Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.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: | \(63.9442019386\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 3x^{9} - 15x^{8} + 43x^{7} + 66x^{6} - 173x^{5} - 127x^{4} + 246x^{3} + 99x^{2} - 82x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.79314\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-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 | ||||||||
\(3\) | −1.79314 | −1.03527 | −0.517635 | − | 0.855602i | \(-0.673187\pi\) | ||||
−0.517635 | + | 0.855602i | \(0.673187\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.09989 | −1.83353 | −0.916763 | − | 0.399432i | \(-0.869207\pi\) | ||||
−0.916763 | + | 0.399432i | \(0.869207\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.215350 | 0.0717832 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.35167 | 1.89819 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.85208 | −0.691732 | −0.345866 | − | 0.938284i | \(-0.612415\pi\) | ||||
−0.345866 | + | 0.938284i | \(0.612415\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.43171 | −0.557873 | −0.278936 | − | 0.960310i | \(-0.589982\pi\) | ||||
−0.278936 | + | 0.960310i | \(0.589982\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.79314 | −0.391295 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.18782 | −0.873221 | −0.436611 | − | 0.899651i | \(-0.643821\pi\) | ||||
−0.436611 | + | 0.899651i | \(0.643821\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.8091 | 2.36182 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.99327 | 0.960955 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.21360 | 0.782445 | 0.391223 | − | 0.920296i | \(-0.372052\pi\) | ||||
0.391223 | + | 0.920296i | \(0.372052\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.03853 | −0.904947 | −0.452473 | − | 0.891778i | \(-0.649458\pi\) | ||||
−0.452473 | + | 0.891778i | \(0.649458\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.79314 | −0.312146 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.09989 | −0.693008 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.01738 | −0.167256 | −0.0836278 | − | 0.996497i | \(-0.526651\pi\) | ||||
−0.0836278 | + | 0.996497i | \(0.526651\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.79314 | 0.287132 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.98517 | 0.622379 | 0.311190 | − | 0.950348i | \(-0.399273\pi\) | ||||
0.311190 | + | 0.950348i | \(0.399273\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.70767 | 1.02291 | 0.511455 | − | 0.859310i | \(-0.329107\pi\) | ||||
0.511455 | + | 0.859310i | \(0.329107\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.882910 | −0.131616 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.2043 | −1.48845 | −0.744224 | − | 0.667930i | \(-0.767180\pi\) | ||||
−0.744224 | + | 0.667930i | \(0.767180\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.11418 | 0.716129 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.40503 | −0.192996 | −0.0964982 | − | 0.995333i | \(-0.530764\pi\) | ||||
−0.0964982 | + | 0.995333i | \(0.530764\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.09989 | −0.552829 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.36040 | 0.577549 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.74222 | 0.226818 | 0.113409 | − | 0.993548i | \(-0.463823\pi\) | ||||
0.113409 | + | 0.993548i | \(0.463823\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.66442 | 0.341144 | 0.170572 | − | 0.985345i | \(-0.445439\pi\) | ||||
0.170572 | + | 0.985345i | \(0.445439\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.215350 | 0.0271315 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.09989 | 0.508529 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.7459 | 1.92367 | 0.961834 | − | 0.273634i | \(-0.0882256\pi\) | ||||
0.961834 | + | 0.273634i | \(0.0882256\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.50935 | 0.904019 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.7880 | −1.39898 | −0.699488 | − | 0.714645i | \(-0.746588\pi\) | ||||
−0.699488 | + | 0.714645i | \(0.746588\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.81536 | 0.446554 | 0.223277 | − | 0.974755i | \(-0.428325\pi\) | ||||
0.223277 | + | 0.974755i | \(0.428325\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −21.1753 | −2.44512 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.6244 | 1.64537 | 0.822685 | − | 0.568497i | \(-0.192475\pi\) | ||||
0.822685 | + | 0.568497i | \(0.192475\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.59967 | −1.06663 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.0350 | 1.43078 | 0.715390 | − | 0.698725i | \(-0.246249\pi\) | ||||
0.715390 | + | 0.698725i | \(0.246249\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.6932 | 1.26831 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.55557 | −0.810042 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.08568 | −0.539081 | −0.269541 | − | 0.962989i | \(-0.586872\pi\) | ||||
−0.269541 | + | 0.962989i | \(0.586872\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.03479 | 0.936864 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.96975 | 1.02287 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.1623 | 1.23489 | 0.617447 | − | 0.786613i | \(-0.288167\pi\) | ||||
0.617447 | + | 0.786613i | \(0.288167\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.215350 | 0.0216435 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.40779 | 0.140081 | 0.0700403 | − | 0.997544i | \(-0.477687\pi\) | ||||
0.0700403 | + | 0.997544i | \(0.477687\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.23231 | −0.909687 | −0.454843 | − | 0.890571i | \(-0.650305\pi\) | ||||
−0.454843 | + | 0.890571i | \(0.650305\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.35167 | 0.717450 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.5588 | −1.02075 | −0.510376 | − | 0.859951i | \(-0.670494\pi\) | ||||
−0.510376 | + | 0.859951i | \(0.670494\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.07093 | 0.389924 | 0.194962 | − | 0.980811i | \(-0.437542\pi\) | ||||
0.194962 | + | 0.980811i | \(0.437542\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.82430 | 0.173155 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.76726 | 0.354394 | 0.177197 | − | 0.984175i | \(-0.443297\pi\) | ||||
