Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1320,2,Mod(661,1320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1320, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1320.661");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1320.w (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.5402530668\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} + 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 661.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1320.661 |
Dual form | 1320.2.w.a.661.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1320\mathbb{Z}\right)^\times\).
\(n\) | \(661\) | \(881\) | \(991\) | \(1057\) | \(1201\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.00000i | 0.707107 | − | 0.707107i | ||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | − | 2.00000i | − | 1.00000i | ||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 1.00000 | + | 1.00000i | 0.408248 | + | 0.408248i | ||||
\(7\) | −2.00000 | −0.755929 | −0.377964 | − | 0.925820i | \(-0.623376\pi\) | ||||
−0.377964 | + | 0.925820i | \(0.623376\pi\) | |||||||
\(8\) | −2.00000 | − | 2.00000i | −0.707107 | − | 0.707107i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 1.00000 | + | 1.00000i | 0.316228 | + | 0.316228i | ||||
\(11\) | − | 1.00000i | − | 0.301511i | ||||||
\(12\) | 2.00000 | 0.577350 | ||||||||
\(13\) | − | 4.00000i | − | 1.10940i | −0.832050 | − | 0.554700i | \(-0.812833\pi\) | ||
0.832050 | − | 0.554700i | \(-0.187167\pi\) | |||||||
\(14\) | −2.00000 | + | 2.00000i | −0.534522 | + | 0.534522i | ||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | −1.00000 | + | 1.00000i | −0.235702 | + | 0.235702i | ||||
\(19\) | − | 4.00000i | − | 0.917663i | −0.888523 | − | 0.458831i | \(-0.848268\pi\) | ||
0.888523 | − | 0.458831i | \(-0.151732\pi\) | |||||||
\(20\) | 2.00000 | 0.447214 | ||||||||
\(21\) | − | 2.00000i | − | 0.436436i | ||||||
\(22\) | −1.00000 | − | 1.00000i | −0.213201 | − | 0.213201i | ||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 2.00000 | − | 2.00000i | 0.408248 | − | 0.408248i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −4.00000 | − | 4.00000i | −0.784465 | − | 0.784465i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 4.00000i | 0.755929i | ||||||||
\(29\) | − | 6.00000i | − | 1.11417i | −0.830455 | − | 0.557086i | \(-0.811919\pi\) | ||
0.830455 | − | 0.557086i | \(-0.188081\pi\) | |||||||
\(30\) | −1.00000 | + | 1.00000i | −0.182574 | + | 0.182574i | ||||
\(31\) | −6.00000 | −1.07763 | −0.538816 | − | 0.842424i | \(-0.681128\pi\) | ||||
−0.538816 | + | 0.842424i | \(0.681128\pi\) | |||||||
\(32\) | −4.00000 | + | 4.00000i | −0.707107 | + | 0.707107i | ||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 2.00000 | − | 2.00000i | 0.342997 | − | 0.342997i | ||||
\(35\) | − | 2.00000i | − | 0.338062i | ||||||
\(36\) | 2.00000i | 0.333333i | ||||||||
\(37\) | − | 4.00000i | − | 0.657596i | −0.944400 | − | 0.328798i | \(-0.893356\pi\) | ||
0.944400 | − | 0.328798i | \(-0.106644\pi\) | |||||||
\(38\) | −4.00000 | − | 4.00000i | −0.648886 | − | 0.648886i | ||||
\(39\) | 4.00000 | 0.640513 | ||||||||
\(40\) | 2.00000 | − | 2.00000i | 0.316228 | − | 0.316228i | ||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | −2.00000 | − | 2.00000i | −0.308607 | − | 0.308607i | ||||
\(43\) | − | 4.00000i | − | 0.609994i | −0.952353 | − | 0.304997i | \(-0.901344\pi\) | ||
0.952353 | − | 0.304997i | \(-0.0986555\pi\) | |||||||
\(44\) | −2.00000 | −0.301511 | ||||||||
\(45\) | − | 1.00000i | − | 0.149071i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | − | 4.00000i | − | 0.577350i | ||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | −1.00000 | + | 1.00000i | −0.141421 | + | 0.141421i | ||||
\(51\) | 2.00000i | 0.280056i | ||||||||
\(52\) | −8.00000 | −1.10940 | ||||||||
\(53\) | − | 14.0000i | − | 1.92305i | −0.274721 | − | 0.961524i | \(-0.588586\pi\) | ||
0.274721 | − | 0.961524i | \(-0.411414\pi\) | |||||||
\(54\) | −1.00000 | − | 1.00000i | −0.136083 | − | 0.136083i | ||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 4.00000 | + | 4.00000i | 0.534522 | + | 0.534522i | ||||
\(57\) | 4.00000 | 0.529813 | ||||||||
\(58\) | −6.00000 | − | 6.00000i | −0.787839 | − | 0.787839i | ||||
\(59\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(60\) | 2.00000i | 0.258199i | ||||||||
\(61\) | 12.0000i | 1.53644i | 0.640184 | + | 0.768221i | \(0.278858\pi\) | ||||
−0.640184 | + | 0.768221i | \(0.721142\pi\) | |||||||
\(62\) | −6.00000 | + | 6.00000i | −0.762001 | + | 0.762001i | ||||
\(63\) | 2.00000 | 0.251976 | ||||||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | 4.00000 | 0.496139 | ||||||||
\(66\) | 1.00000 | − | 1.00000i | 0.123091 | − | 0.123091i | ||||
\(67\) | − | 4.00000i | − | 0.488678i | −0.969690 | − | 0.244339i | \(-0.921429\pi\) | ||
0.969690 | − | 0.244339i | \(-0.0785709\pi\) | |||||||
\(68\) | − | 4.00000i | − | 0.485071i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.00000 | − | 2.00000i | −0.239046 | − | 0.239046i | ||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 2.00000 | + | 2.00000i | 0.235702 | + | 0.235702i | ||||
\(73\) | 10.0000 | 1.17041 | 0.585206 | − | 0.810885i | \(-0.301014\pi\) | ||||
0.585206 | + | 0.810885i | \(0.301014\pi\) | |||||||
\(74\) | −4.00000 | − | 4.00000i | −0.464991 | − | 0.464991i | ||||
\(75\) | − | 1.00000i | − | 0.115470i | ||||||
\(76\) | −8.00000 | −0.917663 | ||||||||
\(77\) | 2.00000i | 0.227921i | ||||||||
\(78\) | 4.00000 | − | 4.00000i | 0.452911 | − | 0.452911i | ||||
\(79\) | 6.00000 | 0.675053 | 0.337526 | − | 0.941316i | \(-0.390410\pi\) | ||||
0.337526 | + | 0.941316i | \(0.390410\pi\) | |||||||
\(80\) | − | 4.00000i | − | 0.447214i | ||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.00000 | − | 2.00000i | 0.220863 | − | 0.220863i | ||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | −4.00000 | −0.436436 | ||||||||
\(85\) | 2.00000i | 0.216930i | ||||||||
\(86\) | −4.00000 | − | 4.00000i | −0.431331 | − | 0.431331i | ||||
\(87\) | 6.00000 | 0.643268 | ||||||||
\(88\) | −2.00000 | + | 2.00000i | −0.213201 | + | 0.213201i | ||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | −1.00000 | − | 1.00000i | −0.105409 | − | 0.105409i | ||||
\(91\) | 8.00000i | 0.838628i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 6.00000i | − | 0.622171i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.00000 | 0.410391 | ||||||||
\(96\) | −4.00000 | − | 4.00000i | −0.408248 | − | 0.408248i | ||||
\(97\) | 6.00000 | 0.609208 | 0.304604 | − | 0.952479i | \(-0.401476\pi\) | ||||
0.304604 | + | 0.952479i | \(0.401476\pi\) | |||||||
\(98\) | −3.00000 | + | 3.00000i | −0.303046 | + | 0.303046i | ||||
\(99\) | 1.00000i | 0.100504i | ||||||||
\(100\) | 2.00000i | 0.200000i | ||||||||
\(101\) | − | 2.00000i | − | 0.199007i | −0.995037 | − | 0.0995037i | \(-0.968274\pi\) | ||
0.995037 | − | 0.0995037i | \(-0.0317255\pi\) | |||||||
\(102\) | 2.00000 | + | 2.00000i | 0.198030 | + | 0.198030i | ||||
\(103\) | −10.0000 | −0.985329 | −0.492665 | − | 0.870219i | \(-0.663977\pi\) | ||||
−0.492665 | + | 0.870219i | \(0.663977\pi\) | |||||||
\(104\) | −8.00000 | + | 8.00000i | −0.784465 | + | 0.784465i | ||||
\(105\) | 2.00000 | 0.195180 | ||||||||
\(106\) | −14.0000 | − | 14.0000i | −1.35980 | − | 1.35980i | ||||
\(107\) | 20.0000i | 1.93347i | 0.255774 | + | 0.966736i | \(0.417670\pi\) | ||||
−0.255774 | + | 0.966736i | \(0.582330\pi\) | |||||||
\(108\) | −2.00000 | −0.192450 | ||||||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 1.00000 | − | 1.00000i | 0.0953463 | − | 0.0953463i | ||||
\(111\) | 4.00000 | 0.379663 | ||||||||
\(112\) | 8.00000 | 0.755929 | ||||||||
\(113\) | −2.00000 | −0.188144 | −0.0940721 | − | 0.995565i | \(-0.529988\pi\) | ||||
−0.0940721 | + | 0.995565i | \(0.529988\pi\) | |||||||
\(114\) | 4.00000 | − | 4.00000i | 0.374634 | − | 0.374634i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −12.0000 | −1.11417 | ||||||||
