Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(419,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.419");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.g (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: | \(3.68908857338\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 419.1 | ||
Root | \(-1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.419 |
Dual form | 462.2.g.b.419.3 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | −1.22474 | − | 1.22474i | −0.707107 | − | 0.707107i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −2.44949 | −1.09545 | −0.547723 | − | 0.836660i | \(-0.684505\pi\) | ||||
−0.547723 | + | 0.836660i | \(0.684505\pi\) | |||||||
\(6\) | −1.22474 | + | 1.22474i | −0.500000 | + | 0.500000i | ||||
\(7\) | −1.00000 | − | 2.44949i | −0.377964 | − | 0.925820i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 3.00000i | 1.00000i | ||||||||
\(10\) | 2.44949i | 0.774597i | ||||||||
\(11\) | 1.00000i | 0.301511i | ||||||||
\(12\) | 1.22474 | + | 1.22474i | 0.353553 | + | 0.353553i | ||||
\(13\) | − | 2.44949i | − | 0.679366i | −0.940540 | − | 0.339683i | \(-0.889680\pi\) | ||
0.940540 | − | 0.339683i | \(-0.110320\pi\) | |||||||
\(14\) | −2.44949 | + | 1.00000i | −0.654654 | + | 0.267261i | ||||
\(15\) | 3.00000 | + | 3.00000i | 0.774597 | + | 0.774597i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 3.00000 | 0.707107 | ||||||||
\(19\) | 7.34847i | 1.68585i | 0.538028 | + | 0.842927i | \(0.319170\pi\) | ||||
−0.538028 | + | 0.842927i | \(0.680830\pi\) | |||||||
\(20\) | 2.44949 | 0.547723 | ||||||||
\(21\) | −1.77526 | + | 4.22474i | −0.387392 | + | 0.921915i | ||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 6.00000i | 1.25109i | 0.780189 | + | 0.625543i | \(0.215123\pi\) | ||||
−0.780189 | + | 0.625543i | \(0.784877\pi\) | |||||||
\(24\) | 1.22474 | − | 1.22474i | 0.250000 | − | 0.250000i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.44949 | −0.480384 | ||||||||
\(27\) | 3.67423 | − | 3.67423i | 0.707107 | − | 0.707107i | ||||
\(28\) | 1.00000 | + | 2.44949i | 0.188982 | + | 0.462910i | ||||
\(29\) | − | 6.00000i | − | 1.11417i | −0.830455 | − | 0.557086i | \(-0.811919\pi\) | ||
0.830455 | − | 0.557086i | \(-0.188081\pi\) | |||||||
\(30\) | 3.00000 | − | 3.00000i | 0.547723 | − | 0.547723i | ||||
\(31\) | 4.89898i | 0.879883i | 0.898027 | + | 0.439941i | \(0.145001\pi\) | ||||
−0.898027 | + | 0.439941i | \(0.854999\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 1.22474 | − | 1.22474i | 0.213201 | − | 0.213201i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.44949 | + | 6.00000i | 0.414039 | + | 1.01419i | ||||
\(36\) | − | 3.00000i | − | 0.500000i | ||||||
\(37\) | 10.0000 | 1.64399 | 0.821995 | − | 0.569495i | \(-0.192861\pi\) | ||||
0.821995 | + | 0.569495i | \(0.192861\pi\) | |||||||
\(38\) | 7.34847 | 1.19208 | ||||||||
\(39\) | −3.00000 | + | 3.00000i | −0.480384 | + | 0.480384i | ||||
\(40\) | − | 2.44949i | − | 0.387298i | ||||||
\(41\) | −9.79796 | −1.53018 | −0.765092 | − | 0.643921i | \(-0.777307\pi\) | ||||
−0.765092 | + | 0.643921i | \(0.777307\pi\) | |||||||
\(42\) | 4.22474 | + | 1.77526i | 0.651892 | + | 0.273928i | ||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | − | 1.00000i | − | 0.150756i | ||||||
\(45\) | − | 7.34847i | − | 1.09545i | ||||||
\(46\) | 6.00000 | 0.884652 | ||||||||
\(47\) | −9.79796 | −1.42918 | −0.714590 | − | 0.699544i | \(-0.753387\pi\) | ||||
−0.714590 | + | 0.699544i | \(0.753387\pi\) | |||||||
\(48\) | −1.22474 | − | 1.22474i | −0.176777 | − | 0.176777i | ||||
\(49\) | −5.00000 | + | 4.89898i | −0.714286 | + | 0.699854i | ||||
\(50\) | − | 1.00000i | − | 0.141421i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.44949i | 0.339683i | ||||||||
\(53\) | − | 6.00000i | − | 0.824163i | −0.911147 | − | 0.412082i | \(-0.864802\pi\) | ||
0.911147 | − | 0.412082i | \(-0.135198\pi\) | |||||||
\(54\) | −3.67423 | − | 3.67423i | −0.500000 | − | 0.500000i | ||||
\(55\) | − | 2.44949i | − | 0.330289i | ||||||
\(56\) | 2.44949 | − | 1.00000i | 0.327327 | − | 0.133631i | ||||
\(57\) | 9.00000 | − | 9.00000i | 1.19208 | − | 1.19208i | ||||
\(58\) | −6.00000 | −0.787839 | ||||||||
\(59\) | 2.44949 | 0.318896 | 0.159448 | − | 0.987206i | \(-0.449029\pi\) | ||||
0.159448 | + | 0.987206i | \(0.449029\pi\) | |||||||
\(60\) | −3.00000 | − | 3.00000i | −0.387298 | − | 0.387298i | ||||
\(61\) | 7.34847i | 0.940875i | 0.882433 | + | 0.470438i | \(0.155904\pi\) | ||||
−0.882433 | + | 0.470438i | \(0.844096\pi\) | |||||||
\(62\) | 4.89898 | 0.622171 | ||||||||
\(63\) | 7.34847 | − | 3.00000i | 0.925820 | − | 0.377964i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 6.00000i | 0.744208i | ||||||||
\(66\) | −1.22474 | − | 1.22474i | −0.150756 | − | 0.150756i | ||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.34847 | − | 7.34847i | 0.884652 | − | 0.884652i | ||||
\(70\) | 6.00000 | − | 2.44949i | 0.717137 | − | 0.292770i | ||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | −3.00000 | −0.353553 | ||||||||
\(73\) | 4.89898i | 0.573382i | 0.958023 | + | 0.286691i | \(0.0925553\pi\) | ||||
−0.958023 | + | 0.286691i | \(0.907445\pi\) | |||||||
\(74\) | − | 10.0000i | − | 1.16248i | ||||||
\(75\) | −1.22474 | − | 1.22474i | −0.141421 | − | 0.141421i | ||||
\(76\) | − | 7.34847i | − | 0.842927i | ||||||
\(77\) | 2.44949 | − | 1.00000i | 0.279145 | − | 0.113961i | ||||
\(78\) | 3.00000 | + | 3.00000i | 0.339683 | + | 0.339683i | ||||
\(79\) | −10.0000 | −1.12509 | −0.562544 | − | 0.826767i | \(-0.690177\pi\) | ||||
−0.562544 | + | 0.826767i | \(0.690177\pi\) | |||||||
\(80\) | −2.44949 | −0.273861 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 9.79796i | 1.08200i | ||||||||
\(83\) | 2.44949 | 0.268866 | 0.134433 | − | 0.990923i | \(-0.457079\pi\) | ||||
0.134433 | + | 0.990923i | \(0.457079\pi\) | |||||||
\(84\) | 1.77526 | − | 4.22474i | 0.193696 | − | 0.460957i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.00000i | 0.862662i | ||||||||
\(87\) | −7.34847 | + | 7.34847i | −0.787839 | + | 0.787839i | ||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −9.79796 | −1.03858 | −0.519291 | − | 0.854598i | \(-0.673804\pi\) | ||||
−0.519291 | + | 0.854598i | \(0.673804\pi\) | |||||||
\(90\) | −7.34847 | −0.774597 | ||||||||
\(91\) | −6.00000 | + | 2.44949i | −0.628971 | + | 0.256776i | ||||
\(92\) | − | 6.00000i | − | 0.625543i | ||||||
\(93\) | 6.00000 | − | 6.00000i | 0.622171 | − | 0.622171i | ||||
\(94\) | 9.79796i | 1.01058i | ||||||||
\(95\) | − | 18.0000i | − | 1.84676i | ||||||
\(96\) | −1.22474 | + | 1.22474i | −0.125000 | + | 0.125000i | ||||
\(97\) | − | 4.89898i | − | 0.497416i | −0.968579 | − | 0.248708i | \(-0.919994\pi\) | ||
0.968579 | − | 0.248708i | \(-0.0800060\pi\) | |||||||
\(98\) | 4.89898 | + | 5.00000i | 0.494872 | + | 0.505076i | ||||
\(99\) | −3.00000 | −0.301511 | ||||||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | 2.44949 | 0.243733 | 0.121867 | − | 0.992546i | \(-0.461112\pi\) | ||||
0.121867 | + | 0.992546i | \(0.461112\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.89898i | 0.482711i | 0.970437 | + | 0.241355i | \(0.0775919\pi\) | ||||
−0.970437 | + | 0.241355i | \(0.922408\pi\) | |||||||
\(104\) | 2.44949 | 0.240192 | ||||||||
\(105\) | 4.34847 | − | 10.3485i | 0.424367 | − | 1.00991i | ||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | −3.67423 | + | 3.67423i | −0.353553 | + | 0.353553i | ||||
\(109\) | −14.0000 | −1.34096 | −0.670478 | − | 0.741929i | \(-0.733911\pi\) | ||||
−0.670478 | + | 0.741929i | \(0.733911\pi\) | |||||||
\(110\) | −2.44949 | −0.233550 | ||||||||
\(111\) | −12.2474 | − | 12.2474i | −1.16248 | − | 1.16248i | ||||
\(112\) | −1.00000 | − | 2.44949i | −0.0944911 | − | 0.231455i | ||||
\(113\) | 18.0000i | 1.69330i | 0.532152 | + | 0.846649i | \(0.321383\pi\) | ||||
−0.532152 | + | 0.846649i | \(0.678617\pi\) | |||||||
\(114\) | −9.00000 | − | 9.00000i | −0.842927 | − | 0.842927i | ||||
\(115\) | − | 14.6969i | − | 1.37050i | ||||||
\(116\) | 6.00000i | 0.557086i | ||||||||
\(117\) | 7.34847 | 0.679366 | ||||||||
