Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8281,2,Mod(1,8281)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8281, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8281.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8281 = 7^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8281.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: | \(66.1241179138\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.6995813.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 6x^{4} + 4x^{3} + 7x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.435907\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8281.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.85816 | −1.31392 | −0.656959 | − | 0.753926i | \(-0.728158\pi\) | ||||
−0.656959 | + | 0.753926i | \(0.728158\pi\) | |||||||
\(3\) | −2.29407 | −1.32448 | −0.662240 | − | 0.749291i | \(-0.730394\pi\) | ||||
−0.662240 | + | 0.749291i | \(0.730394\pi\) | |||||||
\(4\) | 1.45276 | 0.726381 | ||||||||
\(5\) | −0.197362 | −0.0882631 | −0.0441315 | − | 0.999026i | \(-0.514052\pi\) | ||||
−0.0441315 | + | 0.999026i | \(0.514052\pi\) | |||||||
\(6\) | 4.26275 | 1.74026 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.01686 | 0.359513 | ||||||||
\(9\) | 2.26275 | 0.754249 | ||||||||
\(10\) | 0.366731 | 0.115970 | ||||||||
\(11\) | 4.18274 | 1.26114 | 0.630571 | − | 0.776131i | \(-0.282821\pi\) | ||||
0.630571 | + | 0.776131i | \(0.282821\pi\) | |||||||
\(12\) | −3.33274 | −0.962078 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.452762 | 0.116903 | ||||||||
\(16\) | −4.79501 | −1.19875 | ||||||||
\(17\) | −0.841305 | −0.204047 | −0.102023 | − | 0.994782i | \(-0.532532\pi\) | ||||
−0.102023 | + | 0.994782i | \(0.532532\pi\) | |||||||
\(18\) | −4.20455 | −0.991022 | ||||||||
\(19\) | 1.35175 | 0.310113 | 0.155057 | − | 0.987906i | \(-0.450444\pi\) | ||||
0.155057 | + | 0.987906i | \(0.450444\pi\) | |||||||
\(20\) | −0.286720 | −0.0641126 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7.77220 | −1.65704 | ||||||||
\(23\) | −4.11519 | −0.858077 | −0.429038 | − | 0.903286i | \(-0.641147\pi\) | ||||
−0.429038 | + | 0.903286i | \(0.641147\pi\) | |||||||
\(24\) | −2.33274 | −0.476168 | ||||||||
\(25\) | −4.96105 | −0.992210 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.69131 | 0.325492 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.23861 | −1.52987 | −0.764936 | − | 0.644106i | \(-0.777230\pi\) | ||||
−0.764936 | + | 0.644106i | \(0.777230\pi\) | |||||||
\(30\) | −0.841305 | −0.153601 | ||||||||
\(31\) | −1.28070 | −0.230020 | −0.115010 | − | 0.993364i | \(-0.536690\pi\) | ||||
−0.115010 | + | 0.993364i | \(0.536690\pi\) | |||||||
\(32\) | 6.87618 | 1.21555 | ||||||||
\(33\) | −9.59548 | −1.67036 | ||||||||
\(34\) | 1.56328 | 0.268100 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.28723 | 0.547872 | ||||||||
\(37\) | −3.04485 | −0.500570 | −0.250285 | − | 0.968172i | \(-0.580524\pi\) | ||||
−0.250285 | + | 0.968172i | \(0.580524\pi\) | |||||||
\(38\) | −2.51177 | −0.407463 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.200689 | −0.0317317 | ||||||||
\(41\) | 5.39696 | 0.842863 | 0.421431 | − | 0.906860i | \(-0.361528\pi\) | ||||
0.421431 | + | 0.906860i | \(0.361528\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.32778 | 0.812479 | 0.406239 | − | 0.913767i | \(-0.366840\pi\) | ||||
0.406239 | + | 0.913767i | \(0.366840\pi\) | |||||||
\(44\) | 6.07652 | 0.916070 | ||||||||
\(45\) | −0.446581 | −0.0665724 | ||||||||
\(46\) | 7.64669 | 1.12744 | ||||||||
\(47\) | −11.6641 | −1.70138 | −0.850690 | − | 0.525668i | \(-0.823815\pi\) | ||||
−0.850690 | + | 0.525668i | \(0.823815\pi\) | |||||||
\(48\) | 11.0001 | 1.58772 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 9.21843 | 1.30368 | ||||||||
\(51\) | 1.93001 | 0.270256 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.64796 | 0.638447 | 0.319223 | − | 0.947679i | \(-0.396578\pi\) | ||||
0.319223 | + | 0.947679i | \(0.396578\pi\) | |||||||
\(54\) | −3.14272 | −0.427670 | ||||||||
\(55\) | −0.825514 | −0.111312 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.10101 | −0.410739 | ||||||||
\(58\) | 15.3087 | 2.01013 | ||||||||
\(59\) | 6.05811 | 0.788698 | 0.394349 | − | 0.918961i | \(-0.370970\pi\) | ||||
0.394349 | + | 0.918961i | \(0.370970\pi\) | |||||||
\(60\) | 0.657756 | 0.0849160 | ||||||||
\(61\) | 11.3657 | 1.45523 | 0.727614 | − | 0.685986i | \(-0.240629\pi\) | ||||
0.727614 | + | 0.685986i | \(0.240629\pi\) | |||||||
\(62\) | 2.37975 | 0.302228 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.18704 | −0.398380 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 17.8300 | 2.19472 | ||||||||
\(67\) | −13.3970 | −1.63671 | −0.818354 | − | 0.574715i | \(-0.805113\pi\) | ||||
−0.818354 | + | 0.574715i | \(0.805113\pi\) | |||||||
\(68\) | −1.22222 | −0.148216 | ||||||||
\(69\) | 9.44053 | 1.13651 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.97040 | 0.708556 | 0.354278 | − | 0.935140i | \(-0.384727\pi\) | ||||
0.354278 | + | 0.935140i | \(0.384727\pi\) | |||||||
\(72\) | 2.30089 | 0.271162 | ||||||||
\(73\) | 3.88547 | 0.454759 | 0.227380 | − | 0.973806i | \(-0.426984\pi\) | ||||
0.227380 | + | 0.973806i | \(0.426984\pi\) | |||||||
\(74\) | 5.65782 | 0.657708 | ||||||||
\(75\) | 11.3810 | 1.31416 | ||||||||
\(76\) | 1.96377 | 0.225260 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.7334 | −1.20760 | −0.603799 | − | 0.797136i | \(-0.706347\pi\) | ||||
−0.603799 | + | 0.797136i | \(0.706347\pi\) | |||||||
\(80\) | 0.946353 | 0.105806 | ||||||||
\(81\) | −10.6682 | −1.18536 | ||||||||
\(82\) | −10.0284 | −1.10745 | ||||||||
\(83\) | 3.07390 | 0.337404 | 0.168702 | − | 0.985667i | \(-0.446042\pi\) | ||||
0.168702 | + | 0.985667i | \(0.446042\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.166042 | 0.0180098 | ||||||||
\(86\) | −9.89987 | −1.06753 | ||||||||
\(87\) | 18.8999 | 2.02629 | ||||||||
\(88\) | 4.25324 | 0.453397 | ||||||||
\(89\) | −11.9841 | −1.27032 | −0.635159 | − | 0.772382i | \(-0.719065\pi\) | ||||
−0.635159 | + | 0.772382i | \(0.719065\pi\) | |||||||
\(90\) | 0.829819 | 0.0874706 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.97840 | −0.623291 | ||||||||
\(93\) | 2.93801 | 0.304658 | ||||||||
\(94\) | 21.6737 | 2.23547 | ||||||||
\(95\) | −0.266785 | −0.0273715 | ||||||||
\(96\) | −15.7744 | −1.60997 | ||||||||
\(97\) | 19.4727 | 1.97716 | 0.988578 | − | 0.150709i | \(-0.0481558\pi\) | ||||
0.988578 | + | 0.150709i | \(0.0481558\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.46448 | 0.951216 | ||||||||
\(100\) | −7.20722 | −0.720722 | ||||||||
\(101\) | 16.9339 | 1.68499 | 0.842495 | − | 0.538704i | \(-0.181086\pi\) | ||||
0.842495 | + | 0.538704i | \(0.181086\pi\) | |||||||
\(102\) | −3.58627 | −0.355094 | ||||||||
\(103\) | 7.23425 | 0.712811 | 0.356406 | − | 0.934331i | \(-0.384002\pi\) | ||||
0.356406 | + | 0.934331i | \(0.384002\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.63667 | −0.838867 | ||||||||
\(107\) | −9.85249 | −0.952477 | −0.476238 | − | 0.879316i | \(-0.658000\pi\) | ||||
−0.476238 | + | 0.879316i | \(0.658000\pi\) | |||||||