\(117\) | 4.00000i | 0.369800i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.00000 | −0.366679 | ||||||||
\(120\) | 2.00000 | + | 2.00000i | 0.182574 | + | 0.182574i | ||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 12.0000 | + | 12.0000i | 1.08643 | + | 1.08643i | ||||
\(123\) | 2.00000i | 0.180334i | ||||||||
\(124\) | 12.0000i | 1.07763i | ||||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 2.00000 | − | 2.00000i | 0.178174 | − | 0.178174i | ||||
\(127\) | 6.00000 | 0.532414 | 0.266207 | − | 0.963916i | \(-0.414230\pi\) | ||||
0.266207 | + | 0.963916i | \(0.414230\pi\) | |||||||
\(128\) | 8.00000 | + | 8.00000i | 0.707107 | + | 0.707107i | ||||
\(129\) | 4.00000 | 0.352180 | ||||||||
\(130\) | 4.00000 | − | 4.00000i | 0.350823 | − | 0.350823i | ||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | − | 2.00000i | − | 0.174078i | ||||||
\(133\) | 8.00000i | 0.693688i | ||||||||
\(134\) | −4.00000 | − | 4.00000i | −0.345547 | − | 0.345547i | ||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −4.00000 | − | 4.00000i | −0.342997 | − | 0.342997i | ||||
\(137\) | 6.00000 | 0.512615 | 0.256307 | − | 0.966595i | \(-0.417494\pi\) | ||||
0.256307 | + | 0.966595i | \(0.417494\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.0000i | 1.01783i | 0.860818 | + | 0.508913i | \(0.169953\pi\) | ||||
−0.860818 | + | 0.508913i | \(0.830047\pi\) | |||||||
\(140\) | −4.00000 | −0.338062 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.00000 | + | 8.00000i | −0.671345 | + | 0.671345i | ||||
\(143\) | −4.00000 | −0.334497 | ||||||||
\(144\) | 4.00000 | 0.333333 | ||||||||
\(145\) | 6.00000 | 0.498273 | ||||||||
\(146\) | 10.0000 | − | 10.0000i | 0.827606 | − | 0.827606i | ||||
\(147\) | − | 3.00000i | − | 0.247436i | ||||||
\(148\) | −8.00000 | −0.657596 | ||||||||
\(149\) | 2.00000i | 0.163846i | 0.996639 | + | 0.0819232i | \(0.0261062\pi\) | ||||
−0.996639 | + | 0.0819232i | \(0.973894\pi\) | |||||||
\(150\) | −1.00000 | − | 1.00000i | −0.0816497 | − | 0.0816497i | ||||
\(151\) | −22.0000 | −1.79033 | −0.895167 | − | 0.445730i | \(-0.852944\pi\) | ||||
−0.895167 | + | 0.445730i | \(0.852944\pi\) | |||||||
\(152\) | −8.00000 | + | 8.00000i | −0.648886 | + | 0.648886i | ||||
\(153\) | −2.00000 | −0.161690 | ||||||||
\(154\) | 2.00000 | + | 2.00000i | 0.161165 | + | 0.161165i | ||||
\(155\) | − | 6.00000i | − | 0.481932i | ||||||
\(156\) | − | 8.00000i | − | 0.640513i | ||||||
\(157\) | 4.00000i | 0.319235i | 0.987179 | + | 0.159617i | \(0.0510260\pi\) | ||||
−0.987179 | + | 0.159617i | \(0.948974\pi\) | |||||||
\(158\) | 6.00000 | − | 6.00000i | 0.477334 | − | 0.477334i | ||||
\(159\) | 14.0000 | 1.11027 | ||||||||
\(160\) | −4.00000 | − | 4.00000i | −0.316228 | − | 0.316228i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | − | 1.00000i | 0.0785674 | − | 0.0785674i | ||||
\(163\) | 4.00000i | 0.313304i | 0.987654 | + | 0.156652i | \(0.0500701\pi\) | ||||
−0.987654 | + | 0.156652i | \(0.949930\pi\) | |||||||
\(164\) | − | 4.00000i | − | 0.312348i | ||||||
\(165\) | 1.00000i | 0.0778499i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | −4.00000 | + | 4.00000i | −0.308607 | + | 0.308607i | ||||
\(169\) | −3.00000 | −0.230769 | ||||||||
\(170\) | 2.00000 | + | 2.00000i | 0.153393 | + | 0.153393i | ||||
\(171\) | 4.00000i | 0.305888i | ||||||||
\(172\) | −8.00000 | −0.609994 | ||||||||
\(173\) | − | 18.0000i | − | 1.36851i | −0.729241 | − | 0.684257i | \(-0.760127\pi\) | ||
0.729241 | − | 0.684257i | \(-0.239873\pi\) | |||||||
\(174\) | 6.00000 | − | 6.00000i | 0.454859 | − | 0.454859i | ||||
\(175\) | 2.00000 | 0.151186 | ||||||||
\(176\) | 4.00000i | 0.301511i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.00000 | − | 6.00000i | 0.449719 | − | 0.449719i | ||||
\(179\) | − | 24.0000i | − | 1.79384i | −0.442189 | − | 0.896922i | \(-0.645798\pi\) | ||
0.442189 | − | 0.896922i | \(-0.354202\pi\) | |||||||
\(180\) | −2.00000 | −0.149071 | ||||||||
\(181\) | 20.0000i | 1.48659i | 0.668965 | + | 0.743294i | \(0.266738\pi\) | ||||
−0.668965 | + | 0.743294i | \(0.733262\pi\) | |||||||
\(182\) | 8.00000 | + | 8.00000i | 0.592999 | + | 0.592999i | ||||
\(183\) | −12.0000 | −0.887066 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.00000 | 0.294086 | ||||||||
\(186\) | −6.00000 | − | 6.00000i | −0.439941 | − | 0.439941i | ||||
\(187\) | − | 2.00000i | − | 0.146254i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.00000i | 0.145479i | ||||||||
\(190\) | 4.00000 | − | 4.00000i | 0.290191 | − | 0.290191i | ||||
\(191\) | 4.00000 | 0.289430 | 0.144715 | − | 0.989473i | \(-0.453773\pi\) | ||||
0.144715 | + | 0.989473i | \(0.453773\pi\) | |||||||
\(192\) | −8.00000 | −0.577350 | ||||||||
\(193\) | 18.0000 | 1.29567 | 0.647834 | − | 0.761781i | \(-0.275675\pi\) | ||||
0.647834 | + | 0.761781i | \(0.275675\pi\) | |||||||
\(194\) | 6.00000 | − | 6.00000i | 0.430775 | − | 0.430775i | ||||
\(195\) | 4.00000i | 0.286446i | ||||||||
\(196\) | 6.00000i | 0.428571i | ||||||||
\(197\) | − | 18.0000i | − | 1.28245i | −0.767354 | − | 0.641223i | \(-0.778427\pi\) | ||
0.767354 | − | 0.641223i | \(-0.221573\pi\) | |||||||
\(198\) | 1.00000 | + | 1.00000i | 0.0710669 | + | 0.0710669i | ||||
\(199\) | 2.00000 | 0.141776 | 0.0708881 | − | 0.997484i | \(-0.477417\pi\) | ||||
0.0708881 | + | 0.997484i | \(0.477417\pi\) | |||||||
\(200\) | 2.00000 | + | 2.00000i | 0.141421 | + | 0.141421i | ||||
\(201\) | 4.00000 | 0.282138 | ||||||||
\(202\) | −2.00000 | − | 2.00000i | −0.140720 | − | 0.140720i | ||||
\(203\) | 12.0000i | 0.842235i | ||||||||
\(204\) | 4.00000 | 0.280056 | ||||||||
\(205\) | 2.00000i | 0.139686i | ||||||||
\(206\) | −10.0000 | + | 10.0000i | −0.696733 | + | 0.696733i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 16.0000i | 1.10940i | ||||||||
\(209\) | −4.00000 | −0.276686 | ||||||||
\(210\) | 2.00000 | − | 2.00000i | 0.138013 | − | 0.138013i | ||||
\(211\) | 20.0000i | 1.37686i | 0.725304 | + | 0.688428i | \(0.241699\pi\) | ||||
−0.725304 | + | 0.688428i | \(0.758301\pi\) | |||||||
\(212\) | −28.0000 | −1.92305 | ||||||||
\(213\) | − | 8.00000i | − | 0.548151i | ||||||
\(214\) | 20.0000 | + | 20.0000i | 1.36717 | + | 1.36717i | ||||
\(215\) | 4.00000 | 0.272798 | ||||||||
\(216\) | −2.00000 | + | 2.00000i | −0.136083 | + | 0.136083i | ||||
\(217\) | 12.0000 | 0.814613 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.0000i | 0.675737i | ||||||||
\(220\) | − | 2.00000i | − | 0.134840i | ||||||
\(221\) | − | 8.00000i | − | 0.538138i | ||||||
\(222\) | 4.00000 | − | 4.00000i | 0.268462 | − | 0.268462i | ||||
\(223\) | 10.0000 | 0.669650 | 0.334825 | − | 0.942280i | \(-0.391323\pi\) | ||||
0.334825 | + | 0.942280i | \(0.391323\pi\) | |||||||
\(224\) | 8.00000 | − | 8.00000i | 0.534522 | − | 0.534522i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −2.00000 | + | 2.00000i | −0.133038 | + | 0.133038i | ||||
\(227\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(228\) | − | 8.00000i | − | 0.529813i | ||||||
\(229\) | 20.0000i | 1.32164i | 0.750546 | + | 0.660819i | \(0.229791\pi\) | ||||
−0.750546 | + | 0.660819i | \(0.770209\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.00000 | −0.131590 | ||||||||
\(232\) | −12.0000 | + | 12.0000i | −0.787839 | + | 0.787839i | ||||
\(233\) | −6.00000 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | 4.00000 | + | 4.00000i | 0.261488 | + | 0.261488i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.00000i | 0.389742i | ||||||||
\(238\) | −4.00000 | + | 4.00000i | −0.259281 | + | 0.259281i | ||||
\(239\) | 8.00000 | 0.517477 | 0.258738 | − | 0.965947i | \(-0.416693\pi\) | ||||
0.258738 | + | 0.965947i | \(0.416693\pi\) | |||||||
\(240\) | 4.00000 | 0.258199 | ||||||||
\(241\) | 10.0000 | 0.644157 | 0.322078 | − | 0.946713i | \(-0.395619\pi\) | ||||
0.322078 | + | 0.946713i | \(0.395619\pi\) | |||||||
\(242\) | −1.00000 | + | 1.00000i | −0.0642824 | + | 0.0642824i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 24.0000 | 1.53644 | ||||||||
\(245\) | − | 3.00000i | − | 0.191663i | ||||||
