Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [168,2,Mod(125,168)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(168, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("168.125");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 168 = 2^{3} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 168.i (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: | \(1.34148675396\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.10070523904.11 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 10x^{4} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{2}]$ |
Embedding invariants
Embedding label | 125.1 | ||
Root | \(1.68014 + 0.420861i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 168.125 |
Dual form | 168.2.i.d.125.5 |
$q$-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 \(\left(\mathbb{Z}/168\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(85\) | \(113\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 1.00000i | ||||||
\(3\) | −1.68014 | − | 0.420861i | −0.970030 | − | 0.242984i | ||||
\(4\) | −2.00000 | −1.00000 | ||||||||
\(5\) | 3.91044i | 1.74880i | 0.485206 | + | 0.874400i | \(0.338745\pi\) | ||||
−0.485206 | + | 0.874400i | \(0.661255\pi\) | |||||||
\(6\) | −0.595188 | + | 2.37608i | −0.242984 | + | 0.970030i | ||||
\(7\) | −2.64575 | −1.00000 | ||||||||
\(8\) | 2.82843i | 1.00000i | ||||||||
\(9\) | 2.64575 | + | 1.41421i | 0.881917 | + | 0.471405i | ||||
\(10\) | 5.53019 | 1.74880 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 3.36028 | + | 0.841723i | 0.970030 | + | 0.242984i | ||||
\(13\) | −4.55066 | −1.26213 | −0.631063 | − | 0.775732i | \(-0.717381\pi\) | ||||
−0.631063 | + | 0.775732i | \(0.717381\pi\) | |||||||
\(14\) | 3.74166i | 1.00000i | ||||||||
\(15\) | 1.64575 | − | 6.57008i | 0.424931 | − | 1.69639i | ||||
\(16\) | 4.00000 | 1.00000 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 2.00000 | − | 3.74166i | 0.471405 | − | 0.881917i | ||||
\(19\) | −0.979531 | −0.224720 | −0.112360 | − | 0.993668i | \(-0.535841\pi\) | ||||
−0.112360 | + | 0.993668i | \(0.535841\pi\) | |||||||
\(20\) | − | 7.82087i | − | 1.74880i | ||||||
\(21\) | 4.44524 | + | 1.11349i | 0.970030 | + | 0.242984i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.48331i | 1.56038i | 0.625543 | + | 0.780189i | \(0.284877\pi\) | ||||
−0.625543 | + | 0.780189i | \(0.715123\pi\) | |||||||
\(24\) | 1.19038 | − | 4.75216i | 0.242984 | − | 0.970030i | ||||
\(25\) | −10.2915 | −2.05830 | ||||||||
\(26\) | 6.43560i | 1.26213i | ||||||||
\(27\) | −3.85005 | − | 3.48957i | −0.740942 | − | 0.671569i | ||||
\(28\) | 5.29150 | 1.00000 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | −9.29150 | − | 2.32744i | −1.69639 | − | 0.424931i | ||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | − | 5.65685i | − | 1.00000i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 10.3460i | − | 1.74880i | ||||||
\(36\) | −5.29150 | − | 2.82843i | −0.881917 | − | 0.471405i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 1.38527i | 0.224720i | ||||||||
\(39\) | 7.64575 | + | 1.91520i | 1.22430 | + | 0.306677i | ||||
\(40\) | −11.0604 | −1.74880 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 1.57472 | − | 6.28651i | 0.242984 | − | 0.970030i | ||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.53019 | + | 10.3460i | −0.824392 | + | 1.54230i | ||||
\(46\) | 10.5830 | 1.56038 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | −6.72057 | − | 1.68345i | −0.970030 | − | 0.242984i | ||||
\(49\) | 7.00000 | 1.00000 | ||||||||
\(50\) | 14.5544i | 2.05830i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 9.10132 | 1.26213 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | −4.93500 | + | 5.44479i | −0.671569 | + | 0.740942i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 7.48331i | − | 1.00000i | ||||||
\(57\) | 1.64575 | + | 0.412247i | 0.217985 | + | 0.0546034i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 5.29570i | − | 0.689442i | −0.938705 | − | 0.344721i | \(-0.887974\pi\) | ||
0.938705 | − | 0.344721i | \(-0.112026\pi\) | |||||||
\(60\) | −3.29150 | + | 13.1402i | −0.424931 | + | 1.69639i | ||||
\(61\) | 15.6110 | 1.99879 | 0.999394 | − | 0.0347968i | \(-0.0110784\pi\) | ||||
0.999394 | + | 0.0347968i | \(0.0110784\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.00000 | − | 3.74166i | −0.881917 | − | 0.471405i | ||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | − | 17.7951i | − | 2.20721i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.14944 | − | 12.5730i | 0.379148 | − | 1.51361i | ||||
\(70\) | −14.6315 | −1.74880 | ||||||||
\(71\) | 5.65685i | 0.671345i | 0.941979 | + | 0.335673i | \(0.108964\pi\) | ||||
−0.941979 | + | 0.335673i | \(0.891036\pi\) | |||||||
\(72\) | −4.00000 | + | 7.48331i | −0.471405 | + | 0.881917i | ||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 17.2912 | + | 4.33130i | 1.99661 | + | 0.500135i | ||||
\(76\) | 1.95906 | 0.224720 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.70850 | − | 10.8127i | 0.306677 | − | 1.22430i | ||||
\(79\) | −5.29150 | −0.595341 | −0.297670 | − | 0.954669i | \(-0.596210\pi\) | ||||
−0.297670 | + | 0.954669i | \(0.596210\pi\) | |||||||
\(80\) | 15.6417i | 1.74880i | ||||||||
\(81\) | 5.00000 | + | 7.48331i | 0.555556 | + | 0.831479i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 18.1669i | 1.99408i | 0.0769020 | + | 0.997039i | \(0.475497\pi\) | ||||
−0.0769020 | + | 0.997039i | \(0.524503\pi\) | |||||||
\(84\) | −8.89047 | − | 2.22699i | −0.970030 | − | 0.242984i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 14.6315 | + | 7.82087i | 1.54230 | + | 0.824392i | ||||
\(91\) | 12.0399 | 1.26213 | ||||||||
