Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,2,Mod(107,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1350.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.f (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.7798042729\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 270) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 593.1 | ||
Root | \(0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.593 |
Dual form | 1350.2.f.a.107.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.36603 | + | 1.36603i | −0.516309 | + | 0.516309i | −0.916453 | − | 0.400143i | \(-0.868960\pi\) |
0.400143 | + | 0.916453i | \(0.368960\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.31079i | 0.696729i | 0.937359 | + | 0.348365i | \(0.113263\pi\) | ||||
−0.937359 | + | 0.348365i | \(0.886737\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.46410 | + | 3.46410i | 0.960769 | + | 0.960769i | 0.999259 | − | 0.0384901i | \(-0.0122548\pi\) |
−0.0384901 | + | 0.999259i | \(0.512255\pi\) | |||||||
\(14\) | 1.93185 | 0.516309 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −3.86370 | − | 3.86370i | −0.937086 | − | 0.937086i | 0.0610491 | − | 0.998135i | \(-0.480555\pi\) |
−0.998135 | + | 0.0610491i | \(0.980555\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 0.535898i | − | 0.122944i | −0.998109 | − | 0.0614718i | \(-0.980421\pi\) | ||
0.998109 | − | 0.0614718i | \(-0.0195794\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.63397 | − | 1.63397i | 0.348365 | − | 0.348365i | ||||
\(23\) | 1.41421 | − | 1.41421i | 0.294884 | − | 0.294884i | −0.544122 | − | 0.839006i | \(-0.683137\pi\) |
0.839006 | + | 0.544122i | \(0.183137\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 4.89898i | − | 0.960769i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.36603 | − | 1.36603i | −0.258155 | − | 0.258155i | ||||
\(29\) | −3.48477 | −0.647105 | −0.323552 | − | 0.946210i | \(-0.604877\pi\) | ||||
−0.323552 | + | 0.946210i | \(0.604877\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.6603 | −1.91464 | −0.957319 | − | 0.289033i | \(-0.906666\pi\) | ||||
−0.957319 | + | 0.289033i | \(0.906666\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.46410i | 0.937086i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.19615 | + | 8.19615i | −1.34744 | + | 1.34744i | −0.459006 | + | 0.888433i | \(0.651794\pi\) |
−0.888433 | + | 0.459006i | \(0.848206\pi\) | |||||||
\(38\) | −0.378937 | + | 0.378937i | −0.0614718 | + | 0.0614718i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 9.52056i | − | 1.48686i | −0.668813 | − | 0.743431i | \(-0.733197\pi\) | ||
0.668813 | − | 0.743431i | \(-0.266803\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.73205 | + | 4.73205i | 0.721631 | + | 0.721631i | 0.968937 | − | 0.247306i | \(-0.0795454\pi\) |
−0.247306 | + | 0.968937i | \(0.579545\pi\) | |||||||
\(44\) | −2.31079 | −0.348365 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.00000 | −0.294884 | ||||||||
\(47\) | 4.24264 | + | 4.24264i | 0.618853 | + | 0.618853i | 0.945237 | − | 0.326384i | \(-0.105830\pi\) |
−0.326384 | + | 0.945237i | \(0.605830\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.26795i | 0.466850i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.46410 | + | 3.46410i | −0.480384 | + | 0.480384i | ||||
\(53\) | 2.26002 | − | 2.26002i | 0.310438 | − | 0.310438i | −0.534641 | − | 0.845079i | \(-0.679553\pi\) |
0.845079 | + | 0.534641i | \(0.179553\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.93185i | 0.258155i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.46410 | + | 2.46410i | 0.323552 | + | 0.323552i | ||||
\(59\) | −10.1769 | −1.32492 | −0.662460 | − | 0.749098i | \(-0.730487\pi\) | ||||
−0.662460 | + | 0.749098i | \(0.730487\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.53590 | 0.324689 | 0.162344 | − | 0.986734i | \(-0.448094\pi\) | ||||
0.162344 | + | 0.986734i | \(0.448094\pi\) | |||||||
\(62\) | 7.53794 | + | 7.53794i | 0.957319 | + | 0.957319i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.19615 | + | 4.19615i | −0.512642 | + | 0.512642i | −0.915335 | − | 0.402693i | \(-0.868074\pi\) |
0.402693 | + | 0.915335i | \(0.368074\pi\) | |||||||
\(68\) | 3.86370 | − | 3.86370i | 0.468543 | − | 0.468543i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.14110i | 0.491459i | 0.969338 | + | 0.245729i | \(0.0790274\pi\) | ||||
−0.969338 | + | 0.245729i | \(0.920973\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.63397 | − | 7.63397i | −0.893489 | − | 0.893489i | 0.101361 | − | 0.994850i | \(-0.467680\pi\) |
−0.994850 | + | 0.101361i | \(0.967680\pi\) | |||||||
\(74\) | 11.5911 | 1.34744 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.535898 | 0.0614718 | ||||||||
\(77\) | −3.15660 | − | 3.15660i | −0.359728 | − | 0.359728i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.46410i | 0.389742i | 0.980829 | + | 0.194871i | \(0.0624288\pi\) | ||||
−0.980829 | + | 0.194871i | \(0.937571\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.73205 | + | 6.73205i | −0.743431 | + | 0.743431i | ||||
\(83\) | −11.2629 | + | 11.2629i | −1.23627 | + | 1.23627i | −0.274754 | + | 0.961515i | \(0.588596\pi\) |
−0.961515 | + | 0.274754i | \(0.911404\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 6.69213i | − | 0.721631i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.63397 | + | 1.63397i | 0.174182 | + | 0.174182i | ||||
\(89\) | −8.76268 | −0.928843 | −0.464421 | − | 0.885614i | \(-0.653738\pi\) | ||||
−0.464421 | + | 0.885614i | \(0.653738\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.46410 | −0.992107 | ||||||||
\(92\) | 1.41421 | + | 1.41421i | 0.147442 | + | 0.147442i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 6.00000i | − | 0.618853i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.43782 | − | 1.43782i | 0.145989 | − | 0.145989i | −0.630335 | − | 0.776323i | \(-0.717082\pi\) |
0.776323 | + | 0.630335i | \(0.217082\pi\) | |||||||
\(98\) | 2.31079 | − | 2.31079i | 0.233425 | − | 0.233425i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.2103i | 1.21497i | 0.794332 | + | 0.607484i | \(0.207821\pi\) | ||||
−0.794332 | + | 0.607484i | \(0.792179\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.26795 | + | 6.26795i | 0.617599 | + | 0.617599i | 0.944915 | − | 0.327316i | \(-0.106144\pi\) |
−0.327316 | + | 0.944915i | \(0.606144\pi\) | |||||||
\(104\) | 4.89898 | 0.480384 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.19615 | −0.310438 | ||||||||
\(107\) | −8.43451 | − | 8.43451i | −0.815395 | − | 0.815395i | 0.170042 | − | 0.985437i | \(-0.445610\pi\) |
−0.985437 | + | 0.170042i | \(0.945610\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 2.00000i | − | 0.191565i | −0.995402 | − | 0.0957826i | \(-0.969465\pi\) | ||
0.995402 | − | 0.0957826i | \(-0.0305354\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.36603 | − | 1.36603i | 0.129077 | − | 0.129077i | ||||
\(113\) | 2.17209 | − | 2.17209i | 0.204333 | − | 0.204333i | −0.597521 | − | 0.801854i | \(-0.703847\pi\) |
