Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [420,2,Mod(83,420)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(420, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 2, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("420.83");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 420.w (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: | \(3.35371688489\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.12745506816.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 23x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{4}]$ |
Embedding invariants
Embedding label | 83.4 | ||
Root | \(-1.54779 - 1.54779i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 420.83 |
Dual form | 420.2.w.a.167.3 |
$q$-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 \(\left(\mathbb{Z}/420\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(241\) | \(281\) | \(337\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.00000i | −0.707107 | + | 0.707107i | ||||
\(3\) | 1.22474 | + | 1.22474i | 0.707107 | + | 0.707107i | ||||
\(4\) | − | 2.00000i | − | 1.00000i | ||||||
\(5\) | −1.22474 | + | 1.87083i | −0.547723 | + | 0.836660i | ||||
\(6\) | −2.44949 | −1.00000 | ||||||||
\(7\) | 1.87083 | − | 1.87083i | 0.707107 | − | 0.707107i | ||||
\(8\) | 2.00000 | + | 2.00000i | 0.707107 | + | 0.707107i | ||||
\(9\) | 3.00000i | 1.00000i | ||||||||
\(10\) | −0.646084 | − | 3.09557i | −0.204310 | − | 0.978906i | ||||
\(11\) | 5.58258 | 1.68321 | 0.841605 | − | 0.540094i | \(-0.181611\pi\) | ||||
0.841605 | + | 0.540094i | \(0.181611\pi\) | |||||||
\(12\) | 2.44949 | − | 2.44949i | 0.707107 | − | 0.707107i | ||||
\(13\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(14\) | 3.74166i | 1.00000i | ||||||||
\(15\) | −3.79129 | + | 0.791288i | −0.978906 | + | 0.204310i | ||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | −1.80341 | + | 1.80341i | −0.437390 | + | 0.437390i | −0.891133 | − | 0.453743i | \(-0.850089\pi\) |
0.453743 | + | 0.891133i | \(0.350089\pi\) | |||||||
\(18\) | −3.00000 | − | 3.00000i | −0.707107 | − | 0.707107i | ||||
\(19\) | 8.64064i | 1.98230i | 0.132754 | + | 0.991149i | \(0.457618\pi\) | ||||
−0.132754 | + | 0.991149i | \(0.542382\pi\) | |||||||
\(20\) | 3.74166 | + | 2.44949i | 0.836660 | + | 0.547723i | ||||
\(21\) | 4.58258 | 1.00000 | ||||||||
\(22\) | −5.58258 | + | 5.58258i | −1.19021 | + | 1.19021i | ||||
\(23\) | −4.58258 | − | 4.58258i | −0.955533 | − | 0.955533i | 0.0435195 | − | 0.999053i | \(-0.486143\pi\) |
−0.999053 | + | 0.0435195i | \(0.986143\pi\) | |||||||
\(24\) | 4.89898i | 1.00000i | ||||||||
\(25\) | −2.00000 | − | 4.58258i | −0.400000 | − | 0.916515i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.67423 | + | 3.67423i | −0.707107 | + | 0.707107i | ||||
\(28\) | −3.74166 | − | 3.74166i | −0.707107 | − | 0.707107i | ||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 3.00000 | − | 4.58258i | 0.547723 | − | 0.836660i | ||||
\(31\) | 5.03383 | 0.904102 | 0.452051 | − | 0.891992i | \(-0.350693\pi\) | ||||
0.452051 | + | 0.891992i | \(0.350693\pi\) | |||||||
\(32\) | 4.00000 | − | 4.00000i | 0.707107 | − | 0.707107i | ||||
\(33\) | 6.83723 | + | 6.83723i | 1.19021 | + | 1.19021i | ||||
\(34\) | − | 3.60681i | − | 0.618563i | ||||||
\(35\) | 1.20871 | + | 5.79129i | 0.204310 | + | 0.978906i | ||||
\(36\) | 6.00000 | 1.00000 | ||||||||
\(37\) | −0.582576 | + | 0.582576i | −0.0957749 | + | 0.0957749i | −0.753371 | − | 0.657596i | \(-0.771573\pi\) |
0.657596 | + | 0.753371i | \(0.271573\pi\) | |||||||
\(38\) | −8.64064 | − | 8.64064i | −1.40170 | − | 1.40170i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.19115 | + | 1.29217i | −0.978906 | + | 0.204310i | ||||
\(41\) | −3.74166 | −0.584349 | −0.292174 | − | 0.956365i | \(-0.594379\pi\) | ||||
−0.292174 | + | 0.956365i | \(0.594379\pi\) | |||||||
\(42\) | −4.58258 | + | 4.58258i | −0.707107 | + | 0.707107i | ||||
\(43\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(44\) | − | 11.1652i | − | 1.68321i | ||||||
\(45\) | −5.61249 | − | 3.67423i | −0.836660 | − | 0.547723i | ||||
\(46\) | 9.16515 | 1.35133 | ||||||||
\(47\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(48\) | −4.89898 | − | 4.89898i | −0.707107 | − | 0.707107i | ||||
\(49\) | − | 7.00000i | − | 1.00000i | ||||||
\(50\) | 6.58258 | + | 2.58258i | 0.930917 | + | 0.365231i | ||||
\(51\) | −4.41742 | −0.618563 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(54\) | − | 7.34847i | − | 1.00000i | ||||||
\(55\) | −6.83723 | + | 10.4440i | −0.921932 | + | 1.40827i | ||||
\(56\) | 7.48331 | 1.00000 | ||||||||
\(57\) | −10.5826 | + | 10.5826i | −1.40170 | + | 1.40170i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 1.58258 | + | 7.58258i | 0.204310 | + | 0.978906i | ||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | −5.03383 | + | 5.03383i | −0.639296 | + | 0.639296i | ||||
\(63\) | 5.61249 | + | 5.61249i | 0.707107 | + | 0.707107i | ||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −13.6745 | −1.68321 | ||||||||
\(67\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(68\) | 3.60681 | + | 3.60681i | 0.437390 | + | 0.437390i | ||||
\(69\) | − | 11.2250i | − | 1.35133i | ||||||
\(70\) | −7.00000 | − | 4.58258i | −0.836660 | − | 0.547723i | ||||
\(71\) | 15.5826 | 1.84931 | 0.924656 | − | 0.380804i | \(-0.124353\pi\) | ||||
0.924656 | + | 0.380804i | \(0.124353\pi\) | |||||||
\(72\) | −6.00000 | + | 6.00000i | −0.707107 | + | 0.707107i | ||||
\(73\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(74\) | − | 1.16515i | − | 0.135446i | ||||||
\(75\) | 3.16300 | − | 8.06198i | 0.365231 | − | 0.930917i | ||||
\(76\) | 17.2813 | 1.98230 | ||||||||
\(77\) | 10.4440 | − | 10.4440i | 1.19021 | − | 1.19021i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 4.89898 | − | 7.48331i | 0.547723 | − | 0.836660i | ||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 3.74166 | − | 3.74166i | 0.413197 | − | 0.413197i | ||||
\(83\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(84\) | − | 9.16515i | − | 1.00000i | ||||||
\(85\) | −1.16515 | − | 5.58258i | −0.126378 | − | 0.605515i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 11.1652 | + | 11.1652i | 1.19021 | + | 1.19021i | ||||
\(89\) | − | 2.44949i | − | 0.259645i | −0.991537 | − | 0.129823i | \(-0.958559\pi\) | ||
0.991537 | − | 0.129823i | \(-0.0414408\pi\) | |||||||
\(90\) | 9.28672 | − | 1.93825i | 0.978906 | − | 0.204310i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −9.16515 | + | 9.16515i | −0.955533 | + | 0.955533i | ||||