\(118\) | − | 2.44949i | − | 0.225494i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.00000 | + | 3.00000i | −0.273861 | + | 0.273861i | ||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 7.34847 | 0.665299 | ||||||||
\(123\) | 12.0000 | + | 12.0000i | 1.08200 | + | 1.08200i | ||||
\(124\) | − | 4.89898i | − | 0.439941i | ||||||
\(125\) | 9.79796 | 0.876356 | ||||||||
\(126\) | −3.00000 | − | 7.34847i | −0.267261 | − | 0.654654i | ||||
\(127\) | −16.0000 | −1.41977 | −0.709885 | − | 0.704317i | \(-0.751253\pi\) | ||||
−0.709885 | + | 0.704317i | \(0.751253\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 9.79796 | + | 9.79796i | 0.862662 | + | 0.862662i | ||||
\(130\) | 6.00000 | 0.526235 | ||||||||
\(131\) | −2.44949 | −0.214013 | −0.107006 | − | 0.994258i | \(-0.534127\pi\) | ||||
−0.107006 | + | 0.994258i | \(0.534127\pi\) | |||||||
\(132\) | −1.22474 | + | 1.22474i | −0.106600 | + | 0.106600i | ||||
\(133\) | 18.0000 | − | 7.34847i | 1.56080 | − | 0.637193i | ||||
\(134\) | 4.00000i | 0.345547i | ||||||||
\(135\) | −9.00000 | + | 9.00000i | −0.774597 | + | 0.774597i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 12.0000i | − | 1.02523i | −0.858619 | − | 0.512615i | \(-0.828677\pi\) | ||
0.858619 | − | 0.512615i | \(-0.171323\pi\) | |||||||
\(138\) | −7.34847 | − | 7.34847i | −0.625543 | − | 0.625543i | ||||
\(139\) | − | 12.2474i | − | 1.03882i | −0.854527 | − | 0.519408i | \(-0.826153\pi\) | ||
0.854527 | − | 0.519408i | \(-0.173847\pi\) | |||||||
\(140\) | −2.44949 | − | 6.00000i | −0.207020 | − | 0.507093i | ||||
\(141\) | 12.0000 | + | 12.0000i | 1.01058 | + | 1.01058i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.44949 | 0.204837 | ||||||||
\(144\) | 3.00000i | 0.250000i | ||||||||
\(145\) | 14.6969i | 1.22051i | ||||||||
\(146\) | 4.89898 | 0.405442 | ||||||||
\(147\) | 12.1237 | + | 0.123724i | 0.999948 | + | 0.0102046i | ||||
\(148\) | −10.0000 | −0.821995 | ||||||||
\(149\) | − | 18.0000i | − | 1.47462i | −0.675556 | − | 0.737309i | \(-0.736096\pi\) | ||
0.675556 | − | 0.737309i | \(-0.263904\pi\) | |||||||
\(150\) | −1.22474 | + | 1.22474i | −0.100000 | + | 0.100000i | ||||
\(151\) | 16.0000 | 1.30206 | 0.651031 | − | 0.759051i | \(-0.274337\pi\) | ||||
0.651031 | + | 0.759051i | \(0.274337\pi\) | |||||||
\(152\) | −7.34847 | −0.596040 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.00000 | − | 2.44949i | −0.0805823 | − | 0.197386i | ||||
\(155\) | − | 12.0000i | − | 0.963863i | ||||||
\(156\) | 3.00000 | − | 3.00000i | 0.240192 | − | 0.240192i | ||||
\(157\) | − | 12.2474i | − | 0.977453i | −0.872437 | − | 0.488726i | \(-0.837462\pi\) | ||
0.872437 | − | 0.488726i | \(-0.162538\pi\) | |||||||
\(158\) | 10.0000i | 0.795557i | ||||||||
\(159\) | −7.34847 | + | 7.34847i | −0.582772 | + | 0.582772i | ||||
\(160\) | 2.44949i | 0.193649i | ||||||||
\(161\) | 14.6969 | − | 6.00000i | 1.15828 | − | 0.472866i | ||||
\(162\) | 9.00000i | 0.707107i | ||||||||
\(163\) | −16.0000 | −1.25322 | −0.626608 | − | 0.779334i | \(-0.715557\pi\) | ||||
−0.626608 | + | 0.779334i | \(0.715557\pi\) | |||||||
\(164\) | 9.79796 | 0.765092 | ||||||||
\(165\) | −3.00000 | + | 3.00000i | −0.233550 | + | 0.233550i | ||||
\(166\) | − | 2.44949i | − | 0.190117i | ||||||
\(167\) | 14.6969 | 1.13728 | 0.568642 | − | 0.822585i | \(-0.307469\pi\) | ||||
0.568642 | + | 0.822585i | \(0.307469\pi\) | |||||||
\(168\) | −4.22474 | − | 1.77526i | −0.325946 | − | 0.136964i | ||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −22.0454 | −1.68585 | ||||||||
\(172\) | 8.00000 | 0.609994 | ||||||||
\(173\) | 2.44949 | 0.186231 | 0.0931156 | − | 0.995655i | \(-0.470317\pi\) | ||||
0.0931156 | + | 0.995655i | \(0.470317\pi\) | |||||||
\(174\) | 7.34847 | + | 7.34847i | 0.557086 | + | 0.557086i | ||||
\(175\) | −1.00000 | − | 2.44949i | −0.0755929 | − | 0.185164i | ||||
\(176\) | 1.00000i | 0.0753778i | ||||||||
\(177\) | −3.00000 | − | 3.00000i | −0.225494 | − | 0.225494i | ||||
\(178\) | 9.79796i | 0.734388i | ||||||||
\(179\) | 24.0000i | 1.79384i | 0.442189 | + | 0.896922i | \(0.354202\pi\) | ||||
−0.442189 | + | 0.896922i | \(0.645798\pi\) | |||||||
\(180\) | 7.34847i | 0.547723i | ||||||||
\(181\) | 17.1464i | 1.27448i | 0.770664 | + | 0.637242i | \(0.219925\pi\) | ||||
−0.770664 | + | 0.637242i | \(0.780075\pi\) | |||||||
\(182\) | 2.44949 | + | 6.00000i | 0.181568 | + | 0.444750i | ||||
\(183\) | 9.00000 | − | 9.00000i | 0.665299 | − | 0.665299i | ||||
\(184\) | −6.00000 | −0.442326 | ||||||||
\(185\) | −24.4949 | −1.80090 | ||||||||
\(186\) | −6.00000 | − | 6.00000i | −0.439941 | − | 0.439941i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 9.79796 | 0.714590 | ||||||||
\(189\) | −12.6742 | − | 5.32577i | −0.921915 | − | 0.387392i | ||||
\(190\) | −18.0000 | −1.30586 | ||||||||
\(191\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(192\) | 1.22474 | + | 1.22474i | 0.0883883 | + | 0.0883883i | ||||
\(193\) | 16.0000 | 1.15171 | 0.575853 | − | 0.817554i | \(-0.304670\pi\) | ||||
0.575853 | + | 0.817554i | \(0.304670\pi\) | |||||||
\(194\) | −4.89898 | −0.351726 | ||||||||
\(195\) | 7.34847 | − | 7.34847i | 0.526235 | − | 0.526235i | ||||
\(196\) | 5.00000 | − | 4.89898i | 0.357143 | − | 0.349927i | ||||
\(197\) | − | 6.00000i | − | 0.427482i | −0.976890 | − | 0.213741i | \(-0.931435\pi\) | ||
0.976890 | − | 0.213741i | \(-0.0685649\pi\) | |||||||
\(198\) | 3.00000i | 0.213201i | ||||||||
\(199\) | 14.6969i | 1.04184i | 0.853606 | + | 0.520919i | \(0.174411\pi\) | ||||
−0.853606 | + | 0.520919i | \(0.825589\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | 4.89898 | + | 4.89898i | 0.345547 | + | 0.345547i | ||||
\(202\) | − | 2.44949i | − | 0.172345i | ||||||
\(203\) | −14.6969 | + | 6.00000i | −1.03152 | + | 0.421117i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 24.0000 | 1.67623 | ||||||||
\(206\) | 4.89898 | 0.341328 | ||||||||
\(207\) | −18.0000 | −1.25109 | ||||||||
\(208\) | − | 2.44949i | − | 0.169842i | ||||||
\(209\) | −7.34847 | −0.508304 | ||||||||
\(210\) | −10.3485 | − | 4.34847i | −0.714112 | − | 0.300073i | ||||
\(211\) | 16.0000 | 1.10149 | 0.550743 | − | 0.834675i | \(-0.314345\pi\) | ||||
0.550743 | + | 0.834675i | \(0.314345\pi\) | |||||||
\(212\) | 6.00000i | 0.412082i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 19.5959 | 1.33643 | ||||||||
\(216\) | 3.67423 | + | 3.67423i | 0.250000 | + | 0.250000i | ||||
\(217\) | 12.0000 | − | 4.89898i | 0.814613 | − | 0.332564i | ||||
\(218\) | 14.0000i | 0.948200i | ||||||||
\(219\) | 6.00000 | − | 6.00000i | 0.405442 | − | 0.405442i | ||||
\(220\) | 2.44949i | 0.165145i | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −12.2474 | + | 12.2474i | −0.821995 | + | 0.821995i | ||||
\(223\) | 9.79796i | 0.656120i | 0.944657 | + | 0.328060i | \(0.106395\pi\) | ||||
−0.944657 | + | 0.328060i | \(0.893605\pi\) | |||||||
\(224\) | −2.44949 | + | 1.00000i | −0.163663 | + | 0.0668153i | ||||
\(225\) | 3.00000i | 0.200000i | ||||||||
\(226\) | 18.0000 | 1.19734 | ||||||||
\(227\) | −17.1464 | −1.13805 | −0.569024 | − | 0.822321i | \(-0.692679\pi\) | ||||
−0.569024 | + | 0.822321i | \(0.692679\pi\) | |||||||
\(228\) | −9.00000 | + | 9.00000i | −0.596040 | + | 0.596040i | ||||
\(229\) | − | 7.34847i | − | 0.485601i | −0.970076 | − | 0.242800i | \(-0.921934\pi\) | ||
0.970076 | − | 0.242800i | \(-0.0780660\pi\) | |||||||
\(230\) | −14.6969 | −0.969087 | ||||||||
\(231\) | −4.22474 | − | 1.77526i | −0.277968 | − | 0.116803i | ||||
\(232\) | 6.00000 | 0.393919 | ||||||||
\(233\) | − | 12.0000i | − | 0.786146i | −0.919507 | − | 0.393073i | \(-0.871412\pi\) | ||
0.919507 | − | 0.393073i | \(-0.128588\pi\) | |||||||
\(234\) | − | 7.34847i | − | 0.480384i | ||||||
\(235\) | 24.0000 | 1.56559 | ||||||||
\(236\) | −2.44949 | −0.159448 | ||||||||
\(237\) | 12.2474 | + | 12.2474i | 0.795557 | + | 0.795557i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.00000i | 0.388108i | 0.980991 | + | 0.194054i | \(0.0621637\pi\) | ||||
−0.980991 | + | 0.194054i | \(0.937836\pi\) | |||||||
\(240\) | 3.00000 | + | 3.00000i | 0.193649 | + | 0.193649i | ||||
\(241\) | − | 19.5959i | − | 1.26228i | −0.775667 | − | 0.631142i | \(-0.782587\pi\) | ||
0.775667 | − | 0.631142i | \(-0.217413\pi\) | |||||||
