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 | 443.1 | ||
Root | \(0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.443 |
Dual form | 450.2.p.g.257.1 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.965926 | + | 0.258819i | −0.683013 | + | 0.183013i | ||||
\(3\) | −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 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(8\) | −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 | 0.878668 | − | 0.477432i | \(-0.158432\pi\) |
0.0258656 | + | 0.999665i | \(0.491766\pi\) | |||||||
\(12\) | −1.67303 | − | 0.448288i | −0.482963 | − | 0.129410i | ||||
\(13\) | 0.896575 | − | 3.34607i | 0.248665 | − | 0.928032i | −0.722840 | − | 0.691015i | \(-0.757164\pi\) |
0.971506 | − | 0.237016i | \(-0.0761695\pi\) | |||||||
\(14\) | 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 | \(0.490633\pi\) | |||||||
\(18\) | −0.776457 | − | 2.89778i | −0.183013 | − | 0.683013i | ||||
\(19\) | − | 5.00000i | − | 1.14708i | −0.819178 | − | 0.573539i | \(-0.805570\pi\) | ||
0.819178 | − | 0.573539i | \(-0.194430\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.34607 | − | 0.896575i | −0.713384 | − | 0.191151i | ||||
\(23\) | −5.79555 | − | 1.55291i | −1.20846 | − | 0.323805i | −0.402300 | − | 0.915508i | \(-0.631789\pi\) |
−0.806156 | + | 0.591703i | \(0.798456\pi\) | |||||||
\(24\) | 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 | −0.341431 | − | 0.939907i | \(-0.610912\pi\) |
0.984699 | − | 0.174265i | \(-0.0557550\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | − | 3.46410i | −0.359211 | − | 0.622171i | 0.628619 | − | 0.777714i | \(-0.283621\pi\) |
−0.987829 | + | 0.155543i | \(0.950287\pi\) | |||||||
\(32\) | −0.258819 | + | 0.965926i | −0.0457532 | + | 0.170753i | ||||
\(33\) | −1.55291 | − | 5.79555i | −0.270328 | − | 1.00888i | ||||
\(34\) | −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 | \(0.0571389\pi\) | |||||||
\(38\) | 1.29410 | + | 4.82963i | 0.209930 | + | 0.783469i | ||||
\(39\) | −5.19615 | + | 3.00000i | −0.832050 | + | 0.480384i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.50000 | + | 0.866025i | −0.234261 | + | 0.135250i | −0.612536 | − | 0.790443i | \(-0.709851\pi\) |
0.378275 | + | 0.925693i | \(0.376517\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.7112 | − | 3.13801i | 1.78595 | − | 0.478543i | 0.794299 | − | 0.607527i | \(-0.207838\pi\) |
0.991647 | + | 0.128984i | \(0.0411717\pi\) | |||||||
\(44\) | 3.46410 | 0.522233 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.00000 | 0.884652 | ||||||||
\(47\) | 5.79555 | − | 1.55291i | 0.845369 | − | 0.226516i | 0.189961 | − | 0.981792i | \(-0.439164\pi\) |
0.655407 | + | 0.755276i | \(0.272497\pi\) | |||||||
\(48\) | −1.67303 | + | 0.448288i | −0.241481 | + | 0.0647048i | ||||
\(49\) | 6.06218 | − | 3.50000i | 0.866025 | − | 0.500000i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 10.3923i | − | 1.45521i | ||||||
\(52\) | −0.896575 | − | 3.34607i | −0.124333 | − | 0.464016i | ||||
\(53\) | −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 | ||||
\(58\) | −1.79315 | + | 6.69213i | −0.235452 | + | 0.878720i | ||||
\(59\) | −0.866025 | − | 1.50000i | −0.112747 | − | 0.195283i | 0.804130 | − | 0.594454i | \(-0.202632\pi\) |
−0.916877 | + | 0.399170i | \(0.869298\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.00000 | + | 6.92820i | −0.512148 | + | 0.887066i | 0.487753 | + | 0.872982i | \(0.337817\pi\) |
−0.999901 | + | 0.0140840i | \(0.995517\pi\) | |||||||
\(62\) | 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 | ||||
\(67\) | −8.36516 | − | 2.24144i | −1.02197 | − | 0.273835i | −0.291346 | − | 0.956618i | \(-0.594103\pi\) |
−0.730622 | + | 0.682783i | \(0.760770\pi\) | |||||||
\(68\) | 5.79555 | + | 1.55291i | 0.702814 | + | 0.188319i | ||||
\(69\) | 5.19615 | + | 9.00000i | 0.625543 | + | 1.08347i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6.92820i | − | 0.822226i | −0.911584 | − | 0.411113i | \(-0.865140\pi\) | ||
0.911584 | − | 0.411113i | \(-0.134860\pi\) | |||||||
\(72\) | −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 | \(-0.621990\pi\) |
−0.990166 | + | 0.139895i | \(0.955323\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 1.22474 | − | 1.22474i | 0.135250 | − | 0.135250i | ||||
\(83\) | 2.32937 | + | 8.69333i | 0.255682 | + | 0.954217i | 0.967710 | + | 0.252066i | \(0.0811101\pi\) |
−0.712028 | + | 0.702151i | \(0.752223\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −10.5000 | + | 6.06218i | −1.13224 | + | 0.653701i | ||||
\(87\) | −11.5911 | + | 3.10583i | −1.24270 | + | 0.332980i | ||||
\(88\) | −3.34607 | + | 0.896575i | −0.356692 | + | 0.0955753i | ||||
\(89\) | 12.1244 | 1.28518 | 0.642590 | − | 0.766211i | \(-0.277860\pi\) | ||||
0.642590 | + | 0.766211i | \(0.277860\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.79555 | + | 1.55291i | −0.604228 | + | 0.161903i | ||||
\(93\) | −1.79315 | + | 6.69213i | −0.185941 | + | 0.693942i | ||||
\(94\) | −5.19615 | + | 3.00000i | −0.535942 | + | 0.309426i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.50000 | − | 0.866025i | 0.153093 | − | 0.0883883i | ||||
\(97\) | 1.34486 | + | 5.01910i | 0.136550 | + | 0.509612i | 0.999987 | + | 0.00515471i | \(0.00164080\pi\) |
−0.863437 | + | 0.504457i | \(0.831693\pi\) | |||||||
\(98\) | −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 | 0.641774 | − | 0.766894i | \(-0.278199\pi\) |
−0.343263 | + | 0.939239i | \(0.611532\pi\) | |||||||
\(102\) | 2.68973 | + | 10.0382i | 0.266323 | + | 0.993929i | ||||
\(103\) | 0.896575 | − | 3.34607i | 0.0883422 | − | 0.329698i | −0.907584 | − | 0.419871i | \(-0.862075\pi\) |
0.995926 | + | 0.0901732i | \(0.0287421\pi\) | |||||||
\(104\) | 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 | \(0.703678\pi\) | |||||||
\(108\) | 1.34486 | − | 5.01910i | 0.129410 | − | 0.482963i | ||||
\(109\) | 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 | ||||||||
\(113\) | −14.4889 | − | 3.88229i | −1.36300 | − | 0.365215i | −0.498083 | − | 0.867129i | \(-0.665962\pi\) |
−0.864917 | + | 0.501915i | \(0.832629\pi\) | |||||||
\(114\) | 4.33013 | − | 7.50000i | 0.405554 | − | 0.702439i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 6.92820i | − | 0.643268i | ||||||
\(117\) | 10.0382 | + | 2.68973i | 0.928032 | + | 0.248665i | ||||
\(118\) | 1.22474 | + | 1.22474i | 0.112747 | + | 0.112747i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.500000 | + | 0.866025i | 0.0454545 | + | 0.0787296i | ||||