\(93\) | 6.16515 | + | 6.16515i | 0.639296 | + | 0.639296i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −16.1652 | − | 10.5826i | −1.65851 | − | 1.08575i | ||||
\(96\) | 9.79796 | 1.00000 | ||||||||
\(97\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(98\) | 7.00000 | + | 7.00000i | 0.707107 | + | 0.707107i | ||||
\(99\) | 16.7477i | 1.68321i | ||||||||
\(100\) | −9.16515 | + | 4.00000i | −0.916515 | + | 0.400000i | ||||
\(101\) | 7.34847 | 0.731200 | 0.365600 | − | 0.930772i | \(-0.380864\pi\) | ||||
0.365600 | + | 0.930772i | \(0.380864\pi\) | |||||||
\(102\) | 4.41742 | − | 4.41742i | 0.437390 | − | 0.437390i | ||||
\(103\) | −7.48331 | − | 7.48331i | −0.737353 | − | 0.737353i | 0.234712 | − | 0.972065i | \(-0.424585\pi\) |
−0.972065 | + | 0.234712i | \(0.924585\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.61249 | + | 8.57321i | −0.547723 | + | 0.836660i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.7477 | − | 13.7477i | 1.32904 | − | 1.32904i | 0.422837 | − | 0.906206i | \(-0.361034\pi\) |
0.906206 | − | 0.422837i | \(-0.138966\pi\) | |||||||
\(108\) | 7.34847 | + | 7.34847i | 0.707107 | + | 0.707107i | ||||
\(109\) | − | 18.3303i | − | 1.75572i | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||
0.478913 | − | 0.877862i | \(-0.341031\pi\) | |||||||
\(110\) | −3.60681 | − | 17.2813i | −0.343896 | − | 1.64770i | ||||
\(111\) | −1.42701 | −0.135446 | ||||||||
\(112\) | −7.48331 | + | 7.48331i | −0.707107 | + | 0.707107i | ||||
\(113\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(114\) | − | 21.1652i | − | 1.98230i | ||||||
\(115\) | 14.1857 | − | 2.96073i | 1.32282 | − | 0.276089i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.74773i | 0.618563i | ||||||||
\(120\) | −9.16515 | − | 6.00000i | −0.836660 | − | 0.547723i | ||||
\(121\) | 20.1652 | 1.83320 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.58258 | − | 4.58258i | −0.413197 | − | 0.413197i | ||||
\(124\) | − | 10.0677i | − | 0.904102i | ||||||
\(125\) | 11.0227 | + | 1.87083i | 0.985901 | + | 0.167332i | ||||
\(126\) | −11.2250 | −1.00000 | ||||||||
\(127\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(128\) | −8.00000 | − | 8.00000i | −0.707107 | − | 0.707107i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | 13.6745 | − | 13.6745i | 1.19021 | − | 1.19021i | ||||
\(133\) | 16.1652 | + | 16.1652i | 1.40170 | + | 1.40170i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.37386 | − | 11.3739i | −0.204310 | − | 0.978906i | ||||
\(136\) | −7.21362 | −0.618563 | ||||||||
\(137\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(138\) | 11.2250 | + | 11.2250i | 0.955533 | + | 0.955533i | ||||
\(139\) | − | 22.3151i | − | 1.89274i | −0.323082 | − | 0.946371i | \(-0.604719\pi\) | ||
0.323082 | − | 0.946371i | \(-0.395281\pi\) | |||||||
\(140\) | 11.5826 | − | 2.41742i | 0.978906 | − | 0.204310i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −15.5826 | + | 15.5826i | −1.30766 | + | 1.30766i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | − | 12.0000i | − | 1.00000i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.57321 | − | 8.57321i | 0.707107 | − | 0.707107i | ||||
\(148\) | 1.16515 | + | 1.16515i | 0.0957749 | + | 0.0957749i | ||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 4.89898 | + | 11.2250i | 0.400000 | + | 0.916515i | ||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | −17.2813 | + | 17.2813i | −1.40170 | + | 1.40170i | ||||
\(153\) | −5.41022 | − | 5.41022i | −0.437390 | − | 0.437390i | ||||
\(154\) | 20.8881i | 1.68321i | ||||||||
\(155\) | −6.16515 | + | 9.41742i | −0.495197 | + | 0.756426i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.58434 | + | 12.3823i | 0.204310 | + | 0.978906i | ||||
\(161\) | −17.1464 | −1.35133 | ||||||||
\(162\) | 9.00000 | − | 9.00000i | 0.707107 | − | 0.707107i | ||||
\(163\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(164\) | 7.48331i | 0.584349i | ||||||||
\(165\) | −21.1652 | + | 4.41742i | −1.64770 | + | 0.343896i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(168\) | 9.16515 | + | 9.16515i | 0.707107 | + | 0.707107i | ||||
\(169\) | 13.0000i | 1.00000i | ||||||||
\(170\) | 6.74773 | + | 4.41742i | 0.517527 | + | 0.338801i | ||||
\(171\) | −25.9219 | −1.98230 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.8711 | − | 11.8711i | −0.902540 | − | 0.902540i | 0.0931156 | − | 0.995655i | \(-0.470317\pi\) |
−0.995655 | + | 0.0931156i | \(0.970317\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.3149 | − | 4.83156i | −0.930917 | − | 0.365231i | ||||
\(176\) | −22.3303 | −1.68321 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.44949 | + | 2.44949i | 0.183597 | + | 0.183597i | ||||
\(179\) | 26.7477i | 1.99922i | 0.0279439 | + | 0.999609i | \(0.491104\pi\) | ||||
−0.0279439 | + | 0.999609i | \(0.508896\pi\) | |||||||
\(180\) | −7.34847 | + | 11.2250i | −0.547723 | + | 0.836660i | ||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 18.3303i | − | 1.35133i | ||||||
\(185\) | −0.376393 | − | 1.80341i | −0.0276729 | − | 0.132589i | ||||
\(186\) | −12.3303 | −0.904102 | ||||||||
\(187\) | −10.0677 | + | 10.0677i | −0.736219 | + | 0.736219i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.7477i | 1.00000i | ||||||||
\(190\) | 26.7477 | − | 5.58258i | 1.94048 | − | 0.405003i | ||||
\(191\) | −14.4174 | −1.04321 | −0.521604 | − | 0.853188i | \(-0.674666\pi\) | ||||
−0.521604 | + | 0.853188i | \(0.674666\pi\) | |||||||
\(192\) | −9.79796 | + | 9.79796i | −0.707107 | + | 0.707107i | ||||
\(193\) | −11.7477 | − | 11.7477i | −0.845620 | − | 0.845620i | 0.143963 | − | 0.989583i | \(-0.454015\pi\) |
−0.989583 | + | 0.143963i | \(0.954015\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −1.00000 | ||||||||
\(197\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(198\) | −16.7477 | − | 16.7477i | −1.19021 | − | 1.19021i | ||||
\(199\) | − | 15.8543i | − | 1.12388i | −0.827178 | − | 0.561939i | \(-0.810055\pi\) | ||
0.827178 | − | 0.561939i | \(-0.189945\pi\) | |||||||
\(200\) | 5.16515 | − | 13.1652i | 0.365231 | − | 0.930917i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.34847 | + | 7.34847i | −0.517036 | + | 0.517036i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 8.83485i | 0.618563i | ||||||||
\(205\) | 4.58258 | − | 7.00000i | 0.320061 | − | 0.488901i | ||||
\(206\) | 14.9666 | 1.04277 | ||||||||
\(207\) | 13.7477 | − | 13.7477i | 0.955533 | − | 0.955533i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 48.2370i | 3.33662i | ||||||||
\(210\) | −2.96073 | − | 14.1857i | −0.204310 | − | 0.978906i | ||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 19.0847 | + | 19.0847i | 1.30766 | + | 1.30766i | ||||
