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 | 293.1 | ||
Root | \(0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.293 |
Dual form | 450.2.p.g.407.1 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{3}{4}\right)\) |
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 | −0.691015 | − | 0.722840i | \(-0.742836\pi\) |
−0.237016 | + | 0.971506i | \(0.576170\pi\) | |||||||
\(14\) | 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 | \(-0.990633\pi\) |
−0.0294245 | − | 0.999567i | \(-0.509367\pi\) | |||||||
\(18\) | −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 | \(-0.868211\pi\) |
0.591703 | − | 0.806156i | \(-0.298456\pi\) | |||||||
\(24\) | −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 | −0.178545 | − | 0.983932i | \(-0.557139\pi\) |
0.983932 | + | 0.178545i | \(0.0571389\pi\) | |||||||
\(38\) | 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 | \(0.458828\pi\) |
−0.607527 | + | 0.794299i | \(0.707838\pi\) | |||||||
\(44\) | −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 | \(-0.772497\pi\) |
0.981792 | − | 0.189961i | \(-0.0608363\pi\) | |||||||
\(48\) | 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 | −0.352892 | − | 0.935664i | \(-0.614802\pi\) |
0.935664 | + | 0.352892i | \(0.114802\pi\) | |||||||
\(54\) | 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 | \(0.0941030\pi\) |
−0.682783 | + | 0.730622i | \(0.739230\pi\) | |||||||
\(68\) | 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 | \(0.00109011\pi\) |
0.00342468 | + | 0.999994i | \(0.498910\pi\) | |||||||
\(74\) | 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 | 0.702151 | − | 0.712028i | \(-0.252223\pi\) |
0.252066 | + | 0.967710i | \(0.418890\pi\) | |||||||
\(84\) | 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 | −0.00515471 | − | 0.999987i | \(-0.501641\pi\) |
−0.504457 | + | 0.863437i | \(0.668307\pi\) | |||||||
\(98\) | 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 | −0.419871 | − | 0.907584i | \(-0.637925\pi\) |
0.0901732 | + | 0.995926i | \(0.471258\pi\) | |||||||
\(104\) | −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 | 0.597095 | − | 0.802171i | \(-0.296322\pi\) |
−0.802171 | + | 0.597095i | \(0.796322\pi\) | |||||||
\(108\) | −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 | \(-0.834038\pi\) |
0.501915 | − | 0.864917i | \(-0.332629\pi\) | |||||||
\(114\) | −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 | −0.301420 | − | 0.953491i | \(-0.597461\pi\) |
0.953491 | + | 0.301420i | \(0.0974607\pi\) | |||||||
\(128\) | 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 | \(0.208946\pi\) |
−0.991192 | + | 0.132434i | \(0.957721\pi\) | |||||||
\(138\) | −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 | 0.920875 | − | 0.389857i | \(-0.127476\pi\) |
−0.992430 | + | 0.122812i | \(0.960809\pi\) | |||||||
\(158\) | 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 | 0.753443 | − | 0.657513i | \(-0.228392\pi\) |
−0.657513 | + | 0.753443i | \(0.728392\pi\) | |||||||
\(164\) | 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 | 0.219242 | − | 0.975670i | \(-0.429641\pi\) |
0.677705 | + | 0.735334i | \(0.262975\pi\) | |||||||
\(168\) | 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 | \(0.0764212\pi\) |
0.237785 | + | 0.971318i | \(0.423579\pi\) | |||||||
\(198\) | −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 | −0.879538 | − | 0.475828i | \(-0.842148\pi\) |
0.999617 | + | 0.0276899i | \(0.00881510\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.0000 | 0.997785 | ||||||||
\(227\) | −0.776457 | + | 2.89778i | −0.0515353 | + | 0.192332i | −0.986894 | − | 0.161367i | \(-0.948410\pi\) |
0.935359 | + | 0.353699i | \(0.115076\pi\) | |||||||
\(228\) | 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 | −0.884140 | − | 0.467223i | \(-0.845255\pi\) |
0.467223 | + | 0.884140i | \(0.345255\pi\) | |||||||