\(242\) | 1.00000i | 0.0642824i | ||||||||
\(243\) | 11.0227 | + | 11.0227i | 0.707107 | + | 0.707107i | ||||
\(244\) | − | 7.34847i | − | 0.470438i | ||||||
\(245\) | 12.2474 | − | 12.0000i | 0.782461 | − | 0.766652i | ||||
\(246\) | 12.0000 | − | 12.0000i | 0.765092 | − | 0.765092i | ||||
\(247\) | 18.0000 | 1.14531 | ||||||||
\(248\) | −4.89898 | −0.311086 | ||||||||
\(249\) | −3.00000 | − | 3.00000i | −0.190117 | − | 0.190117i | ||||
\(250\) | − | 9.79796i | − | 0.619677i | ||||||
\(251\) | −12.2474 | −0.773052 | −0.386526 | − | 0.922278i | \(-0.626325\pi\) | ||||
−0.386526 | + | 0.922278i | \(0.626325\pi\) | |||||||
\(252\) | −7.34847 | + | 3.00000i | −0.462910 | + | 0.188982i | ||||
\(253\) | −6.00000 | −0.377217 | ||||||||
\(254\) | 16.0000i | 1.00393i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −19.5959 | −1.22236 | −0.611180 | − | 0.791492i | \(-0.709305\pi\) | ||||
−0.611180 | + | 0.791492i | \(0.709305\pi\) | |||||||
\(258\) | 9.79796 | − | 9.79796i | 0.609994 | − | 0.609994i | ||||
\(259\) | −10.0000 | − | 24.4949i | −0.621370 | − | 1.52204i | ||||
\(260\) | − | 6.00000i | − | 0.372104i | ||||||
\(261\) | 18.0000 | 1.11417 | ||||||||
\(262\) | 2.44949i | 0.151330i | ||||||||
\(263\) | 24.0000i | 1.47990i | 0.672660 | + | 0.739952i | \(0.265152\pi\) | ||||
−0.672660 | + | 0.739952i | \(0.734848\pi\) | |||||||
\(264\) | 1.22474 | + | 1.22474i | 0.0753778 | + | 0.0753778i | ||||
\(265\) | 14.6969i | 0.902826i | ||||||||
\(266\) | −7.34847 | − | 18.0000i | −0.450564 | − | 1.10365i | ||||
\(267\) | 12.0000 | + | 12.0000i | 0.734388 | + | 0.734388i | ||||
\(268\) | 4.00000 | 0.244339 | ||||||||
\(269\) | −2.44949 | −0.149348 | −0.0746740 | − | 0.997208i | \(-0.523792\pi\) | ||||
−0.0746740 | + | 0.997208i | \(0.523792\pi\) | |||||||
\(270\) | 9.00000 | + | 9.00000i | 0.547723 | + | 0.547723i | ||||
\(271\) | 4.89898i | 0.297592i | 0.988868 | + | 0.148796i | \(0.0475397\pi\) | ||||
−0.988868 | + | 0.148796i | \(0.952460\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.3485 | + | 4.34847i | 0.626318 | + | 0.263181i | ||||
\(274\) | −12.0000 | −0.724947 | ||||||||
\(275\) | 1.00000i | 0.0603023i | ||||||||
\(276\) | −7.34847 | + | 7.34847i | −0.442326 | + | 0.442326i | ||||
\(277\) | 2.00000 | 0.120168 | 0.0600842 | − | 0.998193i | \(-0.480863\pi\) | ||||
0.0600842 | + | 0.998193i | \(0.480863\pi\) | |||||||
\(278\) | −12.2474 | −0.734553 | ||||||||
\(279\) | −14.6969 | −0.879883 | ||||||||
\(280\) | −6.00000 | + | 2.44949i | −0.358569 | + | 0.146385i | ||||
\(281\) | 12.0000i | 0.715860i | 0.933748 | + | 0.357930i | \(0.116517\pi\) | ||||
−0.933748 | + | 0.357930i | \(0.883483\pi\) | |||||||
\(282\) | 12.0000 | − | 12.0000i | 0.714590 | − | 0.714590i | ||||
\(283\) | − | 2.44949i | − | 0.145607i | −0.997346 | − | 0.0728035i | \(-0.976805\pi\) | ||
0.997346 | − | 0.0728035i | \(-0.0231946\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −22.0454 | + | 22.0454i | −1.30586 | + | 1.30586i | ||||
\(286\) | − | 2.44949i | − | 0.144841i | ||||||
\(287\) | 9.79796 | + | 24.0000i | 0.578355 | + | 1.41668i | ||||
\(288\) | 3.00000 | 0.176777 | ||||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 14.6969 | 0.863034 | ||||||||
\(291\) | −6.00000 | + | 6.00000i | −0.351726 | + | 0.351726i | ||||
\(292\) | − | 4.89898i | − | 0.286691i | ||||||
\(293\) | 17.1464 | 1.00171 | 0.500853 | − | 0.865533i | \(-0.333020\pi\) | ||||
0.500853 | + | 0.865533i | \(0.333020\pi\) | |||||||
\(294\) | 0.123724 | − | 12.1237i | 0.00721575 | − | 0.707070i | ||||
\(295\) | −6.00000 | −0.349334 | ||||||||
\(296\) | 10.0000i | 0.581238i | ||||||||
\(297\) | 3.67423 | + | 3.67423i | 0.213201 | + | 0.213201i | ||||
\(298\) | −18.0000 | −1.04271 | ||||||||
\(299\) | 14.6969 | 0.849946 | ||||||||
\(300\) | 1.22474 | + | 1.22474i | 0.0707107 | + | 0.0707107i | ||||
\(301\) | 8.00000 | + | 19.5959i | 0.461112 | + | 1.12949i | ||||
\(302\) | − | 16.0000i | − | 0.920697i | ||||||
\(303\) | −3.00000 | − | 3.00000i | −0.172345 | − | 0.172345i | ||||
\(304\) | 7.34847i | 0.421464i | ||||||||
\(305\) | − | 18.0000i | − | 1.03068i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 31.8434i | − | 1.81740i | −0.417453 | − | 0.908698i | \(-0.637077\pi\) | ||
0.417453 | − | 0.908698i | \(-0.362923\pi\) | |||||||
\(308\) | −2.44949 | + | 1.00000i | −0.139573 | + | 0.0569803i | ||||
\(309\) | 6.00000 | − | 6.00000i | 0.341328 | − | 0.341328i | ||||
\(310\) | −12.0000 | −0.681554 | ||||||||
\(311\) | −14.6969 | −0.833387 | −0.416693 | − | 0.909047i | \(-0.636811\pi\) | ||||
−0.416693 | + | 0.909047i | \(0.636811\pi\) | |||||||
\(312\) | −3.00000 | − | 3.00000i | −0.169842 | − | 0.169842i | ||||
\(313\) | 4.89898i | 0.276907i | 0.990369 | + | 0.138453i | \(0.0442131\pi\) | ||||
−0.990369 | + | 0.138453i | \(0.955787\pi\) | |||||||
\(314\) | −12.2474 | −0.691164 | ||||||||
\(315\) | −18.0000 | + | 7.34847i | −1.01419 | + | 0.414039i | ||||
\(316\) | 10.0000 | 0.562544 | ||||||||
\(317\) | − | 6.00000i | − | 0.336994i | −0.985702 | − | 0.168497i | \(-0.946109\pi\) | ||
0.985702 | − | 0.168497i | \(-0.0538913\pi\) | |||||||
\(318\) | 7.34847 | + | 7.34847i | 0.412082 | + | 0.412082i | ||||
\(319\) | 6.00000 | 0.335936 | ||||||||
\(320\) | 2.44949 | 0.136931 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.00000 | − | 14.6969i | −0.334367 | − | 0.819028i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 9.00000 | 0.500000 | ||||||||
\(325\) | − | 2.44949i | − | 0.135873i | ||||||
\(326\) | 16.0000i | 0.886158i | ||||||||
\(327\) | 17.1464 | + | 17.1464i | 0.948200 | + | 0.948200i | ||||
\(328\) | − | 9.79796i | − | 0.541002i | ||||||
\(329\) | 9.79796 | + | 24.0000i | 0.540179 | + | 1.32316i | ||||
\(330\) | 3.00000 | + | 3.00000i | 0.165145 | + | 0.165145i | ||||
\(331\) | −20.0000 | −1.09930 | −0.549650 | − | 0.835395i | \(-0.685239\pi\) | ||||
−0.549650 | + | 0.835395i | \(0.685239\pi\) | |||||||
\(332\) | −2.44949 | −0.134433 | ||||||||
\(333\) | 30.0000i | 1.64399i | ||||||||
\(334\) | − | 14.6969i | − | 0.804181i | ||||||
\(335\) | 9.79796 | 0.535320 | ||||||||
\(336\) | −1.77526 | + | 4.22474i | −0.0968481 | + | 0.230479i | ||||
\(337\) | −20.0000 | −1.08947 | −0.544735 | − | 0.838608i | \(-0.683370\pi\) | ||||
−0.544735 | + | 0.838608i | \(0.683370\pi\) | |||||||
\(338\) | − | 7.00000i | − | 0.380750i | ||||||
\(339\) | 22.0454 | − | 22.0454i | 1.19734 | − | 1.19734i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.89898 | −0.265295 | ||||||||
\(342\) | 22.0454i | 1.19208i | ||||||||
\(343\) | 17.0000 | + | 7.34847i | 0.917914 | + | 0.396780i | ||||
\(344\) | − | 8.00000i | − | 0.431331i | ||||||
\(345\) | −18.0000 | + | 18.0000i | −0.969087 | + | 0.969087i | ||||
\(346\) | − | 2.44949i | − | 0.131685i | ||||||
\(347\) | − | 12.0000i | − | 0.644194i | −0.946707 | − | 0.322097i | \(-0.895612\pi\) | ||
0.946707 | − | 0.322097i | \(-0.104388\pi\) | |||||||
\(348\) | 7.34847 | − | 7.34847i | 0.393919 | − | 0.393919i | ||||
\(349\) | − | 7.34847i | − | 0.393355i | −0.980468 | − | 0.196677i | \(-0.936985\pi\) | ||
0.980468 | − | 0.196677i | \(-0.0630151\pi\) | |||||||
\(350\) | −2.44949 | + | 1.00000i | −0.130931 | + | 0.0534522i | ||||
\(351\) | −9.00000 | − | 9.00000i | −0.480384 | − | 0.480384i | ||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −19.5959 | −1.04299 | −0.521493 | − | 0.853256i | \(-0.674625\pi\) | ||||
−0.521493 | + | 0.853256i | \(0.674625\pi\) | |||||||
\(354\) | −3.00000 | + | 3.00000i | −0.159448 | + | 0.159448i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 9.79796 | 0.519291 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 24.0000 | 1.26844 | ||||||||
\(359\) | − | 18.0000i | − | 0.950004i | −0.879985 | − | 0.475002i | \(-0.842447\pi\) | ||
0.879985 | − | 0.475002i | \(-0.157553\pi\) | |||||||
\(360\) | 7.34847 | 0.387298 | ||||||||
\(361\) | −35.0000 | −1.84211 | ||||||||
\(362\) | 17.1464 | 0.901196 | ||||||||
\(363\) | 1.22474 | + | 1.22474i | 0.0642824 | + | 0.0642824i | ||||
\(364\) | 6.00000 | − | 2.44949i | 0.314485 | − | 0.128388i | ||||
\(365\) | − | 12.0000i | − | 0.628109i | ||||||
\(366\) | −9.00000 | − | 9.00000i | −0.470438 | − | 0.470438i | ||||