\(214\) | 27.4955i | 1.87955i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −14.6969 | −1.00000 | ||||||||
\(217\) | 9.41742 | − | 9.41742i | 0.639296 | − | 0.639296i | ||||
\(218\) | 18.3303 | + | 18.3303i | 1.24148 | + | 1.24148i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 20.8881 | + | 13.6745i | 1.40827 | + | 0.921932i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1.42701 | − | 1.42701i | 0.0957749 | − | 0.0957749i | ||||
\(223\) | −9.79796 | − | 9.79796i | −0.656120 | − | 0.656120i | 0.298340 | − | 0.954460i | \(-0.403567\pi\) |
−0.954460 | + | 0.298340i | \(0.903567\pi\) | |||||||
\(224\) | − | 14.9666i | − | 1.00000i | ||||||
\(225\) | 13.7477 | − | 6.00000i | 0.916515 | − | 0.400000i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(228\) | 21.1652 | + | 21.1652i | 1.40170 | + | 1.40170i | ||||
\(229\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(230\) | −11.2250 | + | 17.1464i | −0.740153 | + | 1.13060i | ||||
\(231\) | 25.5826 | 1.68321 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.74773 | − | 6.74773i | −0.437390 | − | 0.437390i | ||||
\(239\) | − | 3.25227i | − | 0.210372i | −0.994453 | − | 0.105186i | \(-0.966456\pi\) | ||
0.994453 | − | 0.105186i | \(-0.0335438\pi\) | |||||||
\(240\) | 15.1652 | − | 3.16515i | 0.978906 | − | 0.204310i | ||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | −20.1652 | + | 20.1652i | −1.29627 | + | 1.29627i | ||||
\(243\) | −11.0227 | − | 11.0227i | −0.707107 | − | 0.707107i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 13.0958 | + | 8.57321i | 0.836660 | + | 0.547723i | ||||
\(246\) | 9.16515 | 0.584349 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 10.0677 | + | 10.0677i | 0.639296 | + | 0.639296i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −12.8935 | + | 9.15188i | −0.815459 | + | 0.578815i | ||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | 11.2250 | − | 11.2250i | 0.707107 | − | 0.707107i | ||||
\(253\) | −25.5826 | − | 25.5826i | −1.60836 | − | 1.60836i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.41022 | − | 8.26424i | 0.338801 | − | 0.517527i | ||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | −14.0509 | + | 14.0509i | −0.876468 | + | 0.876468i | −0.993167 | − | 0.116699i | \(-0.962769\pi\) |
0.116699 | + | 0.993167i | \(0.462769\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.17980i | 0.135446i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.00000 | − | 1.00000i | −0.0616626 | − | 0.0616626i | 0.675603 | − | 0.737266i | \(-0.263883\pi\) |
−0.737266 | + | 0.675603i | \(0.763883\pi\) | |||||||
\(264\) | 27.3489i | 1.68321i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −32.3303 | −1.98230 | ||||||||
\(267\) | 3.00000 | − | 3.00000i | 0.183597 | − | 0.183597i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 26.9444i | − | 1.64283i | −0.570332 | − | 0.821414i | \(-0.693186\pi\) | ||
0.570332 | − | 0.821414i | \(-0.306814\pi\) | |||||||
\(270\) | 13.7477 | + | 9.00000i | 0.836660 | + | 0.547723i | ||||
\(271\) | 29.5287 | 1.79374 | 0.896871 | − | 0.442292i | \(-0.145835\pi\) | ||||
0.896871 | + | 0.442292i | \(0.145835\pi\) | |||||||
\(272\) | 7.21362 | − | 7.21362i | 0.437390 | − | 0.437390i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −11.1652 | − | 25.5826i | −0.673284 | − | 1.54269i | ||||
\(276\) | −22.4499 | −1.35133 | ||||||||
\(277\) | −20.5826 | + | 20.5826i | −1.23669 | + | 1.23669i | −0.275340 | + | 0.961347i | \(0.588791\pi\) |
−0.961347 | + | 0.275340i | \(0.911209\pi\) | |||||||
\(278\) | 22.3151 | + | 22.3151i | 1.33837 | + | 1.33837i | ||||
\(279\) | 15.1015i | 0.904102i | ||||||||
\(280\) | −9.16515 | + | 14.0000i | −0.547723 | + | 0.836660i | ||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.6969 | + | 14.6969i | 0.873642 | + | 0.873642i | 0.992867 | − | 0.119225i | \(-0.0380410\pi\) |
−0.119225 | + | 0.992867i | \(0.538041\pi\) | |||||||
\(284\) | − | 31.1652i | − | 1.84931i | ||||||
\(285\) | −6.83723 | − | 32.7591i | −0.405003 | − | 1.94048i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.00000 | + | 7.00000i | −0.413197 | + | 0.413197i | ||||
\(288\) | 12.0000 | + | 12.0000i | 0.707107 | + | 0.707107i | ||||
\(289\) | 10.4955i | 0.617380i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.1185 | − | 24.1185i | −1.40902 | − | 1.40902i | −0.765065 | − | 0.643953i | \(-0.777293\pi\) |
−0.643953 | − | 0.765065i | \(-0.722707\pi\) | |||||||
\(294\) | 17.1464i | 1.00000i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.33030 | −0.135446 | ||||||||
\(297\) | −20.5117 | + | 20.5117i | −1.19021 | + | 1.19021i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −16.1240 | − | 6.32599i | −0.930917 | − | 0.365231i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.00000 | + | 9.00000i | 0.517036 | + | 0.517036i | ||||
\(304\) | − | 34.5625i | − | 1.98230i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 10.8204 | 0.618563 | ||||||||
\(307\) | 3.74166 | − | 3.74166i | 0.213548 | − | 0.213548i | −0.592225 | − | 0.805773i | \(-0.701750\pi\) |
0.805773 | + | 0.592225i | \(0.201750\pi\) | |||||||
\(308\) | −20.8881 | − | 20.8881i | −1.19021 | − | 1.19021i | ||||
\(309\) | − | 18.3303i | − | 1.04277i | ||||||
\(310\) | −3.25227 | − | 15.5826i | −0.184717 | − | 0.885031i | ||||
\(311\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −17.3739 | + | 3.62614i | −0.978906 | + | 0.204310i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −14.9666 | − | 9.79796i | −0.836660 | − | 0.547723i | ||||
\(321\) | 33.6749 | 1.87955 | ||||||||
\(322\) | 17.1464 | − | 17.1464i | 0.955533 | − | 0.955533i | ||||
\(323\) | −15.5826 | − | 15.5826i | −0.867038 | − | 0.867038i | ||||
\(324\) | 18.0000i | 1.00000i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 22.4499 | − | 22.4499i | 1.24148 | − | 1.24148i | ||||
\(328\) | −7.48331 | − | 7.48331i | −0.413197 | − | 0.413197i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 16.7477 | − | 25.5826i | 0.921932 | − | 1.40827i | ||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.74773 | − | 1.74773i | −0.0957749 | − | 0.0957749i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −18.3303 | −1.00000 | ||||||||
\(337\) | 17.3303 | − | 17.3303i | 0.944042 | − | 0.944042i | −0.0544735 | − | 0.998515i | \(-0.517348\pi\) |
0.998515 | + | 0.0544735i | \(0.0173480\pi\) | |||||||
\(338\) | −13.0000 | − | 13.0000i | −0.707107 | − | 0.707107i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −11.1652 | + | 2.33030i | −0.605515 | + | 0.126378i | ||||