\(246\) | 2.00000 | + | 2.00000i | 0.127515 | + | 0.127515i | ||||
\(247\) | −16.0000 | −1.01806 | ||||||||
\(248\) | 12.0000 | + | 12.0000i | 0.762001 | + | 0.762001i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.00000 | − | 1.00000i | −0.0632456 | − | 0.0632456i | ||||
\(251\) | − | 4.00000i | − | 0.252478i | −0.992000 | − | 0.126239i | \(-0.959709\pi\) | ||
0.992000 | − | 0.126239i | \(-0.0402906\pi\) | |||||||
\(252\) | − | 4.00000i | − | 0.251976i | ||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 6.00000 | − | 6.00000i | 0.376473 | − | 0.376473i | ||||
\(255\) | −2.00000 | −0.125245 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 22.0000 | 1.37232 | 0.686161 | − | 0.727450i | \(-0.259294\pi\) | ||||
0.686161 | + | 0.727450i | \(0.259294\pi\) | |||||||
\(258\) | 4.00000 | − | 4.00000i | 0.249029 | − | 0.249029i | ||||
\(259\) | 8.00000i | 0.497096i | ||||||||
\(260\) | − | 8.00000i | − | 0.496139i | ||||||
\(261\) | 6.00000i | 0.371391i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | −2.00000 | − | 2.00000i | −0.123091 | − | 0.123091i | ||||
\(265\) | 14.0000 | 0.860013 | ||||||||
\(266\) | 8.00000 | + | 8.00000i | 0.490511 | + | 0.490511i | ||||
\(267\) | 6.00000i | 0.367194i | ||||||||
\(268\) | −8.00000 | −0.488678 | ||||||||
\(269\) | − | 18.0000i | − | 1.09748i | −0.835993 | − | 0.548740i | \(-0.815108\pi\) | ||
0.835993 | − | 0.548740i | \(-0.184892\pi\) | |||||||
\(270\) | 1.00000 | − | 1.00000i | 0.0608581 | − | 0.0608581i | ||||
\(271\) | −22.0000 | −1.33640 | −0.668202 | − | 0.743980i | \(-0.732936\pi\) | ||||
−0.668202 | + | 0.743980i | \(0.732936\pi\) | |||||||
\(272\) | −8.00000 | −0.485071 | ||||||||
\(273\) | −8.00000 | −0.484182 | ||||||||
\(274\) | 6.00000 | − | 6.00000i | 0.362473 | − | 0.362473i | ||||
\(275\) | 1.00000i | 0.0603023i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.0000i | 0.721010i | 0.932757 | + | 0.360505i | \(0.117396\pi\) | ||||
−0.932757 | + | 0.360505i | \(0.882604\pi\) | |||||||
\(278\) | 12.0000 | + | 12.0000i | 0.719712 | + | 0.719712i | ||||
\(279\) | 6.00000 | 0.359211 | ||||||||
\(280\) | −4.00000 | + | 4.00000i | −0.239046 | + | 0.239046i | ||||
\(281\) | 22.0000 | 1.31241 | 0.656205 | − | 0.754583i | \(-0.272161\pi\) | ||||
0.656205 | + | 0.754583i | \(0.272161\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.00000i | 0.237775i | 0.992908 | + | 0.118888i | \(0.0379328\pi\) | ||||
−0.992908 | + | 0.118888i | \(0.962067\pi\) | |||||||
\(284\) | 16.0000i | 0.949425i | ||||||||
\(285\) | 4.00000i | 0.236940i | ||||||||
\(286\) | −4.00000 | + | 4.00000i | −0.236525 | + | 0.236525i | ||||
\(287\) | −4.00000 | −0.236113 | ||||||||
\(288\) | 4.00000 | − | 4.00000i | 0.235702 | − | 0.235702i | ||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 6.00000 | − | 6.00000i | 0.352332 | − | 0.352332i | ||||
\(291\) | 6.00000i | 0.351726i | ||||||||
\(292\) | − | 20.0000i | − | 1.17041i | ||||||
\(293\) | 14.0000i | 0.817889i | 0.912559 | + | 0.408944i | \(0.134103\pi\) | ||||
−0.912559 | + | 0.408944i | \(0.865897\pi\) | |||||||
\(294\) | −3.00000 | − | 3.00000i | −0.174964 | − | 0.174964i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8.00000 | + | 8.00000i | −0.464991 | + | 0.464991i | ||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 2.00000 | + | 2.00000i | 0.115857 | + | 0.115857i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −2.00000 | −0.115470 | ||||||||
\(301\) | 8.00000i | 0.461112i | ||||||||
\(302\) | −22.0000 | + | 22.0000i | −1.26596 | + | 1.26596i | ||||
\(303\) | 2.00000 | 0.114897 | ||||||||
\(304\) | 16.0000i | 0.917663i | ||||||||
\(305\) | −12.0000 | −0.687118 | ||||||||
\(306\) | −2.00000 | + | 2.00000i | −0.114332 | + | 0.114332i | ||||
\(307\) | − | 20.0000i | − | 1.14146i | −0.821138 | − | 0.570730i | \(-0.806660\pi\) | ||
0.821138 | − | 0.570730i | \(-0.193340\pi\) | |||||||
\(308\) | 4.00000 | 0.227921 | ||||||||
\(309\) | − | 10.0000i | − | 0.568880i | ||||||
\(310\) | −6.00000 | − | 6.00000i | −0.340777 | − | 0.340777i | ||||
\(311\) | 20.0000 | 1.13410 | 0.567048 | − | 0.823685i | \(-0.308085\pi\) | ||||
0.567048 | + | 0.823685i | \(0.308085\pi\) | |||||||
\(312\) | −8.00000 | − | 8.00000i | −0.452911 | − | 0.452911i | ||||
\(313\) | 6.00000 | 0.339140 | 0.169570 | − | 0.985518i | \(-0.445762\pi\) | ||||
0.169570 | + | 0.985518i | \(0.445762\pi\) | |||||||
\(314\) | 4.00000 | + | 4.00000i | 0.225733 | + | 0.225733i | ||||
\(315\) | 2.00000i | 0.112687i | ||||||||
\(316\) | − | 12.0000i | − | 0.675053i | ||||||
\(317\) | − | 34.0000i | − | 1.90963i | −0.297200 | − | 0.954815i | \(-0.596053\pi\) | ||
0.297200 | − | 0.954815i | \(-0.403947\pi\) | |||||||
\(318\) | 14.0000 | − | 14.0000i | 0.785081 | − | 0.785081i | ||||
\(319\) | −6.00000 | −0.335936 | ||||||||
\(320\) | −8.00000 | −0.447214 | ||||||||
\(321\) | −20.0000 | −1.11629 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 8.00000i | − | 0.445132i | ||||||
\(324\) | − | 2.00000i | − | 0.111111i | ||||||
\(325\) | 4.00000i | 0.221880i | ||||||||
\(326\) | 4.00000 | + | 4.00000i | 0.221540 | + | 0.221540i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.00000 | − | 4.00000i | −0.220863 | − | 0.220863i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.00000 | + | 1.00000i | 0.0550482 | + | 0.0550482i | ||||
\(331\) | 12.0000i | 0.659580i | 0.944054 | + | 0.329790i | \(0.106978\pi\) | ||||
−0.944054 | + | 0.329790i | \(0.893022\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.00000i | 0.219199i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.00000 | 0.218543 | ||||||||
\(336\) | 8.00000i | 0.436436i | ||||||||
\(337\) | −2.00000 | −0.108947 | −0.0544735 | − | 0.998515i | \(-0.517348\pi\) | ||||
−0.0544735 | + | 0.998515i | \(0.517348\pi\) | |||||||
\(338\) | −3.00000 | + | 3.00000i | −0.163178 | + | 0.163178i | ||||
\(339\) | − | 2.00000i | − | 0.108625i | ||||||
\(340\) | 4.00000 | 0.216930 | ||||||||
\(341\) | 6.00000i | 0.324918i | ||||||||
\(342\) | 4.00000 | + | 4.00000i | 0.216295 | + | 0.216295i | ||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | −8.00000 | + | 8.00000i | −0.431331 | + | 0.431331i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.0000 | − | 18.0000i | −0.967686 | − | 0.967686i | ||||
\(347\) | − | 16.0000i | − | 0.858925i | −0.903085 | − | 0.429463i | \(-0.858703\pi\) | ||
0.903085 | − | 0.429463i | \(-0.141297\pi\) | |||||||
\(348\) | − | 12.0000i | − | 0.643268i | ||||||
\(349\) | − | 28.0000i | − | 1.49881i | −0.662114 | − | 0.749403i | \(-0.730341\pi\) | ||
0.662114 | − | 0.749403i | \(-0.269659\pi\) | |||||||
\(350\) | 2.00000 | − | 2.00000i | 0.106904 | − | 0.106904i | ||||
\(351\) | −4.00000 | −0.213504 | ||||||||
\(352\) | 4.00000 | + | 4.00000i | 0.213201 | + | 0.213201i | ||||
\(353\) | 14.0000 | 0.745145 | 0.372572 | − | 0.928003i | \(-0.378476\pi\) | ||||
0.372572 | + | 0.928003i | \(0.378476\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 8.00000i | − | 0.424596i | ||||||
\(356\) | − | 12.0000i | − | 0.635999i | ||||||
\(357\) | − | 4.00000i | − | 0.211702i | ||||||
\(358\) | −24.0000 | − | 24.0000i | −1.26844 | − | 1.26844i | ||||
\(359\) | −12.0000 | −0.633336 | −0.316668 | − | 0.948536i | \(-0.602564\pi\) | ||||
−0.316668 | + | 0.948536i | \(0.602564\pi\) | |||||||
\(360\) | −2.00000 | + | 2.00000i | −0.105409 | + | 0.105409i | ||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 20.0000 | + | 20.0000i | 1.05118 | + | 1.05118i | ||||
\(363\) | − | 1.00000i | − | 0.0524864i | ||||||
\(364\) | 16.0000 | 0.838628 | ||||||||
\(365\) | 10.0000i | 0.523424i | ||||||||
\(366\) | −12.0000 | + | 12.0000i | −0.627250 | + | 0.627250i | ||||
\(367\) | −34.0000 | −1.77479 | −0.887393 | − | 0.461014i | \(-0.847486\pi\) | ||||
−0.887393 | + | 0.461014i | \(0.847486\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.00000 | −0.104116 | ||||||||
\(370\) | 4.00000 | − | 4.00000i | 0.207950 | − | 0.207950i | ||||
\(371\) | 28.0000i | 1.45369i | ||||||||
\(372\) | −12.0000 | −0.622171 | ||||||||
