Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 18 x^{14} + 83 x^{13} + 112 x^{12} - 668 x^{11} - 235 x^{10} + 2648 x^{9} - 298 x^{8} - 5422 x^{7} + 2075 x^{6} + 5385 x^{5} - 3163 x^{4} - 1882 x^{3} + \cdots - 20 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Root | \(-2.57436\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.57436 | 1.82035 | 0.910173 | − | 0.414228i | \(-0.135948\pi\) | ||||
0.910173 | + | 0.414228i | \(0.135948\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.62732 | 2.31366 | ||||||||
\(5\) | −2.78465 | −1.24533 | −0.622667 | − | 0.782487i | \(-0.713951\pi\) | ||||
−0.622667 | + | 0.782487i | \(0.713951\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 6.76367 | 2.39132 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −7.16870 | −2.26694 | ||||||||
\(11\) | −1.44556 | −0.435854 | −0.217927 | − | 0.975965i | \(-0.569929\pi\) | ||||
−0.217927 | + | 0.975965i | \(0.569929\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.74033 | 1.31473 | 0.657365 | − | 0.753572i | \(-0.271671\pi\) | ||||
0.657365 | + | 0.753572i | \(0.271671\pi\) | |||||||
\(14\) | −2.57436 | −0.688026 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 8.15746 | 2.03937 | ||||||||
\(17\) | −4.74437 | −1.15068 | −0.575340 | − | 0.817914i | \(-0.695130\pi\) | ||||
−0.575340 | + | 0.817914i | \(0.695130\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.68628 | 1.30452 | 0.652261 | − | 0.757994i | \(-0.273820\pi\) | ||||
0.652261 | + | 0.757994i | \(0.273820\pi\) | |||||||
\(20\) | −12.8855 | −2.88128 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.72140 | −0.793405 | ||||||||
\(23\) | −0.885825 | −0.184707 | −0.0923537 | − | 0.995726i | \(-0.529439\pi\) | ||||
−0.0923537 | + | 0.995726i | \(0.529439\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.75429 | 0.550858 | ||||||||
\(26\) | 12.2033 | 2.39326 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.62732 | −0.874482 | ||||||||
\(29\) | 1.81353 | 0.336764 | 0.168382 | − | 0.985722i | \(-0.446146\pi\) | ||||
0.168382 | + | 0.985722i | \(0.446146\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.74962 | 0.853057 | 0.426528 | − | 0.904474i | \(-0.359736\pi\) | ||||
0.426528 | + | 0.904474i | \(0.359736\pi\) | |||||||
\(32\) | 7.47290 | 1.32103 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −12.2137 | −2.09464 | ||||||||
\(35\) | 2.78465 | 0.470692 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.22583 | 0.859122 | 0.429561 | − | 0.903038i | \(-0.358668\pi\) | ||||
0.429561 | + | 0.903038i | \(0.358668\pi\) | |||||||
\(38\) | 14.6385 | 2.37468 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −18.8345 | −2.97799 | ||||||||
\(41\) | 5.00751 | 0.782042 | 0.391021 | − | 0.920382i | \(-0.372122\pi\) | ||||
0.391021 | + | 0.920382i | \(0.372122\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.34876 | −0.968177 | −0.484088 | − | 0.875019i | \(-0.660849\pi\) | ||||
−0.484088 | + | 0.875019i | \(0.660849\pi\) | |||||||
\(44\) | −6.68909 | −1.00842 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.28043 | −0.336231 | ||||||||
\(47\) | 13.1360 | 1.91609 | 0.958043 | − | 0.286624i | \(-0.0925331\pi\) | ||||
0.958043 | + | 0.286624i | \(0.0925331\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 7.09054 | 1.00275 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 21.9350 | 3.04184 | ||||||||
\(53\) | −8.73749 | −1.20019 | −0.600093 | − | 0.799930i | \(-0.704870\pi\) | ||||
−0.600093 | + | 0.799930i | \(0.704870\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.02539 | 0.542784 | ||||||||
\(56\) | −6.76367 | −0.903833 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.66867 | 0.613027 | ||||||||
\(59\) | 7.36544 | 0.958898 | 0.479449 | − | 0.877570i | \(-0.340836\pi\) | ||||
0.479449 | + | 0.877570i | \(0.340836\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00342 | 0.256511 | 0.128256 | − | 0.991741i | \(-0.459062\pi\) | ||||
0.128256 | + | 0.991741i | \(0.459062\pi\) | |||||||
\(62\) | 12.2272 | 1.55286 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.92299 | 0.365374 | ||||||||
\(65\) | −13.2002 | −1.63728 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.76572 | −0.582226 | −0.291113 | − | 0.956689i | \(-0.594025\pi\) | ||||
−0.291113 | + | 0.956689i | \(0.594025\pi\) | |||||||
\(68\) | −21.9537 | −2.66228 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.16870 | 0.856823 | ||||||||
\(71\) | 13.1659 | 1.56250 | 0.781251 | − | 0.624217i | \(-0.214582\pi\) | ||||
0.781251 | + | 0.624217i | \(0.214582\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.7431 | 1.49147 | 0.745736 | − | 0.666242i | \(-0.232098\pi\) | ||||
0.745736 | + | 0.666242i | \(0.232098\pi\) | |||||||
\(74\) | 13.4532 | 1.56390 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 26.3123 | 3.01822 | ||||||||
\(77\) | 1.44556 | 0.164737 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.77816 | 0.425076 | 0.212538 | − | 0.977153i | \(-0.431827\pi\) | ||||
0.212538 | + | 0.977153i | \(0.431827\pi\) | |||||||
\(80\) | −22.7157 | −2.53969 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 12.8911 | 1.42359 | ||||||||
\(83\) | −13.2837 | −1.45807 | −0.729036 | − | 0.684475i | \(-0.760031\pi\) | ||||
−0.729036 | + | 0.684475i | \(0.760031\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.2114 | 1.43298 | ||||||||
\(86\) | −16.3440 | −1.76242 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −9.77731 | −1.04226 | ||||||||
\(89\) | 2.64036 | 0.279877 | 0.139939 | − | 0.990160i | \(-0.455309\pi\) | ||||
0.139939 | + | 0.990160i | \(0.455309\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.74033 | −0.496921 | ||||||||
\(92\) | −4.09900 | −0.427350 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 33.8168 | 3.48794 | ||||||||
\(95\) | −15.8343 | −1.62457 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.9175 | 1.51464 | 0.757322 | − | 0.653041i | \(-0.226507\pi\) | ||||
0.757322 | + | 0.653041i | \(0.226507\pi\) | |||||||
\(98\) | 2.57436 | 0.260049 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 12.7450 | 1.27450 | ||||||||
\(101\) | 4.76405 | 0.474041 | 0.237020 | − | 0.971505i | \(-0.423829\pi\) | ||||
0.237020 | + | 0.971505i | \(0.423829\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.52975 | 0.347797 | 0.173898 | − | 0.984764i | \(-0.444364\pi\) | ||||
0.173898 | + | 0.984764i | \(0.444364\pi\) | |||||||
\(104\) | 32.0620 | 3.14394 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −22.4934 | −2.18476 | ||||||||
\(107\) | 4.73776 | 0.458017 | 0.229008 | − | 0.973424i | \(-0.426452\pi\) | ||||
0.229008 | + | 0.973424i | \(0.426452\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.8152 | −1.70638 | −0.853191 | − | 0.521598i | \(-0.825336\pi\) | ||||