\(122\) | 2.07055 | − | 7.72741i | 0.187459 | − | 0.699607i | ||||
\(123\) | 2.89778 | + | 0.776457i | 0.261284 | + | 0.0700108i | ||||
\(124\) | −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 | \(0.0974607\pi\) | |||||||
\(128\) | 0.258819 | + | 0.965926i | 0.0228766 | + | 0.0853766i | ||||
\(129\) | −18.1865 | − | 10.5000i | −1.60123 | − | 0.924473i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.00000 | − | 1.73205i | 0.262111 | − | 0.151330i | −0.363186 | − | 0.931717i | \(-0.618311\pi\) |
0.625297 | + | 0.780387i | \(0.284978\pi\) | |||||||
\(132\) | −4.24264 | − | 4.24264i | −0.369274 | − | 0.369274i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 8.66025 | 0.748132 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.00000 | −0.514496 | ||||||||
\(137\) | −8.69333 | + | 2.32937i | −0.742722 | + | 0.199012i | −0.610287 | − | 0.792180i | \(-0.708946\pi\) |
−0.132434 | + | 0.991192i | \(0.542279\pi\) | |||||||
\(138\) | −7.34847 | − | 7.34847i | −0.625543 | − | 0.625543i | ||||
\(139\) | 3.46410 | − | 2.00000i | 0.293821 | − | 0.169638i | −0.345843 | − | 0.938293i | \(-0.612407\pi\) |
0.639664 | + | 0.768655i | \(0.279074\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.00000 | − | 5.19615i | −0.757937 | − | 0.437595i | ||||
\(142\) | 1.79315 | + | 6.69213i | 0.150478 | + | 0.561591i | ||||
\(143\) | 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 | ||||
\(147\) | −11.7112 | − | 3.13801i | −0.965926 | − | 0.258819i | ||||
\(148\) | 1.79315 | − | 6.69213i | 0.147396 | − | 0.550090i | ||||
\(149\) | 5.19615 | + | 9.00000i | 0.425685 | + | 0.737309i | 0.996484 | − | 0.0837813i | \(-0.0266997\pi\) |
−0.570799 | + | 0.821090i | \(0.693366\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | + | 13.8564i | −0.651031 | + | 1.12762i | 0.331842 | + | 0.943335i | \(0.392330\pi\) |
−0.982873 | + | 0.184284i | \(0.941004\pi\) | |||||||
\(152\) | 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 | ||||
\(157\) | 3.34607 | + | 0.896575i | 0.267045 | + | 0.0715545i | 0.389857 | − | 0.920875i | \(-0.372524\pi\) |
−0.122812 | + | 0.992430i | \(0.539191\pi\) | |||||||
\(158\) | 13.5230 | + | 3.62347i | 1.07583 | + | 0.288268i | ||||
\(159\) | 10.3923 | 0.824163 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 8.69333 | − | 2.32937i | 0.683013 | − | 0.183013i | ||||
\(163\) | 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 | ||||
\(167\) | 3.10583 | − | 11.5911i | 0.240336 | − | 0.896947i | −0.735334 | − | 0.677705i | \(-0.762975\pi\) |
0.975670 | − | 0.219242i | \(-0.0703585\pi\) | |||||||
\(168\) | 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 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(174\) | 10.3923 | − | 6.00000i | 0.787839 | − | 0.454859i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.00000 | − | 1.73205i | 0.226134 | − | 0.130558i | ||||
\(177\) | −0.776457 | + | 2.89778i | −0.0583621 | + | 0.217810i | ||||
\(178\) | −11.7112 | + | 3.13801i | −0.877794 | + | 0.235204i | ||||
\(179\) | −22.5167 | −1.68297 | −0.841487 | − | 0.540277i | \(-0.818319\pi\) | ||||
−0.841487 | + | 0.540277i | \(0.818319\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.0000 | 1.18927 | 0.594635 | − | 0.803996i | \(-0.297296\pi\) | ||||
0.594635 | + | 0.803996i | \(0.297296\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.3843 | − | 3.58630i | 0.989393 | − | 0.265107i | ||||
\(184\) | 5.19615 | − | 3.00000i | 0.383065 | − | 0.221163i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | − | 6.92820i | − | 0.508001i | ||||||
\(187\) | 5.37945 | + | 20.0764i | 0.393385 | + | 1.46813i | ||||
\(188\) | 4.24264 | − | 4.24264i | 0.309426 | − | 0.309426i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.0000 | + | 12.1244i | 1.51951 | + | 0.877288i | 0.999736 | + | 0.0229818i | \(0.00731599\pi\) |
0.519771 | + | 0.854306i | \(0.326017\pi\) | |||||||
\(192\) | −1.22474 | + | 1.22474i | −0.0883883 | + | 0.0883883i | ||||
\(193\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(194\) | −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 | \(-0.576421\pi\) | |||||||
\(198\) | 2.68973 | − | 10.0382i | 0.191151 | − | 0.713384i | ||||
\(199\) | 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 | ||||
\(202\) | −3.34607 | − | 0.896575i | −0.235428 | − | 0.0630828i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −5.19615 | − | 9.00000i | −0.363803 | − | 0.630126i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.46410i | 0.241355i | ||||||||
\(207\) | 4.65874 | − | 17.3867i | 0.323805 | − | 1.20846i | ||||
\(208\) | −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 | 0.998221 | − | 0.0596196i | \(-0.0189888\pi\) |
−0.550743 | + | 0.834675i | \(0.685655\pi\) | |||||||
\(212\) | −1.55291 | + | 5.79555i | −0.106655 | + | 0.398040i | ||||
\(213\) | −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 | ||||||||
\(218\) | −5.17638 | − | 19.3185i | −0.350589 | − | 1.30842i | ||||
\(219\) | − | 21.0000i | − | 1.41905i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.0000 | − | 10.3923i | 1.21081 | − | 0.699062i | ||||
\(222\) | 11.5911 | − | 3.10583i | 0.777944 | − | 0.208450i | ||||
\(223\) | −6.69213 | + | 1.79315i | −0.448138 | + | 0.120078i | −0.475828 | − | 0.879538i | \(-0.657852\pi\) |
0.0276899 | + | 0.999617i | \(0.491185\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.0000 | 0.997785 | ||||||||
\(227\) | −2.89778 | + | 0.776457i | −0.192332 | + | 0.0515353i | −0.353699 | − | 0.935359i | \(-0.615076\pi\) |
0.161367 | + | 0.986894i | \(0.448410\pi\) | |||||||
\(228\) | −2.24144 | + | 8.36516i | −0.148443 | + | 0.553996i | ||||
\(229\) | 13.8564 | − | 8.00000i | 0.915657 | − | 0.528655i | 0.0334101 | − | 0.999442i | \(-0.489363\pi\) |
0.882247 | + | 0.470787i | \(0.156030\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.79315 | + | 6.69213i | 0.117726 | + | 0.439360i | ||||
\(233\) | 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 | ||||
\(237\) | 6.27603 | + | 23.4225i | 0.407672 | + | 1.52145i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.19615 | − | 9.00000i | −0.336111 | − | 0.582162i | 0.647586 | − | 0.761992i | \(-0.275778\pi\) |
−0.983698 | + | 0.179830i | \(0.942445\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.500000 | − | 0.866025i | 0.0322078 | − | 0.0557856i | −0.849472 | − | 0.527633i | \(-0.823079\pi\) |
0.881680 | + | 0.471848i | \(0.156413\pi\) | |||||||
\(242\) | −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 | ||||||||