\(108\) | 2.45707 | 0.236431 | ||||||||
\(109\) | 13.8159 | 1.32332 | 0.661662 | − | 0.749802i | \(-0.269851\pi\) | ||||
0.661662 | + | 0.749802i | \(0.269851\pi\) | |||||||
\(110\) | 1.53394 | 0.146255 | ||||||||
\(111\) | 6.98509 | 0.662995 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.26864 | −0.401560 | −0.200780 | − | 0.979636i | \(-0.564348\pi\) | ||||
−0.200780 | + | 0.979636i | \(0.564348\pi\) | |||||||
\(114\) | 5.76218 | 0.539677 | ||||||||
\(115\) | 0.812183 | 0.0757365 | ||||||||
\(116\) | −11.9687 | −1.11127 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.2569 | −1.03629 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.460394 | 0.0420280 | ||||||||
\(121\) | 6.49529 | 0.590481 | ||||||||
\(122\) | −21.1193 | −1.91205 | ||||||||
\(123\) | −12.3810 | −1.11636 | ||||||||
\(124\) | −1.86055 | −0.167082 | ||||||||
\(125\) | 1.96593 | 0.175839 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.19024 | −0.194352 | −0.0971761 | − | 0.995267i | \(-0.530981\pi\) | ||||
−0.0971761 | + | 0.995267i | \(0.530981\pi\) | |||||||
\(128\) | −7.83033 | −0.692110 | ||||||||
\(129\) | −12.2223 | −1.07611 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.27612 | −0.198865 | −0.0994326 | − | 0.995044i | \(-0.531703\pi\) | ||||
−0.0994326 | + | 0.995044i | \(0.531703\pi\) | |||||||
\(132\) | −13.9400 | −1.21332 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 24.8938 | 2.15050 | ||||||||
\(135\) | −0.333800 | −0.0287289 | ||||||||
\(136\) | −0.855486 | −0.0733573 | ||||||||
\(137\) | −13.4480 | −1.14894 | −0.574469 | − | 0.818526i | \(-0.694791\pi\) | ||||
−0.574469 | + | 0.818526i | \(0.694791\pi\) | |||||||
\(138\) | −17.5420 | −1.49328 | ||||||||
\(139\) | −4.04540 | −0.343126 | −0.171563 | − | 0.985173i | \(-0.554882\pi\) | ||||
−0.171563 | + | 0.985173i | \(0.554882\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 26.7582 | 2.25344 | ||||||||
\(142\) | −11.0940 | −0.930984 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −10.8499 | −0.904157 | ||||||||
\(145\) | 1.62599 | 0.135031 | ||||||||
\(146\) | −7.21982 | −0.597517 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.42344 | −0.363605 | ||||||||
\(149\) | −15.3519 | −1.25768 | −0.628840 | − | 0.777535i | \(-0.716470\pi\) | ||||
−0.628840 | + | 0.777535i | \(0.716470\pi\) | |||||||
\(150\) | −21.1477 | −1.72670 | ||||||||
\(151\) | −6.12108 | −0.498127 | −0.249063 | − | 0.968487i | \(-0.580123\pi\) | ||||
−0.249063 | + | 0.968487i | \(0.580123\pi\) | |||||||
\(152\) | 1.37454 | 0.111490 | ||||||||
\(153\) | −1.90366 | −0.153902 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.252762 | 0.0203023 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.53668 | −0.362067 | −0.181033 | − | 0.983477i | \(-0.557944\pi\) | ||||
−0.181033 | + | 0.983477i | \(0.557944\pi\) | |||||||
\(158\) | 19.9443 | 1.58669 | ||||||||
\(159\) | −10.6627 | −0.845611 | ||||||||
\(160\) | −1.35710 | −0.107288 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 19.8233 | 1.55746 | ||||||||
\(163\) | −1.82254 | −0.142752 | −0.0713762 | − | 0.997449i | \(-0.522739\pi\) | ||||
−0.0713762 | + | 0.997449i | \(0.522739\pi\) | |||||||
\(164\) | 7.84049 | 0.612240 | ||||||||
\(165\) | 1.89379 | 0.147431 | ||||||||
\(166\) | −5.71180 | −0.443322 | ||||||||
\(167\) | −10.7079 | −0.828606 | −0.414303 | − | 0.910139i | \(-0.635975\pi\) | ||||
−0.414303 | + | 0.910139i | \(0.635975\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −0.308533 | −0.0236634 | ||||||||
\(171\) | 3.05867 | 0.233903 | ||||||||
\(172\) | 7.74000 | 0.590169 | ||||||||
\(173\) | 13.4927 | 1.02583 | 0.512915 | − | 0.858439i | \(-0.328566\pi\) | ||||
0.512915 | + | 0.858439i | \(0.328566\pi\) | |||||||
\(174\) | −35.1191 | −2.66237 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −20.0563 | −1.51180 | ||||||||
\(177\) | −13.8977 | −1.04462 | ||||||||
\(178\) | 22.2685 | 1.66909 | ||||||||
\(179\) | 10.4692 | 0.782502 | 0.391251 | − | 0.920284i | \(-0.372042\pi\) | ||||
0.391251 | + | 0.920284i | \(0.372042\pi\) | |||||||
\(180\) | −0.648776 | −0.0483569 | ||||||||
\(181\) | −12.5209 | −0.930674 | −0.465337 | − | 0.885133i | \(-0.654067\pi\) | ||||
−0.465337 | + | 0.885133i | \(0.654067\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −26.0737 | −1.92742 | ||||||||
\(184\) | −4.18455 | −0.308489 | ||||||||
\(185\) | 0.600938 | 0.0441819 | ||||||||
\(186\) | −5.45930 | −0.400295 | ||||||||
\(187\) | −3.51896 | −0.257332 | ||||||||
\(188\) | −16.9451 | −1.23585 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.495729 | 0.0359640 | ||||||||
\(191\) | 13.1137 | 0.948874 | 0.474437 | − | 0.880290i | \(-0.342652\pi\) | ||||
0.474437 | + | 0.880290i | \(0.342652\pi\) | |||||||
\(192\) | 7.31129 | 0.527647 | ||||||||
\(193\) | −1.04157 | −0.0749740 | −0.0374870 | − | 0.999297i | \(-0.511935\pi\) | ||||
−0.0374870 | + | 0.999297i | \(0.511935\pi\) | |||||||
\(194\) | −36.1835 | −2.59782 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.47833 | −0.105327 | −0.0526635 | − | 0.998612i | \(-0.516771\pi\) | ||||
−0.0526635 | + | 0.998612i | \(0.516771\pi\) | |||||||
\(198\) | −17.5865 | −1.24982 | ||||||||
\(199\) | −14.0999 | −0.999512 | −0.499756 | − | 0.866166i | \(-0.666577\pi\) | ||||
−0.499756 | + | 0.866166i | \(0.666577\pi\) | |||||||
\(200\) | −5.04467 | −0.356712 | ||||||||
\(201\) | 30.7337 | 2.16779 | ||||||||
\(202\) | −31.4660 | −2.21394 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.80385 | 0.196309 | ||||||||
\(205\) | −1.06516 | −0.0743937 | ||||||||
\(206\) | −13.4424 | −0.936576 | ||||||||
\(207\) | −9.31164 | −0.647204 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.65402 | 0.391097 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.4692 | 1.82222 | 0.911108 | − | 0.412167i | \(-0.135228\pi\) | ||||
0.911108 | + | 0.412167i | \(0.135228\pi\) | |||||||
\(212\) | 6.75239 | 0.463756 | ||||||||
\(213\) | −13.6965 | −0.938468 | ||||||||
\(214\) | 18.3075 | 1.25148 | ||||||||
\(215\) | −1.05150 | −0.0717119 | ||||||||
\(216\) | 1.71981 | 0.117019 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −25.6722 | −1.73874 | ||||||||
\(219\) | −8.91352 | −0.602320 | ||||||||
\(220\) | −1.19928 | −0.0808552 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −12.9794 | −0.871122 | ||||||||
\(223\) | −0.728048 | −0.0487537 | −0.0243769 | − | 0.999703i | \(-0.507760\pi\) | ||||
−0.0243769 | + | 0.999703i | \(0.507760\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.2256 | −0.748373 | ||||||||
\(226\) | 7.93182 | 0.527617 | ||||||||
\(227\) | −2.85195 | −0.189291 | −0.0946454 | − | 0.995511i | \(-0.530172\pi\) | ||||
−0.0946454 | + | 0.995511i | \(0.530172\pi\) | |||||||
\(228\) | −4.50503 | −0.298353 | ||||||||
\(229\) | 3.17352 | 0.209712 | 0.104856 | − | 0.994487i | \(-0.466562\pi\) | ||||
0.104856 | + | 0.994487i | \(0.466562\pi\) | |||||||
\(230\) | −1.50917 | −0.0995116 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.37748 | −0.550009 | ||||||||
\(233\) | 13.4071 | 0.878327 | 0.439163 | − | 0.898407i | \(-0.355275\pi\) | ||||
0.439163 | + | 0.898407i | \(0.355275\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.30205 | 0.150169 | ||||||||