−0.853191 | + | 0.521598i | \(0.825336\pi\) | |||||||
\(110\) | 10.3628 | 0.988054 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −8.15746 | −0.770808 | ||||||||
\(113\) | 16.8253 | 1.58279 | 0.791394 | − | 0.611307i | \(-0.209356\pi\) | ||||
0.791394 | + | 0.611307i | \(0.209356\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.46672 | 0.230022 | ||||||||
\(116\) | 8.39178 | 0.779157 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 18.9613 | 1.74553 | ||||||||
\(119\) | 4.74437 | 0.434916 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.91035 | −0.810032 | ||||||||
\(122\) | 5.15752 | 0.466940 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 21.9780 | 1.97368 | ||||||||
\(125\) | 6.25352 | 0.559332 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | −7.42097 | −0.655927 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −33.9820 | −2.98042 | ||||||||
\(131\) | 3.37663 | 0.295017 | 0.147509 | − | 0.989061i | \(-0.452875\pi\) | ||||
0.147509 | + | 0.989061i | \(0.452875\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.68628 | −0.493063 | ||||||||
\(134\) | −12.2687 | −1.05985 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −32.0894 | −2.75164 | ||||||||
\(137\) | 22.4118 | 1.91477 | 0.957386 | − | 0.288811i | \(-0.0932598\pi\) | ||||
0.957386 | + | 0.288811i | \(0.0932598\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.35723 | 0.708851 | 0.354426 | − | 0.935084i | \(-0.384676\pi\) | ||||
0.354426 | + | 0.935084i | \(0.384676\pi\) | |||||||
\(140\) | 12.8855 | 1.08902 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 33.8937 | 2.84430 | ||||||||
\(143\) | −6.85244 | −0.573030 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.05005 | −0.419384 | ||||||||
\(146\) | 32.8054 | 2.71499 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 24.1816 | 1.98772 | ||||||||
\(149\) | −15.1765 | −1.24331 | −0.621654 | − | 0.783292i | \(-0.713539\pi\) | ||||
−0.621654 | + | 0.783292i | \(0.713539\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.08540 | −0.576602 | −0.288301 | − | 0.957540i | \(-0.593090\pi\) | ||||
−0.288301 | + | 0.957540i | \(0.593090\pi\) | |||||||
\(152\) | 38.4601 | 3.11953 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.72140 | 0.299879 | ||||||||
\(155\) | −13.2260 | −1.06234 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.8656 | −0.946975 | −0.473488 | − | 0.880800i | \(-0.657005\pi\) | ||||
−0.473488 | + | 0.880800i | \(0.657005\pi\) | |||||||
\(158\) | 9.72633 | 0.773785 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −20.8094 | −1.64513 | ||||||||
\(161\) | 0.885825 | 0.0698128 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.21744 | 0.173683 | 0.0868416 | − | 0.996222i | \(-0.472323\pi\) | ||||
0.0868416 | + | 0.996222i | \(0.472323\pi\) | |||||||
\(164\) | 23.1714 | 1.80938 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −34.1969 | −2.65420 | ||||||||
\(167\) | −5.09063 | −0.393925 | −0.196962 | − | 0.980411i | \(-0.563108\pi\) | ||||
−0.196962 | + | 0.980411i | \(0.563108\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.47071 | 0.728516 | ||||||||
\(170\) | 34.0110 | 2.60852 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −29.3777 | −2.24003 | ||||||||
\(173\) | −4.99185 | −0.379524 | −0.189762 | − | 0.981830i | \(-0.560772\pi\) | ||||
−0.189762 | + | 0.981830i | \(0.560772\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.75429 | −0.208205 | ||||||||
\(176\) | −11.7921 | −0.888865 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.79722 | 0.509473 | ||||||||
\(179\) | 16.1437 | 1.20663 | 0.603317 | − | 0.797502i | \(-0.293846\pi\) | ||||
0.603317 | + | 0.797502i | \(0.293846\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.5581 | 1.45374 | 0.726870 | − | 0.686775i | \(-0.240974\pi\) | ||||
0.726870 | + | 0.686775i | \(0.240974\pi\) | |||||||
\(182\) | −12.2033 | −0.904569 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.99143 | −0.441694 | ||||||||
\(185\) | −14.5521 | −1.06989 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.85829 | 0.501528 | ||||||||
\(188\) | 60.7846 | 4.43317 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −40.7632 | −2.95728 | ||||||||
\(191\) | −1.86303 | −0.134804 | −0.0674019 | − | 0.997726i | \(-0.521471\pi\) | ||||
−0.0674019 | + | 0.997726i | \(0.521471\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.9749 | 0.861974 | 0.430987 | − | 0.902358i | \(-0.358165\pi\) | ||||
0.430987 | + | 0.902358i | \(0.358165\pi\) | |||||||
\(194\) | 38.4031 | 2.75718 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.62732 | 0.330523 | ||||||||
\(197\) | 1.66527 | 0.118646 | 0.0593228 | − | 0.998239i | \(-0.481106\pi\) | ||||
0.0593228 | + | 0.998239i | \(0.481106\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.1338 | −0.931029 | −0.465514 | − | 0.885040i | \(-0.654131\pi\) | ||||
−0.465514 | + | 0.885040i | \(0.654131\pi\) | |||||||
\(200\) | 18.6291 | 1.31728 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.2644 | 0.862918 | ||||||||
\(203\) | −1.81353 | −0.127285 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.9442 | −0.973903 | ||||||||
\(206\) | 9.08685 | 0.633111 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 38.6690 | 2.68122 | ||||||||
\(209\) | −8.21988 | −0.568581 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.92135 | 0.269957 | 0.134978 | − | 0.990849i | \(-0.456903\pi\) | ||||
0.134978 | + | 0.990849i | \(0.456903\pi\) | |||||||
\(212\) | −40.4312 | −2.77683 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 12.1967 | 0.833749 | ||||||||
\(215\) | 17.6791 | 1.20570 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.74962 | −0.322425 | ||||||||
\(218\) | −45.8626 | −3.10621 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 18.6268 | 1.25582 | ||||||||
\(221\) | −22.4899 | −1.51283 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.53320 | 0.303565 | 0.151783 | − | 0.988414i | \(-0.451499\pi\) | ||||
0.151783 | + | 0.988414i | \(0.451499\pi\) | |||||||
\(224\) | −7.47290 | −0.499304 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 43.3142 | 2.88122 | ||||||||
\(227\) | −18.1116 | −1.20211 | −0.601055 | − | 0.799208i | \(-0.705253\pi\) | ||||
−0.601055 | + | 0.799208i | \(0.705253\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.5931 | 1.09650 | 0.548250 | − | 0.836314i | \(-0.315294\pi\) | ||||
0.548250 | + | 0.836314i | \(0.315294\pi\) | |||||||
\(230\) | 6.35021 | 0.418721 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12.2661 | 0.805309 | ||||||||
\(233\) | 14.4081 | 0.943906 | 0.471953 | − | 0.881624i | \(-0.343549\pi\) | ||||