0.801854 | + | 0.597521i | \(0.203847\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 3.48477i | − | 0.323552i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.19615 | + | 7.19615i | 0.662460 | + | 0.662460i | ||||
\(119\) | 10.5558 | 0.967652 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.66025 | 0.514569 | ||||||||
\(122\) | −1.79315 | − | 1.79315i | −0.162344 | − | 0.162344i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 10.6603i | − | 0.957319i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.83013 | − | 9.83013i | 0.872283 | − | 0.872283i | −0.120438 | − | 0.992721i | \(-0.538430\pi\) |
0.992721 | + | 0.120438i | \(0.0384299\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.7651i | 1.11529i | 0.830079 | + | 0.557645i | \(0.188295\pi\) | ||||
−0.830079 | + | 0.557645i | \(0.811705\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.732051 | + | 0.732051i | 0.0634769 | + | 0.0634769i | ||||
\(134\) | 5.93426 | 0.512642 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.46410 | −0.468543 | ||||||||
\(137\) | −2.44949 | − | 2.44949i | −0.209274 | − | 0.209274i | 0.594685 | − | 0.803959i | \(-0.297277\pi\) |
−0.803959 | + | 0.594685i | \(0.797277\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.8564i | 1.51456i | 0.653090 | + | 0.757280i | \(0.273472\pi\) | ||||
−0.653090 | + | 0.757280i | \(0.726528\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.92820 | − | 2.92820i | 0.245729 | − | 0.245729i | ||||
\(143\) | −8.00481 | + | 8.00481i | −0.669396 | + | 0.669396i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10.7961i | 0.893489i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.19615 | − | 8.19615i | −0.673720 | − | 0.673720i | ||||
\(149\) | −0.240237 | −0.0196810 | −0.00984048 | − | 0.999952i | \(-0.503132\pi\) | ||||
−0.00984048 | + | 0.999952i | \(0.503132\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.53590 | −0.124990 | −0.0624948 | − | 0.998045i | \(-0.519906\pi\) | ||||
−0.0624948 | + | 0.998045i | \(0.519906\pi\) | |||||||
\(152\) | −0.378937 | − | 0.378937i | −0.0307359 | − | 0.0307359i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.46410i | 0.359728i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.0000 | + | 12.0000i | −0.957704 | + | 0.957704i | −0.999141 | − | 0.0414369i | \(-0.986806\pi\) |
0.0414369 | + | 0.999141i | \(0.486806\pi\) | |||||||
\(158\) | 2.44949 | − | 2.44949i | 0.194871 | − | 0.194871i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.86370i | 0.304502i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.46410 | + | 1.46410i | 0.114677 | + | 0.114677i | 0.762117 | − | 0.647440i | \(-0.224160\pi\) |
−0.647440 | + | 0.762117i | \(0.724160\pi\) | |||||||
\(164\) | 9.52056 | 0.743431 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.9282 | 1.23627 | ||||||||
\(167\) | −2.17209 | − | 2.17209i | −0.168081 | − | 0.168081i | 0.618054 | − | 0.786135i | \(-0.287921\pi\) |
−0.786135 | + | 0.618054i | \(0.787921\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.0000i | 0.846154i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.73205 | + | 4.73205i | −0.360815 | + | 0.360815i | ||||
\(173\) | −2.50026 | + | 2.50026i | −0.190091 | + | 0.190091i | −0.795735 | − | 0.605644i | \(-0.792915\pi\) |
0.605644 | + | 0.795735i | \(0.292915\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 2.31079i | − | 0.174182i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.19615 | + | 6.19615i | 0.464421 | + | 0.464421i | ||||
\(179\) | 6.83083 | 0.510560 | 0.255280 | − | 0.966867i | \(-0.417832\pi\) | ||||
0.255280 | + | 0.966867i | \(0.417832\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.07180 | 0.0796660 | 0.0398330 | − | 0.999206i | \(-0.487317\pi\) | ||||
0.0398330 | + | 0.999206i | \(0.487317\pi\) | |||||||
\(182\) | 6.69213 | + | 6.69213i | 0.496054 | + | 0.496054i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 2.00000i | − | 0.147442i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.92820 | − | 8.92820i | 0.652895 | − | 0.652895i | ||||
\(188\) | −4.24264 | + | 4.24264i | −0.309426 | + | 0.309426i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 26.0106i | 1.88206i | 0.338317 | + | 0.941032i | \(0.390142\pi\) | ||||
−0.338317 | + | 0.941032i | \(0.609858\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.0263 | − | 11.0263i | −0.793689 | − | 0.793689i | 0.188403 | − | 0.982092i | \(-0.439669\pi\) |
−0.982092 | + | 0.188403i | \(0.939669\pi\) | |||||||
\(194\) | −2.03339 | −0.145989 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.26795 | −0.233425 | ||||||||
\(197\) | 5.46739 | + | 5.46739i | 0.389535 | + | 0.389535i | 0.874522 | − | 0.484987i | \(-0.161175\pi\) |
−0.484987 | + | 0.874522i | \(0.661175\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 20.3205i | − | 1.44048i | −0.693724 | − | 0.720241i | \(-0.744031\pi\) | ||
0.693724 | − | 0.720241i | \(-0.255969\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.63397 | − | 8.63397i | 0.607484 | − | 0.607484i | ||||
\(203\) | 4.76028 | − | 4.76028i | 0.334106 | − | 0.334106i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 8.86422i | − | 0.617599i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.46410 | − | 3.46410i | −0.240192 | − | 0.240192i | ||||
\(209\) | 1.23835 | 0.0856583 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.3205 | 0.917022 | 0.458511 | − | 0.888689i | \(-0.348383\pi\) | ||||
0.458511 | + | 0.888689i | \(0.348383\pi\) | |||||||
\(212\) | 2.26002 | + | 2.26002i | 0.155219 | + | 0.155219i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 11.9282i | 0.815395i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.5622 | − | 14.5622i | 0.988545 | − | 0.988545i | ||||
\(218\) | −1.41421 | + | 1.41421i | −0.0957826 | + | 0.0957826i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 26.7685i | − | 1.80065i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.73205 | − | 7.73205i | −0.517776 | − | 0.517776i | 0.399122 | − | 0.916898i | \(-0.369315\pi\) |
−0.916898 | + | 0.399122i | \(0.869315\pi\) | |||||||
\(224\) | −1.93185 | −0.129077 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.07180 | −0.204333 | ||||||||
\(227\) | 8.10634 | + | 8.10634i | 0.538037 | + | 0.538037i | 0.922952 | − | 0.384915i | \(-0.125769\pi\) |
−0.384915 | + | 0.922952i | \(0.625769\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 22.3923i | − | 1.47973i | −0.672758 | − | 0.739863i | \(-0.734890\pi\) | ||
0.672758 | − | 0.739863i | \(-0.265110\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.46410 | + | 2.46410i | −0.161776 | + | 0.161776i | ||||
\(233\) | 14.0406 | − | 14.0406i | 0.919830 | − | 0.919830i | −0.0771864 | − | 0.997017i | \(-0.524594\pi\) |
0.997017 | + | 0.0771864i | \(0.0245937\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 10.1769i | − | 0.662460i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −7.46410 | − | 7.46410i | −0.483826 | − | 0.483826i | ||||
\(239\) | −20.0764 | −1.29863 | −0.649317 | − | 0.760518i | \(-0.724945\pi\) | ||||
−0.649317 | + | 0.760518i | \(0.724945\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.00000 | 0.257663 | 0.128831 | − | 0.991667i | \(-0.458877\pi\) | ||||
0.128831 | + | 0.991667i | \(0.458877\pi\) | |||||||
