Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4840,2,Mod(1,4840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4840.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4840 = 2^{3} \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4840.a (trivial) |
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: | yes |
Analytic conductor: | \(38.6475945783\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.25903625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 3x^{5} - 7x^{4} + 17x^{3} + 16x^{2} - 20x - 5 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 440) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.29082\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4840.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −2.29082 | −1.32260 | −0.661302 | − | 0.750119i | \(-0.729996\pi\) | ||||
−0.661302 | + | 0.750119i | \(0.729996\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.66366 | −1.76270 | −0.881348 | − | 0.472467i | \(-0.843363\pi\) | ||||
−0.881348 | + | 0.472467i | \(0.843363\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.24785 | 0.749284 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.94269 | −1.64821 | −0.824103 | − | 0.566440i | \(-0.808320\pi\) | ||||
−0.824103 | + | 0.566440i | \(0.808320\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.29082 | 0.591487 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.30331 | 0.801171 | 0.400586 | − | 0.916259i | \(-0.368807\pi\) | ||||
0.400586 | + | 0.916259i | \(0.368807\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.19195 | 0.961699 | 0.480850 | − | 0.876803i | \(-0.340328\pi\) | ||||
0.480850 | + | 0.876803i | \(0.340328\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 10.6836 | 2.33135 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.71184 | −0.356942 | −0.178471 | − | 0.983945i | \(-0.557115\pi\) | ||||
−0.178471 | + | 0.983945i | \(0.557115\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.72304 | 0.331598 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.76702 | 1.44230 | 0.721149 | − | 0.692780i | \(-0.243614\pi\) | ||||
0.721149 | + | 0.692780i | \(0.243614\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.97204 | −0.533794 | −0.266897 | − | 0.963725i | \(-0.585998\pi\) | ||||
−0.266897 | + | 0.963725i | \(0.585998\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.66366 | 0.788302 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.68500 | −0.934608 | −0.467304 | − | 0.884097i | \(-0.654775\pi\) | ||||
−0.467304 | + | 0.884097i | \(0.654775\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 13.6136 | 2.17993 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.14758 | 0.960090 | 0.480045 | − | 0.877244i | \(-0.340620\pi\) | ||||
0.480045 | + | 0.877244i | \(0.340620\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.42353 | 0.674582 | 0.337291 | − | 0.941401i | \(-0.390489\pi\) | ||||
0.337291 | + | 0.941401i | \(0.390489\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.24785 | −0.335090 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.13243 | 0.602776 | 0.301388 | − | 0.953502i | \(-0.402550\pi\) | ||||
0.301388 | + | 0.953502i | \(0.402550\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.7497 | 2.10710 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.56730 | −1.05963 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.10104 | 1.11276 | 0.556381 | − | 0.830927i | \(-0.312189\pi\) | ||||
0.556381 | + | 0.830927i | \(0.312189\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.60300 | −1.27195 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.21515 | −0.809144 | −0.404572 | − | 0.914506i | \(-0.632580\pi\) | ||||
−0.404572 | + | 0.914506i | \(0.632580\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.52758 | 0.195587 | 0.0977934 | − | 0.995207i | \(-0.468822\pi\) | ||||
0.0977934 | + | 0.995207i | \(0.468822\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10.4832 | −1.32076 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.94269 | 0.737100 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.46447 | −0.911931 | −0.455965 | − | 0.889998i | \(-0.650706\pi\) | ||||
−0.455965 | + | 0.889998i | \(0.650706\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.92151 | 0.472094 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.23747 | −0.265539 | −0.132770 | − | 0.991147i | \(-0.542387\pi\) | ||||
−0.132770 | + | 0.991147i | \(0.542387\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.49400 | 0.877106 | 0.438553 | − | 0.898705i | \(-0.355491\pi\) | ||||
0.438553 | + | 0.898705i | \(0.355491\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.29082 | −0.264521 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −17.5316 | −1.97246 | −0.986230 | − | 0.165378i | \(-0.947116\pi\) | ||||
−0.986230 | + | 0.165378i | \(0.947116\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.6907 | −1.18786 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.0785 | −1.21603 | −0.608014 | − | 0.793926i | \(-0.708034\pi\) | ||||
−0.608014 | + | 0.793926i | \(0.708034\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.30331 | −0.358295 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −17.7928 | −1.90759 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.8171 | 1.35861 | 0.679305 | − | 0.733856i | \(-0.262281\pi\) | ||||
0.679305 | + | 0.733856i | \(0.262281\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 27.7147 | 2.90529 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.80840 | 0.705998 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.19195 | −0.430085 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.53760 | −0.968396 | −0.484198 | − | 0.874958i | \(-0.660889\pi\) | ||||
−0.484198 | + | 0.874958i | \(0.660889\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.7259 | 1.06727 | 0.533635 | − | 0.845715i | \(-0.320826\pi\) | ||||
0.533635 | + | 0.845715i | \(0.320826\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.57865 | 0.254082 | 0.127041 | − | 0.991897i | \(-0.459452\pi\) | ||||
