528i | −0.581402 | + | 0.581402i | ||||
\(214\) | 2.59808 | − | 1.50000i | 0.177601 | − | 0.102538i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 5.19615i | − | 0.353553i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 19.3185 | + | 5.17638i | 1.30842 | + | 0.350589i | ||||
\(219\) | − | 21.0000i | − | 1.41905i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.0000 | + | 10.3923i | 1.21081 | + | 0.699062i | ||||
\(222\) | −3.10583 | + | 11.5911i | −0.208450 | + | 0.777944i | ||||
\(223\) | −1.79315 | + | 6.69213i | −0.120078 | + | 0.448138i | −0.999617 | − | 0.0276899i | \(-0.991185\pi\) |
0.879538 | + | 0.475828i | \(0.157852\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.0000 | 0.997785 | ||||||||
\(227\) | 0.776457 | − | 2.89778i | 0.0515353 | − | 0.192332i | −0.935359 | − | 0.353699i | \(-0.884924\pi\) |
0.986894 | + | 0.161367i | \(0.0515903\pi\) | |||||||
\(228\) | −8.36516 | + | 2.24144i | −0.553996 | + | 0.148443i | ||||
\(229\) | −13.8564 | − | 8.00000i | −0.915657 | − | 0.528655i | −0.0334101 | − | 0.999442i | \(-0.510637\pi\) |
−0.882247 | + | 0.470787i | \(0.843970\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.69213 | + | 1.79315i | 0.439360 | + | 0.117726i | ||||
\(233\) | 6.36396 | − | 6.36396i | 0.416917 | − | 0.416917i | −0.467223 | − | 0.884140i | \(-0.654745\pi\) |
0.884140 | + | 0.467223i | \(0.154745\pi\) | |||||||
\(234\) | 10.3923 | 0.679366 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.50000 | + | 0.866025i | −0.0976417 | + | 0.0563735i | ||||
\(237\) | 23.4225 | + | 6.27603i | 1.52145 | + | 0.407672i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.19615 | − | 9.00000i | 0.336111 | − | 0.582162i | −0.647586 | − | 0.761992i | \(-0.724222\pi\) |
0.983698 | + | 0.179830i | \(0.0575549\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.500000 | + | 0.866025i | 0.0322078 | + | 0.0557856i | 0.881680 | − | 0.471848i | \(-0.156413\pi\) |
−0.849472 | + | 0.527633i | \(0.823079\pi\) | |||||||
\(242\) | −0.707107 | − | 0.707107i | −0.0454545 | − | 0.0454545i | ||||
\(243\) | −11.0227 | − | 11.0227i | −0.707107 | − | 0.707107i | ||||
\(244\) | 8.00000i | 0.512148i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.00000 | −0.191273 | ||||||||
\(247\) | −4.48288 | − | 16.7303i | −0.285239 | − | 1.06453i | ||||
\(248\) | −1.03528 | − | 3.86370i | −0.0657401 | − | 0.245345i | ||||
\(249\) | −7.79423 | − | 13.5000i | −0.493939 | − | 0.855528i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 5.19615i | − | 0.327978i | −0.986462 | − | 0.163989i | \(-0.947564\pi\) | ||
0.986462 | − | 0.163989i | \(-0.0524362\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.6969 | + | 14.6969i | 0.923989 | + | 0.923989i | ||||
\(254\) | 5.19615 | + | 9.00000i | 0.326036 | + | 0.564710i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 14.4889 | − | 3.88229i | 0.903792 | − | 0.242170i | 0.223148 | − | 0.974785i | \(-0.428367\pi\) |
0.680644 | + | 0.732614i | \(0.261700\pi\) | |||||||
\(258\) | −5.43520 | − | 20.2844i | −0.338381 | − | 1.26285i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.0000 | − | 10.3923i | 1.11417 | − | 0.643268i | ||||
\(262\) | 2.44949 | − | 2.44949i | 0.151330 | − | 0.151330i | ||||
\(263\) | 11.5911 | + | 3.10583i | 0.714738 | + | 0.191514i | 0.597823 | − | 0.801628i | \(-0.296033\pi\) |
0.116916 | + | 0.993142i | \(0.462699\pi\) | |||||||
\(264\) | −5.19615 | + | 3.00000i | −0.319801 | + | 0.184637i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.8492 | − | 14.8492i | −0.908759 | − | 0.908759i | ||||
\(268\) | −2.24144 | + | 8.36516i | −0.136918 | + | 0.510984i | ||||
\(269\) | 13.8564 | 0.844840 | 0.422420 | − | 0.906400i | \(-0.361181\pi\) | ||||
0.422420 | + | 0.906400i | \(0.361181\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.0000 | −0.607457 | −0.303728 | − | 0.952759i | \(-0.598232\pi\) | ||||
−0.303728 | + | 0.952759i | \(0.598232\pi\) | |||||||
\(272\) | −1.55291 | + | 5.79555i | −0.0941593 | + | 0.351407i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.79423 | − | 4.50000i | −0.470867 | − | 0.271855i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 9.00000 | − | 5.19615i | 0.541736 | − | 0.312772i | ||||
\(277\) | −6.69213 | − | 1.79315i | −0.402091 | − | 0.107740i | 0.0521052 | − | 0.998642i | \(-0.483407\pi\) |
−0.454196 | + | 0.890902i | \(0.650074\pi\) | |||||||
\(278\) | −2.82843 | + | 2.82843i | −0.169638 | + | 0.169638i | ||||
\(279\) | −10.3923 | − | 6.00000i | −0.622171 | − | 0.359211i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.0000 | + | 10.3923i | −1.07379 | + | 0.619953i | −0.929214 | − | 0.369541i | \(-0.879515\pi\) |
−0.144575 | + | 0.989494i | \(0.546182\pi\) | |||||||
\(282\) | 2.68973 | + | 10.0382i | 0.160171 | + | 0.597766i | ||||
\(283\) | 11.7112 | − | 3.13801i | 0.696160 | − | 0.186536i | 0.106650 | − | 0.994297i | \(-0.465988\pi\) |
0.589510 | + | 0.807761i | \(0.299321\pi\) | |||||||
\(284\) | 3.46410 | − | 6.00000i | 0.205557 | − | 0.356034i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.00000 | − | 10.3923i | −0.354787 | − | 0.614510i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.776457 | + | 2.89778i | 0.0457532 | + | 0.170753i | ||||
\(289\) | 19.0000i | 1.11765i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.50000 | + | 7.79423i | 0.263795 | + | 0.456906i | ||||
\(292\) | 3.13801 | + | 11.7112i | 0.183638 | + | 0.685348i | ||||
\(293\) | 1.55291 | + | 5.79555i | 0.0907222 | + | 0.338580i | 0.996336 | − | 0.0855230i | \(-0.0272561\pi\) |
−0.905614 | + | 0.424103i | \(0.860589\pi\) | |||||||
\(294\) | −12.1244 | −0.707107 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 6.92820i | − | 0.402694i | ||||||
\(297\) | −4.65874 | + | 17.3867i | −0.270328 | + | 1.00888i | ||||
\(298\) | 7.34847 | + | 7.34847i | 0.425685 | + | 0.425685i | ||||
\(299\) | 10.3923 | + | 18.0000i | 0.601003 | + | 1.04097i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −15.4548 | + | 4.14110i | −0.889325 | + | 0.238294i | ||||
\(303\) | 5.79555 | + | 1.55291i | 0.332946 | + | 0.0892126i | ||||
\(304\) | 4.33013 | − | 2.50000i | 0.248350 | − | 0.143385i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 9.00000 | + | 15.5885i | 0.514496 | + | 0.891133i | ||||
\(307\) | 17.1464 | − | 17.1464i | 0.978598 | − | 0.978598i | −0.0211774 | − | 0.999776i | \(-0.506741\pi\) |
0.999776 | + | 0.0211774i | \(0.00674148\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.19615 | + | 3.00000i | 0.295599 | + | 0.170664i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.0000 | − | 12.1244i | −1.19080 | − | 0.687509i | −0.232313 | − | 0.972641i | \(-0.574629\pi\) |
−0.958488 | + | 0.285132i | \(0.907963\pi\) | |||||||