\(92\) | − | 14.9666i | − | 1.56038i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 3.83039i | − | 0.392990i | ||||||
\(96\) | −2.38075 | + | 9.50432i | −0.242984 | + | 0.970030i | ||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | − | 9.89949i | − | 1.00000i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 20.5830 | 2.05830 | ||||||||
\(101\) | 8.96077i | 0.891630i | 0.895125 | + | 0.445815i | \(0.147086\pi\) | ||||
−0.895125 | + | 0.445815i | \(0.852914\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | − | 12.8712i | − | 1.26213i | ||||||
\(105\) | −4.35425 | + | 17.3828i | −0.424931 | + | 1.69639i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 7.70010 | + | 6.97915i | 0.740942 | + | 0.671569i | ||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −10.5830 | −1.00000 | ||||||||
\(113\) | 14.1421i | 1.33038i | 0.746674 | + | 0.665190i | \(0.231650\pi\) | ||||
−0.746674 | + | 0.665190i | \(0.768350\pi\) | |||||||
\(114\) | 0.583005 | − | 2.32744i | 0.0546034 | − | 0.217985i | ||||
\(115\) | −29.2630 | −2.72879 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −12.0399 | − | 6.43560i | −1.11309 | − | 0.594972i | ||||
\(118\) | −7.48925 | −0.689442 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 18.5830 | + | 4.65489i | 1.69639 | + | 0.424931i | ||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | − | 22.0773i | − | 1.99879i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 20.6921i | − | 1.85076i | ||||||
\(126\) | −5.29150 | + | 9.89949i | −0.471405 | + | 0.881917i | ||||
\(127\) | 2.00000 | 0.177471 | 0.0887357 | − | 0.996055i | \(-0.471717\pi\) | ||||
0.0887357 | + | 0.996055i | \(0.471717\pi\) | |||||||
\(128\) | 11.3137i | 1.00000i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −25.1660 | −2.20721 | ||||||||
\(131\) | 13.1166i | 1.14600i | 0.819555 | + | 0.573000i | \(0.194221\pi\) | ||||
−0.819555 | + | 0.573000i | \(0.805779\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.59160 | 0.224720 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 13.6458 | − | 15.0554i | 1.17444 | − | 1.29576i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 14.9666i | − | 1.27869i | −0.768922 | − | 0.639343i | \(-0.779207\pi\) | ||
0.768922 | − | 0.639343i | \(-0.220793\pi\) | |||||||
\(138\) | −17.7809 | − | 4.45398i | −1.51361 | − | 0.379148i | ||||
\(139\) | 19.1822 | 1.62701 | 0.813505 | − | 0.581558i | \(-0.197557\pi\) | ||||
0.813505 | + | 0.581558i | \(0.197557\pi\) | |||||||
\(140\) | 20.6921i | 1.74880i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.00000 | 0.671345 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 10.5830 | + | 5.65685i | 0.881917 | + | 0.471405i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −11.7610 | − | 2.94603i | −0.970030 | − | 0.242984i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 6.12538 | − | 24.4534i | 0.500135 | − | 1.99661i | ||||
\(151\) | −10.0000 | −0.813788 | −0.406894 | − | 0.913475i | \(-0.633388\pi\) | ||||
−0.406894 | + | 0.913475i | \(0.633388\pi\) | |||||||
\(152\) | − | 2.77053i | − | 0.224720i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −15.2915 | − | 3.83039i | −1.22430 | − | 0.306677i | ||||
\(157\) | −17.5701 | −1.40225 | −0.701123 | − | 0.713040i | \(-0.747318\pi\) | ||||
−0.701123 | + | 0.713040i | \(0.747318\pi\) | |||||||
\(158\) | 7.48331i | 0.595341i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 22.1208 | 1.74880 | ||||||||
\(161\) | − | 19.7990i | − | 1.56038i | ||||||
\(162\) | 10.5830 | − | 7.07107i | 0.831479 | − | 0.555556i | ||||
\(163\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 25.6919 | 1.99408 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | −3.14944 | + | 12.5730i | −0.242984 | + | 0.970030i | ||||
\(169\) | 7.70850 | 0.592961 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.59160 | − | 1.38527i | −0.198184 | − | 0.105934i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 24.6025i | − | 1.87049i | −0.353995 | − | 0.935247i | \(-0.615177\pi\) | ||
0.353995 | − | 0.935247i | \(-0.384823\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 27.2288 | 2.05830 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.22876 | + | 8.89753i | −0.167524 | + | 0.668779i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 11.0604 | − | 20.6921i | 0.824392 | − | 1.54230i | ||||
\(181\) | −24.7124 | −1.83686 | −0.918428 | − | 0.395589i | \(-0.870540\pi\) | ||||
−0.918428 | + | 0.395589i | \(0.870540\pi\) | |||||||
\(182\) | − | 17.0270i | − | 1.26213i | ||||||
\(183\) | −26.2288 | − | 6.57008i | −1.93889 | − | 0.485675i | ||||
\(184\) | −21.1660 | −1.56038 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.1863 | + | 9.23254i | 0.740942 | + | 0.671569i | ||||
\(190\) | −5.41699 | −0.392990 | ||||||||
\(191\) | 22.6274i | 1.63726i | 0.574320 | + | 0.818631i | \(0.305267\pi\) | ||||
−0.574320 | + | 0.818631i | \(0.694733\pi\) | |||||||
\(192\) | 13.4411 | + | 3.36689i | 0.970030 | + | 0.242984i | ||||
\(193\) | 26.4575 | 1.90445 | 0.952227 | − | 0.305392i | \(-0.0987875\pi\) | ||||
0.952227 | + | 0.305392i | \(0.0987875\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.48925 | + | 29.8982i | −0.536317 | + | 2.14106i | ||||
\(196\) | −14.0000 | −1.00000 | ||||||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | − | 29.1088i | − | 2.05830i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.6724 | 0.891630 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.5830 | + | 19.7990i | −0.735570 | + | 1.37612i | ||||