\(247\) | −16.7303 | − | 4.48288i | −1.06453 | − | 0.285239i | ||||
\(248\) | 3.86370 | + | 1.03528i | 0.245345 | + | 0.0657401i | ||||
\(249\) | 7.79423 | − | 13.5000i | 0.493939 | − | 0.855528i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.19615i | 0.327978i | 0.986462 | + | 0.163989i | \(0.0524362\pi\) | ||||
−0.986462 | + | 0.163989i | \(0.947564\pi\) | |||||||
\(252\) | 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 | ||||
\(257\) | −3.88229 | + | 14.4889i | −0.242170 | + | 0.903792i | 0.732614 | + | 0.680644i | \(0.238300\pi\) |
−0.974785 | + | 0.223148i | \(0.928367\pi\) | |||||||
\(258\) | 20.2844 | + | 5.43520i | 1.26285 | + | 0.338381i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.0000 | + | 10.3923i | 1.11417 | + | 0.643268i | ||||
\(262\) | −2.44949 | + | 2.44949i | −0.151330 | + | 0.151330i | ||||
\(263\) | −3.10583 | − | 11.5911i | −0.191514 | − | 0.714738i | −0.993142 | − | 0.116916i | \(-0.962699\pi\) |
0.801628 | − | 0.597823i | \(-0.203967\pi\) | |||||||
\(264\) | 5.19615 | + | 3.00000i | 0.319801 | + | 0.184637i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.8492 | − | 14.8492i | −0.908759 | − | 0.908759i | ||||
\(268\) | −8.36516 | + | 2.24144i | −0.510984 | + | 0.136918i | ||||
\(269\) | −13.8564 | −0.844840 | −0.422420 | − | 0.906400i | \(-0.638819\pi\) | ||||
−0.422420 | + | 0.906400i | \(0.638819\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.0000 | −0.607457 | −0.303728 | − | 0.952759i | \(-0.598232\pi\) | ||||
−0.303728 | + | 0.952759i | \(0.598232\pi\) | |||||||
\(272\) | 5.79555 | − | 1.55291i | 0.351407 | − | 0.0941593i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.79423 | − | 4.50000i | 0.470867 | − | 0.271855i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 9.00000 | + | 5.19615i | 0.541736 | + | 0.312772i | ||||
\(277\) | −1.79315 | − | 6.69213i | −0.107740 | − | 0.402091i | 0.890902 | − | 0.454196i | \(-0.150074\pi\) |
−0.998642 | + | 0.0521052i | \(0.983407\pi\) | |||||||
\(278\) | −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 | −0.144575 | − | 0.989494i | \(-0.546182\pi\) |
−0.929214 | + | 0.369541i | \(0.879515\pi\) | |||||||
\(282\) | 10.0382 | + | 2.68973i | 0.597766 | + | 0.160171i | ||||
\(283\) | 3.13801 | − | 11.7112i | 0.186536 | − | 0.696160i | −0.807761 | − | 0.589510i | \(-0.799321\pi\) |
0.994297 | − | 0.106650i | \(-0.0340125\pi\) | |||||||
\(284\) | −3.46410 | − | 6.00000i | −0.205557 | − | 0.356034i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.00000 | + | 10.3923i | −0.354787 | + | 0.614510i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.89778 | − | 0.776457i | −0.170753 | − | 0.0457532i | ||||
\(289\) | 19.0000i | 1.11765i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.50000 | − | 7.79423i | 0.263795 | − | 0.456906i | ||||
\(292\) | 11.7112 | + | 3.13801i | 0.685348 | + | 0.183638i | ||||
\(293\) | −5.79555 | − | 1.55291i | −0.338580 | − | 0.0907222i | 0.0855230 | − | 0.996336i | \(-0.472744\pi\) |
−0.424103 | + | 0.905614i | \(0.639411\pi\) | |||||||
\(294\) | 12.1244 | 0.707107 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.92820i | 0.402694i | ||||||||
\(297\) | 17.3867 | − | 4.65874i | 1.00888 | − | 0.270328i | ||||
\(298\) | −7.34847 | − | 7.34847i | −0.425685 | − | 0.425685i | ||||
\(299\) | −10.3923 | + | 18.0000i | −0.601003 | + | 1.04097i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4.14110 | − | 15.4548i | 0.238294 | − | 0.889325i | ||||
\(303\) | −1.55291 | − | 5.79555i | −0.0892126 | − | 0.332946i | ||||
\(304\) | −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 | −0.958488 | − | 0.285132i | \(-0.907963\pi\) |
−0.232313 | + | 0.972641i | \(0.574629\pi\) | |||||||
\(312\) | 1.55291 | − | 5.79555i | 0.0879165 | − | 0.328109i | ||||
\(313\) | −31.7876 | + | 8.51747i | −1.79674 | + | 0.481436i | −0.993462 | − | 0.114165i | \(-0.963581\pi\) |
−0.803281 | + | 0.595601i | \(0.796914\pi\) | |||||||
\(314\) | −3.46410 | −0.195491 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.0000 | −0.787562 | ||||||||
\(317\) | 11.5911 | − | 3.10583i | 0.651022 | − | 0.174441i | 0.0818309 | − | 0.996646i | \(-0.473923\pi\) |
0.569191 | + | 0.822206i | \(0.307257\pi\) | |||||||
\(318\) | −10.0382 | + | 2.68973i | −0.562914 | + | 0.150832i | ||||
\(319\) | 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 | ||||
\(328\) | 0.448288 | − | 1.67303i | 0.0247525 | − | 0.0923778i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.500000 | − | 0.866025i | 0.0274825 | − | 0.0476011i | −0.851957 | − | 0.523612i | \(-0.824584\pi\) |
0.879440 | + | 0.476011i | \(0.157918\pi\) | |||||||
\(332\) | 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 | ||||||||
\(337\) | −6.69213 | − | 1.79315i | −0.364544 | − | 0.0976792i | 0.0718974 | − | 0.997412i | \(-0.477095\pi\) |
−0.436441 | + | 0.899733i | \(0.643761\pi\) | |||||||
\(338\) | −0.965926 | − | 0.258819i | −0.0525394 | − | 0.0140779i | ||||
\(339\) | 12.9904 | + | 22.5000i | 0.705541 | + | 1.22203i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 13.8564i | − | 0.750366i | ||||||
\(342\) | −14.4889 | + | 3.88229i | −0.783469 | + | 0.209930i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −6.06218 | + | 10.5000i | −0.326851 | + | 0.566122i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.10583 | + | 11.5911i | −0.166730 | + | 0.622243i | 0.831084 | + | 0.556147i | \(0.187721\pi\) |
−0.997813 | + | 0.0660960i | \(0.978946\pi\) | |||||||
\(348\) | −8.48528 | + | 8.48528i | −0.454859 | + | 0.454859i | ||||
\(349\) | 22.5167 | + | 13.0000i | 1.20529 | + | 0.695874i | 0.961727 | − | 0.274011i | \(-0.0883505\pi\) |
0.243563 | + | 0.969885i | \(0.421684\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.00000 | − | 15.5885i | −0.480384 | − | 0.832050i | ||||
\(352\) | −2.44949 | + | 2.44949i | −0.130558 | + | 0.130558i | ||||
\(353\) | −2.32937 | − | 8.69333i | −0.123980 | − | 0.462699i | 0.875821 | − | 0.482635i | \(-0.160320\pi\) |
−0.999801 | + | 0.0199361i | \(0.993654\pi\) | |||||||
\(354\) | − | 3.00000i | − | 0.159448i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 10.5000 | − | 6.06218i | 0.556499 | − | 0.321295i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 21.7494 | − | 5.82774i | 1.14949 | − | 0.308006i | ||||
\(359\) | −27.7128 | −1.46263 | −0.731313 | − | 0.682042i | \(-0.761092\pi\) | ||||
−0.731313 | + | 0.682042i | \(0.761092\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.00000 | −0.315789 | ||||||||
\(362\) | −15.4548 | + | 4.14110i | −0.812287 | + | 0.217652i | ||||