\(341\) | 28.1017 | 1.52179 | ||||||||
\(342\) | 25.9219 | − | 25.9219i | 1.40170 | − | 1.40170i | ||||
\(343\) | −13.0958 | − | 13.0958i | −0.707107 | − | 0.707107i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 21.0000 | + | 13.7477i | 1.13060 | + | 0.740153i | ||||
\(346\) | 23.7421 | 1.27638 | ||||||||
\(347\) | 13.0000 | − | 13.0000i | 0.697877 | − | 0.697877i | −0.266076 | − | 0.963952i | \(-0.585727\pi\) |
0.963952 | + | 0.266076i | \(0.0857271\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | 17.1464 | − | 7.48331i | 0.916515 | − | 0.400000i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 22.3303 | − | 22.3303i | 1.19021 | − | 1.19021i | ||||
\(353\) | 0.376393 | + | 0.376393i | 0.0200334 | + | 0.0200334i | 0.717053 | − | 0.697019i | \(-0.245491\pi\) |
−0.697019 | + | 0.717053i | \(0.745491\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −19.0847 | + | 29.1523i | −1.01291 | + | 1.54725i | ||||
\(356\) | −4.89898 | −0.259645 | ||||||||
\(357\) | −8.26424 | + | 8.26424i | −0.437390 | + | 0.437390i | ||||
\(358\) | −26.7477 | − | 26.7477i | −1.41366 | − | 1.41366i | ||||
\(359\) | 36.7477i | 1.93947i | 0.244158 | + | 0.969735i | \(0.421488\pi\) | ||||
−0.244158 | + | 0.969735i | \(0.578512\pi\) | |||||||
\(360\) | −3.87650 | − | 18.5734i | −0.204310 | − | 0.978906i | ||||
\(361\) | −55.6606 | −2.92951 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 24.6972 | + | 24.6972i | 1.29627 | + | 1.29627i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.5959 | + | 19.5959i | −1.02290 | + | 1.02290i | −0.0231670 | + | 0.999732i | \(0.507375\pi\) |
−0.999732 | + | 0.0231670i | \(0.992625\pi\) | |||||||
\(368\) | 18.3303 | + | 18.3303i | 0.955533 | + | 0.955533i | ||||
\(369\) | − | 11.2250i | − | 0.584349i | ||||||
\(370\) | 2.17980 | + | 1.42701i | 0.113322 | + | 0.0741869i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 12.3303 | − | 12.3303i | 0.639296 | − | 0.639296i | ||||
\(373\) | 26.1652 | + | 26.1652i | 1.35478 | + | 1.35478i | 0.880227 | + | 0.474554i | \(0.157390\pi\) |
0.474554 | + | 0.880227i | \(0.342610\pi\) | |||||||
\(374\) | − | 20.1353i | − | 1.04117i | ||||||
\(375\) | 11.2087 | + | 15.7913i | 0.578815 | + | 0.815459i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −13.7477 | − | 13.7477i | −0.707107 | − | 0.707107i | ||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | −21.1652 | + | 32.3303i | −1.08575 | + | 1.65851i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 14.4174 | − | 14.4174i | 0.737660 | − | 0.737660i | ||||
\(383\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(384\) | − | 19.5959i | − | 1.00000i | ||||||
\(385\) | 6.74773 | + | 32.3303i | 0.343896 | + | 1.64770i | ||||
\(386\) | 23.4955 | 1.19589 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.5285 | 0.835882 | ||||||||
\(392\) | 14.0000 | − | 14.0000i | 0.707107 | − | 0.707107i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 33.4955 | 1.68321 | ||||||||
\(397\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(398\) | 15.8543 | + | 15.8543i | 0.794702 | + | 0.794702i | ||||
\(399\) | 39.5964i | 1.98230i | ||||||||
\(400\) | 8.00000 | + | 18.3303i | 0.400000 | + | 0.916515i | ||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | − | 14.6969i | − | 0.731200i | ||||||
\(405\) | 11.0227 | − | 16.8375i | 0.547723 | − | 0.836660i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.25227 | + | 3.25227i | −0.161209 | + | 0.161209i | ||||
\(408\) | −8.83485 | − | 8.83485i | −0.437390 | − | 0.437390i | ||||
\(409\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(410\) | 2.41742 | + | 11.5826i | 0.119388 | + | 0.572023i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −14.9666 | + | 14.9666i | −0.737353 | + | 0.737353i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 27.4955i | 1.35133i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 27.3303 | − | 27.3303i | 1.33837 | − | 1.33837i | ||||
\(418\) | −48.2370 | − | 48.2370i | −2.35935 | − | 2.35935i | ||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 17.1464 | + | 11.2250i | 0.836660 | + | 0.547723i | ||||
\(421\) | 9.16515 | 0.446682 | 0.223341 | − | 0.974740i | \(-0.428304\pi\) | ||||
0.223341 | + | 0.974740i | \(0.428304\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.8711 | + | 4.65743i | 0.575831 | + | 0.225919i | ||||
\(426\) | −38.1694 | −1.84931 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −27.4955 | − | 27.4955i | −1.32904 | − | 1.32904i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.4174 | −1.17615 | −0.588073 | − | 0.808808i | \(-0.700113\pi\) | ||||
−0.588073 | + | 0.808808i | \(0.700113\pi\) | |||||||
\(432\) | 14.6969 | − | 14.6969i | 0.707107 | − | 0.707107i | ||||
\(433\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(434\) | 18.8348i | 0.904102i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −36.6606 | −1.75572 | ||||||||
\(437\) | 39.5964 | − | 39.5964i | 1.89415 | − | 1.89415i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 33.1355i | 1.58147i | 0.612157 | + | 0.790736i | \(0.290302\pi\) | ||||
−0.612157 | + | 0.790736i | \(0.709698\pi\) | |||||||
\(440\) | −34.5625 | + | 7.21362i | −1.64770 | + | 0.343896i | ||||
\(441\) | 21.0000 | 1.00000 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.0000 | + | 19.0000i | 0.902717 | + | 0.902717i | 0.995670 | − | 0.0929532i | \(-0.0296307\pi\) |
−0.0929532 | + | 0.995670i | \(0.529631\pi\) | |||||||
\(444\) | 2.85403i | 0.135446i | ||||||||
\(445\) | 4.58258 | + | 3.00000i | 0.217235 | + | 0.142214i | ||||
\(446\) | 19.5959 | 0.927894 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 14.9666 | + | 14.9666i | 0.707107 | + | 0.707107i | ||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | −7.74773 | + | 19.7477i | −0.365231 | + | 0.930917i | ||||
\(451\) | −20.8881 | −0.983582 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −42.3303 | −1.98230 | ||||||||
\(457\) | 7.33030 | − | 7.33030i | 0.342897 | − | 0.342897i | −0.514558 | − | 0.857455i | \(-0.672044\pi\) |
0.857455 | + | 0.514558i | \(0.172044\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 13.2523i | − | 0.618563i | ||||||
\(460\) | −5.92146 | − | 28.3714i | −0.276089 | − | 1.32282i | ||||
\(461\) | −41.1582 | −1.91693 | −0.958465 | − | 0.285210i | \(-0.907937\pi\) | ||||
−0.958465 | + | 0.285210i | \(0.907937\pi\) | |||||||
\(462\) | −25.5826 | + | 25.5826i | −1.19021 | + | 1.19021i | ||||
\(463\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −19.0847 | + | 3.98320i | −0.885031 | + | 0.184717i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 39.5964 | − | 17.2813i | 1.81681 | − | 0.792919i | ||||