\(208\) | −18.2026 | −1.26213 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 24.5830 | + | 6.15784i | 1.69639 | + | 0.424931i | ||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.38075 | − | 9.50432i | 0.163126 | − | 0.651225i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 9.87000 | − | 10.8896i | 0.671569 | − | 0.740942i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(224\) | 14.9666i | 1.00000i | ||||||||
\(225\) | −27.2288 | − | 14.5544i | −1.81525 | − | 0.970292i | ||||
\(226\) | 20.0000 | 1.33038 | ||||||||
\(227\) | − | 15.3964i | − | 1.02189i | −0.859612 | − | 0.510947i | \(-0.829295\pi\) | ||
0.859612 | − | 0.510947i | \(-0.170705\pi\) | |||||||
\(228\) | −3.29150 | − | 0.824494i | −0.217985 | − | 0.0546034i | ||||
\(229\) | 8.46878 | 0.559633 | 0.279817 | − | 0.960053i | \(-0.409726\pi\) | ||||
0.279817 | + | 0.960053i | \(0.409726\pi\) | |||||||
\(230\) | 41.3842i | 2.72879i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 29.9333i | 1.96099i | 0.196537 | + | 0.980497i | \(0.437031\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | −9.10132 | + | 17.0270i | −0.594972 | + | 1.11309i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 10.5914i | 0.689442i | ||||||||
\(237\) | 8.89047 | + | 2.22699i | 0.577498 | + | 0.144659i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.48331i | 0.484055i | 0.970269 | + | 0.242028i | \(0.0778125\pi\) | ||||
−0.970269 | + | 0.242028i | \(0.922188\pi\) | |||||||
\(240\) | 6.58301 | − | 26.2803i | 0.424931 | − | 1.69639i | ||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | 15.5563i | 1.00000i | ||||||||
\(243\) | −5.25127 | − | 14.6773i | −0.336869 | − | 0.941551i | ||||
\(244\) | −31.2221 | −1.99879 | ||||||||
\(245\) | 27.3730i | 1.74880i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.45751 | 0.283625 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.64575 | − | 30.5230i | 0.484530 | − | 1.93432i | ||||
\(250\) | −29.2630 | −1.85076 | ||||||||
\(251\) | 23.2172i | 1.46546i | 0.680520 | + | 0.732730i | \(0.261754\pi\) | ||||
−0.680520 | + | 0.732730i | \(0.738246\pi\) | |||||||
\(252\) | 14.0000 | + | 7.48331i | 0.881917 | + | 0.471405i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − | 2.82843i | − | 0.177471i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 35.5901i | 2.20721i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 18.5496 | 1.14600 | ||||||||
\(263\) | − | 28.2843i | − | 1.74408i | −0.489432 | − | 0.872041i | \(-0.662796\pi\) | ||
0.489432 | − | 0.872041i | \(-0.337204\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 3.66507i | − | 0.224720i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 32.4234i | 1.97689i | 0.151585 | + | 0.988444i | \(0.451562\pi\) | ||||
−0.151585 | + | 0.988444i | \(0.548438\pi\) | |||||||
\(270\) | −21.2915 | − | 19.2980i | −1.29576 | − | 1.17444i | ||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −20.2288 | − | 5.06713i | −1.22430 | − | 0.306677i | ||||
\(274\) | −21.1660 | −1.27869 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.29888 | + | 25.1461i | −0.379148 | + | 1.51361i | ||||
\(277\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(278\) | − | 27.1277i | − | 1.62701i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 29.2630 | 1.74880 | ||||||||
\(281\) | − | 14.9666i | − | 0.892834i | −0.894825 | − | 0.446417i | \(-0.852700\pi\) | ||
0.894825 | − | 0.446417i | \(-0.147300\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 32.2016 | 1.91419 | 0.957094 | − | 0.289779i | \(-0.0935819\pi\) | ||||
0.957094 | + | 0.289779i | \(0.0935819\pi\) | |||||||
\(284\) | − | 11.3137i | − | 0.671345i | ||||||
\(285\) | −1.61206 | + | 6.43560i | −0.0954905 | + | 0.381212i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 8.00000 | − | 14.9666i | 0.471405 | − | 0.881917i | ||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 14.5018i | − | 0.847206i | −0.905848 | − | 0.423603i | \(-0.860765\pi\) | ||
0.905848 | − | 0.423603i | \(-0.139235\pi\) | |||||||
\(294\) | −4.16632 | + | 16.6326i | −0.242984 | + | 0.970030i | ||||
\(295\) | 20.7085 | 1.20570 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 34.0540i | − | 1.96939i | ||||||
\(300\) | −34.5824 | − | 8.66259i | −1.99661 | − | 0.500135i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 14.1421i | 0.813788i | ||||||||
\(303\) | 3.77124 | − | 15.0554i | 0.216652 | − | 0.864908i | ||||
\(304\) | −3.91813 | −0.224720 | ||||||||
\(305\) | 61.0460i | 3.49548i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.9990 | −0.798964 | −0.399482 | − | 0.916741i | \(-0.630810\pi\) | ||||
−0.399482 | + | 0.916741i | \(0.630810\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | −5.41699 | + | 21.6255i | −0.306677 | + | 1.22430i | ||||
\(313\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(314\) | 24.8479i | 1.40225i | ||||||||
\(315\) | 14.6315 | − | 27.3730i | 0.824392 | − | 1.54230i | ||||
\(316\) | 10.5830 | 0.595341 | ||||||||
\(317\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − | 31.2835i | − | 1.74880i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −28.0000 | −1.56038 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −10.0000 | − | 14.9666i | −0.555556 | − | 0.831479i | ||||
\(325\) | 46.8331 | 2.59783 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | − | 36.3338i | − | 1.99408i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 17.7809 | + | 4.45398i | 0.970030 | + | 0.242984i | ||||
\(337\) | 26.4575 | 1.44123 | 0.720616 | − | 0.693334i | \(-0.243859\pi\) | ||||
0.720616 | + | 0.693334i | \(0.243859\pi\) | |||||||
\(338\) | − | 10.9015i | − | 0.592961i | ||||||
\(339\) | 5.95188 | − | 23.7608i | 0.323262 | − | 1.29051i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −1.95906 | + | 3.66507i | −0.105934 | + | 0.198184i | ||||
