Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,2,Mod(2177,2880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2880, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 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("2880.2177");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.w (of order \(4\), degree \(2\), not 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: | \(22.9969157821\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | no (minimal twist has level 1440) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 2753.4 | ||
Root | \(0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2880.2753 |
Dual form | 2880.2.w.n.2177.4 |
$q$-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 \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(2431\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.12132 | − | 0.707107i | 0.948683 | − | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.46410 | − | 3.46410i | 1.30931 | − | 1.30931i | 0.387392 | − | 0.921915i | \(-0.373376\pi\) |
0.921915 | − | 0.387392i | \(-0.126624\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.89898i | 1.47710i | 0.674200 | + | 0.738549i | \(0.264489\pi\) | ||||
−0.674200 | + | 0.738549i | \(0.735511\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | − | 1.00000i | −0.277350 | − | 0.277350i | 0.554700 | − | 0.832050i | \(-0.312833\pi\) |
−0.832050 | + | 0.554700i | \(0.812833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.82843 | − | 2.82843i | −0.685994 | − | 0.685994i | 0.275350 | − | 0.961344i | \(-0.411206\pi\) |
−0.961344 | + | 0.275350i | \(0.911206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 6.92820i | − | 1.58944i | −0.606977 | − | 0.794719i | \(-0.707618\pi\) | ||
0.606977 | − | 0.794719i | \(-0.292382\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.00000 | − | 3.00000i | 0.800000 | − | 0.600000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.07107 | 1.31306 | 0.656532 | − | 0.754298i | \(-0.272023\pi\) | ||||
0.656532 | + | 0.754298i | \(0.272023\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.92820 | −1.24434 | −0.622171 | − | 0.782881i | \(-0.713749\pi\) | ||||
−0.622171 | + | 0.782881i | \(0.713749\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.89898 | − | 9.79796i | 0.828079 | − | 1.65616i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | + | 1.00000i | −0.164399 | + | 0.164399i | −0.784512 | − | 0.620113i | \(-0.787087\pi\) |
0.620113 | + | 0.784512i | \(0.287087\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 9.89949i | − | 1.54604i | −0.634381 | − | 0.773021i | \(-0.718745\pi\) | ||
0.634381 | − | 0.773021i | \(-0.281255\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.92820 | + | 6.92820i | 1.05654 | + | 1.05654i | 0.998303 | + | 0.0582384i | \(0.0185483\pi\) |
0.0582384 | + | 0.998303i | \(0.481452\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.89898 | + | 4.89898i | 0.714590 | + | 0.714590i | 0.967492 | − | 0.252902i | \(-0.0813851\pi\) |
−0.252902 | + | 0.967492i | \(0.581385\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 17.0000i | − | 2.42857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.82843 | − | 2.82843i | 0.388514 | − | 0.388514i | −0.485643 | − | 0.874157i | \(-0.661414\pi\) |
0.874157 | + | 0.485643i | \(0.161414\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.46410 | + | 10.3923i | 0.467099 | + | 1.40130i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.89898 | −0.637793 | −0.318896 | − | 0.947790i | \(-0.603312\pi\) | ||||
−0.318896 | + | 0.947790i | \(0.603312\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.82843 | − | 1.41421i | −0.350823 | − | 0.175412i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.92820 | + | 6.92820i | −0.846415 | + | 0.846415i | −0.989684 | − | 0.143269i | \(-0.954239\pi\) |
0.143269 | + | 0.989684i | \(0.454239\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.00000 | − | 7.00000i | −0.819288 | − | 0.819288i | 0.166717 | − | 0.986005i | \(-0.446683\pi\) |
−0.986005 | + | 0.166717i | \(0.946683\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 16.9706 | + | 16.9706i | 1.93398 | + | 1.93398i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 6.92820i | − | 0.779484i | −0.920924 | − | 0.389742i | \(-0.872564\pi\) | ||
0.920924 | − | 0.389742i | \(-0.127436\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.89898 | + | 4.89898i | −0.537733 | + | 0.537733i | −0.922862 | − | 0.385130i | \(-0.874157\pi\) |
0.385130 | + | 0.922862i | \(0.374157\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.00000 | − | 4.00000i | −0.867722 | − | 0.433861i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.89949 | 1.04934 | 0.524672 | − | 0.851304i | \(-0.324188\pi\) | ||||
0.524672 | + | 0.851304i | \(0.324188\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.92820 | −0.726273 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.89898 | − | 14.6969i | −0.502625 | − | 1.50787i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.00000 | − | 5.00000i | 0.507673 | − | 0.507673i | −0.406138 | − | 0.913812i | \(-0.633125\pi\) |
0.913812 | + | 0.406138i | \(0.133125\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.24264i | 0.422159i | 0.977469 | + | 0.211079i | \(0.0676978\pi\) | ||||
−0.977469 | + | 0.211079i | \(0.932302\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.46410 | + | 3.46410i | 0.341328 | + | 0.341328i | 0.856866 | − | 0.515538i | \(-0.172408\pi\) |