\(373\) | − | 24.0000i | − | 1.24267i | −0.783544 | − | 0.621336i | \(-0.786590\pi\) | ||
0.783544 | − | 0.621336i | \(-0.213410\pi\) | |||||||
\(374\) | −2.00000 | − | 2.00000i | −0.103418 | − | 0.103418i | ||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −24.0000 | −1.23606 | ||||||||
\(378\) | 2.00000 | + | 2.00000i | 0.102869 | + | 0.102869i | ||||
\(379\) | 36.0000i | 1.84920i | 0.380945 | + | 0.924598i | \(0.375599\pi\) | ||||
−0.380945 | + | 0.924598i | \(0.624401\pi\) | |||||||
\(380\) | − | 8.00000i | − | 0.410391i | ||||||
\(381\) | 6.00000i | 0.307389i | ||||||||
\(382\) | 4.00000 | − | 4.00000i | 0.204658 | − | 0.204658i | ||||
\(383\) | 20.0000 | 1.02195 | 0.510976 | − | 0.859595i | \(-0.329284\pi\) | ||||
0.510976 | + | 0.859595i | \(0.329284\pi\) | |||||||
\(384\) | −8.00000 | + | 8.00000i | −0.408248 | + | 0.408248i | ||||
\(385\) | −2.00000 | −0.101929 | ||||||||
\(386\) | 18.0000 | − | 18.0000i | 0.916176 | − | 0.916176i | ||||
\(387\) | 4.00000i | 0.203331i | ||||||||
\(388\) | − | 12.0000i | − | 0.609208i | ||||||
\(389\) | − | 10.0000i | − | 0.507020i | −0.967333 | − | 0.253510i | \(-0.918415\pi\) | ||
0.967333 | − | 0.253510i | \(-0.0815851\pi\) | |||||||
\(390\) | 4.00000 | + | 4.00000i | 0.202548 | + | 0.202548i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 6.00000 | + | 6.00000i | 0.303046 | + | 0.303046i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −18.0000 | − | 18.0000i | −0.906827 | − | 0.906827i | ||||
\(395\) | 6.00000i | 0.301893i | ||||||||
\(396\) | 2.00000 | 0.100504 | ||||||||
\(397\) | − | 28.0000i | − | 1.40528i | −0.711546 | − | 0.702640i | \(-0.752005\pi\) | ||
0.711546 | − | 0.702640i | \(-0.247995\pi\) | |||||||
\(398\) | 2.00000 | − | 2.00000i | 0.100251 | − | 0.100251i | ||||
\(399\) | −8.00000 | −0.400501 | ||||||||
\(400\) | 4.00000 | 0.200000 | ||||||||
\(401\) | −34.0000 | −1.69788 | −0.848939 | − | 0.528490i | \(-0.822758\pi\) | ||||
−0.848939 | + | 0.528490i | \(0.822758\pi\) | |||||||
\(402\) | 4.00000 | − | 4.00000i | 0.199502 | − | 0.199502i | ||||
\(403\) | 24.0000i | 1.19553i | ||||||||
\(404\) | −4.00000 | −0.199007 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | 12.0000 | + | 12.0000i | 0.595550 | + | 0.595550i | ||||
\(407\) | −4.00000 | −0.198273 | ||||||||
\(408\) | 4.00000 | − | 4.00000i | 0.198030 | − | 0.198030i | ||||
\(409\) | 10.0000 | 0.494468 | 0.247234 | − | 0.968956i | \(-0.420478\pi\) | ||||
0.247234 | + | 0.968956i | \(0.420478\pi\) | |||||||
\(410\) | 2.00000 | + | 2.00000i | 0.0987730 | + | 0.0987730i | ||||
\(411\) | 6.00000i | 0.295958i | ||||||||
\(412\) | 20.0000i | 0.985329i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 16.0000 | + | 16.0000i | 0.784465 | + | 0.784465i | ||||
\(417\) | −12.0000 | −0.587643 | ||||||||
\(418\) | −4.00000 | + | 4.00000i | −0.195646 | + | 0.195646i | ||||
\(419\) | − | 4.00000i | − | 0.195413i | −0.995215 | − | 0.0977064i | \(-0.968849\pi\) | ||
0.995215 | − | 0.0977064i | \(-0.0311506\pi\) | |||||||
\(420\) | − | 4.00000i | − | 0.195180i | ||||||
\(421\) | − | 12.0000i | − | 0.584844i | −0.956289 | − | 0.292422i | \(-0.905539\pi\) | ||
0.956289 | − | 0.292422i | \(-0.0944612\pi\) | |||||||
\(422\) | 20.0000 | + | 20.0000i | 0.973585 | + | 0.973585i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −28.0000 | + | 28.0000i | −1.35980 | + | 1.35980i | ||||
\(425\) | −2.00000 | −0.0970143 | ||||||||
\(426\) | −8.00000 | − | 8.00000i | −0.387601 | − | 0.387601i | ||||
\(427\) | − | 24.0000i | − | 1.16144i | ||||||
\(428\) | 40.0000 | 1.93347 | ||||||||
\(429\) | − | 4.00000i | − | 0.193122i | ||||||
\(430\) | 4.00000 | − | 4.00000i | 0.192897 | − | 0.192897i | ||||
\(431\) | 12.0000 | 0.578020 | 0.289010 | − | 0.957326i | \(-0.406674\pi\) | ||||
0.289010 | + | 0.957326i | \(0.406674\pi\) | |||||||
\(432\) | 4.00000i | 0.192450i | ||||||||
\(433\) | −2.00000 | −0.0961139 | −0.0480569 | − | 0.998845i | \(-0.515303\pi\) | ||||
−0.0480569 | + | 0.998845i | \(0.515303\pi\) | |||||||
\(434\) | 12.0000 | − | 12.0000i | 0.576018 | − | 0.576018i | ||||
\(435\) | 6.00000i | 0.287678i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 10.0000 | + | 10.0000i | 0.477818 | + | 0.477818i | ||||
\(439\) | 14.0000 | 0.668184 | 0.334092 | − | 0.942541i | \(-0.391570\pi\) | ||||
0.334092 | + | 0.942541i | \(0.391570\pi\) | |||||||
\(440\) | −2.00000 | − | 2.00000i | −0.0953463 | − | 0.0953463i | ||||
\(441\) | 3.00000 | 0.142857 | ||||||||
\(442\) | −8.00000 | − | 8.00000i | −0.380521 | − | 0.380521i | ||||
\(443\) | − | 8.00000i | − | 0.380091i | −0.981775 | − | 0.190046i | \(-0.939136\pi\) | ||
0.981775 | − | 0.190046i | \(-0.0608636\pi\) | |||||||
\(444\) | − | 8.00000i | − | 0.379663i | ||||||
\(445\) | 6.00000i | 0.284427i | ||||||||
\(446\) | 10.0000 | − | 10.0000i | 0.473514 | − | 0.473514i | ||||
\(447\) | −2.00000 | −0.0945968 | ||||||||
\(448\) | − | 16.0000i | − | 0.755929i | ||||||
\(449\) | 6.00000 | 0.283158 | 0.141579 | − | 0.989927i | \(-0.454782\pi\) | ||||
0.141579 | + | 0.989927i | \(0.454782\pi\) | |||||||
\(450\) | 1.00000 | − | 1.00000i | 0.0471405 | − | 0.0471405i | ||||
\(451\) | − | 2.00000i | − | 0.0941763i | ||||||
\(452\) | 4.00000i | 0.188144i | ||||||||
\(453\) | − | 22.0000i | − | 1.03365i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.00000 | −0.375046 | ||||||||
\(456\) | −8.00000 | − | 8.00000i | −0.374634 | − | 0.374634i | ||||
\(457\) | 26.0000 | 1.21623 | 0.608114 | − | 0.793849i | \(-0.291926\pi\) | ||||
0.608114 | + | 0.793849i | \(0.291926\pi\) | |||||||
\(458\) | 20.0000 | + | 20.0000i | 0.934539 | + | 0.934539i | ||||
\(459\) | − | 2.00000i | − | 0.0933520i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 10.0000i | − | 0.465746i | −0.972507 | − | 0.232873i | \(-0.925187\pi\) | ||
0.972507 | − | 0.232873i | \(-0.0748127\pi\) | |||||||
\(462\) | −2.00000 | + | 2.00000i | −0.0930484 | + | 0.0930484i | ||||
\(463\) | 2.00000 | 0.0929479 | 0.0464739 | − | 0.998920i | \(-0.485202\pi\) | ||||
0.0464739 | + | 0.998920i | \(0.485202\pi\) | |||||||
\(464\) | 24.0000i | 1.11417i | ||||||||
\(465\) | 6.00000 | 0.278243 | ||||||||
\(466\) | −6.00000 | + | 6.00000i | −0.277945 | + | 0.277945i | ||||
\(467\) | − | 32.0000i | − | 1.48078i | −0.672176 | − | 0.740392i | \(-0.734640\pi\) | ||
0.672176 | − | 0.740392i | \(-0.265360\pi\) | |||||||
\(468\) | 8.00000 | 0.369800 | ||||||||
\(469\) | 8.00000i | 0.369406i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.00000 | −0.184310 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.00000 | −0.183920 | ||||||||
\(474\) | 6.00000 | + | 6.00000i | 0.275589 | + | 0.275589i | ||||
\(475\) | 4.00000i | 0.183533i | ||||||||
\(476\) | 8.00000i | 0.366679i | ||||||||
\(477\) | 14.0000i | 0.641016i | ||||||||
\(478\) | 8.00000 | − | 8.00000i | 0.365911 | − | 0.365911i | ||||
\(479\) | −12.0000 | −0.548294 | −0.274147 | − | 0.961688i | \(-0.588395\pi\) | ||||
−0.274147 | + | 0.961688i | \(0.588395\pi\) | |||||||
\(480\) | 4.00000 | − | 4.00000i | 0.182574 | − | 0.182574i | ||||
\(481\) | −16.0000 | −0.729537 | ||||||||
\(482\) | 10.0000 | − | 10.0000i | 0.455488 | − | 0.455488i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.00000i | 0.0909091i | ||||||||
\(485\) | 6.00000i | 0.272446i | ||||||||
\(486\) | 1.00000 | + | 1.00000i | 0.0453609 | + | 0.0453609i | ||||
\(487\) | −22.0000 | −0.996915 | −0.498458 | − | 0.866914i | \(-0.666100\pi\) | ||||
−0.498458 | + | 0.866914i | \(0.666100\pi\) | |||||||
\(488\) | 24.0000 | − | 24.0000i | 1.08643 | − | 1.08643i | ||||
\(489\) | −4.00000 | −0.180886 | ||||||||
\(490\) | −3.00000 | − | 3.00000i | −0.135526 | − | 0.135526i | ||||
\(491\) | 40.0000i | 1.80517i | 0.430507 | + | 0.902587i | \(0.358335\pi\) | ||||
−0.430507 | + | 0.902587i | \(0.641665\pi\) | |||||||
\(492\) | 4.00000 | 0.180334 | ||||||||
\(493\) | − | 12.0000i | − | 0.540453i | ||||||
\(494\) | −16.0000 | + | 16.0000i | −0.719874 | + | 0.719874i | ||||
\(495\) | −1.00000 | −0.0449467 | ||||||||
\(496\) | 24.0000 | 1.07763 | ||||||||