\(343\) | −18.5203 | −1.00000 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 49.1660 | + | 12.3157i | 2.64701 | + | 0.663054i | ||||
\(346\) | −34.7932 | −1.87049 | ||||||||
\(347\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.6305 | 1.53255 | 0.766277 | − | 0.642510i | \(-0.222107\pi\) | ||||
0.766277 | + | 0.642510i | \(0.222107\pi\) | |||||||
\(350\) | − | 38.5073i | − | 2.05830i | ||||||
\(351\) | 17.5203 | + | 15.8799i | 0.935162 | + | 0.847604i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(354\) | 12.5830 | + | 3.15194i | 0.668779 | + | 0.167524i | ||||
\(355\) | −22.1208 | −1.17405 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 37.4166i | − | 1.97477i | −0.158334 | − | 0.987386i | \(-0.550612\pi\) | ||
0.158334 | − | 0.987386i | \(-0.449388\pi\) | |||||||
\(360\) | −29.2630 | − | 15.6417i | −1.54230 | − | 0.824392i | ||||
\(361\) | −18.0405 | −0.949501 | ||||||||
\(362\) | 34.9486i | 1.83686i | ||||||||
\(363\) | 18.4816 | + | 4.62948i | 0.970030 | + | 0.242984i | ||||
\(364\) | −24.0798 | −1.26213 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −9.29150 | + | 37.0931i | −0.485675 | + | 1.93889i | ||||
\(367\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(368\) | 29.9333i | 1.56038i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.70850 | + | 34.7656i | −0.449705 | + | 1.79529i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 13.0568 | − | 14.4056i | 0.671569 | − | 0.740942i | ||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 7.66079i | 0.392990i | ||||||||
\(381\) | −3.36028 | − | 0.841723i | −0.172153 | − | 0.0431228i | ||||
\(382\) | 32.0000 | 1.63726 | ||||||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | 4.76150 | − | 19.0086i | 0.242984 | − | 0.970030i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 37.4166i | − | 1.90445i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(390\) | 42.2825 | + | 10.5914i | 2.14106 | + | 0.536317i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 19.7990i | 1.00000i | ||||||||
\(393\) | 5.52026 | − | 22.0377i | 0.278460 | − | 1.11165i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 20.6921i | − | 1.04113i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −37.7318 | −1.89370 | −0.946852 | − | 0.321668i | \(-0.895756\pi\) | ||||
−0.946852 | + | 0.321668i | \(0.895756\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.35425 | − | 1.09070i | −0.217985 | − | 0.0546034i | ||||
\(400\) | −41.1660 | −2.05830 | ||||||||
\(401\) | − | 36.7696i | − | 1.83618i | −0.396368 | − | 0.918092i | \(-0.629729\pi\) | ||
0.396368 | − | 0.918092i | \(-0.370271\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | − | 17.9215i | − | 0.891630i | ||||||
\(405\) | −29.2630 | + | 19.5522i | −1.45409 | + | 0.971555i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.29888 | + | 25.1461i | −0.310701 | + | 1.24036i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.0111i | 0.689442i | ||||||||
\(414\) | 28.0000 | + | 14.9666i | 1.37612 | + | 0.735570i | ||||
\(415\) | −71.0405 | −3.48724 | ||||||||
\(416\) | 25.7424i | 1.26213i | ||||||||
\(417\) | −32.2288 | − | 8.07303i | −1.57825 | − | 0.395338i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 38.8590i | − | 1.89839i | −0.314695 | − | 0.949193i | \(-0.601902\pi\) | ||
0.314695 | − | 0.949193i | \(-0.398098\pi\) | |||||||
\(420\) | 8.70850 | − | 34.7656i | 0.424931 | − | 1.69639i | ||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −13.4411 | − | 3.36689i | −0.651225 | − | 0.163126i | ||||
\(427\) | −41.3029 | −1.99879 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 37.4166i | − | 1.80229i | −0.433515 | − | 0.901146i | \(-0.642727\pi\) | ||
0.433515 | − | 0.901146i | \(-0.357273\pi\) | |||||||
\(432\) | −15.4002 | − | 13.9583i | −0.740942 | − | 0.671569i | ||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 7.33014i | − | 0.350648i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.5203 | + | 9.89949i | 0.881917 | + | 0.471405i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 21.1660 | 1.00000 | ||||||||
\(449\) | 29.9333i | 1.41264i | 0.707894 | + | 0.706319i | \(0.249646\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | −20.5830 | + | 38.5073i | −0.970292 | + | 1.81525i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 28.2843i | − | 1.33038i | ||||||
\(453\) | 16.8014 | + | 4.20861i | 0.789399 | + | 0.197738i | ||||
\(454\) | −21.7738 | −1.02189 | ||||||||
\(455\) | 47.0813i | 2.20721i | ||||||||
\(456\) | −1.16601 | + | 4.65489i | −0.0546034 | + | 0.217985i | ||||
\(457\) | −5.29150 | −0.247526 | −0.123763 | − | 0.992312i | \(-0.539496\pi\) | ||||
−0.123763 | + | 0.992312i | \(0.539496\pi\) | |||||||
\(458\) | − | 11.9767i | − | 0.559633i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 58.5260 | 2.72879 | ||||||||
\(461\) | − | 6.19024i | − | 0.288308i | −0.989555 | − | 0.144154i | \(-0.953954\pi\) | ||
0.989555 | − | 0.144154i | \(-0.0460461\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.4575 | 1.22958 | 0.614792 | − | 0.788689i | \(-0.289240\pi\) | ||||
0.614792 | + | 0.788689i | \(0.289240\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 42.3320 | 1.96099 | ||||||||
\(467\) | 41.6295i | 1.92638i | 0.268814 | + | 0.963192i | \(0.413368\pi\) | ||||
−0.268814 | + | 0.963192i | \(0.586632\pi\) | |||||||
\(468\) | 24.0798 | + | 12.8712i | 1.11309 | + | 0.594972i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 29.5203 | + | 7.39458i | 1.36022 | + | 0.340724i | ||||
\(472\) | 14.9785 | 0.689442 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 3.14944 | − | 12.5730i | 0.144659 | − | 0.577498i | ||||