−0.515538 | + | 0.856866i | \(0.672408\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.89898 | + | 4.89898i | 0.473602 | + | 0.473602i | 0.903078 | − | 0.429476i | \(-0.141302\pi\) |
−0.429476 | + | 0.903078i | \(0.641302\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.00000i | 0.766261i | 0.923694 | + | 0.383131i | \(0.125154\pi\) | ||||
−0.923694 | + | 0.383131i | \(0.874846\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.07107 | + | 7.07107i | −0.665190 | + | 0.665190i | −0.956599 | − | 0.291409i | \(-0.905876\pi\) |
0.291409 | + | 0.956599i | \(0.405876\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −19.5959 | −1.79635 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.0000 | −1.18182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.36396 | − | 9.19239i | 0.569210 | − | 0.822192i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.3923 | + | 10.3923i | −0.922168 | + | 0.922168i | −0.997182 | − | 0.0750145i | \(-0.976100\pi\) |
0.0750145 | + | 0.997182i | \(0.476100\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 4.89898i | − | 0.428026i | −0.976831 | − | 0.214013i | \(-0.931347\pi\) | ||
0.976831 | − | 0.214013i | \(-0.0686535\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −24.0000 | − | 24.0000i | −2.08106 | − | 2.08106i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.41421 | + | 1.41421i | 0.120824 | + | 0.120824i | 0.764934 | − | 0.644109i | \(-0.222772\pi\) |
−0.644109 | + | 0.764934i | \(0.722772\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.89898 | − | 4.89898i | 0.409673 | − | 0.409673i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.0000 | − | 5.00000i | 1.24568 | − | 0.415227i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.24264 | 0.347571 | 0.173785 | − | 0.984784i | \(-0.444400\pi\) | ||||
0.173785 | + | 0.984784i | \(0.444400\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.6969 | + | 4.89898i | −1.18049 | + | 0.393496i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.0000 | − | 13.0000i | 1.03751 | − | 1.03751i | 0.0382445 | − | 0.999268i | \(-0.487823\pi\) |
0.999268 | − | 0.0382445i | \(-0.0121766\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.92820 | − | 6.92820i | −0.542659 | − | 0.542659i | 0.381649 | − | 0.924307i | \(-0.375356\pi\) |
−0.924307 | + | 0.381649i | \(0.875356\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.79796 | + | 9.79796i | 0.758189 | + | 0.758189i | 0.975993 | − | 0.217804i | \(-0.0698893\pi\) |
−0.217804 | + | 0.975993i | \(0.569889\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 11.0000i | − | 0.846154i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.41421 | − | 1.41421i | 0.107521 | − | 0.107521i | −0.651300 | − | 0.758820i | \(-0.725776\pi\) |
0.758820 | + | 0.651300i | \(0.225776\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.46410 | − | 24.2487i | 0.261861 | − | 1.83303i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.89898 | −0.366167 | −0.183083 | − | 0.983097i | \(-0.558608\pi\) | ||||
−0.183083 | + | 0.983097i | \(0.558608\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.00000 | 0.594635 | 0.297318 | − | 0.954779i | \(-0.403908\pi\) | ||||
0.297318 | + | 0.954779i | \(0.403908\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.41421 | + | 2.82843i | −0.103975 | + | 0.207950i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.8564 | − | 13.8564i | 1.01328 | − | 1.01328i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.5959i | 1.41791i | 0.705253 | + | 0.708955i | \(0.250833\pi\) | ||||
−0.705253 | + | 0.708955i | \(0.749167\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.00000 | − | 7.00000i | −0.503871 | − | 0.503871i | 0.408768 | − | 0.912639i | \(-0.365959\pi\) |
−0.912639 | + | 0.408768i | \(0.865959\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.41421 | − | 1.41421i | −0.100759 | − | 0.100759i | 0.654931 | − | 0.755689i | \(-0.272698\pi\) |
−0.755689 | + | 0.654931i | \(0.772698\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 13.8564i | − | 0.982255i | −0.871088 | − | 0.491127i | \(-0.836585\pi\) | ||
0.871088 | − | 0.491127i | \(-0.163415\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 24.4949 | − | 24.4949i | 1.71920 | − | 1.71920i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.00000 | − | 21.0000i | −0.488901 | − | 1.46670i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 33.9411 | 2.34776 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.8564 | 0.953914 | 0.476957 | − | 0.878927i | \(-0.341740\pi\) | ||||
0.476957 | + | 0.878927i | \(0.341740\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 19.5959 | + | 9.79796i | 1.33643 | + | 0.668215i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −24.0000 | + | 24.0000i | −1.62923 | + | 1.62923i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.65685i | 0.380521i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.3923 | + | 10.3923i | 0.695920 | + | 0.695920i | 0.963528 | − | 0.267608i | \(-0.0862331\pi\) |
−0.267608 | + | 0.963528i | \(0.586233\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.79796 | + | 9.79796i | 0.650313 | + | 0.650313i | 0.953068 | − | 0.302755i | \(-0.0979064\pi\) |
−0.302755 | + | 0.953068i | \(0.597906\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.0000i | 1.18947i | 0.803921 | + | 0.594737i | \(0.202744\pi\) | ||||