0.127041 | + | 0.991897i | \(0.459452\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10.6836 | −1.04261 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.6297 | 1.70433 | 0.852164 | − | 0.523275i | \(-0.175290\pi\) | ||||
0.852164 | + | 0.523275i | \(0.175290\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.3476 | 1.47004 | 0.735019 | − | 0.678047i | \(-0.237173\pi\) | ||||
0.735019 | + | 0.678047i | \(0.237173\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.0233 | 1.23612 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.316934 | 0.0298147 | 0.0149073 | − | 0.999889i | \(-0.495255\pi\) | ||||
0.0149073 | + | 0.999889i | \(0.495255\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.71184 | 0.159630 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −13.3583 | −1.23497 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −15.4055 | −1.41222 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −14.0830 | −1.26982 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.0671 | −1.60320 | −0.801599 | − | 0.597862i | \(-0.796017\pi\) | ||||
−0.801599 | + | 0.597862i | \(0.796017\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.1335 | −0.892205 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.95176 | 0.694749 | 0.347374 | − | 0.937727i | \(-0.387073\pi\) | ||||
0.347374 | + | 0.937727i | \(0.387073\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −19.5498 | −1.69518 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.72304 | −0.148295 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.07748 | −0.690106 | −0.345053 | − | 0.938583i | \(-0.612139\pi\) | ||||
−0.345053 | + | 0.938583i | \(0.612139\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.3240 | −0.960486 | −0.480243 | − | 0.877135i | \(-0.659452\pi\) | ||||
−0.480243 | + | 0.877135i | \(0.659452\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.46664 | −0.797235 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.76702 | −0.645016 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −33.7889 | −2.78686 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.35175 | −0.192663 | −0.0963314 | − | 0.995349i | \(-0.530711\pi\) | ||||
−0.0963314 | + | 0.995349i | \(0.530711\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.7268 | −1.19845 | −0.599227 | − | 0.800579i | \(-0.704525\pi\) | ||||
−0.599227 | + | 0.800579i | \(0.704525\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.42536 | 0.600305 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.97204 | 0.238720 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.4544 | −1.31320 | −0.656600 | − | 0.754239i | \(-0.728006\pi\) | ||||
−0.656600 | + | 0.754239i | \(0.728006\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −18.5580 | −1.47175 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.98341 | 0.629181 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.26242 | 0.412184 | 0.206092 | − | 0.978533i | \(-0.433925\pi\) | ||||
0.206092 | + | 0.978533i | \(0.433925\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.5495 | 1.66755 | 0.833776 | − | 0.552102i | \(-0.186174\pi\) | ||||
0.833776 | + | 0.552102i | \(0.186174\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 22.3156 | 1.71658 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.42288 | 0.720586 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.08425 | 0.538605 | 0.269303 | − | 0.963056i | \(-0.413207\pi\) | ||||
0.269303 | + | 0.963056i | \(0.413207\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.66366 | −0.352539 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.2378 | 1.07018 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.78759 | 0.656815 | 0.328408 | − | 0.944536i | \(-0.393488\pi\) | ||||
0.328408 | + | 0.944536i | \(0.393488\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.6451 | −0.939904 | −0.469952 | − | 0.882692i | \(-0.655729\pi\) | ||||
−0.469952 | + | 0.882692i | \(0.655729\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.49941 | −0.258684 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.68500 | 0.417969 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.03564 | −0.584507 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.7224 | −1.28235 | −0.641175 | − | 0.767394i | \(-0.721553\pi\) | ||||
−0.641175 | + | 0.767394i | \(0.721553\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.03540 | 0.362456 | 0.181228 | − | 0.983441i | \(-0.441993\pi\) | ||||
0.181228 | + | 0.983441i | \(0.441993\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −13.6136 | −0.974892 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.0557 | 1.07268 | 0.536338 | − | 0.844003i | \(-0.319807\pi\) | ||||
0.536338 | + | 0.844003i | \(0.319807\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.56534 | 0.181852 | 0.0909259 | − | 0.995858i | \(-0.471017\pi\) | ||||
0.0909259 | + | 0.995858i | \(0.471017\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 17.0998 | 1.20612 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −36.2227 | −2.54233 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.14758 | −0.429365 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.84795 | −0.267451 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.71897 | −0.669082 | −0.334541 | − | 0.942381i | \(-0.608581\pi\) | ||||
−0.334541 | + | 0.942381i | \(0.608581\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.12565 | 0.351204 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.42353 | −0.301682 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.8606 | 0.940916 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −17.1674 | −1.16006 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.6306 | −1.32050 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.543504 | 0.0363957 | 0.0181979 | − | 0.999834i | \(-0.494207\pi\) | ||||
0.0181979 | + | 0.999834i | \(0.494207\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.24785 | 0.149857 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.19727 | −0.344955 | −0.172478 | − | 0.985013i | \(-0.555177\pi\) | ||||
−0.172478 | + | 0.985013i | \(0.555177\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.09116 | −0.270352 | −0.135176 | − | 0.990822i | \(-0.543160\pi\) | ||||
