Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1530,2,Mod(647,1530)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1530, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1530.647");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1530.m (of order \(4\), degree \(2\), 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: | \(12.2171115093\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 647.1 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1530.647 |
Dual form | 1530.2.m.e.953.1 |
$q$-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 \(\left(\mathbb{Z}/1530\mathbb{Z}\right)^\times\).
\(n\) | \(307\) | \(1261\) | \(1361\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −0.707107 | − | 2.12132i | −0.316228 | − | 0.948683i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | + | 1.00000i | 0.377964 | + | 0.377964i | 0.870367 | − | 0.492403i | \(-0.163881\pi\) |
−0.492403 | + | 0.870367i | \(0.663881\pi\) | |||||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.00000 | + | 1.00000i | 0.632456 | + | 0.316228i | ||||
\(11\) | − | 2.82843i | − | 0.852803i | −0.904534 | − | 0.426401i | \(-0.859781\pi\) | ||
0.904534 | − | 0.426401i | \(-0.140219\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.00000 | + | 4.00000i | −1.10940 | + | 1.10940i | −0.116171 | + | 0.993229i | \(0.537062\pi\) |
−0.993229 | + | 0.116171i | \(0.962938\pi\) | |||||||
\(14\) | −1.41421 | −0.377964 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 0.707107 | − | 0.707107i | 0.171499 | − | 0.171499i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000i | 0.917663i | 0.888523 | + | 0.458831i | \(0.151732\pi\) | ||||
−0.888523 | + | 0.458831i | \(0.848268\pi\) | |||||||
\(20\) | −2.12132 | + | 0.707107i | −0.474342 | + | 0.158114i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.00000 | + | 2.00000i | 0.426401 | + | 0.426401i | ||||
\(23\) | 5.65685 | + | 5.65685i | 1.17954 | + | 1.17954i | 0.979863 | + | 0.199673i | \(0.0639880\pi\) |
0.199673 | + | 0.979863i | \(0.436012\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.00000 | + | 3.00000i | −0.800000 | + | 0.600000i | ||||
\(26\) | − | 5.65685i | − | 1.10940i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | − | 1.00000i | 0.188982 | − | 0.188982i | ||||
\(29\) | 9.89949 | 1.83829 | 0.919145 | − | 0.393919i | \(-0.128881\pi\) | ||||
0.919145 | + | 0.393919i | \(0.128881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.00000i | 0.171499i | ||||||||
\(35\) | 1.41421 | − | 2.82843i | 0.239046 | − | 0.478091i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.00000 | − | 3.00000i | −0.493197 | − | 0.493197i | 0.416115 | − | 0.909312i | \(-0.363391\pi\) |
−0.909312 | + | 0.416115i | \(0.863391\pi\) | |||||||
\(38\) | −2.82843 | − | 2.82843i | −0.458831 | − | 0.458831i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | − | 2.00000i | 0.158114 | − | 0.316228i | ||||
\(41\) | − | 5.65685i | − | 0.883452i | −0.897150 | − | 0.441726i | \(-0.854366\pi\) | ||
0.897150 | − | 0.441726i | \(-0.145634\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000 | − | 1.00000i | 0.152499 | − | 0.152499i | −0.626734 | − | 0.779233i | \(-0.715609\pi\) |
0.779233 | + | 0.626734i | \(0.215609\pi\) | |||||||
\(44\) | −2.82843 | −0.426401 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.00000 | −1.17954 | ||||||||
\(47\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 5.00000i | − | 0.714286i | ||||||
\(50\) | 0.707107 | − | 4.94975i | 0.100000 | − | 0.700000i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.00000 | + | 4.00000i | 0.554700 | + | 0.554700i | ||||
\(53\) | −4.24264 | − | 4.24264i | −0.582772 | − | 0.582772i | 0.352892 | − | 0.935664i | \(-0.385198\pi\) |
−0.935664 | + | 0.352892i | \(0.885198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.00000 | + | 2.00000i | −0.809040 | + | 0.269680i | ||||
\(56\) | 1.41421i | 0.188982i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.00000 | + | 7.00000i | −0.919145 | + | 0.919145i | ||||
\(59\) | 1.41421 | 0.184115 | 0.0920575 | − | 0.995754i | \(-0.470656\pi\) | ||||
0.0920575 | + | 0.995754i | \(0.470656\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.00000 | 1.02430 | 0.512148 | − | 0.858898i | \(-0.328850\pi\) | ||||
0.512148 | + | 0.858898i | \(0.328850\pi\) | |||||||
\(62\) | −4.24264 | + | 4.24264i | −0.538816 | + | 0.538816i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 11.3137 | + | 5.65685i | 1.40329 | + | 0.701646i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.00000 | + | 9.00000i | 1.09952 | + | 1.09952i | 0.994466 | + | 0.105059i | \(0.0335031\pi\) |
0.105059 | + | 0.994466i | \(0.466497\pi\) | |||||||
\(68\) | −0.707107 | − | 0.707107i | −0.0857493 | − | 0.0857493i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.00000 | + | 3.00000i | 0.119523 | + | 0.358569i | ||||
\(71\) | − | 15.5563i | − | 1.84620i | −0.384561 | − | 0.923099i | \(-0.625647\pi\) | ||
0.384561 | − | 0.923099i | \(-0.374353\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.0000 | − | 12.0000i | 1.40449 | − | 1.40449i | 0.619486 | − | 0.785007i | \(-0.287341\pi\) |
0.785007 | − | 0.619486i | \(-0.212659\pi\) | |||||||
\(74\) | 4.24264 | 0.493197 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.00000 | 0.458831 | ||||||||
\(77\) | 2.82843 | − | 2.82843i | 0.322329 | − | 0.322329i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 8.00000i | − | 0.900070i | −0.893011 | − | 0.450035i | \(-0.851411\pi\) | ||
0.893011 | − | 0.450035i | \(-0.148589\pi\) | |||||||
\(80\) | 0.707107 | + | 2.12132i | 0.0790569 | + | 0.237171i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.00000 | + | 4.00000i | 0.441726 | + | 0.441726i | ||||
\(83\) | 4.24264 | + | 4.24264i | 0.465690 | + | 0.465690i | 0.900515 | − | 0.434825i | \(-0.143190\pi\) |
−0.434825 | + | 0.900515i | \(0.643190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.00000 | − | 1.00000i | −0.216930 | − | 0.108465i | ||||
\(86\) | 1.41421i | 0.152499i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.00000 | − | 2.00000i | 0.213201 | − | 0.213201i | ||||
\(89\) | −7.07107 | −0.749532 | −0.374766 | − | 0.927119i | \(-0.622277\pi\) | ||||
−0.374766 | + | 0.927119i | \(0.622277\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.00000 | −0.838628 | ||||||||
\(92\) | 5.65685 | − | 5.65685i | 0.589768 | − | 0.589768i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.48528 | − | 2.82843i | 0.870572 | − | 0.290191i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.0000 | + | 10.0000i | 1.01535 | + | 1.01535i | 0.999880 | + | 0.0154658i | \(0.00492310\pi\) |
0.0154658 | + | 0.999880i | \(0.495077\pi\) | |||||||
\(98\) | 3.53553 | + | 3.53553i | 0.357143 | + | 0.357143i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.00000 | + | 4.00000i | 0.300000 | + | 0.400000i | ||||
\(101\) | 11.3137i | 1.12576i | 0.826540 | + | 0.562878i | \(0.190306\pi\) | ||||
−0.826540 | + | 0.562878i | \(0.809694\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(104\) | −5.65685 | −0.554700 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | 8.48528 | − | 8.48528i | 0.820303 | − | 0.820303i | −0.165848 | − | 0.986151i | \(-0.553036\pi\) |
0.986151 | + | 0.165848i | \(0.0530362\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.0000i | 1.72409i | 0.506834 | + | 0.862044i | \(0.330816\pi\) | ||||
−0.506834 | + | 0.862044i | \(0.669184\pi\) | |||||||
\(110\) | 2.82843 | − | 5.65685i | 0.269680 | − | 0.539360i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.00000 | − | 1.00000i | −0.0944911 | − | 0.0944911i | ||||
\(113\) | −4.24264 | − | 4.24264i | −0.399114 | − | 0.399114i | 0.478806 | − | 0.877920i | \(-0.341070\pi\) |
−0.877920 | + | 0.478806i | \(0.841070\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.00000 | − | 16.0000i | 0.746004 | − | 1.49201i | ||||