−0.803921 | + | 0.594737i | \(0.797256\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.82843 | − | 2.82843i | 0.185296 | − | 0.185296i | −0.608363 | − | 0.793659i | \(-0.708173\pi\) |
0.793659 | + | 0.608363i | \(0.208173\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.8564 | + | 6.92820i | 0.903892 | + | 0.451946i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.5959 | 1.26755 | 0.633777 | − | 0.773516i | \(-0.281504\pi\) | ||||
0.633777 | + | 0.773516i | \(0.281504\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.00000 | 0.386494 | 0.193247 | − | 0.981150i | \(-0.438098\pi\) | ||||
0.193247 | + | 0.981150i | \(0.438098\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.0208 | − | 36.0624i | −0.767982 | − | 2.30395i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.92820 | + | 6.92820i | −0.440831 | + | 0.440831i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.89898i | 0.309221i | 0.987976 | + | 0.154610i | \(0.0494122\pi\) | ||||
−0.987976 | + | 0.154610i | \(0.950588\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.5563 | + | 15.5563i | 0.970378 | + | 0.970378i | 0.999574 | − | 0.0291953i | \(-0.00929448\pi\) |
−0.0291953 | + | 0.999574i | \(0.509294\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.92820i | 0.430498i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.00000 | − | 8.00000i | 0.245718 | − | 0.491436i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −21.2132 | −1.29339 | −0.646696 | − | 0.762748i | \(-0.723850\pi\) | ||||
−0.646696 | + | 0.762748i | \(0.723850\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.7128 | 1.68343 | 0.841717 | − | 0.539919i | \(-0.181545\pi\) | ||||
0.841717 | + | 0.539919i | \(0.181545\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 14.6969 | + | 19.5959i | 0.886259 | + | 1.18168i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.0000 | − | 11.0000i | 0.660926 | − | 0.660926i | −0.294672 | − | 0.955598i | \(-0.595211\pi\) |
0.955598 | + | 0.294672i | \(0.0952105\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 24.0416i | − | 1.43420i | −0.696969 | − | 0.717102i | \(-0.745468\pi\) | ||
0.696969 | − | 0.717102i | \(-0.254532\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.8564 | − | 13.8564i | −0.823678 | − | 0.823678i | 0.162956 | − | 0.986633i | \(-0.447897\pi\) |
−0.986633 | + | 0.162956i | \(0.947897\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −34.2929 | − | 34.2929i | −2.02424 | − | 2.02424i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 1.00000i | − | 0.0588235i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.89949 | + | 9.89949i | −0.578335 | + | 0.578335i | −0.934444 | − | 0.356110i | \(-0.884103\pi\) |
0.356110 | + | 0.934444i | \(0.384103\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.3923 | + | 3.46410i | −0.605063 | + | 0.201688i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 48.0000 | 2.76667 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.92820 | + | 6.92820i | −0.395413 | + | 0.395413i | −0.876612 | − | 0.481198i | \(-0.840202\pi\) |
0.481198 | + | 0.876612i | \(0.340202\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 29.3939i | − | 1.66677i | −0.552690 | − | 0.833387i | \(-0.686399\pi\) | ||
0.552690 | − | 0.833387i | \(-0.313601\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.0000 | + | 11.0000i | 0.621757 | + | 0.621757i | 0.945980 | − | 0.324224i | \(-0.105103\pi\) |
−0.324224 | + | 0.945980i | \(0.605103\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.82843 | + | 2.82843i | 0.158860 | + | 0.158860i | 0.782062 | − | 0.623201i | \(-0.214168\pi\) |
−0.623201 | + | 0.782062i | \(0.714168\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 34.6410i | 1.93952i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.5959 | + | 19.5959i | −1.09035 | + | 1.09035i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.00000 | − | 1.00000i | −0.388290 | − | 0.0554700i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 33.9411 | 1.87123 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −34.6410 | −1.90404 | −0.952021 | − | 0.306032i | \(-0.900999\pi\) | ||||
−0.952021 | + | 0.306032i | \(0.900999\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.79796 | + | 19.5959i | −0.535320 | + | 1.07064i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.0000 | + | 13.0000i | −0.708155 | + | 0.708155i | −0.966147 | − | 0.257992i | \(-0.916939\pi\) |
0.257992 | + | 0.966147i | \(0.416939\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 33.9411i | − | 1.83801i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −34.6410 | − | 34.6410i | −1.87044 | − | 1.87044i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.5959 | − | 19.5959i | −1.05196 | − | 1.05196i | −0.998574 | − | 0.0533903i | \(-0.982997\pi\) |
−0.0533903 | − | 0.998574i | \(-0.517003\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.7990 | + | 19.7990i | −1.05379 | + | 1.05379i | −0.0553255 | + | 0.998468i | \(0.517620\pi\) |
−0.998468 | + | 0.0553255i | \(0.982380\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.79796 | 0.517116 | 0.258558 | − | 0.965996i | \(-0.416753\pi\) | ||||
0.258558 | + | 0.965996i | \(0.416753\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −29.0000 | −1.52632 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −19.7990 | − | 9.89949i | −1.03633 | − | 0.518163i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.3923 | − | 10.3923i | 0.542474 | − | 0.542474i | −0.381780 | − | 0.924253i | \(-0.624689\pi\) |