\(312\) | −5.79555 | + | 1.55291i | −0.328109 | + | 0.0879165i | ||||
\(313\) | −8.51747 | + | 31.7876i | −0.481436 | + | 1.79674i | 0.114165 | + | 0.993462i | \(0.463581\pi\) |
−0.595601 | + | 0.803281i | \(0.703086\pi\) | |||||||
\(314\) | 3.46410 | 0.195491 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.0000 | −0.787562 | ||||||||
\(317\) | −3.10583 | + | 11.5911i | −0.174441 | + | 0.651022i | 0.822206 | + | 0.569191i | \(0.192743\pi\) |
−0.996646 | + | 0.0818309i | \(0.973923\pi\) | |||||||
\(318\) | −2.68973 | + | 10.0382i | −0.150832 | + | 0.562914i | ||||
\(319\) | −20.7846 | − | 12.0000i | −1.16371 | − | 0.671871i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.19615i | 0.290021i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 21.2132 | − | 21.2132i | 1.18033 | − | 1.18033i | ||||
\(324\) | 7.79423 | + | 4.50000i | 0.433013 | + | 0.250000i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.50000 | + | 0.866025i | −0.0830773 | + | 0.0479647i | ||||
\(327\) | −24.4949 | + | 24.4949i | −1.35457 | + | 1.35457i | ||||
\(328\) | 1.67303 | − | 0.448288i | 0.0923778 | − | 0.0247525i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.500000 | + | 0.866025i | 0.0274825 | + | 0.0476011i | 0.879440 | − | 0.476011i | \(-0.157918\pi\) |
−0.851957 | + | 0.523612i | \(0.824584\pi\) | |||||||
\(332\) | 6.36396 | + | 6.36396i | 0.349268 | + | 0.349268i | ||||
\(333\) | −14.6969 | − | 14.6969i | −0.805387 | − | 0.805387i | ||||
\(334\) | 12.0000i | 0.656611i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.79315 | − | 6.69213i | −0.0976792 | − | 0.364544i | 0.899733 | − | 0.436441i | \(-0.143761\pi\) |
−0.997412 | + | 0.0718974i | \(0.977095\pi\) | |||||||
\(338\) | 0.258819 | + | 0.965926i | 0.0140779 | + | 0.0525394i | ||||
\(339\) | −12.9904 | + | 22.5000i | −0.705541 | + | 1.22203i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.8564i | 0.750366i | ||||||||
\(342\) | 3.88229 | − | 14.4889i | 0.209930 | − | 0.783469i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6.06218 | + | 10.5000i | 0.326851 | + | 0.566122i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.5911 | − | 3.10583i | 0.622243 | − | 0.166730i | 0.0660960 | − | 0.997813i | \(-0.478946\pi\) |
0.556147 | + | 0.831084i | \(0.312279\pi\) | |||||||
\(348\) | −8.48528 | + | 8.48528i | −0.454859 | + | 0.454859i | ||||
\(349\) | −22.5167 | + | 13.0000i | −1.20529 | + | 0.695874i | −0.961727 | − | 0.274011i | \(-0.911649\pi\) |
−0.243563 | + | 0.969885i | \(0.578316\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.00000 | + | 15.5885i | −0.480384 | + | 0.832050i | ||||
\(352\) | 2.44949 | − | 2.44949i | 0.130558 | − | 0.130558i | ||||
\(353\) | 8.69333 | + | 2.32937i | 0.462699 | + | 0.123980i | 0.482635 | − | 0.875821i | \(-0.339680\pi\) |
−0.0199361 | + | 0.999801i | \(0.506346\pi\) | |||||||
\(354\) | − | 3.00000i | − | 0.159448i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 10.5000 | + | 6.06218i | 0.556499 | + | 0.321295i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.82774 | − | 21.7494i | 0.308006 | − | 1.14949i | ||||
\(359\) | 27.7128 | 1.46263 | 0.731313 | − | 0.682042i | \(-0.238908\pi\) | ||||
0.731313 | + | 0.682042i | \(0.238908\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.00000 | −0.315789 | ||||||||
\(362\) | 4.14110 | − | 15.4548i | 0.217652 | − | 0.812287i | ||||
\(363\) | 1.67303 | − | 0.448288i | 0.0878114 | − | 0.0235290i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −12.0000 | − | 6.92820i | −0.627250 | − | 0.362143i | ||||
\(367\) | 16.7303 | + | 4.48288i | 0.873316 | + | 0.234004i | 0.667521 | − | 0.744591i | \(-0.267355\pi\) |
0.205795 | + | 0.978595i | \(0.434022\pi\) | |||||||
\(368\) | −4.24264 | + | 4.24264i | −0.221163 | + | 0.221163i | ||||
\(369\) | 2.59808 | − | 4.50000i | 0.135250 | − | 0.234261i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 6.69213 | + | 1.79315i | 0.346971 | + | 0.0929705i | ||||
\(373\) | −20.0764 | + | 5.37945i | −1.03952 | + | 0.278538i | −0.737913 | − | 0.674896i | \(-0.764188\pi\) |
−0.301603 | + | 0.953434i | \(0.597522\pi\) | |||||||
\(374\) | 10.3923 | − | 18.0000i | 0.537373 | − | 0.930758i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.00000 | − | 5.19615i | −0.154713 | − | 0.267971i | ||||
\(377\) | −16.9706 | − | 16.9706i | −0.874028 | − | 0.874028i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 8.00000i | − | 0.410932i | −0.978664 | − | 0.205466i | \(-0.934129\pi\) | ||
0.978664 | − | 0.205466i | \(-0.0658711\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.0000 | −0.922168 | ||||||||
\(382\) | −6.27603 | − | 23.4225i | −0.321110 | − | 1.19840i | ||||
\(383\) | −1.55291 | − | 5.79555i | −0.0793502 | − | 0.296139i | 0.914834 | − | 0.403830i | \(-0.132321\pi\) |
−0.994184 | + | 0.107691i | \(0.965654\pi\) | |||||||
\(384\) | −0.866025 | − | 1.50000i | −0.0441942 | − | 0.0765466i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 35.1337 | + | 9.41404i | 1.78595 | + | 0.478543i | ||||
\(388\) | −3.67423 | − | 3.67423i | −0.186531 | − | 0.186531i | ||||
\(389\) | −5.19615 | − | 9.00000i | −0.263455 | − | 0.456318i | 0.703702 | − | 0.710495i | \(-0.251529\pi\) |
−0.967158 | + | 0.254177i | \(0.918196\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.0000 | + | 31.1769i | −0.910299 | + | 1.57668i | ||||
\(392\) | 6.76148 | − | 1.81173i | 0.341506 | − | 0.0915064i | ||||
\(393\) | 1.55291 | + | 5.79555i | 0.0783342 | + | 0.292347i | ||||
\(394\) | −20.7846 | + | 12.0000i | −1.04711 | + | 0.604551i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | − | 10.3923i | − | 0.522233i | ||||||
\(397\) | −17.1464 | + | 17.1464i | −0.860555 | + | 0.860555i | −0.991402 | − | 0.130848i | \(-0.958230\pi\) |
0.130848 | + | 0.991402i | \(0.458230\pi\) | |||||||
\(398\) | 7.72741 | + | 2.07055i | 0.387340 | + | 0.103787i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.0000 | − | 10.3923i | −0.898877 | − | 0.518967i | −0.0220414 | − | 0.999757i | \(-0.507017\pi\) |
−0.876836 | + | 0.480790i | \(0.840350\pi\) | |||||||
\(402\) | −10.6066 | − | 10.6066i | −0.529009 | − | 0.529009i | ||||
\(403\) | −3.58630 | + | 13.3843i | −0.178646 | + | 0.666718i | ||||
\(404\) | −3.46410 | −0.172345 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.21166 | + | 23.1822i | −0.307900 | + | 1.14910i | ||||
\(408\) | −7.34847 | − | 7.34847i | −0.363803 | − | 0.363803i | ||||
\(409\) | 25.1147 | + | 14.5000i | 1.24184 | + | 0.716979i | 0.969469 | − | 0.245212i | \(-0.0788577\pi\) |
0.272374 | + | 0.962191i | \(0.412191\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.5000 | − | 7.79423i | 0.665906 | − | 0.384461i | ||||