\(236\) | 8.80099 | 0.572896 | ||||||||
\(237\) | 24.6231 | 1.59944 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.5538 | 1.00609 | 0.503046 | − | 0.864259i | \(-0.332212\pi\) | ||||
0.503046 | + | 0.864259i | \(0.332212\pi\) | |||||||
\(240\) | −2.17100 | −0.140137 | ||||||||
\(241\) | −7.57574 | −0.487996 | −0.243998 | − | 0.969776i | \(-0.578459\pi\) | ||||
−0.243998 | + | 0.969776i | \(0.578459\pi\) | |||||||
\(242\) | −12.0693 | −0.775844 | ||||||||
\(243\) | 19.3997 | 1.24449 | ||||||||
\(244\) | 16.5117 | 1.05705 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 23.0059 | 1.46680 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1.30229 | −0.0826953 | ||||||||
\(249\) | −7.05173 | −0.446885 | ||||||||
\(250\) | −3.65302 | −0.231038 | ||||||||
\(251\) | −1.27476 | −0.0804624 | −0.0402312 | − | 0.999190i | \(-0.512809\pi\) | ||||
−0.0402312 | + | 0.999190i | \(0.512809\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.2128 | −1.08216 | ||||||||
\(254\) | 4.06982 | 0.255363 | ||||||||
\(255\) | −0.380912 | −0.0238536 | ||||||||
\(256\) | 20.9241 | 1.30776 | ||||||||
\(257\) | 8.48019 | 0.528980 | 0.264490 | − | 0.964388i | \(-0.414796\pi\) | ||||
0.264490 | + | 0.964388i | \(0.414796\pi\) | |||||||
\(258\) | 22.7110 | 1.41392 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −18.6419 | −1.15390 | ||||||||
\(262\) | 4.22939 | 0.261293 | ||||||||
\(263\) | 12.7883 | 0.788560 | 0.394280 | − | 0.918990i | \(-0.370994\pi\) | ||||
0.394280 | + | 0.918990i | \(0.370994\pi\) | |||||||
\(264\) | −9.75722 | −0.600515 | ||||||||
\(265\) | −0.917333 | −0.0563513 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 27.4925 | 1.68251 | ||||||||
\(268\) | −19.4627 | −1.18887 | ||||||||
\(269\) | 4.71172 | 0.287278 | 0.143639 | − | 0.989630i | \(-0.454120\pi\) | ||||
0.143639 | + | 0.989630i | \(0.454120\pi\) | |||||||
\(270\) | 0.620254 | 0.0377475 | ||||||||
\(271\) | −18.0112 | −1.09410 | −0.547052 | − | 0.837098i | \(-0.684250\pi\) | ||||
−0.547052 | + | 0.837098i | \(0.684250\pi\) | |||||||
\(272\) | 4.03407 | 0.244601 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 24.9885 | 1.50961 | ||||||||
\(275\) | −20.7508 | −1.25132 | ||||||||
\(276\) | 13.7148 | 0.825537 | ||||||||
\(277\) | −26.1209 | −1.56945 | −0.784725 | − | 0.619844i | \(-0.787196\pi\) | ||||
−0.784725 | + | 0.619844i | \(0.787196\pi\) | |||||||
\(278\) | 7.51700 | 0.450840 | ||||||||
\(279\) | −2.89790 | −0.173493 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.66197 | 0.218455 | 0.109227 | − | 0.994017i | \(-0.465162\pi\) | ||||
0.109227 | + | 0.994017i | \(0.465162\pi\) | |||||||
\(282\) | −49.7210 | −2.96084 | ||||||||
\(283\) | −7.64527 | −0.454464 | −0.227232 | − | 0.973841i | \(-0.572968\pi\) | ||||
−0.227232 | + | 0.973841i | \(0.572968\pi\) | |||||||
\(284\) | 8.67357 | 0.514682 | ||||||||
\(285\) | 0.612022 | 0.0362531 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 15.5591 | 0.916827 | ||||||||
\(289\) | −16.2922 | −0.958365 | ||||||||
\(290\) | −3.02135 | −0.177420 | ||||||||
\(291\) | −44.6718 | −2.61871 | ||||||||
\(292\) | 5.64466 | 0.330329 | ||||||||
\(293\) | −17.1534 | −1.00211 | −0.501056 | − | 0.865415i | \(-0.667055\pi\) | ||||
−0.501056 | + | 0.865415i | \(0.667055\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.19564 | −0.0696130 | ||||||||
\(296\) | −3.09617 | −0.179961 | ||||||||
\(297\) | 7.07429 | 0.410492 | ||||||||
\(298\) | 28.5264 | 1.65249 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 16.5339 | 0.954583 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 11.3740 | 0.654498 | ||||||||
\(303\) | −38.8476 | −2.23174 | ||||||||
\(304\) | −6.48166 | −0.371749 | ||||||||
\(305\) | −2.24316 | −0.128443 | ||||||||
\(306\) | 3.53731 | 0.202215 | ||||||||
\(307\) | −28.0696 | −1.60201 | −0.801007 | − | 0.598655i | \(-0.795702\pi\) | ||||
−0.801007 | + | 0.598655i | \(0.795702\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.5959 | −0.944105 | ||||||||
\(310\) | −0.469672 | −0.0266756 | ||||||||
\(311\) | 23.5341 | 1.33450 | 0.667248 | − | 0.744836i | \(-0.267472\pi\) | ||||
0.667248 | + | 0.744836i | \(0.267472\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.34860 | 0.189274 | 0.0946370 | − | 0.995512i | \(-0.469831\pi\) | ||||
0.0946370 | + | 0.995512i | \(0.469831\pi\) | |||||||
\(314\) | 8.42989 | 0.475726 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15.5930 | −0.877177 | ||||||||
\(317\) | 7.27834 | 0.408793 | 0.204396 | − | 0.978888i | \(-0.434477\pi\) | ||||
0.204396 | + | 0.978888i | \(0.434477\pi\) | |||||||
\(318\) | 19.8131 | 1.11106 | ||||||||
\(319\) | −34.4600 | −1.92939 | ||||||||
\(320\) | 0.629002 | 0.0351623 | ||||||||
\(321\) | 22.6023 | 1.26154 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.13724 | −0.0632775 | ||||||||
\(324\) | −15.4984 | −0.861021 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.38658 | 0.187565 | ||||||||
\(327\) | −31.6946 | −1.75272 | ||||||||
\(328\) | 5.48792 | 0.303020 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3.51896 | −0.193712 | ||||||||
\(331\) | 14.3234 | 0.787283 | 0.393642 | − | 0.919264i | \(-0.371215\pi\) | ||||
0.393642 | + | 0.919264i | \(0.371215\pi\) | |||||||
\(332\) | 4.46564 | 0.245084 | ||||||||
\(333\) | −6.88973 | −0.377555 | ||||||||
\(334\) | 19.8971 | 1.08872 | ||||||||
\(335\) | 2.64407 | 0.144461 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.1802 | 0.935868 | 0.467934 | − | 0.883764i | \(-0.344999\pi\) | ||||
0.467934 | + | 0.883764i | \(0.344999\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.79255 | 0.531858 | ||||||||
\(340\) | 0.241220 | 0.0130820 | ||||||||
\(341\) | −5.35683 | −0.290089 | ||||||||
\(342\) | −5.68351 | −0.307329 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5.41758 | 0.292096 | ||||||||
\(345\) | −1.86320 | −0.100312 | ||||||||
\(346\) | −25.0716 | −1.34786 | ||||||||
\(347\) | −7.70278 | −0.413507 | −0.206753 | − | 0.978393i | \(-0.566290\pi\) | ||||
−0.206753 | + | 0.978393i | \(0.566290\pi\) | |||||||
\(348\) | 27.4571 | 1.47186 | ||||||||
\(349\) | 22.3701 | 1.19744 | 0.598721 | − | 0.800958i | \(-0.295676\pi\) | ||||
0.598721 | + | 0.800958i | \(0.295676\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 28.7613 | 1.53298 | ||||||||
\(353\) | −22.2623 | −1.18490 | −0.592451 | − | 0.805606i | \(-0.701840\pi\) | ||||
−0.592451 | + | 0.805606i | \(0.701840\pi\) | |||||||
\(354\) | 25.8242 | 1.37254 | ||||||||
\(355\) | −1.17833 | −0.0625393 | ||||||||
\(356\) | −17.4101 | −0.922735 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −19.4534 | −1.02814 | ||||||||
\(359\) | 2.75842 | 0.145584 | 0.0727920 | − | 0.997347i | \(-0.476809\pi\) | ||||
0.0727920 | + | 0.997347i | \(0.476809\pi\) | |||||||
\(360\) | −0.454108 | −0.0239336 | ||||||||
\(361\) | −17.1728 | −0.903830 | ||||||||
\(362\) | 23.2659 | 1.22283 | ||||||||
\(363\) | −14.9006 | −0.782081 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.766844 | −0.0401385 | ||||||||
\(366\) | 48.4491 | 2.53248 | ||||||||
\(367\) | 14.1497 | 0.738609 | 0.369304 | − | 0.929308i | \(-0.379596\pi\) | ||||