\(242\) | −4.00240 | − | 4.00240i | −0.257284 | − | 0.257284i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.53590i | 0.162344i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.85641 | − | 1.85641i | 0.118120 | − | 0.118120i | ||||
\(248\) | −7.53794 | + | 7.53794i | −0.478660 | + | 0.478660i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 19.4201i | − | 1.22578i | −0.790167 | − | 0.612891i | \(-0.790006\pi\) | ||
0.790167 | − | 0.612891i | \(-0.209994\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.26795 | + | 3.26795i | 0.205454 | + | 0.205454i | ||||
\(254\) | −13.9019 | −0.872283 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.04008 | − | 9.04008i | −0.563905 | − | 0.563905i | 0.366509 | − | 0.930414i | \(-0.380553\pi\) |
−0.930414 | + | 0.366509i | \(0.880553\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 22.3923i | − | 1.39139i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.02628 | − | 9.02628i | 0.557645 | − | 0.557645i | ||||
\(263\) | −9.89949 | + | 9.89949i | −0.610429 | + | 0.610429i | −0.943058 | − | 0.332629i | \(-0.892064\pi\) |
0.332629 | + | 0.943058i | \(0.392064\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 1.03528i | − | 0.0634769i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.19615 | − | 4.19615i | −0.256321 | − | 0.256321i | ||||
\(269\) | −21.7680 | −1.32722 | −0.663609 | − | 0.748079i | \(-0.730976\pi\) | ||||
−0.663609 | + | 0.748079i | \(0.730976\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.3923 | 1.54247 | 0.771236 | − | 0.636549i | \(-0.219639\pi\) | ||||
0.771236 | + | 0.636549i | \(0.219639\pi\) | |||||||
\(272\) | 3.86370 | + | 3.86370i | 0.234271 | + | 0.234271i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.46410i | 0.209274i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.85641 | − | 7.85641i | 0.472046 | − | 0.472046i | −0.430530 | − | 0.902576i | \(-0.641673\pi\) |
0.902576 | + | 0.430530i | \(0.141673\pi\) | |||||||
\(278\) | 12.6264 | − | 12.6264i | 0.757280 | − | 0.757280i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.58630i | 0.213941i | 0.994262 | + | 0.106970i | \(0.0341150\pi\) | ||||
−0.994262 | + | 0.106970i | \(0.965885\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.26795 | + | 5.26795i | 0.313147 | + | 0.313147i | 0.846128 | − | 0.532980i | \(-0.178928\pi\) |
−0.532980 | + | 0.846128i | \(0.678928\pi\) | |||||||
\(284\) | −4.14110 | −0.245729 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.3205 | 0.669396 | ||||||||
\(287\) | 13.0053 | + | 13.0053i | 0.767680 | + | 0.767680i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.8564i | 0.756259i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.63397 | − | 7.63397i | 0.446745 | − | 0.446745i | ||||
\(293\) | −8.48528 | + | 8.48528i | −0.495715 | + | 0.495715i | −0.910101 | − | 0.414386i | \(-0.863996\pi\) |
0.414386 | + | 0.910101i | \(0.363996\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 11.5911i | 0.673720i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.169873 | + | 0.169873i | 0.00984048 | + | 0.00984048i | ||||
\(299\) | 9.79796 | 0.566631 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.9282 | −0.745169 | ||||||||
\(302\) | 1.08604 | + | 1.08604i | 0.0624948 | + | 0.0624948i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.535898i | 0.0307359i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(308\) | 3.15660 | − | 3.15660i | 0.179864 | − | 0.179864i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.03528i | 0.0587051i | 0.999569 | + | 0.0293526i | \(0.00934455\pi\) | ||||
−0.999569 | + | 0.0293526i | \(0.990655\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.973721 | + | 0.973721i | 0.0550379 | + | 0.0550379i | 0.734090 | − | 0.679052i | \(-0.237609\pi\) |
−0.679052 | + | 0.734090i | \(0.737609\pi\) | |||||||
\(314\) | 16.9706 | 0.957704 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.46410 | −0.194871 | ||||||||
\(317\) | 3.91447 | + | 3.91447i | 0.219859 | + | 0.219859i | 0.808439 | − | 0.588580i | \(-0.200313\pi\) |
−0.588580 | + | 0.808439i | \(0.700313\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 8.05256i | − | 0.450857i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.73205 | − | 2.73205i | 0.152251 | − | 0.152251i | ||||
\(323\) | −2.07055 | + | 2.07055i | −0.115209 | + | 0.115209i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 2.07055i | − | 0.114677i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.73205 | − | 6.73205i | −0.371715 | − | 0.371715i | ||||
\(329\) | −11.5911 | −0.639039 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.535898 | 0.0294556 | 0.0147278 | − | 0.999892i | \(-0.495312\pi\) | ||||
0.0147278 | + | 0.999892i | \(0.495312\pi\) | |||||||
\(332\) | −11.2629 | − | 11.2629i | −0.618134 | − | 0.618134i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.07180i | 0.168081i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.46410 | − | 6.46410i | 0.352122 | − | 0.352122i | −0.508777 | − | 0.860899i | \(-0.669902\pi\) |
0.860899 | + | 0.508777i | \(0.169902\pi\) | |||||||
\(338\) | 7.77817 | − | 7.77817i | 0.423077 | − | 0.423077i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 24.6336i | − | 1.33398i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.0263 | − | 14.0263i | −0.757348 | − | 0.757348i | ||||
\(344\) | 6.69213 | 0.360815 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.53590 | 0.190091 | ||||||||
\(347\) | −8.01841 | − | 8.01841i | −0.430451 | − | 0.430451i | 0.458331 | − | 0.888782i | \(-0.348448\pi\) |
−0.888782 | + | 0.458331i | \(0.848448\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 26.3923i | − | 1.41275i | −0.707839 | − | 0.706374i | \(-0.750330\pi\) | ||
0.707839 | − | 0.706374i | \(-0.249670\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.63397 | + | 1.63397i | −0.0870911 | + | 0.0870911i | ||||
\(353\) | 5.55532 | − | 5.55532i | 0.295680 | − | 0.295680i | −0.543639 | − | 0.839319i | \(-0.682954\pi\) |
0.839319 | + | 0.543639i | \(0.182954\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 8.76268i | − | 0.464421i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.83013 | − | 4.83013i | −0.255280 | − | 0.255280i | ||||
\(359\) | 20.6312 | 1.08887 | 0.544436 | − | 0.838802i | \(-0.316744\pi\) | ||||
0.544436 | + | 0.838802i | \(0.316744\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.7128 | 0.984885 | ||||||||
\(362\) | −0.757875 | − | 0.757875i | −0.0398330 | − | 0.0398330i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 9.46410i | − | 0.496054i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.0263 | + | 16.0263i | −0.836565 | + | 0.836565i | −0.988405 | − | 0.151840i | \(-0.951480\pi\) |
0.151840 | + | 0.988405i | \(0.451480\pi\) | |||||||
\(368\) | −1.41421 | + | 1.41421i | −0.0737210 | + | 0.0737210i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.17449i | 0.320564i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.3923 | + | 12.3923i | 0.641649 | + | 0.641649i | 0.950961 | − | 0.309312i | \(-0.100099\pi\) |
−0.309312 | + | 0.950961i | \(0.600099\pi\) | |||||||