\(475\) | 10.0808 | 0.462541 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10.5830 | 0.484055 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | −37.1660 | − | 9.30978i | −1.69639 | − | 0.424931i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.33263 | + | 33.2651i | −0.379148 | + | 1.51361i | ||||
\(484\) | 22.0000 | 1.00000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −20.7569 | + | 7.42642i | −0.941551 | + | 0.336869i | ||||
\(487\) | 38.0000 | 1.72194 | 0.860972 | − | 0.508652i | \(-0.169856\pi\) | ||||
0.860972 | + | 0.508652i | \(0.169856\pi\) | |||||||
\(488\) | 44.1547i | 1.99879i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 38.7113 | 1.74880 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | − | 6.30388i | − | 0.283625i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 14.9666i | − | 0.671345i | ||||||
\(498\) | −43.1660 | − | 10.8127i | −1.93432 | − | 0.484530i | ||||
\(499\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(500\) | 41.3842i | 1.85076i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 32.8341 | 1.46546 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 10.5830 | − | 19.7990i | 0.471405 | − | 0.881917i | ||||
\(505\) | −35.0405 | −1.55928 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.9514 | − | 3.24421i | −0.575190 | − | 0.144080i | ||||
\(508\) | −4.00000 | −0.177471 | ||||||||
\(509\) | 37.4737i | 1.66099i | 0.557024 | + | 0.830497i | \(0.311943\pi\) | ||||
−0.557024 | + | 0.830497i | \(0.688057\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 22.6274i | − | 1.00000i | ||||||
\(513\) | 3.77124 | + | 3.41815i | 0.166504 | + | 0.150915i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.3542 | + | 41.3357i | −0.454501 | + | 1.81444i | ||||
\(520\) | 50.3320 | 2.20721 | ||||||||
\(521\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.0594 | 1.09577 | 0.547885 | − | 0.836554i | \(-0.315433\pi\) | ||||
0.547885 | + | 0.836554i | \(0.315433\pi\) | |||||||
\(524\) | − | 26.2331i | − | 1.14600i | ||||||
\(525\) | −45.7482 | − | 11.4595i | −1.99661 | − | 0.500135i | ||||
\(526\) | −40.0000 | −1.74408 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −33.0000 | −1.43478 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.48925 | − | 14.0111i | 0.325006 | − | 0.608030i | ||||
\(532\) | −5.18319 | −0.224720 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 45.8536 | 1.97689 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −27.2915 | + | 30.1107i | −1.17444 | + | 1.29576i | ||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 41.5203 | + | 10.4005i | 1.78180 | + | 0.446327i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −7.16601 | + | 28.6078i | −0.306677 | + | 1.22430i | ||||
\(547\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(548\) | 29.9333i | 1.27869i | ||||||||
\(549\) | 41.3029 | + | 22.0773i | 1.76277 | + | 0.942238i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 35.5619 | + | 8.90796i | 1.51361 | + | 0.379148i | ||||
\(553\) | 14.0000 | 0.595341 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −38.3643 | −1.62701 | ||||||||
\(557\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | − | 41.3842i | − | 1.74880i | ||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −21.1660 | −0.892834 | ||||||||
\(563\) | 46.6799i | 1.96732i | 0.180032 | + | 0.983661i | \(0.442380\pi\) | ||||
−0.180032 | + | 0.983661i | \(0.557620\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −55.3019 | −2.32657 | ||||||||
\(566\) | − | 45.5400i | − | 1.91419i | ||||||
\(567\) | −13.2288 | − | 19.7990i | −0.555556 | − | 0.831479i | ||||
\(568\) | −16.0000 | −0.671345 | ||||||||
\(569\) | − | 2.82843i | − | 0.118574i | −0.998241 | − | 0.0592869i | \(-0.981117\pi\) | ||
0.998241 | − | 0.0592869i | \(-0.0188827\pi\) | |||||||
\(570\) | 9.10132 | + | 2.27980i | 0.381212 | + | 0.0954905i | ||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.52301 | − | 38.0173i | 0.397829 | − | 1.58819i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 77.0146i | − | 3.21173i | ||||||
\(576\) | −21.1660 | − | 11.3137i | −0.881917 | − | 0.471405i | ||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | 24.0416i | 1.00000i | ||||||||
\(579\) | −44.4524 | − | 11.1349i | −1.84738 | − | 0.462753i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 48.0651i | − | 1.99408i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 25.1660 | − | 47.0813i | 1.04049 | − | 1.94657i | ||||
\(586\) | −20.5087 | −0.847206 | ||||||||
\(587\) | 36.5792i | 1.50978i | 0.655849 | + | 0.754892i | \(0.272311\pi\) | ||||
−0.655849 | + | 0.754892i | \(0.727689\pi\) | |||||||
\(588\) | 23.5220 | + | 5.89206i | 0.970030 | + | 0.242984i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | − | 29.2862i | − | 1.20570i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −48.1596 | −1.96939 | ||||||||
\(599\) | − | 11.3137i | − | 0.462266i | −0.972922 | − | 0.231133i | \(-0.925757\pi\) | ||
0.972922 | − | 0.231133i | \(-0.0742432\pi\) | |||||||
\(600\) | −12.2508 | + | 48.9068i | −0.500135 | + | 1.99661i | ||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 20.0000 | 0.813788 | ||||||||
\(605\) | − | 43.0148i | − | 1.74880i | ||||||
\(606\) | −21.2915 | − | 5.33334i | −0.864908 | − | 0.216652i | ||||
\(607\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(608\) | 5.54107i | 0.224720i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 86.3320 | 3.49548 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(614\) | 19.7975i | 0.798964i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.1421i | 0.569341i | 0.958625 | + | 0.284670i | \(0.0918842\pi\) | ||||