\(476\) | 13.4955 | 0.618563 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.25227 | + | 3.25227i | 0.148756 | + | 0.148756i | ||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | −12.0000 | + | 18.3303i | −0.547723 | + | 0.836660i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −21.0000 | − | 21.0000i | −0.955533 | − | 0.955533i | ||||
\(484\) | − | 40.3303i | − | 1.83320i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 22.0454 | 1.00000 | ||||||||
\(487\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −21.6690 | + | 4.52259i | −0.978906 | + | 0.204310i | ||||
\(491\) | 35.5826 | 1.60582 | 0.802910 | − | 0.596101i | \(-0.203284\pi\) | ||||
0.802910 | + | 0.596101i | \(0.203284\pi\) | |||||||
\(492\) | −9.16515 | + | 9.16515i | −0.413197 | + | 0.413197i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −31.3321 | − | 20.5117i | −1.40827 | − | 0.921932i | ||||
\(496\) | −20.1353 | −0.904102 | ||||||||
\(497\) | 29.1523 | − | 29.1523i | 1.30766 | − | 1.30766i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | 3.74166 | − | 22.0454i | 0.167332 | − | 0.985901i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(504\) | 22.4499i | 1.00000i | ||||||||
\(505\) | −9.00000 | + | 13.7477i | −0.400495 | + | 0.611766i | ||||
\(506\) | 51.1652 | 2.27457 | ||||||||
\(507\) | −15.9217 | + | 15.9217i | −0.707107 | + | 0.707107i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.1916i | 1.16092i | 0.814288 | + | 0.580461i | \(0.197128\pi\) | ||||
−0.814288 | + | 0.580461i | \(0.802872\pi\) | |||||||
\(510\) | 2.85403 | + | 13.6745i | 0.126378 | + | 0.605515i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −16.0000 | + | 16.0000i | −0.707107 | + | 0.707107i | ||||
\(513\) | −31.7477 | − | 31.7477i | −1.40170 | − | 1.40170i | ||||
\(514\) | − | 28.1017i | − | 1.23951i | ||||||
\(515\) | 23.1652 | − | 4.83485i | 1.02078 | − | 0.213049i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −2.17980 | − | 2.17980i | −0.0957749 | − | 0.0957749i | ||||
\(519\) | − | 29.0780i | − | 1.27638i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −41.6413 | −1.82434 | −0.912170 | − | 0.409812i | \(-0.865594\pi\) | ||||
−0.912170 | + | 0.409812i | \(0.865594\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.9333 | + | 29.9333i | 1.30889 | + | 1.30889i | 0.922217 | + | 0.386673i | \(0.126376\pi\) |
0.386673 | + | 0.922217i | \(0.373624\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9.16515 | − | 21.0000i | −0.400000 | − | 0.916515i | ||||
\(526\) | 2.00000 | 0.0872041 | ||||||||
\(527\) | −9.07803 | + | 9.07803i | −0.395445 | + | 0.395445i | ||||
\(528\) | −27.3489 | − | 27.3489i | −1.19021 | − | 1.19021i | ||||
\(529\) | 19.0000i | 0.826087i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 32.3303 | − | 32.3303i | 1.40170 | − | 1.40170i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 6.00000i | 0.259645i | ||||||||
\(535\) | 8.88218 | + | 42.5571i | 0.384010 | + | 1.83990i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −32.7591 | + | 32.7591i | −1.41366 | + | 1.41366i | ||||
\(538\) | 26.9444 | + | 26.9444i | 1.16166 | + | 1.16166i | ||||
\(539\) | − | 39.0780i | − | 1.68321i | ||||||
\(540\) | −22.7477 | + | 4.74773i | −0.978906 | + | 0.204310i | ||||
\(541\) | −8.00000 | −0.343947 | −0.171973 | − | 0.985102i | \(-0.555014\pi\) | ||||
−0.171973 | + | 0.985102i | \(0.555014\pi\) | |||||||
\(542\) | −29.5287 | + | 29.5287i | −1.26837 | + | 1.26837i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 14.4272i | 0.618563i | ||||||||
\(545\) | 34.2929 | + | 22.4499i | 1.46894 | + | 0.961650i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 36.7477 | + | 14.4174i | 1.56693 | + | 0.614761i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 22.4499 | − | 22.4499i | 0.955533 | − | 0.955533i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 41.1652i | − | 1.74894i | ||||||
\(555\) | 1.74773 | − | 2.66970i | 0.0741869 | − | 0.113322i | ||||
\(556\) | −44.6302 | −1.89274 | ||||||||
\(557\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(558\) | −15.1015 | − | 15.1015i | −0.639296 | − | 0.639296i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −4.83485 | − | 23.1652i | −0.204310 | − | 0.978906i | ||||
\(561\) | −24.6606 | −1.04117 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −29.3939 | −1.23552 | ||||||||
\(567\) | −16.8375 | + | 16.8375i | −0.707107 | + | 0.707107i | ||||
\(568\) | 31.1652 | + | 31.1652i | 1.30766 | + | 1.30766i | ||||
\(569\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | 39.5964 | + | 25.9219i | 1.65851 | + | 1.08575i | ||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.6577 | − | 17.6577i | −0.737660 | − | 0.737660i | ||||
\(574\) | − | 14.0000i | − | 0.584349i | ||||||
\(575\) | −11.8348 | + | 30.1652i | −0.493547 | + | 1.25797i | ||||
\(576\) | −24.0000 | −1.00000 | ||||||||
\(577\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(578\) | −10.4955 | − | 10.4955i | −0.436553 | − | 0.436553i | ||||
\(579\) | − | 28.7759i | − | 1.19589i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 48.2370 | 1.99265 | ||||||||
\(587\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(588\) | −17.1464 | − | 17.1464i | −0.707107 | − | 0.707107i | ||||
\(589\) | 43.4955i | 1.79220i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.33030 | − | 2.33030i | 0.0957749 | − | 0.0957749i | ||||
\(593\) | 25.5455 | + | 25.5455i | 1.04903 | + | 1.04903i | 0.998734 | + | 0.0502942i | \(0.0160159\pi\) |
0.0502942 | + | 0.998734i | \(0.483984\pi\) | |||||||
\(594\) | − | 41.0234i | − | 1.68321i | ||||||
\(595\) | −12.6238 | − | 8.26424i | −0.517527 | − | 0.338801i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 19.4174 | − | 19.4174i | 0.794702 | − | 0.794702i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 19.0780i | − | 0.779507i | −0.920919 | − | 0.389754i | \(-0.872560\pi\) | ||
0.920919 | − | 0.389754i | \(-0.127440\pi\) | |||||||
\(600\) | 22.4499 | − | 9.79796i | 0.916515 | − | 0.400000i | ||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −24.6972 | + | 37.7255i | −1.00408 | + | 1.53376i | ||||
\(606\) | −18.0000 | −0.731200 | ||||||||
\(607\) | 29.3939 | − | 29.3939i | 1.19306 | − | 1.19306i | 0.216857 | − | 0.976203i | \(-0.430419\pi\) |
0.976203 | − | 0.216857i | \(-0.0695807\pi\) | |||||||
\(608\) | 34.5625 | + | 34.5625i | 1.40170 | + | 1.40170i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −10.8204 | + | 10.8204i | −0.437390 | + | 0.437390i | ||||