\(363\) | 0.448288 | − | 1.67303i | 0.0235290 | − | 0.0878114i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −12.0000 | + | 6.92820i | −0.627250 | + | 0.362143i | ||||
\(367\) | 4.48288 | + | 16.7303i | 0.234004 | + | 0.873316i | 0.978595 | + | 0.205795i | \(0.0659779\pi\) |
−0.744591 | + | 0.667521i | \(0.767355\pi\) | |||||||
\(368\) | −4.24264 | + | 4.24264i | −0.221163 | + | 0.221163i | ||||
\(369\) | −2.59808 | − | 4.50000i | −0.135250 | − | 0.234261i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.79315 | + | 6.69213i | 0.0929705 | + | 0.346971i | ||||
\(373\) | −5.37945 | + | 20.0764i | −0.278538 | + | 1.03952i | 0.674896 | + | 0.737913i | \(0.264188\pi\) |
−0.953434 | + | 0.301603i | \(0.902478\pi\) | |||||||
\(374\) | −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 | ||||||||
\(382\) | −23.4225 | − | 6.27603i | −1.19840 | − | 0.321110i | ||||
\(383\) | 5.79555 | + | 1.55291i | 0.296139 | + | 0.0793502i | 0.403830 | − | 0.914834i | \(-0.367679\pi\) |
−0.107691 | + | 0.994184i | \(0.534346\pi\) | |||||||
\(384\) | 0.866025 | − | 1.50000i | 0.0441942 | − | 0.0765466i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.41404 | + | 35.1337i | 0.478543 | + | 1.78595i | ||||
\(388\) | 3.67423 | + | 3.67423i | 0.186531 | + | 0.186531i | ||||
\(389\) | 5.19615 | − | 9.00000i | 0.263455 | − | 0.456318i | −0.703702 | − | 0.710495i | \(-0.748471\pi\) |
0.967158 | + | 0.254177i | \(0.0818045\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.0000 | − | 31.1769i | −0.910299 | − | 1.57668i | ||||
\(392\) | −1.81173 | + | 6.76148i | −0.0915064 | + | 0.341506i | ||||
\(393\) | −5.79555 | − | 1.55291i | −0.292347 | − | 0.0783342i | ||||
\(394\) | 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 | \(0.0417700\pi\) | |||||||
\(398\) | −2.07055 | − | 7.72741i | −0.103787 | − | 0.387340i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.0000 | + | 10.3923i | −0.898877 | + | 0.518967i | −0.876836 | − | 0.480790i | \(-0.840350\pi\) |
−0.0220414 | + | 0.999757i | \(0.507017\pi\) | |||||||
\(402\) | −10.6066 | − | 10.6066i | −0.529009 | − | 0.529009i | ||||
\(403\) | −13.3843 | + | 3.58630i | −0.666718 | + | 0.178646i | ||||
\(404\) | 3.46410 | 0.172345 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 23.1822 | − | 6.21166i | 1.14910 | − | 0.307900i | ||||
\(408\) | 7.34847 | + | 7.34847i | 0.363803 | + | 0.363803i | ||||
\(409\) | −25.1147 | + | 14.5000i | −1.24184 | + | 0.716979i | −0.969469 | − | 0.245212i | \(-0.921142\pi\) |
−0.272374 | + | 0.962191i | \(0.587809\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.5000 | + | 7.79423i | 0.665906 | + | 0.384461i | ||||
\(412\) | −0.896575 | − | 3.34607i | −0.0441711 | − | 0.164849i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 18.0000i | 0.884652i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.00000 | + | 1.73205i | 0.147087 | + | 0.0849208i | ||||
\(417\) | −6.69213 | − | 1.79315i | −0.327715 | − | 0.0878110i | ||||
\(418\) | −4.48288 | + | 16.7303i | −0.219265 | + | 0.818307i | ||||
\(419\) | 12.9904 | + | 22.5000i | 0.634622 | + | 1.09920i | 0.986595 | + | 0.163187i | \(0.0521774\pi\) |
−0.351974 | + | 0.936010i | \(0.614489\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.00000 | − | 6.92820i | 0.194948 | − | 0.337660i | −0.751935 | − | 0.659237i | \(-0.770879\pi\) |
0.946883 | + | 0.321577i | \(0.104213\pi\) | |||||||
\(422\) | −9.19239 | − | 9.19239i | −0.447478 | − | 0.447478i | ||||
\(423\) | 4.65874 | + | 17.3867i | 0.226516 | + | 0.845369i | ||||
\(424\) | − | 6.00000i | − | 0.291386i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.00000 | − | 10.3923i | 0.290701 | − | 0.503509i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2.89778 | + | 0.776457i | 0.140069 | + | 0.0375315i | ||||
\(429\) | −20.7846 | −1.00349 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.8564i | 0.667440i | 0.942672 | + | 0.333720i | \(0.108304\pi\) | ||||
−0.942672 | + | 0.333720i | \(0.891696\pi\) | |||||||
\(432\) | −1.34486 | − | 5.01910i | −0.0647048 | − | 0.241481i | ||||
\(433\) | 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 | ||||
\(437\) | −7.76457 | + | 28.9778i | −0.371430 | + | 1.38619i | ||||
\(438\) | 5.43520 | + | 20.2844i | 0.259704 | + | 0.969228i | ||||
\(439\) | −22.5167 | − | 13.0000i | −1.07466 | − | 0.620456i | −0.145210 | − | 0.989401i | \(-0.546386\pi\) |
−0.929451 | + | 0.368945i | \(0.879719\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.5000 | + | 18.1865i | 0.500000 | + | 0.866025i | ||||
\(442\) | −14.6969 | + | 14.6969i | −0.699062 | + | 0.699062i | ||||
\(443\) | 9.31749 | + | 34.7733i | 0.442687 | + | 1.65213i | 0.721972 | + | 0.691922i | \(0.243236\pi\) |
−0.279285 | + | 0.960208i | \(0.590097\pi\) | |||||||
\(444\) | −10.3923 | + | 6.00000i | −0.493197 | + | 0.284747i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6.00000 | − | 3.46410i | 0.284108 | − | 0.164030i | ||||
\(447\) | 4.65874 | − | 17.3867i | 0.220351 | − | 0.822361i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.66025 | −0.408703 | −0.204351 | − | 0.978898i | \(-0.565508\pi\) | ||||
−0.204351 | + | 0.978898i | \(0.565508\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.00000 | −0.282529 | ||||||||
\(452\) | −14.4889 | + | 3.88229i | −0.681500 | + | 0.182607i | ||||
\(453\) | 26.7685 | − | 7.17260i | 1.25769 | − | 0.336998i | ||||
\(454\) | 2.59808 | − | 1.50000i | 0.121934 | − | 0.0703985i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | − | 8.66025i | − | 0.405554i | ||||||
\(457\) | 1.34486 | + | 5.01910i | 0.0629100 | + | 0.234783i | 0.990221 | − | 0.139509i | \(-0.0445523\pi\) |
−0.927311 | + | 0.374292i | \(0.877886\pi\) | |||||||
\(458\) | −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 | −0.403137 | − | 0.915140i | \(-0.632080\pi\) |
−0.994103 | + | 0.108443i | \(0.965413\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.79315 | − | 6.69213i | 0.0833348 | − | 0.311010i | −0.911659 | − | 0.410948i | \(-0.865198\pi\) |
0.994994 | + | 0.0999382i | \(0.0318645\pi\) | |||||||
\(464\) | −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 | \(0.588498\pi\) | |||||||
\(468\) | 10.0382 | − | 2.68973i | 0.464016 | − | 0.124333i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.00000 | − | 5.19615i | −0.138233 | − | 0.239426i | ||||
\(472\) | 1.67303 | + | 0.448288i | 0.0770076 | + | 0.0206341i | ||||
\(473\) | 40.5689 | + | 10.8704i | 1.86536 | + | 0.499822i | ||||
\(474\) | −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 | \(-0.962830\pi\) |