0.369304 | + | 0.929308i | \(0.379596\pi\) | |||||||
\(368\) | 19.7324 | 1.02862 | ||||||||
\(369\) | 12.2119 | 0.635729 | ||||||||
\(370\) | −1.11664 | −0.0580514 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.26823 | 0.221298 | ||||||||
\(373\) | −5.04284 | −0.261109 | −0.130554 | − | 0.991441i | \(-0.541676\pi\) | ||||
−0.130554 | + | 0.991441i | \(0.541676\pi\) | |||||||
\(374\) | 6.53879 | 0.338113 | ||||||||
\(375\) | −4.50999 | −0.232895 | ||||||||
\(376\) | −11.8607 | −0.611668 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.05964 | 0.311263 | 0.155631 | − | 0.987815i | \(-0.450259\pi\) | ||||
0.155631 | + | 0.987815i | \(0.450259\pi\) | |||||||
\(380\) | −0.387575 | −0.0198822 | ||||||||
\(381\) | 5.02456 | 0.257416 | ||||||||
\(382\) | −24.3674 | −1.24674 | ||||||||
\(383\) | −4.54105 | −0.232037 | −0.116018 | − | 0.993247i | \(-0.537013\pi\) | ||||
−0.116018 | + | 0.993247i | \(0.537013\pi\) | |||||||
\(384\) | 17.9633 | 0.916686 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.93541 | 0.0985098 | ||||||||
\(387\) | 12.0554 | 0.612811 | ||||||||
\(388\) | 28.2893 | 1.43617 | ||||||||
\(389\) | 4.50765 | 0.228547 | 0.114273 | − | 0.993449i | \(-0.463546\pi\) | ||||
0.114273 | + | 0.993449i | \(0.463546\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.46213 | 0.175088 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.22157 | 0.263393 | ||||||||
\(394\) | 2.74698 | 0.138391 | ||||||||
\(395\) | 2.11836 | 0.106586 | ||||||||
\(396\) | 13.7496 | 0.690945 | ||||||||
\(397\) | 4.00349 | 0.200929 | 0.100465 | − | 0.994941i | \(-0.467967\pi\) | ||||
0.100465 | + | 0.994941i | \(0.467967\pi\) | |||||||
\(398\) | 26.1998 | 1.31328 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 23.7883 | 1.18941 | ||||||||
\(401\) | −12.6135 | −0.629887 | −0.314944 | − | 0.949110i | \(-0.601986\pi\) | ||||
−0.314944 | + | 0.949110i | \(0.601986\pi\) | |||||||
\(402\) | −57.1081 | −2.84829 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 24.6010 | 1.22394 | ||||||||
\(405\) | 2.10550 | 0.104623 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.7358 | −0.631290 | ||||||||
\(408\) | 1.96254 | 0.0971604 | ||||||||
\(409\) | 20.6952 | 1.02331 | 0.511657 | − | 0.859190i | \(-0.329032\pi\) | ||||
0.511657 | + | 0.859190i | \(0.329032\pi\) | |||||||
\(410\) | 1.97923 | 0.0977472 | ||||||||
\(411\) | 30.8506 | 1.52175 | ||||||||
\(412\) | 10.5096 | 0.517773 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 17.3025 | 0.850373 | ||||||||
\(415\) | −0.606672 | −0.0297803 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.28042 | 0.454464 | ||||||||
\(418\) | −10.5061 | −0.513869 | ||||||||
\(419\) | 21.8175 | 1.06586 | 0.532928 | − | 0.846161i | \(-0.321092\pi\) | ||||
0.532928 | + | 0.846161i | \(0.321092\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.42727 | −0.459457 | −0.229728 | − | 0.973255i | \(-0.573784\pi\) | ||||
−0.229728 | + | 0.973255i | \(0.573784\pi\) | |||||||
\(422\) | −49.1841 | −2.39424 | ||||||||
\(423\) | −26.3928 | −1.28326 | ||||||||
\(424\) | 4.72631 | 0.229530 | ||||||||
\(425\) | 4.17376 | 0.202457 | ||||||||
\(426\) | 25.4503 | 1.23307 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −14.3133 | −0.691861 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.95386 | 0.0942235 | ||||||||
\(431\) | −20.4275 | −0.983960 | −0.491980 | − | 0.870607i | \(-0.663727\pi\) | ||||
−0.491980 | + | 0.870607i | \(0.663727\pi\) | |||||||
\(432\) | −8.10983 | −0.390184 | ||||||||
\(433\) | −26.3486 | −1.26623 | −0.633117 | − | 0.774056i | \(-0.718225\pi\) | ||||
−0.633117 | + | 0.774056i | \(0.718225\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.73014 | −0.178846 | ||||||||
\(436\) | 20.0712 | 0.961238 | ||||||||
\(437\) | −5.56272 | −0.266101 | ||||||||
\(438\) | 16.5628 | 0.791399 | ||||||||
\(439\) | −25.1310 | −1.19944 | −0.599720 | − | 0.800210i | \(-0.704721\pi\) | ||||
−0.599720 | + | 0.800210i | \(0.704721\pi\) | |||||||
\(440\) | −0.839429 | −0.0400182 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.5199 | 0.879907 | 0.439953 | − | 0.898021i | \(-0.354995\pi\) | ||||
0.439953 | + | 0.898021i | \(0.354995\pi\) | |||||||
\(444\) | 10.1477 | 0.481587 | ||||||||
\(445\) | 2.36522 | 0.112122 | ||||||||
\(446\) | 1.35283 | 0.0640584 | ||||||||
\(447\) | 35.2184 | 1.66577 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.6431 | −0.549471 | −0.274736 | − | 0.961520i | \(-0.588590\pi\) | ||||
−0.274736 | + | 0.961520i | \(0.588590\pi\) | |||||||
\(450\) | 20.8590 | 0.983301 | ||||||||
\(451\) | 22.5740 | 1.06297 | ||||||||
\(452\) | −6.20132 | −0.291685 | ||||||||
\(453\) | 14.0422 | 0.659759 | ||||||||
\(454\) | 5.29939 | 0.248713 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.15328 | −0.147666 | ||||||||
\(457\) | −20.5184 | −0.959812 | −0.479906 | − | 0.877320i | \(-0.659329\pi\) | ||||
−0.479906 | + | 0.877320i | \(0.659329\pi\) | |||||||
\(458\) | −5.89691 | −0.275544 | ||||||||
\(459\) | −1.42291 | −0.0664156 | ||||||||
\(460\) | 1.17991 | 0.0550136 | ||||||||
\(461\) | 2.04075 | 0.0950473 | 0.0475236 | − | 0.998870i | \(-0.484867\pi\) | ||||
0.0475236 | + | 0.998870i | \(0.484867\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.03155 | −0.140888 | −0.0704441 | − | 0.997516i | \(-0.522442\pi\) | ||||
−0.0704441 | + | 0.997516i | \(0.522442\pi\) | |||||||
\(464\) | 39.5042 | 1.83394 | ||||||||
\(465\) | −0.579853 | −0.0268900 | ||||||||
\(466\) | −24.9125 | −1.15405 | ||||||||
\(467\) | 12.9274 | 0.598210 | 0.299105 | − | 0.954220i | \(-0.403312\pi\) | ||||
0.299105 | + | 0.954220i | \(0.403312\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4.27757 | −0.197310 | ||||||||
\(471\) | 10.4075 | 0.479550 | ||||||||
\(472\) | 6.16022 | 0.283547 | ||||||||
\(473\) | 22.2847 | 1.02465 | ||||||||
\(474\) | −45.7537 | −2.10153 | ||||||||
\(475\) | −6.70611 | −0.307697 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.5172 | 0.481548 | ||||||||
\(478\) | −28.9015 | −1.32192 | ||||||||
\(479\) | 36.5821 | 1.67148 | 0.835740 | − | 0.549126i | \(-0.185039\pi\) | ||||
0.835740 | + | 0.549126i | \(0.185039\pi\) | |||||||
\(480\) | 3.11328 | 0.142101 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 14.0769 | 0.641187 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.43611 | 0.428914 | ||||||||
\(485\) | −3.84318 | −0.174510 | ||||||||
\(486\) | −36.0478 | −1.63516 | ||||||||
\(487\) | −36.7496 | −1.66528 | −0.832642 | − | 0.553812i | \(-0.813173\pi\) | ||||
−0.832642 | + | 0.553812i | \(0.813173\pi\) | |||||||
\(488\) | 11.5573 | 0.523173 | ||||||||
\(489\) | 4.18103 | 0.189073 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.19797 | −0.369969 | −0.184985 | − | 0.982741i | \(-0.559224\pi\) | ||||
−0.184985 | + | 0.982741i | \(0.559224\pi\) | |||||||
\(492\) | −17.9866 | −0.810900 | ||||||||
\(493\) | 6.93119 | 0.312165 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.86793 | −0.0839572 | ||||||||
\(496\) | 6.14096 | 0.275737 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 13.1033 | 0.587171 | ||||||||
\(499\) | 43.2532 | 1.93628 | 0.968141 | − | 0.250407i | \(-0.0805645\pi\) | ||||