\(116\) | − | 9.89949i | − | 0.919145i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.00000 | + | 1.00000i | −0.0920575 | + | 0.0920575i | ||||
\(119\) | 1.41421 | 0.129641 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.00000 | 0.272727 | ||||||||
\(122\) | −5.65685 | + | 5.65685i | −0.512148 | + | 0.512148i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 6.00000i | − | 0.538816i | ||||||
\(125\) | 9.19239 | + | 6.36396i | 0.822192 | + | 0.569210i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −12.0000 | + | 4.00000i | −1.05247 | + | 0.350823i | ||||
\(131\) | − | 5.65685i | − | 0.494242i | −0.968985 | − | 0.247121i | \(-0.920516\pi\) | ||
0.968985 | − | 0.247121i | \(-0.0794845\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.00000 | + | 4.00000i | −0.346844 | + | 0.346844i | ||||
\(134\) | −12.7279 | −1.09952 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.00000 | 0.0857493 | ||||||||
\(137\) | −2.82843 | + | 2.82843i | −0.241649 | + | 0.241649i | −0.817532 | − | 0.575883i | \(-0.804658\pi\) |
0.575883 | + | 0.817532i | \(0.304658\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.0000i | 1.35710i | 0.734553 | + | 0.678551i | \(0.237392\pi\) | ||||
−0.734553 | + | 0.678551i | \(0.762608\pi\) | |||||||
\(140\) | −2.82843 | − | 1.41421i | −0.239046 | − | 0.119523i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 11.0000 | + | 11.0000i | 0.923099 | + | 0.923099i | ||||
\(143\) | 11.3137 | + | 11.3137i | 0.946100 | + | 0.946100i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.00000 | − | 21.0000i | −0.581318 | − | 1.74396i | ||||
\(146\) | 16.9706i | 1.40449i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.00000 | + | 3.00000i | −0.246598 | + | 0.246598i | ||||
\(149\) | −11.3137 | −0.926855 | −0.463428 | − | 0.886135i | \(-0.653381\pi\) | ||||
−0.463428 | + | 0.886135i | \(0.653381\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.0000 | 1.30206 | 0.651031 | − | 0.759051i | \(-0.274337\pi\) | ||||
0.651031 | + | 0.759051i | \(0.274337\pi\) | |||||||
\(152\) | −2.82843 | + | 2.82843i | −0.229416 | + | 0.229416i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.00000i | 0.322329i | ||||||||
\(155\) | −4.24264 | − | 12.7279i | −0.340777 | − | 1.02233i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.00000 | + | 8.00000i | 0.638470 | + | 0.638470i | 0.950178 | − | 0.311708i | \(-0.100901\pi\) |
−0.311708 | + | 0.950178i | \(0.600901\pi\) | |||||||
\(158\) | 5.65685 | + | 5.65685i | 0.450035 | + | 0.450035i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.00000 | − | 1.00000i | −0.158114 | − | 0.0790569i | ||||
\(161\) | 11.3137i | 0.891645i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.00000 | + | 6.00000i | −0.469956 | + | 0.469956i | −0.901900 | − | 0.431944i | \(-0.857828\pi\) |
0.431944 | + | 0.901900i | \(0.357828\pi\) | |||||||
\(164\) | −5.65685 | −0.441726 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.00000 | −0.465690 | ||||||||
\(167\) | −15.5563 | + | 15.5563i | −1.20379 | + | 1.20379i | −0.230781 | + | 0.973006i | \(0.574128\pi\) |
−0.973006 | + | 0.230781i | \(0.925872\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 19.0000i | − | 1.46154i | ||||||
\(170\) | 2.12132 | − | 0.707107i | 0.162698 | − | 0.0542326i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.00000 | − | 1.00000i | −0.0762493 | − | 0.0762493i | ||||
\(173\) | 11.3137 | + | 11.3137i | 0.860165 | + | 0.860165i | 0.991357 | − | 0.131192i | \(-0.0418803\pi\) |
−0.131192 | + | 0.991357i | \(0.541880\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.00000 | − | 1.00000i | −0.529150 | − | 0.0755929i | ||||
\(176\) | 2.82843i | 0.213201i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.00000 | − | 5.00000i | 0.374766 | − | 0.374766i | ||||
\(179\) | −18.3848 | −1.37414 | −0.687071 | − | 0.726590i | \(-0.741104\pi\) | ||||
−0.687071 | + | 0.726590i | \(0.741104\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 5.65685 | − | 5.65685i | 0.419314 | − | 0.419314i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.00000i | 0.589768i | ||||||||
\(185\) | −4.24264 | + | 8.48528i | −0.311925 | + | 0.623850i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.00000 | − | 2.00000i | −0.146254 | − | 0.146254i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.00000 | + | 8.00000i | −0.290191 | + | 0.580381i | ||||
\(191\) | − | 14.1421i | − | 1.02329i | −0.859197 | − | 0.511645i | \(-0.829036\pi\) | ||
0.859197 | − | 0.511645i | \(-0.170964\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.00000 | − | 6.00000i | 0.431889 | − | 0.431889i | −0.457381 | − | 0.889271i | \(-0.651213\pi\) |
0.889271 | + | 0.457381i | \(0.151213\pi\) | |||||||
\(194\) | −14.1421 | −1.01535 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.00000 | −0.357143 | ||||||||
\(197\) | −8.48528 | + | 8.48528i | −0.604551 | + | 0.604551i | −0.941517 | − | 0.336966i | \(-0.890599\pi\) |
0.336966 | + | 0.941517i | \(0.390599\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 14.0000i | − | 0.992434i | −0.868199 | − | 0.496217i | \(-0.834722\pi\) | ||
0.868199 | − | 0.496217i | \(-0.165278\pi\) | |||||||
\(200\) | −4.94975 | − | 0.707107i | −0.350000 | − | 0.0500000i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.00000 | − | 8.00000i | −0.562878 | − | 0.562878i | ||||
\(203\) | 9.89949 | + | 9.89949i | 0.694808 | + | 0.694808i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.0000 | + | 4.00000i | −0.838116 | + | 0.279372i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.00000 | − | 4.00000i | 0.277350 | − | 0.277350i | ||||
\(209\) | 11.3137 | 0.782586 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(212\) | −4.24264 | + | 4.24264i | −0.291386 | + | 0.291386i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 12.0000i | 0.820303i | ||||||||
\(215\) | −2.82843 | − | 1.41421i | −0.192897 | − | 0.0964486i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.00000 | + | 6.00000i | 0.407307 | + | 0.407307i | ||||
\(218\) | −12.7279 | − | 12.7279i | −0.862044 | − | 0.862044i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.00000 | + | 6.00000i | 0.134840 | + | 0.404520i | ||||
\(221\) | 5.65685i | 0.380521i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.00000 | − | 8.00000i | 0.535720 | − | 0.535720i | −0.386549 | − | 0.922269i | \(-0.626333\pi\) |
0.922269 | + | 0.386549i | \(0.126333\pi\) | |||||||
\(224\) | 1.41421 | 0.0944911 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.00000 | 0.399114 | ||||||||
\(227\) | 8.48528 | − | 8.48528i | 0.563188 | − | 0.563188i | −0.367024 | − | 0.930212i | \(-0.619623\pi\) |
0.930212 | + | 0.367024i | \(0.119623\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.0000i | 0.925146i | 0.886581 | + | 0.462573i | \(0.153074\pi\) | ||||
−0.886581 | + | 0.462573i | \(0.846926\pi\) | |||||||
\(230\) | 5.65685 | + | 16.9706i | 0.373002 | + | 1.11901i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.00000 | + | 7.00000i | 0.459573 | + | 0.459573i | ||||
\(233\) | 1.41421 | + | 1.41421i | 0.0926482 | + | 0.0926482i | 0.751912 | − | 0.659264i | \(-0.229132\pi\) |
−0.659264 | + | 0.751912i | \(0.729132\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 1.41421i | − | 0.0920575i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.00000 | + | 1.00000i | −0.0648204 | + | 0.0648204i | ||||
\(239\) | 28.2843 | 1.82956 | 0.914779 | − | 0.403955i | \(-0.132365\pi\) | ||||
0.914779 | + | 0.403955i | \(0.132365\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.0000 | −0.901819 | −0.450910 | − | 0.892570i | \(-0.648900\pi\) | ||||
−0.450910 | + | 0.892570i | \(0.648900\pi\) | |||||||
\(242\) | −2.12132 | + | 2.12132i | −0.136364 | + | 0.136364i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 8.00000i | − | 0.512148i | ||||||