0.597493 | + | 0.801874i | \(0.296164\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.0000 | − | 20.7846i | −0.547153 | − | 0.947697i | ||||
\(482\) | −0.258819 | + | 0.965926i | −0.0117889 | + | 0.0439967i | ||||
\(483\) | 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 | \(0.300174\pi\) | |||||||
\(488\) | −2.07055 | − | 7.72741i | −0.0937295 | − | 0.349803i | ||||
\(489\) | − | 3.00000i | − | 0.135665i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.5000 | − | 14.7224i | 1.15080 | − | 0.664414i | 0.201717 | − | 0.979444i | \(-0.435348\pi\) |
0.949082 | + | 0.315030i | \(0.102015\pi\) | |||||||
\(492\) | 2.89778 | − | 0.776457i | 0.130642 | − | 0.0350054i | ||||
\(493\) | 40.1528 | − | 10.7589i | 1.80839 | − | 0.484557i | ||||
\(494\) | 17.3205 | 0.779287 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.03459 | + | 15.0573i | −0.180794 | + | 0.674733i | ||||
\(499\) | −11.2583 | + | 6.50000i | −0.503992 | + | 0.290980i | −0.730361 | − | 0.683062i | \(-0.760648\pi\) |
0.226369 | + | 0.974042i | \(0.427315\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.0000 | + | 10.3923i | −0.804181 | + | 0.464294i | ||||
\(502\) | −1.34486 | − | 5.01910i | −0.0600242 | − | 0.224013i | ||||
\(503\) | −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 | ||||
\(507\) | −0.448288 | − | 1.67303i | −0.0199092 | − | 0.0743020i | ||||
\(508\) | 2.68973 | − | 10.0382i | 0.119337 | − | 0.445373i | ||||
\(509\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(510\) | 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 | ||||||||
\(517\) | 20.0764 | + | 5.37945i | 0.882959 | + | 0.236588i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.7846i | 0.910590i | 0.890341 | + | 0.455295i | \(0.150466\pi\) | ||||
−0.890341 | + | 0.455295i | \(0.849534\pi\) | |||||||
\(522\) | −20.0764 | − | 5.37945i | −0.878720 | − | 0.235452i | ||||
\(523\) | −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 | ||||
\(527\) | 6.21166 | − | 23.1822i | 0.270584 | − | 1.00983i | ||||
\(528\) | −5.79555 | − | 1.55291i | −0.252219 | − | 0.0675819i | ||||
\(529\) | 11.2583 | + | 6.50000i | 0.489493 | + | 0.282609i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.50000 | − | 2.59808i | 0.195283 | − | 0.112747i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.55291 | + | 5.79555i | 0.0672642 | + | 0.251033i | ||||
\(534\) | 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 | ||||
\(538\) | 13.3843 | − | 3.58630i | 0.577036 | − | 0.154616i | ||||
\(539\) | 24.2487 | 1.04447 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.0000 | 1.37579 | 0.687894 | − | 0.725811i | \(-0.258536\pi\) | ||||
0.687894 | + | 0.725811i | \(0.258536\pi\) | |||||||
\(542\) | 9.65926 | − | 2.58819i | 0.414901 | − | 0.111172i | ||||
\(543\) | −19.5959 | − | 19.5959i | −0.840941 | − | 0.840941i | ||||
\(544\) | −5.19615 | + | 3.00000i | −0.222783 | + | 0.128624i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.82774 | − | 21.7494i | −0.249176 | − | 0.929938i | −0.971238 | − | 0.238110i | \(-0.923472\pi\) |
0.722062 | − | 0.691828i | \(-0.243195\pi\) | |||||||
\(548\) | −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 | ||||
\(552\) | −10.0382 | − | 2.68973i | −0.427254 | − | 0.114482i | ||||
\(553\) | 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 | ||||
\(562\) | 20.0764 | + | 5.37945i | 0.846871 | + | 0.226919i | ||||
\(563\) | −20.2844 | − | 5.43520i | −0.854887 | − | 0.229066i | −0.195346 | − | 0.980734i | \(-0.562583\pi\) |
−0.659542 | + | 0.751668i | \(0.729250\pi\) | |||||||
\(564\) | −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 | −0.232401 | − | 0.972620i | \(-0.574658\pi\) |
0.958514 | − | 0.285045i | \(-0.0920086\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.500000 | + | 0.866025i | 0.0209243 | + | 0.0362420i | 0.876298 | − | 0.481770i | \(-0.160006\pi\) |
−0.855374 | + | 0.518012i | \(0.826672\pi\) | |||||||
\(572\) | 3.10583 | − | 11.5911i | 0.129861 | − | 0.484649i | ||||
\(573\) | −10.8704 | − | 40.5689i | −0.454117 | − | 1.69479i | ||||
\(574\) | 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 | \(-0.0233919\pi\) | |||||||
\(578\) | −4.91756 | − | 18.3526i | −0.204544 | − | 0.763367i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2.32937 | + | 8.69333i | −0.0965556 | + | 0.360350i | ||||
\(583\) | −20.0764 | + | 5.37945i | −0.831479 | + | 0.222794i | ||||
\(584\) | −12.1244 | −0.501709 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.00000 | 0.247858 | ||||||||
\(587\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(588\) | −11.7112 | + | 3.13801i | −0.482963 | + | 0.129410i | ||||
\(589\) | −17.3205 | + | 10.0000i | −0.713679 | + | 0.412043i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 41.5692i | 1.70993i | ||||||||
\(592\) | −1.79315 | − | 6.69213i | −0.0736980 | − | 0.275045i | ||||
\(593\) | 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 | ||||
\(598\) | 5.37945 | − | 20.0764i | 0.219982 | − | 0.820985i | ||||
\(599\) | 13.8564 | + | 24.0000i | 0.566157 | + | 0.980613i | 0.996941 | + | 0.0781581i | \(0.0249039\pi\) |
−0.430784 | + | 0.902455i | \(0.641763\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.0000 | − | 22.5167i | 0.530281 | − | 0.918474i | −0.469095 | − | 0.883148i | \(-0.655420\pi\) |
0.999376 | − | 0.0353259i | \(-0.0112469\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.72432 | − | 25.0955i | 0.273835 | − | 1.02197i | ||||
\(604\) | 16.0000i | 0.651031i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.00000 | + | 5.19615i | 0.121867 | + | 0.211079i | ||||
\(607\) | 23.4225 | + | 6.27603i | 0.950688 | + | 0.254736i | 0.700654 | − | 0.713501i | \(-0.252892\pi\) |
0.250034 | + | 0.968237i | \(0.419558\pi\) | |||||||
\(608\) | 4.82963 | + | 1.29410i | 0.195867 | + | 0.0524825i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 20.7846i | − | 0.840855i | ||||||
\(612\) | −4.65874 | + | 17.3867i | −0.188319 | + | 0.702814i | ||||
\(613\) | 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 | ||||||||
\(617\) | −2.32937 | + | 8.69333i | −0.0937770 | + | 0.349980i | −0.996831 | − | 0.0795462i | \(-0.974653\pi\) |
0.903054 | + | 0.429527i | \(0.141320\pi\) | |||||||
\(618\) | 4.24264 | − | 4.24264i | 0.170664 | − | 0.170664i | ||||
\(619\) | −14.7224 | − | 8.50000i | −0.591744 | − | 0.341644i | 0.174042 | − | 0.984738i | \(-0.444317\pi\) |
−0.765787 | + | 0.643094i | \(0.777650\pi\) | |||||||
\(620\) | 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 | ||||