\(412\) | −3.34607 | − | 0.896575i | −0.164849 | − | 0.0441711i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 18.0000i | 0.884652i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.00000 | − | 1.73205i | 0.147087 | − | 0.0849208i | ||||
\(417\) | −1.79315 | − | 6.69213i | −0.0878110 | − | 0.327715i | ||||
\(418\) | −16.7303 | + | 4.48288i | −0.818307 | + | 0.219265i | ||||
\(419\) | −12.9904 | + | 22.5000i | −0.634622 | + | 1.09920i | 0.351974 | + | 0.936010i | \(0.385511\pi\) |
−0.986595 | + | 0.163187i | \(0.947823\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.00000 | + | 6.92820i | 0.194948 | + | 0.337660i | 0.946883 | − | 0.321577i | \(-0.104213\pi\) |
−0.751935 | + | 0.659237i | \(0.770879\pi\) | |||||||
\(422\) | −9.19239 | − | 9.19239i | −0.447478 | − | 0.447478i | ||||
\(423\) | −17.3867 | − | 4.65874i | −0.845369 | − | 0.226516i | ||||
\(424\) | − | 6.00000i | − | 0.291386i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.00000 | + | 10.3923i | 0.290701 | + | 0.503509i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.776457 | − | 2.89778i | −0.0375315 | − | 0.140069i | ||||
\(429\) | 20.7846 | 1.00349 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 13.8564i | − | 0.667440i | −0.942672 | − | 0.333720i | \(-0.891696\pi\) | ||
0.942672 | − | 0.333720i | \(-0.108304\pi\) | |||||||
\(432\) | −5.01910 | − | 1.34486i | −0.241481 | − | 0.0647048i | ||||
\(433\) | −4.89898 | − | 4.89898i | −0.235430 | − | 0.235430i | 0.579525 | − | 0.814955i | \(-0.303238\pi\) |
−0.814955 | + | 0.579525i | \(0.803238\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.0000 | − | 17.3205i | 0.478913 | − | 0.829502i | ||||
\(437\) | 28.9778 | − | 7.76457i | 1.38619 | − | 0.371430i | ||||
\(438\) | −20.2844 | − | 5.43520i | −0.969228 | − | 0.259704i | ||||
\(439\) | 22.5167 | − | 13.0000i | 1.07466 | − | 0.620456i | 0.145210 | − | 0.989401i | \(-0.453614\pi\) |
0.929451 | + | 0.368945i | \(0.120281\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.5000 | − | 18.1865i | 0.500000 | − | 0.866025i | ||||
\(442\) | 14.6969 | − | 14.6969i | 0.699062 | − | 0.699062i | ||||
\(443\) | −34.7733 | − | 9.31749i | −1.65213 | − | 0.442687i | −0.691922 | − | 0.721972i | \(-0.743236\pi\) |
−0.960208 | + | 0.279285i | \(0.909903\pi\) | |||||||
\(444\) | 10.3923 | + | 6.00000i | 0.493197 | + | 0.284747i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6.00000 | + | 3.46410i | 0.284108 | + | 0.164030i | ||||
\(447\) | −17.3867 | + | 4.65874i | −0.822361 | + | 0.220351i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.66025 | 0.408703 | 0.204351 | − | 0.978898i | \(-0.434492\pi\) | ||||
0.204351 | + | 0.978898i | \(0.434492\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.00000 | −0.282529 | ||||||||
\(452\) | 3.88229 | − | 14.4889i | 0.182607 | − | 0.681500i | ||||
\(453\) | 7.17260 | − | 26.7685i | 0.336998 | − | 1.25769i | ||||
\(454\) | −2.59808 | − | 1.50000i | −0.121934 | − | 0.0703985i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.66025i | 0.405554i | ||||||||
\(457\) | 5.01910 | + | 1.34486i | 0.234783 | + | 0.0629100i | 0.374292 | − | 0.927311i | \(-0.377886\pi\) |
−0.139509 | + | 0.990221i | \(0.544552\pi\) | |||||||
\(458\) | −11.3137 | + | 11.3137i | −0.528655 | + | 0.528655i | ||||
\(459\) | −31.1769 | −1.45521 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.0000 | + | 17.3205i | −1.39724 | + | 0.806696i | −0.994103 | − | 0.108443i | \(-0.965413\pi\) |
−0.403137 | + | 0.915140i | \(0.632080\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.69213 | − | 1.79315i | 0.311010 | − | 0.0833348i | −0.0999382 | − | 0.994994i | \(-0.531864\pi\) |
0.410948 | + | 0.911659i | \(0.365198\pi\) | |||||||
\(464\) | 3.46410 | − | 6.00000i | 0.160817 | − | 0.278543i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.50000 | − | 7.79423i | −0.208458 | − | 0.361061i | ||||
\(467\) | 14.8492 | + | 14.8492i | 0.687141 | + | 0.687141i | 0.961599 | − | 0.274458i | \(-0.0884985\pi\) |
−0.274458 | + | 0.961599i | \(0.588498\pi\) | |||||||
\(468\) | 2.68973 | − | 10.0382i | 0.124333 | − | 0.464016i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.00000 | + | 5.19615i | −0.138233 | + | 0.239426i | ||||
\(472\) | 0.448288 | + | 1.67303i | 0.0206341 | + | 0.0770076i | ||||
\(473\) | −10.8704 | − | 40.5689i | −0.499822 | − | 1.86536i | ||||
\(474\) | 12.1244 | − | 21.0000i | 0.556890 | − | 0.964562i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.7279 | − | 12.7279i | −0.582772 | − | 0.582772i | ||||
\(478\) | −7.34847 | − | 7.34847i | −0.336111 | − | 0.336111i | ||||
\(479\) | 8.66025 | + | 15.0000i | 0.395697 | + | 0.685367i | 0.993190 | − | 0.116507i | \(-0.0371697\pi\) |
−0.597493 | + | 0.801874i | \(0.703836\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.0000 | + | 20.7846i | −0.547153 | + | 0.947697i | ||||
\(482\) | 0.965926 | − | 0.258819i | 0.0439967 | − | 0.0117889i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.866025 | + | 0.500000i | −0.0393648 | + | 0.0227273i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −13.5000 | + | 7.79423i | −0.612372 | + | 0.353553i | ||||
\(487\) | 4.89898 | − | 4.89898i | 0.221994 | − | 0.221994i | −0.587344 | − | 0.809338i | \(-0.699826\pi\) |
0.809338 | + | 0.587344i | \(0.199826\pi\) | |||||||
\(488\) | 7.72741 | + | 2.07055i | 0.349803 | + | 0.0937295i | ||||
\(489\) | − | 3.00000i | − | 0.135665i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.5000 | + | 14.7224i | 1.15080 | + | 0.664414i | 0.949082 | − | 0.315030i | \(-0.102015\pi\) |
0.201717 | + | 0.979444i | \(0.435348\pi\) | |||||||
\(492\) | −0.776457 | + | 2.89778i | −0.0350054 | + | 0.130642i | ||||
\(493\) | 10.7589 | − | 40.1528i | 0.484557 | − | 1.80839i | ||||
\(494\) | −17.3205 | −0.779287 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −15.0573 | + | 4.03459i | −0.674733 | + | 0.180794i | ||||
\(499\) | 11.2583 | + | 6.50000i | 0.503992 | + | 0.290980i | 0.730361 | − | 0.683062i | \(-0.239352\pi\) |
−0.226369 | + | 0.974042i | \(0.572685\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.0000 | − | 10.3923i | −0.804181 | − | 0.464294i | ||||
\(502\) | −5.01910 | − | 1.34486i | −0.224013 | − | 0.0600242i | ||||
\(503\) | −29.6985 | + | 29.6985i | −1.32419 | + | 1.32419i | −0.413841 | + | 0.910349i | \(0.635813\pi\) |
−0.910349 | + | 0.413841i | \(0.864187\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 18.0000 | − | 10.3923i | 0.800198 | − | 0.461994i | ||||
\(507\) | −1.67303 | − | 0.448288i | −0.0743020 | − | 0.0199092i | ||||
\(508\) | 10.0382 | − | 2.68973i | 0.445373 | − | 0.119337i | ||||
\(509\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 18.3712 | + | 18.3712i | 0.811107 | + | 0.811107i | ||||
\(514\) | − | 15.0000i | − | 0.661622i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −21.0000 | −0.924473 | ||||||||