\(245\) | −10.6066 | + | 3.53553i | −0.677631 | + | 0.225877i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.0000 | − | 16.0000i | −1.01806 | − | 1.01806i | ||||
\(248\) | 4.24264 | + | 4.24264i | 0.269408 | + | 0.269408i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.0000 | + | 2.00000i | −0.695701 | + | 0.126491i | ||||
\(251\) | − | 15.5563i | − | 0.981908i | −0.871185 | − | 0.490954i | \(-0.836648\pi\) | ||
0.871185 | − | 0.490954i | \(-0.163352\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.0000 | − | 16.0000i | 1.00591 | − | 1.00591i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −1.41421 | + | 1.41421i | −0.0882162 | + | 0.0882162i | −0.749838 | − | 0.661622i | \(-0.769869\pi\) |
0.661622 | + | 0.749838i | \(0.269869\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 6.00000i | − | 0.372822i | ||||||
\(260\) | 5.65685 | − | 11.3137i | 0.350823 | − | 0.701646i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.00000 | + | 4.00000i | 0.247121 | + | 0.247121i | ||||
\(263\) | 8.48528 | + | 8.48528i | 0.523225 | + | 0.523225i | 0.918544 | − | 0.395319i | \(-0.129366\pi\) |
−0.395319 | + | 0.918544i | \(0.629366\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.00000 | + | 12.0000i | −0.368577 | + | 0.737154i | ||||
\(266\) | − | 5.65685i | − | 0.346844i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.00000 | − | 9.00000i | 0.549762 | − | 0.549762i | ||||
\(269\) | 4.24264 | 0.258678 | 0.129339 | − | 0.991600i | \(-0.458714\pi\) | ||||
0.129339 | + | 0.991600i | \(0.458714\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.00000 | −0.242983 | −0.121491 | − | 0.992592i | \(-0.538768\pi\) | ||||
−0.121491 | + | 0.992592i | \(0.538768\pi\) | |||||||
\(272\) | −0.707107 | + | 0.707107i | −0.0428746 | + | 0.0428746i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 4.00000i | − | 0.241649i | ||||||
\(275\) | 8.48528 | + | 11.3137i | 0.511682 | + | 0.682242i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.0000 | − | 15.0000i | −0.901263 | − | 0.901263i | 0.0942828 | − | 0.995545i | \(-0.469944\pi\) |
−0.995545 | + | 0.0942828i | \(0.969944\pi\) | |||||||
\(278\) | −11.3137 | − | 11.3137i | −0.678551 | − | 0.678551i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.00000 | − | 1.00000i | 0.179284 | − | 0.0597614i | ||||
\(281\) | 15.5563i | 0.928014i | 0.885832 | + | 0.464007i | \(0.153589\pi\) | ||||
−0.885832 | + | 0.464007i | \(0.846411\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.0000 | + | 12.0000i | −0.713326 | + | 0.713326i | −0.967230 | − | 0.253904i | \(-0.918285\pi\) |
0.253904 | + | 0.967230i | \(0.418285\pi\) | |||||||
\(284\) | −15.5563 | −0.923099 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −16.0000 | −0.946100 | ||||||||
\(287\) | 5.65685 | − | 5.65685i | 0.333914 | − | 0.333914i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 1.00000i | − | 0.0588235i | ||||||
\(290\) | 19.7990 | + | 9.89949i | 1.16264 | + | 0.581318i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −12.0000 | − | 12.0000i | −0.702247 | − | 0.702247i | ||||
\(293\) | 21.2132 | + | 21.2132i | 1.23929 | + | 1.23929i | 0.960292 | + | 0.278996i | \(0.0900018\pi\) |
0.278996 | + | 0.960292i | \(0.409998\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.00000 | − | 3.00000i | −0.0582223 | − | 0.174667i | ||||
\(296\) | − | 4.24264i | − | 0.246598i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.00000 | − | 8.00000i | 0.463428 | − | 0.463428i | ||||
\(299\) | −45.2548 | −2.61715 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.00000 | 0.115278 | ||||||||
\(302\) | −11.3137 | + | 11.3137i | −0.651031 | + | 0.651031i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 4.00000i | − | 0.229416i | ||||||
\(305\) | −5.65685 | − | 16.9706i | −0.323911 | − | 0.971732i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.00000 | − | 7.00000i | −0.399511 | − | 0.399511i | 0.478549 | − | 0.878061i | \(-0.341163\pi\) |
−0.878061 | + | 0.478549i | \(0.841163\pi\) | |||||||
\(308\) | −2.82843 | − | 2.82843i | −0.161165 | − | 0.161165i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 12.0000 | + | 6.00000i | 0.681554 | + | 0.340777i | ||||
\(311\) | − | 21.2132i | − | 1.20289i | −0.798914 | − | 0.601445i | \(-0.794592\pi\) | ||
0.798914 | − | 0.601445i | \(-0.205408\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.00000 | + | 6.00000i | −0.339140 | + | 0.339140i | −0.856044 | − | 0.516904i | \(-0.827085\pi\) |
0.516904 | + | 0.856044i | \(0.327085\pi\) | |||||||
\(314\) | −11.3137 | −0.638470 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | −7.07107 | + | 7.07107i | −0.397151 | + | 0.397151i | −0.877227 | − | 0.480076i | \(-0.840609\pi\) |
0.480076 | + | 0.877227i | \(0.340609\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 28.0000i | − | 1.56770i | ||||||
\(320\) | 2.12132 | − | 0.707107i | 0.118585 | − | 0.0395285i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.00000 | − | 8.00000i | −0.445823 | − | 0.445823i | ||||
\(323\) | 2.82843 | + | 2.82843i | 0.157378 | + | 0.157378i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.00000 | − | 28.0000i | 0.221880 | − | 1.55316i | ||||
\(326\) | − | 8.48528i | − | 0.469956i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.00000 | − | 4.00000i | 0.220863 | − | 0.220863i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −34.0000 | −1.86881 | −0.934405 | − | 0.356214i | \(-0.884068\pi\) | ||||
−0.934405 | + | 0.356214i | \(0.884068\pi\) | |||||||
\(332\) | 4.24264 | − | 4.24264i | 0.232845 | − | 0.232845i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 22.0000i | − | 1.20379i | ||||||
\(335\) | 12.7279 | − | 25.4558i | 0.695401 | − | 1.39080i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.00000 | + | 4.00000i | 0.217894 | + | 0.217894i | 0.807610 | − | 0.589716i | \(-0.200761\pi\) |
−0.589716 | + | 0.807610i | \(0.700761\pi\) | |||||||
\(338\) | 13.4350 | + | 13.4350i | 0.730769 | + | 0.730769i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.00000 | + | 2.00000i | −0.0542326 | + | 0.108465i | ||||
\(341\) | − | 16.9706i | − | 0.919007i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.0000 | − | 12.0000i | 0.647939 | − | 0.647939i | ||||
\(344\) | 1.41421 | 0.0762493 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −16.0000 | −0.860165 | ||||||||
\(347\) | 25.4558 | − | 25.4558i | 1.36654 | − | 1.36654i | 0.501223 | − | 0.865318i | \(-0.332883\pi\) |
0.865318 | − | 0.501223i | \(-0.167117\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 14.0000i | − | 0.749403i | −0.927146 | − | 0.374701i | \(-0.877745\pi\) | ||
0.927146 | − | 0.374701i | \(-0.122255\pi\) | |||||||
\(350\) | 5.65685 | − | 4.24264i | 0.302372 | − | 0.226779i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.00000 | − | 2.00000i | −0.106600 | − | 0.106600i | ||||
\(353\) | 22.6274 | + | 22.6274i | 1.20434 | + | 1.20434i | 0.972835 | + | 0.231501i | \(0.0743638\pi\) |
0.231501 | + | 0.972835i | \(0.425636\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −33.0000 | + | 11.0000i | −1.75146 | + | 0.583819i | ||||
\(356\) | 7.07107i | 0.374766i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.0000 | − | 13.0000i | 0.687071 | − | 0.687071i | ||||
\(359\) | −36.7696 | −1.94062 | −0.970311 | − | 0.241859i | \(-0.922243\pi\) | ||||
−0.970311 | + | 0.241859i | \(0.922243\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 1.41421 | − | 1.41421i | 0.0743294 | − | 0.0743294i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.00000i | 0.419314i | ||||||||
\(365\) | −33.9411 | − | 16.9706i | −1.77656 | − | 0.888280i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.0000 | + | 11.0000i | 0.574195 | + | 0.574195i | 0.933298 | − | 0.359103i | \(-0.116917\pi\) |
−0.359103 | + | 0.933298i | \(0.616917\pi\) | |||||||