\(613\) | −13.8348 | − | 13.8348i | −0.558784 | − | 0.558784i | 0.370177 | − | 0.928961i | \(-0.379297\pi\) |
−0.928961 | + | 0.370177i | \(0.879297\pi\) | |||||||
\(614\) | 7.48331i | 0.302002i | ||||||||
\(615\) | 14.1857 | − | 2.96073i | 0.572023 | − | 0.119388i | ||||
\(616\) | 41.7762 | 1.68321 | ||||||||
\(617\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(618\) | 18.3303 | + | 18.3303i | 0.737353 | + | 0.737353i | ||||
\(619\) | − | 46.8100i | − | 1.88145i | −0.339167 | − | 0.940726i | \(-0.610145\pi\) | ||
0.339167 | − | 0.940726i | \(-0.389855\pi\) | |||||||
\(620\) | 18.8348 | + | 12.3303i | 0.756426 | + | 0.495197i | ||||
\(621\) | 33.6749 | 1.35133 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.58258 | − | 4.58258i | −0.183597 | − | 0.183597i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.0000 | + | 18.3303i | −0.680000 | + | 0.733212i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −59.0780 | + | 59.0780i | −2.35935 | + | 2.35935i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 2.10124i | − | 0.0837820i | ||||||
\(630\) | 13.7477 | − | 21.0000i | 0.547723 | − | 0.836660i | ||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 46.7477i | 1.84931i | ||||||||
\(640\) | 24.7646 | − | 5.16867i | 0.978906 | − | 0.204310i | ||||
\(641\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(642\) | −33.6749 | + | 33.6749i | −1.32904 | + | 1.32904i | ||||
\(643\) | −26.1916 | − | 26.1916i | −1.03290 | − | 1.03290i | −0.999440 | − | 0.0334557i | \(-0.989349\pi\) |
−0.0334557 | − | 0.999440i | \(-0.510651\pi\) | |||||||
\(644\) | 34.2929i | 1.35133i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 31.1652 | 1.22618 | ||||||||
\(647\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(648\) | −18.0000 | − | 18.0000i | −0.707107 | − | 0.707107i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 23.0679 | 0.904102 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(654\) | 44.8999i | 1.75572i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 14.9666 | 0.584349 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 49.0780i | − | 1.91181i | −0.293678 | − | 0.955904i | \(-0.594879\pi\) | ||
0.293678 | − | 0.955904i | \(-0.405121\pi\) | |||||||
\(660\) | 8.83485 | + | 42.3303i | 0.343896 | + | 1.64770i | ||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −50.0404 | + | 10.4440i | −1.94048 | + | 0.405003i | ||||
\(666\) | 3.49545 | 0.135446 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 24.0000i | − | 0.927894i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 18.3303 | − | 18.3303i | 0.707107 | − | 0.707107i | ||||
\(673\) | 8.25227 | + | 8.25227i | 0.318102 | + | 0.318102i | 0.848038 | − | 0.529936i | \(-0.177784\pi\) |
−0.529936 | + | 0.848038i | \(0.677784\pi\) | |||||||
\(674\) | 34.6606i | 1.33508i | ||||||||
\(675\) | 24.1859 | + | 9.48899i | 0.930917 | + | 0.365231i | ||||
\(676\) | 26.0000 | 1.00000 | ||||||||
\(677\) | 4.65743 | − | 4.65743i | 0.179000 | − | 0.179000i | −0.611920 | − | 0.790920i | \(-0.709603\pi\) |
0.790920 | + | 0.611920i | \(0.209603\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 8.83485 | − | 13.4955i | 0.338801 | − | 0.517527i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −28.1017 | + | 28.1017i | −1.07607 | + | 1.07607i | ||||
\(683\) | 29.0000 | + | 29.0000i | 1.10965 | + | 1.10965i | 0.993196 | + | 0.116459i | \(0.0371542\pi\) |
0.116459 | + | 0.993196i | \(0.462846\pi\) | |||||||
\(684\) | 51.8438i | 1.98230i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 26.1916 | 1.00000 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −34.7477 | + | 7.25227i | −1.32282 | + | 0.276089i | ||||
\(691\) | −7.88785 | −0.300068 | −0.150034 | − | 0.988681i | \(-0.547938\pi\) | ||||
−0.150034 | + | 0.988681i | \(0.547938\pi\) | |||||||
\(692\) | −23.7421 | + | 23.7421i | −0.902540 | + | 0.902540i | ||||
\(693\) | 31.3321 | + | 31.3321i | 1.19021 | + | 1.19021i | ||||
\(694\) | 26.0000i | 0.986947i | ||||||||
\(695\) | 41.7477 | + | 27.3303i | 1.58358 | + | 1.03670i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.74773 | − | 6.74773i | 0.255588 | − | 0.255588i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −9.66311 | + | 24.6297i | −0.365231 | + | 0.930917i | ||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.03383 | − | 5.03383i | −0.189854 | − | 0.189854i | ||||
\(704\) | 44.6606i | 1.68321i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.752785 | −0.0283315 | ||||||||
\(707\) | 13.7477 | − | 13.7477i | 0.517036 | − | 0.517036i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 18.3303i | − | 0.688409i | −0.938895 | − | 0.344204i | \(-0.888149\pi\) | ||
0.938895 | − | 0.344204i | \(-0.111851\pi\) | |||||||
\(710\) | −10.0677 | − | 48.2370i | −0.377832 | − | 1.81030i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.89898 | − | 4.89898i | 0.183597 | − | 0.183597i | ||||
\(713\) | −23.0679 | − | 23.0679i | −0.863899 | − | 0.863899i | ||||
\(714\) | − | 16.5285i | − | 0.618563i | ||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 53.4955 | 1.99922 | ||||||||
\(717\) | 3.98320 | − | 3.98320i | 0.148756 | − | 0.148756i | ||||
\(718\) | −36.7477 | − | 36.7477i | −1.37141 | − | 1.37141i | ||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 22.4499 | + | 14.6969i | 0.836660 | + | 0.547723i | ||||
\(721\) | −28.0000 | −1.04277 | ||||||||
\(722\) | 55.6606 | − | 55.6606i | 2.07147 | − | 2.07147i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −49.3943 | −1.83320 | ||||||||
\(727\) | −7.34847 | + | 7.34847i | −0.272540 | + | 0.272540i | −0.830122 | − | 0.557582i | \(-0.811729\pi\) |
0.557582 | + | 0.830122i | \(0.311729\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 27.0000i | − | 1.00000i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(734\) | − | 39.1918i | − | 1.44660i | ||||||
\(735\) | 5.53901 | + | 26.5390i | 0.204310 | + | 0.978906i | ||||
\(736\) | −36.6606 | −1.35133 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 11.2250 | + | 11.2250i | 0.413197 | + | 0.413197i | ||||
\(739\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(740\) | −3.60681 | + | 0.752785i | −0.132589 | + | 0.0276729i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −31.0000 | − | 31.0000i | −1.13728 | − | 1.13728i | −0.988936 | − | 0.148344i | \(-0.952606\pi\) |
−0.148344 | − | 0.988936i | \(-0.547394\pi\) | |||||||
\(744\) | 24.6606i | 0.904102i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −52.3303 | −1.91595 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 20.1353 | + | 20.1353i | 0.736219 | + | 0.736219i | ||||
\(749\) | − | 51.4393i | − | 1.87955i | ||||||