\(517\) | 5.37945 | + | 20.0764i | 0.236588 | + | 0.882959i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 20.7846i | − | 0.910590i | −0.890341 | − | 0.455295i | \(-0.849534\pi\) | ||
0.890341 | − | 0.455295i | \(-0.150466\pi\) | |||||||
\(522\) | −5.37945 | − | 20.0764i | −0.235452 | − | 0.878720i | ||||
\(523\) | 3.67423 | + | 3.67423i | 0.160663 | + | 0.160663i | 0.782860 | − | 0.622197i | \(-0.213760\pi\) |
−0.622197 | + | 0.782860i | \(0.713760\pi\) | |||||||
\(524\) | −1.73205 | − | 3.00000i | −0.0756650 | − | 0.131056i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.00000 | − | 10.3923i | 0.261612 | − | 0.453126i | ||||
\(527\) | −23.1822 | + | 6.21166i | −1.00983 | + | 0.270584i | ||||
\(528\) | 1.55291 | + | 5.79555i | 0.0675819 | + | 0.252219i | ||||
\(529\) | −11.2583 | + | 6.50000i | −0.489493 | + | 0.282609i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.50000 | + | 2.59808i | 0.195283 | + | 0.112747i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.79555 | − | 1.55291i | −0.251033 | − | 0.0672642i | ||||
\(534\) | −18.1865 | + | 10.5000i | −0.787008 | + | 0.454379i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 7.50000 | + | 4.33013i | 0.323951 | + | 0.187033i | ||||
\(537\) | 27.5772 | + | 27.5772i | 1.19004 | + | 1.19004i | ||||
\(538\) | 3.58630 | − | 13.3843i | 0.154616 | − | 0.577036i | ||||
\(539\) | −24.2487 | −1.04447 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.0000 | 1.37579 | 0.687894 | − | 0.725811i | \(-0.258536\pi\) | ||||
0.687894 | + | 0.725811i | \(0.258536\pi\) | |||||||
\(542\) | −2.58819 | + | 9.65926i | −0.111172 | + | 0.414901i | ||||
\(543\) | 19.5959 | + | 19.5959i | 0.840941 | + | 0.840941i | ||||
\(544\) | 5.19615 | + | 3.00000i | 0.222783 | + | 0.128624i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.7494 | − | 5.82774i | −0.929938 | − | 0.249176i | −0.238110 | − | 0.971238i | \(-0.576528\pi\) |
−0.691828 | + | 0.722062i | \(0.743195\pi\) | |||||||
\(548\) | −6.36396 | + | 6.36396i | −0.271855 | + | 0.271855i | ||||
\(549\) | 20.7846 | − | 12.0000i | 0.887066 | − | 0.512148i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −30.0000 | + | 17.3205i | −1.27804 | + | 0.737878i | ||||
\(552\) | −2.68973 | − | 10.0382i | −0.114482 | − | 0.427254i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.46410 | + | 6.00000i | −0.147176 | + | 0.254916i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.00000 | + | 3.46410i | 0.0848189 | + | 0.146911i | ||||
\(557\) | −16.9706 | − | 16.9706i | −0.719066 | − | 0.719066i | 0.249348 | − | 0.968414i | \(-0.419784\pi\) |
−0.968414 | + | 0.249348i | \(0.919784\pi\) | |||||||
\(558\) | −8.48528 | + | 8.48528i | −0.359211 | + | 0.359211i | ||||
\(559\) | − | 42.0000i | − | 1.77641i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18.0000 | + | 31.1769i | 0.759961 | + | 1.31629i | ||||
\(562\) | 5.37945 | + | 20.0764i | 0.226919 | + | 0.846871i | ||||
\(563\) | 5.43520 | + | 20.2844i | 0.229066 | + | 0.854887i | 0.980734 | + | 0.195346i | \(0.0625829\pi\) |
−0.751668 | + | 0.659542i | \(0.770750\pi\) | |||||||
\(564\) | 10.3923 | 0.437595 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 12.1244i | − | 0.509625i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.89898 | − | 4.89898i | −0.205557 | − | 0.205557i | ||||
\(569\) | −17.3205 | − | 30.0000i | −0.726113 | − | 1.25767i | −0.958514 | − | 0.285045i | \(-0.907991\pi\) |
0.232401 | − | 0.972620i | \(-0.425342\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.500000 | − | 0.866025i | 0.0209243 | − | 0.0362420i | −0.855374 | − | 0.518012i | \(-0.826672\pi\) |
0.876298 | + | 0.481770i | \(0.160006\pi\) | |||||||
\(572\) | −11.5911 | + | 3.10583i | −0.484649 | + | 0.129861i | ||||
\(573\) | 40.5689 | + | 10.8704i | 1.69479 | + | 0.454117i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.00000 | 0.125000 | ||||||||
\(577\) | −25.7196 | + | 25.7196i | −1.07072 | + | 1.07072i | −0.0734217 | + | 0.997301i | \(0.523392\pi\) |
−0.997301 | + | 0.0734217i | \(0.976608\pi\) | |||||||
\(578\) | 18.3526 | + | 4.91756i | 0.763367 | + | 0.204544i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 8.69333 | − | 2.32937i | 0.360350 | − | 0.0965556i | ||||
\(583\) | −5.37945 | + | 20.0764i | −0.222794 | + | 0.831479i | ||||
\(584\) | 12.1244 | 0.501709 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.00000 | 0.247858 | ||||||||
\(587\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(588\) | −3.13801 | + | 11.7112i | −0.129410 | + | 0.482963i | ||||
\(589\) | 17.3205 | + | 10.0000i | 0.713679 | + | 0.412043i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 41.5692i | − | 1.70993i | ||||||
\(592\) | −6.69213 | − | 1.79315i | −0.275045 | − | 0.0736980i | ||||
\(593\) | 23.3345 | − | 23.3345i | 0.958234 | − | 0.958234i | −0.0409281 | − | 0.999162i | \(-0.513031\pi\) |
0.999162 | + | 0.0409281i | \(0.0130314\pi\) | |||||||
\(594\) | 15.5885 | + | 9.00000i | 0.639602 | + | 0.369274i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.00000 | − | 5.19615i | 0.368654 | − | 0.212843i | ||||
\(597\) | −9.79796 | + | 9.79796i | −0.401004 | + | 0.401004i | ||||
\(598\) | 20.0764 | − | 5.37945i | 0.820985 | − | 0.219982i | ||||
\(599\) | −13.8564 | + | 24.0000i | −0.566157 | + | 0.980613i | 0.430784 | + | 0.902455i | \(0.358237\pi\) |
−0.996941 | + | 0.0781581i | \(0.975096\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.0000 | + | 22.5167i | 0.530281 | + | 0.918474i | 0.999376 | + | 0.0353259i | \(0.0112469\pi\) |
−0.469095 | + | 0.883148i | \(0.655420\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 25.0955 | − | 6.72432i | 1.02197 | − | 0.273835i | ||||
\(604\) | 16.0000i | 0.651031i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.00000 | − | 5.19615i | 0.121867 | − | 0.211079i | ||||
\(607\) | 6.27603 | + | 23.4225i | 0.254736 | + | 0.950688i | 0.968237 | + | 0.250034i | \(0.0804418\pi\) |
−0.713501 | + | 0.700654i | \(0.752892\pi\) | |||||||
\(608\) | −1.29410 | − | 4.82963i | −0.0524825 | − | 0.195867i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.7846i | 0.840855i | ||||||||
\(612\) | 17.3867 | − | 4.65874i | 0.702814 | − | 0.188319i | ||||
\(613\) | −2.44949 | − | 2.44949i | −0.0989340 | − | 0.0989340i | 0.655907 | − | 0.754841i | \(-0.272286\pi\) |
−0.754841 | + | 0.655907i | \(0.772286\pi\) | |||||||
\(614\) | −12.1244 | − | 21.0000i | −0.489299 | − | 0.847491i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.69333 | − | 2.32937i | 0.349980 | − | 0.0937770i | −0.0795462 | − | 0.996831i | \(-0.525347\pi\) |
0.429527 | + | 0.903054i | \(0.358680\pi\) | |||||||
\(618\) | 4.24264 | − | 4.24264i | 0.170664 | − | 0.170664i | ||||