\(368\) | −5.65685 | − | 5.65685i | −0.294884 | − | 0.294884i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.00000 | − | 9.00000i | −0.155963 | − | 0.467888i | ||||
\(371\) | − | 8.48528i | − | 0.440534i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.0000 | − | 18.0000i | 0.932005 | − | 0.932005i | −0.0658264 | − | 0.997831i | \(-0.520968\pi\) |
0.997831 | + | 0.0658264i | \(0.0209684\pi\) | |||||||
\(374\) | 2.82843 | 0.146254 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −39.5980 | + | 39.5980i | −2.03940 | + | 2.03940i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.0000i | 1.64373i | 0.569683 | + | 0.821865i | \(0.307066\pi\) | ||||
−0.569683 | + | 0.821865i | \(0.692934\pi\) | |||||||
\(380\) | −2.82843 | − | 8.48528i | −0.145095 | − | 0.435286i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 10.0000 | + | 10.0000i | 0.511645 | + | 0.511645i | ||||
\(383\) | −8.48528 | − | 8.48528i | −0.433578 | − | 0.433578i | 0.456266 | − | 0.889843i | \(-0.349187\pi\) |
−0.889843 | + | 0.456266i | \(0.849187\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.00000 | − | 4.00000i | −0.407718 | − | 0.203859i | ||||
\(386\) | 8.48528i | 0.431889i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10.0000 | − | 10.0000i | 0.507673 | − | 0.507673i | ||||
\(389\) | −5.65685 | −0.286814 | −0.143407 | − | 0.989664i | \(-0.545806\pi\) | ||||
−0.143407 | + | 0.989664i | \(0.545806\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.00000 | 0.404577 | ||||||||
\(392\) | 3.53553 | − | 3.53553i | 0.178571 | − | 0.178571i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 12.0000i | − | 0.604551i | ||||||
\(395\) | −16.9706 | + | 5.65685i | −0.853882 | + | 0.284627i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.00000 | + | 5.00000i | 0.250943 | + | 0.250943i | 0.821357 | − | 0.570414i | \(-0.193217\pi\) |
−0.570414 | + | 0.821357i | \(0.693217\pi\) | |||||||
\(398\) | 9.89949 | + | 9.89949i | 0.496217 | + | 0.496217i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.00000 | − | 3.00000i | 0.200000 | − | 0.150000i | ||||
\(401\) | − | 19.7990i | − | 0.988714i | −0.869259 | − | 0.494357i | \(-0.835403\pi\) | ||
0.869259 | − | 0.494357i | \(-0.164597\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −24.0000 | + | 24.0000i | −1.19553 | + | 1.19553i | ||||
\(404\) | 11.3137 | 0.562878 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −14.0000 | −0.694808 | ||||||||
\(407\) | −8.48528 | + | 8.48528i | −0.420600 | + | 0.420600i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.0000i | 0.692255i | 0.938187 | + | 0.346128i | \(0.112504\pi\) | ||||
−0.938187 | + | 0.346128i | \(0.887496\pi\) | |||||||
\(410\) | 5.65685 | − | 11.3137i | 0.279372 | − | 0.558744i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.41421 | + | 1.41421i | 0.0695889 | + | 0.0695889i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.00000 | − | 12.0000i | 0.294528 | − | 0.589057i | ||||
\(416\) | 5.65685i | 0.277350i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8.00000 | + | 8.00000i | −0.391293 | + | 0.391293i | ||||
\(419\) | −11.3137 | −0.552711 | −0.276355 | − | 0.961056i | \(-0.589127\pi\) | ||||
−0.276355 | + | 0.961056i | \(0.589127\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.00000 | 0.292422 | 0.146211 | − | 0.989253i | \(-0.453292\pi\) | ||||
0.146211 | + | 0.989253i | \(0.453292\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 6.00000i | − | 0.291386i | ||||||
\(425\) | −0.707107 | + | 4.94975i | −0.0342997 | + | 0.240098i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.00000 | + | 8.00000i | 0.387147 | + | 0.387147i | ||||
\(428\) | −8.48528 | − | 8.48528i | −0.410152 | − | 0.410152i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.00000 | − | 1.00000i | 0.144673 | − | 0.0482243i | ||||
\(431\) | − | 4.24264i | − | 0.204361i | −0.994766 | − | 0.102180i | \(-0.967418\pi\) | ||
0.994766 | − | 0.102180i | \(-0.0325819\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.0000 | + | 15.0000i | −0.720854 | + | 0.720854i | −0.968779 | − | 0.247925i | \(-0.920251\pi\) |
0.247925 | + | 0.968779i | \(0.420251\pi\) | |||||||
\(434\) | −8.48528 | −0.407307 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.0000 | 0.862044 | ||||||||
\(437\) | −22.6274 | + | 22.6274i | −1.08242 | + | 1.08242i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 8.00000i | − | 0.381819i | −0.981608 | − | 0.190910i | \(-0.938856\pi\) | ||
0.981608 | − | 0.190910i | \(-0.0611437\pi\) | |||||||
\(440\) | −5.65685 | − | 2.82843i | −0.269680 | − | 0.134840i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.00000 | − | 4.00000i | −0.190261 | − | 0.190261i | ||||
\(443\) | 15.5563 | + | 15.5563i | 0.739104 | + | 0.739104i | 0.972405 | − | 0.233300i | \(-0.0749525\pi\) |
−0.233300 | + | 0.972405i | \(0.574953\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.00000 | + | 15.0000i | 0.237023 | + | 0.711068i | ||||
\(446\) | 11.3137i | 0.535720i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.00000 | + | 1.00000i | −0.0472456 | + | 0.0472456i | ||||
\(449\) | 2.82843 | 0.133482 | 0.0667409 | − | 0.997770i | \(-0.478740\pi\) | ||||
0.0667409 | + | 0.997770i | \(0.478740\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.0000 | −0.753411 | ||||||||
\(452\) | −4.24264 | + | 4.24264i | −0.199557 | + | 0.199557i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 12.0000i | 0.563188i | ||||||||
\(455\) | 5.65685 | + | 16.9706i | 0.265197 | + | 0.795592i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.00000 | − | 9.00000i | −0.421002 | − | 0.421002i | 0.464546 | − | 0.885549i | \(-0.346217\pi\) |
−0.885549 | + | 0.464546i | \(0.846217\pi\) | |||||||
\(458\) | −9.89949 | − | 9.89949i | −0.462573 | − | 0.462573i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −16.0000 | − | 8.00000i | −0.746004 | − | 0.373002i | ||||
\(461\) | 8.48528i | 0.395199i | 0.980283 | + | 0.197599i | \(0.0633145\pi\) | ||||
−0.980283 | + | 0.197599i | \(0.936685\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.0000 | + | 12.0000i | −0.557687 | + | 0.557687i | −0.928648 | − | 0.370961i | \(-0.879028\pi\) |
0.370961 | + | 0.928648i | \(0.379028\pi\) | |||||||
\(464\) | −9.89949 | −0.459573 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.00000 | −0.0926482 | ||||||||
\(467\) | −8.48528 | + | 8.48528i | −0.392652 | + | 0.392652i | −0.875632 | − | 0.482980i | \(-0.839555\pi\) |
0.482980 | + | 0.875632i | \(0.339555\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.0000i | 0.831163i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.00000 | + | 1.00000i | 0.0460287 | + | 0.0460287i | ||||
\(473\) | −2.82843 | − | 2.82843i | −0.130051 | − | 0.130051i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.0000 | − | 16.0000i | −0.550598 | − | 0.734130i | ||||
\(476\) | − | 1.41421i | − | 0.0648204i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −20.0000 | + | 20.0000i | −0.914779 | + | 0.914779i | ||||
\(479\) | −9.89949 | −0.452319 | −0.226160 | − | 0.974090i | \(-0.572617\pi\) | ||||
−0.226160 | + | 0.974090i | \(0.572617\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.0000 | 1.09431 | ||||||||
\(482\) | 9.89949 | − | 9.89949i | 0.450910 | − | 0.450910i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 3.00000i | − | 0.136364i | ||||||
\(485\) | 14.1421 | − | 28.2843i | 0.642161 | − | 1.28432i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.0000 | − | 17.0000i | −0.770344 | − | 0.770344i | 0.207823 | − | 0.978166i | \(-0.433362\pi\) |
−0.978166 | + | 0.207823i | \(0.933362\pi\) | |||||||
\(488\) | 5.65685 | + | 5.65685i | 0.256074 | + | 0.256074i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 5.00000 | − | 10.0000i | 0.225877 | − | 0.451754i | ||||
\(491\) | 1.41421i | 0.0638226i | 0.999491 | + | 0.0319113i | \(0.0101594\pi\) | ||||