\(497\) | 16.0000 | 0.717698 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.0000i | 0.895323i | 0.894203 | + | 0.447661i | \(0.147743\pi\) | ||||
−0.894203 | + | 0.447661i | \(0.852257\pi\) | |||||||
\(500\) | −2.00000 | −0.0894427 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.00000 | − | 4.00000i | −0.178529 | − | 0.178529i | ||||
\(503\) | 28.0000 | 1.24846 | 0.624229 | − | 0.781241i | \(-0.285413\pi\) | ||||
0.624229 | + | 0.781241i | \(0.285413\pi\) | |||||||
\(504\) | −4.00000 | − | 4.00000i | −0.178174 | − | 0.178174i | ||||
\(505\) | 2.00000 | 0.0889988 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 3.00000i | − | 0.133235i | ||||||
\(508\) | − | 12.0000i | − | 0.532414i | ||||||
\(509\) | − | 42.0000i | − | 1.86162i | −0.365507 | − | 0.930809i | \(-0.619104\pi\) | ||
0.365507 | − | 0.930809i | \(-0.380896\pi\) | |||||||
\(510\) | −2.00000 | + | 2.00000i | −0.0885615 | + | 0.0885615i | ||||
\(511\) | −20.0000 | −0.884748 | ||||||||
\(512\) | 16.0000 | − | 16.0000i | 0.707107 | − | 0.707107i | ||||
\(513\) | −4.00000 | −0.176604 | ||||||||
\(514\) | 22.0000 | − | 22.0000i | 0.970378 | − | 0.970378i | ||||
\(515\) | − | 10.0000i | − | 0.440653i | ||||||
\(516\) | − | 8.00000i | − | 0.352180i | ||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 8.00000 | + | 8.00000i | 0.351500 | + | 0.351500i | ||||
\(519\) | 18.0000 | 0.790112 | ||||||||
\(520\) | −8.00000 | − | 8.00000i | −0.350823 | − | 0.350823i | ||||
\(521\) | 42.0000 | 1.84005 | 0.920027 | − | 0.391856i | \(-0.128167\pi\) | ||||
0.920027 | + | 0.391856i | \(0.128167\pi\) | |||||||
\(522\) | 6.00000 | + | 6.00000i | 0.262613 | + | 0.262613i | ||||
\(523\) | − | 36.0000i | − | 1.57417i | −0.616844 | − | 0.787085i | \(-0.711589\pi\) | ||
0.616844 | − | 0.787085i | \(-0.288411\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.00000i | 0.0872872i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.0000 | −0.522728 | ||||||||
\(528\) | −4.00000 | −0.174078 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 14.0000 | − | 14.0000i | 0.608121 | − | 0.608121i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 16.0000 | 0.693688 | ||||||||
\(533\) | − | 8.00000i | − | 0.346518i | ||||||
\(534\) | 6.00000 | + | 6.00000i | 0.259645 | + | 0.259645i | ||||
\(535\) | −20.0000 | −0.864675 | ||||||||
\(536\) | −8.00000 | + | 8.00000i | −0.345547 | + | 0.345547i | ||||
\(537\) | 24.0000 | 1.03568 | ||||||||
\(538\) | −18.0000 | − | 18.0000i | −0.776035 | − | 0.776035i | ||||
\(539\) | 3.00000i | 0.129219i | ||||||||
\(540\) | − | 2.00000i | − | 0.0860663i | ||||||
\(541\) | 16.0000i | 0.687894i | 0.938989 | + | 0.343947i | \(0.111764\pi\) | ||||
−0.938989 | + | 0.343947i | \(0.888236\pi\) | |||||||
\(542\) | −22.0000 | + | 22.0000i | −0.944981 | + | 0.944981i | ||||
\(543\) | −20.0000 | −0.858282 | ||||||||
\(544\) | −8.00000 | + | 8.00000i | −0.342997 | + | 0.342997i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −8.00000 | + | 8.00000i | −0.342368 | + | 0.342368i | ||||
\(547\) | − | 44.0000i | − | 1.88130i | −0.339372 | − | 0.940652i | \(-0.610215\pi\) | ||
0.339372 | − | 0.940652i | \(-0.389785\pi\) | |||||||
\(548\) | − | 12.0000i | − | 0.512615i | ||||||
\(549\) | − | 12.0000i | − | 0.512148i | ||||||
\(550\) | 1.00000 | + | 1.00000i | 0.0426401 | + | 0.0426401i | ||||
\(551\) | −24.0000 | −1.02243 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.0000 | −0.510292 | ||||||||
\(554\) | 12.0000 | + | 12.0000i | 0.509831 | + | 0.509831i | ||||
\(555\) | 4.00000i | 0.169791i | ||||||||
\(556\) | 24.0000 | 1.01783 | ||||||||
\(557\) | 22.0000i | 0.932170i | 0.884740 | + | 0.466085i | \(0.154336\pi\) | ||||
−0.884740 | + | 0.466085i | \(0.845664\pi\) | |||||||
\(558\) | 6.00000 | − | 6.00000i | 0.254000 | − | 0.254000i | ||||
\(559\) | −16.0000 | −0.676728 | ||||||||
\(560\) | 8.00000i | 0.338062i | ||||||||
\(561\) | 2.00000 | 0.0844401 | ||||||||
\(562\) | 22.0000 | − | 22.0000i | 0.928014 | − | 0.928014i | ||||
\(563\) | − | 16.0000i | − | 0.674320i | −0.941447 | − | 0.337160i | \(-0.890534\pi\) | ||
0.941447 | − | 0.337160i | \(-0.109466\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 2.00000i | − | 0.0841406i | ||||||
\(566\) | 4.00000 | + | 4.00000i | 0.168133 | + | 0.168133i | ||||
\(567\) | −2.00000 | −0.0839921 | ||||||||
\(568\) | 16.0000 | + | 16.0000i | 0.671345 | + | 0.671345i | ||||
\(569\) | −30.0000 | −1.25767 | −0.628833 | − | 0.777541i | \(-0.716467\pi\) | ||||
−0.628833 | + | 0.777541i | \(0.716467\pi\) | |||||||
\(570\) | 4.00000 | + | 4.00000i | 0.167542 | + | 0.167542i | ||||
\(571\) | 28.0000i | 1.17176i | 0.810397 | + | 0.585882i | \(0.199252\pi\) | ||||
−0.810397 | + | 0.585882i | \(0.800748\pi\) | |||||||
\(572\) | 8.00000i | 0.334497i | ||||||||
\(573\) | 4.00000i | 0.167102i | ||||||||
\(574\) | −4.00000 | + | 4.00000i | −0.166957 | + | 0.166957i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | − | 8.00000i | − | 0.333333i | ||||||
\(577\) | −34.0000 | −1.41544 | −0.707719 | − | 0.706494i | \(-0.750276\pi\) | ||||
−0.707719 | + | 0.706494i | \(0.750276\pi\) | |||||||
\(578\) | −13.0000 | + | 13.0000i | −0.540729 | + | 0.540729i | ||||
\(579\) | 18.0000i | 0.748054i | ||||||||
\(580\) | − | 12.0000i | − | 0.498273i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 6.00000 | + | 6.00000i | 0.248708 | + | 0.248708i | ||||
\(583\) | −14.0000 | −0.579821 | ||||||||
\(584\) | −20.0000 | − | 20.0000i | −0.827606 | − | 0.827606i | ||||
\(585\) | −4.00000 | −0.165380 | ||||||||
\(586\) | 14.0000 | + | 14.0000i | 0.578335 | + | 0.578335i | ||||
\(587\) | 28.0000i | 1.15568i | 0.816149 | + | 0.577842i | \(0.196105\pi\) | ||||
−0.816149 | + | 0.577842i | \(0.803895\pi\) | |||||||
\(588\) | −6.00000 | −0.247436 | ||||||||
\(589\) | 24.0000i | 0.988903i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.0000 | 0.740421 | ||||||||
\(592\) | 16.0000i | 0.657596i | ||||||||
\(593\) | 14.0000 | 0.574911 | 0.287456 | − | 0.957794i | \(-0.407191\pi\) | ||||
0.287456 | + | 0.957794i | \(0.407191\pi\) | |||||||
\(594\) | −1.00000 | + | 1.00000i | −0.0410305 | + | 0.0410305i | ||||
\(595\) | − | 4.00000i | − | 0.163984i | ||||||
\(596\) | 4.00000 | 0.163846 | ||||||||
\(597\) | 2.00000i | 0.0818546i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.0000 | −0.980613 | −0.490307 | − | 0.871550i | \(-0.663115\pi\) | ||||
−0.490307 | + | 0.871550i | \(0.663115\pi\) | |||||||
\(600\) | −2.00000 | + | 2.00000i | −0.0816497 | + | 0.0816497i | ||||
\(601\) | −38.0000 | −1.55005 | −0.775026 | − | 0.631929i | \(-0.782263\pi\) | ||||
−0.775026 | + | 0.631929i | \(0.782263\pi\) | |||||||
\(602\) | 8.00000 | + | 8.00000i | 0.326056 | + | 0.326056i | ||||
\(603\) | 4.00000i | 0.162893i | ||||||||
\(604\) | 44.0000i | 1.79033i | ||||||||
\(605\) | − | 1.00000i | − | 0.0406558i | ||||||
\(606\) | 2.00000 | − | 2.00000i | 0.0812444 | − | 0.0812444i | ||||
\(607\) | 14.0000 | 0.568242 | 0.284121 | − | 0.958788i | \(-0.408298\pi\) | ||||
0.284121 | + | 0.958788i | \(0.408298\pi\) | |||||||
\(608\) | 16.0000 | + | 16.0000i | 0.648886 | + | 0.648886i | ||||
\(609\) | −12.0000 | −0.486265 | ||||||||
\(610\) | −12.0000 | + | 12.0000i | −0.485866 | + | 0.485866i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 4.00000i | 0.161690i | ||||||||
\(613\) | 8.00000i | 0.323117i | 0.986863 | + | 0.161558i | \(0.0516520\pi\) | ||||
−0.986863 | + | 0.161558i | \(0.948348\pi\) | |||||||
\(614\) | −20.0000 | − | 20.0000i | −0.807134 | − | 0.807134i | ||||
\(615\) | −2.00000 | −0.0806478 | ||||||||
\(616\) | 4.00000 | − | 4.00000i | 0.161165 | − | 0.161165i | ||||
\(617\) | −30.0000 | −1.20775 | −0.603877 | − | 0.797077i | \(-0.706378\pi\) | ||||
−0.603877 | + | 0.797077i | \(0.706378\pi\) | |||||||
\(618\) | −10.0000 | − | 10.0000i | −0.402259 | − | 0.402259i | ||||
\(619\) | − | 44.0000i | − | 1.76851i | −0.467005 | − | 0.884255i | \(-0.654667\pi\) | ||
0.467005 | − | 0.884255i | \(-0.345333\pi\) | |||||||