0.177197 | + | 0.984175i | \(0.443297\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 17.1696 | 1.60107 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.215350 | −0.0199091 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.85208 | −0.261450 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.14597 | −0.644330 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −27.9165 | −2.49693 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.6398 | 1.03286 | 0.516431 | − | 0.856329i | \(-0.327260\pi\) | ||||
0.516431 | + | 0.856329i | \(0.327260\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.0278 | −1.05899 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.2068 | 1.32862 | 0.664311 | − | 0.747457i | \(-0.268725\pi\) | ||||
0.664311 | + | 0.747457i | \(0.268725\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.43171 | −0.210856 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −20.4718 | −1.76194 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.9323 | 1.19032 | 0.595159 | − | 0.803608i | \(-0.297089\pi\) | ||||
0.595159 | + | 0.803608i | \(0.297089\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.67440 | −0.311659 | −0.155829 | − | 0.987784i | \(-0.549805\pi\) | ||||
−0.155829 | + | 0.987784i | \(0.549805\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 18.2977 | 1.54094 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −17.2753 | −1.43463 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.79314 | −0.147896 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.6662 | 0.955736 | 0.477868 | − | 0.878432i | \(-0.341410\pi\) | ||||
0.477868 | + | 0.878432i | \(0.341410\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.6065 | −1.83969 | −0.919846 | − | 0.392280i | \(-0.871686\pi\) | ||||
−0.919846 | + | 0.392280i | \(0.871686\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.614195 | −0.0496548 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 20.6574 | 1.65924 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.25830 | −0.738893 | −0.369446 | − | 0.929252i | \(-0.620453\pi\) | ||||
−0.369446 | + | 0.929252i | \(0.620453\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.51942 | 0.199803 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.18782 | −0.330047 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.49778 | 0.665598 | 0.332799 | − | 0.942998i | \(-0.392007\pi\) | ||||
0.332799 | + | 0.942998i | \(0.392007\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.35167 | 0.572327 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.51364 | −0.736188 | −0.368094 | − | 0.929789i | \(-0.619990\pi\) | ||||
−0.368094 | + | 0.929789i | \(0.619990\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.523668 | −0.0400459 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.5824 | −0.880594 | −0.440297 | − | 0.897852i | \(-0.645127\pi\) | ||||
−0.440297 | + | 0.897852i | \(0.645127\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.8091 | 0.892683 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.12405 | −0.234818 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.2718 | −0.842494 | −0.421247 | − | 0.906946i | \(-0.638407\pi\) | ||||
−0.421247 | + | 0.906946i | \(0.638407\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.8861 | 1.10647 | 0.553236 | − | 0.833024i | \(-0.313393\pi\) | ||||
0.553236 | + | 0.833024i | \(0.313393\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.77767 | −0.353176 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.17113 | 0.306667 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.85208 | −0.208565 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.99327 | 0.363207 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.4505 | 0.828531 | 0.414265 | − | 0.910156i | \(-0.364039\pi\) | ||||
0.414265 | + | 0.910156i | \(0.364039\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.04999 | −0.579451 | −0.289726 | − | 0.957110i | \(-0.593564\pi\) | ||||
−0.289726 | + | 0.957110i | \(0.593564\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.35167 | −0.526464 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.19564 | 0.370174 | 0.185087 | − | 0.982722i | \(-0.440743\pi\) | ||||
0.185087 | + | 0.982722i | \(0.440743\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.1305 | 1.85235 | 0.926173 | − | 0.377100i | \(-0.123079\pi\) | ||||
0.926173 | + | 0.377100i | \(0.123079\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −28.2346 | −1.99152 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.21360 | 0.295737 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.3388 | −1.14115 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.901846 | −0.0626826 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.43171 | −0.168205 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.02320 | −0.414654 | −0.207327 | − | 0.978272i | \(-0.566476\pi\) | ||||
−0.207327 | + | 0.978272i | \(0.566476\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 21.1375 | 1.44832 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −27.5007 | −1.87553 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.03853 | −0.342038 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.84147 | −0.462304 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.85208 | 0.191852 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.7386 | −1.45572 | −0.727862 | − | 0.685723i | \(-0.759486\pi\) | ||||
−0.727862 | + | 0.685723i | \(0.759486\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.54308 | 0.169539 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.19258 | −0.411016 | −0.205508 | − | 0.978655i | \(-0.565885\pi\) | ||||
−0.205508 | + | 0.978655i | \(0.565885\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.40410 | 0.224949 | 0.112475 | − | 0.993655i | \(-0.464122\pi\) | ||||
0.112475 | + | 0.993655i | \(0.464122\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.79314 | −0.117980 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.4067 | −0.812792 | −0.406396 | − | 0.913697i | \(-0.633215\pi\) | ||||
−0.406396 | + | 0.913697i | \(0.633215\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 41.8364 | 2.72911 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −26.2235 | −1.70340 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.45750 | 0.547070 | 0.273535 | − | 0.961862i | \(-0.411807\pi\) | ||||