\(619\) | 14.7224 | − | 8.50000i | 0.591744 | − | 0.341644i | −0.174042 | − | 0.984738i | \(-0.555683\pi\) |
0.765787 | + | 0.643094i | \(0.222350\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −27.0000 | − | 15.5885i | −1.08347 | − | 0.625543i | ||||
\(622\) | −17.1464 | + | 17.1464i | −0.687509 | + | 0.687509i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 6.00000i | 0.240192i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 28.5000 | + | 16.4545i | 1.13909 | + | 0.657653i | ||||
\(627\) | 7.76457 | − | 28.9778i | 0.310087 | − | 1.15726i | ||||
\(628\) | 0.896575 | − | 3.34607i | 0.0357773 | − | 0.133523i | ||||
\(629\) | −41.5692 | −1.65747 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.0000 | −0.636950 | −0.318475 | − | 0.947931i | \(-0.603171\pi\) | ||||
−0.318475 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(632\) | −3.62347 | + | 13.5230i | −0.144134 | + | 0.537915i | ||||
\(633\) | 21.7494 | − | 5.82774i | 0.864462 | − | 0.231632i | ||||
\(634\) | 10.3923 | + | 6.00000i | 0.412731 | + | 0.238290i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.00000 | + | 5.19615i | 0.356873 | + | 0.206041i | ||||
\(637\) | −23.4225 | − | 6.27603i | −0.928032 | − | 0.248665i | ||||
\(638\) | −16.9706 | + | 16.9706i | −0.671871 | + | 0.671871i | ||||
\(639\) | −20.7846 | −0.822226 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.5000 | − | 11.2583i | 0.770204 | − | 0.444677i | −0.0627436 | − | 0.998030i | \(-0.519985\pi\) |
0.832947 | + | 0.553352i | \(0.186652\pi\) | |||||||
\(642\) | 5.01910 | + | 1.34486i | 0.198088 | + | 0.0530775i | ||||
\(643\) | −45.1719 | + | 12.1038i | −1.78141 | + | 0.477326i | −0.990839 | − | 0.135050i | \(-0.956880\pi\) |
−0.790566 | + | 0.612376i | \(0.790214\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15.0000 | − | 25.9808i | −0.590167 | − | 1.02220i | ||||
\(647\) | 29.6985 | + | 29.6985i | 1.16757 | + | 1.16757i | 0.982778 | + | 0.184790i | \(0.0591604\pi\) |
0.184790 | + | 0.982778i | \(0.440840\pi\) | |||||||
\(648\) | 6.36396 | − | 6.36396i | 0.250000 | − | 0.250000i | ||||
\(649\) | − | 6.00000i | − | 0.235521i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.448288 | + | 1.67303i | 0.0175563 | + | 0.0655210i | ||||
\(653\) | 7.76457 | + | 28.9778i | 0.303851 | + | 1.13399i | 0.933930 | + | 0.357457i | \(0.116356\pi\) |
−0.630079 | + | 0.776531i | \(0.716977\pi\) | |||||||
\(654\) | 17.3205 | + | 30.0000i | 0.677285 | + | 1.17309i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 1.73205i | − | 0.0676252i | ||||||
\(657\) | 25.7196 | − | 25.7196i | 1.00342 | − | 1.00342i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.79423 | − | 13.5000i | −0.303620 | − | 0.525885i | 0.673333 | − | 0.739339i | \(-0.264862\pi\) |
−0.976953 | + | 0.213454i | \(0.931529\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.0000 | − | 43.3013i | 0.972387 | − | 1.68422i | 0.284087 | − | 0.958799i | \(-0.408310\pi\) |
0.688301 | − | 0.725426i | \(-0.258357\pi\) | |||||||
\(662\) | 0.965926 | − | 0.258819i | 0.0375418 | − | 0.0100593i | ||||
\(663\) | 9.31749 | + | 34.7733i | 0.361861 | + | 1.35048i | ||||
\(664\) | 7.79423 | − | 4.50000i | 0.302475 | − | 0.174634i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −18.0000 | + | 10.3923i | −0.697486 | + | 0.402694i | ||||
\(667\) | 29.3939 | − | 29.3939i | 1.13814 | − | 1.13814i | ||||
\(668\) | 11.5911 | + | 3.10583i | 0.448474 | + | 0.120168i | ||||
\(669\) | −10.3923 | + | 6.00000i | −0.401790 | + | 0.231973i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.0000 | − | 13.8564i | −0.926510 | − | 0.534921i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.96575 | − | 33.4607i | 0.345604 | − | 1.28981i | −0.546300 | − | 0.837590i | \(-0.683964\pi\) |
0.891904 | − | 0.452224i | \(-0.149369\pi\) | |||||||
\(674\) | −6.92820 | −0.266864 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −1.55291 | + | 5.79555i | −0.0596833 | + | 0.222741i | −0.989326 | − | 0.145722i | \(-0.953449\pi\) |
0.929642 | + | 0.368464i | \(0.120116\pi\) | |||||||
\(678\) | 18.3712 | + | 18.3712i | 0.705541 | + | 0.705541i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.50000 | − | 2.59808i | 0.172440 | − | 0.0995585i | ||||
\(682\) | 13.3843 | + | 3.58630i | 0.512510 | + | 0.137327i | ||||
\(683\) | 2.12132 | − | 2.12132i | 0.0811701 | − | 0.0811701i | −0.665356 | − | 0.746526i | \(-0.731720\pi\) |
0.746526 | + | 0.665356i | \(0.231720\pi\) | |||||||
\(684\) | −12.9904 | − | 7.50000i | −0.496700 | − | 0.286770i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.17260 | − | 26.7685i | −0.273652 | − | 1.02128i | ||||
\(688\) | 11.7112 | − | 3.13801i | 0.446486 | − | 0.119636i | ||||
\(689\) | −10.3923 | + | 18.0000i | −0.395915 | + | 0.685745i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.5000 | + | 30.3109i | 0.665731 | + | 1.15308i | 0.979086 | + | 0.203445i | \(0.0652137\pi\) |
−0.313355 | + | 0.949636i | \(0.601453\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 12.0000i | − | 0.455514i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 6.00000 | + | 10.3923i | 0.227429 | + | 0.393919i | ||||
\(697\) | −2.68973 | − | 10.0382i | −0.101881 | − | 0.380224i | ||||
\(698\) | 6.72930 | + | 25.1141i | 0.254708 | + | 0.950582i | ||||
\(699\) | 15.5885 | 0.589610 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 6.92820i | − | 0.261675i | −0.991404 | − | 0.130837i | \(-0.958233\pi\) | ||
0.991404 | − | 0.130837i | \(-0.0417666\pi\) | |||||||
\(702\) | 12.7279 | + | 12.7279i | 0.480384 | + | 0.480384i | ||||
\(703\) | 24.4949 | + | 24.4949i | 0.923843 | + | 0.923843i | ||||
\(704\) | −1.73205 | − | 3.00000i | −0.0652791 | − | 0.113067i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.50000 | − | 7.79423i | 0.169360 | − | 0.293340i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.89778 | − | 0.776457i | −0.108905 | − | 0.0291810i | ||||
\(709\) | 39.8372 | − | 23.0000i | 1.49612 | − | 0.863783i | 0.496126 | − | 0.868250i | \(-0.334755\pi\) |
0.999990 | + | 0.00446726i | \(0.00142198\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 21.0000 | + | 36.3731i | 0.787562 | + | 1.36410i | ||||
\(712\) | 8.57321 | − | 8.57321i | 0.321295 | − | 0.321295i | ||||
\(713\) | −23.1822 | − | 6.21166i | −0.868181 | − | 0.232628i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −19.5000 | − | 11.2583i | −0.728749 | − | 0.420744i | ||||
\(717\) | 17.3867 | − | 4.65874i | 0.649317 | − | 0.173984i | ||||
\(718\) | 7.17260 | − | 26.7685i | 0.267679 | − | 0.998992i | ||||
\(719\) | −6.92820 | −0.258378 | −0.129189 | − | 0.991620i | \(-0.541237\pi\) | ||||
−0.129189 | + | 0.991620i | \(0.541237\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.55291 | + | 5.79555i | −0.0577935 | + | 0.215688i | ||||