−0.135176 | + | 0.990822i | \(0.543160\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.9446 | −0.913541 | −0.456771 | − | 0.889584i | \(-0.650994\pi\) | ||||
−0.456771 | + | 0.889584i | \(0.650994\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.13243 | −0.269570 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 40.1618 | 2.60879 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.523568 | −0.0338668 | −0.0169334 | − | 0.999857i | \(-0.505390\pi\) | ||||
−0.0169334 | + | 0.999857i | \(0.505390\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.38011 | 0.410979 | 0.205489 | − | 0.978659i | \(-0.434121\pi\) | ||||
0.205489 | + | 0.978659i | \(0.434121\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 19.3214 | 1.23947 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.7497 | −0.942323 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −24.9115 | −1.58508 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 25.3789 | 1.60832 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.6413 | 0.861030 | 0.430515 | − | 0.902583i | \(-0.358332\pi\) | ||||
0.430515 | + | 0.902583i | \(0.358332\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.56730 | 0.473882 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.40705 | −0.150148 | −0.0750738 | − | 0.997178i | \(-0.523919\pi\) | ||||
−0.0750738 | + | 0.997178i | \(0.523919\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 26.5129 | 1.64743 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 17.4591 | 1.08069 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.7841 | 0.726641 | 0.363321 | − | 0.931664i | \(-0.381643\pi\) | ||||
0.363321 | + | 0.931664i | \(0.381643\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.10104 | −0.497643 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −29.3617 | −1.79691 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.1436 | −0.923324 | −0.461662 | − | 0.887056i | \(-0.652747\pi\) | ||||
−0.461662 | + | 0.887056i | \(0.652747\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.5739 | 0.642316 | 0.321158 | − | 0.947026i | \(-0.395928\pi\) | ||||
0.321158 | + | 0.947026i | \(0.395928\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −63.4893 | −3.84255 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.1516 | 1.51121 | 0.755606 | − | 0.655026i | \(-0.227342\pi\) | ||||
0.755606 | + | 0.655026i | \(0.227342\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.68070 | −0.399963 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.322966 | 0.0192666 | 0.00963328 | − | 0.999954i | \(-0.496934\pi\) | ||||
0.00963328 | + | 0.999954i | \(0.496934\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.3723 | −1.27045 | −0.635227 | − | 0.772325i | \(-0.719094\pi\) | ||||
−0.635227 | + | 0.772325i | \(0.719094\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.60300 | 0.568832 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −28.6702 | −1.69235 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.08811 | −0.358124 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 21.8489 | 1.28081 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.5001 | 0.613424 | 0.306712 | − | 0.951802i | \(-0.400771\pi\) | ||||
0.306712 | + | 0.951802i | \(0.400771\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.21515 | 0.361860 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.1729 | 0.588315 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.6298 | −1.18908 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −24.5712 | −1.41158 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.52758 | −0.0874691 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.0598 | 1.65853 | 0.829266 | − | 0.558854i | \(-0.188759\pi\) | ||||
0.829266 | + | 0.558854i | \(0.188759\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.90722 | −0.336050 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.9483 | −1.13116 | −0.565582 | − | 0.824692i | \(-0.691348\pi\) | ||||
−0.565582 | + | 0.824692i | \(0.691348\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.4800 | 0.988030 | 0.494015 | − | 0.869453i | \(-0.335529\pi\) | ||||
0.494015 | + | 0.869453i | \(0.335529\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.4832 | 0.590662 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −29.8295 | −1.67539 | −0.837696 | − | 0.546136i | \(-0.816098\pi\) | ||||
−0.837696 | + | 0.546136i | \(0.816098\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −40.3865 | −2.25415 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.8473 | 0.770486 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.94269 | −0.329641 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −35.1587 | −1.94428 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −19.2722 | −1.06251 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.4740 | 1.62004 | 0.810018 | − | 0.586405i | \(-0.199457\pi\) | ||||
0.810018 | + | 0.586405i | \(0.199457\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.7790 | −0.700287 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.46447 | 0.407828 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.9682 | −1.14221 | −0.571106 | − | 0.820877i | \(-0.693485\pi\) | ||||
−0.571106 | + | 0.820877i | \(0.693485\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.726039 | −0.0394330 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −36.1419 | −1.95148 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.92151 | −0.211127 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.27059 | 0.390306 | 0.195153 | − | 0.980773i | \(-0.437480\pi\) | ||||
0.195153 | + | 0.980773i | \(0.437480\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.2432 | −1.03006 | −0.515032 | − | 0.857171i | \(-0.672220\pi\) | ||||
−0.515032 | + | 0.857171i | \(0.672220\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.2395 | −0.546542 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.5882 | 0.776454 | 0.388227 | − | 0.921564i | \(-0.373088\pi\) | ||||
0.388227 | + | 0.921564i | \(0.373088\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.23747 | 0.118753 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 35.2913 | 1.86781 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.56617 | −0.135437 | −0.0677187 | − | 0.997704i | \(-0.521572\pi\) | ||||