\(627\) | −28.9778 | + | 7.76457i | −1.15726 | + | 0.310087i | ||||
\(628\) | 3.34607 | − | 0.896575i | 0.133523 | − | 0.0357773i | ||||
\(629\) | 41.5692 | 1.65747 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.0000 | −0.636950 | −0.318475 | − | 0.947931i | \(-0.603171\pi\) | ||||
−0.318475 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(632\) | 13.5230 | − | 3.62347i | 0.537915 | − | 0.144134i | ||||
\(633\) | 5.82774 | − | 21.7494i | 0.231632 | − | 0.864462i | ||||
\(634\) | −10.3923 | + | 6.00000i | −0.412731 | + | 0.238290i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.00000 | − | 5.19615i | 0.356873 | − | 0.206041i | ||||
\(637\) | −6.27603 | − | 23.4225i | −0.248665 | − | 0.928032i | ||||
\(638\) | −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 | 0.832947 | − | 0.553352i | \(-0.186652\pi\) |
−0.0627436 | + | 0.998030i | \(0.519985\pi\) | |||||||
\(642\) | 1.34486 | + | 5.01910i | 0.0530775 | + | 0.198088i | ||||
\(643\) | −12.1038 | + | 45.1719i | −0.477326 | + | 1.78141i | 0.135050 | + | 0.990839i | \(0.456880\pi\) |
−0.612376 | + | 0.790566i | \(0.709786\pi\) | |||||||
\(644\) | 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 | ||||||||
\(652\) | 1.67303 | + | 0.448288i | 0.0655210 | + | 0.0175563i | ||||
\(653\) | −28.9778 | − | 7.76457i | −1.13399 | − | 0.303851i | −0.357457 | − | 0.933930i | \(-0.616356\pi\) |
−0.776531 | + | 0.630079i | \(0.783023\pi\) | |||||||
\(654\) | −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 | \(-0.735138\pi\) |
0.976953 | + | 0.213454i | \(0.0684713\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.0000 | + | 43.3013i | 0.972387 | + | 1.68422i | 0.688301 | + | 0.725426i | \(0.258357\pi\) |
0.284087 | + | 0.958799i | \(0.408310\pi\) | |||||||
\(662\) | −0.258819 | + | 0.965926i | −0.0100593 | + | 0.0375418i | ||||
\(663\) | −34.7733 | − | 9.31749i | −1.35048 | − | 0.361861i | ||||
\(664\) | −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 | ||||
\(668\) | −3.10583 | − | 11.5911i | −0.120168 | − | 0.448474i | ||||
\(669\) | 10.3923 | + | 6.00000i | 0.401790 | + | 0.231973i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.0000 | + | 13.8564i | −0.926510 | + | 0.534921i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33.4607 | − | 8.96575i | 1.28981 | − | 0.345604i | 0.452224 | − | 0.891904i | \(-0.350631\pi\) |
0.837590 | + | 0.546300i | \(0.183964\pi\) | |||||||
\(674\) | 6.92820 | 0.266864 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 5.79555 | − | 1.55291i | 0.222741 | − | 0.0596833i | −0.145722 | − | 0.989326i | \(-0.546551\pi\) |
0.368464 | + | 0.929642i | \(0.379884\pi\) | |||||||
\(678\) | −18.3712 | − | 18.3712i | −0.705541 | − | 0.705541i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.50000 | + | 2.59808i | 0.172440 | + | 0.0995585i | ||||
\(682\) | 3.58630 | + | 13.3843i | 0.137327 | + | 0.512510i | ||||
\(683\) | 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 | ||||||||
\(687\) | −26.7685 | − | 7.17260i | −1.02128 | − | 0.273652i | ||||
\(688\) | 3.13801 | − | 11.7112i | 0.119636 | − | 0.446486i | ||||
\(689\) | 10.3923 | + | 18.0000i | 0.395915 | + | 0.685745i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.5000 | − | 30.3109i | 0.665731 | − | 1.15308i | −0.313355 | − | 0.949636i | \(-0.601453\pi\) |
0.979086 | − | 0.203445i | \(-0.0652137\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 12.0000i | − | 0.455514i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 6.00000 | − | 10.3923i | 0.227429 | − | 0.393919i | ||||
\(697\) | −10.0382 | − | 2.68973i | −0.380224 | − | 0.101881i | ||||
\(698\) | −25.1141 | − | 6.72930i | −0.950582 | − | 0.254708i | ||||
\(699\) | −15.5885 | −0.589610 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.92820i | 0.261675i | 0.991404 | + | 0.130837i | \(0.0417666\pi\) | ||||
−0.991404 | + | 0.130837i | \(0.958233\pi\) | |||||||
\(702\) | 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 | ||||||||
\(708\) | 0.776457 | + | 2.89778i | 0.0291810 | + | 0.108905i | ||||
\(709\) | −39.8372 | − | 23.0000i | −1.49612 | − | 0.863783i | −0.496126 | − | 0.868250i | \(-0.665245\pi\) |
−0.999990 | + | 0.00446726i | \(0.998578\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 21.0000 | − | 36.3731i | 0.787562 | − | 1.36410i | ||||
\(712\) | −8.57321 | + | 8.57321i | −0.321295 | + | 0.321295i | ||||
\(713\) | 6.21166 | + | 23.1822i | 0.232628 | + | 0.868181i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −19.5000 | + | 11.2583i | −0.728749 | + | 0.420744i | ||||
\(717\) | −4.65874 | + | 17.3867i | −0.173984 | + | 0.649317i | ||||
\(718\) | 26.7685 | − | 7.17260i | 0.998992 | − | 0.267679i | ||||
\(719\) | 6.92820 | 0.258378 | 0.129189 | − | 0.991620i | \(-0.458763\pi\) | ||||
0.129189 | + | 0.991620i | \(0.458763\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 5.79555 | − | 1.55291i | 0.215688 | − | 0.0577935i | ||||
\(723\) | −1.67303 | + | 0.448288i | −0.0622208 | + | 0.0166720i | ||||
\(724\) | 13.8564 | − | 8.00000i | 0.514969 | − | 0.297318i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.73205i | 0.0642824i | ||||||||
\(727\) | −8.96575 | − | 33.4607i | −0.332521 | − | 1.24099i | −0.906531 | − | 0.422139i | \(-0.861280\pi\) |
0.574010 | − | 0.818848i | \(-0.305387\pi\) | |||||||
\(728\) | 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 | ||||
\(733\) | 8.06918 | − | 30.1146i | 0.298042 | − | 1.11231i | −0.640729 | − | 0.767767i | \(-0.721368\pi\) |
0.938771 | − | 0.344541i | \(-0.111965\pi\) | |||||||
\(734\) | −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 | ||||||||
\(743\) | −11.5911 | − | 3.10583i | −0.425237 | − | 0.113942i | 0.0398527 | − | 0.999206i | \(-0.487311\pi\) |
−0.465089 | + | 0.885264i | \(0.653978\pi\) | |||||||
\(744\) | −3.46410 | − | 6.00000i | −0.127000 | − | 0.219971i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 20.7846i | − | 0.760979i | ||||||
\(747\) | −26.0800 | + | 6.98811i | −0.954217 | + | 0.255682i | ||||
\(748\) | 14.6969 | + | 14.6969i | 0.537373 | + | 0.537373i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.0000 | + | 32.9090i | 0.693320 | + | 1.20087i | 0.970744 | + | 0.240118i | \(0.0771860\pi\) |
−0.277424 | + | 0.960748i | \(0.589481\pi\) | |||||||
\(752\) | 1.55291 | − | 5.79555i | 0.0566290 | − | 0.211342i | ||||
\(753\) | 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 | \(0.373290\pi\) | |||||||
\(758\) | 2.07055 | + | 7.72741i | 0.0752058 | + | 0.280672i | ||||