\(367\) | − | 9.79796i | − | 0.511449i | −0.966750 | − | 0.255725i | \(-0.917686\pi\) | ||
0.966750 | − | 0.255725i | \(-0.0823140\pi\) | |||||||
\(368\) | 6.00000i | 0.312772i | ||||||||
\(369\) | − | 29.3939i | − | 1.53018i | ||||||
\(370\) | 24.4949i | 1.27343i | ||||||||
\(371\) | −14.6969 | + | 6.00000i | −0.763027 | + | 0.311504i | ||||
\(372\) | −6.00000 | + | 6.00000i | −0.311086 | + | 0.311086i | ||||
\(373\) | 26.0000 | 1.34623 | 0.673114 | − | 0.739538i | \(-0.264956\pi\) | ||||
0.673114 | + | 0.739538i | \(0.264956\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.0000 | − | 12.0000i | −0.619677 | − | 0.619677i | ||||
\(376\) | − | 9.79796i | − | 0.505291i | ||||||
\(377\) | −14.6969 | −0.756931 | ||||||||
\(378\) | −5.32577 | + | 12.6742i | −0.273928 | + | 0.651892i | ||||
\(379\) | −20.0000 | −1.02733 | −0.513665 | − | 0.857991i | \(-0.671713\pi\) | ||||
−0.513665 | + | 0.857991i | \(0.671713\pi\) | |||||||
\(380\) | 18.0000i | 0.923381i | ||||||||
\(381\) | 19.5959 | + | 19.5959i | 1.00393 | + | 1.00393i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | 1.22474 | − | 1.22474i | 0.0625000 | − | 0.0625000i | ||||
\(385\) | −6.00000 | + | 2.44949i | −0.305788 | + | 0.124838i | ||||
\(386\) | − | 16.0000i | − | 0.814379i | ||||||
\(387\) | − | 24.0000i | − | 1.21999i | ||||||
\(388\) | 4.89898i | 0.248708i | ||||||||
\(389\) | − | 30.0000i | − | 1.52106i | −0.649303 | − | 0.760530i | \(-0.724939\pi\) | ||
0.649303 | − | 0.760530i | \(-0.275061\pi\) | |||||||
\(390\) | −7.34847 | − | 7.34847i | −0.372104 | − | 0.372104i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −4.89898 | − | 5.00000i | −0.247436 | − | 0.252538i | ||||
\(393\) | 3.00000 | + | 3.00000i | 0.151330 | + | 0.151330i | ||||
\(394\) | −6.00000 | −0.302276 | ||||||||
\(395\) | 24.4949 | 1.23247 | ||||||||
\(396\) | 3.00000 | 0.150756 | ||||||||
\(397\) | 26.9444i | 1.35230i | 0.736764 | + | 0.676150i | \(0.236353\pi\) | ||||
−0.736764 | + | 0.676150i | \(0.763647\pi\) | |||||||
\(398\) | 14.6969 | 0.736691 | ||||||||
\(399\) | −31.0454 | − | 13.0454i | −1.55421 | − | 0.653087i | ||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 18.0000i | 0.898877i | 0.893311 | + | 0.449439i | \(0.148376\pi\) | ||||
−0.893311 | + | 0.449439i | \(0.851624\pi\) | |||||||
\(402\) | 4.89898 | − | 4.89898i | 0.244339 | − | 0.244339i | ||||
\(403\) | 12.0000 | 0.597763 | ||||||||
\(404\) | −2.44949 | −0.121867 | ||||||||
\(405\) | 22.0454 | 1.09545 | ||||||||
\(406\) | 6.00000 | + | 14.6969i | 0.297775 | + | 0.729397i | ||||
\(407\) | 10.0000i | 0.495682i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 29.3939i | − | 1.45343i | −0.686937 | − | 0.726717i | \(-0.741045\pi\) | ||
0.686937 | − | 0.726717i | \(-0.258955\pi\) | |||||||
\(410\) | − | 24.0000i | − | 1.18528i | ||||||
\(411\) | −14.6969 | + | 14.6969i | −0.724947 | + | 0.724947i | ||||
\(412\) | − | 4.89898i | − | 0.241355i | ||||||
\(413\) | −2.44949 | − | 6.00000i | −0.120532 | − | 0.295241i | ||||
\(414\) | 18.0000i | 0.884652i | ||||||||
\(415\) | −6.00000 | −0.294528 | ||||||||
\(416\) | −2.44949 | −0.120096 | ||||||||
\(417\) | −15.0000 | + | 15.0000i | −0.734553 | + | 0.734553i | ||||
\(418\) | 7.34847i | 0.359425i | ||||||||
\(419\) | 26.9444 | 1.31632 | 0.658160 | − | 0.752878i | \(-0.271335\pi\) | ||||
0.658160 | + | 0.752878i | \(0.271335\pi\) | |||||||
\(420\) | −4.34847 | + | 10.3485i | −0.212184 | + | 0.504954i | ||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | − | 16.0000i | − | 0.778868i | ||||||
\(423\) | − | 29.3939i | − | 1.42918i | ||||||
\(424\) | 6.00000 | 0.291386 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.0000 | − | 7.34847i | 0.871081 | − | 0.355617i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.00000 | − | 3.00000i | −0.144841 | − | 0.144841i | ||||
\(430\) | − | 19.5959i | − | 0.944999i | ||||||
\(431\) | 18.0000i | 0.867029i | 0.901146 | + | 0.433515i | \(0.142727\pi\) | ||||
−0.901146 | + | 0.433515i | \(0.857273\pi\) | |||||||
\(432\) | 3.67423 | − | 3.67423i | 0.176777 | − | 0.176777i | ||||
\(433\) | − | 4.89898i | − | 0.235430i | −0.993047 | − | 0.117715i | \(-0.962443\pi\) | ||
0.993047 | − | 0.117715i | \(-0.0375569\pi\) | |||||||
\(434\) | −4.89898 | − | 12.0000i | −0.235159 | − | 0.576018i | ||||
\(435\) | 18.0000 | − | 18.0000i | 0.863034 | − | 0.863034i | ||||
\(436\) | 14.0000 | 0.670478 | ||||||||
\(437\) | −44.0908 | −2.10915 | ||||||||
\(438\) | −6.00000 | − | 6.00000i | −0.286691 | − | 0.286691i | ||||
\(439\) | − | 24.4949i | − | 1.16908i | −0.811366 | − | 0.584539i | \(-0.801275\pi\) | ||
0.811366 | − | 0.584539i | \(-0.198725\pi\) | |||||||
\(440\) | 2.44949 | 0.116775 | ||||||||
\(441\) | −14.6969 | − | 15.0000i | −0.699854 | − | 0.714286i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 12.0000i | − | 0.570137i | −0.958507 | − | 0.285069i | \(-0.907984\pi\) | ||
0.958507 | − | 0.285069i | \(-0.0920164\pi\) | |||||||
\(444\) | 12.2474 | + | 12.2474i | 0.581238 | + | 0.581238i | ||||
\(445\) | 24.0000 | 1.13771 | ||||||||
\(446\) | 9.79796 | 0.463947 | ||||||||
\(447\) | −22.0454 | + | 22.0454i | −1.04271 | + | 1.04271i | ||||
\(448\) | 1.00000 | + | 2.44949i | 0.0472456 | + | 0.115728i | ||||
\(449\) | − | 12.0000i | − | 0.566315i | −0.959073 | − | 0.283158i | \(-0.908618\pi\) | ||
0.959073 | − | 0.283158i | \(-0.0913819\pi\) | |||||||
\(450\) | 3.00000 | 0.141421 | ||||||||
\(451\) | − | 9.79796i | − | 0.461368i | ||||||
\(452\) | − | 18.0000i | − | 0.846649i | ||||||
\(453\) | −19.5959 | − | 19.5959i | −0.920697 | − | 0.920697i | ||||
\(454\) | 17.1464i | 0.804722i | ||||||||
\(455\) | 14.6969 | − | 6.00000i | 0.689003 | − | 0.281284i | ||||
\(456\) | 9.00000 | + | 9.00000i | 0.421464 | + | 0.421464i | ||||
\(457\) | −32.0000 | −1.49690 | −0.748448 | − | 0.663193i | \(-0.769201\pi\) | ||||
−0.748448 | + | 0.663193i | \(0.769201\pi\) | |||||||
\(458\) | −7.34847 | −0.343371 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 14.6969i | 0.685248i | ||||||||
\(461\) | −22.0454 | −1.02676 | −0.513378 | − | 0.858162i | \(-0.671606\pi\) | ||||
−0.513378 | + | 0.858162i | \(0.671606\pi\) | |||||||
\(462\) | −1.77526 | + | 4.22474i | −0.0825923 | + | 0.196553i | ||||
\(463\) | −22.0000 | −1.02243 | −0.511213 | − | 0.859454i | \(-0.670804\pi\) | ||||
−0.511213 | + | 0.859454i | \(0.670804\pi\) | |||||||
\(464\) | − | 6.00000i | − | 0.278543i | ||||||
\(465\) | −14.6969 | + | 14.6969i | −0.681554 | + | 0.681554i | ||||
\(466\) | −12.0000 | −0.555889 | ||||||||
\(467\) | 7.34847 | 0.340047 | 0.170023 | − | 0.985440i | \(-0.445616\pi\) | ||||
0.170023 | + | 0.985440i | \(0.445616\pi\) | |||||||
\(468\) | −7.34847 | −0.339683 | ||||||||
\(469\) | 4.00000 | + | 9.79796i | 0.184703 | + | 0.452428i | ||||
\(470\) | − | 24.0000i | − | 1.10704i | ||||||
\(471\) | −15.0000 | + | 15.0000i | −0.691164 | + | 0.691164i | ||||
\(472\) | 2.44949i | 0.112747i | ||||||||
\(473\) | − | 8.00000i | − | 0.367840i | ||||||
\(474\) | 12.2474 | − | 12.2474i | 0.562544 | − | 0.562544i | ||||
\(475\) | 7.34847i | 0.337171i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.0000 | 0.824163 | ||||||||
\(478\) | 6.00000 | 0.274434 | ||||||||
\(479\) | −4.89898 | −0.223840 | −0.111920 | − | 0.993717i | \(-0.535700\pi\) | ||||
−0.111920 | + | 0.993717i | \(0.535700\pi\) | |||||||
\(480\) | 3.00000 | − | 3.00000i | 0.136931 | − | 0.136931i | ||||
\(481\) | − | 24.4949i | − | 1.11687i | ||||||
\(482\) | −19.5959 | −0.892570 | ||||||||
\(483\) | −25.3485 | − | 10.6515i | −1.15340 | − | 0.484661i | ||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 12.0000i | 0.544892i | ||||||||
\(486\) | 11.0227 | − | 11.0227i | 0.500000 | − | 0.500000i | ||||
\(487\) | 16.0000 | 0.725029 | 0.362515 | − | 0.931978i | \(-0.381918\pi\) | ||||
0.362515 | + | 0.931978i | \(0.381918\pi\) | |||||||
\(488\) | −7.34847 | −0.332650 | ||||||||
\(489\) | 19.5959 | + | 19.5959i | 0.886158 | + | 0.886158i | ||||
\(490\) | −12.0000 | − | 12.2474i | −0.542105 | − | 0.553283i | ||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | −12.0000 | − | 12.0000i | −0.541002 | − | 0.541002i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | − | 18.0000i | − | 0.809858i | ||||||