−0.999491 | + | 0.0319113i | \(0.989841\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.00000 | − | 7.00000i | 0.315264 | − | 0.315264i | ||||
\(494\) | 22.6274 | 1.01806 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.00000 | −0.269408 | ||||||||
\(497\) | 15.5563 | − | 15.5563i | 0.697798 | − | 0.697798i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 4.00000i | − | 0.179065i | −0.995984 | − | 0.0895323i | \(-0.971463\pi\) | ||
0.995984 | − | 0.0895323i | \(-0.0285372\pi\) | |||||||
\(500\) | 6.36396 | − | 9.19239i | 0.284605 | − | 0.411096i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 11.0000 | + | 11.0000i | 0.490954 | + | 0.490954i | ||||
\(503\) | −16.9706 | − | 16.9706i | −0.756680 | − | 0.756680i | 0.219037 | − | 0.975717i | \(-0.429709\pi\) |
−0.975717 | + | 0.219037i | \(0.929709\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.0000 | − | 8.00000i | 1.06799 | − | 0.355995i | ||||
\(506\) | 22.6274i | 1.00591i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.2843 | 1.25368 | 0.626839 | − | 0.779149i | \(-0.284348\pi\) | ||||
0.626839 | + | 0.779149i | \(0.284348\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.0000 | 1.06170 | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 2.00000i | − | 0.0882162i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 4.24264 | + | 4.24264i | 0.186411 | + | 0.186411i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.00000 | + | 12.0000i | 0.175412 | + | 0.526235i | ||||
\(521\) | − | 19.7990i | − | 0.867409i | −0.901055 | − | 0.433705i | \(-0.857206\pi\) | ||
0.901055 | − | 0.433705i | \(-0.142794\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.0000 | + | 15.0000i | −0.655904 | + | 0.655904i | −0.954408 | − | 0.298504i | \(-0.903512\pi\) |
0.298504 | + | 0.954408i | \(0.403512\pi\) | |||||||
\(524\) | −5.65685 | −0.247121 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.0000 | −0.523225 | ||||||||
\(527\) | 4.24264 | − | 4.24264i | 0.184812 | − | 0.184812i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 41.0000i | 1.78261i | ||||||||
\(530\) | −4.24264 | − | 12.7279i | −0.184289 | − | 0.552866i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.00000 | + | 4.00000i | 0.173422 | + | 0.173422i | ||||
\(533\) | 22.6274 | + | 22.6274i | 0.980102 | + | 0.980102i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24.0000 | − | 12.0000i | −1.03761 | − | 0.518805i | ||||
\(536\) | 12.7279i | 0.549762i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.00000 | + | 3.00000i | −0.129339 | + | 0.129339i | ||||
\(539\) | −14.1421 | −0.609145 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.0000 | 1.71973 | 0.859867 | − | 0.510518i | \(-0.170546\pi\) | ||||
0.859867 | + | 0.510518i | \(0.170546\pi\) | |||||||
\(542\) | 2.82843 | − | 2.82843i | 0.121491 | − | 0.121491i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 1.00000i | − | 0.0428746i | ||||||
\(545\) | 38.1838 | − | 12.7279i | 1.63561 | − | 0.545204i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.0000 | − | 32.0000i | −1.36822 | − | 1.36822i | −0.862976 | − | 0.505246i | \(-0.831402\pi\) |
−0.505246 | − | 0.862976i | \(-0.668598\pi\) | |||||||
\(548\) | 2.82843 | + | 2.82843i | 0.120824 | + | 0.120824i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −14.0000 | − | 2.00000i | −0.596962 | − | 0.0852803i | ||||
\(551\) | 39.5980i | 1.68693i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.00000 | − | 8.00000i | 0.340195 | − | 0.340195i | ||||
\(554\) | 21.2132 | 0.901263 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.0000 | 0.678551 | ||||||||
\(557\) | 1.41421 | − | 1.41421i | 0.0599222 | − | 0.0599222i | −0.676511 | − | 0.736433i | \(-0.736509\pi\) |
0.736433 | + | 0.676511i | \(0.236509\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.00000i | 0.338364i | ||||||||
\(560\) | −1.41421 | + | 2.82843i | −0.0597614 | + | 0.119523i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −11.0000 | − | 11.0000i | −0.464007 | − | 0.464007i | ||||
\(563\) | −4.24264 | − | 4.24264i | −0.178806 | − | 0.178806i | 0.612029 | − | 0.790835i | \(-0.290353\pi\) |
−0.790835 | + | 0.612029i | \(0.790353\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.00000 | + | 12.0000i | −0.252422 | + | 0.504844i | ||||
\(566\) | − | 16.9706i | − | 0.713326i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.0000 | − | 11.0000i | 0.461550 | − | 0.461550i | ||||
\(569\) | −18.3848 | −0.770730 | −0.385365 | − | 0.922764i | \(-0.625924\pi\) | ||||
−0.385365 | + | 0.922764i | \(0.625924\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.0000 | 0.836974 | 0.418487 | − | 0.908223i | \(-0.362561\pi\) | ||||
0.418487 | + | 0.908223i | \(0.362561\pi\) | |||||||
\(572\) | 11.3137 | − | 11.3137i | 0.473050 | − | 0.473050i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 8.00000i | 0.333914i | ||||||||
\(575\) | −39.5980 | − | 5.65685i | −1.65135 | − | 0.235907i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.00000 | − | 9.00000i | −0.374675 | − | 0.374675i | 0.494502 | − | 0.869177i | \(-0.335351\pi\) |
−0.869177 | + | 0.494502i | \(0.835351\pi\) | |||||||
\(578\) | 0.707107 | + | 0.707107i | 0.0294118 | + | 0.0294118i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −21.0000 | + | 7.00000i | −0.871978 | + | 0.290659i | ||||
\(581\) | 8.48528i | 0.352029i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.0000 | + | 12.0000i | −0.496989 | + | 0.496989i | ||||
\(584\) | 16.9706 | 0.702247 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −30.0000 | −1.23929 | ||||||||
\(587\) | −18.3848 | + | 18.3848i | −0.758821 | + | 0.758821i | −0.976108 | − | 0.217287i | \(-0.930279\pi\) |
0.217287 | + | 0.976108i | \(0.430279\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.0000i | 0.988903i | ||||||||
\(590\) | 2.82843 | + | 1.41421i | 0.116445 | + | 0.0582223i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.00000 | + | 3.00000i | 0.123299 | + | 0.123299i | ||||
\(593\) | −32.5269 | − | 32.5269i | −1.33572 | − | 1.33572i | −0.900159 | − | 0.435561i | \(-0.856550\pi\) |
−0.435561 | − | 0.900159i | \(-0.643450\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.00000 | − | 3.00000i | −0.0409960 | − | 0.122988i | ||||
\(596\) | 11.3137i | 0.463428i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 32.0000 | − | 32.0000i | 1.30858 | − | 1.30858i | ||||
\(599\) | −2.82843 | −0.115566 | −0.0577832 | − | 0.998329i | \(-0.518403\pi\) | ||||
−0.0577832 | + | 0.998329i | \(0.518403\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.0000 | −0.407909 | −0.203954 | − | 0.978980i | \(-0.565379\pi\) | ||||
−0.203954 | + | 0.978980i | \(0.565379\pi\) | |||||||
\(602\) | −1.41421 | + | 1.41421i | −0.0576390 | + | 0.0576390i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 16.0000i | − | 0.651031i | ||||||
\(605\) | −2.12132 | − | 6.36396i | −0.0862439 | − | 0.258732i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.0000 | − | 15.0000i | −0.608831 | − | 0.608831i | 0.333809 | − | 0.942641i | \(-0.391666\pi\) |
−0.942641 | + | 0.333809i | \(0.891666\pi\) | |||||||
\(608\) | 2.82843 | + | 2.82843i | 0.114708 | + | 0.114708i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 16.0000 | + | 8.00000i | 0.647821 | + | 0.323911i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.0000 | − | 30.0000i | 1.21169 | − | 1.21169i | 0.241218 | − | 0.970471i | \(-0.422453\pi\) |
0.970471 | − | 0.241218i | \(-0.0775467\pi\) | |||||||
\(614\) | 9.89949 | 0.399511 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.00000 | 0.161165 | ||||||||
\(617\) | −21.2132 | + | 21.2132i | −0.854011 | + | 0.854011i | −0.990624 | − | 0.136613i | \(-0.956378\pi\) |
0.136613 | + | 0.990624i | \(0.456378\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.00000i | 0.321547i | 0.986991 | + | 0.160774i | \(0.0513989\pi\) | ||||