\(759\) | 36.0000i | 1.30672i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.50000 | − | 0.866025i | 0.0543750 | − | 0.0313934i | −0.472566 | − | 0.881295i | \(-0.656672\pi\) |
0.526941 | + | 0.849902i | \(0.323339\pi\) | |||||||
\(762\) | 17.3867 | − | 4.65874i | 0.629852 | − | 0.168768i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 24.2487 | 0.877288 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.00000 | −0.216789 | ||||||||
\(767\) | −5.79555 | + | 1.55291i | −0.209265 | + | 0.0560725i | ||||
\(768\) | −0.448288 | + | 1.67303i | −0.0161762 | + | 0.0603704i | ||||
\(769\) | −42.4352 | + | 24.5000i | −1.53025 | + | 0.883493i | −0.530904 | + | 0.847432i | \(0.678148\pi\) |
−0.999350 | + | 0.0360609i | \(0.988519\pi\) | |||||||
\(770\) | 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 | ||||||||
\(778\) | −2.68973 | + | 10.0382i | −0.0964314 | + | 0.359887i | ||||
\(779\) | 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 | ||||
\(783\) | −9.31749 | − | 34.7733i | −0.332980 | − | 1.24270i | ||||
\(784\) | − | 7.00000i | − | 0.250000i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6.00000 | 0.214013 | ||||||||
\(787\) | 30.1146 | + | 8.06918i | 1.07347 | + | 0.287635i | 0.751918 | − | 0.659257i | \(-0.229129\pi\) |
0.321551 | + | 0.946892i | \(0.395796\pi\) | |||||||
\(788\) | −23.1822 | − | 6.21166i | −0.825832 | − | 0.221281i | ||||
\(789\) | −10.3923 | + | 18.0000i | −0.369976 | + | 0.640817i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2.68973 | − | 10.0382i | −0.0955753 | − | 0.356692i | ||||
\(793\) | 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 | ||||
\(797\) | −1.55291 | + | 5.79555i | −0.0550070 | + | 0.205289i | −0.987960 | − | 0.154709i | \(-0.950556\pi\) |
0.932953 | + | 0.359998i | \(0.117223\pi\) | |||||||
\(798\) | 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 | ||||
\(803\) | 10.8704 | + | 40.5689i | 0.383608 | + | 1.43164i | ||||
\(804\) | 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 | ||||
\(808\) | −3.34607 | + | 0.896575i | −0.117714 | + | 0.0315414i | ||||
\(809\) | 29.4449 | 1.03523 | 0.517613 | − | 0.855615i | \(-0.326821\pi\) | ||||
0.517613 | + | 0.855615i | \(0.326821\pi\) | |||||||
\(810\) | 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 | ||||
\(817\) | −15.6901 | − | 58.5561i | −0.548926 | − | 2.04862i | ||||
\(818\) | 20.5061 | − | 20.5061i | 0.716979 | − | 0.716979i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −48.0000 | − | 27.7128i | −1.67521 | − | 0.967184i | −0.964645 | − | 0.263554i | \(-0.915105\pi\) |
−0.710567 | − | 0.703630i | \(-0.751561\pi\) | |||||||
\(822\) | −15.0573 | − | 4.03459i | −0.525183 | − | 0.140722i | ||||
\(823\) | −0.896575 | + | 3.34607i | −0.0312527 | + | 0.116637i | −0.979790 | − | 0.200029i | \(-0.935896\pi\) |
0.948537 | + | 0.316665i | \(0.102563\pi\) | |||||||
\(824\) | 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 | \(0.666014\pi\) | |||||||
\(828\) | −4.65874 | − | 17.3867i | −0.161903 | − | 0.604228i | ||||
\(829\) | − | 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 | ||||
\(832\) | −3.34607 | − | 0.896575i | −0.116004 | − | 0.0310832i | ||||
\(833\) | 40.5689 | + | 10.8704i | 1.40563 | + | 0.376637i | ||||
\(834\) | 6.92820 | 0.239904 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 17.3205i | − | 0.599042i | ||||||
\(837\) | −20.0764 | − | 5.37945i | −0.693942 | − | 0.185941i | ||||
\(838\) | −18.3712 | − | 18.3712i | −0.634622 | − | 0.634622i | ||||
\(839\) | 6.92820 | − | 12.0000i | 0.239188 | − | 0.414286i | −0.721293 | − | 0.692630i | \(-0.756452\pi\) |
0.960482 | + | 0.278344i | \(0.0897854\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.50000 | − | 16.4545i | −0.327586 | − | 0.567396i | ||||
\(842\) | −2.07055 | + | 7.72741i | −0.0713559 | + | 0.266304i | ||||
\(843\) | 9.31749 | + | 34.7733i | 0.320911 | + | 1.19766i | ||||
\(844\) | 11.2583 | + | 6.50000i | 0.387528 | + | 0.223739i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9.00000 | − | 15.5885i | −0.309426 | − | 0.535942i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.55291 | + | 5.79555i | 0.0533273 | + | 0.199020i | ||||
\(849\) | −18.1865 | + | 10.5000i | −0.624160 | + | 0.360359i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36.0000 | + | 20.7846i | −1.23406 | + | 0.712487i | ||||
\(852\) | −3.10583 | + | 11.5911i | −0.106404 | + | 0.397105i | ||||
\(853\) | −3.34607 | + | 0.896575i | −0.114567 | + | 0.0306982i | −0.315647 | − | 0.948877i | \(-0.602222\pi\) |
0.201080 | + | 0.979575i | \(0.435555\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.00000 | −0.102538 | ||||||||
\(857\) | 14.4889 | − | 3.88229i | 0.494931 | − | 0.132616i | −0.00271550 | − | 0.999996i | \(-0.500864\pi\) |
0.497646 | + | 0.867380i | \(0.334198\pi\) | |||||||
\(858\) | 20.0764 | − | 5.37945i | 0.685397 | − | 0.183651i | ||||
\(859\) | −11.2583 | + | 6.50000i | −0.384129 | + | 0.221777i | −0.679613 | − | 0.733571i | \(-0.737852\pi\) |
0.295484 | + | 0.955348i | \(0.404519\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.58630 | − | 13.3843i | −0.122150 | − | 0.455870i | ||||
\(863\) | −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 | ||||
\(873\) | −15.0573 | + | 4.03459i | −0.509612 | + | 0.136550i | ||||
\(874\) | − | 30.0000i | − | 1.01477i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.5000 | − | 18.1865i | −0.354762 | − | 0.614466i | ||||
\(877\) | −10.0382 | − | 2.68973i | −0.338966 | − | 0.0908256i | 0.0853209 | − | 0.996354i | \(-0.472808\pi\) |
−0.424287 | + | 0.905528i | \(0.639475\pi\) | |||||||
\(878\) | 25.1141 | + | 6.72930i | 0.847559 | + | 0.227103i | ||||
\(879\) | 5.19615 | + | 9.00000i | 0.175262 | + | 0.303562i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.92820i | 0.233417i | 0.993166 | + | 0.116709i | \(0.0372343\pi\) | ||||
−0.993166 | + | 0.116709i | \(0.962766\pi\) | |||||||
\(882\) | −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 | ||||
\(887\) | 1.55291 | − | 5.79555i | 0.0521418 | − | 0.194596i | −0.934942 | − | 0.354800i | \(-0.884549\pi\) |
0.987084 | + | 0.160205i | \(0.0512155\pi\) | |||||||
\(888\) | 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 | ||||
\(893\) | −7.76457 | − | 28.9778i | −0.259831 | − | 0.969704i | ||||
\(894\) | 18.0000i | 0.602010i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 34.7733 | − | 9.31749i | 1.16105 | − | 0.311102i | ||||
\(898\) | 8.36516 | − | 2.24144i | 0.279149 | − | 0.0747978i | ||||