\(495\) | 7.34847 | 0.330289 | ||||||||
\(496\) | 4.89898i | 0.219971i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −3.00000 | + | 3.00000i | −0.134433 | + | 0.134433i | ||||
\(499\) | −32.0000 | −1.43252 | −0.716258 | − | 0.697835i | \(-0.754147\pi\) | ||||
−0.716258 | + | 0.697835i | \(0.754147\pi\) | |||||||
\(500\) | −9.79796 | −0.438178 | ||||||||
\(501\) | −18.0000 | − | 18.0000i | −0.804181 | − | 0.804181i | ||||
\(502\) | 12.2474i | 0.546630i | ||||||||
\(503\) | −19.5959 | −0.873739 | −0.436869 | − | 0.899525i | \(-0.643913\pi\) | ||||
−0.436869 | + | 0.899525i | \(0.643913\pi\) | |||||||
\(504\) | 3.00000 | + | 7.34847i | 0.133631 | + | 0.327327i | ||||
\(505\) | −6.00000 | −0.266996 | ||||||||
\(506\) | 6.00000i | 0.266733i | ||||||||
\(507\) | −8.57321 | − | 8.57321i | −0.380750 | − | 0.380750i | ||||
\(508\) | 16.0000 | 0.709885 | ||||||||
\(509\) | 17.1464 | 0.760002 | 0.380001 | − | 0.924986i | \(-0.375924\pi\) | ||||
0.380001 | + | 0.924986i | \(0.375924\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.0000 | − | 4.89898i | 0.530849 | − | 0.216718i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 27.0000 | + | 27.0000i | 1.19208 | + | 1.19208i | ||||
\(514\) | 19.5959i | 0.864339i | ||||||||
\(515\) | − | 12.0000i | − | 0.528783i | ||||||
\(516\) | −9.79796 | − | 9.79796i | −0.431331 | − | 0.431331i | ||||
\(517\) | − | 9.79796i | − | 0.430914i | ||||||
\(518\) | −24.4949 | + | 10.0000i | −1.07624 | + | 0.439375i | ||||
\(519\) | −3.00000 | − | 3.00000i | −0.131685 | − | 0.131685i | ||||
\(520\) | −6.00000 | −0.263117 | ||||||||
\(521\) | 44.0908 | 1.93165 | 0.965827 | − | 0.259188i | \(-0.0834550\pi\) | ||||
0.965827 | + | 0.259188i | \(0.0834550\pi\) | |||||||
\(522\) | − | 18.0000i | − | 0.787839i | ||||||
\(523\) | 22.0454i | 0.963978i | 0.876177 | + | 0.481989i | \(0.160086\pi\) | ||||
−0.876177 | + | 0.481989i | \(0.839914\pi\) | |||||||
\(524\) | 2.44949 | 0.107006 | ||||||||
\(525\) | −1.77526 | + | 4.22474i | −0.0774785 | + | 0.184383i | ||||
\(526\) | 24.0000 | 1.04645 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 1.22474 | − | 1.22474i | 0.0533002 | − | 0.0533002i | ||||
\(529\) | −13.0000 | −0.565217 | ||||||||
\(530\) | 14.6969 | 0.638394 | ||||||||
\(531\) | 7.34847i | 0.318896i | ||||||||
\(532\) | −18.0000 | + | 7.34847i | −0.780399 | + | 0.318597i | ||||
\(533\) | 24.0000i | 1.03956i | ||||||||
\(534\) | 12.0000 | − | 12.0000i | 0.519291 | − | 0.519291i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 4.00000i | − | 0.172774i | ||||||
\(537\) | 29.3939 | − | 29.3939i | 1.26844 | − | 1.26844i | ||||
\(538\) | 2.44949i | 0.105605i | ||||||||
\(539\) | −4.89898 | − | 5.00000i | −0.211014 | − | 0.215365i | ||||
\(540\) | 9.00000 | − | 9.00000i | 0.387298 | − | 0.387298i | ||||
\(541\) | −34.0000 | −1.46177 | −0.730887 | − | 0.682498i | \(-0.760893\pi\) | ||||
−0.730887 | + | 0.682498i | \(0.760893\pi\) | |||||||
\(542\) | 4.89898 | 0.210429 | ||||||||
\(543\) | 21.0000 | − | 21.0000i | 0.901196 | − | 0.901196i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 34.2929 | 1.46894 | ||||||||
\(546\) | 4.34847 | − | 10.3485i | 0.186097 | − | 0.442874i | ||||
\(547\) | 8.00000 | 0.342055 | 0.171028 | − | 0.985266i | \(-0.445291\pi\) | ||||
0.171028 | + | 0.985266i | \(0.445291\pi\) | |||||||
\(548\) | 12.0000i | 0.512615i | ||||||||
\(549\) | −22.0454 | −0.940875 | ||||||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | 44.0908 | 1.87833 | ||||||||
\(552\) | 7.34847 | + | 7.34847i | 0.312772 | + | 0.312772i | ||||
\(553\) | 10.0000 | + | 24.4949i | 0.425243 | + | 1.04163i | ||||
\(554\) | − | 2.00000i | − | 0.0849719i | ||||||
\(555\) | 30.0000 | + | 30.0000i | 1.27343 | + | 1.27343i | ||||
\(556\) | 12.2474i | 0.519408i | ||||||||
\(557\) | 18.0000i | 0.762684i | 0.924434 | + | 0.381342i | \(0.124538\pi\) | ||||
−0.924434 | + | 0.381342i | \(0.875462\pi\) | |||||||
\(558\) | 14.6969i | 0.622171i | ||||||||
\(559\) | 19.5959i | 0.828819i | ||||||||
\(560\) | 2.44949 | + | 6.00000i | 0.103510 | + | 0.253546i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 12.0000 | 0.506189 | ||||||||
\(563\) | 17.1464 | 0.722636 | 0.361318 | − | 0.932443i | \(-0.382327\pi\) | ||||
0.361318 | + | 0.932443i | \(0.382327\pi\) | |||||||
\(564\) | −12.0000 | − | 12.0000i | −0.505291 | − | 0.505291i | ||||
\(565\) | − | 44.0908i | − | 1.85491i | ||||||
\(566\) | −2.44949 | −0.102960 | ||||||||
\(567\) | 9.00000 | + | 22.0454i | 0.377964 | + | 0.925820i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.00000i | 0.251533i | 0.992060 | + | 0.125767i | \(0.0401390\pi\) | ||||
−0.992060 | + | 0.125767i | \(0.959861\pi\) | |||||||
\(570\) | 22.0454 | + | 22.0454i | 0.923381 | + | 0.923381i | ||||
\(571\) | 32.0000 | 1.33916 | 0.669579 | − | 0.742741i | \(-0.266474\pi\) | ||||
0.669579 | + | 0.742741i | \(0.266474\pi\) | |||||||
\(572\) | −2.44949 | −0.102418 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 24.0000 | − | 9.79796i | 1.00174 | − | 0.408959i | ||||
\(575\) | 6.00000i | 0.250217i | ||||||||
\(576\) | − | 3.00000i | − | 0.125000i | ||||||
\(577\) | − | 29.3939i | − | 1.22368i | −0.790980 | − | 0.611842i | \(-0.790429\pi\) | ||
0.790980 | − | 0.611842i | \(-0.209571\pi\) | |||||||
\(578\) | 17.0000i | 0.707107i | ||||||||
\(579\) | −19.5959 | − | 19.5959i | −0.814379 | − | 0.814379i | ||||
\(580\) | − | 14.6969i | − | 0.610257i | ||||||
\(581\) | −2.44949 | − | 6.00000i | −0.101622 | − | 0.248922i | ||||
\(582\) | 6.00000 | + | 6.00000i | 0.248708 | + | 0.248708i | ||||
\(583\) | 6.00000 | 0.248495 | ||||||||
\(584\) | −4.89898 | −0.202721 | ||||||||
\(585\) | −18.0000 | −0.744208 | ||||||||
\(586\) | − | 17.1464i | − | 0.708312i | ||||||
\(587\) | −41.6413 | −1.71872 | −0.859361 | − | 0.511370i | \(-0.829138\pi\) | ||||
−0.859361 | + | 0.511370i | \(0.829138\pi\) | |||||||
\(588\) | −12.1237 | − | 0.123724i | −0.499974 | − | 0.00510231i | ||||
\(589\) | −36.0000 | −1.48335 | ||||||||
\(590\) | 6.00000i | 0.247016i | ||||||||
\(591\) | −7.34847 | + | 7.34847i | −0.302276 | + | 0.302276i | ||||
\(592\) | 10.0000 | 0.410997 | ||||||||
\(593\) | 24.4949 | 1.00588 | 0.502942 | − | 0.864320i | \(-0.332251\pi\) | ||||
0.502942 | + | 0.864320i | \(0.332251\pi\) | |||||||
\(594\) | 3.67423 | − | 3.67423i | 0.150756 | − | 0.150756i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 18.0000i | 0.737309i | ||||||||
\(597\) | 18.0000 | − | 18.0000i | 0.736691 | − | 0.736691i | ||||
\(598\) | − | 14.6969i | − | 0.601003i | ||||||
\(599\) | − | 24.0000i | − | 0.980613i | −0.871550 | − | 0.490307i | \(-0.836885\pi\) | ||
0.871550 | − | 0.490307i | \(-0.163115\pi\) | |||||||
\(600\) | 1.22474 | − | 1.22474i | 0.0500000 | − | 0.0500000i | ||||
\(601\) | − | 4.89898i | − | 0.199834i | −0.994996 | − | 0.0999168i | \(-0.968142\pi\) | ||
0.994996 | − | 0.0999168i | \(-0.0318577\pi\) | |||||||
\(602\) | 19.5959 | − | 8.00000i | 0.798670 | − | 0.326056i | ||||
\(603\) | − | 12.0000i | − | 0.488678i | ||||||
\(604\) | −16.0000 | −0.651031 | ||||||||
\(605\) | 2.44949 | 0.0995859 | ||||||||
\(606\) | −3.00000 | + | 3.00000i | −0.121867 | + | 0.121867i | ||||
\(607\) | 34.2929i | 1.39190i | 0.718088 | + | 0.695952i | \(0.245017\pi\) | ||||
−0.718088 | + | 0.695952i | \(0.754983\pi\) | |||||||
\(608\) | 7.34847 | 0.298020 | ||||||||
\(609\) | 25.3485 | + | 10.6515i | 1.02717 | + | 0.431622i | ||||
\(610\) | −18.0000 | −0.728799 | ||||||||
\(611\) | 24.0000i | 0.970936i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.00000 | 0.0807792 | 0.0403896 | − | 0.999184i | \(-0.487140\pi\) | ||||
0.0403896 | + | 0.999184i | \(0.487140\pi\) | |||||||
\(614\) | −31.8434 | −1.28509 | ||||||||
\(615\) | −29.3939 | − | 29.3939i | −1.18528 | − | 1.18528i | ||||
\(616\) | 1.00000 | + | 2.44949i | 0.0402911 | + | 0.0986928i | ||||
\(617\) | 30.0000i | 1.20775i | 0.797077 | + | 0.603877i | \(0.206378\pi\) | ||||
−0.797077 | + | 0.603877i | \(0.793622\pi\) | |||||||
\(618\) | −6.00000 | − | 6.00000i | −0.241355 | − | 0.241355i | ||||
\(619\) | 26.9444i | 1.08299i | 0.840705 | + | 0.541493i | \(0.182141\pi\) | ||||