0.471953 | + | 0.881624i | \(0.343549\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −36.5793 | −2.38617 | ||||||||
\(236\) | 34.0823 | 2.21857 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 12.2137 | 0.791698 | ||||||||
\(239\) | −18.7529 | −1.21302 | −0.606511 | − | 0.795075i | \(-0.707431\pi\) | ||||
−0.606511 | + | 0.795075i | \(0.707431\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.1134 | −1.23120 | −0.615601 | − | 0.788058i | \(-0.711087\pi\) | ||||
−0.615601 | + | 0.788058i | \(0.711087\pi\) | |||||||
\(242\) | −22.9384 | −1.47454 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.27046 | 0.593480 | ||||||||
\(245\) | −2.78465 | −0.177905 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.9548 | 1.71510 | ||||||||
\(248\) | 32.1248 | 2.03993 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 16.0988 | 1.01818 | ||||||||
\(251\) | 11.8661 | 0.748981 | 0.374491 | − | 0.927231i | \(-0.377818\pi\) | ||||
0.374491 | + | 0.927231i | \(0.377818\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.28052 | 0.0805054 | ||||||||
\(254\) | −2.57436 | −0.161530 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −24.9502 | −1.55939 | ||||||||
\(257\) | −31.6311 | −1.97310 | −0.986548 | − | 0.163470i | \(-0.947731\pi\) | ||||
−0.986548 | + | 0.163470i | \(0.947731\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.22583 | −0.324718 | ||||||||
\(260\) | −61.0814 | −3.78811 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.69265 | 0.537034 | ||||||||
\(263\) | 6.20289 | 0.382487 | 0.191243 | − | 0.981543i | \(-0.438748\pi\) | ||||
0.191243 | + | 0.981543i | \(0.438748\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 24.3309 | 1.49463 | ||||||||
\(266\) | −14.6385 | −0.897546 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −22.0525 | −1.34707 | ||||||||
\(269\) | 16.2838 | 0.992841 | 0.496421 | − | 0.868082i | \(-0.334647\pi\) | ||||
0.496421 | + | 0.868082i | \(0.334647\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.3251 | −0.991679 | −0.495840 | − | 0.868414i | \(-0.665140\pi\) | ||||
−0.495840 | + | 0.868414i | \(0.665140\pi\) | |||||||
\(272\) | −38.7021 | −2.34666 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 57.6961 | 3.48555 | ||||||||
\(275\) | −3.98150 | −0.240094 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.19322 | −0.492283 | −0.246141 | − | 0.969234i | \(-0.579163\pi\) | ||||
−0.246141 | + | 0.969234i | \(0.579163\pi\) | |||||||
\(278\) | 21.5145 | 1.29035 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 18.8345 | 1.12557 | ||||||||
\(281\) | −14.9657 | −0.892777 | −0.446389 | − | 0.894839i | \(-0.647290\pi\) | ||||
−0.446389 | + | 0.894839i | \(0.647290\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.946807 | −0.0562818 | −0.0281409 | − | 0.999604i | \(-0.508959\pi\) | ||||
−0.0281409 | + | 0.999604i | \(0.508959\pi\) | |||||||
\(284\) | 60.9228 | 3.61510 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −17.6406 | −1.04311 | ||||||||
\(287\) | −5.00751 | −0.295584 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.50909 | 0.324064 | ||||||||
\(290\) | −13.0006 | −0.763423 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 58.9666 | 3.45076 | ||||||||
\(293\) | −23.1429 | −1.35202 | −0.676012 | − | 0.736891i | \(-0.736293\pi\) | ||||
−0.676012 | + | 0.736891i | \(0.736293\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.5102 | −1.19415 | ||||||||
\(296\) | 35.3458 | 2.05443 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −39.0698 | −2.26325 | ||||||||
\(299\) | −4.19910 | −0.242840 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.34876 | 0.365936 | ||||||||
\(302\) | −18.2404 | −1.04961 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 46.3856 | 2.66040 | ||||||||
\(305\) | −5.57882 | −0.319443 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.7783 | −0.957588 | −0.478794 | − | 0.877927i | \(-0.658926\pi\) | ||||
−0.478794 | + | 0.877927i | \(0.658926\pi\) | |||||||
\(308\) | 6.68909 | 0.381146 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −34.0486 | −1.93383 | ||||||||
\(311\) | −10.2652 | −0.582088 | −0.291044 | − | 0.956710i | \(-0.594003\pi\) | ||||
−0.291044 | + | 0.956710i | \(0.594003\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.3636 | 1.49016 | 0.745079 | − | 0.666976i | \(-0.232412\pi\) | ||||
0.745079 | + | 0.666976i | \(0.232412\pi\) | |||||||
\(314\) | −30.5462 | −1.72382 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 17.4827 | 0.983481 | ||||||||
\(317\) | 6.89867 | 0.387468 | 0.193734 | − | 0.981054i | \(-0.437940\pi\) | ||||
0.193734 | + | 0.981054i | \(0.437940\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.62157 | −0.146780 | ||||||||
\(320\) | −8.13952 | −0.455013 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.28043 | 0.127083 | ||||||||
\(323\) | −26.9779 | −1.50109 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.0562 | 0.724230 | ||||||||
\(326\) | 5.70848 | 0.316164 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 33.8691 | 1.87011 | ||||||||
\(329\) | −13.1360 | −0.724213 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.07030 | −0.388619 | −0.194309 | − | 0.980940i | \(-0.562247\pi\) | ||||
−0.194309 | + | 0.980940i | \(0.562247\pi\) | |||||||
\(332\) | −61.4678 | −3.37348 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −13.1051 | −0.717080 | ||||||||
\(335\) | 13.2709 | 0.725066 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.3787 | −0.674312 | −0.337156 | − | 0.941449i | \(-0.609465\pi\) | ||||
−0.337156 | + | 0.941449i | \(0.609465\pi\) | |||||||
\(338\) | 24.3810 | 1.32615 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 61.1336 | 3.31543 | ||||||||
\(341\) | −6.86587 | −0.371808 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −42.9409 | −2.31522 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.8508 | −0.690864 | ||||||||
\(347\) | 15.0504 | 0.807948 | 0.403974 | − | 0.914770i | \(-0.367629\pi\) | ||||
0.403974 | + | 0.914770i | \(0.367629\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.7118 | 1.26926 | 0.634631 | − | 0.772816i | \(-0.281152\pi\) | ||||
0.634631 | + | 0.772816i | \(0.281152\pi\) | |||||||
\(350\) | −7.09054 | −0.379005 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −10.8025 | −0.575778 | ||||||||
\(353\) | −22.5750 | −1.20154 | −0.600772 | − | 0.799420i | \(-0.705140\pi\) | ||||
−0.600772 | + | 0.799420i | \(0.705140\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −36.6624 | −1.94584 | ||||||||
\(356\) | 12.2178 | 0.647541 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 41.5595 | 2.19649 | ||||||||
\(359\) | 30.2864 | 1.59846 | 0.799228 | − | 0.601029i | \(-0.205242\pi\) | ||||