0.924253 | + | 0.381780i | \(0.124689\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 19.5959i | − | 1.01737i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.00000 | − | 7.00000i | −0.362446 | − | 0.362446i | 0.502267 | − | 0.864713i | \(-0.332500\pi\) |
−0.864713 | + | 0.502267i | \(0.832500\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.07107 | − | 7.07107i | −0.364179 | − | 0.364179i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.7128i | 1.42351i | 0.702427 | + | 0.711756i | \(0.252100\pi\) | ||||
−0.702427 | + | 0.711756i | \(0.747900\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.6969 | + | 14.6969i | −0.750978 | + | 0.750978i | −0.974662 | − | 0.223683i | \(-0.928192\pi\) |
0.223683 | + | 0.974662i | \(0.428192\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 48.0000 | + | 24.0000i | 2.44631 | + | 1.22315i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.24264 | −0.215110 | −0.107555 | − | 0.994199i | \(-0.534302\pi\) | ||||
−0.107555 | + | 0.994199i | \(0.534302\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.89898 | − | 14.6969i | −0.246494 | − | 0.739483i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.00000 | − | 5.00000i | 0.250943 | − | 0.250943i | −0.570414 | − | 0.821357i | \(-0.693217\pi\) |
0.821357 | + | 0.570414i | \(0.193217\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.2132i | 1.05934i | 0.848205 | + | 0.529668i | \(0.177684\pi\) | ||||
−0.848205 | + | 0.529668i | \(0.822316\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.92820 | + | 6.92820i | 0.345118 | + | 0.345118i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.89898 | − | 4.89898i | −0.242833 | − | 0.242833i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.00000i | 0.395575i | 0.980245 | + | 0.197787i | \(0.0633755\pi\) | ||||
−0.980245 | + | 0.197787i | \(0.936624\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −16.9706 | + | 16.9706i | −0.835067 | + | 0.835067i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.92820 | + | 13.8564i | −0.340092 | + | 0.680184i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.89898 | −0.239331 | −0.119665 | − | 0.992814i | \(-0.538182\pi\) | ||||
−0.119665 | + | 0.992814i | \(0.538182\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.0000 | −1.46211 | −0.731055 | − | 0.682318i | \(-0.760972\pi\) | ||||
−0.731055 | + | 0.682318i | \(0.760972\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −19.7990 | − | 2.82843i | −0.960392 | − | 0.137199i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.5959i | 0.943902i | 0.881625 | + | 0.471951i | \(0.156450\pi\) | ||||
−0.881625 | + | 0.471951i | \(0.843550\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.00000 | + | 7.00000i | 0.336399 | + | 0.336399i | 0.855010 | − | 0.518611i | \(-0.173551\pi\) |
−0.518611 | + | 0.855010i | \(0.673551\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.7128i | 1.32266i | 0.750095 | + | 0.661330i | \(0.230008\pi\) | ||||
−0.750095 | + | 0.661330i | \(0.769992\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.79796 | + | 9.79796i | −0.465515 | + | 0.465515i | −0.900458 | − | 0.434943i | \(-0.856769\pi\) |
0.434943 | + | 0.900458i | \(0.356769\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21.0000 | − | 7.00000i | 0.995495 | − | 0.331832i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.2132 | 1.00111 | 0.500556 | − | 0.865704i | \(-0.333129\pi\) | ||||
0.500556 | + | 0.865704i | \(0.333129\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 48.4974 | 2.28365 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.6969 | + | 4.89898i | −0.689003 | + | 0.229668i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.0000 | + | 23.0000i | −1.07589 | + | 1.07589i | −0.0790217 | + | 0.996873i | \(0.525180\pi\) |
−0.996873 | + | 0.0790217i | \(0.974820\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.7279i | 0.592798i | 0.955064 | + | 0.296399i | \(0.0957859\pi\) | ||||
−0.955064 | + | 0.296399i | \(0.904214\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.46410 | + | 3.46410i | 0.160990 | + | 0.160990i | 0.783005 | − | 0.622015i | \(-0.213686\pi\) |
−0.622015 | + | 0.783005i | \(0.713686\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.4949 | − | 24.4949i | −1.13349 | − | 1.13349i | −0.989593 | − | 0.143896i | \(-0.954037\pi\) |
−0.143896 | − | 0.989593i | \(-0.545963\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 48.0000i | 2.21643i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −33.9411 | + | 33.9411i | −1.56061 | + | 1.56061i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.7846 | − | 27.7128i | −0.953663 | − | 1.27155i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.5959 | 0.895360 | 0.447680 | − | 0.894194i | \(-0.352250\pi\) | ||||
0.447680 | + | 0.894194i | \(0.352250\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.00000 | 0.0911922 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.07107 | − | 14.1421i | 0.321081 | − | 0.642161i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.3205 | − | 17.3205i | 0.784867 | − | 0.784867i | −0.195781 | − | 0.980648i | \(-0.562724\pi\) |