\(899\) | −27.7128 | −0.924274 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.0000 | −1.19933 | ||||||||
\(902\) | 5.79555 | − | 1.55291i | 0.192971 | − | 0.0517064i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12.9904 | − | 7.50000i | 0.432054 | − | 0.249446i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −24.0000 | + | 13.8564i | −0.797347 | + | 0.460348i | ||||
\(907\) | 8.51747 | + | 31.7876i | 0.282818 | + | 1.05549i | 0.950419 | + | 0.310972i | \(0.100654\pi\) |
−0.667601 | + | 0.744519i | \(0.732679\pi\) | |||||||
\(908\) | −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 | 0.727462 | − | 0.686148i | \(-0.240700\pi\) |
−0.230490 | + | 0.973075i | \(0.574033\pi\) | |||||||
\(912\) | 2.24144 | + | 8.36516i | 0.0742215 | + | 0.276998i | ||||
\(913\) | −8.06918 | + | 30.1146i | −0.267051 | + | 0.996647i | ||||
\(914\) | −2.59808 | − | 4.50000i | −0.0859367 | − | 0.148847i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.00000 | − | 13.8564i | 0.264327 | − | 0.457829i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −30.1146 | + | 8.06918i | −0.993929 | + | 0.266323i | ||||
\(919\) | − | 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 | ||||||||
\(922\) | 33.4607 | + | 8.96575i | 1.10197 | + | 0.295271i | ||||
\(923\) | −23.1822 | − | 6.21166i | −0.763052 | − | 0.204459i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6.92820i | 0.227675i | ||||||||
\(927\) | 10.0382 | + | 2.68973i | 0.329698 | + | 0.0883422i | ||||
\(928\) | 4.89898 | + | 4.89898i | 0.160817 | + | 0.160817i | ||||
\(929\) | −27.7128 | + | 48.0000i | −0.909228 | + | 1.57483i | −0.0940887 | + | 0.995564i | \(0.529994\pi\) |
−0.815139 | + | 0.579265i | \(0.803340\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.5000 | − | 30.3109i | −0.573539 | − | 0.993399i | ||||
\(932\) | 2.32937 | − | 8.69333i | 0.0763011 | − | 0.284760i | ||||
\(933\) | 40.5689 | + | 10.8704i | 1.32817 | + | 0.355881i | ||||
\(934\) | −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 | 0.219049 | − | 0.975714i | \(-0.429705\pi\) |
0.954517 | + | 0.298155i | \(0.0963712\pi\) | |||||||
\(942\) | 4.24264 | + | 4.24264i | 0.138233 | + | 0.138233i | ||||
\(943\) | 10.0382 | − | 2.68973i | 0.326889 | − | 0.0875895i | ||||
\(944\) | −1.73205 | −0.0563735 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −42.0000 | −1.36554 | ||||||||
\(947\) | −14.4889 | + | 3.88229i | −0.470826 | + | 0.126157i | −0.486427 | − | 0.873721i | \(-0.661700\pi\) |
0.0156019 | + | 0.999878i | \(0.495034\pi\) | |||||||
\(948\) | 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 | ||||
\(957\) | −40.1528 | − | 10.7589i | −1.29796 | − | 0.347786i | ||||
\(958\) | 4.48288 | − | 16.7303i | 0.144835 | − | 0.540532i | ||||
\(959\) | 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 | ||||||||
\(967\) | −6.69213 | − | 1.79315i | −0.215204 | − | 0.0576638i | 0.149606 | − | 0.988746i | \(-0.452200\pi\) |
−0.364810 | + | 0.931082i | \(0.618866\pi\) | |||||||
\(968\) | −0.965926 | − | 0.258819i | −0.0310460 | − | 0.00831876i | ||||
\(969\) | −51.9615 | −1.66924 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.5167i | 0.722594i | 0.932451 | + | 0.361297i | \(0.117666\pi\) | ||||
−0.932451 | + | 0.361297i | \(0.882334\pi\) | |||||||
\(972\) | 15.0573 | + | 4.03459i | 0.482963 | + | 0.129410i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 3.46410 | − | 6.00000i | 0.110997 | − | 0.192252i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.00000 | + | 6.92820i | 0.128037 | + | 0.221766i | ||||
\(977\) | −0.776457 | + | 2.89778i | −0.0248411 | + | 0.0927081i | −0.977233 | − | 0.212167i | \(-0.931948\pi\) |
0.952392 | + | 0.304875i | \(0.0986147\pi\) | |||||||
\(978\) | 0.776457 | + | 2.89778i | 0.0248284 | + | 0.0926607i | ||||
\(979\) | 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 | ||||
\(983\) | 10.8704 | + | 40.5689i | 0.346712 | + | 1.29395i | 0.890600 | + | 0.454788i | \(0.150285\pi\) |
−0.543888 | + | 0.839158i | \(0.683048\pi\) | |||||||
\(984\) | −2.59808 | + | 1.50000i | −0.0828236 | + | 0.0478183i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −36.0000 | + | 20.7846i | −1.14647 | + | 0.661917i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −16.7303 | + | 4.48288i | −0.532263 | + | 0.142619i | ||||
\(989\) | −72.7461 | −2.31319 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40.0000 | −1.27064 | −0.635321 | − | 0.772248i | \(-0.719132\pi\) | ||||
−0.635321 | + | 0.772248i | \(0.719132\pi\) | |||||||
\(992\) | 3.86370 | − | 1.03528i | 0.122673 | − | 0.0328701i | ||||
\(993\) | −1.67303 | + | 0.448288i | −0.0530921 | + | 0.0142260i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 15.5885i | − | 0.493939i | ||||||
\(997\) | 2.68973 | + | 10.0382i | 0.0851845 | + | 0.317913i | 0.995349 | − | 0.0963340i | \(-0.0307117\pi\) |
−0.910165 | + | 0.414247i | \(0.864045\pi\) | |||||||
\(998\) | 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.443.1 | yes | 8 | |
3.2 | odd | 2 | 1350.2.q.c.143.2 | 8 | |||
5.2 | odd | 4 | inner | 450.2.p.g.407.1 | yes | 8 | |
5.3 | odd | 4 | inner | 450.2.p.g.407.2 | yes | 8 | |
5.4 | even | 2 | inner | 450.2.p.g.443.2 | yes | 8 | |
9.4 | even | 3 | 1350.2.q.c.1043.2 | 8 | |||
9.5 | odd | 6 | inner | 450.2.p.g.293.1 | yes | 8 | |
15.2 | even | 4 | 1350.2.q.c.1007.2 | 8 | |||
15.8 | even | 4 | 1350.2.q.c.1007.1 | 8 | |||
15.14 | odd | 2 | 1350.2.q.c.143.1 | 8 | |||
45.4 | even | 6 | 1350.2.q.c.1043.1 | 8 | |||
45.13 | odd | 12 | 1350.2.q.c.557.1 | 8 | |||
45.14 | odd | 6 | inner | 450.2.p.g.293.2 | yes | 8 | |
45.22 | odd | 12 | 1350.2.q.c.557.2 | 8 | |||
45.23 | even | 12 | inner | 450.2.p.g.257.2 | yes | 8 | |
45.32 | even | 12 | inner | 450.2.p.g.257.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.2.p.g.257.1 | ✓ | 8 | 45.32 | even | 12 | inner | |
450.2.p.g.257.2 | yes | 8 | 45.23 | even | 12 | inner | |
450.2.p.g.293.1 | yes | 8 | 9.5 | odd | 6 | inner | |
450.2.p.g.293.2 | yes | 8 | 45.14 | odd | 6 | inner | |
450.2.p.g.407.1 | yes | 8 | 5.2 | odd | 4 | inner | |
450.2.p.g.407.2 | yes | 8 | 5.3 | odd | 4 | inner | |
450.2.p.g.443.1 | yes | 8 | 1.1 | even | 1 | trivial | |
450.2.p.g.443.2 | yes | 8 | 5.4 | even | 2 | inner | |
1350.2.q.c.143.1 | 8 | 15.14 | odd | 2 | |||
1350.2.q.c.143.2 | 8 | 3.2 | odd | 2 | |||
1350.2.q.c.557.1 | 8 | 45.13 | odd | 12 | |||
1350.2.q.c.557.2 | 8 | 45.22 | odd | 12 | |||
1350.2.q.c.1007.1 | 8 | 15.8 | even | 4 | |||
1350.2.q.c.1007.2 | 8 | 15.2 | even | 4 | |||
1350.2.q.c.1043.1 | 8 | 45.4 | even | 6 | |||
1350.2.q.c.1043.2 | 8 | 9.4 | even | 3 |