\(374\) | −12.6264 | −0.652895 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.00000 | 0.309426 | ||||||||
\(377\) | −12.0716 | − | 12.0716i | −0.621718 | − | 0.621718i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.00000i | 0.410932i | 0.978664 | + | 0.205466i | \(0.0658711\pi\) | ||||
−0.978664 | + | 0.205466i | \(0.934129\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 18.3923 | − | 18.3923i | 0.941032 | − | 0.941032i | ||||
\(383\) | 24.9754 | − | 24.9754i | 1.27618 | − | 1.27618i | 0.333394 | − | 0.942787i | \(-0.391806\pi\) |
0.942787 | − | 0.333394i | \(-0.108194\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 15.5935i | 0.793689i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.43782 | + | 1.43782i | 0.0729944 | + | 0.0729944i | ||||
\(389\) | 8.90138 | 0.451318 | 0.225659 | − | 0.974206i | \(-0.427546\pi\) | ||||
0.225659 | + | 0.974206i | \(0.427546\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.9282 | −0.552663 | ||||||||
\(392\) | 2.31079 | + | 2.31079i | 0.116712 | + | 0.116712i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 7.73205i | − | 0.389535i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.92820 | − | 8.92820i | 0.448094 | − | 0.448094i | −0.446627 | − | 0.894720i | \(-0.647375\pi\) |
0.894720 | + | 0.446627i | \(0.147375\pi\) | |||||||
\(398\) | −14.3688 | + | 14.3688i | −0.720241 | + | 0.720241i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 1.31268i | − | 0.0655520i | −0.999463 | − | 0.0327760i | \(-0.989565\pi\) | ||
0.999463 | − | 0.0327760i | \(-0.0104348\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −36.9282 | − | 36.9282i | −1.83952 | − | 1.83952i | ||||
\(404\) | −12.2103 | −0.607484 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.73205 | −0.334106 | ||||||||
\(407\) | −18.9396 | − | 18.9396i | −0.938800 | − | 0.938800i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.6603i | 1.02158i | 0.859704 | + | 0.510792i | \(0.170648\pi\) | ||||
−0.859704 | + | 0.510792i | \(0.829352\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.26795 | + | 6.26795i | −0.308800 | + | 0.308800i | ||||
\(413\) | 13.9019 | − | 13.9019i | 0.684068 | − | 0.684068i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.89898i | 0.240192i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.875644 | − | 0.875644i | −0.0428292 | − | 0.0428292i | ||||
\(419\) | 37.7033 | 1.84193 | 0.920963 | − | 0.389650i | \(-0.127404\pi\) | ||||
0.920963 | + | 0.389650i | \(0.127404\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.85641 | 0.480372 | 0.240186 | − | 0.970727i | \(-0.422792\pi\) | ||||
0.240186 | + | 0.970727i | \(0.422792\pi\) | |||||||
\(422\) | −9.41902 | − | 9.41902i | −0.458511 | − | 0.458511i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 3.19615i | − | 0.155219i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.46410 | + | 3.46410i | −0.167640 | + | 0.167640i | ||||
\(428\) | 8.43451 | − | 8.43451i | 0.407698 | − | 0.407698i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.0363i | 0.531600i | 0.964028 | + | 0.265800i | \(0.0856361\pi\) | ||||
−0.964028 | + | 0.265800i | \(0.914364\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.16987 | + | 1.16987i | 0.0562205 | + | 0.0562205i | 0.734658 | − | 0.678438i | \(-0.237343\pi\) |
−0.678438 | + | 0.734658i | \(0.737343\pi\) | |||||||
\(434\) | −20.5940 | −0.988545 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | 0.0957826 | ||||||||
\(437\) | −0.757875 | − | 0.757875i | −0.0362541 | − | 0.0362541i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.2487i | 0.918691i | 0.888258 | + | 0.459345i | \(0.151916\pi\) | ||||
−0.888258 | + | 0.459345i | \(0.848084\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −18.9282 | + | 18.9282i | −0.900323 | + | 0.900323i | ||||
\(443\) | −8.66115 | + | 8.66115i | −0.411504 | + | 0.411504i | −0.882262 | − | 0.470759i | \(-0.843980\pi\) |
0.470759 | + | 0.882262i | \(0.343980\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.9348i | 0.517776i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.36603 | + | 1.36603i | 0.0645386 | + | 0.0645386i | ||||
\(449\) | −29.1165 | −1.37409 | −0.687046 | − | 0.726614i | \(-0.741093\pi\) | ||||
−0.687046 | + | 0.726614i | \(0.741093\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.0000 | 1.03594 | ||||||||
\(452\) | 2.17209 | + | 2.17209i | 0.102166 | + | 0.102166i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 11.4641i | − | 0.538037i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.2942 | − | 24.2942i | 1.13644 | − | 1.13644i | 0.147352 | − | 0.989084i | \(-0.452925\pi\) |
0.989084 | − | 0.147352i | \(-0.0470750\pi\) | |||||||
\(458\) | −15.8338 | + | 15.8338i | −0.739863 | + | 0.739863i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 30.6694i | − | 1.42842i | −0.699934 | − | 0.714208i | \(-0.746787\pi\) | ||
0.699934 | − | 0.714208i | \(-0.253213\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.29423 | + | 7.29423i | 0.338992 | + | 0.338992i | 0.855988 | − | 0.516996i | \(-0.172950\pi\) |
−0.516996 | + | 0.855988i | \(0.672950\pi\) | |||||||
\(464\) | 3.48477 | 0.161776 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −19.8564 | −0.919830 | ||||||||
\(467\) | 9.19239 | + | 9.19239i | 0.425373 | + | 0.425373i | 0.887049 | − | 0.461676i | \(-0.152752\pi\) |
−0.461676 | + | 0.887049i | \(0.652752\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 11.4641i | − | 0.529363i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.19615 | + | 7.19615i | −0.331230 | + | 0.331230i | ||||
\(473\) | −10.9348 | + | 10.9348i | −0.502781 | + | 0.502781i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 10.5558i | 0.483826i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 14.1962 | + | 14.1962i | 0.649317 | + | 0.649317i | ||||
\(479\) | 25.7332 | 1.17578 | 0.587891 | − | 0.808940i | \(-0.299958\pi\) | ||||
0.587891 | + | 0.808940i | \(0.299958\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −56.7846 | −2.58916 | ||||||||
\(482\) | −2.82843 | − | 2.82843i | −0.128831 | − | 0.128831i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.66025i | 0.257284i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.8038 | − | 12.8038i | 0.580198 | − | 0.580198i | −0.354760 | − | 0.934957i | \(-0.615437\pi\) |
0.934957 | + | 0.354760i | \(0.115437\pi\) | |||||||
\(488\) | 1.79315 | − | 1.79315i | 0.0811721 | − | 0.0811721i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.9773i | 1.08208i | 0.840997 | + | 0.541039i | \(0.181969\pi\) | ||||
−0.840997 | + | 0.541039i | \(0.818031\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.4641 | + | 13.4641i | 0.606393 | + | 0.606393i | ||||
\(494\) | −2.62536 | −0.118120 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.6603 | 0.478660 | ||||||||
\(497\) | −5.65685 | − | 5.65685i | −0.253745 | − | 0.253745i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.14359i | 0.364557i | 0.983247 | + | 0.182279i | \(0.0583473\pi\) | ||||
−0.983247 | + | 0.182279i | \(0.941653\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −13.7321 | + | 13.7321i | −0.612891 | + | 0.612891i | ||||
\(503\) | −15.8338 | + | 15.8338i | −0.705992 | + | 0.705992i | −0.965690 | − | 0.259698i | \(-0.916377\pi\) |