0.799228 | + | 0.601029i | \(0.205242\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.3338 | 0.701780 | ||||||||
\(362\) | 50.3495 | 2.64631 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −21.9350 | −1.14971 | ||||||||
\(365\) | −35.4852 | −1.85738 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.31654 | 0.120922 | 0.0604612 | − | 0.998171i | \(-0.480743\pi\) | ||||
0.0604612 | + | 0.998171i | \(0.480743\pi\) | |||||||
\(368\) | −7.22609 | −0.376686 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −37.4624 | −1.94758 | ||||||||
\(371\) | 8.73749 | 0.453628 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.2206 | 1.35765 | 0.678826 | − | 0.734299i | \(-0.262489\pi\) | ||||
0.678826 | + | 0.734299i | \(0.262489\pi\) | |||||||
\(374\) | 17.6557 | 0.912955 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 88.8477 | 4.58197 | ||||||||
\(377\) | 8.59672 | 0.442754 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.95185 | −0.459825 | −0.229913 | − | 0.973211i | \(-0.573844\pi\) | ||||
−0.229913 | + | 0.973211i | \(0.573844\pi\) | |||||||
\(380\) | −73.2705 | −3.75870 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.79610 | −0.245390 | ||||||||
\(383\) | −20.6076 | −1.05300 | −0.526500 | − | 0.850175i | \(-0.676496\pi\) | ||||
−0.526500 | + | 0.850175i | \(0.676496\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.02539 | −0.205153 | ||||||||
\(386\) | 30.8278 | 1.56909 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 69.0282 | 3.50437 | ||||||||
\(389\) | 11.0810 | 0.561828 | 0.280914 | − | 0.959733i | \(-0.409362\pi\) | ||||
0.280914 | + | 0.959733i | \(0.409362\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.20269 | 0.212539 | ||||||||
\(392\) | 6.76367 | 0.341617 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.28701 | 0.215976 | ||||||||
\(395\) | −10.5209 | −0.529362 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.2409 | −1.26680 | −0.633402 | − | 0.773823i | \(-0.718342\pi\) | ||||
−0.633402 | + | 0.773823i | \(0.718342\pi\) | |||||||
\(398\) | −33.8111 | −1.69480 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 22.4680 | 1.12340 | ||||||||
\(401\) | 6.42176 | 0.320687 | 0.160344 | − | 0.987061i | \(-0.448740\pi\) | ||||
0.160344 | + | 0.987061i | \(0.448740\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.5147 | 1.12154 | ||||||||
\(404\) | 22.0448 | 1.09677 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.66867 | −0.231702 | ||||||||
\(407\) | −7.55427 | −0.374451 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.8312 | 1.07948 | 0.539742 | − | 0.841830i | \(-0.318522\pi\) | ||||
0.539742 | + | 0.841830i | \(0.318522\pi\) | |||||||
\(410\) | −35.8973 | −1.77284 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 16.3333 | 0.804684 | ||||||||
\(413\) | −7.36544 | −0.362430 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 36.9904 | 1.81579 | ||||||||
\(416\) | 35.4240 | 1.73680 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −21.1609 | −1.03501 | ||||||||
\(419\) | −21.5047 | −1.05057 | −0.525286 | − | 0.850926i | \(-0.676042\pi\) | ||||
−0.525286 | + | 0.850926i | \(0.676042\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.18572 | 0.204000 | 0.102000 | − | 0.994784i | \(-0.467476\pi\) | ||||
0.102000 | + | 0.994784i | \(0.467476\pi\) | |||||||
\(422\) | 10.0950 | 0.491415 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −59.0975 | −2.87003 | ||||||||
\(425\) | −13.0674 | −0.633862 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.00342 | −0.0969522 | ||||||||
\(428\) | 21.9231 | 1.05970 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 45.5123 | 2.19480 | ||||||||
\(431\) | 14.6079 | 0.703638 | 0.351819 | − | 0.936068i | \(-0.385563\pi\) | ||||
0.351819 | + | 0.936068i | \(0.385563\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −31.6255 | −1.51983 | −0.759913 | − | 0.650025i | \(-0.774759\pi\) | ||||
−0.759913 | + | 0.650025i | \(0.774759\pi\) | |||||||
\(434\) | −12.2272 | −0.586925 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −82.4364 | −3.94799 | ||||||||
\(437\) | −5.03705 | −0.240955 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.74432 | 0.321889 | 0.160944 | − | 0.986963i | \(-0.448546\pi\) | ||||
0.160944 | + | 0.986963i | \(0.448546\pi\) | |||||||
\(440\) | 27.2264 | 1.29797 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −57.8970 | −2.75388 | ||||||||
\(443\) | 18.9280 | 0.899294 | 0.449647 | − | 0.893206i | \(-0.351550\pi\) | ||||
0.449647 | + | 0.893206i | \(0.351550\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.35248 | −0.348541 | ||||||||
\(446\) | 11.6701 | 0.552594 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.92299 | −0.138098 | ||||||||
\(449\) | −10.7611 | −0.507846 | −0.253923 | − | 0.967224i | \(-0.581721\pi\) | ||||
−0.253923 | + | 0.967224i | \(0.581721\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.23867 | −0.340856 | ||||||||
\(452\) | 77.8559 | 3.66203 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −46.6258 | −2.18825 | ||||||||
\(455\) | 13.2002 | 0.618833 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.44982 | −0.301710 | −0.150855 | − | 0.988556i | \(-0.548203\pi\) | ||||
−0.150855 | + | 0.988556i | \(0.548203\pi\) | |||||||
\(458\) | 42.7165 | 1.99601 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 11.4143 | 0.532194 | ||||||||
\(461\) | −5.25564 | −0.244779 | −0.122390 | − | 0.992482i | \(-0.539056\pi\) | ||||
−0.122390 | + | 0.992482i | \(0.539056\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.1048 | −1.07377 | −0.536886 | − | 0.843655i | \(-0.680399\pi\) | ||||
−0.536886 | + | 0.843655i | \(0.680399\pi\) | |||||||
\(464\) | 14.7938 | 0.686785 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 37.0916 | 1.71824 | ||||||||
\(467\) | −8.23695 | −0.381160 | −0.190580 | − | 0.981672i | \(-0.561037\pi\) | ||||
−0.190580 | + | 0.981672i | \(0.561037\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.76572 | 0.220061 | ||||||||
\(470\) | −94.1682 | −4.34365 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 49.8174 | 2.29303 | ||||||||
\(473\) | 9.17753 | 0.421983 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.6617 | 0.718607 | ||||||||
\(476\) | 21.9537 | 1.00625 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −48.2766 | −2.20812 | ||||||||
\(479\) | −32.9121 | −1.50379 | −0.751897 | − | 0.659281i | \(-0.770861\pi\) | ||||
−0.751897 | + | 0.659281i | \(0.770861\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.7722 | 1.12951 | ||||||||
\(482\) | −49.2048 | −2.24122 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −41.2310 | −1.87414 | ||||||||