\(723\) | −0.448288 | + | 1.67303i | −0.0166720 | + | 0.0622208i | ||||
\(724\) | −13.8564 | − | 8.00000i | −0.514969 | − | 0.297318i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | − | 1.73205i | − | 0.0642824i | ||||||
\(727\) | −33.4607 | − | 8.96575i | −1.24099 | − | 0.332521i | −0.422139 | − | 0.906531i | \(-0.638720\pi\) |
−0.818848 | + | 0.574010i | \(0.805387\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 27.0000i | − | 1.00000i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 63.0000 | − | 36.3731i | 2.33014 | − | 1.34531i | ||||
\(732\) | −9.79796 | + | 9.79796i | −0.362143 | + | 0.362143i | ||||
\(733\) | 30.1146 | − | 8.06918i | 1.11231 | − | 0.298042i | 0.344541 | − | 0.938771i | \(-0.388035\pi\) |
0.767767 | + | 0.640729i | \(0.221368\pi\) | |||||||
\(734\) | 8.66025 | − | 15.0000i | 0.319656 | − | 0.553660i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.00000 | + | 5.19615i | 0.110581 | + | 0.191533i | ||||
\(737\) | −21.2132 | − | 21.2132i | −0.781398 | − | 0.781398i | ||||
\(738\) | −3.67423 | − | 3.67423i | −0.135250 | − | 0.135250i | ||||
\(739\) | − | 23.0000i | − | 0.846069i | −0.906114 | − | 0.423034i | \(-0.860965\pi\) | ||
0.906114 | − | 0.423034i | \(-0.139035\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.0000 | − | 25.9808i | 0.551039 | − | 0.954427i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.10583 | + | 11.5911i | 0.113942 | + | 0.425237i | 0.999206 | − | 0.0398527i | \(-0.0126889\pi\) |
−0.885264 | + | 0.465089i | \(0.846022\pi\) | |||||||
\(744\) | 3.46410 | − | 6.00000i | 0.127000 | − | 0.219971i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 20.7846i | 0.760979i | ||||||||
\(747\) | 6.98811 | − | 26.0800i | 0.255682 | − | 0.954217i | ||||
\(748\) | −14.6969 | − | 14.6969i | −0.537373 | − | 0.537373i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.0000 | − | 32.9090i | 0.693320 | − | 1.20087i | −0.277424 | − | 0.960748i | \(-0.589481\pi\) |
0.970744 | − | 0.240118i | \(-0.0771860\pi\) | |||||||
\(752\) | −5.79555 | + | 1.55291i | −0.211342 | + | 0.0566290i | ||||
\(753\) | 6.36396 | − | 6.36396i | 0.231916 | − | 0.231916i | ||||
\(754\) | −20.7846 | + | 12.0000i | −0.756931 | + | 0.437014i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.6969 | − | 14.6969i | 0.534169 | − | 0.534169i | −0.387641 | − | 0.921810i | \(-0.626710\pi\) |
0.921810 | + | 0.387641i | \(0.126710\pi\) | |||||||
\(758\) | −7.72741 | − | 2.07055i | −0.280672 | − | 0.0752058i | ||||
\(759\) | 36.0000i | 1.30672i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.50000 | + | 0.866025i | 0.0543750 | + | 0.0313934i | 0.526941 | − | 0.849902i | \(-0.323339\pi\) |
−0.472566 | + | 0.881295i | \(0.656672\pi\) | |||||||
\(762\) | −4.65874 | + | 17.3867i | −0.168768 | + | 0.629852i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −24.2487 | −0.877288 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.00000 | −0.216789 | ||||||||
\(767\) | 1.55291 | − | 5.79555i | 0.0560725 | − | 0.209265i | ||||
\(768\) | −1.67303 | + | 0.448288i | −0.0603704 | + | 0.0161762i | ||||
\(769\) | 42.4352 | + | 24.5000i | 1.53025 | + | 0.883493i | 0.999350 | + | 0.0360609i | \(0.0114810\pi\) |
0.530904 | + | 0.847432i | \(0.321852\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.5000 | + | 12.9904i | 0.810318 | + | 0.467837i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −29.6985 | + | 29.6985i | −1.06818 | + | 1.06818i | −0.0706813 | + | 0.997499i | \(0.522517\pi\) |
−0.997499 | + | 0.0706813i | \(0.977483\pi\) | |||||||
\(774\) | 18.1865 | − | 31.5000i | 0.653701 | − | 1.13224i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.50000 | + | 2.59808i | −0.161541 | + | 0.0932655i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10.0382 | + | 2.68973i | −0.359887 | + | 0.0964314i | ||||
\(779\) | −4.33013 | + | 7.50000i | −0.155143 | + | 0.268715i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.0000 | + | 20.7846i | 0.429394 | + | 0.743732i | ||||
\(782\) | 25.4558 | + | 25.4558i | 0.910299 | + | 0.910299i | ||||
\(783\) | 34.7733 | + | 9.31749i | 1.24270 | + | 0.332980i | ||||
\(784\) | − | 7.00000i | − | 0.250000i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6.00000 | 0.214013 | ||||||||
\(787\) | 8.06918 | + | 30.1146i | 0.287635 | + | 1.07347i | 0.946892 | + | 0.321551i | \(0.104204\pi\) |
−0.659257 | + | 0.751918i | \(0.729129\pi\) | |||||||
\(788\) | 6.21166 | + | 23.1822i | 0.221281 | + | 0.825832i | ||||
\(789\) | 10.3923 | + | 18.0000i | 0.369976 | + | 0.640817i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −10.0382 | − | 2.68973i | −0.356692 | − | 0.0955753i | ||||
\(793\) | −19.5959 | − | 19.5959i | −0.695871 | − | 0.695871i | ||||
\(794\) | 12.1244 | + | 21.0000i | 0.430277 | + | 0.745262i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.00000 | − | 6.92820i | 0.141776 | − | 0.245564i | ||||
\(797\) | 5.79555 | − | 1.55291i | 0.205289 | − | 0.0550070i | −0.154709 | − | 0.987960i | \(-0.549444\pi\) |
0.359998 | + | 0.932953i | \(0.382777\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −31.1769 | + | 18.0000i | −1.10296 | + | 0.636794i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 36.3731i | − | 1.28518i | ||||||
\(802\) | −14.6969 | + | 14.6969i | −0.518967 | + | 0.518967i | ||||
\(803\) | −40.5689 | − | 10.8704i | −1.43164 | − | 0.383608i | ||||
\(804\) | −12.9904 | + | 7.50000i | −0.458135 | + | 0.264505i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 12.0000 | + | 6.92820i | 0.422682 | + | 0.244036i | ||||
\(807\) | 16.9706 | + | 16.9706i | 0.597392 | + | 0.597392i | ||||
\(808\) | −0.896575 | + | 3.34607i | −0.0315414 | + | 0.117714i | ||||
\(809\) | −29.4449 | −1.03523 | −0.517613 | − | 0.855615i | \(-0.673179\pi\) | ||||
−0.517613 | + | 0.855615i | \(0.673179\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.0000 | 0.877869 | 0.438934 | − | 0.898519i | \(-0.355356\pi\) | ||||
0.438934 | + | 0.898519i | \(0.355356\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.2474 | − | 12.2474i | −0.429537 | − | 0.429537i | ||||
\(814\) | 20.7846 | + | 12.0000i | 0.728500 | + | 0.420600i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −9.00000 | + | 5.19615i | −0.315063 | + | 0.181902i | ||||
\(817\) | −58.5561 | − | 15.6901i | −2.04862 | − | 0.548926i | ||||
\(818\) | 20.5061 | − | 20.5061i | 0.716979 | − | 0.716979i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −48.0000 | + | 27.7128i | −1.67521 | + | 0.967184i | −0.710567 | + | 0.703630i | \(0.751561\pi\) |
−0.964645 | + | 0.263554i | \(0.915105\pi\) | |||||||
\(822\) | −4.03459 | − | 15.0573i | −0.140722 | − | 0.525183i | ||||
\(823\) | −3.34607 | + | 0.896575i | −0.116637 | + | 0.0312527i | −0.316665 | − | 0.948537i | \(-0.602563\pi\) |