0.273535 | + | 0.961862i | \(0.411807\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.2861 | −1.82207 | −0.911033 | − | 0.412334i | \(-0.864714\pi\) | ||||
−0.911033 | + | 0.412334i | \(0.864714\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.23375 | 0.143295 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.09989 | −0.261932 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.43171 | 0.154726 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −23.3736 | −1.48124 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.7992 | 1.06036 | 0.530179 | − | 0.847886i | \(-0.322125\pi\) | ||||
0.530179 | + | 0.847886i | \(0.322125\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.18782 | −0.263286 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −20.9676 | −1.31304 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.02687 | −0.188811 | −0.0944053 | − | 0.995534i | \(-0.530095\pi\) | ||||
−0.0944053 | + | 0.995534i | \(0.530095\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.01738 | −0.0632167 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.907397 | 0.0561665 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.7871 | 1.34345 | 0.671726 | − | 0.740799i | \(-0.265553\pi\) | ||||
0.671726 | + | 0.740799i | \(0.265553\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.76049 | 0.353864 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.11934 | 0.558094 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.03465 | −0.245997 | −0.122998 | − | 0.992407i | \(-0.539251\pi\) | ||||
−0.122998 | + | 0.992407i | \(0.539251\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.5642 | 1.06695 | 0.533474 | − | 0.845816i | \(-0.320886\pi\) | ||||
0.533474 | + | 0.845816i | \(0.320886\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.79314 | 0.108526 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.8091 | 0.712115 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.3895 | −0.684330 | −0.342165 | − | 0.939640i | \(-0.611160\pi\) | ||||
−0.342165 | + | 0.939640i | \(0.611160\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.08505 | −0.0649600 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.9580 | −1.36956 | −0.684781 | − | 0.728749i | \(-0.740102\pi\) | ||||
−0.684781 | + | 0.728749i | \(0.740102\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.4918 | 0.861447 | 0.430723 | − | 0.902484i | \(-0.358258\pi\) | ||||
0.430723 | + | 0.902484i | \(0.358258\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −17.8771 | −1.05895 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.98517 | 0.235237 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.86562 | −0.521507 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −21.8087 | −1.27845 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.4556 | 0.610823 | 0.305412 | − | 0.952220i | \(-0.401206\pi\) | ||||
0.305412 | + | 0.952220i | \(0.401206\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.14292 | −0.415877 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.99327 | 0.289739 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.18782 | 0.242188 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.70767 | 0.386624 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.52437 | −0.145021 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.9238 | −0.625495 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.4302 | −0.709426 | −0.354713 | − | 0.934975i | \(-0.615422\pi\) | ||||
−0.354713 | + | 0.934975i | \(0.615422\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.5548 | 0.941771 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.36867 | 0.134315 | 0.0671575 | − | 0.997742i | \(-0.478607\pi\) | ||||
0.0671575 | + | 0.997742i | \(0.478607\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.1821 | −1.31033 | −0.655166 | − | 0.755485i | \(-0.727401\pi\) | ||||
−0.655166 | + | 0.755485i | \(0.727401\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.882910 | −0.0497463 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.0219 | −0.899878 | −0.449939 | − | 0.893059i | \(-0.648554\pi\) | ||||
−0.449939 | + | 0.893059i | \(0.648554\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.21360 | 0.235916 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.9333 | 1.05675 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.93544 | 0.385898 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.8091 | −0.655050 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.29975 | −0.403677 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.2043 | −0.562580 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.52695 | −0.193859 | −0.0969295 | − | 0.995291i | \(-0.530902\pi\) | ||||
−0.0969295 | + | 0.995291i | \(0.530902\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.219092 | −0.0120061 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −64.5564 | −3.52710 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.07357 | −0.0584808 | −0.0292404 | − | 0.999572i | \(-0.509309\pi\) | ||||
−0.0292404 | + | 0.999572i | \(0.509309\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.75522 | −0.366893 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.03853 | −0.272852 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −30.7875 | −1.65754 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 33.9847 | 1.82439 | 0.912196 | − | 0.409754i | \(-0.134385\pi\) | ||||
0.912196 | + | 0.409754i | \(0.134385\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.7599 | 0.843609 | 0.421805 | − | 0.906687i | \(-0.361397\pi\) | ||||
0.421805 | + | 0.906687i | \(0.361397\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.99327 | −0.266521 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −34.7330 | −1.84865 | −0.924326 | − | 0.381604i | \(-0.875372\pi\) | ||||
−0.924326 | + | 0.381604i | \(0.875372\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 48.3294 | 2.56506 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.11418 | 0.270671 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.6306 | 0.561060 | 0.280530 | − | 0.959845i | \(-0.409490\pi\) | ||||
0.280530 | + | 0.959845i | \(0.409490\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.0868 | −0.688778 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.79314 | −0.0941154 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.6425 | −0.818768 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.7445 | −0.821855 | −0.410928 | − | 0.911668i | \(-0.634795\pi\) | ||||