0.968141 | + | 0.250407i | \(0.0805645\pi\) | |||||||
\(500\) | 2.85604 | 0.127726 | ||||||||
\(501\) | 24.5648 | 1.09747 | ||||||||
\(502\) | 2.36872 | 0.105721 | ||||||||
\(503\) | −0.0181922 | −0.000811149 0 | −0.000405575 | − | 1.00000i | \(-0.500129\pi\) | ||||
−0.000405575 | 1.00000i | \(0.500129\pi\) | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.34212 | −0.148722 | ||||||||
\(506\) | 31.9841 | 1.42187 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.18190 | −0.141174 | ||||||||
\(509\) | 43.1006 | 1.91040 | 0.955200 | − | 0.295960i | \(-0.0956394\pi\) | ||||
0.955200 | + | 0.295960i | \(0.0956394\pi\) | |||||||
\(510\) | 0.707795 | 0.0313417 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −23.2197 | −1.02617 | ||||||||
\(513\) | 2.28623 | 0.100939 | ||||||||
\(514\) | −15.7576 | −0.695036 | ||||||||
\(515\) | −1.42777 | −0.0629149 | ||||||||
\(516\) | −17.7561 | −0.781668 | ||||||||
\(517\) | −48.7877 | −2.14568 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −30.9531 | −1.35869 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.9540 | −0.918012 | −0.459006 | − | 0.888433i | \(-0.651794\pi\) | ||||
−0.459006 | + | 0.888433i | \(0.651794\pi\) | |||||||
\(522\) | 34.6397 | 1.51614 | ||||||||
\(523\) | 34.7403 | 1.51909 | 0.759543 | − | 0.650457i | \(-0.225423\pi\) | ||||
0.759543 | + | 0.650457i | \(0.225423\pi\) | |||||||
\(524\) | −3.30666 | −0.144452 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −23.7627 | −1.03610 | ||||||||
\(527\) | 1.07746 | 0.0469349 | ||||||||
\(528\) | 46.0104 | 2.00235 | ||||||||
\(529\) | −6.06520 | −0.263704 | ||||||||
\(530\) | 1.70455 | 0.0740410 | ||||||||
\(531\) | 13.7080 | 0.594875 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −51.0854 | −2.21068 | ||||||||
\(535\) | 1.94451 | 0.0840685 | ||||||||
\(536\) | −13.6228 | −0.588417 | ||||||||
\(537\) | −24.0170 | −1.03641 | ||||||||
\(538\) | −8.75513 | −0.377460 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.484932 | −0.0208682 | ||||||||
\(541\) | 3.29846 | 0.141812 | 0.0709059 | − | 0.997483i | \(-0.477411\pi\) | ||||
0.0709059 | + | 0.997483i | \(0.477411\pi\) | |||||||
\(542\) | 33.4678 | 1.43756 | ||||||||
\(543\) | 28.7239 | 1.23266 | ||||||||
\(544\) | −5.78497 | −0.248029 | ||||||||
\(545\) | −2.72674 | −0.116801 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.9417 | 0.938161 | 0.469080 | − | 0.883155i | \(-0.344585\pi\) | ||||
0.469080 | + | 0.883155i | \(0.344585\pi\) | |||||||
\(548\) | −19.5367 | −0.834567 | ||||||||
\(549\) | 25.7177 | 1.09761 | ||||||||
\(550\) | 38.5583 | 1.64413 | ||||||||
\(551\) | −11.1366 | −0.474434 | ||||||||
\(552\) | 9.59965 | 0.408588 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 48.5368 | 2.06213 | ||||||||
\(555\) | −1.37859 | −0.0585180 | ||||||||
\(556\) | −5.87700 | −0.249240 | ||||||||
\(557\) | 14.2866 | 0.605342 | 0.302671 | − | 0.953095i | \(-0.402122\pi\) | ||||
0.302671 | + | 0.953095i | \(0.402122\pi\) | |||||||
\(558\) | 5.38476 | 0.227955 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.07273 | 0.340831 | ||||||||
\(562\) | −6.80453 | −0.287032 | ||||||||
\(563\) | −6.78784 | −0.286073 | −0.143037 | − | 0.989717i | \(-0.545687\pi\) | ||||
−0.143037 | + | 0.989717i | \(0.545687\pi\) | |||||||
\(564\) | 38.8733 | 1.63686 | ||||||||
\(565\) | 0.842468 | 0.0354429 | ||||||||
\(566\) | 14.2061 | 0.597128 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.07103 | 0.254735 | ||||||||
\(569\) | −17.3212 | −0.726143 | −0.363072 | − | 0.931761i | \(-0.618272\pi\) | ||||
−0.363072 | + | 0.931761i | \(0.618272\pi\) | |||||||
\(570\) | −1.13724 | −0.0476336 | ||||||||
\(571\) | −13.0116 | −0.544520 | −0.272260 | − | 0.962224i | \(-0.587771\pi\) | ||||
−0.272260 | + | 0.962224i | \(0.587771\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −30.0837 | −1.25676 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.4157 | 0.851392 | ||||||||
\(576\) | −7.21147 | −0.300478 | ||||||||
\(577\) | −0.731535 | −0.0304542 | −0.0152271 | − | 0.999884i | \(-0.504847\pi\) | ||||
−0.0152271 | + | 0.999884i | \(0.504847\pi\) | |||||||
\(578\) | 30.2735 | 1.25921 | ||||||||
\(579\) | 2.38944 | 0.0993017 | ||||||||
\(580\) | 2.36218 | 0.0980842 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 83.0073 | 3.44076 | ||||||||
\(583\) | 19.4412 | 0.805173 | ||||||||
\(584\) | 3.95096 | 0.163492 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 31.8738 | 1.31669 | ||||||||
\(587\) | −8.52284 | −0.351775 | −0.175888 | − | 0.984410i | \(-0.556280\pi\) | ||||
−0.175888 | + | 0.984410i | \(0.556280\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.73119 | −0.0713323 | ||||||||
\(590\) | 2.22170 | 0.0914657 | ||||||||
\(591\) | 3.39140 | 0.139503 | ||||||||
\(592\) | 14.6001 | 0.600059 | ||||||||
\(593\) | −31.3093 | −1.28572 | −0.642860 | − | 0.765984i | \(-0.722252\pi\) | ||||
−0.642860 | + | 0.765984i | \(0.722252\pi\) | |||||||
\(594\) | −13.1452 | −0.539353 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −22.3027 | −0.913554 | ||||||||
\(597\) | 32.3460 | 1.32383 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.750232 | −0.0306537 | −0.0153268 | − | 0.999883i | \(-0.504879\pi\) | ||||
−0.0153268 | + | 0.999883i | \(0.504879\pi\) | |||||||
\(600\) | 11.5728 | 0.472458 | ||||||||
\(601\) | 9.55305 | 0.389677 | 0.194838 | − | 0.980835i | \(-0.437582\pi\) | ||||
0.194838 | + | 0.980835i | \(0.437582\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −30.3141 | −1.23449 | ||||||||
\(604\) | −8.89248 | −0.361830 | ||||||||
\(605\) | −1.28193 | −0.0521177 | ||||||||
\(606\) | 72.1851 | 2.93232 | ||||||||
\(607\) | −22.2395 | −0.902672 | −0.451336 | − | 0.892354i | \(-0.649052\pi\) | ||||
−0.451336 | + | 0.892354i | \(0.649052\pi\) | |||||||
\(608\) | 9.29489 | 0.376958 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.16815 | 0.168764 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2.76557 | −0.111791 | ||||||||
\(613\) | 8.27987 | 0.334421 | 0.167210 | − | 0.985921i | \(-0.446524\pi\) | ||||
0.167210 | + | 0.985921i | \(0.446524\pi\) | |||||||
\(614\) | 52.1578 | 2.10492 | ||||||||
\(615\) | 2.44354 | 0.0985330 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.3312 | −0.818503 | −0.409252 | − | 0.912422i | \(-0.634210\pi\) | ||||
−0.409252 | + | 0.912422i | \(0.634210\pi\) | |||||||
\(618\) | 30.8378 | 1.24048 | ||||||||
\(619\) | 5.34097 | 0.214672 | 0.107336 | − | 0.994223i | \(-0.465768\pi\) | ||||
0.107336 | + | 0.994223i | \(0.465768\pi\) | |||||||
\(620\) | 0.367203 | 0.0147472 | ||||||||
\(621\) | −6.96005 | −0.279297 | ||||||||
\(622\) | −43.7301 | −1.75342 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.4172 | 0.976690 | ||||||||
\(626\) | −6.22224 | −0.248691 | ||||||||
\(627\) | −12.9707 | −0.518000 | ||||||||
\(628\) | −6.59072 | −0.262998 | ||||||||
\(629\) | 2.56165 | 0.102140 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.46662 | −0.257432 | −0.128716 | − | 0.991681i | \(-0.541086\pi\) | ||||
−0.128716 | + | 0.991681i | \(0.541086\pi\) | |||||||
\(632\) | −10.9143 | −0.434147 | ||||||||
\(633\) | −60.7222 | −2.41349 | ||||||||