\(485\) | −41.5401 | −1.88624 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.480422 | 0.0217700 | 0.0108850 | − | 0.999941i | \(-0.496535\pi\) | ||||
0.0108850 | + | 0.999941i | \(0.496535\pi\) | |||||||
\(488\) | 13.5505 | 0.613400 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −7.16870 | −0.323849 | ||||||||
\(491\) | 15.2161 | 0.686694 | 0.343347 | − | 0.939209i | \(-0.388439\pi\) | ||||
0.343347 | + | 0.939209i | \(0.388439\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.60406 | −0.387507 | ||||||||
\(494\) | 69.3914 | 3.12207 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 38.7448 | 1.73969 | ||||||||
\(497\) | −13.1659 | −0.590571 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.10495 | −0.228529 | −0.114264 | − | 0.993450i | \(-0.536451\pi\) | ||||
−0.114264 | + | 0.993450i | \(0.536451\pi\) | |||||||
\(500\) | 28.9370 | 1.29410 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 30.5476 | 1.36341 | ||||||||
\(503\) | −17.3084 | −0.771741 | −0.385871 | − | 0.922553i | \(-0.626099\pi\) | ||||
−0.385871 | + | 0.922553i | \(0.626099\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.2662 | −0.590339 | ||||||||
\(506\) | 3.29651 | 0.146548 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.62732 | −0.205304 | ||||||||
\(509\) | 32.5988 | 1.44492 | 0.722458 | − | 0.691415i | \(-0.243012\pi\) | ||||
0.722458 | + | 0.691415i | \(0.243012\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.7431 | −0.563723 | ||||||||
\(512\) | −49.3889 | −2.18270 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −81.4299 | −3.59172 | ||||||||
\(515\) | −9.82913 | −0.433123 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.9890 | −0.835133 | ||||||||
\(518\) | −13.4532 | −0.591098 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −89.2816 | −3.91526 | ||||||||
\(521\) | 20.6553 | 0.904925 | 0.452463 | − | 0.891783i | \(-0.350546\pi\) | ||||
0.452463 | + | 0.891783i | \(0.350546\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 42.8597 | 1.87412 | 0.937061 | − | 0.349166i | \(-0.113535\pi\) | ||||
0.937061 | + | 0.349166i | \(0.113535\pi\) | |||||||
\(524\) | 15.6247 | 0.682570 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.9685 | 0.696258 | ||||||||
\(527\) | −22.5340 | −0.981595 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.2153 | −0.965883 | ||||||||
\(530\) | 62.6364 | 2.72075 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −26.3123 | −1.14078 | ||||||||
\(533\) | 23.7372 | 1.02817 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.1930 | −0.570384 | ||||||||
\(536\) | −32.2338 | −1.39229 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 41.9204 | 1.80732 | ||||||||
\(539\) | −1.44556 | −0.0622648 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.7567 | −0.763419 | −0.381709 | − | 0.924282i | \(-0.624664\pi\) | ||||
−0.381709 | + | 0.924282i | \(0.624664\pi\) | |||||||
\(542\) | −42.0267 | −1.80520 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −35.4542 | −1.52009 | ||||||||
\(545\) | 49.6090 | 2.12502 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.99775 | −0.299202 | −0.149601 | − | 0.988746i | \(-0.547799\pi\) | ||||
−0.149601 | + | 0.988746i | \(0.547799\pi\) | |||||||
\(548\) | 103.707 | 4.43013 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −10.2498 | −0.437054 | ||||||||
\(551\) | 10.3122 | 0.439316 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.77816 | −0.160664 | ||||||||
\(554\) | −21.0923 | −0.896125 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 38.6716 | 1.64004 | ||||||||
\(557\) | −31.1241 | −1.31877 | −0.659384 | − | 0.751806i | \(-0.729183\pi\) | ||||
−0.659384 | + | 0.751806i | \(0.729183\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −30.0952 | −1.27289 | ||||||||
\(560\) | 22.7157 | 0.959914 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −38.5270 | −1.62516 | ||||||||
\(563\) | 40.6243 | 1.71211 | 0.856055 | − | 0.516884i | \(-0.172908\pi\) | ||||
0.856055 | + | 0.516884i | \(0.172908\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −46.8525 | −1.97110 | ||||||||
\(566\) | −2.43742 | −0.102452 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 89.0497 | 3.73644 | ||||||||
\(569\) | −45.2818 | −1.89831 | −0.949155 | − | 0.314809i | \(-0.898060\pi\) | ||||
−0.949155 | + | 0.314809i | \(0.898060\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.5280 | 0.566131 | 0.283065 | − | 0.959101i | \(-0.408649\pi\) | ||||
0.283065 | + | 0.959101i | \(0.408649\pi\) | |||||||
\(572\) | −31.7085 | −1.32580 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −12.8911 | −0.538065 | ||||||||
\(575\) | −2.43982 | −0.101748 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.8904 | 1.07783 | 0.538916 | − | 0.842360i | \(-0.318834\pi\) | ||||
0.538916 | + | 0.842360i | \(0.318834\pi\) | |||||||
\(578\) | 14.1824 | 0.589909 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −23.3682 | −0.970311 | ||||||||
\(581\) | 13.2837 | 0.551100 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.6306 | 0.523106 | ||||||||
\(584\) | 86.1904 | 3.56658 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −59.5782 | −2.46115 | ||||||||
\(587\) | −46.0434 | −1.90041 | −0.950207 | − | 0.311621i | \(-0.899128\pi\) | ||||
−0.950207 | + | 0.311621i | \(0.899128\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.0077 | 1.11283 | ||||||||
\(590\) | −52.8006 | −2.17377 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 42.6295 | 1.75206 | ||||||||
\(593\) | −27.1990 | −1.11693 | −0.558465 | − | 0.829528i | \(-0.688610\pi\) | ||||
−0.558465 | + | 0.829528i | \(0.688610\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.2114 | −0.541616 | ||||||||
\(596\) | −70.2266 | −2.87659 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −10.8100 | −0.442054 | ||||||||
\(599\) | −26.4774 | −1.08184 | −0.540918 | − | 0.841075i | \(-0.681923\pi\) | ||||
−0.540918 | + | 0.841075i | \(0.681923\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.4346 | 0.833546 | 0.416773 | − | 0.909011i | \(-0.363161\pi\) | ||||
0.416773 | + | 0.909011i | \(0.363161\pi\) | |||||||
\(602\) | 16.3440 | 0.666131 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −32.7864 | −1.33406 | ||||||||
\(605\) | 24.8122 | 1.00876 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 38.3850 | 1.55800 | 0.779000 | − | 0.627024i | \(-0.215727\pi\) | ||||
0.779000 | + | 0.627024i | \(0.215727\pi\) | |||||||
\(608\) | 42.4930 | 1.72332 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14.3619 | −0.581496 | ||||||||
\(611\) | 62.2691 | 2.51914 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.1100 | −1.25652 | −0.628260 | − | 0.778003i | \(-0.716233\pi\) | ||||
−0.628260 | + | 0.778003i | \(0.716233\pi\) | |||||||