−0.410928 | + | 0.911668i | \(0.634795\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.858206 | 0.0446764 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.40503 | −0.0729458 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.84884 | −0.302841 | −0.151421 | − | 0.988469i | \(-0.548385\pi\) | ||||
−0.151421 | + | 0.988469i | \(0.548385\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 50.0582 | 2.58499 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.21360 | −0.217011 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.7116 | −0.652950 | −0.326475 | − | 0.945206i | \(-0.605861\pi\) | ||||
−0.326475 | + | 0.945206i | \(0.605861\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −20.8717 | −1.06929 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.8627 | −1.01493 | −0.507467 | − | 0.861671i | \(-0.669418\pi\) | ||||
−0.507467 | + | 0.861671i | \(0.669418\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.09989 | −0.208950 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.44449 | 0.0734278 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.1385 | −1.32527 | −0.662636 | − | 0.748941i | \(-0.730562\pi\) | ||||
−0.662636 | + | 0.748941i | \(0.730562\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.9440 | 0.604035 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −27.2679 | −1.37548 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −59.9583 | −3.01683 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.0511 | −1.45803 | −0.729017 | − | 0.684496i | \(-0.760022\pi\) | ||||
−0.729017 | + | 0.684496i | \(0.760022\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.36040 | 0.218293 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.930773 | −0.0464806 | −0.0232403 | − | 0.999730i | \(-0.507398\pi\) | ||||
−0.0232403 | + | 0.999730i | \(0.507398\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.03853 | 0.250987 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 39.3576 | 1.95569 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.01738 | −0.0504295 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.9392 | −0.887036 | −0.443518 | − | 0.896266i | \(-0.646270\pi\) | ||||
−0.443518 | + | 0.896266i | \(0.646270\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −24.9826 | −1.23230 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.74222 | 0.0857291 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −53.4422 | −2.62337 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.58872 | 0.322651 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.6006 | −0.908699 | −0.454350 | − | 0.890823i | \(-0.650128\pi\) | ||||
−0.454350 | + | 0.890823i | \(0.650128\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.4998 | −1.73015 | −0.865076 | − | 0.501640i | \(-0.832730\pi\) | ||||
−0.865076 | + | 0.501640i | \(0.832730\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.19749 | −0.106846 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −33.6805 | −1.63374 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.66442 | 0.128940 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.79314 | 0.0865736 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.64974 | 0.368475 | 0.184237 | − | 0.982882i | \(-0.441018\pi\) | ||||
0.184237 | + | 0.982882i | \(0.441018\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.22294 | −0.347112 | −0.173556 | − | 0.984824i | \(-0.555526\pi\) | ||||
−0.173556 | + | 0.984824i | \(0.555526\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 30.9770 | 1.48523 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.1836 | 0.487146 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 38.9496 | 1.85896 | 0.929482 | − | 0.368868i | \(-0.120255\pi\) | ||||
0.929482 | + | 0.368868i | \(0.120255\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.215350 | 0.0102547 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.09099 | −0.289392 | −0.144696 | − | 0.989476i | \(-0.546220\pi\) | ||||
−0.144696 | + | 0.989476i | \(0.546220\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 20.8507 | 0.988419 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −20.9192 | −0.989444 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.5301 | −0.685716 | −0.342858 | − | 0.939387i | \(-0.611395\pi\) | ||||
−0.342858 | + | 0.939387i | \(0.611395\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.98517 | 0.187654 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 40.5366 | 1.90458 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.09989 | 0.192206 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.88912 | −0.0883692 | −0.0441846 | − | 0.999023i | \(-0.514069\pi\) | ||||
−0.0441846 | + | 0.999023i | \(0.514069\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −14.2412 | −0.664723 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.0023 | 1.11790 | 0.558949 | − | 0.829202i | \(-0.311205\pi\) | ||||
0.558949 | + | 0.829202i | \(0.311205\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.0569 | 0.467386 | 0.233693 | − | 0.972310i | \(-0.424919\pi\) | ||||
0.233693 | + | 0.972310i | \(0.424919\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −37.0416 | −1.71776 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −33.8616 | −1.56693 | −0.783463 | − | 0.621438i | \(-0.786549\pi\) | ||||
−0.783463 | + | 0.621438i | \(0.786549\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.7459 | 0.727078 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.6014 | 0.764953 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.70767 | 0.308419 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −28.7163 | −1.31759 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.302574 | −0.0138539 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.6911 | −0.716945 | −0.358472 | − | 0.933540i | \(-0.616702\pi\) | ||||
−0.358472 | + | 0.933540i | \(0.616702\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.01738 | 0.0463883 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.50935 | 0.341687 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −49.8641 | −2.26421 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.8974 | −1.08290 | −0.541448 | − | 0.840735i | \(-0.682124\pi\) | ||||