−0.958625 | + | 0.284670i | \(0.908116\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.3244 | 1.05807 | 0.529034 | − | 0.848601i | \(-0.322554\pi\) | ||||
0.529034 | + | 0.848601i | \(0.322554\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 26.1136 | − | 28.8111i | 1.04790 | − | 1.15615i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 30.5830 | + | 7.66079i | 1.22430 | + | 0.306677i | ||||
\(625\) | 29.4575 | 1.17830 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 35.1402 | 1.40225 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −38.7113 | − | 20.6921i | −1.54230 | − | 0.824392i | ||||
\(631\) | −37.0405 | −1.47456 | −0.737280 | − | 0.675587i | \(-0.763890\pi\) | ||||
−0.737280 | + | 0.675587i | \(0.763890\pi\) | |||||||
\(632\) | − | 14.9666i | − | 0.595341i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.82087i | 0.310362i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −31.8546 | −1.26213 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.00000 | + | 14.9666i | −0.316475 | + | 0.592071i | ||||
\(640\) | −44.2415 | −1.74880 | ||||||||
\(641\) | 48.0833i | 1.89917i | 0.313503 | + | 0.949587i | \(0.398498\pi\) | ||||
−0.313503 | + | 0.949587i | \(0.601502\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.2640 | −0.601955 | −0.300978 | − | 0.953631i | \(-0.597313\pi\) | ||||
−0.300978 | + | 0.953631i | \(0.597313\pi\) | |||||||
\(644\) | 39.5980i | 1.56038i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | −21.1660 | + | 14.1421i | −0.831479 | + | 0.555556i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − | 66.2320i | − | 2.59783i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −51.2915 | −2.00412 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.5895 | −1.18980 | −0.594898 | − | 0.803801i | \(-0.702807\pi\) | ||||
−0.594898 | + | 0.803801i | \(0.702807\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −51.3838 | −1.99408 | ||||||||
\(665\) | 10.1343i | 0.392990i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 6.29888 | − | 25.1461i | 0.242984 | − | 0.970030i | ||||
\(673\) | 26.0000 | 1.00223 | 0.501113 | − | 0.865382i | \(-0.332924\pi\) | ||||
0.501113 | + | 0.865382i | \(0.332924\pi\) | |||||||
\(674\) | − | 37.4166i | − | 1.44123i | ||||||
\(675\) | 39.6228 | + | 35.9130i | 1.52508 | + | 1.38229i | ||||
\(676\) | −15.4170 | −0.592961 | ||||||||
\(677\) | − | 9.45150i | − | 0.363251i | −0.983368 | − | 0.181625i | \(-0.941864\pi\) | ||
0.983368 | − | 0.181625i | \(-0.0581358\pi\) | |||||||
\(678\) | −33.6028 | − | 8.41723i | −1.29051 | − | 0.323262i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.47974 | + | 25.8681i | −0.248304 | + | 0.991267i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(684\) | 5.18319 | + | 2.77053i | 0.198184 | + | 0.105934i | ||||
\(685\) | 58.5260 | 2.23616 | ||||||||
\(686\) | 26.1916i | 1.00000i | ||||||||
\(687\) | −14.2288 | − | 3.56418i | −0.542861 | − | 0.135982i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 17.4170 | − | 69.5312i | 0.663054 | − | 2.64701i | ||||
\(691\) | 52.3633 | 1.99199 | 0.995997 | − | 0.0893857i | \(-0.0284904\pi\) | ||||
0.995997 | + | 0.0893857i | \(0.0284904\pi\) | |||||||
\(692\) | 49.2050i | 1.87049i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 75.0106i | 2.84532i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | − | 40.4896i | − | 1.53255i | ||||||
\(699\) | 12.5978 | − | 50.2921i | 0.476491 | − | 1.90222i | ||||
\(700\) | −54.4575 | −2.05830 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 22.4575 | − | 24.7774i | 0.847604 | − | 0.935162i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 23.7080i | − | 0.891630i | ||||||
\(708\) | 4.45751 | − | 17.7951i | 0.167524 | − | 0.668779i | ||||
\(709\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(710\) | 31.2835i | 1.17405i | ||||||||
\(711\) | −14.0000 | − | 7.48331i | −0.525041 | − | 0.280646i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.14944 | − | 12.5730i | 0.117618 | − | 0.469548i | ||||
\(718\) | −52.9150 | −1.97477 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | −22.1208 | + | 41.3842i | −0.824392 | + | 1.54230i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 25.5131i | 0.949501i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 49.4247 | 1.83686 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 6.54707 | − | 26.1369i | 0.242984 | − | 0.970030i | ||||
\(727\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(728\) | 34.0540i | 1.26213i | ||||||||
\(729\) | 2.64575 | + | 26.8701i | 0.0979908 | + | 0.995187i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 52.4575 | + | 13.1402i | 1.93889 | + | 0.485675i | ||||
\(733\) | 42.9150 | 1.58510 | 0.792551 | − | 0.609806i | \(-0.208753\pi\) | ||||
0.792551 | + | 0.609806i | \(0.208753\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 11.5203 | − | 45.9906i | 0.424931 | − | 1.69639i | ||||
\(736\) | 42.3320 | 1.56038 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.48925 | − | 1.87600i | −0.275125 | − | 0.0689164i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.48331i | 0.274536i | 0.990534 | + | 0.137268i | \(0.0438322\pi\) | ||||
−0.990534 | + | 0.137268i | \(0.956168\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −25.6919 | + | 48.0651i | −0.940017 | + | 1.75861i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 49.1660 | + | 12.3157i | 1.79529 | + | 0.449705i | ||||
\(751\) | 50.0000 | 1.82453 | 0.912263 | − | 0.409605i | \(-0.134333\pi\) | ||||
0.912263 | + | 0.409605i | \(0.134333\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.77124 | − | 39.0083i | 0.356084 | − | 1.42154i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 39.1044i | − | 1.42315i | ||||||