0.259698 | + | 0.965690i | \(0.416377\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 4.62158i | − | 0.205454i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.83013 | + | 9.83013i | 0.436141 | + | 0.436141i | ||||
\(509\) | 20.7699 | 0.920609 | 0.460305 | − | 0.887761i | \(-0.347740\pi\) | ||||
0.460305 | + | 0.887761i | \(0.347740\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.8564 | 0.922633 | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 12.7846i | 0.563905i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.80385 | + | 9.80385i | −0.431173 | + | 0.431173i | ||||
\(518\) | −15.8338 | + | 15.8338i | −0.695695 | + | 0.695695i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 13.3843i | − | 0.586375i | −0.956055 | − | 0.293188i | \(-0.905284\pi\) | ||
0.956055 | − | 0.293188i | \(-0.0947160\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.5359 | + | 14.5359i | 0.635610 | + | 0.635610i | 0.949470 | − | 0.313859i | \(-0.101622\pi\) |
−0.313859 | + | 0.949470i | \(0.601622\pi\) | |||||||
\(524\) | −12.7651 | −0.557645 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14.0000 | 0.610429 | ||||||||
\(527\) | 41.1881 | + | 41.1881i | 1.79418 | + | 1.79418i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.0000i | 0.826087i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.732051 | + | 0.732051i | −0.0317384 | + | 0.0317384i | ||||
\(533\) | 32.9802 | − | 32.9802i | 1.42853 | − | 1.42853i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.93426i | 0.256321i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15.3923 | + | 15.3923i | 0.663609 | + | 0.663609i | ||||
\(539\) | −7.55154 | −0.325268 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.32051 | −0.314733 | −0.157367 | − | 0.987540i | \(-0.550300\pi\) | ||||
−0.157367 | + | 0.987540i | \(0.550300\pi\) | |||||||
\(542\) | −17.9551 | − | 17.9551i | −0.771236 | − | 0.771236i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 5.46410i | − | 0.234271i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.9282 | + | 12.9282i | −0.552770 | + | 0.552770i | −0.927239 | − | 0.374469i | \(-0.877825\pi\) |
0.374469 | + | 0.927239i | \(0.377825\pi\) | |||||||
\(548\) | 2.44949 | − | 2.44949i | 0.104637 | − | 0.104637i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.86748i | 0.0795573i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.73205 | − | 4.73205i | −0.201227 | − | 0.201227i | ||||
\(554\) | −11.1106 | −0.472046 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −17.8564 | −0.757280 | ||||||||
\(557\) | 10.3664 | + | 10.3664i | 0.439237 | + | 0.439237i | 0.891755 | − | 0.452518i | \(-0.149474\pi\) |
−0.452518 | + | 0.891755i | \(0.649474\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.7846i | 1.38664i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.53590 | − | 2.53590i | 0.106970 | − | 0.106970i | ||||
\(563\) | −12.1595 | + | 12.1595i | −0.512462 | + | 0.512462i | −0.915280 | − | 0.402818i | \(-0.868031\pi\) |
0.402818 | + | 0.915280i | \(0.368031\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 7.45001i | − | 0.313147i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.92820 | + | 2.92820i | 0.122865 | + | 0.122865i | ||||
\(569\) | −36.0117 | −1.50969 | −0.754844 | − | 0.655904i | \(-0.772287\pi\) | ||||
−0.754844 | + | 0.655904i | \(0.772287\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.46410 | 0.228666 | 0.114333 | − | 0.993443i | \(-0.463527\pi\) | ||||
0.114333 | + | 0.993443i | \(0.463527\pi\) | |||||||
\(572\) | −8.00481 | − | 8.00481i | −0.334698 | − | 0.334698i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 18.3923i | − | 0.767680i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.39230 | + | 5.39230i | −0.224485 | + | 0.224485i | −0.810384 | − | 0.585899i | \(-0.800741\pi\) |
0.585899 | + | 0.810384i | \(0.300741\pi\) | |||||||
\(578\) | 9.09085 | − | 9.09085i | 0.378130 | − | 0.378130i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 30.7709i | − | 1.27659i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.22243 | + | 5.22243i | 0.216291 | + | 0.216291i | ||||
\(584\) | −10.7961 | −0.446745 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.0000 | 0.495715 | ||||||||
\(587\) | 27.2726 | + | 27.2726i | 1.12566 | + | 1.12566i | 0.990875 | + | 0.134784i | \(0.0430340\pi\) |
0.134784 | + | 0.990875i | \(0.456966\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.71281i | 0.235392i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.19615 | − | 8.19615i | 0.336860 | − | 0.336860i | ||||
\(593\) | −13.7632 | + | 13.7632i | −0.565187 | + | 0.565187i | −0.930776 | − | 0.365589i | \(-0.880867\pi\) |
0.365589 | + | 0.930776i | \(0.380867\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 0.240237i | − | 0.00984048i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.92820 | − | 6.92820i | −0.283315 | − | 0.283315i | ||||
\(599\) | 12.3490 | 0.504566 | 0.252283 | − | 0.967654i | \(-0.418819\pi\) | ||||
0.252283 | + | 0.967654i | \(0.418819\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.0000 | −0.530281 | −0.265141 | − | 0.964210i | \(-0.585418\pi\) | ||||
−0.265141 | + | 0.964210i | \(0.585418\pi\) | |||||||
\(602\) | 9.14162 | + | 9.14162i | 0.372585 | + | 0.372585i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 1.53590i | − | 0.0624948i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.58846 | + | 9.58846i | −0.389183 | + | 0.389183i | −0.874396 | − | 0.485213i | \(-0.838742\pi\) |
0.485213 | + | 0.874396i | \(0.338742\pi\) | |||||||
\(608\) | 0.378937 | − | 0.378937i | 0.0153679 | − | 0.0153679i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29.3939i | 1.18915i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.339746 | − | 0.339746i | −0.0137222 | − | 0.0137222i | 0.700212 | − | 0.713935i | \(-0.253089\pi\) |
−0.713935 | + | 0.700212i | \(0.753089\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.46410 | −0.179864 | ||||||||
\(617\) | 4.72311 | + | 4.72311i | 0.190145 | + | 0.190145i | 0.795759 | − | 0.605614i | \(-0.207072\pi\) |
−0.605614 | + | 0.795759i | \(0.707072\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 28.3923i | − | 1.14118i | −0.821234 | − | 0.570592i | \(-0.806714\pi\) | ||
0.821234 | − | 0.570592i | \(-0.193286\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.732051 | − | 0.732051i | 0.0293526 | − | 0.0293526i | ||||
\(623\) | 11.9700 | − | 11.9700i | 0.479570 | − | 0.479570i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 1.37705i | − | 0.0550379i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −12.0000 | − | 12.0000i | −0.478852 | − | 0.478852i | ||||
\(629\) | 63.3350 | 2.52533 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.9090 | −1.38970 | −0.694852 | − | 0.719153i | \(-0.744530\pi\) | ||||
−0.694852 | + | 0.719153i | \(0.744530\pi\) | |||||||
\(632\) | 2.44949 | + | 2.44949i | 0.0974355 | + | 0.0974355i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 5.53590i | − | 0.219859i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.3205 | + | 11.3205i | −0.448535 | + | 0.448535i | ||||