\(620\) | −12.0000 | −0.481932 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 20.0000 | − | 20.0000i | 0.801927 | − | 0.801927i | ||||
\(623\) | −12.0000 | −0.480770 | ||||||||
\(624\) | −16.0000 | −0.640513 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 6.00000 | − | 6.00000i | 0.239808 | − | 0.239808i | ||||
\(627\) | − | 4.00000i | − | 0.159745i | ||||||
\(628\) | 8.00000 | 0.319235 | ||||||||
\(629\) | − | 8.00000i | − | 0.318981i | ||||||
\(630\) | 2.00000 | + | 2.00000i | 0.0796819 | + | 0.0796819i | ||||
\(631\) | 30.0000 | 1.19428 | 0.597141 | − | 0.802137i | \(-0.296303\pi\) | ||||
0.597141 | + | 0.802137i | \(0.296303\pi\) | |||||||
\(632\) | −12.0000 | − | 12.0000i | −0.477334 | − | 0.477334i | ||||
\(633\) | −20.0000 | −0.794929 | ||||||||
\(634\) | −34.0000 | − | 34.0000i | −1.35031 | − | 1.35031i | ||||
\(635\) | 6.00000i | 0.238103i | ||||||||
\(636\) | − | 28.0000i | − | 1.11027i | ||||||
\(637\) | 12.0000i | 0.475457i | ||||||||
\(638\) | −6.00000 | + | 6.00000i | −0.237542 | + | 0.237542i | ||||
\(639\) | 8.00000 | 0.316475 | ||||||||
\(640\) | −8.00000 | + | 8.00000i | −0.316228 | + | 0.316228i | ||||
\(641\) | −18.0000 | −0.710957 | −0.355479 | − | 0.934684i | \(-0.615682\pi\) | ||||
−0.355479 | + | 0.934684i | \(0.615682\pi\) | |||||||
\(642\) | −20.0000 | + | 20.0000i | −0.789337 | + | 0.789337i | ||||
\(643\) | 28.0000i | 1.10421i | 0.833774 | + | 0.552106i | \(0.186176\pi\) | ||||
−0.833774 | + | 0.552106i | \(0.813824\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.00000i | 0.157500i | ||||||||
\(646\) | −8.00000 | − | 8.00000i | −0.314756 | − | 0.314756i | ||||
\(647\) | −32.0000 | −1.25805 | −0.629025 | − | 0.777385i | \(-0.716546\pi\) | ||||
−0.629025 | + | 0.777385i | \(0.716546\pi\) | |||||||
\(648\) | −2.00000 | − | 2.00000i | −0.0785674 | − | 0.0785674i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 4.00000 | + | 4.00000i | 0.156893 | + | 0.156893i | ||||
\(651\) | 12.0000i | 0.470317i | ||||||||
\(652\) | 8.00000 | 0.313304 | ||||||||
\(653\) | 26.0000i | 1.01746i | 0.860927 | + | 0.508729i | \(0.169885\pi\) | ||||
−0.860927 | + | 0.508729i | \(0.830115\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −8.00000 | −0.312348 | ||||||||
\(657\) | −10.0000 | −0.390137 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 2.00000 | 0.0778499 | ||||||||
\(661\) | 8.00000i | 0.311164i | 0.987823 | + | 0.155582i | \(0.0497253\pi\) | ||||
−0.987823 | + | 0.155582i | \(0.950275\pi\) | |||||||
\(662\) | 12.0000 | + | 12.0000i | 0.466393 | + | 0.466393i | ||||
\(663\) | 8.00000 | 0.310694 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.00000 | −0.310227 | ||||||||
\(666\) | 4.00000 | + | 4.00000i | 0.154997 | + | 0.154997i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.0000i | 0.386622i | ||||||||
\(670\) | 4.00000 | − | 4.00000i | 0.154533 | − | 0.154533i | ||||
\(671\) | 12.0000 | 0.463255 | ||||||||
\(672\) | 8.00000 | + | 8.00000i | 0.308607 | + | 0.308607i | ||||
\(673\) | 6.00000 | 0.231283 | 0.115642 | − | 0.993291i | \(-0.463108\pi\) | ||||
0.115642 | + | 0.993291i | \(0.463108\pi\) | |||||||
\(674\) | −2.00000 | + | 2.00000i | −0.0770371 | + | 0.0770371i | ||||
\(675\) | 1.00000i | 0.0384900i | ||||||||
\(676\) | 6.00000i | 0.230769i | ||||||||
\(677\) | 18.0000i | 0.691796i | 0.938272 | + | 0.345898i | \(0.112426\pi\) | ||||
−0.938272 | + | 0.345898i | \(0.887574\pi\) | |||||||
\(678\) | −2.00000 | − | 2.00000i | −0.0768095 | − | 0.0768095i | ||||
\(679\) | −12.0000 | −0.460518 | ||||||||
\(680\) | 4.00000 | − | 4.00000i | 0.153393 | − | 0.153393i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.00000 | + | 6.00000i | 0.229752 | + | 0.229752i | ||||
\(683\) | 8.00000i | 0.306111i | 0.988218 | + | 0.153056i | \(0.0489114\pi\) | ||||
−0.988218 | + | 0.153056i | \(0.951089\pi\) | |||||||
\(684\) | 8.00000 | 0.305888 | ||||||||
\(685\) | 6.00000i | 0.229248i | ||||||||
\(686\) | 20.0000 | − | 20.0000i | 0.763604 | − | 0.763604i | ||||
\(687\) | −20.0000 | −0.763048 | ||||||||
\(688\) | 16.0000i | 0.609994i | ||||||||
\(689\) | −56.0000 | −2.13343 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 36.0000i | − | 1.36950i | −0.728776 | − | 0.684752i | \(-0.759910\pi\) | ||
0.728776 | − | 0.684752i | \(-0.240090\pi\) | |||||||
\(692\) | −36.0000 | −1.36851 | ||||||||
\(693\) | − | 2.00000i | − | 0.0759737i | ||||||
\(694\) | −16.0000 | − | 16.0000i | −0.607352 | − | 0.607352i | ||||
\(695\) | −12.0000 | −0.455186 | ||||||||
\(696\) | −12.0000 | − | 12.0000i | −0.454859 | − | 0.454859i | ||||
\(697\) | 4.00000 | 0.151511 | ||||||||
\(698\) | −28.0000 | − | 28.0000i | −1.05982 | − | 1.05982i | ||||
\(699\) | − | 6.00000i | − | 0.226941i | ||||||
\(700\) | − | 4.00000i | − | 0.151186i | ||||||
\(701\) | 34.0000i | 1.28416i | 0.766637 | + | 0.642081i | \(0.221929\pi\) | ||||
−0.766637 | + | 0.642081i | \(0.778071\pi\) | |||||||
\(702\) | −4.00000 | + | 4.00000i | −0.150970 | + | 0.150970i | ||||
\(703\) | −16.0000 | −0.603451 | ||||||||
\(704\) | 8.00000 | 0.301511 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.0000 | − | 14.0000i | 0.526897 | − | 0.526897i | ||||
\(707\) | 4.00000i | 0.150435i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 52.0000i | 1.95290i | 0.215742 | + | 0.976450i | \(0.430783\pi\) | ||||
−0.215742 | + | 0.976450i | \(0.569217\pi\) | |||||||
\(710\) | −8.00000 | − | 8.00000i | −0.300235 | − | 0.300235i | ||||
\(711\) | −6.00000 | −0.225018 | ||||||||
\(712\) | −12.0000 | − | 12.0000i | −0.449719 | − | 0.449719i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −4.00000 | − | 4.00000i | −0.149696 | − | 0.149696i | ||||
\(715\) | − | 4.00000i | − | 0.149592i | ||||||
\(716\) | −48.0000 | −1.79384 | ||||||||
\(717\) | 8.00000i | 0.298765i | ||||||||
\(718\) | −12.0000 | + | 12.0000i | −0.447836 | + | 0.447836i | ||||
\(719\) | 48.0000 | 1.79010 | 0.895049 | − | 0.445968i | \(-0.147140\pi\) | ||||
0.895049 | + | 0.445968i | \(0.147140\pi\) | |||||||
\(720\) | 4.00000i | 0.149071i | ||||||||
\(721\) | 20.0000 | 0.744839 | ||||||||
\(722\) | 3.00000 | − | 3.00000i | 0.111648 | − | 0.111648i | ||||
\(723\) | 10.0000i | 0.371904i | ||||||||
\(724\) | 40.0000 | 1.48659 | ||||||||
\(725\) | 6.00000i | 0.222834i | ||||||||
\(726\) | −1.00000 | − | 1.00000i | −0.0371135 | − | 0.0371135i | ||||
\(727\) | −6.00000 | −0.222528 | −0.111264 | − | 0.993791i | \(-0.535490\pi\) | ||||
−0.111264 | + | 0.993791i | \(0.535490\pi\) | |||||||
\(728\) | 16.0000 | − | 16.0000i | 0.592999 | − | 0.592999i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 10.0000 | + | 10.0000i | 0.370117 | + | 0.370117i | ||||
\(731\) | − | 8.00000i | − | 0.295891i | ||||||
\(732\) | 24.0000i | 0.887066i | ||||||||
\(733\) | 20.0000i | 0.738717i | 0.929287 | + | 0.369358i | \(0.120423\pi\) | ||||
−0.929287 | + | 0.369358i | \(0.879577\pi\) | |||||||
\(734\) | −34.0000 | + | 34.0000i | −1.25496 | + | 1.25496i | ||||
\(735\) | 3.00000 | 0.110657 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.00000 | −0.147342 | ||||||||
\(738\) | −2.00000 | + | 2.00000i | −0.0736210 | + | 0.0736210i | ||||
\(739\) | − | 28.0000i | − | 1.03000i | −0.857191 | − | 0.514998i | \(-0.827793\pi\) | ||
0.857191 | − | 0.514998i | \(-0.172207\pi\) | |||||||
\(740\) | − | 8.00000i | − | 0.294086i | ||||||
\(741\) | − | 16.0000i | − | 0.587775i | ||||||
\(742\) | 28.0000 | + | 28.0000i | 1.02791 | + | 1.02791i | ||||
\(743\) | −24.0000 | −0.880475 | −0.440237 | − | 0.897881i | \(-0.645106\pi\) | ||||
−0.440237 | + | 0.897881i | \(0.645106\pi\) | |||||||
\(744\) | −12.0000 | + | 12.0000i | −0.439941 | + | 0.439941i | ||||
\(745\) | −2.00000 | −0.0732743 | ||||||||
\(746\) | −24.0000 | − | 24.0000i | −0.878702 | − | 0.878702i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.00000 | −0.146254 | ||||||||
\(749\) | − | 40.0000i | − | 1.46157i | ||||||
\(750\) | 1.00000 | − | 1.00000i | 0.0365148 | − | 0.0365148i | ||||
\(751\) | 10.0000 | 0.364905 | 0.182453 | − | 0.983215i | \(-0.441596\pi\) | ||||