−0.840705 | + | 0.541493i | \(0.817859\pi\) | |||||||
\(620\) | 12.0000i | 0.481932i | ||||||||
\(621\) | 22.0454 | + | 22.0454i | 0.884652 | + | 0.884652i | ||||
\(622\) | 14.6969i | 0.589294i | ||||||||
\(623\) | 9.79796 | + | 24.0000i | 0.392547 | + | 0.961540i | ||||
\(624\) | −3.00000 | + | 3.00000i | −0.120096 | + | 0.120096i | ||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | 4.89898 | 0.195803 | ||||||||
\(627\) | 9.00000 | + | 9.00000i | 0.359425 | + | 0.359425i | ||||
\(628\) | 12.2474i | 0.488726i | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 7.34847 | + | 18.0000i | 0.292770 | + | 0.717137i | ||||
\(631\) | −34.0000 | −1.35352 | −0.676759 | − | 0.736204i | \(-0.736616\pi\) | ||||
−0.676759 | + | 0.736204i | \(0.736616\pi\) | |||||||
\(632\) | − | 10.0000i | − | 0.397779i | ||||||
\(633\) | −19.5959 | − | 19.5959i | −0.778868 | − | 0.778868i | ||||
\(634\) | −6.00000 | −0.238290 | ||||||||
\(635\) | 39.1918 | 1.55528 | ||||||||
\(636\) | 7.34847 | − | 7.34847i | 0.291386 | − | 0.291386i | ||||
\(637\) | 12.0000 | + | 12.2474i | 0.475457 | + | 0.485262i | ||||
\(638\) | − | 6.00000i | − | 0.237542i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 2.44949i | − | 0.0968246i | ||||||
\(641\) | 30.0000i | 1.18493i | 0.805597 | + | 0.592464i | \(0.201845\pi\) | ||||
−0.805597 | + | 0.592464i | \(0.798155\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.8434i | 1.25578i | 0.778302 | + | 0.627890i | \(0.216081\pi\) | ||||
−0.778302 | + | 0.627890i | \(0.783919\pi\) | |||||||
\(644\) | −14.6969 | + | 6.00000i | −0.579141 | + | 0.236433i | ||||
\(645\) | −24.0000 | − | 24.0000i | −0.944999 | − | 0.944999i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.5959 | 0.770395 | 0.385198 | − | 0.922834i | \(-0.374133\pi\) | ||||
0.385198 | + | 0.922834i | \(0.374133\pi\) | |||||||
\(648\) | − | 9.00000i | − | 0.353553i | ||||||
\(649\) | 2.44949i | 0.0961509i | ||||||||
\(650\) | −2.44949 | −0.0960769 | ||||||||
\(651\) | −20.6969 | − | 8.69694i | −0.811177 | − | 0.340860i | ||||
\(652\) | 16.0000 | 0.626608 | ||||||||
\(653\) | 6.00000i | 0.234798i | 0.993085 | + | 0.117399i | \(0.0374557\pi\) | ||||
−0.993085 | + | 0.117399i | \(0.962544\pi\) | |||||||
\(654\) | 17.1464 | − | 17.1464i | 0.670478 | − | 0.670478i | ||||
\(655\) | 6.00000 | 0.234439 | ||||||||
\(656\) | −9.79796 | −0.382546 | ||||||||
\(657\) | −14.6969 | −0.573382 | ||||||||
\(658\) | 24.0000 | − | 9.79796i | 0.935617 | − | 0.381964i | ||||
\(659\) | 12.0000i | 0.467454i | 0.972302 | + | 0.233727i | \(0.0750921\pi\) | ||||
−0.972302 | + | 0.233727i | \(0.924908\pi\) | |||||||
\(660\) | 3.00000 | − | 3.00000i | 0.116775 | − | 0.116775i | ||||
\(661\) | − | 12.2474i | − | 0.476371i | −0.971220 | − | 0.238185i | \(-0.923447\pi\) | ||
0.971220 | − | 0.238185i | \(-0.0765525\pi\) | |||||||
\(662\) | 20.0000i | 0.777322i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.44949i | 0.0950586i | ||||||||
\(665\) | −44.0908 | + | 18.0000i | −1.70977 | + | 0.698010i | ||||
\(666\) | 30.0000 | 1.16248 | ||||||||
\(667\) | 36.0000 | 1.39393 | ||||||||
\(668\) | −14.6969 | −0.568642 | ||||||||
\(669\) | 12.0000 | − | 12.0000i | 0.463947 | − | 0.463947i | ||||
\(670\) | − | 9.79796i | − | 0.378528i | ||||||
\(671\) | −7.34847 | −0.283685 | ||||||||
\(672\) | 4.22474 | + | 1.77526i | 0.162973 | + | 0.0684820i | ||||
\(673\) | 10.0000 | 0.385472 | 0.192736 | − | 0.981251i | \(-0.438264\pi\) | ||||
0.192736 | + | 0.981251i | \(0.438264\pi\) | |||||||
\(674\) | 20.0000i | 0.770371i | ||||||||
\(675\) | 3.67423 | − | 3.67423i | 0.141421 | − | 0.141421i | ||||
\(676\) | −7.00000 | −0.269231 | ||||||||
\(677\) | −12.2474 | −0.470708 | −0.235354 | − | 0.971910i | \(-0.575625\pi\) | ||||
−0.235354 | + | 0.971910i | \(0.575625\pi\) | |||||||
\(678\) | −22.0454 | − | 22.0454i | −0.846649 | − | 0.846649i | ||||
\(679\) | −12.0000 | + | 4.89898i | −0.460518 | + | 0.188006i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.0000 | + | 21.0000i | 0.804722 | + | 0.804722i | ||||
\(682\) | 4.89898i | 0.187592i | ||||||||
\(683\) | − | 24.0000i | − | 0.918334i | −0.888350 | − | 0.459167i | \(-0.848148\pi\) | ||
0.888350 | − | 0.459167i | \(-0.151852\pi\) | |||||||
\(684\) | 22.0454 | 0.842927 | ||||||||
\(685\) | 29.3939i | 1.12308i | ||||||||
\(686\) | 7.34847 | − | 17.0000i | 0.280566 | − | 0.649063i | ||||
\(687\) | −9.00000 | + | 9.00000i | −0.343371 | + | 0.343371i | ||||
\(688\) | −8.00000 | −0.304997 | ||||||||
\(689\) | −14.6969 | −0.559909 | ||||||||
\(690\) | 18.0000 | + | 18.0000i | 0.685248 | + | 0.685248i | ||||
\(691\) | 12.2474i | 0.465915i | 0.972487 | + | 0.232957i | \(0.0748403\pi\) | ||||
−0.972487 | + | 0.232957i | \(0.925160\pi\) | |||||||
\(692\) | −2.44949 | −0.0931156 | ||||||||
\(693\) | 3.00000 | + | 7.34847i | 0.113961 | + | 0.279145i | ||||
\(694\) | −12.0000 | −0.455514 | ||||||||
\(695\) | 30.0000i | 1.13796i | ||||||||
\(696\) | −7.34847 | − | 7.34847i | −0.278543 | − | 0.278543i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −7.34847 | −0.278144 | ||||||||
\(699\) | −14.6969 | + | 14.6969i | −0.555889 | + | 0.555889i | ||||
\(700\) | 1.00000 | + | 2.44949i | 0.0377964 | + | 0.0925820i | ||||
\(701\) | − | 6.00000i | − | 0.226617i | −0.993560 | − | 0.113308i | \(-0.963855\pi\) | ||
0.993560 | − | 0.113308i | \(-0.0361448\pi\) | |||||||
\(702\) | −9.00000 | + | 9.00000i | −0.339683 | + | 0.339683i | ||||
\(703\) | 73.4847i | 2.77153i | ||||||||
\(704\) | − | 1.00000i | − | 0.0376889i | ||||||
\(705\) | −29.3939 | − | 29.3939i | −1.10704 | − | 1.10704i | ||||
\(706\) | 19.5959i | 0.737502i | ||||||||
\(707\) | −2.44949 | − | 6.00000i | −0.0921225 | − | 0.225653i | ||||
\(708\) | 3.00000 | + | 3.00000i | 0.112747 | + | 0.112747i | ||||
\(709\) | 34.0000 | 1.27690 | 0.638448 | − | 0.769665i | \(-0.279577\pi\) | ||||
0.638448 | + | 0.769665i | \(0.279577\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 30.0000i | − | 1.12509i | ||||||
\(712\) | − | 9.79796i | − | 0.367194i | ||||||
\(713\) | −29.3939 | −1.10081 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.00000 | −0.224387 | ||||||||
\(716\) | − | 24.0000i | − | 0.896922i | ||||||
\(717\) | 7.34847 | − | 7.34847i | 0.274434 | − | 0.274434i | ||||
\(718\) | −18.0000 | −0.671754 | ||||||||
\(719\) | 19.5959 | 0.730804 | 0.365402 | − | 0.930850i | \(-0.380931\pi\) | ||||
0.365402 | + | 0.930850i | \(0.380931\pi\) | |||||||
\(720\) | − | 7.34847i | − | 0.273861i | ||||||
\(721\) | 12.0000 | − | 4.89898i | 0.446903 | − | 0.182448i | ||||
\(722\) | 35.0000i | 1.30257i | ||||||||
\(723\) | −24.0000 | + | 24.0000i | −0.892570 | + | 0.892570i | ||||
\(724\) | − | 17.1464i | − | 0.637242i | ||||||
\(725\) | − | 6.00000i | − | 0.222834i | ||||||
\(726\) | 1.22474 | − | 1.22474i | 0.0454545 | − | 0.0454545i | ||||
\(727\) | − | 14.6969i | − | 0.545079i | −0.962145 | − | 0.272540i | \(-0.912136\pi\) | ||
0.962145 | − | 0.272540i | \(-0.0878636\pi\) | |||||||
\(728\) | −2.44949 | − | 6.00000i | −0.0907841 | − | 0.222375i | ||||
\(729\) | − | 27.0000i | − | 1.00000i | ||||||
\(730\) | −12.0000 | −0.444140 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −9.00000 | + | 9.00000i | −0.332650 | + | 0.332650i | ||||
\(733\) | − | 36.7423i | − | 1.35711i | −0.734550 | − | 0.678555i | \(-0.762607\pi\) | ||
0.734550 | − | 0.678555i | \(-0.237393\pi\) | |||||||
\(734\) | −9.79796 | −0.361649 | ||||||||
\(735\) | −29.6969 | − | 0.303062i | −1.09539 | − | 0.0111786i | ||||
\(736\) | 6.00000 | 0.221163 | ||||||||
\(737\) | − | 4.00000i | − | 0.147342i | ||||||
\(738\) | −29.3939 | −1.08200 | ||||||||
\(739\) | −4.00000 | −0.147142 | −0.0735712 | − | 0.997290i | \(-0.523440\pi\) | ||||
−0.0735712 | + | 0.997290i | \(0.523440\pi\) | |||||||
\(740\) | 24.4949 | 0.900450 | ||||||||
\(741\) | −22.0454 | − | 22.0454i | −0.809858 | − | 0.809858i | ||||
\(742\) | 6.00000 | + | 14.6969i | 0.220267 | + | 0.539542i | ||||
\(743\) | − | 6.00000i | − | 0.220119i | −0.993925 | − | 0.110059i | \(-0.964896\pi\) | ||
0.993925 | − | 0.110059i | \(-0.0351041\pi\) | |||||||
\(744\) | 6.00000 | + | 6.00000i | 0.219971 | + | 0.219971i | ||||