\(750\) | −27.0000 | − | 4.58258i | −0.985901 | − | 0.167332i | ||||
\(751\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 27.4955 | 1.00000 | ||||||||
\(757\) | −28.4955 | + | 28.4955i | −1.03568 | + | 1.03568i | −0.0363456 | + | 0.999339i | \(0.511572\pi\) |
−0.999339 | + | 0.0363456i | \(0.988428\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 62.6643i | − | 2.27457i | ||||||
\(760\) | −11.1652 | − | 53.4955i | −0.405003 | − | 1.94048i | ||||
\(761\) | −41.1582 | −1.49198 | −0.745992 | − | 0.665955i | \(-0.768024\pi\) | ||||
−0.745992 | + | 0.665955i | \(0.768024\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −34.2929 | − | 34.2929i | −1.24148 | − | 1.24148i | ||||
\(764\) | 28.8348i | 1.04321i | ||||||||
\(765\) | 16.7477 | − | 3.49545i | 0.605515 | − | 0.126378i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 19.5959 | + | 19.5959i | 0.707107 | + | 0.707107i | ||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | −39.0780 | − | 25.5826i | −1.40827 | − | 0.921932i | ||||
\(771\) | −34.4174 | −1.23951 | ||||||||
\(772\) | −23.4955 | + | 23.4955i | −0.845620 | + | 0.845620i | ||||
\(773\) | 37.7930 | + | 37.7930i | 1.35932 | + | 1.35932i | 0.874757 | + | 0.484561i | \(0.161021\pi\) |
0.484561 | + | 0.874757i | \(0.338979\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.0677 | − | 23.0679i | −0.361641 | − | 0.828623i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.66970 | + | 2.66970i | −0.0957749 | + | 0.0957749i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 32.3303i | − | 1.15835i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 86.9909 | 3.11278 | ||||||||
\(782\) | −16.5285 | + | 16.5285i | −0.591058 | + | 0.591058i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 28.0000i | 1.00000i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.9666 | + | 14.9666i | −0.533503 | + | 0.533503i | −0.921613 | − | 0.388110i | \(-0.873128\pi\) |
0.388110 | + | 0.921613i | \(0.373128\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 2.44949i | − | 0.0872041i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −33.4955 | + | 33.4955i | −1.19021 | + | 1.19021i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −31.7085 | −1.12388 | ||||||||
\(797\) | −26.2983 | + | 26.2983i | −0.931534 | + | 0.931534i | −0.997802 | − | 0.0662682i | \(-0.978891\pi\) |
0.0662682 | + | 0.997802i | \(0.478891\pi\) | |||||||
\(798\) | −39.5964 | − | 39.5964i | −1.40170 | − | 1.40170i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −26.3303 | − | 10.3303i | −0.930917 | − | 0.365231i | ||||
\(801\) | 7.34847 | 0.259645 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.0000 | − | 32.0780i | 0.740153 | − | 1.13060i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 33.0000 | − | 33.0000i | 1.16166 | − | 1.16166i | ||||
\(808\) | 14.6969 | + | 14.6969i | 0.517036 | + | 0.517036i | ||||
\(809\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(810\) | 5.81475 | + | 27.8602i | 0.204310 | + | 0.978906i | ||||
\(811\) | −56.8776 | −1.99724 | −0.998622 | − | 0.0524767i | \(-0.983288\pi\) | ||||
−0.998622 | + | 0.0524767i | \(0.983288\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 36.1652 | + | 36.1652i | 1.26837 | + | 1.26837i | ||||
\(814\) | − | 6.50455i | − | 0.227984i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 17.6697 | 0.618563 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −14.0000 | − | 9.16515i | −0.488901 | − | 0.320061i | ||||
\(821\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(824\) | − | 29.9333i | − | 1.04277i | ||||||
\(825\) | 17.6577 | − | 45.0066i | 0.614761 | − | 1.56693i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32.0780 | + | 32.0780i | −1.11546 | + | 1.11546i | −0.123064 | + | 0.992399i | \(0.539272\pi\) |
−0.992399 | + | 0.123064i | \(0.960728\pi\) | |||||||
\(828\) | −27.4955 | − | 27.4955i | −0.955533 | − | 0.955533i | ||||
\(829\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −50.4168 | −1.74894 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12.6238 | + | 12.6238i | 0.437390 | + | 0.437390i | ||||
\(834\) | 54.6606i | 1.89274i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 96.4740 | 3.33662 | ||||||||
\(837\) | −18.4955 | + | 18.4955i | −0.639296 | + | 0.639296i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | −28.3714 | + | 5.92146i | −0.978906 | + | 0.204310i | ||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | −9.16515 | + | 9.16515i | −0.315852 | + | 0.315852i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −24.3208 | − | 15.9217i | −0.836660 | − | 0.547723i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 37.7255 | − | 37.7255i | 1.29627 | − | 1.29627i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 36.0000i | 1.23552i | ||||||||
\(850\) | −16.5285 | + | 7.21362i | −0.566922 | + | 0.247425i | ||||
\(851\) | 5.33939 | 0.183032 | ||||||||
\(852\) | 38.1694 | − | 38.1694i | 1.30766 | − | 1.30766i | ||||
\(853\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 31.7477 | − | 48.4955i | 1.08575 | − | 1.65851i | ||||
\(856\) | 54.9909 | 1.87955 | ||||||||
\(857\) | 41.3998 | − | 41.3998i | 1.41419 | − | 1.41419i | 0.702969 | − | 0.711220i | \(-0.251857\pi\) |
0.711220 | − | 0.702969i | \(-0.248143\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 46.0572i | 1.57145i | 0.618575 | + | 0.785726i | \(0.287710\pi\) | ||||
−0.618575 | + | 0.785726i | \(0.712290\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −17.1464 | −0.584349 | ||||||||
\(862\) | 24.4174 | − | 24.4174i | 0.831661 | − | 0.831661i | ||||
\(863\) | 41.2432 | + | 41.2432i | 1.40393 | + | 1.40393i | 0.787068 | + | 0.616866i | \(0.211598\pi\) |
0.616866 | + | 0.787068i | \(0.288402\pi\) | |||||||
\(864\) | 29.3939i | 1.00000i | ||||||||
\(865\) | 36.7477 | − | 7.66970i | 1.24946 | − | 0.260778i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.8543 | + | 12.8543i | −0.436553 | + | 0.436553i | ||||
\(868\) | −18.8348 | − | 18.8348i | −0.639296 | − | 0.639296i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 36.6606 | − | 36.6606i | 1.24148 | − | 1.24148i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 79.1927i | 2.67873i | ||||||||
\(875\) | 24.1216 | − | 17.1216i | 0.815459 | − | 0.578815i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38.4955 | + | 38.4955i | −1.29990 | + | 1.29990i | −0.371444 | + | 0.928456i | \(0.621137\pi\) |
−0.928456 | + | 0.371444i | \(0.878863\pi\) | |||||||
\(878\) | −33.1355 | − | 33.1355i | −1.11827 | − | 1.11827i | ||||
\(879\) | − | 59.0780i | − | 1.99265i | ||||||