0.200029 | + | 0.979790i | \(0.435896\pi\) | |||||||
\(824\) | −1.73205 | + | 3.00000i | −0.0603388 | + | 0.104510i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.6066 | + | 10.6066i | 0.368828 | + | 0.368828i | 0.867050 | − | 0.498222i | \(-0.166014\pi\) |
−0.498222 | + | 0.867050i | \(0.666014\pi\) | |||||||
\(828\) | 17.3867 | + | 4.65874i | 0.604228 | + | 0.161903i | ||||
\(829\) | − | 38.0000i | − | 1.31979i | −0.751356 | − | 0.659897i | \(-0.770600\pi\) | ||
0.751356 | − | 0.659897i | \(-0.229400\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.00000 | − | 10.3923i | −0.208138 | − | 0.360505i | ||||
\(832\) | −0.896575 | − | 3.34607i | −0.0310832 | − | 0.116004i | ||||
\(833\) | −10.8704 | − | 40.5689i | −0.376637 | − | 1.40563i | ||||
\(834\) | −6.92820 | −0.239904 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 17.3205i | 0.599042i | ||||||||
\(837\) | −5.37945 | − | 20.0764i | −0.185941 | − | 0.693942i | ||||
\(838\) | 18.3712 | + | 18.3712i | 0.634622 | + | 0.634622i | ||||
\(839\) | −6.92820 | − | 12.0000i | −0.239188 | − | 0.414286i | 0.721293 | − | 0.692630i | \(-0.243548\pi\) |
−0.960482 | + | 0.278344i | \(0.910215\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.50000 | + | 16.4545i | −0.327586 | + | 0.567396i | ||||
\(842\) | 7.72741 | − | 2.07055i | 0.266304 | − | 0.0713559i | ||||
\(843\) | −34.7733 | − | 9.31749i | −1.19766 | − | 0.320911i | ||||
\(844\) | −11.2583 | + | 6.50000i | −0.387528 | + | 0.223739i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9.00000 | + | 15.5885i | −0.309426 | + | 0.535942i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.79555 | − | 1.55291i | −0.199020 | − | 0.0533273i | ||||
\(849\) | 18.1865 | + | 10.5000i | 0.624160 | + | 0.360359i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36.0000 | − | 20.7846i | −1.23406 | − | 0.712487i | ||||
\(852\) | 11.5911 | − | 3.10583i | 0.397105 | − | 0.106404i | ||||
\(853\) | −0.896575 | + | 3.34607i | −0.0306982 | + | 0.114567i | −0.979575 | − | 0.201080i | \(-0.935555\pi\) |
0.948877 | + | 0.315647i | \(0.102222\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.00000 | −0.102538 | ||||||||
\(857\) | −3.88229 | + | 14.4889i | −0.132616 | + | 0.494931i | −0.999996 | − | 0.00271550i | \(-0.999136\pi\) |
0.867380 | + | 0.497646i | \(0.165802\pi\) | |||||||
\(858\) | 5.37945 | − | 20.0764i | 0.183651 | − | 0.685397i | ||||
\(859\) | 11.2583 | + | 6.50000i | 0.384129 | + | 0.221777i | 0.679613 | − | 0.733571i | \(-0.262148\pi\) |
−0.295484 | + | 0.955348i | \(0.595481\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −13.3843 | − | 3.58630i | −0.455870 | − | 0.122150i | ||||
\(863\) | −4.24264 | + | 4.24264i | −0.144421 | + | 0.144421i | −0.775621 | − | 0.631199i | \(-0.782563\pi\) |
0.631199 | + | 0.775621i | \(0.282563\pi\) | |||||||
\(864\) | −2.59808 | + | 4.50000i | −0.0883883 | + | 0.153093i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −6.00000 | + | 3.46410i | −0.203888 | + | 0.117715i | ||||
\(867\) | −23.2702 | + | 23.2702i | −0.790296 | + | 0.790296i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.2487 | − | 42.0000i | 0.822581 | − | 1.42475i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.0000 | − | 25.9808i | −0.508256 | − | 0.880325i | ||||
\(872\) | −14.1421 | − | 14.1421i | −0.478913 | − | 0.478913i | ||||
\(873\) | −4.03459 | + | 15.0573i | −0.136550 | + | 0.509612i | ||||
\(874\) | − | 30.0000i | − | 1.01477i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.5000 | + | 18.1865i | −0.354762 | + | 0.614466i | ||||
\(877\) | −2.68973 | − | 10.0382i | −0.0908256 | − | 0.338966i | 0.905528 | − | 0.424287i | \(-0.139475\pi\) |
−0.996354 | + | 0.0853209i | \(0.972808\pi\) | |||||||
\(878\) | −6.72930 | − | 25.1141i | −0.227103 | − | 0.847559i | ||||
\(879\) | −5.19615 | + | 9.00000i | −0.175262 | + | 0.303562i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 6.92820i | − | 0.233417i | −0.993166 | − | 0.116709i | \(-0.962766\pi\) | ||
0.993166 | − | 0.116709i | \(-0.0372343\pi\) | |||||||
\(882\) | −14.8492 | − | 14.8492i | −0.500000 | − | 0.500000i | ||||
\(883\) | −36.7423 | − | 36.7423i | −1.23648 | − | 1.23648i | −0.961431 | − | 0.275048i | \(-0.911306\pi\) |
−0.275048 | − | 0.961431i | \(-0.588694\pi\) | |||||||
\(884\) | −10.3923 | − | 18.0000i | −0.349531 | − | 0.605406i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −18.0000 | + | 31.1769i | −0.604722 | + | 1.04741i | ||||
\(887\) | −5.79555 | + | 1.55291i | −0.194596 | + | 0.0521418i | −0.354800 | − | 0.934942i | \(-0.615451\pi\) |
0.160205 | + | 0.987084i | \(0.448785\pi\) | |||||||
\(888\) | 8.48528 | − | 8.48528i | 0.284747 | − | 0.284747i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −27.0000 | + | 15.5885i | −0.904534 | + | 0.522233i | ||||
\(892\) | 4.89898 | − | 4.89898i | 0.164030 | − | 0.164030i | ||||
\(893\) | 28.9778 | + | 7.76457i | 0.969704 | + | 0.259831i | ||||
\(894\) | 18.0000i | 0.602010i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.31749 | + | 34.7733i | −0.311102 | + | 1.16105i | ||||
\(898\) | 2.24144 | − | 8.36516i | 0.0747978 | − | 0.279149i | ||||
\(899\) | 27.7128 | 0.924274 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.0000 | −1.19933 | ||||||||
\(902\) | −1.55291 | + | 5.79555i | −0.0517064 | + | 0.192971i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.9904 | − | 7.50000i | −0.432054 | − | 0.249446i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −24.0000 | − | 13.8564i | −0.797347 | − | 0.460348i | ||||
\(907\) | 31.7876 | + | 8.51747i | 1.05549 | + | 0.282818i | 0.744519 | − | 0.667601i | \(-0.232679\pi\) |
0.310972 | + | 0.950419i | \(0.399346\pi\) | |||||||
\(908\) | −2.12132 | + | 2.12132i | −0.0703985 | + | 0.0703985i | ||||
\(909\) | 5.19615 | + | 9.00000i | 0.172345 | + | 0.298511i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.0000 | − | 8.66025i | 0.496972 | − | 0.286927i | −0.230490 | − | 0.973075i | \(-0.574033\pi\) |
0.727462 | + | 0.686148i | \(0.240700\pi\) | |||||||
\(912\) | 8.36516 | + | 2.24144i | 0.276998 | + | 0.0742215i | ||||
\(913\) | −30.1146 | + | 8.06918i | −0.996647 | + | 0.267051i | ||||
\(914\) | 2.59808 | − | 4.50000i | 0.0859367 | − | 0.148847i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.00000 | + | 13.8564i | 0.264327 | + | 0.457829i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −8.06918 | + | 30.1146i | −0.266323 | + | 0.993929i | ||||
\(919\) | − | 2.00000i | − | 0.0659739i | −0.999456 | − | 0.0329870i | \(-0.989498\pi\) | ||
0.999456 | − | 0.0329870i | \(-0.0105020\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 42.0000 | 1.38395 | ||||||||
\(922\) | 8.96575 | + | 33.4607i | 0.295271 | + | 1.10197i | ||||