\(745\) | 44.0908i | 1.61536i | ||||||||
\(746\) | − | 26.0000i | − | 0.951928i | ||||||
\(747\) | 7.34847i | 0.268866i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −12.0000 | + | 12.0000i | −0.438178 | + | 0.438178i | ||||
\(751\) | 40.0000 | 1.45962 | 0.729810 | − | 0.683650i | \(-0.239608\pi\) | ||||
0.729810 | + | 0.683650i | \(0.239608\pi\) | |||||||
\(752\) | −9.79796 | −0.357295 | ||||||||
\(753\) | 15.0000 | + | 15.0000i | 0.546630 | + | 0.546630i | ||||
\(754\) | 14.6969i | 0.535231i | ||||||||
\(755\) | −39.1918 | −1.42634 | ||||||||
\(756\) | 12.6742 | + | 5.32577i | 0.460957 | + | 0.193696i | ||||
\(757\) | 22.0000 | 0.799604 | 0.399802 | − | 0.916602i | \(-0.369079\pi\) | ||||
0.399802 | + | 0.916602i | \(0.369079\pi\) | |||||||
\(758\) | 20.0000i | 0.726433i | ||||||||
\(759\) | 7.34847 | + | 7.34847i | 0.266733 | + | 0.266733i | ||||
\(760\) | 18.0000 | 0.652929 | ||||||||
\(761\) | −19.5959 | −0.710351 | −0.355176 | − | 0.934800i | \(-0.615579\pi\) | ||||
−0.355176 | + | 0.934800i | \(0.615579\pi\) | |||||||
\(762\) | 19.5959 | − | 19.5959i | 0.709885 | − | 0.709885i | ||||
\(763\) | 14.0000 | + | 34.2929i | 0.506834 | + | 1.24148i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 6.00000i | − | 0.216647i | ||||||
\(768\) | −1.22474 | − | 1.22474i | −0.0441942 | − | 0.0441942i | ||||
\(769\) | − | 9.79796i | − | 0.353323i | −0.984272 | − | 0.176662i | \(-0.943470\pi\) | ||
0.984272 | − | 0.176662i | \(-0.0565299\pi\) | |||||||
\(770\) | 2.44949 | + | 6.00000i | 0.0882735 | + | 0.216225i | ||||
\(771\) | 24.0000 | + | 24.0000i | 0.864339 | + | 0.864339i | ||||
\(772\) | −16.0000 | −0.575853 | ||||||||
\(773\) | −22.0454 | −0.792918 | −0.396459 | − | 0.918052i | \(-0.629761\pi\) | ||||
−0.396459 | + | 0.918052i | \(0.629761\pi\) | |||||||
\(774\) | −24.0000 | −0.862662 | ||||||||
\(775\) | 4.89898i | 0.175977i | ||||||||
\(776\) | 4.89898 | 0.175863 | ||||||||
\(777\) | −17.7526 | + | 42.2474i | −0.636869 | + | 1.51562i | ||||
\(778\) | −30.0000 | −1.07555 | ||||||||
\(779\) | − | 72.0000i | − | 2.57967i | ||||||
\(780\) | −7.34847 | + | 7.34847i | −0.263117 | + | 0.263117i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −22.0454 | − | 22.0454i | −0.787839 | − | 0.787839i | ||||
\(784\) | −5.00000 | + | 4.89898i | −0.178571 | + | 0.174964i | ||||
\(785\) | 30.0000i | 1.07075i | ||||||||
\(786\) | 3.00000 | − | 3.00000i | 0.107006 | − | 0.107006i | ||||
\(787\) | − | 17.1464i | − | 0.611204i | −0.952159 | − | 0.305602i | \(-0.901142\pi\) | ||
0.952159 | − | 0.305602i | \(-0.0988577\pi\) | |||||||
\(788\) | 6.00000i | 0.213741i | ||||||||
\(789\) | 29.3939 | − | 29.3939i | 1.04645 | − | 1.04645i | ||||
\(790\) | − | 24.4949i | − | 0.871489i | ||||||
\(791\) | 44.0908 | − | 18.0000i | 1.56769 | − | 0.640006i | ||||
\(792\) | − | 3.00000i | − | 0.106600i | ||||||
\(793\) | 18.0000 | 0.639199 | ||||||||
\(794\) | 26.9444 | 0.956221 | ||||||||
\(795\) | 18.0000 | − | 18.0000i | 0.638394 | − | 0.638394i | ||||
\(796\) | − | 14.6969i | − | 0.520919i | ||||||
\(797\) | 31.8434 | 1.12795 | 0.563975 | − | 0.825792i | \(-0.309271\pi\) | ||||
0.563975 | + | 0.825792i | \(0.309271\pi\) | |||||||
\(798\) | −13.0454 | + | 31.0454i | −0.461802 | + | 1.09900i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | − | 1.00000i | − | 0.0353553i | ||||||
\(801\) | − | 29.3939i | − | 1.03858i | ||||||
\(802\) | 18.0000 | 0.635602 | ||||||||
\(803\) | −4.89898 | −0.172881 | ||||||||
\(804\) | −4.89898 | − | 4.89898i | −0.172774 | − | 0.172774i | ||||
\(805\) | −36.0000 | + | 14.6969i | −1.26883 | + | 0.517999i | ||||
\(806\) | − | 12.0000i | − | 0.422682i | ||||||
\(807\) | 3.00000 | + | 3.00000i | 0.105605 | + | 0.105605i | ||||
\(808\) | 2.44949i | 0.0861727i | ||||||||
\(809\) | 30.0000i | 1.05474i | 0.849635 | + | 0.527372i | \(0.176823\pi\) | ||||
−0.849635 | + | 0.527372i | \(0.823177\pi\) | |||||||
\(810\) | − | 22.0454i | − | 0.774597i | ||||||
\(811\) | 56.3383i | 1.97830i | 0.146896 | + | 0.989152i | \(0.453072\pi\) | ||||
−0.146896 | + | 0.989152i | \(0.546928\pi\) | |||||||
\(812\) | 14.6969 | − | 6.00000i | 0.515761 | − | 0.210559i | ||||
\(813\) | 6.00000 | − | 6.00000i | 0.210429 | − | 0.210429i | ||||
\(814\) | 10.0000 | 0.350500 | ||||||||
\(815\) | 39.1918 | 1.37283 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 58.7878i | − | 2.05672i | ||||||
\(818\) | −29.3939 | −1.02773 | ||||||||
\(819\) | −7.34847 | − | 18.0000i | −0.256776 | − | 0.628971i | ||||
\(820\) | −24.0000 | −0.838116 | ||||||||
\(821\) | 6.00000i | 0.209401i | 0.994504 | + | 0.104701i | \(0.0333885\pi\) | ||||
−0.994504 | + | 0.104701i | \(0.966612\pi\) | |||||||
\(822\) | 14.6969 | + | 14.6969i | 0.512615 | + | 0.512615i | ||||
\(823\) | 2.00000 | 0.0697156 | 0.0348578 | − | 0.999392i | \(-0.488902\pi\) | ||||
0.0348578 | + | 0.999392i | \(0.488902\pi\) | |||||||
\(824\) | −4.89898 | −0.170664 | ||||||||
\(825\) | 1.22474 | − | 1.22474i | 0.0426401 | − | 0.0426401i | ||||
\(826\) | −6.00000 | + | 2.44949i | −0.208767 | + | 0.0852286i | ||||
\(827\) | 12.0000i | 0.417281i | 0.977992 | + | 0.208640i | \(0.0669038\pi\) | ||||
−0.977992 | + | 0.208640i | \(0.933096\pi\) | |||||||
\(828\) | 18.0000 | 0.625543 | ||||||||
\(829\) | 51.4393i | 1.78656i | 0.449500 | + | 0.893280i | \(0.351602\pi\) | ||||
−0.449500 | + | 0.893280i | \(0.648398\pi\) | |||||||
\(830\) | 6.00000i | 0.208263i | ||||||||
\(831\) | −2.44949 | − | 2.44949i | −0.0849719 | − | 0.0849719i | ||||
\(832\) | 2.44949i | 0.0849208i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 15.0000 | + | 15.0000i | 0.519408 | + | 0.519408i | ||||
\(835\) | −36.0000 | −1.24583 | ||||||||
\(836\) | 7.34847 | 0.254152 | ||||||||
\(837\) | 18.0000 | + | 18.0000i | 0.622171 | + | 0.622171i | ||||
\(838\) | − | 26.9444i | − | 0.930778i | ||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 10.3485 | + | 4.34847i | 0.357056 | + | 0.150036i | ||||
\(841\) | −7.00000 | −0.241379 | ||||||||
\(842\) | 10.0000i | 0.344623i | ||||||||
\(843\) | 14.6969 | − | 14.6969i | 0.506189 | − | 0.506189i | ||||
\(844\) | −16.0000 | −0.550743 | ||||||||
\(845\) | −17.1464 | −0.589855 | ||||||||
\(846\) | −29.3939 | −1.01058 | ||||||||
\(847\) | 1.00000 | + | 2.44949i | 0.0343604 | + | 0.0841655i | ||||
\(848\) | − | 6.00000i | − | 0.206041i | ||||||
\(849\) | −3.00000 | + | 3.00000i | −0.102960 | + | 0.102960i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 60.0000i | 2.05677i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.1464i | 0.587083i | 0.955946 | + | 0.293541i | \(0.0948338\pi\) | ||||
−0.955946 | + | 0.293541i | \(0.905166\pi\) | |||||||
\(854\) | −7.34847 | − | 18.0000i | −0.251459 | − | 0.615947i | ||||
\(855\) | 54.0000 | 1.84676 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 48.9898 | 1.67346 | 0.836730 | − | 0.547616i | \(-0.184465\pi\) | ||||
0.836730 | + | 0.547616i | \(0.184465\pi\) | |||||||
\(858\) | −3.00000 | + | 3.00000i | −0.102418 | + | 0.102418i | ||||
\(859\) | − | 22.0454i | − | 0.752180i | −0.926583 | − | 0.376090i | \(-0.877268\pi\) | ||
0.926583 | − | 0.376090i | \(-0.122732\pi\) | |||||||
\(860\) | −19.5959 | −0.668215 | ||||||||
\(861\) | 17.3939 | − | 41.3939i | 0.592782 | − | 1.41070i | ||||
\(862\) | 18.0000 | 0.613082 | ||||||||
\(863\) | − | 24.0000i | − | 0.816970i | −0.912765 | − | 0.408485i | \(-0.866057\pi\) | ||
0.912765 | − | 0.408485i | \(-0.133943\pi\) | |||||||
\(864\) | −3.67423 | − | 3.67423i | −0.125000 | − | 0.125000i | ||||
\(865\) | −6.00000 | −0.204006 | ||||||||
\(866\) | −4.89898 | −0.166474 | ||||||||
\(867\) | 20.8207 | + | 20.8207i | 0.707107 | + | 0.707107i | ||||
\(868\) | −12.0000 | + | 4.89898i | −0.407307 | + | 0.166282i | ||||
\(869\) | − | 10.0000i | − | 0.339227i | ||||||
\(870\) | −18.0000 | − | 18.0000i | −0.610257 | − | 0.610257i | ||||
\(871\) | 9.79796i | 0.331991i | ||||||||
\(872\) | − | 14.0000i | − | 0.474100i | ||||||
\(873\) | 14.6969 | 0.497416 | ||||||||
\(874\) | 44.0908i | 1.49139i | ||||||||
\(875\) | −9.79796 | − | 24.0000i | −0.331231 | − | 0.811348i | ||||
\(876\) | −6.00000 | + | 6.00000i | −0.202721 | + | 0.202721i | ||||