\(634\) | −13.5243 | −0.537120 | ||||||||
\(635\) | 0.432271 | 0.0171541 | ||||||||
\(636\) | −15.4904 | −0.614236 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 64.0322 | 2.53506 | ||||||||
\(639\) | 13.5095 | 0.534428 | ||||||||
\(640\) | 1.54541 | 0.0610877 | ||||||||
\(641\) | 23.3289 | 0.921434 | 0.460717 | − | 0.887547i | \(-0.347592\pi\) | ||||
0.460717 | + | 0.887547i | \(0.347592\pi\) | |||||||
\(642\) | −41.9987 | −1.65756 | ||||||||
\(643\) | −3.58878 | −0.141527 | −0.0707637 | − | 0.997493i | \(-0.522544\pi\) | ||||
−0.0707637 | + | 0.997493i | \(0.522544\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.41222 | 0.0949810 | ||||||||
\(646\) | 2.11317 | 0.0831415 | ||||||||
\(647\) | 39.6524 | 1.55890 | 0.779448 | − | 0.626467i | \(-0.215500\pi\) | ||||
0.779448 | + | 0.626467i | \(0.215500\pi\) | |||||||
\(648\) | −10.8480 | −0.426151 | ||||||||
\(649\) | 25.3395 | 0.994661 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.64772 | −0.103693 | ||||||||
\(653\) | 18.1355 | 0.709699 | 0.354849 | − | 0.934923i | \(-0.384532\pi\) | ||||
0.354849 | + | 0.934923i | \(0.384532\pi\) | |||||||
\(654\) | 58.8938 | 2.30293 | ||||||||
\(655\) | 0.449219 | 0.0175525 | ||||||||
\(656\) | −25.8784 | −1.01038 | ||||||||
\(657\) | 8.79183 | 0.343002 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.4810 | 0.525147 | 0.262573 | − | 0.964912i | \(-0.415429\pi\) | ||||
0.262573 | + | 0.964912i | \(0.415429\pi\) | |||||||
\(660\) | 2.75122 | 0.107091 | ||||||||
\(661\) | 10.3122 | 0.401099 | 0.200549 | − | 0.979684i | \(-0.435727\pi\) | ||||
0.200549 | + | 0.979684i | \(0.435727\pi\) | |||||||
\(662\) | −26.6151 | −1.03443 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.12571 | 0.121301 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 12.8022 | 0.496076 | ||||||||
\(667\) | 33.9035 | 1.31275 | ||||||||
\(668\) | −15.5561 | −0.601884 | ||||||||
\(669\) | 1.67019 | 0.0645733 | ||||||||
\(670\) | −4.91310 | −0.189810 | ||||||||
\(671\) | 47.5397 | 1.83525 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.23056 | −0.355812 | −0.177906 | − | 0.984048i | \(-0.556932\pi\) | ||||
−0.177906 | + | 0.984048i | \(0.556932\pi\) | |||||||
\(674\) | −31.9237 | −1.22965 | ||||||||
\(675\) | −8.39066 | −0.322956 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.0934 | 0.810687 | 0.405343 | − | 0.914165i | \(-0.367152\pi\) | ||||
0.405343 | + | 0.914165i | \(0.367152\pi\) | |||||||
\(678\) | −18.1961 | −0.698818 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.168841 | 0.00647474 | ||||||||
\(681\) | 6.54258 | 0.250712 | ||||||||
\(682\) | 9.95385 | 0.381153 | ||||||||
\(683\) | 38.2212 | 1.46249 | 0.731246 | − | 0.682113i | \(-0.238939\pi\) | ||||
0.731246 | + | 0.682113i | \(0.238939\pi\) | |||||||
\(684\) | 4.44353 | 0.169902 | ||||||||
\(685\) | 2.65412 | 0.101409 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.28027 | −0.277760 | ||||||||
\(688\) | −25.5467 | −0.973960 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 3.46213 | 0.131801 | ||||||||
\(691\) | −26.2322 | −0.997920 | −0.498960 | − | 0.866625i | \(-0.666285\pi\) | ||||
−0.498960 | + | 0.866625i | \(0.666285\pi\) | |||||||
\(692\) | 19.6017 | 0.745144 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.3130 | 0.543314 | ||||||||
\(695\) | 0.798409 | 0.0302854 | ||||||||
\(696\) | 19.2185 | 0.728476 | ||||||||
\(697\) | −4.54049 | −0.171983 | ||||||||
\(698\) | −41.5672 | −1.57334 | ||||||||
\(699\) | −30.7567 | −1.16333 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −46.7346 | −1.76514 | −0.882570 | − | 0.470180i | \(-0.844189\pi\) | ||||
−0.882570 | + | 0.470180i | \(0.844189\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.11588 | −0.155233 | ||||||||
\(704\) | −13.3306 | −0.502414 | ||||||||
\(705\) | −5.28105 | −0.198896 | ||||||||
\(706\) | 41.3669 | 1.55687 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −20.1901 | −0.758789 | ||||||||
\(709\) | 47.4464 | 1.78189 | 0.890944 | − | 0.454113i | \(-0.150044\pi\) | ||||
0.890944 | + | 0.454113i | \(0.150044\pi\) | |||||||
\(710\) | 2.18953 | 0.0821715 | ||||||||
\(711\) | −24.2869 | −0.910830 | ||||||||
\(712\) | −12.1861 | −0.456695 | ||||||||
\(713\) | 5.27032 | 0.197375 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 15.2092 | 0.568395 | ||||||||
\(717\) | −35.6815 | −1.33255 | ||||||||
\(718\) | −5.12560 | −0.191286 | ||||||||
\(719\) | 49.2380 | 1.83627 | 0.918133 | − | 0.396273i | \(-0.129696\pi\) | ||||
0.918133 | + | 0.396273i | \(0.129696\pi\) | |||||||
\(720\) | 2.14136 | 0.0798037 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 31.9098 | 1.18756 | ||||||||
\(723\) | 17.3793 | 0.646342 | ||||||||
\(724\) | −18.1900 | −0.676024 | ||||||||
\(725\) | 40.8722 | 1.51795 | ||||||||
\(726\) | 27.6878 | 1.02759 | ||||||||
\(727\) | 32.0495 | 1.18865 | 0.594325 | − | 0.804225i | \(-0.297419\pi\) | ||||
0.594325 | + | 0.804225i | \(0.297419\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.4996 | −0.462947 | ||||||||
\(730\) | 1.42492 | 0.0527387 | ||||||||
\(731\) | −4.48229 | −0.165783 | ||||||||
\(732\) | −37.8789 | −1.40004 | ||||||||
\(733\) | 28.2010 | 1.04163 | 0.520813 | − | 0.853670i | \(-0.325629\pi\) | ||||
0.520813 | + | 0.853670i | \(0.325629\pi\) | |||||||
\(734\) | −26.2924 | −0.970472 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −28.2968 | −1.04303 | ||||||||
\(737\) | −56.0362 | −2.06412 | ||||||||
\(738\) | −22.6918 | −0.835295 | ||||||||
\(739\) | 42.5370 | 1.56475 | 0.782375 | − | 0.622808i | \(-0.214008\pi\) | ||||
0.782375 | + | 0.622808i | \(0.214008\pi\) | |||||||
\(740\) | 0.873021 | 0.0320929 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.9142 | −0.583836 | −0.291918 | − | 0.956443i | \(-0.594294\pi\) | ||||
−0.291918 | + | 0.956443i | \(0.594294\pi\) | |||||||
\(744\) | 2.98753 | 0.109528 | ||||||||
\(745\) | 3.02989 | 0.111007 | ||||||||
\(746\) | 9.37042 | 0.343075 | ||||||||
\(747\) | 6.95546 | 0.254487 | ||||||||
\(748\) | −5.11221 | −0.186921 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 8.38028 | 0.306005 | ||||||||
\(751\) | 18.1996 | 0.664114 | 0.332057 | − | 0.943259i | \(-0.392257\pi\) | ||||
0.332057 | + | 0.943259i | \(0.392257\pi\) | |||||||
\(752\) | 55.9293 | 2.03953 | ||||||||
\(753\) | 2.92440 | 0.106571 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.20807 | 0.0439662 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −44.9004 | −1.63193 | −0.815967 | − | 0.578099i | \(-0.803795\pi\) | ||||
−0.815967 | + | 0.578099i | \(0.803795\pi\) | |||||||
\(758\) | −11.2598 | −0.408974 | ||||||||
\(759\) | 39.4872 | 1.43330 | ||||||||
\(760\) | −0.271282 | −0.00984042 | ||||||||
\(761\) | −26.4888 | −0.960217 | −0.480108 | − | 0.877209i | \(-0.659403\pi\) | ||||
−0.480108 | + | 0.877209i | \(0.659403\pi\) | |||||||
\(762\) | −9.33644 | −0.338223 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 19.0511 | 0.689244 | ||||||||
\(765\) | 0.375711 | 0.0135839 | ||||||||
\(766\) | 8.43800 | 0.304877 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −48.0013 | −1.73210 | ||||||||