\(638\) | −5.69402 | + | 5.69402i | −0.225428 | + | 0.225428i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 11.0363i | − | 0.435908i | −0.975959 | − | 0.217954i | \(-0.930062\pi\) | ||
0.975959 | − | 0.217954i | \(-0.0699383\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.46410 | + | 3.46410i | 0.136611 | + | 0.136611i | 0.772105 | − | 0.635495i | \(-0.219204\pi\) |
−0.635495 | + | 0.772105i | \(0.719204\pi\) | |||||||
\(644\) | −3.86370 | −0.152251 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.92820 | 0.115209 | ||||||||
\(647\) | 18.5606 | + | 18.5606i | 0.729694 | + | 0.729694i | 0.970559 | − | 0.240865i | \(-0.0774310\pi\) |
−0.240865 | + | 0.970559i | \(0.577431\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 23.5167i | − | 0.923110i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.46410 | + | 1.46410i | −0.0573386 | + | 0.0573386i | ||||
\(653\) | 14.3688 | − | 14.3688i | 0.562293 | − | 0.562293i | −0.367665 | − | 0.929958i | \(-0.619843\pi\) |
0.929958 | + | 0.367665i | \(0.119843\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9.52056i | 0.371715i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8.19615 | + | 8.19615i | 0.319519 | + | 0.319519i | ||||
\(659\) | −26.4540 | −1.03050 | −0.515250 | − | 0.857040i | \(-0.672301\pi\) | ||||
−0.515250 | + | 0.857040i | \(0.672301\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.3923 | 0.715378 | 0.357689 | − | 0.933841i | \(-0.383565\pi\) | ||||
0.357689 | + | 0.933841i | \(0.383565\pi\) | |||||||
\(662\) | −0.378937 | − | 0.378937i | −0.0147278 | − | 0.0147278i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15.9282i | 0.618134i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.92820 | + | 4.92820i | −0.190821 | + | 0.190821i | ||||
\(668\) | 2.17209 | − | 2.17209i | 0.0840406 | − | 0.0840406i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.85993i | 0.226220i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.0263 | + | 16.0263i | 0.617768 | + | 0.617768i | 0.944958 | − | 0.327191i | \(-0.106102\pi\) |
−0.327191 | + | 0.944958i | \(0.606102\pi\) | |||||||
\(674\) | −9.14162 | −0.352122 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.0000 | −0.423077 | ||||||||
\(677\) | 9.69642 | + | 9.69642i | 0.372664 | + | 0.372664i | 0.868447 | − | 0.495783i | \(-0.165119\pi\) |
−0.495783 | + | 0.868447i | \(0.665119\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.92820i | 0.150751i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −17.4186 | + | 17.4186i | −0.666992 | + | 0.666992i | ||||
\(683\) | −12.0716 | + | 12.0716i | −0.461906 | + | 0.461906i | −0.899280 | − | 0.437374i | \(-0.855909\pi\) |
0.437374 | + | 0.899280i | \(0.355909\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 19.8362i | 0.757348i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.73205 | − | 4.73205i | −0.180408 | − | 0.180408i | ||||
\(689\) | 15.6579 | 0.596518 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.6410 | −1.31781 | −0.658903 | − | 0.752228i | \(-0.728979\pi\) | ||||
−0.658903 | + | 0.752228i | \(0.728979\pi\) | |||||||
\(692\) | −2.50026 | − | 2.50026i | −0.0950455 | − | 0.0950455i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11.3397i | 0.430451i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −36.7846 | + | 36.7846i | −1.39332 | + | 1.39332i | ||||
\(698\) | −18.6622 | + | 18.6622i | −0.706374 | + | 0.706374i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.1151i | 1.32628i | 0.748496 | + | 0.663140i | \(0.230776\pi\) | ||||
−0.748496 | + | 0.663140i | \(0.769224\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.39230 | + | 4.39230i | 0.165659 | + | 0.165659i | ||||
\(704\) | 2.31079 | 0.0870911 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.85641 | −0.295680 | ||||||||
\(707\) | −16.6796 | − | 16.6796i | −0.627299 | − | 0.627299i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.7846i | 1.08103i | 0.841335 | + | 0.540514i | \(0.181770\pi\) | ||||
−0.841335 | + | 0.540514i | \(0.818230\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.19615 | + | 6.19615i | −0.232211 | + | 0.232211i | ||||
\(713\) | −15.0759 | + | 15.0759i | −0.564596 | + | 0.564596i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.83083i | 0.255280i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −14.5885 | − | 14.5885i | −0.544436 | − | 0.544436i | ||||
\(719\) | 20.3538 | 0.759068 | 0.379534 | − | 0.925178i | \(-0.376084\pi\) | ||||
0.379534 | + | 0.925178i | \(0.376084\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.1244 | −0.637744 | ||||||||
\(722\) | −13.2320 | − | 13.2320i | −0.492442 | − | 0.492442i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.07180i | 0.0398330i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.0263 | + | 20.0263i | −0.742734 | + | 0.742734i | −0.973103 | − | 0.230370i | \(-0.926006\pi\) |
0.230370 | + | 0.973103i | \(0.426006\pi\) | |||||||
\(728\) | −6.69213 | + | 6.69213i | −0.248027 | + | 0.248027i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 36.5665i | − | 1.35246i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.1244 | − | 13.1244i | −0.484759 | − | 0.484759i | 0.421889 | − | 0.906648i | \(-0.361367\pi\) |
−0.906648 | + | 0.421889i | \(0.861367\pi\) | |||||||
\(734\) | 22.6646 | 0.836565 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.00000 | 0.0737210 | ||||||||
\(737\) | −9.69642 | − | 9.69642i | −0.357172 | − | 0.357172i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.9282i | 0.843428i | 0.906729 | + | 0.421714i | \(0.138571\pi\) | ||||
−0.906729 | + | 0.421714i | \(0.861429\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.36603 | − | 4.36603i | 0.160282 | − | 0.160282i | ||||
\(743\) | −33.2576 | + | 33.2576i | −1.22010 | + | 1.22010i | −0.252507 | + | 0.967595i | \(0.581255\pi\) |
−0.967595 | + | 0.252507i | \(0.918745\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 17.5254i | − | 0.641649i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.92820 | + | 8.92820i | 0.326447 | + | 0.326447i | ||||
\(749\) | 23.0435 | 0.841992 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.5885 | 1.22566 | 0.612830 | − | 0.790215i | \(-0.290031\pi\) | ||||
0.612830 | + | 0.790215i | \(0.290031\pi\) | |||||||
\(752\) | −4.24264 | − | 4.24264i | −0.154713 | − | 0.154713i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 17.0718i | 0.621718i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.19615 | + | 8.19615i | −0.297894 | + | 0.297894i | −0.840189 | − | 0.542294i | \(-0.817556\pi\) |
0.542294 | + | 0.840189i | \(0.317556\pi\) | |||||||
\(758\) | 5.65685 | − | 5.65685i | 0.205466 | − | 0.205466i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.6990i | 1.25784i | 0.777471 | + | 0.628919i | \(0.216502\pi\) | ||||
−0.777471 | + | 0.628919i | \(0.783498\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.73205 | + | 2.73205i | 0.0989069 | + | 0.0989069i | ||||
\(764\) | −26.0106 | −0.941032 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −35.3205 | −1.27618 | ||||||||
\(767\) | −35.2538 | − | 35.2538i | −1.27294 | − | 1.27294i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.78461i | 0.352842i | 0.984315 | + | 0.176421i | \(0.0564520\pi\) | ||||