−0.541448 | + | 0.840735i | \(0.682124\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15.2377 | −0.689073 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.60891 | 0.298256 | 0.149128 | − | 0.988818i | \(-0.452353\pi\) | ||||
0.149128 | + | 0.988818i | \(0.452353\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.0175 | −0.541243 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.882910 | −0.0396838 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.7880 | −0.528763 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.2334 | 0.547643 | 0.273822 | − | 0.961781i | \(-0.411712\pi\) | ||||
0.273822 | + | 0.961781i | \(0.411712\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.0593 | 0.762153 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.8269 | −1.37450 | −0.687252 | − | 0.726419i | \(-0.741183\pi\) | ||||
−0.687252 | + | 0.726419i | \(0.741183\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.77179 | −0.256841 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.79314 | −0.0796361 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.27765 | 0.233928 | 0.116964 | − | 0.993136i | \(-0.462684\pi\) | ||||
0.116964 | + | 0.993136i | \(0.462684\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.81536 | 0.168781 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.1422 | −0.536090 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 37.8515 | 1.66793 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.2043 | −0.448784 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.7689 | 0.911652 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.4010 | 1.33189 | 0.665946 | − | 0.746000i | \(-0.268028\pi\) | ||||
0.665946 | + | 0.746000i | \(0.268028\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.0070 | 0.481301 | 0.240651 | − | 0.970612i | \(-0.422639\pi\) | ||||
0.240651 | + | 0.970612i | \(0.422639\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −21.1753 | −0.924168 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.3703 | 0.625981 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.46215 | −0.237485 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.375187 | 0.0162817 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.98517 | −0.172617 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 43.2897 | 1.87158 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.2119 | 0.872208 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.2639 | −0.527266 | −0.263633 | − | 0.964623i | \(-0.584921\pi\) | ||||
−0.263633 | + | 0.964623i | \(0.584921\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −26.6928 | −1.14550 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.6904 | −0.714937 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.5691 | 0.793959 | 0.396979 | − | 0.917828i | \(-0.370058\pi\) | ||||
0.396979 | + | 0.917828i | \(0.370058\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.573781 | 0.0244884 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.2463 | −0.436505 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.6244 | 0.621892 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.47941 | −0.317483 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.9013 | 0.504274 | 0.252137 | − | 0.967692i | \(-0.418867\pi\) | ||||
0.252137 | + | 0.967692i | \(0.418867\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.70767 | −0.283704 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.11418 | 0.215921 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.3475 | −0.731110 | −0.365555 | − | 0.930790i | \(-0.619121\pi\) | ||||
−0.365555 | + | 0.930790i | \(0.619121\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.4453 | −0.649790 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.59967 | −0.403148 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.45530 | 0.102932 | 0.0514658 | − | 0.998675i | \(-0.483611\pi\) | ||||
0.0514658 | + | 0.998675i | \(0.483611\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.9694 | 1.25418 | 0.627091 | − | 0.778946i | \(-0.284246\pi\) | ||||
0.627091 | + | 0.778946i | \(0.284246\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20.5324 | −0.857753 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −49.4544 | −2.06239 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.74606 | 0.197581 | 0.0987905 | − | 0.995108i | \(-0.468503\pi\) | ||||
0.0987905 | + | 0.995108i | \(0.468503\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.4348 | 0.599888 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.0350 | 0.540784 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.40503 | −0.0581906 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.882910 | 0.0365038 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −38.1637 | −1.57518 | −0.787592 | − | 0.616198i | \(-0.788672\pi\) | ||||
−0.787592 | + | 0.616198i | \(0.788672\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.2523 | 0.504845 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.31651 | −0.383230 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 35.4574 | 1.45606 | 0.728031 | − | 0.685544i | \(-0.240436\pi\) | ||||
0.728031 | + | 0.685544i | \(0.240436\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.6932 | 0.479376 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −46.8557 | −1.91768 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.5036 | −0.878612 | −0.439306 | − | 0.898337i | \(-0.644776\pi\) | ||||
−0.439306 | + | 0.898337i | \(0.644776\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.3470 | −0.626016 | −0.313008 | − | 0.949750i | \(-0.601337\pi\) | ||||
−0.313008 | + | 0.949750i | \(0.601337\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.39088 | 0.138087 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.09989 | −0.166684 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −38.3757 | −1.55762 | −0.778811 | − | 0.627258i | \(-0.784177\pi\) | ||||
−0.778811 | + | 0.627258i | \(0.784177\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.55557 | −0.306167 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.2043 | 0.412821 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.4970 | 0.504749 | 0.252375 | − | 0.967630i | \(-0.418788\pi\) | ||||
0.252375 | + | 0.967630i | \(0.418788\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 29.2977 | 1.18140 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.1442 | −0.408390 | −0.204195 | − | 0.978930i | \(-0.565458\pi\) | ||||