\(923\) | 6.21166 | + | 23.1822i | 0.204459 | + | 0.763052i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 6.92820i | − | 0.227675i | ||||||
\(927\) | 2.68973 | + | 10.0382i | 0.0883422 | + | 0.329698i | ||||
\(928\) | −4.89898 | − | 4.89898i | −0.160817 | − | 0.160817i | ||||
\(929\) | 27.7128 | + | 48.0000i | 0.909228 | + | 1.57483i | 0.815139 | + | 0.579265i | \(0.196660\pi\) |
0.0940887 | + | 0.995564i | \(0.470006\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.5000 | + | 30.3109i | −0.573539 | + | 0.993399i | ||||
\(932\) | −8.69333 | + | 2.32937i | −0.284760 | + | 0.0763011i | ||||
\(933\) | −10.8704 | − | 40.5689i | −0.355881 | − | 1.32817i | ||||
\(934\) | 18.1865 | − | 10.5000i | 0.595082 | − | 0.343570i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −9.00000 | − | 5.19615i | −0.294174 | − | 0.169842i | ||||
\(937\) | −3.67423 | + | 3.67423i | −0.120032 | + | 0.120032i | −0.764571 | − | 0.644539i | \(-0.777049\pi\) |
0.644539 | + | 0.764571i | \(0.277049\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −49.3634 | + | 28.5000i | −1.61092 | + | 0.930062i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.0000 | + | 20.7846i | 1.17357 | + | 0.677559i | 0.954517 | − | 0.298155i | \(-0.0963712\pi\) |
0.219049 | + | 0.975714i | \(0.429705\pi\) | |||||||
\(942\) | 4.24264 | + | 4.24264i | 0.138233 | + | 0.138233i | ||||
\(943\) | 2.68973 | − | 10.0382i | 0.0875895 | − | 0.326889i | ||||
\(944\) | 1.73205 | 0.0563735 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −42.0000 | −1.36554 | ||||||||
\(947\) | 3.88229 | − | 14.4889i | 0.126157 | − | 0.470826i | −0.873721 | − | 0.486427i | \(-0.838300\pi\) |
0.999878 | + | 0.0156019i | \(0.00496644\pi\) | |||||||
\(948\) | −17.1464 | − | 17.1464i | −0.556890 | − | 0.556890i | ||||
\(949\) | −36.3731 | − | 21.0000i | −1.18072 | − | 0.681689i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.0000 | + | 10.3923i | −0.583690 | + | 0.336994i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.24264 | + | 4.24264i | −0.137433 | + | 0.137433i | −0.772476 | − | 0.635044i | \(-0.780982\pi\) |
0.635044 | + | 0.772476i | \(0.280982\pi\) | |||||||
\(954\) | −15.5885 | + | 9.00000i | −0.504695 | + | 0.291386i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9.00000 | + | 5.19615i | −0.291081 | + | 0.168056i | ||||
\(957\) | −10.7589 | − | 40.1528i | −0.347786 | − | 1.29796i | ||||
\(958\) | 16.7303 | − | 4.48288i | 0.540532 | − | 0.144835i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | + | 12.9904i | 0.241935 | + | 0.419045i | ||||
\(962\) | 16.9706 | + | 16.9706i | 0.547153 | + | 0.547153i | ||||
\(963\) | −6.36396 | + | 6.36396i | −0.205076 | + | 0.205076i | ||||
\(964\) | − | 1.00000i | − | 0.0322078i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.79315 | − | 6.69213i | −0.0576638 | − | 0.215204i | 0.931082 | − | 0.364810i | \(-0.118866\pi\) |
−0.988746 | + | 0.149606i | \(0.952200\pi\) | |||||||
\(968\) | 0.258819 | + | 0.965926i | 0.00831876 | + | 0.0310460i | ||||
\(969\) | 51.9615 | 1.66924 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 22.5167i | − | 0.722594i | −0.932451 | − | 0.361297i | \(-0.882334\pi\) | ||
0.932451 | − | 0.361297i | \(-0.117666\pi\) | |||||||
\(972\) | 4.03459 | + | 15.0573i | 0.129410 | + | 0.482963i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −3.46410 | − | 6.00000i | −0.110997 | − | 0.192252i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.00000 | − | 6.92820i | 0.128037 | − | 0.221766i | ||||
\(977\) | 2.89778 | − | 0.776457i | 0.0927081 | − | 0.0248411i | −0.212167 | − | 0.977233i | \(-0.568052\pi\) |
0.304875 | + | 0.952392i | \(0.401385\pi\) | |||||||
\(978\) | −2.89778 | − | 0.776457i | −0.0926607 | − | 0.0248284i | ||||
\(979\) | −36.3731 | + | 21.0000i | −1.16249 | + | 0.671163i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −60.0000 | −1.91565 | ||||||||
\(982\) | 20.8207 | − | 20.8207i | 0.664414 | − | 0.664414i | ||||
\(983\) | −40.5689 | − | 10.8704i | −1.29395 | − | 0.346712i | −0.454788 | − | 0.890600i | \(-0.650285\pi\) |
−0.839158 | + | 0.543888i | \(0.816952\pi\) | |||||||
\(984\) | 2.59808 | + | 1.50000i | 0.0828236 | + | 0.0478183i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −36.0000 | − | 20.7846i | −1.14647 | − | 0.661917i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.48288 | + | 16.7303i | −0.142619 | + | 0.532263i | ||||
\(989\) | 72.7461 | 2.31319 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40.0000 | −1.27064 | −0.635321 | − | 0.772248i | \(-0.719132\pi\) | ||||
−0.635321 | + | 0.772248i | \(0.719132\pi\) | |||||||
\(992\) | −1.03528 | + | 3.86370i | −0.0328701 | + | 0.122673i | ||||
\(993\) | −0.448288 | + | 1.67303i | −0.0142260 | + | 0.0530921i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 15.5885i | 0.493939i | ||||||||
\(997\) | 10.0382 | + | 2.68973i | 0.317913 | + | 0.0851845i | 0.414247 | − | 0.910165i | \(-0.364045\pi\) |
−0.0963340 | + | 0.995349i | \(0.530712\pi\) | |||||||
\(998\) | 9.19239 | − | 9.19239i | 0.290980 | − | 0.290980i | ||||
\(999\) | − | 36.0000i | − | 1.13899i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 450.2.p.g.293.2 | yes | 8 | |
3.2 | odd | 2 | 1350.2.q.c.1043.1 | 8 | |||
5.2 | odd | 4 | inner | 450.2.p.g.257.2 | yes | 8 | |
5.3 | odd | 4 | inner | 450.2.p.g.257.1 | ✓ | 8 | |
5.4 | even | 2 | inner | 450.2.p.g.293.1 | yes | 8 | |
9.2 | odd | 6 | inner | 450.2.p.g.443.2 | yes | 8 | |
9.7 | even | 3 | 1350.2.q.c.143.1 | 8 | |||
15.2 | even | 4 | 1350.2.q.c.557.1 | 8 | |||
15.8 | even | 4 | 1350.2.q.c.557.2 | 8 | |||
15.14 | odd | 2 | 1350.2.q.c.1043.2 | 8 | |||
45.2 | even | 12 | inner | 450.2.p.g.407.2 | yes | 8 | |
45.7 | odd | 12 | 1350.2.q.c.1007.1 | 8 | |||
45.29 | odd | 6 | inner | 450.2.p.g.443.1 | yes | 8 | |
45.34 | even | 6 | 1350.2.q.c.143.2 | 8 | |||
45.38 | even | 12 | inner | 450.2.p.g.407.1 | yes | 8 | |
45.43 | odd | 12 | 1350.2.q.c.1007.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.2.p.g.257.1 | ✓ | 8 | 5.3 | odd | 4 | inner | |
450.2.p.g.257.2 | yes | 8 | 5.2 | odd | 4 | inner | |
450.2.p.g.293.1 | yes | 8 | 5.4 | even | 2 | inner | |
450.2.p.g.293.2 | yes | 8 | 1.1 | even | 1 | trivial | |
450.2.p.g.407.1 | yes | 8 | 45.38 | even | 12 | inner | |
450.2.p.g.407.2 | yes | 8 | 45.2 | even | 12 | inner | |
450.2.p.g.443.1 | yes | 8 | 45.29 | odd | 6 | inner | |
450.2.p.g.443.2 | yes | 8 | 9.2 | odd | 6 | inner | |
1350.2.q.c.143.1 | 8 | 9.7 | even | 3 | |||
1350.2.q.c.143.2 | 8 | 45.34 | even | 6 | |||
1350.2.q.c.557.1 | 8 | 15.2 | even | 4 | |||
1350.2.q.c.557.2 | 8 | 15.8 | even | 4 | |||
1350.2.q.c.1007.1 | 8 | 45.7 | odd | 12 | |||
1350.2.q.c.1007.2 | 8 | 45.43 | odd | 12 | |||
1350.2.q.c.1043.1 | 8 | 3.2 | odd | 2 | |||
1350.2.q.c.1043.2 | 8 | 15.14 | odd | 2 |