−0.986991 | + | 0.160774i | \(0.948601\pi\) | |||||||
\(620\) | −12.7279 | + | 4.24264i | −0.511166 | + | 0.170389i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15.0000 | + | 15.0000i | 0.601445 | + | 0.601445i | ||||
\(623\) | −7.07107 | − | 7.07107i | −0.283296 | − | 0.283296i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.00000 | − | 24.0000i | 0.280000 | − | 0.960000i | ||||
\(626\) | − | 8.48528i | − | 0.339140i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.00000 | − | 8.00000i | 0.319235 | − | 0.319235i | ||||
\(629\) | −4.24264 | −0.169165 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.0000 | −0.636950 | −0.318475 | − | 0.947931i | \(-0.603171\pi\) | ||||
−0.318475 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(632\) | 5.65685 | − | 5.65685i | 0.225018 | − | 0.225018i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 10.0000i | − | 0.397151i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.0000 | + | 20.0000i | 0.792429 | + | 0.792429i | ||||
\(638\) | 19.7990 | + | 19.7990i | 0.783850 | + | 0.783850i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.00000 | + | 2.00000i | −0.0395285 | + | 0.0790569i | ||||
\(641\) | − | 2.82843i | − | 0.111716i | −0.998439 | − | 0.0558581i | \(-0.982211\pi\) | ||
0.998439 | − | 0.0558581i | \(-0.0177894\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.0000 | − | 10.0000i | 0.394362 | − | 0.394362i | −0.481877 | − | 0.876239i | \(-0.660045\pi\) |
0.876239 | + | 0.481877i | \(0.160045\pi\) | |||||||
\(644\) | 11.3137 | 0.445823 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.00000 | −0.157378 | ||||||||
\(647\) | 25.4558 | − | 25.4558i | 1.00077 | − | 1.00077i | 0.000772798 | − | 1.00000i | \(-0.499754\pi\) |
1.00000 | 0.000772798i | \(-0.000245989\pi\) | ||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 4.00000i | − | 0.157014i | ||||||
\(650\) | 16.9706 | + | 22.6274i | 0.665640 | + | 0.887520i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.00000 | + | 6.00000i | 0.234978 | + | 0.234978i | ||||
\(653\) | −2.82843 | − | 2.82843i | −0.110685 | − | 0.110685i | 0.649595 | − | 0.760280i | \(-0.274938\pi\) |
−0.760280 | + | 0.649595i | \(0.774938\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.0000 | + | 4.00000i | −0.468879 | + | 0.156293i | ||||
\(656\) | 5.65685i | 0.220863i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.07107 | −0.275450 | −0.137725 | − | 0.990471i | \(-0.543979\pi\) | ||||
−0.137725 | + | 0.990471i | \(0.543979\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.0000 | 0.700119 | 0.350059 | − | 0.936727i | \(-0.386161\pi\) | ||||
0.350059 | + | 0.936727i | \(0.386161\pi\) | |||||||
\(662\) | 24.0416 | − | 24.0416i | 0.934405 | − | 0.934405i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.00000i | 0.232845i | ||||||||
\(665\) | 11.3137 | + | 5.65685i | 0.438727 | + | 0.219363i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 56.0000 | + | 56.0000i | 2.16833 | + | 2.16833i | ||||
\(668\) | 15.5563 | + | 15.5563i | 0.601893 | + | 0.601893i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9.00000 | + | 27.0000i | 0.347700 | + | 1.04310i | ||||
\(671\) | − | 22.6274i | − | 0.873522i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.00000 | − | 2.00000i | 0.0770943 | − | 0.0770943i | −0.667508 | − | 0.744602i | \(-0.732639\pi\) |
0.744602 | + | 0.667508i | \(0.232639\pi\) | |||||||
\(674\) | −5.65685 | −0.217894 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −19.0000 | −0.730769 | ||||||||
\(677\) | −12.7279 | + | 12.7279i | −0.489174 | + | 0.489174i | −0.908045 | − | 0.418872i | \(-0.862426\pi\) |
0.418872 | + | 0.908045i | \(0.362426\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.0000i | 0.767530i | ||||||||
\(680\) | −0.707107 | − | 2.12132i | −0.0271163 | − | 0.0813489i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 12.0000 | + | 12.0000i | 0.459504 | + | 0.459504i | ||||
\(683\) | −2.82843 | − | 2.82843i | −0.108227 | − | 0.108227i | 0.650920 | − | 0.759147i | \(-0.274383\pi\) |
−0.759147 | + | 0.650920i | \(0.774383\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.00000 | + | 4.00000i | 0.305664 | + | 0.152832i | ||||
\(686\) | 16.9706i | 0.647939i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.00000 | + | 1.00000i | −0.0381246 | + | 0.0381246i | ||||
\(689\) | 33.9411 | 1.29305 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(692\) | 11.3137 | − | 11.3137i | 0.430083 | − | 0.430083i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 36.0000i | 1.36654i | ||||||||
\(695\) | 33.9411 | − | 11.3137i | 1.28746 | − | 0.429153i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.00000 | − | 4.00000i | −0.151511 | − | 0.151511i | ||||
\(698\) | 9.89949 | + | 9.89949i | 0.374701 | + | 0.374701i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.00000 | + | 7.00000i | −0.0377964 | + | 0.264575i | ||||
\(701\) | − | 2.82843i | − | 0.106828i | −0.998572 | − | 0.0534141i | \(-0.982990\pi\) | ||
0.998572 | − | 0.0534141i | \(-0.0170103\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.0000 | − | 12.0000i | 0.452589 | − | 0.452589i | ||||
\(704\) | 2.82843 | 0.106600 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −32.0000 | −1.20434 | ||||||||
\(707\) | −11.3137 | + | 11.3137i | −0.425496 | + | 0.425496i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 46.0000i | 1.72757i | 0.503864 | + | 0.863783i | \(0.331911\pi\) | ||||
−0.503864 | + | 0.863783i | \(0.668089\pi\) | |||||||
\(710\) | 15.5563 | − | 31.1127i | 0.583819 | − | 1.16764i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.00000 | − | 5.00000i | −0.187383 | − | 0.187383i | ||||
\(713\) | 33.9411 | + | 33.9411i | 1.27111 | + | 1.27111i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.0000 | − | 32.0000i | 0.598366 | − | 1.19673i | ||||
\(716\) | 18.3848i | 0.687071i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 26.0000 | − | 26.0000i | 0.970311 | − | 0.970311i | ||||
\(719\) | 52.3259 | 1.95143 | 0.975713 | − | 0.219051i | \(-0.0702961\pi\) | ||||
0.975713 | + | 0.219051i | \(0.0702961\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.12132 | + | 2.12132i | −0.0789474 | + | 0.0789474i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.00000i | 0.0743294i | ||||||||
\(725\) | −39.5980 | + | 29.6985i | −1.47063 | + | 1.10297i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(728\) | −5.65685 | − | 5.65685i | −0.209657 | − | 0.209657i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 36.0000 | − | 12.0000i | 1.33242 | − | 0.444140i | ||||
\(731\) | − | 1.41421i | − | 0.0523066i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.0000 | − | 22.0000i | 0.812589 | − | 0.812589i | −0.172433 | − | 0.985021i | \(-0.555163\pi\) |
0.985021 | + | 0.172433i | \(0.0551627\pi\) | |||||||
\(734\) | −15.5563 | −0.574195 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.00000 | 0.294884 | ||||||||
\(737\) | 25.4558 | − | 25.4558i | 0.937678 | − | 0.937678i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.0000i | 1.10357i | 0.833987 | + | 0.551784i | \(0.186053\pi\) | ||||
−0.833987 | + | 0.551784i | \(0.813947\pi\) | |||||||
\(740\) | 8.48528 | + | 4.24264i | 0.311925 | + | 0.155963i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.00000 | + | 6.00000i | 0.220267 | + | 0.220267i | ||||
\(743\) | −12.7279 | − | 12.7279i | −0.466942 | − | 0.466942i | 0.433980 | − | 0.900922i | \(-0.357109\pi\) |
−0.900922 | + | 0.433980i | \(0.857109\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.00000 | + | 24.0000i | 0.293097 | + | 0.879292i | ||||
\(746\) | 25.4558i | 0.932005i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.00000 | + | 2.00000i | −0.0731272 | + | 0.0731272i | ||||
\(749\) | 16.9706 | 0.620091 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 56.0000i | − | 2.03940i | ||||||