0.980648 | + | 0.195781i | \(0.0627240\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.4949i | 1.10544i | 0.833367 | + | 0.552720i | \(0.186410\pi\) | ||||
−0.833367 | + | 0.552720i | \(0.813590\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.0000 | − | 20.0000i | −0.900755 | − | 0.900755i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 6.92820i | − | 0.310149i | −0.987903 | − | 0.155074i | \(-0.950438\pi\) | ||
0.987903 | − | 0.155074i | \(-0.0495618\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.89898 | + | 4.89898i | −0.218435 | + | 0.218435i | −0.807839 | − | 0.589404i | \(-0.799363\pi\) |
0.589404 | + | 0.807839i | \(0.299363\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.00000 | + | 9.00000i | 0.133498 | + | 0.400495i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.07107 | −0.313420 | −0.156710 | − | 0.987645i | \(-0.550089\pi\) | ||||
−0.156710 | + | 0.987645i | \(0.550089\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −48.4974 | −2.14540 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.79796 | + | 4.89898i | 0.431750 | + | 0.215875i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −24.0000 | + | 24.0000i | −1.05552 | + | 1.05552i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 38.1838i | − | 1.67286i | −0.548073 | − | 0.836431i | \(-0.684638\pi\) | ||
0.548073 | − | 0.836431i | \(-0.315362\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 19.5959 | + | 19.5959i | 0.853612 | + | 0.853612i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000i | 1.00000i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.89949 | + | 9.89949i | −0.428795 | + | 0.428795i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.8564 | + | 6.92820i | 0.599065 | + | 0.299532i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 83.2827 | 3.58724 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.0000 | 1.71973 | 0.859867 | − | 0.510518i | \(-0.170546\pi\) | ||||
0.859867 | + | 0.510518i | \(0.170546\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.65685 | + | 16.9706i | 0.242313 | + | 0.726939i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 48.9898i | − | 2.08704i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24.0000 | − | 24.0000i | −1.02058 | − | 1.02058i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.1127 | + | 31.1127i | 1.31829 | + | 1.31829i | 0.915131 | + | 0.403156i | \(0.132087\pi\) |
0.403156 | + | 0.915131i | \(0.367913\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 13.8564i | − | 0.586064i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.0000 | + | 20.0000i | −0.420703 | + | 0.841406i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −38.1838 | −1.60075 | −0.800373 | − | 0.599502i | \(-0.795365\pi\) | ||||
−0.800373 | + | 0.599502i | \(0.795365\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.7846 | 0.869809 | 0.434904 | − | 0.900477i | \(-0.356782\pi\) | ||||
0.434904 | + | 0.900477i | \(0.356782\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.00000 | + | 1.00000i | −0.0416305 | + | 0.0416305i | −0.727616 | − | 0.685985i | \(-0.759372\pi\) |
0.685985 | + | 0.727616i | \(0.259372\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 33.9411i | 1.40812i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.8564 | + | 13.8564i | 0.573874 | + | 0.573874i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.89898 | + | 4.89898i | 0.202203 | + | 0.202203i | 0.800943 | − | 0.598741i | \(-0.204332\pi\) |
−0.598741 | + | 0.800943i | \(0.704332\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 48.0000i | 1.97781i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.3848 | + | 18.3848i | −0.754972 | + | 0.754972i | −0.975403 | − | 0.220430i | \(-0.929254\pi\) |
0.220430 | + | 0.975403i | \(0.429254\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −41.5692 | + | 13.8564i | −1.70417 | + | 0.568057i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.0000 | 0.978980 | 0.489490 | − | 0.872009i | \(-0.337183\pi\) | ||||
0.489490 | + | 0.872009i | \(0.337183\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −27.5772 | + | 9.19239i | −1.12117 | + | 0.373724i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.1769 | − | 31.1769i | 1.26543 | − | 1.26543i | 0.317010 | − | 0.948422i | \(-0.397321\pi\) |
0.948422 | − | 0.317010i | \(-0.102679\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 9.79796i | − | 0.396383i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.00000 | + | 7.00000i | 0.282727 | + | 0.282727i | 0.834196 | − | 0.551468i | \(-0.185932\pi\) |
−0.551468 | + | 0.834196i | \(0.685932\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.1421 | + | 14.1421i | 0.569341 | + | 0.569341i | 0.931944 | − | 0.362603i | \(-0.118112\pi\) |
−0.362603 | + | 0.931944i | \(0.618112\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 13.8564i | − | 0.556936i | −0.960446 | − | 0.278468i | \(-0.910173\pi\) | ||
0.960446 | − | 0.278468i | \(-0.0898266\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 34.2929 | − | 34.2929i | 1.37391 | − | 1.37391i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.00000 | − | 24.0000i | 0.280000 | − | 0.960000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.65685 | 0.225554 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.6410 | 1.37904 | 0.689519 | − | 0.724268i | \(-0.257822\pi\) | ||||