−0.0677187 | + | 0.997704i | \(0.521572\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.42756 | −0.0751348 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.49400 | −0.392254 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.7911 | −1.13748 | −0.568742 | − | 0.822516i | \(-0.692570\pi\) | ||||
−0.568742 | + | 0.822516i | \(0.692570\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.8188 | 0.719380 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −37.7804 | −1.96146 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.7684 | −1.02357 | −0.511783 | − | 0.859115i | \(-0.671015\pi\) | ||||
−0.511783 | + | 0.859115i | \(0.671015\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.29082 | 0.118297 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −46.1570 | −2.37721 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.5393 | −0.695467 | −0.347733 | − | 0.937594i | \(-0.613049\pi\) | ||||
−0.347733 | + | 0.937594i | \(0.613049\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 41.3885 | 2.12040 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.3937 | 0.735483 | 0.367742 | − | 0.929928i | \(-0.380131\pi\) | ||||
0.367742 | + | 0.929928i | \(0.380131\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.94343 | 0.505453 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.2204 | −0.771705 | −0.385853 | − | 0.922560i | \(-0.626093\pi\) | ||||
−0.385853 | + | 0.922560i | \(0.626093\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.65473 | −0.285972 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.2160 | −0.918878 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 17.5316 | 0.882111 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −37.0013 | −1.85704 | −0.928520 | − | 0.371282i | \(-0.878918\pi\) | ||||
−0.928520 | + | 0.371282i | \(0.878918\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 44.7851 | 2.24206 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.6104 | −1.22898 | −0.614492 | − | 0.788923i | \(-0.710639\pi\) | ||||
−0.614492 | + | 0.788923i | \(0.710639\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.6619 | 0.879802 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.6907 | 0.531226 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.3346 | −0.906586 | −0.453293 | − | 0.891362i | \(-0.649751\pi\) | ||||
−0.453293 | + | 0.891362i | \(0.649751\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.5040 | 0.912737 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 28.9853 | 1.42628 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.0785 | 0.543824 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 25.9411 | 1.27034 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.6524 | 1.15550 | 0.577748 | − | 0.816215i | \(-0.303932\pi\) | ||||
0.577748 | + | 0.816215i | \(0.303932\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.6921 | 0.569840 | 0.284920 | − | 0.958551i | \(-0.408033\pi\) | ||||
0.284920 | + | 0.958551i | \(0.408033\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.28908 | 0.451651 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.30331 | 0.160234 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.12412 | −0.344760 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.42118 | 0.261129 | 0.130565 | − | 0.991440i | \(-0.458321\pi\) | ||||
0.130565 | + | 0.991440i | \(0.458321\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.0482 | −0.675116 | −0.337558 | − | 0.941305i | \(-0.609601\pi\) | ||||
−0.337558 | + | 0.941305i | \(0.609601\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 17.7928 | 0.853101 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.17593 | −0.343271 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.4133 | −0.640184 | −0.320092 | − | 0.947386i | \(-0.603714\pi\) | ||||
−0.320092 | + | 0.947386i | \(0.603714\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 33.1551 | 1.57881 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −28.1807 | −1.33891 | −0.669453 | − | 0.742855i | \(-0.733471\pi\) | ||||
−0.669453 | + | 0.742855i | \(0.733471\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.8171 | −0.607589 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.38743 | 0.254817 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −37.5023 | −1.76984 | −0.884921 | − | 0.465741i | \(-0.845788\pi\) | ||||
−0.884921 | + | 0.465741i | \(0.845788\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 33.7365 | 1.58508 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −27.7147 | −1.29928 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.5343 | −0.726666 | −0.363333 | − | 0.931659i | \(-0.618361\pi\) | ||||
−0.363333 | + | 0.931659i | \(0.618361\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.69173 | 0.265667 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.4407 | 0.952018 | 0.476009 | − | 0.879440i | \(-0.342083\pi\) | ||||
0.476009 | + | 0.879440i | \(0.342083\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.64734 | −0.448350 | −0.224175 | − | 0.974549i | \(-0.571969\pi\) | ||||
−0.224175 | + | 0.974549i | \(0.571969\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.80840 | −0.315732 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.9773 | 0.646790 | 0.323395 | − | 0.946264i | \(-0.395176\pi\) | ||||
0.323395 | + | 0.946264i | \(0.395176\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 34.8117 | 1.60746 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 37.6939 | 1.73685 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.19195 | 0.192340 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.2099 | 0.833775 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.7475 | −1.31351 | −0.656754 | − | 0.754105i | \(-0.728071\pi\) | ||||
−0.656754 | + | 0.754105i | \(0.728071\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 33.7842 | 1.54043 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −18.2886 | −0.832158 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.53760 | 0.433080 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.2994 | 0.466709 | 0.233355 | − | 0.972392i | \(-0.425030\pi\) | ||||