\(755\) | −11.3137 | − | 33.9411i | −0.411748 | − | 1.23524i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.00000 | + | 8.00000i | 0.290765 | + | 0.290765i | 0.837382 | − | 0.546617i | \(-0.184085\pi\) |
−0.546617 | + | 0.837382i | \(0.684085\pi\) | |||||||
\(758\) | −22.6274 | − | 22.6274i | −0.821865 | − | 0.821865i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.00000 | + | 4.00000i | 0.290191 | + | 0.145095i | ||||
\(761\) | 15.5563i | 0.563917i | 0.959427 | + | 0.281959i | \(0.0909841\pi\) | ||||
−0.959427 | + | 0.281959i | \(0.909016\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.0000 | + | 18.0000i | −0.651644 | + | 0.651644i | ||||
\(764\) | −14.1421 | −0.511645 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.0000 | 0.433578 | ||||||||
\(767\) | −5.65685 | + | 5.65685i | −0.204257 | + | 0.204257i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.0000i | 1.08183i | 0.841078 | + | 0.540914i | \(0.181921\pi\) | ||||
−0.841078 | + | 0.540914i | \(0.818079\pi\) | |||||||
\(770\) | 8.48528 | − | 2.82843i | 0.305788 | − | 0.101929i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.00000 | − | 6.00000i | −0.215945 | − | 0.215945i | ||||
\(773\) | −9.89949 | − | 9.89949i | −0.356060 | − | 0.356060i | 0.506298 | − | 0.862358i | \(-0.331013\pi\) |
−0.862358 | + | 0.506298i | \(0.831013\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24.0000 | + | 18.0000i | −0.862105 | + | 0.646579i | ||||
\(776\) | 14.1421i | 0.507673i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.00000 | − | 4.00000i | 0.143407 | − | 0.143407i | ||||
\(779\) | 22.6274 | 0.810711 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −44.0000 | −1.57444 | ||||||||
\(782\) | −5.65685 | + | 5.65685i | −0.202289 | + | 0.202289i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.00000i | 0.178571i | ||||||||
\(785\) | 11.3137 | − | 22.6274i | 0.403804 | − | 0.807607i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.0000 | + | 30.0000i | 1.06938 | + | 1.06938i | 0.997406 | + | 0.0719783i | \(0.0229312\pi\) |
0.0719783 | + | 0.997406i | \(0.477069\pi\) | |||||||
\(788\) | 8.48528 | + | 8.48528i | 0.302276 | + | 0.302276i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.00000 | − | 16.0000i | 0.284627 | − | 0.569254i | ||||
\(791\) | − | 8.48528i | − | 0.301702i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.0000 | + | 32.0000i | −1.13635 | + | 1.13635i | ||||
\(794\) | −7.07107 | −0.250943 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14.0000 | −0.496217 | ||||||||
\(797\) | −12.7279 | + | 12.7279i | −0.450846 | + | 0.450846i | −0.895635 | − | 0.444789i | \(-0.853279\pi\) |
0.444789 | + | 0.895635i | \(0.353279\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.707107 | + | 4.94975i | −0.0250000 | + | 0.175000i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 14.0000 | + | 14.0000i | 0.494357 | + | 0.494357i | ||||
\(803\) | −33.9411 | − | 33.9411i | −1.19776 | − | 1.19776i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 24.0000 | − | 8.00000i | 0.845889 | − | 0.281963i | ||||
\(806\) | − | 33.9411i | − | 1.19553i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8.00000 | + | 8.00000i | −0.281439 | + | 0.281439i | ||||
\(809\) | −39.5980 | −1.39219 | −0.696095 | − | 0.717949i | \(-0.745081\pi\) | ||||
−0.696095 | + | 0.717949i | \(0.745081\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 52.0000 | 1.82597 | 0.912983 | − | 0.407997i | \(-0.133772\pi\) | ||||
0.912983 | + | 0.407997i | \(0.133772\pi\) | |||||||
\(812\) | 9.89949 | − | 9.89949i | 0.347404 | − | 0.347404i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 12.0000i | − | 0.420600i | ||||||
\(815\) | 16.9706 | + | 8.48528i | 0.594453 | + | 0.297226i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.00000 | + | 4.00000i | 0.139942 | + | 0.139942i | ||||
\(818\) | −9.89949 | − | 9.89949i | −0.346128 | − | 0.346128i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.00000 | + | 12.0000i | 0.139686 | + | 0.419058i | ||||
\(821\) | − | 12.7279i | − | 0.444208i | −0.975023 | − | 0.222104i | \(-0.928708\pi\) | ||
0.975023 | − | 0.222104i | \(-0.0712924\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.0000 | + | 15.0000i | −0.522867 | + | 0.522867i | −0.918436 | − | 0.395569i | \(-0.870547\pi\) |
0.395569 | + | 0.918436i | \(0.370547\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.00000 | −0.0695889 | ||||||||
\(827\) | −19.7990 | + | 19.7990i | −0.688478 | + | 0.688478i | −0.961896 | − | 0.273417i | \(-0.911846\pi\) |
0.273417 | + | 0.961896i | \(0.411846\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.00000i | 0.0694629i | 0.999397 | + | 0.0347314i | \(0.0110576\pi\) | ||||
−0.999397 | + | 0.0347314i | \(0.988942\pi\) | |||||||
\(830\) | 4.24264 | + | 12.7279i | 0.147264 | + | 0.441793i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.00000 | − | 4.00000i | −0.138675 | − | 0.138675i | ||||
\(833\) | −3.53553 | − | 3.53553i | −0.122499 | − | 0.122499i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 44.0000 | + | 22.0000i | 1.52268 | + | 0.761341i | ||||
\(836\) | − | 11.3137i | − | 0.391293i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.00000 | − | 8.00000i | 0.276355 | − | 0.276355i | ||||
\(839\) | 32.5269 | 1.12295 | 0.561477 | − | 0.827492i | \(-0.310233\pi\) | ||||
0.561477 | + | 0.827492i | \(0.310233\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 69.0000 | 2.37931 | ||||||||
\(842\) | −4.24264 | + | 4.24264i | −0.146211 | + | 0.146211i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −40.3051 | + | 13.4350i | −1.38654 | + | 0.462179i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.00000 | + | 3.00000i | 0.103081 | + | 0.103081i | ||||
\(848\) | 4.24264 | + | 4.24264i | 0.145693 | + | 0.145693i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.00000 | − | 4.00000i | −0.102899 | − | 0.137199i | ||||
\(851\) | − | 33.9411i | − | 1.16349i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.0000 | + | 21.0000i | −0.719026 | + | 0.719026i | −0.968406 | − | 0.249380i | \(-0.919773\pi\) |
0.249380 | + | 0.968406i | \(0.419773\pi\) | |||||||
\(854\) | −11.3137 | −0.387147 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.0000 | 0.410152 | ||||||||
\(857\) | −26.8701 | + | 26.8701i | −0.917864 | + | 0.917864i | −0.996874 | − | 0.0790101i | \(-0.974824\pi\) |
0.0790101 | + | 0.996874i | \(0.474824\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 30.0000i | − | 1.02359i | −0.859109 | − | 0.511793i | \(-0.828981\pi\) | ||
0.859109 | − | 0.511793i | \(-0.171019\pi\) | |||||||
\(860\) | −1.41421 | + | 2.82843i | −0.0482243 | + | 0.0964486i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.00000 | + | 3.00000i | 0.102180 | + | 0.102180i | ||||
\(863\) | −11.3137 | − | 11.3137i | −0.385123 | − | 0.385123i | 0.487821 | − | 0.872944i | \(-0.337792\pi\) |
−0.872944 | + | 0.487821i | \(0.837792\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.0000 | − | 32.0000i | 0.544016 | − | 1.08803i | ||||
\(866\) | − | 21.2132i | − | 0.720854i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.00000 | − | 6.00000i | 0.203653 | − | 0.203653i | ||||
\(869\) | −22.6274 | −0.767583 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −72.0000 | −2.43963 | ||||||||
\(872\) | −12.7279 | + | 12.7279i | −0.431022 | + | 0.431022i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 32.0000i | − | 1.08242i | ||||||
\(875\) | 2.82843 | + | 15.5563i | 0.0956183 | + | 0.525901i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27.0000 | − | 27.0000i | −0.911725 | − | 0.911725i | 0.0846827 | − | 0.996408i | \(-0.473012\pi\) |
−0.996408 | + | 0.0846827i | \(0.973012\pi\) | |||||||
\(878\) | 5.65685 | + | 5.65685i | 0.190910 | + | 0.190910i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.00000 | − | 2.00000i | 0.202260 | − | 0.0674200i | ||||