0.689519 | + | 0.724268i | \(0.257822\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.6969 | + | 29.3939i | −0.583230 | + | 1.16646i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.0000 | + | 17.0000i | −0.673565 | + | 0.673565i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 15.5563i | − | 0.614439i | −0.951639 | − | 0.307219i | \(-0.900601\pi\) | ||
0.951639 | − | 0.307219i | \(-0.0993986\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.8564 | + | 13.8564i | 0.546443 | + | 0.546443i | 0.925410 | − | 0.378967i | \(-0.123721\pi\) |
−0.378967 | + | 0.925410i | \(0.623721\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.4949 | + | 24.4949i | 0.962994 | + | 0.962994i | 0.999339 | − | 0.0363455i | \(-0.0115717\pi\) |
−0.0363455 | + | 0.999339i | \(0.511572\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 24.0000i | − | 0.942082i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.1127 | + | 31.1127i | −1.21753 | + | 1.21753i | −0.249041 | + | 0.968493i | \(0.580115\pi\) |
−0.968493 | + | 0.249041i | \(0.919885\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.46410 | − | 10.3923i | −0.135354 | − | 0.406061i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.89898 | 0.190837 | 0.0954186 | − | 0.995437i | \(-0.469581\pi\) | ||||
0.0954186 | + | 0.995437i | \(0.469581\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −67.8823 | − | 33.9411i | −2.63236 | − | 1.31618i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.0000 | + | 25.0000i | 0.963679 | + | 0.963679i | 0.999363 | − | 0.0356839i | \(-0.0113610\pi\) |
−0.0356839 | + | 0.999363i | \(0.511361\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.82843 | − | 2.82843i | −0.108705 | − | 0.108705i | 0.650662 | − | 0.759367i | \(-0.274491\pi\) |
−0.759367 | + | 0.650662i | \(0.774491\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 34.6410i | − | 1.32940i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.4949 | + | 24.4949i | −0.937271 | + | 0.937271i | −0.998145 | − | 0.0608742i | \(-0.980611\pi\) |
0.0608742 | + | 0.998145i | \(0.480611\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.00000 | + | 2.00000i | 0.152832 | + | 0.0764161i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.65685 | −0.215509 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.7846 | −0.790684 | −0.395342 | − | 0.918534i | \(-0.629374\pi\) | ||||
−0.395342 | + | 0.918534i | \(0.629374\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.0000 | + | 28.0000i | −1.06058 | + | 1.06058i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 26.8701i | − | 1.01487i | −0.861691 | − | 0.507434i | \(-0.830594\pi\) | ||
0.861691 | − | 0.507434i | \(-0.169406\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.92820 | + | 6.92820i | 0.261302 | + | 0.261302i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.6969 | + | 14.6969i | 0.552735 | + | 0.552735i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.0000i | 1.12667i | 0.826227 | + | 0.563337i | \(0.190483\pi\) | ||||
−0.826227 | + | 0.563337i | \(0.809517\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.92820 | − | 13.8564i | 0.259100 | − | 0.518200i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −39.1918 | −1.46161 | −0.730804 | − | 0.682587i | \(-0.760855\pi\) | ||||
−0.730804 | + | 0.682587i | \(0.760855\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.0000 | 0.893807 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 28.2843 | − | 21.2132i | 1.05045 | − | 0.787839i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.3205 | + | 17.3205i | −0.642382 | + | 0.642382i | −0.951140 | − | 0.308758i | \(-0.900087\pi\) |
0.308758 | + | 0.951140i | \(0.400087\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 39.1918i | − | 1.44956i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.0000 | + | 31.0000i | 1.14501 | + | 1.14501i | 0.987520 | + | 0.157491i | \(0.0503404\pi\) |
0.157491 | + | 0.987520i | \(0.449660\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −33.9411 | − | 33.9411i | −1.25024 | − | 1.25024i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 48.4974i | − | 1.78401i | −0.452029 | − | 0.892003i | \(-0.649300\pi\) | ||
0.452029 | − | 0.892003i | \(-0.350700\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.2929 | + | 34.2929i | −1.25808 | + | 1.25808i | −0.306076 | + | 0.952007i | \(0.599016\pi\) |
−0.952007 | + | 0.306076i | \(0.900984\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.00000 | − | 3.00000i | 0.329734 | − | 0.109911i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 33.9411 | 1.24018 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.7846 | −0.758441 | −0.379221 | − | 0.925306i | \(-0.623808\pi\) | ||||
−0.379221 | + | 0.925306i | \(0.623808\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.0000 | + | 19.0000i | −0.690567 | + | 0.690567i | −0.962357 | − | 0.271790i | \(-0.912384\pi\) |
0.271790 | + | 0.962357i | \(0.412384\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 4.24264i | − | 0.153796i | −0.997039 | − | 0.0768978i | \(-0.975498\pi\) | ||
0.997039 | − | 0.0768978i | \(-0.0245015\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 27.7128 | + | 27.7128i | 1.00327 | + | 1.00327i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.89898 | + | 4.89898i | 0.176892 | + | 0.176892i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.0000i | 0.865462i | 0.901523 | + | 0.432731i | \(0.142450\pi\) | ||||