0.233355 | + | 0.972392i | \(0.425030\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.0552 | −0.545157 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.35859 | 0.332088 | 0.166044 | − | 0.986118i | \(-0.446901\pi\) | ||||
0.166044 | + | 0.986118i | \(0.446901\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25.6569 | 1.15553 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.4348 | 0.468065 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.83645 | 0.126977 | 0.0634885 | − | 0.997983i | \(-0.479777\pi\) | ||||
0.0634885 | + | 0.997983i | \(0.479777\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −49.3661 | −2.20551 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.8353 | 0.616887 | 0.308444 | − | 0.951243i | \(-0.400192\pi\) | ||||
0.308444 | + | 0.951243i | \(0.400192\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.7259 | −0.477297 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −51.1209 | −2.27036 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.9515 | 1.10596 | 0.552978 | − | 0.833196i | \(-0.313491\pi\) | ||||
0.552978 | + | 0.833196i | \(0.313491\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −34.9494 | −1.54607 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.22288 | 0.318898 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.57865 | −0.113629 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.2287 | −0.712362 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.72550 | 0.0755955 | 0.0377978 | − | 0.999285i | \(-0.487966\pi\) | ||||
0.0377978 | + | 0.999285i | \(0.487966\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.9448 | 0.653489 | 0.326745 | − | 0.945113i | \(-0.394048\pi\) | ||||
0.326745 | + | 0.945113i | \(0.394048\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 10.6836 | 0.466270 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.81758 | −0.427660 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.0696 | −0.872592 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.9707 | −0.606279 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −36.5331 | −1.58243 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.6297 | −0.762199 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −20.1308 | −0.868707 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.0200 | 1.72059 | 0.860297 | − | 0.509793i | \(-0.170278\pi\) | ||||
0.860297 | + | 0.509793i | \(0.170278\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 28.9677 | 1.24312 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15.3476 | −0.657421 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.9990 | −0.983368 | −0.491684 | − | 0.870774i | \(-0.663618\pi\) | ||||
−0.491684 | + | 0.870774i | \(0.663618\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.43378 | 0.146550 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 32.5589 | 1.38706 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 81.7614 | 3.47685 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13.0233 | −0.552808 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.9261 | −0.505323 | −0.252662 | − | 0.967555i | \(-0.581306\pi\) | ||||
−0.252662 | + | 0.967555i | \(0.581306\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −26.2877 | −1.11185 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 39.2951 | 1.65609 | 0.828046 | − | 0.560660i | \(-0.189453\pi\) | ||||
0.828046 | + | 0.560660i | \(0.189453\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.316934 | −0.0133335 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 49.8578 | 2.09383 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.1895 | 0.720621 | 0.360310 | − | 0.932832i | \(-0.382671\pi\) | ||||
0.360310 | + | 0.932832i | \(0.382671\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.4297 | 1.10605 | 0.553025 | − | 0.833165i | \(-0.313473\pi\) | ||||
0.553025 | + | 0.833165i | \(0.313473\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 40.5989 | 1.69604 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.71184 | −0.0713885 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.3838 | 0.432284 | 0.216142 | − | 0.976362i | \(-0.430653\pi\) | ||||
0.216142 | + | 0.976362i | \(0.430653\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.5352 | −0.479386 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 51.6665 | 2.14349 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 13.3583 | 0.552297 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.2848 | −0.878517 | −0.439258 | − | 0.898361i | \(-0.644759\pi\) | ||||
−0.439258 | + | 0.898361i | \(0.644759\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.4586 | −0.513349 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −34.4900 | −1.41873 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.74652 | 0.277046 | 0.138523 | − | 0.990359i | \(-0.455764\pi\) | ||||
0.138523 | + | 0.990359i | \(0.455764\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.4055 | 0.631565 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.87672 | −0.240518 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.09390 | −0.167272 | −0.0836361 | − | 0.996496i | \(-0.526653\pi\) | ||||
−0.0836361 | + | 0.996496i | \(0.526653\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.46697 | −0.100630 | −0.0503149 | − | 0.998733i | \(-0.516022\pi\) | ||||
−0.0503149 | + | 0.998733i | \(0.516022\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16.7790 | −0.683295 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.9423 | −1.13414 | −0.567072 | − | 0.823668i | \(-0.691924\pi\) | ||||
−0.567072 | + | 0.823668i | \(0.691924\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 82.9796 | 3.36250 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24.5577 | −0.993499 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.9146 | 1.57174 | 0.785872 | − | 0.618389i | \(-0.212214\pi\) | ||||
0.785872 | + | 0.618389i | \(0.212214\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 14.0830 | 0.567881 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.639294 | −0.0257370 | −0.0128685 | − | 0.999917i | \(-0.504096\pi\) | ||||