\(881\) | 2.82843i | 0.0952921i | 0.998864 | + | 0.0476461i | \(0.0151720\pi\) | ||||
−0.998864 | + | 0.0476461i | \(0.984828\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.0000 | + | 11.0000i | −0.370179 | + | 0.370179i | −0.867543 | − | 0.497363i | \(-0.834302\pi\) |
0.497363 | + | 0.867543i | \(0.334302\pi\) | |||||||
\(884\) | 5.65685 | 0.190261 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −22.0000 | −0.739104 | ||||||||
\(887\) | 5.65685 | − | 5.65685i | 0.189939 | − | 0.189939i | −0.605731 | − | 0.795670i | \(-0.707119\pi\) |
0.795670 | + | 0.605731i | \(0.207119\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −14.1421 | − | 7.07107i | −0.474045 | − | 0.237023i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.00000 | − | 8.00000i | −0.267860 | − | 0.267860i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.0000 | + | 39.0000i | 0.434542 | + | 1.30363i | ||||
\(896\) | − | 1.41421i | − | 0.0472456i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.00000 | + | 2.00000i | −0.0667409 | + | 0.0667409i | ||||
\(899\) | 59.3970 | 1.98100 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.00000 | −0.199889 | ||||||||
\(902\) | 11.3137 | − | 11.3137i | 0.376705 | − | 0.376705i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 6.00000i | − | 0.199557i | ||||||
\(905\) | 1.41421 | + | 4.24264i | 0.0470100 | + | 0.141030i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.0000 | − | 14.0000i | −0.464862 | − | 0.464862i | 0.435383 | − | 0.900245i | \(-0.356613\pi\) |
−0.900245 | + | 0.435383i | \(0.856613\pi\) | |||||||
\(908\) | −8.48528 | − | 8.48528i | −0.281594 | − | 0.281594i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −16.0000 | − | 8.00000i | −0.530395 | − | 0.265197i | ||||
\(911\) | 12.7279i | 0.421695i | 0.977519 | + | 0.210847i | \(0.0676223\pi\) | ||||
−0.977519 | + | 0.210847i | \(0.932378\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.0000 | − | 12.0000i | 0.397142 | − | 0.397142i | ||||
\(914\) | 12.7279 | 0.421002 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.0000 | 0.462573 | ||||||||
\(917\) | 5.65685 | − | 5.65685i | 0.186806 | − | 0.186806i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 52.0000i | − | 1.71532i | −0.514216 | − | 0.857661i | \(-0.671917\pi\) | ||
0.514216 | − | 0.857661i | \(-0.328083\pi\) | |||||||
\(920\) | 16.9706 | − | 5.65685i | 0.559503 | − | 0.186501i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6.00000 | − | 6.00000i | −0.197599 | − | 0.197599i | ||||
\(923\) | 62.2254 | + | 62.2254i | 2.04817 | + | 2.04817i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.0000 | + | 3.00000i | 0.690476 | + | 0.0986394i | ||||
\(926\) | − | 16.9706i | − | 0.557687i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.00000 | − | 7.00000i | 0.229786 | − | 0.229786i | ||||
\(929\) | −5.65685 | −0.185595 | −0.0927977 | − | 0.995685i | \(-0.529581\pi\) | ||||
−0.0927977 | + | 0.995685i | \(0.529581\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.0000 | 0.655474 | ||||||||
\(932\) | 1.41421 | − | 1.41421i | 0.0463241 | − | 0.0463241i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 12.0000i | − | 0.392652i | ||||||
\(935\) | −2.82843 | + | 5.65685i | −0.0924995 | + | 0.184999i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.00000 | + | 5.00000i | 0.163343 | + | 0.163343i | 0.784046 | − | 0.620703i | \(-0.213153\pi\) |
−0.620703 | + | 0.784046i | \(0.713153\pi\) | |||||||
\(938\) | −12.7279 | − | 12.7279i | −0.415581 | − | 0.415581i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.3848i | 0.599327i | 0.954045 | + | 0.299663i | \(0.0968743\pi\) | ||||
−0.954045 | + | 0.299663i | \(0.903126\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.0000 | − | 32.0000i | 1.04206 | − | 1.04206i | ||||
\(944\) | −1.41421 | −0.0460287 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.00000 | 0.130051 | ||||||||
\(947\) | 14.1421 | − | 14.1421i | 0.459558 | − | 0.459558i | −0.438953 | − | 0.898510i | \(-0.644650\pi\) |
0.898510 | + | 0.438953i | \(0.144650\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 96.0000i | 3.11629i | ||||||||
\(950\) | 19.7990 | + | 2.82843i | 0.642364 | + | 0.0917663i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.00000 | + | 1.00000i | 0.0324102 | + | 0.0324102i | ||||
\(953\) | 25.4558 | + | 25.4558i | 0.824596 | + | 0.824596i | 0.986763 | − | 0.162168i | \(-0.0518485\pi\) |
−0.162168 | + | 0.986763i | \(0.551849\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −30.0000 | + | 10.0000i | −0.970777 | + | 0.323592i | ||||
\(956\) | − | 28.2843i | − | 0.914779i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.00000 | − | 7.00000i | 0.226160 | − | 0.226160i | ||||
\(959\) | −5.65685 | −0.182669 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | −16.9706 | + | 16.9706i | −0.547153 | + | 0.547153i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 14.0000i | 0.450910i | ||||||||
\(965\) | −16.9706 | − | 8.48528i | −0.546302 | − | 0.273151i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.00000 | − | 2.00000i | −0.0643157 | − | 0.0643157i | 0.674217 | − | 0.738533i | \(-0.264481\pi\) |
−0.738533 | + | 0.674217i | \(0.764481\pi\) | |||||||
\(968\) | 2.12132 | + | 2.12132i | 0.0681818 | + | 0.0681818i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10.0000 | + | 30.0000i | 0.321081 | + | 0.963242i | ||||
\(971\) | − | 43.8406i | − | 1.40691i | −0.710739 | − | 0.703456i | \(-0.751639\pi\) | ||
0.710739 | − | 0.703456i | \(-0.248361\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.0000 | + | 16.0000i | −0.512936 | + | 0.512936i | ||||
\(974\) | 24.0416 | 0.770344 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.00000 | −0.256074 | ||||||||
\(977\) | −33.9411 | + | 33.9411i | −1.08587 | + | 1.08587i | −0.0899242 | + | 0.995949i | \(0.528662\pi\) |
−0.995949 | + | 0.0899242i | \(0.971338\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.0000i | 0.639203i | ||||||||
\(980\) | 3.53553 | + | 10.6066i | 0.112938 | + | 0.338815i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.00000 | − | 1.00000i | −0.0319113 | − | 0.0319113i | ||||
\(983\) | −9.89949 | − | 9.89949i | −0.315745 | − | 0.315745i | 0.531385 | − | 0.847130i | \(-0.321672\pi\) |
−0.847130 | + | 0.531385i | \(0.821672\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24.0000 | + | 12.0000i | 0.764704 | + | 0.382352i | ||||
\(986\) | 9.89949i | 0.315264i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −16.0000 | + | 16.0000i | −0.509028 | + | 0.509028i | ||||
\(989\) | 11.3137 | 0.359755 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.00000 | −0.0635321 | −0.0317660 | − | 0.999495i | \(-0.510113\pi\) | ||||
−0.0317660 | + | 0.999495i | \(0.510113\pi\) | |||||||
\(992\) | 4.24264 | − | 4.24264i | 0.134704 | − | 0.134704i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 22.0000i | 0.697798i | ||||||||
\(995\) | −29.6985 | + | 9.89949i | −0.941505 | + | 0.313835i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.0000 | − | 17.0000i | −0.538395 | − | 0.538395i | 0.384662 | − | 0.923057i | \(-0.374318\pi\) |
−0.923057 | + | 0.384662i | \(0.874318\pi\) | |||||||
\(998\) | 2.82843 | + | 2.82843i | 0.0895323 | + | 0.0895323i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1530.2.m.e.647.1 | ✓ | 4 | |
3.2 | odd | 2 | inner | 1530.2.m.e.647.2 | yes | 4 | |
5.3 | odd | 4 | inner | 1530.2.m.e.953.2 | yes | 4 | |
15.8 | even | 4 | inner | 1530.2.m.e.953.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1530.2.m.e.647.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1530.2.m.e.647.2 | yes | 4 | 3.2 | odd | 2 | inner | |
1530.2.m.e.953.1 | yes | 4 | 15.8 | even | 4 | inner | |
1530.2.m.e.953.2 | yes | 4 | 5.3 | odd | 4 | inner |