\(614\) | −43.1933 | −1.74314 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.77731 | 0.393939 | ||||||||
\(617\) | 3.99996 | 0.161032 | 0.0805161 | − | 0.996753i | \(-0.474343\pi\) | ||||
0.0805161 | + | 0.996753i | \(0.474343\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −37.4699 | −1.50604 | −0.753021 | − | 0.657996i | \(-0.771404\pi\) | ||||
−0.753021 | + | 0.657996i | \(0.771404\pi\) | |||||||
\(620\) | −61.2011 | −2.45790 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −26.4264 | −1.05960 | ||||||||
\(623\) | −2.64036 | −0.105784 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1853 | −1.24741 | ||||||||
\(626\) | 67.8694 | 2.71260 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −54.9058 | −2.19098 | ||||||||
\(629\) | −24.7933 | −0.988574 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.9103 | −0.951853 | −0.475926 | − | 0.879485i | \(-0.657887\pi\) | ||||
−0.475926 | + | 0.879485i | \(0.657887\pi\) | |||||||
\(632\) | 25.5542 | 1.01649 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 17.7596 | 0.705326 | ||||||||
\(635\) | 2.78465 | 0.110506 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.74033 | 0.187819 | ||||||||
\(638\) | −6.74886 | −0.267190 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 20.6648 | 0.816849 | ||||||||
\(641\) | −29.3723 | −1.16014 | −0.580069 | − | 0.814567i | \(-0.696974\pi\) | ||||
−0.580069 | + | 0.814567i | \(0.696974\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.61735 | −0.142654 | −0.0713272 | − | 0.997453i | \(-0.522723\pi\) | ||||
−0.0713272 | + | 0.997453i | \(0.522723\pi\) | |||||||
\(644\) | 4.09900 | 0.161523 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −69.4507 | −2.73250 | ||||||||
\(647\) | −12.6711 | −0.498152 | −0.249076 | − | 0.968484i | \(-0.580127\pi\) | ||||
−0.249076 | + | 0.968484i | \(0.580127\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.6472 | −0.417939 | ||||||||
\(650\) | 33.6115 | 1.31835 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.2608 | 0.401844 | ||||||||
\(653\) | −16.5935 | −0.649355 | −0.324678 | − | 0.945825i | \(-0.605256\pi\) | ||||
−0.324678 | + | 0.945825i | \(0.605256\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.40273 | −0.367395 | ||||||||
\(656\) | 40.8486 | 1.59487 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −33.8168 | −1.31832 | ||||||||
\(659\) | 15.9424 | 0.621028 | 0.310514 | − | 0.950569i | \(-0.399499\pi\) | ||||
0.310514 | + | 0.950569i | \(0.399499\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.7378 | −1.00109 | −0.500543 | − | 0.865712i | \(-0.666866\pi\) | ||||
−0.500543 | + | 0.865712i | \(0.666866\pi\) | |||||||
\(662\) | −18.2015 | −0.707421 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −89.8463 | −3.48671 | ||||||||
\(665\) | 15.8343 | 0.614029 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.60647 | −0.0622027 | ||||||||
\(668\) | −23.5560 | −0.911408 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 34.1640 | 1.31987 | ||||||||
\(671\) | −2.89607 | −0.111801 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.7394 | −0.606709 | −0.303355 | − | 0.952878i | \(-0.598107\pi\) | ||||
−0.303355 | + | 0.952878i | \(0.598107\pi\) | |||||||
\(674\) | −31.8673 | −1.22748 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 43.8240 | 1.68554 | ||||||||
\(677\) | 6.89543 | 0.265013 | 0.132506 | − | 0.991182i | \(-0.457697\pi\) | ||||
0.132506 | + | 0.991182i | \(0.457697\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.9175 | −0.572482 | ||||||||
\(680\) | 89.3578 | 3.42671 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −17.6752 | −0.676819 | ||||||||
\(683\) | 10.6634 | 0.408025 | 0.204013 | − | 0.978968i | \(-0.434602\pi\) | ||||
0.204013 | + | 0.978968i | \(0.434602\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −62.4092 | −2.38453 | ||||||||
\(686\) | −2.57436 | −0.0982895 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −51.7898 | −1.97447 | ||||||||
\(689\) | −41.4186 | −1.57792 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.2270 | −0.389052 | −0.194526 | − | 0.980897i | \(-0.562317\pi\) | ||||
−0.194526 | + | 0.980897i | \(0.562317\pi\) | |||||||
\(692\) | −23.0989 | −0.878089 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 38.7451 | 1.47075 | ||||||||
\(695\) | −23.2720 | −0.882757 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −23.7575 | −0.899879 | ||||||||
\(698\) | 61.0426 | 2.31049 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −12.7450 | −0.481716 | ||||||||
\(701\) | 2.61443 | 0.0987457 | 0.0493729 | − | 0.998780i | \(-0.484278\pi\) | ||||
0.0493729 | + | 0.998780i | \(0.484278\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 29.7156 | 1.12074 | ||||||||
\(704\) | −4.22537 | −0.159250 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −58.1161 | −2.18723 | ||||||||
\(707\) | −4.76405 | −0.179171 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.2028 | 0.458286 | 0.229143 | − | 0.973393i | \(-0.426408\pi\) | ||||
0.229143 | + | 0.973393i | \(0.426408\pi\) | |||||||
\(710\) | −94.3822 | −3.54210 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 17.8585 | 0.669275 | ||||||||
\(713\) | −4.20733 | −0.157566 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.0817 | 0.713614 | ||||||||
\(716\) | 74.7019 | 2.79174 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 77.9681 | 2.90974 | ||||||||
\(719\) | 45.8176 | 1.70871 | 0.854354 | − | 0.519691i | \(-0.173953\pi\) | ||||
0.854354 | + | 0.519691i | \(0.173953\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.52975 | −0.131455 | ||||||||
\(722\) | 34.3260 | 1.27748 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 90.5015 | 3.36346 | ||||||||
\(725\) | 4.99499 | 0.185509 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.20108 | 0.229985 | 0.114993 | − | 0.993366i | \(-0.463316\pi\) | ||||
0.114993 | + | 0.993366i | \(0.463316\pi\) | |||||||
\(728\) | −32.0620 | −1.18830 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −91.3517 | −3.38108 | ||||||||
\(731\) | 30.1209 | 1.11406 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.0136 | −1.03471 | −0.517353 | − | 0.855772i | \(-0.673083\pi\) | ||||
−0.517353 | + | 0.855772i | \(0.673083\pi\) | |||||||
\(734\) | 5.96361 | 0.220121 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.61968 | −0.244005 | ||||||||
\(737\) | 6.88915 | 0.253765 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.5172 | 0.681166 | 0.340583 | − | 0.940214i | \(-0.389376\pi\) | ||||
0.340583 | + | 0.940214i | \(0.389376\pi\) | |||||||
\(740\) | −67.3374 | −2.47537 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 22.4934 | 0.825760 | ||||||||