−0.984315 | + | 0.176421i | \(0.943548\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 11.0263 | − | 11.0263i | 0.396844 | − | 0.396844i | ||||
\(773\) | 31.0112 | − | 31.0112i | 1.11539 | − | 1.11539i | 0.122986 | − | 0.992408i | \(-0.460753\pi\) |
0.992408 | − | 0.122986i | \(-0.0392469\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 2.03339i | − | 0.0729944i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.29423 | − | 6.29423i | −0.225659 | − | 0.225659i | ||||
\(779\) | −5.10205 | −0.182800 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.56922 | −0.342414 | ||||||||
\(782\) | 7.72741 | + | 7.72741i | 0.276331 | + | 0.276331i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 3.26795i | − | 0.116712i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.9282 | + | 16.9282i | −0.603425 | + | 0.603425i | −0.941220 | − | 0.337795i | \(-0.890319\pi\) |
0.337795 | + | 0.941220i | \(0.390319\pi\) | |||||||
\(788\) | −5.46739 | + | 5.46739i | −0.194768 | + | 0.194768i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.93426i | 0.210998i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.78461 | + | 8.78461i | 0.311951 | + | 0.311951i | ||||
\(794\) | −12.6264 | −0.448094 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20.3205 | 0.720241 | ||||||||
\(797\) | 10.7825 | + | 10.7825i | 0.381935 | + | 0.381935i | 0.871799 | − | 0.489864i | \(-0.162954\pi\) |
−0.489864 | + | 0.871799i | \(0.662954\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 32.7846i | − | 1.15984i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −0.928203 | + | 0.928203i | −0.0327760 | + | 0.0327760i | ||||
\(803\) | 17.6405 | − | 17.6405i | 0.622520 | − | 0.622520i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 52.2244i | 1.83952i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8.63397 | + | 8.63397i | 0.303742 | + | 0.303742i | ||||
\(809\) | −5.17638 | −0.181992 | −0.0909959 | − | 0.995851i | \(-0.529005\pi\) | ||||
−0.0909959 | + | 0.995851i | \(0.529005\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.0718 | −0.529242 | −0.264621 | − | 0.964352i | \(-0.585247\pi\) | ||||
−0.264621 | + | 0.964352i | \(0.585247\pi\) | |||||||
\(812\) | 4.76028 | + | 4.76028i | 0.167053 | + | 0.167053i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 26.7846i | 0.938800i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.53590 | − | 2.53590i | 0.0887199 | − | 0.0887199i | ||||
\(818\) | 14.6090 | − | 14.6090i | 0.510792 | − | 0.510792i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 40.0512i | − | 1.39780i | −0.715220 | − | 0.698899i | \(-0.753674\pi\) | ||
0.715220 | − | 0.698899i | \(-0.246326\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.7058 | + | 15.7058i | 0.547469 | + | 0.547469i | 0.925708 | − | 0.378239i | \(-0.123470\pi\) |
−0.378239 | + | 0.925708i | \(0.623470\pi\) | |||||||
\(824\) | 8.86422 | 0.308800 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −19.6603 | −0.684068 | ||||||||
\(827\) | −29.2180 | − | 29.2180i | −1.01601 | − | 1.01601i | −0.999870 | − | 0.0161401i | \(-0.994862\pi\) |
−0.0161401 | − | 0.999870i | \(-0.505138\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 37.3205i | − | 1.29619i | −0.761557 | − | 0.648097i | \(-0.775565\pi\) | ||
0.761557 | − | 0.648097i | \(-0.224435\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.46410 | − | 3.46410i | 0.120096 | − | 0.120096i | ||||
\(833\) | 12.6264 | − | 12.6264i | 0.437478 | − | 0.437478i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.23835i | 0.0428292i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −26.6603 | − | 26.6603i | −0.920963 | − | 0.920963i | ||||
\(839\) | 0.554803 | 0.0191539 | 0.00957696 | − | 0.999954i | \(-0.496952\pi\) | ||||
0.00957696 | + | 0.999954i | \(0.496952\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.8564 | −0.581255 | ||||||||
\(842\) | −6.96953 | − | 6.96953i | −0.240186 | − | 0.240186i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 13.3205i | 0.458511i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.73205 | + | 7.73205i | −0.265676 | + | 0.265676i | ||||
\(848\) | −2.26002 | + | 2.26002i | −0.0776094 | + | 0.0776094i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 23.1822i | 0.794676i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.1244 | + | 35.1244i | 1.20264 | + | 1.20264i | 0.973362 | + | 0.229273i | \(0.0736348\pi\) |
0.229273 | + | 0.973362i | \(0.426365\pi\) | |||||||
\(854\) | 4.89898 | 0.167640 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11.9282 | −0.407698 | ||||||||
\(857\) | −16.0096 | − | 16.0096i | −0.546878 | − | 0.546878i | 0.378658 | − | 0.925536i | \(-0.376386\pi\) |
−0.925536 | + | 0.378658i | \(0.876386\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.32051i | 0.113294i | 0.998394 | + | 0.0566471i | \(0.0180410\pi\) | ||||
−0.998394 | + | 0.0566471i | \(0.981959\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.80385 | − | 7.80385i | 0.265800 | − | 0.265800i | ||||
\(863\) | 5.17638 | − | 5.17638i | 0.176206 | − | 0.176206i | −0.613494 | − | 0.789700i | \(-0.710236\pi\) |
0.789700 | + | 0.613494i | \(0.210236\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 1.65445i | − | 0.0562205i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 14.5622 | + | 14.5622i | 0.494273 | + | 0.494273i | ||||
\(869\) | −8.00481 | −0.271545 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29.0718 | −0.985060 | ||||||||
\(872\) | −1.41421 | − | 1.41421i | −0.0478913 | − | 0.0478913i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.07180i | 0.0362541i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.73205 | − | 4.73205i | 0.159790 | − | 0.159790i | −0.622684 | − | 0.782474i | \(-0.713958\pi\) |
0.782474 | + | 0.622684i | \(0.213958\pi\) | |||||||
\(878\) | 13.6109 | − | 13.6109i | 0.459345 | − | 0.459345i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 16.2127i | − | 0.546219i | −0.961983 | − | 0.273110i | \(-0.911948\pi\) | ||
0.961983 | − | 0.273110i | \(-0.0880522\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.12436 | + | 5.12436i | 0.172448 | + | 0.172448i | 0.788054 | − | 0.615606i | \(-0.211089\pi\) |
−0.615606 | + | 0.788054i | \(0.711089\pi\) | |||||||
\(884\) | 26.7685 | 0.900323 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.2487 | 0.411504 | ||||||||
\(887\) | 4.41851 | + | 4.41851i | 0.148359 | + | 0.148359i | 0.777385 | − | 0.629026i | \(-0.216546\pi\) |
−0.629026 | + | 0.777385i | \(0.716546\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 26.8564i | 0.900735i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.73205 | − | 7.73205i | 0.258888 | − | 0.258888i | ||||
\(893\) | 2.27362 | − | 2.27362i | 0.0760839 | − | 0.0760839i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 1.93185i | − | 0.0645386i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 20.5885 | + | 20.5885i | 0.687046 | + | 0.687046i | ||||
\(899\) | 37.1485 | 1.23897 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.4641 | −0.581814 | ||||||||