\(877\) | 2.00000 | 0.0675352 | 0.0337676 | − | 0.999430i | \(-0.489249\pi\) | ||||
0.0337676 | + | 0.999430i | \(0.489249\pi\) | |||||||
\(878\) | −24.4949 | −0.826663 | ||||||||
\(879\) | −21.0000 | − | 21.0000i | −0.708312 | − | 0.708312i | ||||
\(880\) | − | 2.44949i | − | 0.0825723i | ||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | −15.0000 | + | 14.6969i | −0.505076 | + | 0.494872i | ||||
\(883\) | 16.0000 | 0.538443 | 0.269221 | − | 0.963078i | \(-0.413234\pi\) | ||||
0.269221 | + | 0.963078i | \(0.413234\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.34847 | + | 7.34847i | 0.247016 | + | 0.247016i | ||||
\(886\) | −12.0000 | −0.403148 | ||||||||
\(887\) | 44.0908 | 1.48042 | 0.740212 | − | 0.672373i | \(-0.234725\pi\) | ||||
0.740212 | + | 0.672373i | \(0.234725\pi\) | |||||||
\(888\) | 12.2474 | − | 12.2474i | 0.410997 | − | 0.410997i | ||||
\(889\) | 16.0000 | + | 39.1918i | 0.536623 | + | 1.31445i | ||||
\(890\) | − | 24.0000i | − | 0.804482i | ||||||
\(891\) | − | 9.00000i | − | 0.301511i | ||||||
\(892\) | − | 9.79796i | − | 0.328060i | ||||||
\(893\) | − | 72.0000i | − | 2.40939i | ||||||
\(894\) | 22.0454 | + | 22.0454i | 0.737309 | + | 0.737309i | ||||
\(895\) | − | 58.7878i | − | 1.96506i | ||||||
\(896\) | 2.44949 | − | 1.00000i | 0.0818317 | − | 0.0334077i | ||||
\(897\) | −18.0000 | − | 18.0000i | −0.601003 | − | 0.601003i | ||||
\(898\) | −12.0000 | −0.400445 | ||||||||
\(899\) | 29.3939 | 0.980341 | ||||||||
\(900\) | − | 3.00000i | − | 0.100000i | ||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −9.79796 | −0.326236 | ||||||||
\(903\) | 14.2020 | − | 33.7980i | 0.472614 | − | 1.12473i | ||||
\(904\) | −18.0000 | −0.598671 | ||||||||
\(905\) | − | 42.0000i | − | 1.39613i | ||||||
\(906\) | −19.5959 | + | 19.5959i | −0.651031 | + | 0.651031i | ||||
\(907\) | −32.0000 | −1.06254 | −0.531271 | − | 0.847202i | \(-0.678286\pi\) | ||||
−0.531271 | + | 0.847202i | \(0.678286\pi\) | |||||||
\(908\) | 17.1464 | 0.569024 | ||||||||
\(909\) | 7.34847i | 0.243733i | ||||||||
\(910\) | −6.00000 | − | 14.6969i | −0.198898 | − | 0.487199i | ||||
\(911\) | − | 42.0000i | − | 1.39152i | −0.718273 | − | 0.695761i | \(-0.755067\pi\) | ||
0.718273 | − | 0.695761i | \(-0.244933\pi\) | |||||||
\(912\) | 9.00000 | − | 9.00000i | 0.298020 | − | 0.298020i | ||||
\(913\) | 2.44949i | 0.0810663i | ||||||||
\(914\) | 32.0000i | 1.05847i | ||||||||
\(915\) | −22.0454 | + | 22.0454i | −0.728799 | + | 0.728799i | ||||
\(916\) | 7.34847i | 0.242800i | ||||||||
\(917\) | 2.44949 | + | 6.00000i | 0.0808893 | + | 0.198137i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.0000 | 1.12156 | 0.560778 | − | 0.827966i | \(-0.310502\pi\) | ||||
0.560778 | + | 0.827966i | \(0.310502\pi\) | |||||||
\(920\) | 14.6969 | 0.484544 | ||||||||
\(921\) | −39.0000 | + | 39.0000i | −1.28509 | + | 1.28509i | ||||
\(922\) | 22.0454i | 0.726027i | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 4.22474 | + | 1.77526i | 0.138984 | + | 0.0584016i | ||||
\(925\) | 10.0000 | 0.328798 | ||||||||
\(926\) | 22.0000i | 0.722965i | ||||||||
\(927\) | −14.6969 | −0.482711 | ||||||||
\(928\) | −6.00000 | −0.196960 | ||||||||
\(929\) | −44.0908 | −1.44657 | −0.723286 | − | 0.690548i | \(-0.757369\pi\) | ||||
−0.723286 | + | 0.690548i | \(0.757369\pi\) | |||||||
\(930\) | 14.6969 | + | 14.6969i | 0.481932 | + | 0.481932i | ||||
\(931\) | −36.0000 | − | 36.7423i | −1.17985 | − | 1.20418i | ||||
\(932\) | 12.0000i | 0.393073i | ||||||||
\(933\) | 18.0000 | + | 18.0000i | 0.589294 | + | 0.589294i | ||||
\(934\) | − | 7.34847i | − | 0.240449i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.34847i | 0.240192i | ||||||||
\(937\) | − | 24.4949i | − | 0.800213i | −0.916469 | − | 0.400107i | \(-0.868973\pi\) | ||
0.916469 | − | 0.400107i | \(-0.131027\pi\) | |||||||
\(938\) | 9.79796 | − | 4.00000i | 0.319915 | − | 0.130605i | ||||
\(939\) | 6.00000 | − | 6.00000i | 0.195803 | − | 0.195803i | ||||
\(940\) | −24.0000 | −0.782794 | ||||||||
\(941\) | 26.9444 | 0.878362 | 0.439181 | − | 0.898399i | \(-0.355269\pi\) | ||||
0.439181 | + | 0.898399i | \(0.355269\pi\) | |||||||
\(942\) | 15.0000 | + | 15.0000i | 0.488726 | + | 0.488726i | ||||
\(943\) | − | 58.7878i | − | 1.91439i | ||||||
\(944\) | 2.44949 | 0.0797241 | ||||||||
\(945\) | 31.0454 | + | 13.0454i | 1.00991 | + | 0.424367i | ||||
\(946\) | −8.00000 | −0.260102 | ||||||||
\(947\) | − | 48.0000i | − | 1.55979i | −0.625910 | − | 0.779895i | \(-0.715272\pi\) | ||
0.625910 | − | 0.779895i | \(-0.284728\pi\) | |||||||
\(948\) | −12.2474 | − | 12.2474i | −0.397779 | − | 0.397779i | ||||
\(949\) | 12.0000 | 0.389536 | ||||||||
\(950\) | 7.34847 | 0.238416 | ||||||||
\(951\) | −7.34847 | + | 7.34847i | −0.238290 | + | 0.238290i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | − | 18.0000i | − | 0.582772i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 6.00000i | − | 0.194054i | ||||||
\(957\) | −7.34847 | − | 7.34847i | −0.237542 | − | 0.237542i | ||||
\(958\) | 4.89898i | 0.158279i | ||||||||
\(959\) | −29.3939 | + | 12.0000i | −0.949178 | + | 0.387500i | ||||
\(960\) | −3.00000 | − | 3.00000i | −0.0968246 | − | 0.0968246i | ||||
\(961\) | 7.00000 | 0.225806 | ||||||||
\(962\) | −24.4949 | −0.789747 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 19.5959i | 0.631142i | ||||||||
\(965\) | −39.1918 | −1.26163 | ||||||||
\(966\) | −10.6515 | + | 25.3485i | −0.342707 | + | 0.815574i | ||||
\(967\) | 56.0000 | 1.80084 | 0.900419 | − | 0.435023i | \(-0.143260\pi\) | ||||
0.900419 | + | 0.435023i | \(0.143260\pi\) | |||||||
\(968\) | − | 1.00000i | − | 0.0321412i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 12.0000 | 0.385297 | ||||||||
\(971\) | 22.0454 | 0.707471 | 0.353735 | − | 0.935346i | \(-0.384911\pi\) | ||||
0.353735 | + | 0.935346i | \(0.384911\pi\) | |||||||
\(972\) | −11.0227 | − | 11.0227i | −0.353553 | − | 0.353553i | ||||
\(973\) | −30.0000 | + | 12.2474i | −0.961756 | + | 0.392635i | ||||
\(974\) | − | 16.0000i | − | 0.512673i | ||||||
\(975\) | −3.00000 | + | 3.00000i | −0.0960769 | + | 0.0960769i | ||||
\(976\) | 7.34847i | 0.235219i | ||||||||
\(977\) | 60.0000i | 1.91957i | 0.280736 | + | 0.959785i | \(0.409421\pi\) | ||||
−0.280736 | + | 0.959785i | \(0.590579\pi\) | |||||||
\(978\) | 19.5959 | − | 19.5959i | 0.626608 | − | 0.626608i | ||||
\(979\) | − | 9.79796i | − | 0.313144i | ||||||
\(980\) | −12.2474 | + | 12.0000i | −0.391230 | + | 0.383326i | ||||
\(981\) | − | 42.0000i | − | 1.34096i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −39.1918 | −1.25003 | −0.625013 | − | 0.780615i | \(-0.714906\pi\) | ||||
−0.625013 | + | 0.780615i | \(0.714906\pi\) | |||||||
\(984\) | −12.0000 | + | 12.0000i | −0.382546 | + | 0.382546i | ||||
\(985\) | 14.6969i | 0.468283i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 17.3939 | − | 41.3939i | 0.553653 | − | 1.31758i | ||||
\(988\) | −18.0000 | −0.572656 | ||||||||
\(989\) | − | 48.0000i | − | 1.52631i | ||||||
\(990\) | − | 7.34847i | − | 0.233550i | ||||||
\(991\) | −2.00000 | −0.0635321 | −0.0317660 | − | 0.999495i | \(-0.510113\pi\) | ||||
−0.0317660 | + | 0.999495i | \(0.510113\pi\) | |||||||
\(992\) | 4.89898 | 0.155543 | ||||||||
\(993\) | 24.4949 | + | 24.4949i | 0.777322 | + | 0.777322i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 36.0000i | − | 1.14128i | ||||||
\(996\) | 3.00000 | + | 3.00000i | 0.0950586 | + | 0.0950586i | ||||
\(997\) | − | 17.1464i | − | 0.543033i | −0.962434 | − | 0.271516i | \(-0.912475\pi\) | ||
0.962434 | − | 0.271516i | \(-0.0875251\pi\) | |||||||
\(998\) | 32.0000i | 1.01294i | ||||||||
\(999\) | 36.7423 | − | 36.7423i | 1.16248 | − | 1.16248i |
(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 | 462.2.g.b.419.1 | ✓ | 4 | |
3.2 | odd | 2 | inner | 462.2.g.b.419.4 | yes | 4 | |
7.6 | odd | 2 | inner | 462.2.g.b.419.2 | yes | 4 | |
21.20 | even | 2 | inner | 462.2.g.b.419.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.g.b.419.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
462.2.g.b.419.2 | yes | 4 | 7.6 | odd | 2 | inner | |
462.2.g.b.419.3 | yes | 4 | 21.20 | even | 2 | inner | |
462.2.g.b.419.4 | yes | 4 | 3.2 | odd | 2 | inner |