\(234\) | 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 | −0.680644 | − | 0.732614i | \(-0.738300\pi\) |
−0.223148 | + | 0.974785i | \(0.571633\pi\) | |||||||
\(258\) | 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 | −0.116916 | − | 0.993142i | \(-0.537301\pi\) |
−0.597823 | + | 0.801628i | \(0.703967\pi\) | |||||||
\(264\) | −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 | 0.454196 | − | 0.890902i | \(-0.349926\pi\) |
−0.0521052 | + | 0.998642i | \(0.516593\pi\) | |||||||
\(278\) | 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 | −0.589510 | − | 0.807761i | \(-0.700679\pi\) |
−0.106650 | + | 0.994297i | \(0.534012\pi\) | |||||||
\(284\) | 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 | 0.905614 | − | 0.424103i | \(-0.139411\pi\) |
−0.996336 | + | 0.0855230i | \(0.972744\pi\) | |||||||
\(294\) | −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 | −0.999776 | − | 0.0211774i | \(-0.993259\pi\) |
0.0211774 | + | 0.999776i | \(0.493259\pi\) | |||||||
\(308\) | 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 | \(-0.536419\pi\) |
0.595601 | − | 0.803281i | \(-0.296914\pi\) | |||||||
\(314\) | 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 | \(-0.807257\pi\) |
0.996646 | − | 0.0818309i | \(-0.0260767\pi\) | |||||||
\(318\) | 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 | 0.997412 | − | 0.0718974i | \(-0.0229054\pi\) |
−0.899733 | + | 0.436441i | \(0.856239\pi\) | |||||||
\(338\) | −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 | −0.556147 | − | 0.831084i | \(-0.687721\pi\) |
−0.0660960 | + | 0.997813i | \(0.521054\pi\) | |||||||
\(348\) | 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 | 0.0199361 | − | 0.999801i | \(-0.493654\pi\) |
−0.482635 | + | 0.875821i | \(0.660320\pi\) | |||||||
\(354\) | − | 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 | −0.205795 | − | 0.978595i | \(-0.565978\pi\) |
−0.667521 | + | 0.744591i | \(0.732645\pi\) | |||||||
\(368\) | 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 | 0.301603 | − | 0.953434i | \(-0.402478\pi\) |
0.737913 | + | 0.674896i | \(0.235812\pi\) | |||||||
\(374\) | 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 | 0.994184 | − | 0.107691i | \(-0.0343456\pi\) |
−0.914834 | + | 0.403830i | \(0.867679\pi\) | |||||||
\(384\) | −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 | −0.130848 | − | 0.991402i | \(-0.541770\pi\) |
0.991402 | + | 0.130848i | \(0.0417700\pi\) | |||||||
\(398\) | −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 | 0.814955 | − | 0.579525i | \(-0.196762\pi\) |
−0.579525 | + | 0.814955i | \(0.696762\pi\) | |||||||
\(434\) | 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 | 0.960208 | − | 0.279285i | \(-0.0900973\pi\) |
0.691922 | + | 0.721972i | \(0.256764\pi\) | |||||||
\(444\) | 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 | 0.139509 | − | 0.990221i | \(-0.455448\pi\) |
−0.374292 | + | 0.927311i | \(0.622114\pi\) | |||||||
\(458\) | 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 | −0.410948 | − | 0.911659i | \(-0.634802\pi\) |
0.0999382 | + | 0.994994i | \(0.468136\pi\) | |||||||
\(464\) | 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 | 0.274458 | − | 0.961599i | \(-0.411502\pi\) |
−0.961599 | + | 0.274458i | \(0.911502\pi\) | |||||||
\(468\) | −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 | −0.809338 | − | 0.587344i | \(-0.800174\pi\) |
0.587344 | + | 0.809338i | \(0.300174\pi\) | |||||||
\(488\) | −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 | \(-0.364187\pi\) |
0.910349 | − | 0.413841i | \(-0.135813\pi\) | |||||||
\(504\) | 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 | 0.622197 | − | 0.782860i | \(-0.286240\pi\) |
−0.782860 | + | 0.622197i | \(0.786240\pi\) | |||||||
\(524\) | −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 | 0.691828 | − | 0.722062i | \(-0.256805\pi\) |
0.238110 | + | 0.971238i | \(0.423472\pi\) | |||||||