\(769\) | 13.9625 | 0.503502 | 0.251751 | − | 0.967792i | \(-0.418994\pi\) | ||||
0.251751 | + | 0.967792i | \(0.418994\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.4541 | −0.700623 | ||||||||
\(772\) | −1.51316 | −0.0544597 | ||||||||
\(773\) | 12.8113 | 0.460790 | 0.230395 | − | 0.973097i | \(-0.425998\pi\) | ||||
0.230395 | + | 0.973097i | \(0.425998\pi\) | |||||||
\(774\) | −22.4009 | −0.805184 | ||||||||
\(775\) | 6.35361 | 0.228228 | ||||||||
\(776\) | 19.8010 | 0.710813 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.37594 | −0.300292 | ||||||||
\(779\) | 7.29534 | 0.261383 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.9726 | 0.893590 | ||||||||
\(782\) | −6.43320 | −0.230051 | ||||||||
\(783\) | −13.9340 | −0.497961 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.895370 | 0.0319571 | ||||||||
\(786\) | −9.70251 | −0.346077 | ||||||||
\(787\) | −27.3199 | −0.973848 | −0.486924 | − | 0.873444i | \(-0.661881\pi\) | ||||
−0.486924 | + | 0.873444i | \(0.661881\pi\) | |||||||
\(788\) | −2.14767 | −0.0765075 | ||||||||
\(789\) | −29.3372 | −1.04443 | ||||||||
\(790\) | −3.93626 | −0.140046 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 9.62401 | 0.341974 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −7.43912 | −0.264005 | ||||||||
\(795\) | 2.10442 | 0.0746362 | ||||||||
\(796\) | −20.4837 | −0.726027 | ||||||||
\(797\) | 29.4003 | 1.04141 | 0.520707 | − | 0.853736i | \(-0.325668\pi\) | ||||
0.520707 | + | 0.853736i | \(0.325668\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.81305 | 0.347161 | ||||||||
\(800\) | −34.1131 | −1.20608 | ||||||||
\(801\) | −27.1171 | −0.958136 | ||||||||
\(802\) | 23.4379 | 0.827621 | ||||||||
\(803\) | 16.2519 | 0.573517 | ||||||||
\(804\) | 44.6487 | 1.57464 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.8090 | −0.380495 | ||||||||
\(808\) | 17.2194 | 0.605775 | ||||||||
\(809\) | −6.01233 | −0.211382 | −0.105691 | − | 0.994399i | \(-0.533706\pi\) | ||||
−0.105691 | + | 0.994399i | \(0.533706\pi\) | |||||||
\(810\) | −3.91236 | −0.137466 | ||||||||
\(811\) | 8.44807 | 0.296652 | 0.148326 | − | 0.988939i | \(-0.452612\pi\) | ||||
0.148326 | + | 0.988939i | \(0.452612\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 41.3190 | 1.44912 | ||||||||
\(814\) | 23.6652 | 0.829464 | ||||||||
\(815\) | 0.359701 | 0.0125998 | ||||||||
\(816\) | −9.25442 | −0.323969 | ||||||||
\(817\) | 7.20184 | 0.251960 | ||||||||
\(818\) | −38.4551 | −1.34455 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.54742 | −0.0540382 | ||||||||
\(821\) | 34.2635 | 1.19581 | 0.597903 | − | 0.801569i | \(-0.296001\pi\) | ||||
0.597903 | + | 0.801569i | \(0.296001\pi\) | |||||||
\(822\) | −57.3253 | −1.99945 | ||||||||
\(823\) | −6.23732 | −0.217419 | −0.108710 | − | 0.994074i | \(-0.534672\pi\) | ||||
−0.108710 | + | 0.994074i | \(0.534672\pi\) | |||||||
\(824\) | 7.35618 | 0.256265 | ||||||||
\(825\) | 47.6037 | 1.65735 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19.5232 | −0.678889 | −0.339445 | − | 0.940626i | \(-0.610239\pi\) | ||||
−0.339445 | + | 0.940626i | \(0.610239\pi\) | |||||||
\(828\) | −13.5276 | −0.470117 | ||||||||
\(829\) | −32.6766 | −1.13491 | −0.567453 | − | 0.823406i | \(-0.692071\pi\) | ||||
−0.567453 | + | 0.823406i | \(0.692071\pi\) | |||||||
\(830\) | 1.12729 | 0.0391289 | ||||||||
\(831\) | 59.9230 | 2.07871 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −17.2445 | −0.597128 | ||||||||
\(835\) | 2.11334 | 0.0731353 | ||||||||
\(836\) | 8.21395 | 0.284085 | ||||||||
\(837\) | −2.16606 | −0.0748698 | ||||||||
\(838\) | −40.5405 | −1.40045 | ||||||||
\(839\) | 24.7427 | 0.854212 | 0.427106 | − | 0.904202i | \(-0.359533\pi\) | ||||
0.427106 | + | 0.904202i | \(0.359533\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 38.8748 | 1.34051 | ||||||||
\(842\) | 17.5174 | 0.603689 | ||||||||
\(843\) | −8.40080 | −0.289339 | ||||||||
\(844\) | 38.4535 | 1.32362 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 49.0422 | 1.68610 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −22.2870 | −0.765339 | ||||||||
\(849\) | 17.5388 | 0.601929 | ||||||||
\(850\) | −7.75551 | −0.266012 | ||||||||
\(851\) | 12.5301 | 0.429528 | ||||||||
\(852\) | −19.8978 | −0.681686 | ||||||||
\(853\) | 18.2245 | 0.623994 | 0.311997 | − | 0.950083i | \(-0.399002\pi\) | ||||
0.311997 | + | 0.950083i | \(0.399002\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.603667 | −0.0206450 | ||||||||
\(856\) | −10.0186 | −0.342427 | ||||||||
\(857\) | −2.54679 | −0.0869967 | −0.0434984 | − | 0.999053i | \(-0.513850\pi\) | ||||
−0.0434984 | + | 0.999053i | \(0.513850\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −54.0090 | −1.84276 | −0.921382 | − | 0.388657i | \(-0.872939\pi\) | ||||
−0.921382 | + | 0.388657i | \(0.872939\pi\) | |||||||
\(860\) | −1.52758 | −0.0520902 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 37.9577 | 1.29284 | ||||||||
\(863\) | −1.24309 | −0.0423153 | −0.0211576 | − | 0.999776i | \(-0.506735\pi\) | ||||
−0.0211576 | + | 0.999776i | \(0.506735\pi\) | |||||||
\(864\) | 11.6297 | 0.395652 | ||||||||
\(865\) | −2.66295 | −0.0905429 | ||||||||
\(866\) | 48.9600 | 1.66373 | ||||||||
\(867\) | 37.3754 | 1.26934 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −44.8949 | −1.52295 | ||||||||
\(870\) | 6.93119 | 0.234989 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 14.0488 | 0.475752 | ||||||||
\(873\) | 44.0619 | 1.49127 | ||||||||
\(874\) | 10.3364 | 0.349635 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12.9492 | −0.437514 | ||||||||
\(877\) | −0.802661 | −0.0271039 | −0.0135520 | − | 0.999908i | \(-0.504314\pi\) | ||||
−0.0135520 | + | 0.999908i | \(0.504314\pi\) | |||||||
\(878\) | 46.6975 | 1.57597 | ||||||||
\(879\) | 39.3511 | 1.32728 | ||||||||
\(880\) | 3.95835 | 0.133436 | ||||||||
\(881\) | 37.0636 | 1.24870 | 0.624352 | − | 0.781143i | \(-0.285363\pi\) | ||||
0.624352 | + | 0.781143i | \(0.285363\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.8671 | −0.769539 | −0.384770 | − | 0.923013i | \(-0.625719\pi\) | ||||
−0.384770 | + | 0.923013i | \(0.625719\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.74288 | 0.0922010 | ||||||||
\(886\) | −34.4130 | −1.15613 | ||||||||
\(887\) | 49.2573 | 1.65390 | 0.826950 | − | 0.562276i | \(-0.190074\pi\) | ||||
0.826950 | + | 0.562276i | \(0.190074\pi\) | |||||||
\(888\) | 7.10283 | 0.238355 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −4.39496 | −0.147319 | ||||||||
\(891\) | −44.6223 | −1.49490 | ||||||||
\(892\) | −1.05768 | −0.0354138 | ||||||||
\(893\) | −15.7669 | −0.527620 | ||||||||
\(894\) | −65.4414 | −2.18869 | ||||||||
\(895\) | −2.06622 | −0.0690661 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 21.6347 | 0.721961 | ||||||||
\(899\) | 10.5512 | 0.351902 | ||||||||
\(900\) | −16.3081 | −0.543604 | ||||||||
\(901\) | −3.91036 | −0.130273 | ||||||||
\(902\) | −41.9462 | −1.39666 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.34059 | −0.144366 | ||||||||
\(905\) | 2.47116 | 0.0821442 | ||||||||
\(906\) | −26.0926 | −0.866870 | ||||||||
\(907\) | −5.00455 | −0.166173 | −0.0830867 | − | 0.996542i | \(-0.526478\pi\) | ||||