−0.0128685 | + | 0.999917i | \(0.504096\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.2927 | −0.775440 | −0.387720 | − | 0.921777i | \(-0.626737\pi\) | ||||
−0.387720 | + | 0.921777i | \(0.626737\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.94955 | −0.118361 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −59.7746 | −2.39482 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.7793 | −0.748781 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.3865 | 0.652336 | 0.326168 | − | 0.945312i | \(-0.394242\pi\) | ||||
0.326168 | + | 0.945312i | \(0.394242\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 22.2644 | 0.884931 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 18.0671 | 0.716972 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −87.6528 | −3.47293 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.02951 | −0.198964 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.13171 | −0.360681 | −0.180341 | − | 0.983604i | \(-0.557720\pi\) | ||||
−0.180341 | + | 0.983604i | \(0.557720\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 39.5059 | 1.55796 | 0.778981 | − | 0.627047i | \(-0.215737\pi\) | ||||
0.778981 | + | 0.627047i | \(0.215737\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.1335 | 0.399006 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.26785 | 0.167786 | 0.0838932 | − | 0.996475i | \(-0.473265\pi\) | ||||
0.0838932 | + | 0.996475i | \(0.473265\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −31.7520 | −1.24446 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.36846 | −0.170951 | −0.0854755 | − | 0.996340i | \(-0.527241\pi\) | ||||
−0.0854755 | + | 0.996340i | \(0.527241\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.95176 | −0.310701 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.8454 | 0.657201 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.146275 | 0.00569808 | 0.00284904 | − | 0.999996i | \(-0.499093\pi\) | ||||
0.00284904 | + | 0.999996i | \(0.499093\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.7505 | 1.62391 | 0.811953 | − | 0.583723i | \(-0.198405\pi\) | ||||
0.811953 | + | 0.583723i | \(0.198405\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 44.9701 | 1.74649 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 19.5498 | 0.758109 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.2959 | −0.514818 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.24507 | −0.0481372 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.58869 | −0.0997866 | −0.0498933 | − | 0.998755i | \(-0.515888\pi\) | ||||
−0.0498933 | + | 0.998755i | \(0.515888\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.72304 | 0.0663197 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −45.0415 | −1.73108 | −0.865542 | − | 0.500836i | \(-0.833026\pi\) | ||||
−0.865542 | + | 0.500836i | \(0.833026\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 44.4801 | 1.70699 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.9060 | 0.456239 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −34.4943 | −1.31989 | −0.659944 | − | 0.751314i | \(-0.729420\pi\) | ||||
−0.659944 | + | 0.751314i | \(0.729420\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.07748 | 0.308625 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.37212 | 0.357569 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −48.1420 | −1.83406 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.2062 | 0.844764 | 0.422382 | − | 0.906418i | \(-0.361194\pi\) | ||||
0.422382 | + | 0.906418i | \(0.361194\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.3240 | 0.429542 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.3074 | 0.769197 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 31.9446 | 1.20825 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.01026 | −0.302543 | −0.151272 | − | 0.988492i | \(-0.548337\pi\) | ||||
−0.151272 | + | 0.988492i | \(0.548337\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −23.8312 | −0.898812 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.46664 | 0.356534 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −50.0220 | −1.88127 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.7422 | 0.478544 | 0.239272 | − | 0.970953i | \(-0.423091\pi\) | ||||
0.239272 | + | 0.970953i | \(0.423091\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −39.4085 | −1.47793 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.08764 | 0.190534 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.19940 | 0.0447924 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.15517 | −0.229549 | −0.114775 | − | 0.993392i | \(-0.536615\pi\) | ||||
−0.114775 | + | 0.993392i | \(0.536615\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.0259 | −0.447869 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14.6157 | −0.543563 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.76702 | 0.288460 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.77647 | −0.362589 | −0.181295 | − | 0.983429i | \(-0.558029\pi\) | ||||
−0.181295 | + | 0.983429i | \(0.558029\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.1897 | −0.451469 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.6123 | 0.540455 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.1966 | 0.819849 | 0.409925 | − | 0.912119i | \(-0.365555\pi\) | ||||
0.409925 | + | 0.912119i | \(0.365555\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 33.7889 | 1.24632 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.7597 | −0.763657 | −0.381828 | − | 0.924233i | \(-0.624705\pi\) | ||||
−0.381828 | + | 0.924233i | \(0.624705\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 57.0676 | 2.09643 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.6946 | 1.27282 | 0.636410 | − | 0.771351i | \(-0.280419\pi\) | ||||
0.636410 | + | 0.771351i | \(0.280419\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.35175 | 0.0861614 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −24.9029 | −0.911150 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −82.2189 | −3.00421 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.6367 | −0.753043 | −0.376521 | − | 0.926408i | \(-0.622880\pi\) | ||||