\(548\) | 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 | 0.968414 | − | 0.249348i | \(-0.0802163\pi\) |
−0.249348 | + | 0.968414i | \(0.580216\pi\) | |||||||
\(558\) | 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 | \(-0.937417\pi\) |
0.751668 | − | 0.659542i | \(-0.229250\pi\) | |||||||
\(564\) | 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 | \(-0.476608\pi\) |
0.997301 | − | 0.0734217i | \(-0.0233919\pi\) | |||||||
\(578\) | −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 | −0.999162 | − | 0.0409281i | \(-0.986969\pi\) |
0.0409281 | + | 0.999162i | \(0.486969\pi\) | |||||||
\(594\) | 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 | \(-0.919558\pi\) |
0.713501 | − | 0.700654i | \(-0.247108\pi\) | |||||||
\(608\) | 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 | 0.754841 | − | 0.655907i | \(-0.227714\pi\) |
−0.655907 | + | 0.754841i | \(0.727714\pi\) | |||||||
\(614\) | −12.1244 | − | 21.0000i | −0.489299 | − | 0.847491i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.69333 | + | 2.32937i | −0.349980 | + | 0.0937770i | −0.429527 | − | 0.903054i | \(-0.641320\pi\) |
0.0795462 | + | 0.996831i | \(0.474653\pi\) | |||||||
\(618\) | −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 | 0.790566 | − | 0.612376i | \(-0.209786\pi\) |
0.990839 | + | 0.135050i | \(0.0431196\pi\) | |||||||
\(644\) | 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 | \(-0.940840\pi\) |
−0.184790 | − | 0.982778i | \(-0.559160\pi\) | |||||||
\(648\) | −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 | \(-0.883644\pi\) |
0.630079 | − | 0.776531i | \(-0.283023\pi\) | |||||||
\(654\) | 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 | \(0.316036\pi\) |
−0.891904 | + | 0.452224i | \(0.850631\pi\) | |||||||
\(674\) | −6.92820 | −0.266864 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 1.55291 | − | 5.79555i | 0.0596833 | − | 0.222741i | −0.929642 | − | 0.368464i | \(-0.879884\pi\) |
0.989326 | + | 0.145722i | \(0.0465506\pi\) | |||||||
\(678\) | −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 | −0.746526 | − | 0.665356i | \(-0.768280\pi\) |
0.665356 | + | 0.746526i | \(0.268280\pi\) | |||||||
\(684\) | −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 | 0.818848 | − | 0.574010i | \(-0.194613\pi\) |
0.422139 | + | 0.906531i | \(0.361280\pi\) | |||||||
\(728\) | 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 | −0.767767 | − | 0.640729i | \(-0.778632\pi\) |
−0.344541 | + | 0.938771i | \(0.611965\pi\) | |||||||
\(734\) | 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 | 0.885264 | − | 0.465089i | \(-0.153978\pi\) |
−0.999206 | + | 0.0398527i | \(0.987311\pi\) | |||||||
\(744\) | 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 | −0.921810 | − | 0.387641i | \(-0.873290\pi\) |
0.387641 | + | 0.921810i | \(0.373290\pi\) | |||||||
\(758\) | 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 | \(-0.477483\pi\) |
0.997499 | − | 0.0706813i | \(-0.0225173\pi\) | |||||||
\(774\) | 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 | \(-0.895796\pi\) |
0.659257 | − | 0.751918i | \(-0.270871\pi\) | |||||||
\(788\) | −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 | −0.359998 | − | 0.932953i | \(-0.617223\pi\) |
0.154709 | + | 0.987960i | \(0.450556\pi\) | |||||||
\(798\) | 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 | −0.200029 | − | 0.979790i | \(-0.564104\pi\) |
0.316665 | + | 0.948537i | \(0.397437\pi\) | |||||||
\(824\) | −1.73205 | + | 3.00000i | −0.0603388 | + | 0.104510i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10.6066 | − | 10.6066i | −0.368828 | − | 0.368828i | 0.498222 | − | 0.867050i | \(-0.333986\pi\) |
−0.867050 | + | 0.498222i | \(0.833986\pi\) | |||||||
\(828\) | −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 | −0.948877 | − | 0.315647i | \(-0.897778\pi\) |