−0.204195 | + | 0.978930i | \(0.565458\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.1922 | 0.811593 | 0.405796 | − | 0.913964i | \(-0.366994\pi\) | ||||
0.405796 | + | 0.913964i | \(0.366994\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −20.9109 | −0.839126 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.08568 | −0.203754 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 55.4091 | 2.21636 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.36040 | 0.174138 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.90164 | 0.115696 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 48.0614 | 1.91330 | 0.956648 | − | 0.291248i | \(-0.0940705\pi\) | ||||
0.956648 | + | 0.291248i | \(0.0940705\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.8004 | 0.429279 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −47.7218 | −1.89378 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.53854 | −0.100423 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.9390 | 0.906037 | 0.453019 | − | 0.891501i | \(-0.350347\pi\) | ||||
0.453019 | + | 0.891501i | \(0.350347\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.3284 | 0.998853 | 0.499427 | − | 0.866356i | \(-0.333544\pi\) | ||||
0.499427 | + | 0.866356i | \(0.333544\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 49.3126 | 1.94168 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.3832 | 0.526146 | 0.263073 | − | 0.964776i | \(-0.415264\pi\) | ||||
0.263073 | + | 0.964776i | \(0.415264\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.74222 | 0.0683882 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.03479 | 0.354101 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.15602 | −0.123505 | −0.0617523 | − | 0.998092i | \(-0.519669\pi\) | ||||
−0.0617523 | + | 0.998092i | \(0.519669\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −62.3461 | −2.43606 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.821636 | 0.0320551 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −32.8595 | −1.28003 | −0.640013 | − | 0.768364i | \(-0.721071\pi\) | ||||
−0.640013 | + | 0.768364i | \(0.721071\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.06631 | −0.235952 | −0.117976 | − | 0.993016i | \(-0.537641\pi\) | ||||
−0.117976 | + | 0.993016i | \(0.537641\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.11418 | −0.198618 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.96975 | 0.386610 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.6458 | −0.683248 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 38.9804 | 1.50707 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.66442 | 0.102859 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.3601 | 0.399353 | 0.199676 | − | 0.979862i | \(-0.436011\pi\) | ||||
0.199676 | + | 0.979862i | \(0.436011\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 58.9659 | 2.26960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.7326 | 0.450919 | 0.225459 | − | 0.974253i | \(-0.427612\pi\) | ||||
0.225459 | + | 0.974253i | \(0.427612\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.1623 | 0.466746 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.1042 | 0.425512 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.6615 | −0.407950 | −0.203975 | − | 0.978976i | \(-0.565386\pi\) | ||||
−0.203975 | + | 0.978976i | \(0.565386\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −57.1209 | −2.18248 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.10402 | −0.232883 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.40503 | 0.0535276 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.1921 | 1.18660 | 0.593302 | − | 0.804980i | \(-0.297824\pi\) | ||||
0.593302 | + | 0.804980i | \(0.297824\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.215350 | 0.00818046 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.0646 | 0.571434 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.3660 | −0.430520 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 22.2470 | 0.841458 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.9873 | −1.43476 | −0.717379 | − | 0.696683i | \(-0.754659\pi\) | ||||
−0.717379 | + | 0.696683i | \(0.754659\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.47396 | 0.0933073 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −75.0186 | −2.82536 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.40779 | 0.0529455 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.8018 | −0.631006 | −0.315503 | − | 0.948925i | \(-0.602173\pi\) | ||||
−0.315503 | + | 0.948925i | \(0.602173\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.14935 | 0.118110 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21.1005 | 0.790219 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.09989 | 0.153327 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.1655 | −0.566365 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.40347 | 0.238809 | 0.119405 | − | 0.992846i | \(-0.461901\pi\) | ||||
0.119405 | + | 0.992846i | \(0.461901\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.23231 | −0.343829 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 50.7209 | 1.88633 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 49.7587 | 1.84799 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.1475 | −0.710141 | −0.355071 | − | 0.934839i | \(-0.615543\pi\) | ||||
−0.355071 | + | 0.934839i | \(0.615543\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.7936 | 0.918281 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −19.1308 | −0.707580 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 44.1429 | 1.63045 | 0.815227 | − | 0.579142i | \(-0.196612\pi\) | ||||
0.815227 | + | 0.579142i | \(0.196612\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.35167 | 0.271171 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15.7459 | 0.580008 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.7229 | −0.651947 | −0.325973 | − | 0.945379i | \(-0.605692\pi\) | ||||
−0.325973 | + | 0.945379i | \(0.605692\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.36040 | −0.160183 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.0867 | 1.32389 | 0.661946 | − | 0.749552i | \(-0.269731\pi\) | ||||