−0.0830867 | + | 0.996542i | \(0.526478\pi\) | |||||||
\(908\) | −4.14321 | −0.137497 | ||||||||
\(909\) | 38.3172 | 1.27090 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 49.0582 | 1.62537 | 0.812685 | − | 0.582703i | \(-0.198005\pi\) | ||||
0.812685 | + | 0.582703i | \(0.198005\pi\) | |||||||
\(912\) | 14.8694 | 0.492374 | ||||||||
\(913\) | 12.8573 | 0.425515 | ||||||||
\(914\) | 38.1266 | 1.26111 | ||||||||
\(915\) | 5.14596 | 0.170120 | ||||||||
\(916\) | 4.61037 | 0.152331 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.64399 | 0.0872646 | ||||||||
\(919\) | 29.6056 | 0.976598 | 0.488299 | − | 0.872676i | \(-0.337618\pi\) | ||||
0.488299 | + | 0.872676i | \(0.337618\pi\) | |||||||
\(920\) | 0.825873 | 0.0272282 | ||||||||
\(921\) | 64.3935 | 2.12184 | ||||||||
\(922\) | −3.79205 | −0.124884 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.1056 | 0.496670 | ||||||||
\(926\) | 5.63311 | 0.185116 | ||||||||
\(927\) | 16.3693 | 0.537637 | ||||||||
\(928\) | −56.6502 | −1.85963 | ||||||||
\(929\) | 16.8305 | 0.552191 | 0.276095 | − | 0.961130i | \(-0.410959\pi\) | ||||
0.276095 | + | 0.961130i | \(0.410959\pi\) | |||||||
\(930\) | 1.07746 | 0.0353313 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 19.4773 | 0.638000 | ||||||||
\(933\) | −53.9888 | −1.76751 | ||||||||
\(934\) | −24.0212 | −0.785998 | ||||||||
\(935\) | 0.694510 | 0.0227129 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −44.0131 | −1.43784 | −0.718922 | − | 0.695091i | \(-0.755364\pi\) | ||||
−0.718922 | + | 0.695091i | \(0.755364\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.68191 | −0.250690 | ||||||||
\(940\) | 3.34433 | 0.109080 | ||||||||
\(941\) | 53.0675 | 1.72995 | 0.864976 | − | 0.501814i | \(-0.167334\pi\) | ||||
0.864976 | + | 0.501814i | \(0.167334\pi\) | |||||||
\(942\) | −19.3387 | −0.630090 | ||||||||
\(943\) | −22.2095 | −0.723241 | ||||||||
\(944\) | −29.0487 | −0.945453 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −41.4086 | −1.34631 | ||||||||
\(947\) | 27.8817 | 0.906034 | 0.453017 | − | 0.891502i | \(-0.350348\pi\) | ||||
0.453017 | + | 0.891502i | \(0.350348\pi\) | |||||||
\(948\) | 35.7715 | 1.16180 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 12.4610 | 0.404289 | ||||||||
\(951\) | −16.6970 | −0.541438 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −36.3568 | −1.17771 | −0.588856 | − | 0.808238i | \(-0.700421\pi\) | ||||
−0.588856 | + | 0.808238i | \(0.700421\pi\) | |||||||
\(954\) | −19.5426 | −0.632715 | ||||||||
\(955\) | −2.58815 | −0.0837505 | ||||||||
\(956\) | 22.5960 | 0.730807 | ||||||||
\(957\) | 79.0535 | 2.55544 | ||||||||
\(958\) | −67.9754 | −2.19619 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.44297 | −0.0465718 | ||||||||
\(961\) | −29.3598 | −0.947091 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −22.2937 | −0.718405 | ||||||||
\(964\) | −11.0057 | −0.354471 | ||||||||
\(965\) | 0.205567 | 0.00661744 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.2681 | 0.490988 | 0.245494 | − | 0.969398i | \(-0.421050\pi\) | ||||
0.245494 | + | 0.969398i | \(0.421050\pi\) | |||||||
\(968\) | 6.60477 | 0.212285 | ||||||||
\(969\) | 2.60890 | 0.0838099 | ||||||||
\(970\) | 7.14125 | 0.229292 | ||||||||
\(971\) | 36.8920 | 1.18392 | 0.591961 | − | 0.805967i | \(-0.298354\pi\) | ||||
0.591961 | + | 0.805967i | \(0.298354\pi\) | |||||||
\(972\) | 28.1831 | 0.903975 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 68.2867 | 2.18805 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −54.4986 | −1.74446 | ||||||||
\(977\) | 0.443914 | 0.0142021 | 0.00710104 | − | 0.999975i | \(-0.497740\pi\) | ||||
0.00710104 | + | 0.999975i | \(0.497740\pi\) | |||||||
\(978\) | −7.76904 | −0.248426 | ||||||||
\(979\) | −50.1265 | −1.60205 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 31.2619 | 0.998117 | ||||||||
\(982\) | 15.2332 | 0.486109 | ||||||||
\(983\) | 45.5603 | 1.45315 | 0.726575 | − | 0.687088i | \(-0.241111\pi\) | ||||
0.726575 | + | 0.687088i | \(0.241111\pi\) | |||||||
\(984\) | −12.5897 | −0.401344 | ||||||||
\(985\) | 0.291767 | 0.00929648 | ||||||||
\(986\) | −12.8793 | −0.410160 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21.9248 | −0.697169 | ||||||||
\(990\) | 3.47092 | 0.110313 | ||||||||
\(991\) | 53.6295 | 1.70360 | 0.851799 | − | 0.523869i | \(-0.175512\pi\) | ||||
0.851799 | + | 0.523869i | \(0.175512\pi\) | |||||||
\(992\) | −8.80632 | −0.279601 | ||||||||
\(993\) | −32.8588 | −1.04274 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.78278 | 0.0882200 | ||||||||
\(996\) | −10.2445 | −0.324609 | ||||||||
\(997\) | −29.0852 | −0.921139 | −0.460569 | − | 0.887624i | \(-0.652355\pi\) | ||||
−0.460569 | + | 0.887624i | \(0.652355\pi\) | |||||||
\(998\) | −80.3715 | −2.54412 | ||||||||
\(999\) | −5.14977 | −0.162932 |
(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 | 8281.2.a.cf.1.1 | 6 | ||
7.3 | odd | 6 | 1183.2.e.g.170.6 | 12 | |||
7.5 | odd | 6 | 1183.2.e.g.508.6 | 12 | |||
7.6 | odd | 2 | 8281.2.a.ce.1.1 | 6 | |||
13.4 | even | 6 | 637.2.f.j.393.1 | 12 | |||
13.10 | even | 6 | 637.2.f.j.295.1 | 12 | |||
13.12 | even | 2 | 8281.2.a.ca.1.6 | 6 | |||
91.4 | even | 6 | 637.2.h.l.471.6 | 12 | |||
91.10 | odd | 6 | 91.2.g.b.9.1 | ✓ | 12 | ||
91.12 | odd | 6 | 1183.2.e.h.508.1 | 12 | |||
91.17 | odd | 6 | 91.2.h.b.16.6 | yes | 12 | ||
91.23 | even | 6 | 637.2.h.l.165.6 | 12 | |||
91.30 | even | 6 | 637.2.g.l.263.1 | 12 | |||
91.38 | odd | 6 | 1183.2.e.h.170.1 | 12 | |||
91.62 | odd | 6 | 637.2.f.k.295.1 | 12 | |||
91.69 | odd | 6 | 637.2.f.k.393.1 | 12 | |||
91.75 | odd | 6 | 91.2.h.b.74.6 | yes | 12 | ||
91.82 | odd | 6 | 91.2.g.b.81.1 | yes | 12 | ||
91.88 | even | 6 | 637.2.g.l.373.1 | 12 | |||
91.90 | odd | 2 | 8281.2.a.bz.1.6 | 6 | |||
273.17 | even | 6 | 819.2.s.d.289.1 | 12 | |||
273.101 | even | 6 | 819.2.n.d.100.6 | 12 | |||
273.173 | even | 6 | 819.2.n.d.172.6 | 12 | |||
273.257 | even | 6 | 819.2.s.d.802.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.g.b.9.1 | ✓ | 12 | 91.10 | odd | 6 | ||
91.2.g.b.81.1 | yes | 12 | 91.82 | odd | 6 | ||
91.2.h.b.16.6 | yes | 12 | 91.17 | odd | 6 | ||
91.2.h.b.74.6 | yes | 12 | 91.75 | odd | 6 | ||
637.2.f.j.295.1 | 12 | 13.10 | even | 6 | |||
637.2.f.j.393.1 | 12 | 13.4 | even | 6 | |||
637.2.f.k.295.1 | 12 | 91.62 | odd | 6 | |||
637.2.f.k.393.1 | 12 | 91.69 | odd | 6 | |||
637.2.g.l.263.1 | 12 | 91.30 | even | 6 | |||
637.2.g.l.373.1 | 12 | 91.88 | even | 6 | |||
637.2.h.l.165.6 | 12 | 91.23 | even | 6 | |||
637.2.h.l.471.6 | 12 | 91.4 | even | 6 | |||
819.2.n.d.100.6 | 12 | 273.101 | even | 6 | |||
819.2.n.d.172.6 | 12 | 273.173 | even | 6 | |||
819.2.s.d.289.1 | 12 | 273.17 | even | 6 | |||
819.2.s.d.802.1 | 12 | 273.257 | even | 6 | |||
1183.2.e.g.170.6 | 12 | 7.3 | odd | 6 | |||
1183.2.e.g.508.6 | 12 | 7.5 | odd | 6 | |||
1183.2.e.h.170.1 | 12 | 91.38 | odd | 6 | |||
1183.2.e.h.508.1 | 12 | 91.12 | odd | 6 | |||
8281.2.a.bz.1.6 | 6 | 91.90 | odd | 2 | |||
8281.2.a.ca.1.6 | 6 | 13.12 | even | 2 | |||
8281.2.a.ce.1.1 | 6 | 7.6 | odd | 2 | |||
8281.2.a.cf.1.1 | 6 | 1.1 | even | 1 | trivial |