−0.376521 | + | 0.926408i | \(0.622880\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −31.2497 | −1.13880 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.7268 | 0.535965 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.6794 | −0.860642 | −0.430321 | − | 0.902676i | \(-0.641600\pi\) | ||||
−0.430321 | + | 0.902676i | \(0.641600\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −46.5039 | −1.68576 | −0.842882 | − | 0.538098i | \(-0.819143\pi\) | ||||
−0.842882 | + | 0.538098i | \(0.819143\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −71.5761 | −2.59123 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.42536 | −0.268465 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 36.9347 | 1.33364 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.48780 | −0.306078 | −0.153039 | − | 0.988220i | \(-0.548906\pi\) | ||||
−0.153039 | + | 0.988220i | \(0.548906\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.51412 | 0.198586 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 44.8095 | 1.61168 | 0.805842 | − | 0.592130i | \(-0.201713\pi\) | ||||
0.805842 | + | 0.592130i | \(0.201713\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.97204 | −0.106759 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −60.7362 | −2.17890 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25.7703 | 0.923318 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 13.3828 | 0.478264 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.4544 | 0.587281 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.50207 | −0.160481 | −0.0802407 | − | 0.996776i | \(-0.525569\pi\) | ||||
−0.0802407 | + | 0.996776i | \(0.525569\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −26.9953 | −0.961059 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.47807 | −0.0525542 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.07795 | −0.322367 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 18.5580 | 0.658185 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34.7713 | 1.23166 | 0.615832 | − | 0.787878i | \(-0.288820\pi\) | ||||
0.615832 | + | 0.787878i | \(0.288820\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.6507 | 0.482927 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 28.8110 | 1.01799 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.98341 | −0.281378 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 34.6913 | 1.22119 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −53.5499 | −1.88271 | −0.941357 | − | 0.337413i | \(-0.890448\pi\) | ||||
−0.941357 | + | 0.337413i | \(0.890448\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.5535 | 0.616387 | 0.308193 | − | 0.951324i | \(-0.400276\pi\) | ||||
0.308193 | + | 0.951324i | \(0.400276\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −24.2228 | −0.849530 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.26242 | −0.184334 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.5432 | 0.648744 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 62.2985 | 2.17688 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.3663 | −0.431586 | −0.215793 | − | 0.976439i | \(-0.569234\pi\) | ||||
−0.215793 | + | 0.976439i | \(0.569234\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.0358 | −0.489258 | −0.244629 | − | 0.969617i | \(-0.578666\pi\) | ||||
−0.244629 | + | 0.969617i | \(0.578666\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.8085 | 0.897450 | 0.448725 | − | 0.893670i | \(-0.351878\pi\) | ||||
0.448725 | + | 0.893670i | \(0.351878\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.0081 | 0.486522 | 0.243261 | − | 0.969961i | \(-0.421783\pi\) | ||||
0.243261 | + | 0.969961i | \(0.421783\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −57.6177 | −1.99874 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 48.7229 | 1.68815 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.5495 | −0.745752 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.12093 | −0.177005 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.80179 | 0.234824 | 0.117412 | − | 0.993083i | \(-0.462540\pi\) | ||||
0.117412 | + | 0.993083i | \(0.462540\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31.3265 | 1.08023 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.739857 | −0.0254820 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −22.3156 | −0.767679 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 48.9602 | 1.68031 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.73178 | 0.333601 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 46.8963 | 1.60570 | 0.802849 | − | 0.596183i | \(-0.203317\pi\) | ||||
0.802849 | + | 0.596183i | \(0.203317\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.42288 | −0.322256 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.79309 | 0.0954100 | 0.0477050 | − | 0.998861i | \(-0.484809\pi\) | ||||
0.0477050 | + | 0.998861i | \(0.484809\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.83184 | 0.198980 | 0.0994898 | − | 0.995039i | \(-0.468279\pi\) | ||||
0.0994898 | + | 0.995039i | \(0.468279\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 65.6782 | 2.23831 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.8495 | 1.52670 | 0.763348 | − | 0.645987i | \(-0.223554\pi\) | ||||
0.763348 | + | 0.645987i | \(0.223554\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.08425 | −0.240872 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.9468 | 0.473657 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 44.3591 | 1.50305 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −21.4391 | −0.725604 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.66366 | 0.157660 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.8686 | 0.535846 | 0.267923 | − | 0.963440i | \(-0.413663\pi\) | ||||
0.267923 | + | 0.963440i | \(0.413663\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −24.0539 | −0.811318 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.1411 | −1.01548 | −0.507740 | − | 0.861510i | \(-0.669519\pi\) | ||||
−0.507740 | + | 0.861510i | \(0.669519\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42.7708 | −1.43935 | −0.719676 | − | 0.694310i | \(-0.755710\pi\) | ||||