\(880\) | 27.3489 | − | 41.7762i | 0.921932 | − | 1.40827i | ||||
\(881\) | 56.3383 | 1.89808 | 0.949042 | − | 0.315149i | \(-0.102055\pi\) | ||||
0.949042 | + | 0.315149i | \(0.102055\pi\) | |||||||
\(882\) | −21.0000 | + | 21.0000i | −0.707107 | + | 0.707107i | ||||
\(883\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −38.0000 | −1.27663 | ||||||||
\(887\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(888\) | −2.85403 | − | 2.85403i | −0.0957749 | − | 0.0957749i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −7.58258 | + | 1.58258i | −0.254169 | + | 0.0530481i | ||||
\(891\) | −50.2432 | −1.68321 | ||||||||
\(892\) | −19.5959 | + | 19.5959i | −0.656120 | + | 0.656120i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −50.0404 | − | 32.7591i | −1.67267 | − | 1.09502i | ||||
\(896\) | −29.9333 | −1.00000 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −12.0000 | − | 27.4955i | −0.400000 | − | 0.916515i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 20.8881 | − | 20.8881i | 0.695497 | − | 0.695497i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 22.0454i | 0.731200i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.2432 | −1.00200 | −0.501001 | − | 0.865447i | \(-0.667035\pi\) | ||||
−0.501001 | + | 0.865447i | \(0.667035\pi\) | |||||||
\(912\) | 42.3303 | − | 42.3303i | 1.40170 | − | 1.40170i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 14.6606i | 0.484930i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 13.2523 | + | 13.2523i | 0.437390 | + | 0.437390i | ||||
\(919\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(920\) | 34.2929 | + | 22.4499i | 1.13060 | + | 0.740153i | ||||
\(921\) | 9.16515 | 0.302002 | ||||||||
\(922\) | 41.1582 | − | 41.1582i | 1.35547 | − | 1.35547i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | − | 51.1652i | − | 1.68321i | ||||||
\(925\) | 3.83485 | + | 1.50455i | 0.126089 | + | 0.0494692i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 22.4499 | − | 22.4499i | 0.737353 | − | 0.737353i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 48.6415i | − | 1.59588i | −0.602739 | − | 0.797939i | \(-0.705924\pi\) | ||
0.602739 | − | 0.797939i | \(-0.294076\pi\) | |||||||
\(930\) | 15.1015 | − | 23.0679i | 0.495197 | − | 0.756426i | ||||
\(931\) | 60.4845 | 1.98230 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.50455 | − | 31.1652i | −0.212721 | − | 1.01921i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.74166 | −0.121975 | −0.0609873 | − | 0.998139i | \(-0.519425\pi\) | ||||
−0.0609873 | + | 0.998139i | \(0.519425\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.1464 | + | 17.1464i | 0.558365 | + | 0.558365i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −25.7196 | − | 16.8375i | −0.836660 | − | 0.547723i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −37.0000 | + | 37.0000i | −1.20234 | + | 1.20234i | −0.228885 | + | 0.973453i | \(0.573508\pi\) |
−0.973453 | + | 0.228885i | \(0.926492\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −22.3151 | + | 56.8776i | −0.723997 | + | 1.84535i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −13.4955 | + | 13.4955i | −0.437390 | + | 0.437390i | ||||
\(953\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.6577 | − | 26.9725i | 0.571389 | − | 0.872811i | ||||
\(956\) | −6.50455 | −0.210372 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −6.33030 | − | 30.3303i | −0.204310 | − | 0.978906i | ||||
\(961\) | −5.66061 | −0.182600 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 41.2432 | + | 41.2432i | 1.32904 | + | 1.32904i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 36.3660 | − | 7.59002i | 1.17066 | − | 0.244331i | ||||
\(966\) | 42.0000 | 1.35133 | ||||||||
\(967\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(968\) | 40.3303 | + | 40.3303i | 1.29627 | + | 1.29627i | ||||
\(969\) | − | 38.1694i | − | 1.22618i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(972\) | −22.0454 | + | 22.0454i | −0.707107 | + | 0.707107i | ||||
\(973\) | −41.7477 | − | 41.7477i | −1.33837 | − | 1.33837i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 13.6745i | − | 0.437038i | ||||||
\(980\) | 17.1464 | − | 26.1916i | 0.547723 | − | 0.836660i | ||||
\(981\) | 54.9909 | 1.75572 | ||||||||
\(982\) | −35.5826 | + | 35.5826i | −1.13549 | + | 1.13549i | ||||
\(983\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(984\) | − | 18.3303i | − | 0.584349i | ||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 51.8438 | − | 10.8204i | 1.64770 | − | 0.343896i | ||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 20.1353 | − | 20.1353i | 0.639296 | − | 0.639296i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 58.3047i | 1.84931i | ||||||||
\(995\) | 29.6606 | + | 19.4174i | 0.940304 | + | 0.615574i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 4.28104i | − | 0.135446i |
(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 | 420.2.w.a.83.4 | yes | 8 | |
3.2 | odd | 2 | 420.2.w.b.83.3 | yes | 8 | ||
4.3 | odd | 2 | 420.2.w.b.83.2 | yes | 8 | ||
5.2 | odd | 4 | inner | 420.2.w.a.167.3 | yes | 8 | |
7.6 | odd | 2 | inner | 420.2.w.a.83.1 | ✓ | 8 | |
12.11 | even | 2 | inner | 420.2.w.a.83.1 | ✓ | 8 | |
15.2 | even | 4 | 420.2.w.b.167.4 | yes | 8 | ||
20.7 | even | 4 | 420.2.w.b.167.1 | yes | 8 | ||
21.20 | even | 2 | 420.2.w.b.83.2 | yes | 8 | ||
28.27 | even | 2 | 420.2.w.b.83.3 | yes | 8 | ||
35.27 | even | 4 | inner | 420.2.w.a.167.2 | yes | 8 | |
60.47 | odd | 4 | inner | 420.2.w.a.167.2 | yes | 8 | |
84.83 | odd | 2 | CM | 420.2.w.a.83.4 | yes | 8 | |
105.62 | odd | 4 | 420.2.w.b.167.1 | yes | 8 | ||
140.27 | odd | 4 | 420.2.w.b.167.4 | yes | 8 | ||
420.167 | even | 4 | inner | 420.2.w.a.167.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.w.a.83.1 | ✓ | 8 | 7.6 | odd | 2 | inner | |
420.2.w.a.83.1 | ✓ | 8 | 12.11 | even | 2 | inner | |
420.2.w.a.83.4 | yes | 8 | 1.1 | even | 1 | trivial | |
420.2.w.a.83.4 | yes | 8 | 84.83 | odd | 2 | CM | |
420.2.w.a.167.2 | yes | 8 | 35.27 | even | 4 | inner | |
420.2.w.a.167.2 | yes | 8 | 60.47 | odd | 4 | inner | |
420.2.w.a.167.3 | yes | 8 | 5.2 | odd | 4 | inner | |
420.2.w.a.167.3 | yes | 8 | 420.167 | even | 4 | inner | |
420.2.w.b.83.2 | yes | 8 | 4.3 | odd | 2 | ||
420.2.w.b.83.2 | yes | 8 | 21.20 | even | 2 | ||
420.2.w.b.83.3 | yes | 8 | 3.2 | odd | 2 | ||
420.2.w.b.83.3 | yes | 8 | 28.27 | even | 2 | ||
420.2.w.b.167.1 | yes | 8 | 20.7 | even | 4 | ||
420.2.w.b.167.1 | yes | 8 | 105.62 | odd | 4 | ||
420.2.w.b.167.4 | yes | 8 | 15.2 | even | 4 | ||
420.2.w.b.167.4 | yes | 8 | 140.27 | odd | 4 |