0.182453 | + | 0.983215i | \(0.441596\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.00000 | 0.145768 | ||||||||
\(754\) | −24.0000 | + | 24.0000i | −0.874028 | + | 0.874028i | ||||
\(755\) | − | 22.0000i | − | 0.800662i | ||||||
\(756\) | 4.00000 | 0.145479 | ||||||||
\(757\) | − | 16.0000i | − | 0.581530i | −0.956795 | − | 0.290765i | \(-0.906090\pi\) | ||
0.956795 | − | 0.290765i | \(-0.0939098\pi\) | |||||||
\(758\) | 36.0000 | + | 36.0000i | 1.30758 | + | 1.30758i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8.00000 | − | 8.00000i | −0.290191 | − | 0.290191i | ||||
\(761\) | −22.0000 | −0.797499 | −0.398750 | − | 0.917060i | \(-0.630556\pi\) | ||||
−0.398750 | + | 0.917060i | \(0.630556\pi\) | |||||||
\(762\) | 6.00000 | + | 6.00000i | 0.217357 | + | 0.217357i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 8.00000i | − | 0.289430i | ||||||
\(765\) | − | 2.00000i | − | 0.0723102i | ||||||
\(766\) | 20.0000 | − | 20.0000i | 0.722629 | − | 0.722629i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 16.0000i | 0.577350i | ||||||||
\(769\) | 18.0000 | 0.649097 | 0.324548 | − | 0.945869i | \(-0.394788\pi\) | ||||
0.324548 | + | 0.945869i | \(0.394788\pi\) | |||||||
\(770\) | −2.00000 | + | 2.00000i | −0.0720750 | + | 0.0720750i | ||||
\(771\) | 22.0000i | 0.792311i | ||||||||
\(772\) | − | 36.0000i | − | 1.29567i | ||||||
\(773\) | − | 46.0000i | − | 1.65451i | −0.561830 | − | 0.827253i | \(-0.689903\pi\) | ||
0.561830 | − | 0.827253i | \(-0.310097\pi\) | |||||||
\(774\) | 4.00000 | + | 4.00000i | 0.143777 | + | 0.143777i | ||||
\(775\) | 6.00000 | 0.215526 | ||||||||
\(776\) | −12.0000 | − | 12.0000i | −0.430775 | − | 0.430775i | ||||
\(777\) | −8.00000 | −0.286998 | ||||||||
\(778\) | −10.0000 | − | 10.0000i | −0.358517 | − | 0.358517i | ||||
\(779\) | − | 8.00000i | − | 0.286630i | ||||||
\(780\) | 8.00000 | 0.286446 | ||||||||
\(781\) | 8.00000i | 0.286263i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.00000 | −0.214423 | ||||||||
\(784\) | 12.0000 | 0.428571 | ||||||||
\(785\) | −4.00000 | −0.142766 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 52.0000i | − | 1.85360i | −0.375555 | − | 0.926800i | \(-0.622548\pi\) | ||
0.375555 | − | 0.926800i | \(-0.377452\pi\) | |||||||
\(788\) | −36.0000 | −1.28245 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.00000 | + | 6.00000i | 0.213470 | + | 0.213470i | ||||
\(791\) | 4.00000 | 0.142224 | ||||||||
\(792\) | 2.00000 | − | 2.00000i | 0.0710669 | − | 0.0710669i | ||||
\(793\) | 48.0000 | 1.70453 | ||||||||
\(794\) | −28.0000 | − | 28.0000i | −0.993683 | − | 0.993683i | ||||
\(795\) | 14.0000i | 0.496529i | ||||||||
\(796\) | − | 4.00000i | − | 0.141776i | ||||||
\(797\) | − | 14.0000i | − | 0.495905i | −0.968772 | − | 0.247953i | \(-0.920242\pi\) | ||
0.968772 | − | 0.247953i | \(-0.0797578\pi\) | |||||||
\(798\) | −8.00000 | + | 8.00000i | −0.283197 | + | 0.283197i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 4.00000 | − | 4.00000i | 0.141421 | − | 0.141421i | ||||
\(801\) | −6.00000 | −0.212000 | ||||||||
\(802\) | −34.0000 | + | 34.0000i | −1.20058 | + | 1.20058i | ||||
\(803\) | − | 10.0000i | − | 0.352892i | ||||||
\(804\) | − | 8.00000i | − | 0.282138i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 24.0000 | + | 24.0000i | 0.845364 | + | 0.845364i | ||||
\(807\) | 18.0000 | 0.633630 | ||||||||
\(808\) | −4.00000 | + | 4.00000i | −0.140720 | + | 0.140720i | ||||
\(809\) | −30.0000 | −1.05474 | −0.527372 | − | 0.849635i | \(-0.676823\pi\) | ||||
−0.527372 | + | 0.849635i | \(0.676823\pi\) | |||||||
\(810\) | 1.00000 | + | 1.00000i | 0.0351364 | + | 0.0351364i | ||||
\(811\) | − | 4.00000i | − | 0.140459i | −0.997531 | − | 0.0702295i | \(-0.977627\pi\) | ||
0.997531 | − | 0.0702295i | \(-0.0223732\pi\) | |||||||
\(812\) | 24.0000 | 0.842235 | ||||||||
\(813\) | − | 22.0000i | − | 0.771574i | ||||||
\(814\) | −4.00000 | + | 4.00000i | −0.140200 | + | 0.140200i | ||||
\(815\) | −4.00000 | −0.140114 | ||||||||
\(816\) | − | 8.00000i | − | 0.280056i | ||||||
\(817\) | −16.0000 | −0.559769 | ||||||||
\(818\) | 10.0000 | − | 10.0000i | 0.349642 | − | 0.349642i | ||||
\(819\) | − | 8.00000i | − | 0.279543i | ||||||
\(820\) | 4.00000 | 0.139686 | ||||||||
\(821\) | 54.0000i | 1.88461i | 0.334751 | + | 0.942306i | \(0.391348\pi\) | ||||
−0.334751 | + | 0.942306i | \(0.608652\pi\) | |||||||
\(822\) | 6.00000 | + | 6.00000i | 0.209274 | + | 0.209274i | ||||
\(823\) | 10.0000 | 0.348578 | 0.174289 | − | 0.984695i | \(-0.444237\pi\) | ||||
0.174289 | + | 0.984695i | \(0.444237\pi\) | |||||||
\(824\) | 20.0000 | + | 20.0000i | 0.696733 | + | 0.696733i | ||||
\(825\) | −1.00000 | −0.0348155 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 20.0000i | − | 0.695468i | −0.937593 | − | 0.347734i | \(-0.886951\pi\) | ||
0.937593 | − | 0.347734i | \(-0.113049\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 28.0000i | − | 0.972480i | −0.873825 | − | 0.486240i | \(-0.838368\pi\) | ||
0.873825 | − | 0.486240i | \(-0.161632\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.0000 | −0.416275 | ||||||||
\(832\) | 32.0000 | 1.10940 | ||||||||
\(833\) | −6.00000 | −0.207888 | ||||||||
\(834\) | −12.0000 | + | 12.0000i | −0.415526 | + | 0.415526i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 8.00000i | 0.276686i | ||||||||
\(837\) | 6.00000i | 0.207390i | ||||||||
\(838\) | −4.00000 | − | 4.00000i | −0.138178 | − | 0.138178i | ||||
\(839\) | 24.0000 | 0.828572 | 0.414286 | − | 0.910147i | \(-0.364031\pi\) | ||||
0.414286 | + | 0.910147i | \(0.364031\pi\) | |||||||
\(840\) | −4.00000 | − | 4.00000i | −0.138013 | − | 0.138013i | ||||
\(841\) | −7.00000 | −0.241379 | ||||||||
\(842\) | −12.0000 | − | 12.0000i | −0.413547 | − | 0.413547i | ||||
\(843\) | 22.0000i | 0.757720i | ||||||||
\(844\) | 40.0000 | 1.37686 | ||||||||
\(845\) | − | 3.00000i | − | 0.103203i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.00000 | 0.0687208 | ||||||||
\(848\) | 56.0000i | 1.92305i | ||||||||
\(849\) | −4.00000 | −0.137280 | ||||||||
\(850\) | −2.00000 | + | 2.00000i | −0.0685994 | + | 0.0685994i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −16.0000 | −0.548151 | ||||||||
\(853\) | − | 16.0000i | − | 0.547830i | −0.961754 | − | 0.273915i | \(-0.911681\pi\) | ||
0.961754 | − | 0.273915i | \(-0.0883186\pi\) | |||||||
\(854\) | −24.0000 | − | 24.0000i | −0.821263 | − | 0.821263i | ||||
\(855\) | −4.00000 | −0.136797 | ||||||||
\(856\) | 40.0000 | − | 40.0000i | 1.36717 | − | 1.36717i | ||||
\(857\) | 38.0000 | 1.29806 | 0.649028 | − | 0.760765i | \(-0.275176\pi\) | ||||
0.649028 | + | 0.760765i | \(0.275176\pi\) | |||||||
\(858\) | −4.00000 | − | 4.00000i | −0.136558 | − | 0.136558i | ||||
\(859\) | − | 20.0000i | − | 0.682391i | −0.939992 | − | 0.341196i | \(-0.889168\pi\) | ||
0.939992 | − | 0.341196i | \(-0.110832\pi\) | |||||||
\(860\) | − | 8.00000i | − | 0.272798i | ||||||
\(861\) | − | 4.00000i | − | 0.136320i | ||||||
\(862\) | 12.0000 | − | 12.0000i | 0.408722 | − | 0.408722i | ||||
\(863\) | 28.0000 | 0.953131 | 0.476566 | − | 0.879139i | \(-0.341881\pi\) | ||||
0.476566 | + | 0.879139i | \(0.341881\pi\) | |||||||
\(864\) | 4.00000 | + | 4.00000i | 0.136083 | + | 0.136083i | ||||
\(865\) | 18.0000 | 0.612018 | ||||||||
\(866\) | −2.00000 | + | 2.00000i | −0.0679628 | + | 0.0679628i | ||||
\(867\) | − | 13.0000i | − | 0.441503i | ||||||
\(868\) | − | 24.0000i | − | 0.814613i | ||||||
\(869\) | − | 6.00000i | − | 0.203536i | ||||||
\(870\) | 6.00000 | + | 6.00000i | 0.203419 | + | 0.203419i | ||||
\(871\) | −16.0000 | −0.542139 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.00000 | −0.203069 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.00000i | 0.0676123i | ||||||||
\(876\) | 20.0000 | 0.675737 | ||||||||
\(877\) | 56.0000i | 1.89099i | 0.325643 | + | 0.945493i | \(0.394419\pi\) | ||||
−0.325643 | + | 0.945493i | \(0.605581\pi\) | |||||||
\(878\) | 14.0000 | − | 14.0000i | 0.472477 | − | 0.472477i | ||||
\(879\) | −14.0000 | −0.472208 | ||||||||