\(756\) | −20.3725 | − | 18.4651i | −0.740942 | − | 0.671569i | ||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10.8340 | 0.392990 | ||||||||
\(761\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(762\) | −1.19038 | + | 4.75216i | −0.0431228 | + | 0.172153i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 45.2548i | − | 1.63726i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24.0989i | 0.870162i | ||||||||
\(768\) | −26.8823 | − | 6.73378i | −0.970030 | − | 0.242984i | ||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −52.9150 | −1.90445 | ||||||||
\(773\) | − | 53.1155i | − | 1.91043i | −0.295912 | − | 0.955215i | \(-0.595624\pi\) | ||
0.295912 | − | 0.955215i | \(-0.404376\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 14.9785 | − | 59.7964i | 0.536317 | − | 2.14106i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 28.0000 | 1.00000 | ||||||||
\(785\) | − | 68.7067i | − | 2.45225i | ||||||
\(786\) | −31.1660 | − | 7.80683i | −1.11165 | − | 0.278460i | ||||
\(787\) | 45.2211 | 1.61196 | 0.805978 | − | 0.591945i | \(-0.201640\pi\) | ||||
0.805978 | + | 0.591945i | \(0.201640\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.9038 | + | 47.5216i | −0.423785 | + | 1.69181i | ||||
\(790\) | −29.2630 | −1.04113 | ||||||||
\(791\) | − | 37.4166i | − | 1.33038i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −71.0405 | −2.52272 | ||||||||
\(794\) | 53.3608i | 1.89370i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 55.8860i | 1.97958i | 0.142521 | + | 0.989792i | \(0.454479\pi\) | ||||
−0.142521 | + | 0.989792i | \(0.545521\pi\) | |||||||
\(798\) | −1.54249 | + | 6.15784i | −0.0546034 | + | 0.217985i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 58.2175i | 2.05830i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −52.0000 | −1.83618 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 77.4227 | 2.72879 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.6458 | − | 54.4759i | 0.480353 | − | 1.91764i | ||||
\(808\) | −25.3449 | −0.891630 | ||||||||
\(809\) | 31.1127i | 1.09386i | 0.837177 | + | 0.546932i | \(0.184204\pi\) | ||||
−0.837177 | + | 0.546932i | \(0.815796\pi\) | |||||||
\(810\) | 27.6510 | + | 41.3842i | 0.971555 | + | 1.45409i | ||||
\(811\) | −48.4452 | −1.70114 | −0.850570 | − | 0.525861i | \(-0.823743\pi\) | ||||
−0.850570 | + | 0.525861i | \(0.823743\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 31.8546 | + | 17.0270i | 1.11309 | + | 0.594972i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(822\) | 35.5619 | + | 8.90796i | 1.24036 | + | 0.310701i | ||||
\(823\) | 26.4575 | 0.922251 | 0.461125 | − | 0.887335i | \(-0.347446\pi\) | ||||
0.461125 | + | 0.887335i | \(0.347446\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 19.8147 | 0.689442 | ||||||||
\(827\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(828\) | 21.1660 | − | 39.5980i | 0.735570 | − | 1.37612i | ||||
\(829\) | 1.32653 | 0.0460723 | 0.0230361 | − | 0.999735i | \(-0.492667\pi\) | ||||
0.0230361 | + | 0.999735i | \(0.492667\pi\) | |||||||
\(830\) | 100.466i | 3.48724i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 36.4053 | 1.26213 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −11.4170 | + | 45.5783i | −0.395338 | + | 1.57825i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −54.9549 | −1.89839 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | −49.1660 | − | 12.3157i | −1.69639 | − | 0.424931i | ||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.29888 | + | 25.1461i | −0.216945 | + | 0.866076i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 30.1436i | 1.03697i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.1033 | 1.00000 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −54.1033 | − | 13.5524i | −1.85682 | − | 0.465118i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −4.76150 | + | 19.0086i | −0.163126 | + | 0.651225i | ||||
\(853\) | −57.8935 | −1.98224 | −0.991118 | − | 0.132987i | \(-0.957543\pi\) | ||||
−0.991118 | + | 0.132987i | \(0.957543\pi\) | |||||||
\(854\) | 58.4112i | 1.99879i | ||||||||
\(855\) | 5.41699 | − | 10.1343i | 0.185257 | − | 0.346585i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −54.3224 | −1.85346 | −0.926728 | − | 0.375734i | \(-0.877391\pi\) | ||||
−0.926728 | + | 0.375734i | \(0.877391\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −52.9150 | −1.80229 | ||||||||
\(863\) | 56.5685i | 1.92562i | 0.270187 | + | 0.962808i | \(0.412914\pi\) | ||||
−0.270187 | + | 0.962808i | \(0.587086\pi\) | |||||||
\(864\) | −19.7400 | + | 21.7792i | −0.671569 | + | 0.740942i | ||||
\(865\) | 96.2065 | 3.27112 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 28.5624 | + | 7.15464i | 0.970030 | + | 0.242984i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −10.3664 | −0.350648 | ||||||||
\(875\) | 54.7461i | 1.85076i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.10326 | + | 24.3651i | −0.205858 | + | 0.821816i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 14.0000 | − | 26.1916i | 0.471405 | − | 0.881917i | ||||
\(883\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −34.7932 | − | 8.71541i | −1.16956 | − | 0.292965i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.29150 | −0.177471 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 29.9333i | − | 1.00000i | ||||||
\(897\) | −14.3320 | + | 57.2156i | −0.478532 | + | 1.91037i | ||||
\(898\) | 42.3320 | 1.41264 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 54.4575 | + | 29.1088i | 1.81525 | + | 0.970292i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −40.0000 | −1.33038 | ||||||||
\(905\) | − | 96.6361i | − | 3.21229i | ||||||