0.661946 | + | 0.749552i | \(0.269731\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −47.8303 | −1.75237 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.80709 | 0.102706 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.5588 | −0.385808 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.0251 | 0.657744 | 0.328872 | − | 0.944375i | \(-0.393332\pi\) | ||||
0.328872 | + | 0.944375i | \(0.393332\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −30.1234 | −1.09776 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 92.6842 | 3.37312 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.8674 | −0.394981 | −0.197491 | − | 0.980305i | \(-0.563279\pi\) | ||||
−0.197491 | + | 0.980305i | \(0.563279\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.50935 | 0.272572 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.2258 | 0.479433 | 0.239717 | − | 0.970843i | \(-0.422945\pi\) | ||||
0.239717 | + | 0.970843i | \(0.422945\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.07093 | 0.147378 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.51813 | 0.0910433 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.74222 | −0.0629080 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.639598 | 0.0230645 | 0.0115322 | − | 0.999934i | \(-0.496329\pi\) | ||||
0.0115322 | + | 0.999934i | \(0.496329\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.42759 | 0.195470 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.945183 | 0.0339959 | 0.0169979 | − | 0.999856i | \(-0.494589\pi\) | ||||
0.0169979 | + | 0.999856i | \(0.494589\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −59.5004 | −2.13732 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.82430 | 0.0654463 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.69079 | −0.347208 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.7880 | −0.421807 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 21.0396 | 0.751895 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 37.9580 | 1.35478 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 51.3127 | 1.82910 | 0.914550 | − | 0.404474i | \(-0.132545\pi\) | ||||
0.914550 | + | 0.404474i | \(0.132545\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −39.0674 | −1.39084 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.76726 | 0.133948 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.66442 | −0.0946162 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.3294 | −0.366345 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.3477 | −0.862439 | −0.431220 | − | 0.902247i | \(-0.641917\pi\) | ||||
−0.431220 | + | 0.902247i | \(0.641917\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 29.1035 | 1.02961 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.09520 | −0.0386970 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.81536 | 0.134641 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.1696 | 0.605149 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.23469 | 0.254673 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 55.0873 | 1.93677 | 0.968384 | − | 0.249466i | \(-0.0802550\pi\) | ||||
0.968384 | + | 0.249466i | \(0.0802550\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.1956 | 0.849624 | 0.424812 | − | 0.905282i | \(-0.360340\pi\) | ||||
0.424812 | + | 0.905282i | \(0.360340\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −31.4950 | −1.10458 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −34.8400 | −1.22039 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.3111 | −0.570654 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.215350 | −0.00752493 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −36.0287 | −1.25741 | −0.628706 | − | 0.777643i | \(-0.716415\pi\) | ||||
−0.628706 | + | 0.777643i | \(0.716415\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.3856 | −0.710597 | −0.355298 | − | 0.934753i | \(-0.615621\pi\) | ||||
−0.355298 | + | 0.934753i | \(0.615621\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −21.1753 | −0.737231 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.60229 | −0.333904 | −0.166952 | − | 0.985965i | \(-0.553393\pi\) | ||||
−0.166952 | + | 0.985965i | \(0.553393\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.2765 | −1.08628 | −0.543140 | − | 0.839642i | \(-0.682765\pi\) | ||||
−0.543140 | + | 0.839642i | \(0.682765\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20.4230 | 0.708466 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.85208 | −0.0988188 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 39.0049 | 1.34982 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −25.1587 | −0.869613 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −48.1484 | −1.66227 | −0.831133 | − | 0.556074i | \(-0.812307\pi\) | ||||
−0.831133 | + | 0.556074i | \(0.812307\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.2456 | −0.387779 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 41.1670 | 1.41787 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.09989 | −0.141040 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −25.9858 | −0.891830 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.26059 | 0.146051 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.2899 | 1.24254 | 0.621272 | − | 0.783595i | \(-0.286616\pi\) | ||||
0.621272 | + | 0.783595i | \(0.286616\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.14698 | 0.0734252 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.25191 | 0.316039 | 0.158020 | − | 0.987436i | \(-0.449489\pi\) | ||||
0.158020 | + | 0.987436i | \(0.449489\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 51.2281 | 1.74788 | 0.873940 | − | 0.486034i | \(-0.161557\pi\) | ||||
0.873940 | + | 0.486034i | \(0.161557\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.14597 | −0.243534 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.9102 | −1.25644 | −0.628219 | − | 0.778036i | \(-0.716216\pi\) | ||||
−0.628219 | + | 0.778036i | \(0.716216\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 47.4866 | 1.61459 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15.8973 | 0.539900 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.6244 | 0.496098 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.7459 | −0.533530 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.61915 | 0.0886447 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −27.9165 | −0.943750 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.2717 | −0.650758 | −0.325379 | − | 0.945584i | \(-0.605492\pi\) | ||||