\(743\) | 38.0750 | 1.39684 | 0.698419 | − | 0.715689i | \(-0.253887\pi\) | ||||
0.698419 | + | 0.715689i | \(0.253887\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 42.2613 | 1.54833 | ||||||||
\(746\) | 67.5013 | 2.47140 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 31.7355 | 1.16037 | ||||||||
\(749\) | −4.73776 | −0.173114 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.6544 | 0.936144 | 0.468072 | − | 0.883690i | \(-0.344949\pi\) | ||||
0.468072 | + | 0.883690i | \(0.344949\pi\) | |||||||
\(752\) | 107.157 | 3.90760 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 22.1310 | 0.805965 | ||||||||
\(755\) | 19.7304 | 0.718062 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.1037 | 1.56663 | 0.783315 | − | 0.621625i | \(-0.213527\pi\) | ||||
0.783315 | + | 0.621625i | \(0.213527\pi\) | |||||||
\(758\) | −23.0453 | −0.837042 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −107.098 | −3.88486 | ||||||||
\(761\) | 41.2866 | 1.49664 | 0.748318 | − | 0.663340i | \(-0.230862\pi\) | ||||
0.748318 | + | 0.663340i | \(0.230862\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.8152 | 0.644952 | ||||||||
\(764\) | −8.62082 | −0.311890 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −53.0514 | −1.91683 | ||||||||
\(767\) | 34.9146 | 1.26069 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.4188 | 1.45754 | 0.728770 | − | 0.684759i | \(-0.240092\pi\) | ||||
0.728770 | + | 0.684759i | \(0.240092\pi\) | |||||||
\(770\) | −10.3628 | −0.373449 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 55.4118 | 1.99432 | ||||||||
\(773\) | −31.2197 | −1.12289 | −0.561447 | − | 0.827513i | \(-0.689755\pi\) | ||||
−0.561447 | + | 0.827513i | \(0.689755\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.0818 | 0.469913 | ||||||||
\(776\) | 100.897 | 3.62200 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 28.5264 | 1.02272 | ||||||||
\(779\) | 28.4741 | 1.02019 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.0321 | −0.681023 | ||||||||
\(782\) | 10.8192 | 0.386895 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 8.15746 | 0.291338 | ||||||||
\(785\) | 33.0415 | 1.17930 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.5112 | −0.588561 | −0.294281 | − | 0.955719i | \(-0.595080\pi\) | ||||
−0.294281 | + | 0.955719i | \(0.595080\pi\) | |||||||
\(788\) | 7.70575 | 0.274506 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −27.0845 | −0.963622 | ||||||||
\(791\) | −16.8253 | −0.598237 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.49686 | 0.337243 | ||||||||
\(794\) | −64.9791 | −2.30602 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −60.7742 | −2.15409 | ||||||||
\(797\) | −21.7364 | −0.769943 | −0.384972 | − | 0.922928i | \(-0.625789\pi\) | ||||
−0.384972 | + | 0.922928i | \(0.625789\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −62.3222 | −2.20480 | ||||||||
\(800\) | 20.5825 | 0.727703 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 16.5319 | 0.583762 | ||||||||
\(803\) | −18.4210 | −0.650063 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.46672 | −0.0869403 | ||||||||
\(806\) | 57.9610 | 2.04159 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 32.2225 | 1.13358 | ||||||||
\(809\) | 24.1216 | 0.848069 | 0.424035 | − | 0.905646i | \(-0.360613\pi\) | ||||
0.424035 | + | 0.905646i | \(0.360613\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.2206 | 1.30699 | 0.653496 | − | 0.756930i | \(-0.273302\pi\) | ||||
0.653496 | + | 0.756930i | \(0.273302\pi\) | |||||||
\(812\) | −8.39178 | −0.294494 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −19.4474 | −0.681631 | ||||||||
\(815\) | −6.17480 | −0.216294 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36.1008 | −1.26301 | ||||||||
\(818\) | 56.2014 | 1.96504 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −64.5242 | −2.25328 | ||||||||
\(821\) | 25.3553 | 0.884907 | 0.442454 | − | 0.896791i | \(-0.354108\pi\) | ||||
0.442454 | + | 0.896791i | \(0.354108\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.1655 | −0.877214 | −0.438607 | − | 0.898679i | \(-0.644528\pi\) | ||||
−0.438607 | + | 0.898679i | \(0.644528\pi\) | |||||||
\(824\) | 23.8741 | 0.831693 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18.9613 | −0.659747 | ||||||||
\(827\) | −37.6398 | −1.30886 | −0.654432 | − | 0.756121i | \(-0.727092\pi\) | ||||
−0.654432 | + | 0.756121i | \(0.727092\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.4051 | −0.361385 | −0.180693 | − | 0.983540i | \(-0.557834\pi\) | ||||
−0.180693 | + | 0.983540i | \(0.557834\pi\) | |||||||
\(830\) | 95.2266 | 3.30536 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 13.8559 | 0.480368 | ||||||||
\(833\) | −4.74437 | −0.164383 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.1756 | 0.490568 | ||||||||
\(836\) | −38.0360 | −1.31550 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −55.3607 | −1.91241 | ||||||||
\(839\) | −2.12792 | −0.0734639 | −0.0367320 | − | 0.999325i | \(-0.511695\pi\) | ||||
−0.0367320 | + | 0.999325i | \(0.511695\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.7111 | −0.886590 | ||||||||
\(842\) | 10.7755 | 0.371350 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 18.1453 | 0.624588 | ||||||||
\(845\) | −26.3726 | −0.907246 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.91035 | 0.306163 | ||||||||
\(848\) | −71.2758 | −2.44762 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −33.6402 | −1.15385 | ||||||||
\(851\) | −4.62918 | −0.158686 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.5959 | −0.910625 | −0.455312 | − | 0.890332i | \(-0.650472\pi\) | ||||
−0.455312 | + | 0.890332i | \(0.650472\pi\) | |||||||
\(854\) | −5.15752 | −0.176487 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 32.0446 | 1.09526 | ||||||||
\(857\) | 37.6643 | 1.28659 | 0.643294 | − | 0.765619i | \(-0.277567\pi\) | ||||
0.643294 | + | 0.765619i | \(0.277567\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.50166 | −0.255953 | −0.127977 | − | 0.991777i | \(-0.540848\pi\) | ||||
−0.127977 | + | 0.991777i | \(0.540848\pi\) | |||||||
\(860\) | 81.8068 | 2.78959 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 37.6060 | 1.28086 | ||||||||
\(863\) | −4.85207 | −0.165167 | −0.0825833 | − | 0.996584i | \(-0.526317\pi\) | ||||
−0.0825833 | + | 0.996584i | \(0.526317\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.9006 | 0.472634 | ||||||||
\(866\) | −81.4155 | −2.76661 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −21.9780 | −0.745982 | ||||||||
\(869\) | −5.46156 | −0.185271 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.5911 | −0.765470 | ||||||||