\(906\) | 5.95188 | − | 23.7608i | 0.197738 | − | 0.789399i | ||||
\(907\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(908\) | 30.7928i | 1.02189i | ||||||||
\(909\) | −12.6724 | + | 23.7080i | −0.420318 | + | 0.786344i | ||||
\(910\) | 66.5830 | 2.20721 | ||||||||
\(911\) | 52.3832i | 1.73553i | 0.496972 | + | 0.867766i | \(0.334445\pi\) | ||||
−0.496972 | + | 0.867766i | \(0.665555\pi\) | |||||||
\(912\) | 6.58301 | + | 1.64899i | 0.217985 | + | 0.0546034i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 7.48331i | 0.247526i | ||||||||
\(915\) | 25.6919 | − | 102.566i | 0.849348 | − | 3.39072i | ||||
\(916\) | −16.9376 | −0.559633 | ||||||||
\(917\) | − | 34.7032i | − | 1.14600i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 58.2065 | 1.92006 | 0.960028 | − | 0.279904i | \(-0.0903025\pi\) | ||||
0.960028 | + | 0.279904i | \(0.0903025\pi\) | |||||||
\(920\) | − | 82.7683i | − | 2.72879i | ||||||
\(921\) | 23.5203 | + | 5.89163i | 0.775019 | + | 0.194136i | ||||
\(922\) | −8.75432 | −0.288308 | ||||||||
\(923\) | − | 25.7424i | − | 0.847322i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 37.4166i | − | 1.22958i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.85672 | −0.224720 | ||||||||
\(932\) | − | 59.8665i | − | 1.96099i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 58.8730 | 1.92638 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 18.2026 | − | 34.0540i | 0.594972 | − | 1.11309i | ||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.0614i | 0.621385i | 0.950510 | + | 0.310693i | \(0.100561\pi\) | ||||
−0.950510 | + | 0.310693i | \(0.899439\pi\) | |||||||
\(942\) | 10.4575 | − | 41.7480i | 0.340724 | − | 1.36022i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | − | 21.1828i | − | 0.689442i | ||||||
\(945\) | −36.1033 | + | 39.8328i | −1.17444 | + | 1.29576i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(948\) | −17.7809 | − | 4.45398i | −0.577498 | − | 0.144659i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | − | 14.2565i | − | 0.462541i | ||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.9333i | 0.969633i | 0.874616 | + | 0.484817i | \(0.161114\pi\) | ||||
−0.874616 | + | 0.484817i | \(0.838886\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −88.4830 | −2.86324 | ||||||||
\(956\) | − | 14.9666i | − | 0.484055i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 39.5980i | 1.27869i | ||||||||
\(960\) | −13.1660 | + | 52.5607i | −0.424931 | + | 1.69639i | ||||
\(961\) | 31.0000 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 103.460i | 3.33051i | ||||||||
\(966\) | 47.0440 | + | 11.7841i | 1.51361 | + | 0.379148i | ||||
\(967\) | −58.0000 | −1.86515 | −0.932577 | − | 0.360971i | \(-0.882445\pi\) | ||||
−0.932577 | + | 0.360971i | \(0.882445\pi\) | |||||||
\(968\) | − | 31.1127i | − | 1.00000i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 62.3216i | − | 2.00000i | −0.00218468 | − | 0.999998i | \(-0.500695\pi\) | ||
0.00218468 | − | 0.999998i | \(-0.499305\pi\) | |||||||
\(972\) | 10.5025 | + | 29.3547i | 0.336869 | + | 0.941551i | ||||
\(973\) | −50.7512 | −1.62701 | ||||||||
\(974\) | − | 53.7401i | − | 1.72194i | ||||||
\(975\) | −78.6863 | − | 19.7103i | −2.51998 | − | 0.631233i | ||||
\(976\) | 62.4442 | 1.99879 | ||||||||
\(977\) | − | 59.8665i | − | 1.91530i | −0.287936 | − | 0.957650i | \(-0.592969\pi\) | ||
0.287936 | − | 0.957650i | \(-0.407031\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | − | 54.7461i | − | 1.74880i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.91503 | −0.283625 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.0405 | −1.17663 | −0.588315 | − | 0.808632i | \(-0.700209\pi\) | ||||
−0.588315 | + | 0.808632i | \(0.700209\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −21.1660 | −0.671345 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −15.2915 | + | 61.0460i | −0.484530 | + | 1.93432i | ||||
\(997\) | 41.6499 | 1.31907 | 0.659533 | − | 0.751675i | \(-0.270754\pi\) | ||||
0.659533 | + | 0.751675i | \(0.270754\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 168.2.i.d.125.1 | ✓ | 8 | |
3.2 | odd | 2 | inner | 168.2.i.d.125.5 | yes | 8 | |
4.3 | odd | 2 | 672.2.i.e.209.8 | 8 | |||
7.6 | odd | 2 | inner | 168.2.i.d.125.4 | yes | 8 | |
8.3 | odd | 2 | 672.2.i.e.209.1 | 8 | |||
8.5 | even | 2 | inner | 168.2.i.d.125.4 | yes | 8 | |
12.11 | even | 2 | 672.2.i.e.209.7 | 8 | |||
21.20 | even | 2 | inner | 168.2.i.d.125.8 | yes | 8 | |
24.5 | odd | 2 | inner | 168.2.i.d.125.8 | yes | 8 | |
24.11 | even | 2 | 672.2.i.e.209.2 | 8 | |||
28.27 | even | 2 | 672.2.i.e.209.1 | 8 | |||
56.13 | odd | 2 | CM | 168.2.i.d.125.1 | ✓ | 8 | |
56.27 | even | 2 | 672.2.i.e.209.8 | 8 | |||
84.83 | odd | 2 | 672.2.i.e.209.2 | 8 | |||
168.83 | odd | 2 | 672.2.i.e.209.7 | 8 | |||
168.125 | even | 2 | inner | 168.2.i.d.125.5 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.i.d.125.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
168.2.i.d.125.1 | ✓ | 8 | 56.13 | odd | 2 | CM | |
168.2.i.d.125.4 | yes | 8 | 7.6 | odd | 2 | inner | |
168.2.i.d.125.4 | yes | 8 | 8.5 | even | 2 | inner | |
168.2.i.d.125.5 | yes | 8 | 3.2 | odd | 2 | inner | |
168.2.i.d.125.5 | yes | 8 | 168.125 | even | 2 | inner | |
168.2.i.d.125.8 | yes | 8 | 21.20 | even | 2 | inner | |
168.2.i.d.125.8 | yes | 8 | 24.5 | odd | 2 | inner | |
672.2.i.e.209.1 | 8 | 8.3 | odd | 2 | |||
672.2.i.e.209.1 | 8 | 28.27 | even | 2 | |||
672.2.i.e.209.2 | 8 | 24.11 | even | 2 | |||
672.2.i.e.209.2 | 8 | 84.83 | odd | 2 | |||
672.2.i.e.209.7 | 8 | 12.11 | even | 2 | |||
672.2.i.e.209.7 | 8 | 168.83 | odd | 2 | |||
672.2.i.e.209.8 | 8 | 4.3 | odd | 2 | |||
672.2.i.e.209.8 | 8 | 56.27 | even | 2 |