0.979575 | + | 0.201080i | \(0.0644451\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.00000 | −0.102538 | ||||||||
\(857\) | 3.88229 | − | 14.4889i | 0.132616 | − | 0.494931i | −0.867380 | − | 0.497646i | \(-0.834198\pi\) |
0.999996 | + | 0.00271550i | \(0.000864371\pi\) | |||||||
\(858\) | −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 | −0.631199 | − | 0.775621i | \(-0.717437\pi\) |
0.775621 | + | 0.631199i | \(0.217437\pi\) | |||||||
\(864\) | −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 | 0.996354 | − | 0.0853209i | \(-0.0271915\pi\) |
−0.905528 | + | 0.424287i | \(0.860525\pi\) | |||||||
\(878\) | 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 | \(0.0886937\pi\) |
0.275048 | + | 0.961431i | \(0.411306\pi\) | |||||||
\(884\) | −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 | −0.160205 | − | 0.987084i | \(-0.551215\pi\) |
0.354800 | + | 0.934942i | \(0.384549\pi\) | |||||||
\(888\) | −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 | −0.310972 | − | 0.950419i | \(-0.600654\pi\) |
−0.744519 | + | 0.667601i | \(0.767321\pi\) | |||||||
\(908\) | 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 | −0.644539 | − | 0.764571i | \(-0.722951\pi\) |
0.764571 | + | 0.644539i | \(0.222951\pi\) | |||||||
\(938\) | 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 | −0.999878 | − | 0.0156019i | \(-0.995034\pi\) |
0.873721 | + | 0.486427i | \(0.161700\pi\) | |||||||
\(948\) | 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 | −0.635044 | − | 0.772476i | \(-0.719018\pi\) |
0.772476 | + | 0.635044i | \(0.219018\pi\) | |||||||
\(954\) | −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 | 0.988746 | − | 0.149606i | \(-0.0478005\pi\) |
−0.931082 | + | 0.364810i | \(0.881134\pi\) | |||||||
\(968\) | −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 | −0.304875 | − | 0.952392i | \(-0.598615\pi\) |
0.212167 | + | 0.977233i | \(0.431948\pi\) | |||||||
\(978\) | 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 | 0.839158 | − | 0.543888i | \(-0.183048\pi\) |
0.454788 | + | 0.890600i | \(0.349715\pi\) | |||||||
\(984\) | 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 | 0.0963340 | − | 0.995349i | \(-0.469288\pi\) |
−0.414247 | + | 0.910165i | \(0.635955\pi\) | |||||||
\(998\) | −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.293.1 | yes | 8 | |
3.2 | odd | 2 | 1350.2.q.c.1043.2 | 8 | |||
5.2 | odd | 4 | inner | 450.2.p.g.257.1 | ✓ | 8 | |
5.3 | odd | 4 | inner | 450.2.p.g.257.2 | yes | 8 | |
5.4 | even | 2 | inner | 450.2.p.g.293.2 | yes | 8 | |
9.2 | odd | 6 | inner | 450.2.p.g.443.1 | yes | 8 | |
9.7 | even | 3 | 1350.2.q.c.143.2 | 8 | |||
15.2 | even | 4 | 1350.2.q.c.557.2 | 8 | |||
15.8 | even | 4 | 1350.2.q.c.557.1 | 8 | |||
15.14 | odd | 2 | 1350.2.q.c.1043.1 | 8 | |||
45.2 | even | 12 | inner | 450.2.p.g.407.1 | yes | 8 | |
45.7 | odd | 12 | 1350.2.q.c.1007.2 | 8 | |||
45.29 | odd | 6 | inner | 450.2.p.g.443.2 | yes | 8 | |
45.34 | even | 6 | 1350.2.q.c.143.1 | 8 | |||
45.38 | even | 12 | inner | 450.2.p.g.407.2 | yes | 8 | |
45.43 | odd | 12 | 1350.2.q.c.1007.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.2.p.g.257.1 | ✓ | 8 | 5.2 | odd | 4 | inner | |
450.2.p.g.257.2 | yes | 8 | 5.3 | odd | 4 | inner | |
450.2.p.g.293.1 | yes | 8 | 1.1 | even | 1 | trivial | |
450.2.p.g.293.2 | yes | 8 | 5.4 | even | 2 | inner | |
450.2.p.g.407.1 | yes | 8 | 45.2 | even | 12 | inner | |
450.2.p.g.407.2 | yes | 8 | 45.38 | even | 12 | inner | |
450.2.p.g.443.1 | yes | 8 | 9.2 | odd | 6 | inner | |
450.2.p.g.443.2 | yes | 8 | 45.29 | odd | 6 | inner | |
1350.2.q.c.143.1 | 8 | 45.34 | even | 6 | |||
1350.2.q.c.143.2 | 8 | 9.7 | even | 3 | |||
1350.2.q.c.557.1 | 8 | 15.8 | even | 4 | |||
1350.2.q.c.557.2 | 8 | 15.2 | even | 4 | |||
1350.2.q.c.1007.1 | 8 | 45.43 | odd | 12 | |||
1350.2.q.c.1007.2 | 8 | 45.7 | odd | 12 | |||
1350.2.q.c.1043.1 | 8 | 15.14 | odd | 2 | |||
1350.2.q.c.1043.2 | 8 | 3.2 | odd | 2 |