\(902\) | −15.5563 | − | 15.5563i | −0.517970 | − | 0.517970i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 3.07180i | − | 0.102166i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.9808 | − | 24.9808i | 0.829473 | − | 0.829473i | −0.157971 | − | 0.987444i | \(-0.550495\pi\) |
0.987444 | + | 0.157971i | \(0.0504953\pi\) | |||||||
\(908\) | −8.10634 | + | 8.10634i | −0.269018 | + | 0.269018i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 36.4922i | − | 1.20904i | −0.796590 | − | 0.604519i | \(-0.793365\pi\) | ||
0.796590 | − | 0.604519i | \(-0.206635\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26.0263 | − | 26.0263i | −0.861344 | − | 0.861344i | ||||
\(914\) | −34.3572 | −1.13644 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 22.3923 | 0.739863 | ||||||||
\(917\) | −17.4374 | − | 17.4374i | −0.575835 | − | 0.575835i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 10.4115i | − | 0.343445i | −0.985145 | − | 0.171723i | \(-0.945067\pi\) | ||
0.985145 | − | 0.171723i | \(-0.0549333\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −21.6865 | + | 21.6865i | −0.714208 | + | 0.714208i | ||||
\(923\) | −14.3452 | + | 14.3452i | −0.472178 | + | 0.472178i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 10.3156i | − | 0.338992i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.46410 | − | 2.46410i | −0.0808881 | − | 0.0808881i | ||||
\(929\) | −56.3655 | −1.84929 | −0.924646 | − | 0.380829i | \(-0.875639\pi\) | ||||
−0.924646 | + | 0.380829i | \(0.875639\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.75129 | 0.0573962 | ||||||||
\(932\) | 14.0406 | + | 14.0406i | 0.459915 | + | 0.459915i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 13.0000i | − | 0.425373i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.1699 | + | 10.1699i | −0.332235 | + | 0.332235i | −0.853435 | − | 0.521200i | \(-0.825485\pi\) |
0.521200 | + | 0.853435i | \(0.325485\pi\) | |||||||
\(938\) | −8.10634 | + | 8.10634i | −0.264682 | + | 0.264682i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.6555i | 0.379958i | 0.981788 | + | 0.189979i | \(0.0608420\pi\) | ||||
−0.981788 | + | 0.189979i | \(0.939158\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.4641 | − | 13.4641i | −0.438451 | − | 0.438451i | ||||
\(944\) | 10.1769 | 0.331230 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 15.4641 | 0.502781 | ||||||||
\(947\) | 39.8618 | + | 39.8618i | 1.29533 | + | 1.29533i | 0.931441 | + | 0.363893i | \(0.118553\pi\) |
0.363893 | + | 0.931441i | \(0.381447\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 52.8897i | − | 1.71687i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.46410 | − | 7.46410i | 0.241913 | − | 0.241913i | ||||
\(953\) | −15.1774 | + | 15.1774i | −0.491645 | + | 0.491645i | −0.908824 | − | 0.417180i | \(-0.863019\pi\) |
0.417180 | + | 0.908824i | \(0.363019\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 20.0764i | − | 0.649317i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −18.1962 | − | 18.1962i | −0.587891 | − | 0.587891i | ||||
\(959\) | 6.69213 | 0.216100 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 82.6410 | 2.66584 | ||||||||
\(962\) | 40.1528 | + | 40.1528i | 1.29458 | + | 1.29458i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.00000i | 0.128831i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.4904 | − | 28.4904i | 0.916189 | − | 0.916189i | −0.0805608 | − | 0.996750i | \(-0.525671\pi\) |
0.996750 | + | 0.0805608i | \(0.0256711\pi\) | |||||||
\(968\) | 4.00240 | − | 4.00240i | 0.128642 | − | 0.128642i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.1808i | 0.936458i | 0.883607 | + | 0.468229i | \(0.155108\pi\) | ||||
−0.883607 | + | 0.468229i | \(0.844892\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.3923 | − | 24.3923i | −0.781981 | − | 0.781981i | ||||
\(974\) | −18.1074 | −0.580198 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.53590 | −0.0811721 | ||||||||
\(977\) | 22.5259 | + | 22.5259i | 0.720667 | + | 0.720667i | 0.968741 | − | 0.248074i | \(-0.0797977\pi\) |
−0.248074 | + | 0.968741i | \(0.579798\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 20.2487i | − | 0.647152i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 16.9545 | − | 16.9545i | 0.541039 | − | 0.541039i | ||||
\(983\) | 3.00429 | − | 3.00429i | 0.0958221 | − | 0.0958221i | −0.657571 | − | 0.753393i | \(-0.728416\pi\) |
0.753393 | + | 0.657571i | \(0.228416\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 19.0411i | − | 0.606393i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.85641 | + | 1.85641i | 0.0590602 | + | 0.0590602i | ||||
\(989\) | 13.3843 | 0.425595 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.3923 | 0.743081 | 0.371541 | − | 0.928417i | \(-0.378830\pi\) | ||||
0.371541 | + | 0.928417i | \(0.378830\pi\) | |||||||
\(992\) | −7.53794 | − | 7.53794i | −0.239330 | − | 0.239330i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.00000i | 0.253745i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.14359 | − | 6.14359i | 0.194570 | − | 0.194570i | −0.603098 | − | 0.797667i | \(-0.706067\pi\) |
0.797667 | + | 0.603098i | \(0.206067\pi\) | |||||||
\(998\) | 5.75839 | − | 5.75839i | 0.182279 | − | 0.182279i | ||||
\(999\) | 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 | 1350.2.f.a.593.1 | 8 | ||
3.2 | odd | 2 | inner | 1350.2.f.a.593.3 | 8 | ||
5.2 | odd | 4 | inner | 1350.2.f.a.107.3 | 8 | ||
5.3 | odd | 4 | 270.2.f.b.107.1 | yes | 8 | ||
5.4 | even | 2 | 270.2.f.b.53.4 | yes | 8 | ||
15.2 | even | 4 | inner | 1350.2.f.a.107.1 | 8 | ||
15.8 | even | 4 | 270.2.f.b.107.4 | yes | 8 | ||
15.14 | odd | 2 | 270.2.f.b.53.1 | ✓ | 8 | ||
20.3 | even | 4 | 2160.2.w.b.1457.1 | 8 | |||
20.19 | odd | 2 | 2160.2.w.b.593.4 | 8 | |||
45.4 | even | 6 | 810.2.m.e.593.1 | 8 | |||
45.13 | odd | 12 | 810.2.m.d.107.1 | 8 | |||
45.14 | odd | 6 | 810.2.m.e.593.2 | 8 | |||
45.23 | even | 12 | 810.2.m.d.107.2 | 8 | |||
45.29 | odd | 6 | 810.2.m.d.53.1 | 8 | |||
45.34 | even | 6 | 810.2.m.d.53.2 | 8 | |||
45.38 | even | 12 | 810.2.m.e.377.1 | 8 | |||
45.43 | odd | 12 | 810.2.m.e.377.2 | 8 | |||
60.23 | odd | 4 | 2160.2.w.b.1457.4 | 8 | |||
60.59 | even | 2 | 2160.2.w.b.593.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
270.2.f.b.53.1 | ✓ | 8 | 15.14 | odd | 2 | ||
270.2.f.b.53.4 | yes | 8 | 5.4 | even | 2 | ||
270.2.f.b.107.1 | yes | 8 | 5.3 | odd | 4 | ||
270.2.f.b.107.4 | yes | 8 | 15.8 | even | 4 | ||
810.2.m.d.53.1 | 8 | 45.29 | odd | 6 | |||
810.2.m.d.53.2 | 8 | 45.34 | even | 6 | |||
810.2.m.d.107.1 | 8 | 45.13 | odd | 12 | |||
810.2.m.d.107.2 | 8 | 45.23 | even | 12 | |||
810.2.m.e.377.1 | 8 | 45.38 | even | 12 | |||
810.2.m.e.377.2 | 8 | 45.43 | odd | 12 | |||
810.2.m.e.593.1 | 8 | 45.4 | even | 6 | |||
810.2.m.e.593.2 | 8 | 45.14 | odd | 6 | |||
1350.2.f.a.107.1 | 8 | 15.2 | even | 4 | inner | ||
1350.2.f.a.107.3 | 8 | 5.2 | odd | 4 | inner | ||
1350.2.f.a.593.1 | 8 | 1.1 | even | 1 | trivial | ||
1350.2.f.a.593.3 | 8 | 3.2 | odd | 2 | inner | ||
2160.2.w.b.593.1 | 8 | 60.59 | even | 2 | |||
2160.2.w.b.593.4 | 8 | 20.19 | odd | 2 | |||
2160.2.w.b.1457.1 | 8 | 20.3 | even | 4 | |||
2160.2.w.b.1457.4 | 8 | 60.23 | odd | 4 |