−0.325379 | + | 0.945584i | \(0.605492\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18.7484 | −0.632367 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.9816 | −0.875342 | −0.437671 | − | 0.899135i | \(-0.644197\pi\) | ||||
−0.437671 | + | 0.899135i | \(0.644197\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.7065 | −0.528566 | −0.264283 | − | 0.964445i | \(-0.585135\pi\) | ||||
−0.264283 | + | 0.964445i | \(0.585135\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.8082 | 0.430544 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.1410 | −0.709844 | −0.354922 | − | 0.934896i | \(-0.615493\pi\) | ||||
−0.354922 | + | 0.934896i | \(0.615493\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.6398 | 0.390385 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.59967 | −0.321601 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 24.8139 | 0.830364 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 46.2131 | 1.54473 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.50935 | −0.250730 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −21.2303 | −0.708072 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.00728 | 0.133502 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.0278 | −0.400260 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −61.0312 | −2.02875 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.4835 | −0.812961 | −0.406480 | − | 0.913660i | \(-0.633244\pi\) | ||||
−0.406480 | + | 0.913660i | \(0.633244\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.303168 | 0.0100554 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.5593 | 0.614896 | 0.307448 | − | 0.951565i | \(-0.400525\pi\) | ||||
0.307448 | + | 0.951565i | \(0.400525\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.0350 | 0.431397 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 19.5879 | 0.647556 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.2068 | 0.502172 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.5489 | −0.875767 | −0.437884 | − | 0.899032i | \(-0.644272\pi\) | ||||
−0.437884 | + | 0.899032i | \(0.644272\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.2890 | 0.734448 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.7880 | 0.388006 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.0143 | −0.395027 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.98818 | −0.0653003 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −55.1128 | −1.80819 | −0.904096 | − | 0.427328i | \(-0.859455\pi\) | ||||
−0.904096 | + | 0.427328i | \(0.859455\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.43171 | −0.0796961 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.24736 | −0.139052 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11.6932 | 0.382409 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.0844 | −0.558122 | −0.279061 | − | 0.960273i | \(-0.590023\pi\) | ||||
−0.279061 | + | 0.960273i | \(0.590023\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 41.5688 | 1.35655 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39.2418 | −1.27924 | −0.639622 | − | 0.768689i | \(-0.720909\pi\) | ||||
−0.639622 | + | 0.768689i | \(0.720909\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.6892 | −0.543475 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −20.4718 | −0.665949 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.2766 | −0.333945 | −0.166973 | − | 0.985962i | \(-0.553399\pi\) | ||||
−0.166973 | + | 0.985962i | \(0.553399\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.81536 | −0.123852 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28.7295 | 0.931617 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −46.4935 | −1.50607 | −0.753037 | − | 0.657979i | \(-0.771412\pi\) | ||||
−0.753037 | + | 0.657979i | \(0.771412\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −46.9459 | −1.51913 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.55557 | −0.244237 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.9323 | 0.449898 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.61321 | −0.181071 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.27382 | −0.0732730 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 33.0041 | 1.06244 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.6936 | −0.440356 | −0.220178 | − | 0.975460i | \(-0.570664\pi\) | ||||
−0.220178 | + | 0.975460i | \(0.570664\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.4362 | −0.399509 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.675977 | −0.0216931 | −0.0108466 | − | 0.999941i | \(-0.503453\pi\) | ||||
−0.0108466 | + | 0.999941i | \(0.503453\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.67440 | −0.117796 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 21.1753 | 0.678154 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 45.2312 | 1.44707 | 0.723537 | − | 0.690286i | \(-0.242515\pi\) | ||||
0.723537 | + | 0.690286i | \(0.242515\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.08568 | −0.162539 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.876674 | 0.0279900 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.25413 | 0.231371 | 0.115685 | − | 0.993286i | \(-0.463094\pi\) | ||||
0.115685 | + | 0.993286i | \(0.463094\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.3015 | −0.678724 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 18.2977 | 0.582422 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −28.0905 | −0.893227 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.17319 | 0.164332 | 0.0821660 | − | 0.996619i | \(-0.473816\pi\) | ||||
0.0821660 | + | 0.996619i | \(0.473816\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.32432 | 0.200696 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −107.132 | −3.39632 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.59884 | 0.145647 | 0.0728233 | − | 0.997345i | \(-0.476799\pi\) | ||||
0.0728233 | + | 0.997345i | \(0.476799\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.08003 | −0.160725 |
(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 | 8008.2.a.s.1.4 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.s.1.4 | ✓ | 10 | 1.1 | even | 1 | trivial |