−0.901523 | + | 0.432731i | \(0.857550\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19.7990 | + | 19.7990i | −0.712120 | + | 0.712120i | −0.966978 | − | 0.254858i | \(-0.917971\pi\) |
0.254858 | + | 0.966978i | \(0.417971\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −27.7128 | + | 20.7846i | −0.995474 | + | 0.746605i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −68.5857 | −2.45734 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.3848 | − | 36.7696i | 0.656181 | − | 1.31236i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.7846 | − | 20.7846i | 0.740891 | − | 0.740891i | −0.231858 | − | 0.972750i | \(-0.574481\pi\) |
0.972750 | + | 0.231858i | \(0.0744806\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 48.9898i | 1.74188i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.3553 | + | 35.3553i | 1.25235 | + | 1.25235i | 0.954664 | + | 0.297687i | \(0.0962151\pi\) |
0.297687 | + | 0.954664i | \(0.403785\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 27.7128i | − | 0.980409i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 34.2929 | − | 34.2929i | 1.21017 | − | 1.21017i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.89949 | −0.348048 | −0.174024 | − | 0.984741i | \(-0.555677\pi\) | ||||
−0.174024 | + | 0.984741i | \(0.555677\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.8564 | 0.486564 | 0.243282 | − | 0.969956i | \(-0.421776\pi\) | ||||
0.243282 | + | 0.969956i | \(0.421776\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19.5959 | − | 9.79796i | −0.686415 | − | 0.343208i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 48.0000 | − | 48.0000i | 1.67931 | − | 1.67931i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1.41421i | − | 0.0493564i | −0.999695 | − | 0.0246782i | \(-0.992144\pi\) | ||
0.999695 | − | 0.0246782i | \(-0.00785611\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.3923 | + | 10.3923i | 0.362253 | + | 0.362253i | 0.864642 | − | 0.502389i | \(-0.167545\pi\) |
−0.502389 | + | 0.864642i | \(0.667545\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.79796 | + | 9.79796i | 0.340708 | + | 0.340708i | 0.856634 | − | 0.515925i | \(-0.172552\pi\) |
−0.515925 | + | 0.856634i | \(0.672552\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 8.00000i | − | 0.277851i | −0.990303 | − | 0.138926i | \(-0.955635\pi\) | ||
0.990303 | − | 0.138926i | \(-0.0443649\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −48.0833 | + | 48.0833i | −1.66599 | + | 1.66599i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 27.7128 | + | 13.8564i | 0.959041 | + | 0.479521i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.79796 | 0.338263 | 0.169132 | − | 0.985593i | \(-0.445904\pi\) | ||||
0.169132 | + | 0.985593i | \(0.445904\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.0000 | 0.724138 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.77817 | − | 23.3345i | −0.267577 | − | 0.802732i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −45.0333 | + | 45.0333i | −1.54736 | + | 1.54736i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.0000 | − | 23.0000i | −0.787505 | − | 0.787505i | 0.193580 | − | 0.981085i | \(-0.437990\pi\) |
−0.981085 | + | 0.193580i | \(0.937990\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.1421 | − | 14.1421i | −0.483086 | − | 0.483086i | 0.423030 | − | 0.906116i | \(-0.360967\pi\) |
−0.906116 | + | 0.423030i | \(0.860967\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.5692i | 1.41832i | 0.705046 | + | 0.709162i | \(0.250926\pi\) | ||||
−0.705046 | + | 0.709162i | \(0.749074\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.79796 | − | 9.79796i | 0.333526 | − | 0.333526i | −0.520398 | − | 0.853924i | \(-0.674216\pi\) |
0.853924 | + | 0.520398i | \(0.174216\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.00000 | − | 4.00000i | 0.0680020 | − | 0.136004i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 33.9411 | 1.15137 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.8564 | 0.469506 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.79796 | − | 53.8888i | −0.331231 | − | 1.82177i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.00000 | + | 5.00000i | −0.168838 | + | 0.168838i | −0.786468 | − | 0.617630i | \(-0.788093\pi\) |
0.617630 | + | 0.786468i | \(0.288093\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.5563i | 0.524107i | 0.965053 | + | 0.262053i | \(0.0843996\pi\) | ||||
−0.965053 | + | 0.262053i | \(0.915600\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.6410 | − | 34.6410i | −1.16576 | − | 1.16576i | −0.983193 | − | 0.182570i | \(-0.941558\pi\) |
−0.182570 | − | 0.983193i | \(-0.558442\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −29.3939 | − | 29.3939i | −0.986950 | − | 0.986950i | 0.0129661 | − | 0.999916i | \(-0.495873\pi\) |
−0.999916 | + | 0.0129661i | \(0.995873\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 72.0000i | 2.41480i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 33.9411 | − | 33.9411i | 1.13580 | − | 1.13580i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.3923 | + | 3.46410i | −0.347376 | + | 0.115792i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −48.9898 | −1.63390 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.0000 | −0.533037 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16.9706 | − | 5.65685i | 0.564121 | − | 0.188040i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.7846 | + | 20.7846i | −0.690142 | + | 0.690142i | −0.962263 | − | 0.272121i | \(-0.912275\pi\) |