\(872\) | −120.496 | −4.08050 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −12.9672 | −0.438621 | ||||||||
\(875\) | −6.25352 | −0.211407 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.17291 | 0.140909 | 0.0704546 | − | 0.997515i | \(-0.477555\pi\) | ||||
0.0704546 | + | 0.997515i | \(0.477555\pi\) | |||||||
\(878\) | 17.3623 | 0.585949 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 32.8370 | 1.10693 | ||||||||
\(881\) | 40.7208 | 1.37192 | 0.685959 | − | 0.727640i | \(-0.259383\pi\) | ||||
0.685959 | + | 0.727640i | \(0.259383\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.4037 | −0.854904 | −0.427452 | − | 0.904038i | \(-0.640589\pi\) | ||||
−0.427452 | + | 0.904038i | \(0.640589\pi\) | |||||||
\(884\) | −104.068 | −3.50018 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 48.7273 | 1.63703 | ||||||||
\(887\) | −11.1346 | −0.373862 | −0.186931 | − | 0.982373i | \(-0.559854\pi\) | ||||
−0.186931 | + | 0.982373i | \(0.559854\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −18.9279 | −0.634465 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 20.9766 | 0.702347 | ||||||||
\(893\) | 74.6952 | 2.49958 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −44.9545 | −1.50266 | ||||||||
\(896\) | 7.42097 | 0.247917 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −27.7028 | −0.924455 | ||||||||
\(899\) | 8.61357 | 0.287279 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 41.4539 | 1.38103 | ||||||||
\(902\) | −18.6349 | −0.620475 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 113.800 | 3.78495 | ||||||||
\(905\) | −54.4624 | −1.81039 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.3986 | −1.17539 | −0.587696 | − | 0.809082i | \(-0.699965\pi\) | ||||
−0.587696 | + | 0.809082i | \(0.699965\pi\) | |||||||
\(908\) | −83.8082 | −2.78127 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 33.9820 | 1.12649 | ||||||||
\(911\) | −7.20575 | −0.238737 | −0.119369 | − | 0.992850i | \(-0.538087\pi\) | ||||
−0.119369 | + | 0.992850i | \(0.538087\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.2024 | 0.635506 | ||||||||
\(914\) | −16.6042 | −0.549217 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 76.7814 | 2.53693 | ||||||||
\(917\) | −3.37663 | −0.111506 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.33954 | −0.209122 | −0.104561 | − | 0.994518i | \(-0.533344\pi\) | ||||
−0.104561 | + | 0.994518i | \(0.533344\pi\) | |||||||
\(920\) | 16.6840 | 0.550057 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −13.5299 | −0.445583 | ||||||||
\(923\) | 62.4106 | 2.05427 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.3935 | 0.473255 | ||||||||
\(926\) | −59.4801 | −1.95464 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 13.5523 | 0.444876 | ||||||||
\(929\) | 34.2525 | 1.12379 | 0.561894 | − | 0.827209i | \(-0.310073\pi\) | ||||
0.561894 | + | 0.827209i | \(0.310073\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.68628 | 0.186360 | ||||||||
\(932\) | 66.6709 | 2.18388 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −21.2049 | −0.693844 | ||||||||
\(935\) | −19.0980 | −0.624570 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.6294 | 0.902614 | 0.451307 | − | 0.892369i | \(-0.350958\pi\) | ||||
0.451307 | + | 0.892369i | \(0.350958\pi\) | |||||||
\(938\) | 12.2687 | 0.400586 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −169.264 | −5.52078 | ||||||||
\(941\) | −14.1355 | −0.460804 | −0.230402 | − | 0.973096i | \(-0.574004\pi\) | ||||
−0.230402 | + | 0.973096i | \(0.574004\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.43578 | −0.144449 | ||||||||
\(944\) | 60.0833 | 1.95554 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 23.6263 | 0.768156 | ||||||||
\(947\) | −40.2007 | −1.30635 | −0.653173 | − | 0.757208i | \(-0.726563\pi\) | ||||
−0.653173 | + | 0.757208i | \(0.726563\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 60.4067 | 1.96088 | ||||||||
\(950\) | 40.3188 | 1.30811 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 32.0894 | 1.04002 | ||||||||
\(953\) | −46.6706 | −1.51181 | −0.755904 | − | 0.654682i | \(-0.772802\pi\) | ||||
−0.755904 | + | 0.654682i | \(0.772802\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.18788 | 0.167876 | ||||||||
\(956\) | −86.7756 | −2.80652 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −84.7276 | −2.73742 | ||||||||
\(959\) | −22.4118 | −0.723716 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.44113 | −0.272295 | ||||||||
\(962\) | 63.7724 | 2.05611 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −88.4439 | −2.84859 | ||||||||
\(965\) | −33.3460 | −1.07345 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.5147 | 0.659708 | 0.329854 | − | 0.944032i | \(-0.393001\pi\) | ||||
0.329854 | + | 0.944032i | \(0.393001\pi\) | |||||||
\(968\) | −60.2666 | −1.93704 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −106.939 | −3.43361 | ||||||||
\(971\) | 34.6513 | 1.11201 | 0.556006 | − | 0.831178i | \(-0.312333\pi\) | ||||
0.556006 | + | 0.831178i | \(0.312333\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.35723 | −0.267921 | ||||||||
\(974\) | 1.23678 | 0.0396289 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 16.3428 | 0.523121 | ||||||||
\(977\) | −21.9087 | −0.700920 | −0.350460 | − | 0.936578i | \(-0.613975\pi\) | ||||
−0.350460 | + | 0.936578i | \(0.613975\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.81680 | −0.121986 | ||||||||
\(980\) | −12.8855 | −0.411612 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 39.1718 | 1.25002 | ||||||||
\(983\) | −37.9579 | −1.21067 | −0.605334 | − | 0.795972i | \(-0.706960\pi\) | ||||
−0.605334 | + | 0.795972i | \(0.706960\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.63720 | −0.147754 | ||||||||
\(986\) | −22.1499 | −0.705398 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 124.729 | 3.96815 | ||||||||
\(989\) | 5.62389 | 0.178829 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.01270 | 0.0321694 | 0.0160847 | − | 0.999871i | \(-0.494880\pi\) | ||||
0.0160847 | + | 0.999871i | \(0.494880\pi\) | |||||||
\(992\) | 35.4934 | 1.12692 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −33.8937 | −1.07504 | ||||||||
\(995\) | 36.5730 | 1.15944 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −46.5112 | −1.47303 | −0.736513 | − | 0.676424i | \(-0.763529\pi\) | ||||
−0.736513 | + | 0.676424i | \(0.763529\pi\) | |||||||
\(998\) | −13.1420 | −0.416001 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8001.2.a.s.1.16 | 16 | ||
3.2 | odd | 2 | 2667.2.a.n.1.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.n.1.1 | ✓ | 16 | 3.2 | odd | 2 | ||
8001.2.a.s.1.16 | 16 | 1.1 | even | 1 | trivial |