\(880\) | −4.00000 | −0.134840 | ||||||||
\(881\) | −38.0000 | −1.28025 | −0.640126 | − | 0.768270i | \(-0.721118\pi\) | ||||
−0.640126 | + | 0.768270i | \(0.721118\pi\) | |||||||
\(882\) | 3.00000 | − | 3.00000i | 0.101015 | − | 0.101015i | ||||
\(883\) | − | 36.0000i | − | 1.21150i | −0.795656 | − | 0.605748i | \(-0.792874\pi\) | ||
0.795656 | − | 0.605748i | \(-0.207126\pi\) | |||||||
\(884\) | −16.0000 | −0.538138 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.00000 | − | 8.00000i | −0.268765 | − | 0.268765i | ||||
\(887\) | 24.0000 | 0.805841 | 0.402921 | − | 0.915235i | \(-0.367995\pi\) | ||||
0.402921 | + | 0.915235i | \(0.367995\pi\) | |||||||
\(888\) | −8.00000 | − | 8.00000i | −0.268462 | − | 0.268462i | ||||
\(889\) | −12.0000 | −0.402467 | ||||||||
\(890\) | 6.00000 | + | 6.00000i | 0.201120 | + | 0.201120i | ||||
\(891\) | − | 1.00000i | − | 0.0335013i | ||||||
\(892\) | − | 20.0000i | − | 0.669650i | ||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −2.00000 | + | 2.00000i | −0.0668900 | + | 0.0668900i | ||||
\(895\) | 24.0000 | 0.802232 | ||||||||
\(896\) | −16.0000 | − | 16.0000i | −0.534522 | − | 0.534522i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.00000 | − | 6.00000i | 0.200223 | − | 0.200223i | ||||
\(899\) | 36.0000i | 1.20067i | ||||||||
\(900\) | − | 2.00000i | − | 0.0666667i | ||||||
\(901\) | − | 28.0000i | − | 0.932815i | ||||||
\(902\) | −2.00000 | − | 2.00000i | −0.0665927 | − | 0.0665927i | ||||
\(903\) | −8.00000 | −0.266223 | ||||||||
\(904\) | 4.00000 | + | 4.00000i | 0.133038 | + | 0.133038i | ||||
\(905\) | −20.0000 | −0.664822 | ||||||||
\(906\) | −22.0000 | − | 22.0000i | −0.730901 | − | 0.730901i | ||||
\(907\) | 20.0000i | 0.664089i | 0.943264 | + | 0.332045i | \(0.107738\pi\) | ||||
−0.943264 | + | 0.332045i | \(0.892262\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.00000i | 0.0663358i | ||||||||
\(910\) | −8.00000 | + | 8.00000i | −0.265197 | + | 0.265197i | ||||
\(911\) | 20.0000 | 0.662630 | 0.331315 | − | 0.943520i | \(-0.392508\pi\) | ||||
0.331315 | + | 0.943520i | \(0.392508\pi\) | |||||||
\(912\) | −16.0000 | −0.529813 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 26.0000 | − | 26.0000i | 0.860004 | − | 0.860004i | ||||
\(915\) | − | 12.0000i | − | 0.396708i | ||||||
\(916\) | 40.0000 | 1.32164 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −2.00000 | − | 2.00000i | −0.0660098 | − | 0.0660098i | ||||
\(919\) | 10.0000 | 0.329870 | 0.164935 | − | 0.986304i | \(-0.447259\pi\) | ||||
0.164935 | + | 0.986304i | \(0.447259\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.0000 | 0.659022 | ||||||||
\(922\) | −10.0000 | − | 10.0000i | −0.329332 | − | 0.329332i | ||||
\(923\) | 32.0000i | 1.05329i | ||||||||
\(924\) | 4.00000i | 0.131590i | ||||||||
\(925\) | 4.00000i | 0.131519i | ||||||||
\(926\) | 2.00000 | − | 2.00000i | 0.0657241 | − | 0.0657241i | ||||
\(927\) | 10.0000 | 0.328443 | ||||||||
\(928\) | 24.0000 | + | 24.0000i | 0.787839 | + | 0.787839i | ||||
\(929\) | 6.00000 | 0.196854 | 0.0984268 | − | 0.995144i | \(-0.468619\pi\) | ||||
0.0984268 | + | 0.995144i | \(0.468619\pi\) | |||||||
\(930\) | 6.00000 | − | 6.00000i | 0.196748 | − | 0.196748i | ||||
\(931\) | 12.0000i | 0.393284i | ||||||||
\(932\) | 12.0000i | 0.393073i | ||||||||
\(933\) | 20.0000i | 0.654771i | ||||||||
\(934\) | −32.0000 | − | 32.0000i | −1.04707 | − | 1.04707i | ||||
\(935\) | 2.00000 | 0.0654070 | ||||||||
\(936\) | 8.00000 | − | 8.00000i | 0.261488 | − | 0.261488i | ||||
\(937\) | 14.0000 | 0.457360 | 0.228680 | − | 0.973502i | \(-0.426559\pi\) | ||||
0.228680 | + | 0.973502i | \(0.426559\pi\) | |||||||
\(938\) | 8.00000 | + | 8.00000i | 0.261209 | + | 0.261209i | ||||
\(939\) | 6.00000i | 0.195803i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.00000i | 0.195594i | 0.995206 | + | 0.0977972i | \(0.0311797\pi\) | ||||
−0.995206 | + | 0.0977972i | \(0.968820\pi\) | |||||||
\(942\) | −4.00000 | + | 4.00000i | −0.130327 | + | 0.130327i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.00000 | −0.0650600 | ||||||||
\(946\) | −4.00000 | + | 4.00000i | −0.130051 | + | 0.130051i | ||||
\(947\) | − | 52.0000i | − | 1.68977i | −0.534946 | − | 0.844886i | \(-0.679668\pi\) | ||
0.534946 | − | 0.844886i | \(-0.320332\pi\) | |||||||
\(948\) | 12.0000 | 0.389742 | ||||||||
\(949\) | − | 40.0000i | − | 1.29845i | ||||||
\(950\) | 4.00000 | + | 4.00000i | 0.129777 | + | 0.129777i | ||||
\(951\) | 34.0000 | 1.10253 | ||||||||
\(952\) | 8.00000 | + | 8.00000i | 0.259281 | + | 0.259281i | ||||
\(953\) | −26.0000 | −0.842223 | −0.421111 | − | 0.907009i | \(-0.638360\pi\) | ||||
−0.421111 | + | 0.907009i | \(0.638360\pi\) | |||||||
\(954\) | 14.0000 | + | 14.0000i | 0.453267 | + | 0.453267i | ||||
\(955\) | 4.00000i | 0.129437i | ||||||||
\(956\) | − | 16.0000i | − | 0.517477i | ||||||
\(957\) | − | 6.00000i | − | 0.193952i | ||||||
\(958\) | −12.0000 | + | 12.0000i | −0.387702 | + | 0.387702i | ||||
\(959\) | −12.0000 | −0.387500 | ||||||||
\(960\) | − | 8.00000i | − | 0.258199i | ||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | −16.0000 | + | 16.0000i | −0.515861 | + | 0.515861i | ||||
\(963\) | − | 20.0000i | − | 0.644491i | ||||||
\(964\) | − | 20.0000i | − | 0.644157i | ||||||
\(965\) | 18.0000i | 0.579441i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.0000 | 0.578841 | 0.289420 | − | 0.957202i | \(-0.406537\pi\) | ||||
0.289420 | + | 0.957202i | \(0.406537\pi\) | |||||||
\(968\) | 2.00000 | + | 2.00000i | 0.0642824 | + | 0.0642824i | ||||
\(969\) | 8.00000 | 0.256997 | ||||||||
\(970\) | 6.00000 | + | 6.00000i | 0.192648 | + | 0.192648i | ||||
\(971\) | 12.0000i | 0.385098i | 0.981287 | + | 0.192549i | \(0.0616755\pi\) | ||||
−0.981287 | + | 0.192549i | \(0.938325\pi\) | |||||||
\(972\) | 2.00000 | 0.0641500 | ||||||||
\(973\) | − | 24.0000i | − | 0.769405i | ||||||
\(974\) | −22.0000 | + | 22.0000i | −0.704925 | + | 0.704925i | ||||
\(975\) | −4.00000 | −0.128103 | ||||||||
\(976\) | − | 48.0000i | − | 1.53644i | ||||||
\(977\) | 58.0000 | 1.85558 | 0.927792 | − | 0.373097i | \(-0.121704\pi\) | ||||
0.927792 | + | 0.373097i | \(0.121704\pi\) | |||||||
\(978\) | −4.00000 | + | 4.00000i | −0.127906 | + | 0.127906i | ||||
\(979\) | − | 6.00000i | − | 0.191761i | ||||||
\(980\) | −6.00000 | −0.191663 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 40.0000 | + | 40.0000i | 1.27645 | + | 1.27645i | ||||
\(983\) | 4.00000 | 0.127580 | 0.0637901 | − | 0.997963i | \(-0.479681\pi\) | ||||
0.0637901 | + | 0.997963i | \(0.479681\pi\) | |||||||
\(984\) | 4.00000 | − | 4.00000i | 0.127515 | − | 0.127515i | ||||
\(985\) | 18.0000 | 0.573528 | ||||||||
\(986\) | −12.0000 | − | 12.0000i | −0.382158 | − | 0.382158i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 32.0000i | 1.01806i | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −1.00000 | + | 1.00000i | −0.0317821 | + | 0.0317821i | ||||
\(991\) | −14.0000 | −0.444725 | −0.222362 | − | 0.974964i | \(-0.571377\pi\) | ||||
−0.222362 | + | 0.974964i | \(0.571377\pi\) | |||||||
\(992\) | 24.0000 | − | 24.0000i | 0.762001 | − | 0.762001i | ||||
\(993\) | −12.0000 | −0.380808 | ||||||||
\(994\) | 16.0000 | − | 16.0000i | 0.507489 | − | 0.507489i | ||||
\(995\) | 2.00000i | 0.0634043i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.0000i | 1.26681i | 0.773819 | + | 0.633406i | \(0.218344\pi\) | ||||
−0.773819 | + | 0.633406i | \(0.781656\pi\) | |||||||
\(998\) | 20.0000 | + | 20.0000i | 0.633089 | + | 0.633089i | ||||
\(999\) | −4.00000 | −0.126554 |
(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 | 1320.2.w.a.661.1 | ✓ | 2 | |
4.3 | odd | 2 | 5280.2.w.b.2641.1 | 2 | |||
8.3 | odd | 2 | 5280.2.w.b.2641.2 | 2 | |||
8.5 | even | 2 | inner | 1320.2.w.a.661.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1320.2.w.a.661.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1320.2.w.a.661.2 | yes | 2 | 8.5 | even | 2 | inner | |
5280.2.w.b.2641.1 | 2 | 4.3 | odd | 2 | |||
5280.2.w.b.2641.2 | 2 | 8.3 | odd | 2 |