0.272121 | + | 0.962263i | \(0.412275\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 29.3939i | − | 0.973863i | −0.873440 | − | 0.486931i | \(-0.838116\pi\) | ||
0.873440 | − | 0.486931i | \(-0.161884\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.0000 | − | 24.0000i | −0.794284 | − | 0.794284i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16.9706 | − | 16.9706i | −0.560417 | − | 0.560417i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.7846i | 0.685621i | 0.939405 | + | 0.342811i | \(0.111379\pi\) | ||||
−0.939405 | + | 0.342811i | \(0.888621\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.00000 | + | 7.00000i | −0.0328798 | + | 0.230159i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12.7279 | −0.417590 | −0.208795 | − | 0.977959i | \(-0.566954\pi\) | ||||
−0.208795 | + | 0.977959i | \(0.566954\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −117.779 | −3.86007 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19.5959 | − | 39.1918i | 0.640855 | − | 1.28171i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.00000 | − | 5.00000i | 0.163343 | − | 0.163343i | −0.620703 | − | 0.784046i | \(-0.713153\pi\) |
0.784046 | + | 0.620703i | \(0.213153\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.2132i | 0.691531i | 0.938321 | + | 0.345765i | \(0.112381\pi\) | ||||
−0.938321 | + | 0.345765i | \(0.887619\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 29.3939 | + | 29.3939i | 0.955173 | + | 0.955173i | 0.999037 | − | 0.0438648i | \(-0.0139671\pi\) |
−0.0438648 | + | 0.999037i | \(0.513967\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.0000i | 0.454459i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35.3553 | − | 35.3553i | 1.14527 | − | 1.14527i | 0.157801 | − | 0.987471i | \(-0.449560\pi\) |
0.987471 | − | 0.157801i | \(-0.0504404\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.8564 | + | 41.5692i | 0.448383 | + | 1.34515i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.79796 | 0.316393 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.0000 | 0.548387 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19.7990 | − | 9.89949i | −0.637352 | − | 0.318676i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.2487 | + | 24.2487i | −0.779786 | + | 0.779786i | −0.979794 | − | 0.200008i | \(-0.935903\pi\) |
0.200008 | + | 0.979794i | \(0.435903\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 44.0908i | 1.41494i | 0.706743 | + | 0.707471i | \(0.250164\pi\) | ||||
−0.706743 | + | 0.707471i | \(0.749836\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.7990 | + | 19.7990i | 0.633426 | + | 0.633426i | 0.948926 | − | 0.315500i | \(-0.102172\pi\) |
−0.315500 | + | 0.948926i | \(0.602172\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 48.4974i | 1.54998i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.89898 | + | 4.89898i | −0.156253 | + | 0.156253i | −0.780904 | − | 0.624651i | \(-0.785241\pi\) |
0.624651 | + | 0.780904i | \(0.285241\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.00000 | − | 2.00000i | −0.127451 | − | 0.0637253i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.7128 | 0.880327 | 0.440163 | − | 0.897918i | \(-0.354921\pi\) | ||||
0.440163 | + | 0.897918i | \(0.354921\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.79796 | − | 29.3939i | −0.310616 | − | 0.931849i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.00000 | − | 7.00000i | 0.221692 | − | 0.221692i | −0.587519 | − | 0.809211i | \(-0.699895\pi\) |
0.809211 | + | 0.587519i | \(0.199895\pi\) | |||||||
\(998\) | 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 | 2880.2.w.n.2753.4 | 8 | ||
3.2 | odd | 2 | inner | 2880.2.w.n.2753.2 | 8 | ||
4.3 | odd | 2 | inner | 2880.2.w.n.2753.3 | 8 | ||
5.2 | odd | 4 | inner | 2880.2.w.n.2177.2 | 8 | ||
8.3 | odd | 2 | 1440.2.w.e.1313.1 | yes | 8 | ||
8.5 | even | 2 | 1440.2.w.e.1313.2 | yes | 8 | ||
12.11 | even | 2 | inner | 2880.2.w.n.2753.1 | 8 | ||
15.2 | even | 4 | inner | 2880.2.w.n.2177.4 | 8 | ||
20.7 | even | 4 | inner | 2880.2.w.n.2177.1 | 8 | ||
24.5 | odd | 2 | 1440.2.w.e.1313.4 | yes | 8 | ||
24.11 | even | 2 | 1440.2.w.e.1313.3 | yes | 8 | ||
40.27 | even | 4 | 1440.2.w.e.737.3 | yes | 8 | ||
40.37 | odd | 4 | 1440.2.w.e.737.4 | yes | 8 | ||
60.47 | odd | 4 | inner | 2880.2.w.n.2177.3 | 8 | ||
120.77 | even | 4 | 1440.2.w.e.737.2 | yes | 8 | ||
120.107 | odd | 4 | 1440.2.w.e.737.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1440.2.w.e.737.1 | ✓ | 8 | 120.107 | odd | 4 | ||
1440.2.w.e.737.2 | yes | 8 | 120.77 | even | 4 | ||
1440.2.w.e.737.3 | yes | 8 | 40.27 | even | 4 | ||
1440.2.w.e.737.4 | yes | 8 | 40.37 | odd | 4 | ||
1440.2.w.e.1313.1 | yes | 8 | 8.3 | odd | 2 | ||
1440.2.w.e.1313.2 | yes | 8 | 8.5 | even | 2 | ||
1440.2.w.e.1313.3 | yes | 8 | 24.11 | even | 2 | ||
1440.2.w.e.1313.4 | yes | 8 | 24.5 | odd | 2 | ||
2880.2.w.n.2177.1 | 8 | 20.7 | even | 4 | inner | ||
2880.2.w.n.2177.2 | 8 | 5.2 | odd | 4 | inner | ||
2880.2.w.n.2177.3 | 8 | 60.47 | odd | 4 | inner | ||
2880.2.w.n.2177.4 | 8 | 15.2 | even | 4 | inner | ||
2880.2.w.n.2753.1 | 8 | 12.11 | even | 2 | inner | ||
2880.2.w.n.2753.2 | 8 | 3.2 | odd | 2 | inner | ||
2880.2.w.n.2753.3 | 8 | 4.3 | odd | 2 | inner | ||
2880.2.w.n.2753.4 | 8 | 1.1 | even | 1 | trivial |