−0.719676 | + | 0.694310i | \(0.755710\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14.2378 | −0.478598 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.66076 | −0.223647 | −0.111823 | − | 0.993728i | \(-0.535669\pi\) | ||||
−0.111823 | + | 0.993728i | \(0.535669\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 84.2588 | 2.82595 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 17.3229 | 0.579689 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.78759 | −0.293737 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −23.3043 | −0.778108 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −23.0839 | −0.769890 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 26.7603 | 0.891514 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 47.2592 | 1.57269 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.6451 | 0.420338 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −37.3310 | −1.23955 | −0.619777 | − | 0.784778i | \(-0.712777\pi\) | ||||
−0.619777 | + | 0.784778i | \(0.712777\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 24.1103 | 0.799688 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.7247 | −0.487852 | −0.243926 | − | 0.969794i | \(-0.578435\pi\) | ||||
−0.243926 | + | 0.969794i | \(0.578435\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.49941 | 0.115687 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −37.0843 | −1.22463 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.0203 | 1.12222 | 0.561112 | − | 0.827740i | \(-0.310374\pi\) | ||||
0.561112 | + | 0.827740i | \(0.310374\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −66.5708 | −2.19358 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.2966 | 0.437664 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.68500 | −0.186922 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.79643 | 0.190380 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.6992 | 0.613502 | 0.306751 | − | 0.951790i | \(-0.400758\pi\) | ||||
0.306751 | + | 0.951790i | \(0.400758\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 61.8299 | 2.02639 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 45.6979 | 1.49608 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.122357 | −0.00399723 | −0.00199862 | − | 0.999998i | \(-0.500636\pi\) | ||||
−0.00199862 | + | 0.999998i | \(0.500636\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −40.0436 | −1.30677 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.8311 | −0.972465 | −0.486233 | − | 0.873829i | \(-0.661629\pi\) | ||||
−0.486233 | + | 0.873829i | \(0.661629\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.5236 | −0.342697 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.03564 | 0.261399 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −49.0368 | −1.59348 | −0.796741 | − | 0.604320i | \(-0.793445\pi\) | ||||
−0.796741 | + | 0.604320i | \(0.793445\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −44.5345 | −1.44565 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 68.3340 | 2.21588 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33.5129 | −1.08559 | −0.542794 | − | 0.839866i | \(-0.682634\pi\) | ||||
−0.542794 | + | 0.839866i | \(0.682634\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.7224 | 0.573485 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 37.6706 | 1.21645 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.1670 | −0.715064 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 39.6290 | 1.27703 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.03540 | −0.162095 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −52.5565 | −1.69010 | −0.845052 | − | 0.534685i | \(-0.820430\pi\) | ||||
−0.845052 | + | 0.534685i | \(0.820430\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −31.7217 | −1.01905 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.28868 | 0.137630 | 0.0688152 | − | 0.997629i | \(-0.478078\pi\) | ||||
0.0688152 | + | 0.997629i | \(0.478078\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 52.8111 | 1.69305 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13.6136 | 0.435985 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.5573 | −0.689678 | −0.344839 | − | 0.938662i | \(-0.612066\pi\) | ||||
−0.344839 | + | 0.938662i | \(0.612066\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 34.4992 | 1.10148 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.3667 | 0.840966 | 0.420483 | − | 0.907300i | \(-0.361861\pi\) | ||||
0.420483 | + | 0.907300i | \(0.361861\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.0557 | −0.479716 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 44.1491 | 1.40528 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.57235 | −0.240787 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −49.3520 | −1.56772 | −0.783858 | − | 0.620940i | \(-0.786751\pi\) | ||||
−0.783858 | + | 0.620940i | \(0.786751\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −67.5195 | −2.14267 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.56534 | −0.0813266 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.83009 | 0.0896300 | 0.0448150 | − | 0.998995i | \(-0.485730\pi\) | ||||
0.0448150 | + | 0.998995i | \(0.485730\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.79545 | −0.309914 |
(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 | 4840.2.a.ba.1.2 | 6 | ||
4.3 | odd | 2 | 9680.2.a.dd.1.5 | 6 | |||
11.7 | odd | 10 | 440.2.y.c.401.3 | yes | 12 | ||
11.8 | odd | 10 | 440.2.y.c.361.3 | ✓ | 12 | ||
11.10 | odd | 2 | 4840.2.a.bb.1.2 | 6 | |||
44.7 | even | 10 | 880.2.bo.i.401.1 | 12 | |||
44.19 | even | 10 | 880.2.bo.i.801.1 | 12 | |||
44.43 | even | 2 | 9680.2.a.dc.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
440.2.y.c.361.3 | ✓ | 12 | 11.8 | odd | 10 | ||
440.2.y.c.401.3 | yes | 12 | 11.7 | odd | 10 | ||
880.2.bo.i.401.1 | 12 | 44.7 | even | 10 | |||
880.2.bo.i.801.1 | 12 | 44.19 | even | 10 | |||
4840.2.a.ba.1.2 | 6 | 1.1 | even | 1 | trivial | ||
4840.2.a.bb.1.2 | 6 | 11.10 | odd | 2 | |||
9680.2.a.dc.1.5 | 6 | 44.43 | even | 2 | |||
9680.2.a.dd.1.5 | 6 | 4.3 | odd | 2 |