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: | \(36\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.63103 | −1.15332 | −0.576658 | − | 0.816986i | \(-0.695643\pi\) | ||||
−0.576658 | + | 0.816986i | \(0.695643\pi\) | |||||||
\(3\) | −1.44692 | −0.835379 | −0.417690 | − | 0.908590i | \(-0.637160\pi\) | ||||
−0.417690 | + | 0.908590i | \(0.637160\pi\) | |||||||
\(4\) | 0.660273 | 0.330136 | ||||||||
\(5\) | 0.621753 | 0.278056 | 0.139028 | − | 0.990288i | \(-0.455602\pi\) | ||||
0.139028 | + | 0.990288i | \(0.455602\pi\) | |||||||
\(6\) | 2.35997 | 0.963456 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.18514 | 0.772564 | ||||||||
\(9\) | −0.906425 | −0.302142 | ||||||||
\(10\) | −1.01410 | −0.320687 | ||||||||
\(11\) | −3.06320 | −0.923588 | −0.461794 | − | 0.886987i | \(-0.652794\pi\) | ||||
−0.461794 | + | 0.886987i | \(0.652794\pi\) | |||||||
\(12\) | −0.955361 | −0.275789 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.899626 | −0.232283 | ||||||||
\(16\) | −4.88459 | −1.22115 | ||||||||
\(17\) | 0.322567 | 0.0782339 | 0.0391169 | − | 0.999235i | \(-0.487546\pi\) | ||||
0.0391169 | + | 0.999235i | \(0.487546\pi\) | |||||||
\(18\) | 1.47841 | 0.348465 | ||||||||
\(19\) | −4.08463 | −0.937079 | −0.468540 | − | 0.883442i | \(-0.655220\pi\) | ||||
−0.468540 | + | 0.883442i | \(0.655220\pi\) | |||||||
\(20\) | 0.410526 | 0.0917965 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.99618 | 1.06519 | ||||||||
\(23\) | −1.64522 | −0.343052 | −0.171526 | − | 0.985180i | \(-0.554870\pi\) | ||||
−0.171526 | + | 0.985180i | \(0.554870\pi\) | |||||||
\(24\) | −3.16172 | −0.645384 | ||||||||
\(25\) | −4.61342 | −0.922685 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.65228 | 1.08778 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.35648 | −0.808977 | −0.404489 | − | 0.914543i | \(-0.632550\pi\) | ||||
−0.404489 | + | 0.914543i | \(0.632550\pi\) | |||||||
\(30\) | 1.46732 | 0.267895 | ||||||||
\(31\) | −5.12069 | −0.919702 | −0.459851 | − | 0.887996i | \(-0.652097\pi\) | ||||
−0.459851 | + | 0.887996i | \(0.652097\pi\) | |||||||
\(32\) | 3.59664 | 0.635803 | ||||||||
\(33\) | 4.43220 | 0.771547 | ||||||||
\(34\) | −0.526117 | −0.0902283 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.598487 | −0.0997479 | ||||||||
\(37\) | −10.1678 | −1.67158 | −0.835790 | − | 0.549049i | \(-0.814990\pi\) | ||||
−0.835790 | + | 0.549049i | \(0.814990\pi\) | |||||||
\(38\) | 6.66218 | 1.08075 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.35862 | 0.214816 | ||||||||
\(41\) | −2.69567 | −0.420993 | −0.210497 | − | 0.977595i | \(-0.567508\pi\) | ||||
−0.210497 | + | 0.977595i | \(0.567508\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.0291770 | 0.00444945 | 0.00222472 | − | 0.999998i | \(-0.499292\pi\) | ||||
0.00222472 | + | 0.999998i | \(0.499292\pi\) | |||||||
\(44\) | −2.02254 | −0.304910 | ||||||||
\(45\) | −0.563572 | −0.0840124 | ||||||||
\(46\) | 2.68341 | 0.395647 | ||||||||
\(47\) | 2.63668 | 0.384599 | 0.192299 | − | 0.981336i | \(-0.438406\pi\) | ||||
0.192299 | + | 0.981336i | \(0.438406\pi\) | |||||||
\(48\) | 7.06760 | 1.02012 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 7.52465 | 1.06415 | ||||||||
\(51\) | −0.466728 | −0.0653550 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.25376 | −0.721659 | −0.360830 | − | 0.932632i | \(-0.617506\pi\) | ||||
−0.360830 | + | 0.932632i | \(0.617506\pi\) | |||||||
\(54\) | −9.21906 | −1.25456 | ||||||||
\(55\) | −1.90455 | −0.256810 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.91013 | 0.782816 | ||||||||
\(58\) | 7.10556 | 0.933006 | ||||||||
\(59\) | −14.6294 | −1.90459 | −0.952293 | − | 0.305185i | \(-0.901282\pi\) | ||||
−0.952293 | + | 0.305185i | \(0.901282\pi\) | |||||||
\(60\) | −0.593999 | −0.0766849 | ||||||||
\(61\) | −7.76622 | −0.994363 | −0.497181 | − | 0.867647i | \(-0.665632\pi\) | ||||
−0.497181 | + | 0.867647i | \(0.665632\pi\) | |||||||
\(62\) | 8.35201 | 1.06071 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.90292 | 0.487865 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −7.22907 | −0.889836 | ||||||||
\(67\) | 10.7043 | 1.30773 | 0.653867 | − | 0.756610i | \(-0.273146\pi\) | ||||
0.653867 | + | 0.756610i | \(0.273146\pi\) | |||||||
\(68\) | 0.212982 | 0.0258278 | ||||||||
\(69\) | 2.38050 | 0.286579 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.706685 | 0.0838681 | 0.0419340 | − | 0.999120i | \(-0.486648\pi\) | ||||
0.0419340 | + | 0.999120i | \(0.486648\pi\) | |||||||
\(72\) | −1.98067 | −0.233424 | ||||||||
\(73\) | 13.6825 | 1.60141 | 0.800705 | − | 0.599059i | \(-0.204459\pi\) | ||||
0.800705 | + | 0.599059i | \(0.204459\pi\) | |||||||
\(74\) | 16.5841 | 1.92786 | ||||||||
\(75\) | 6.67525 | 0.770792 | ||||||||
\(76\) | −2.69697 | −0.309364 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.49414 | −0.843157 | −0.421578 | − | 0.906792i | \(-0.638524\pi\) | ||||
−0.421578 | + | 0.906792i | \(0.638524\pi\) | |||||||
\(80\) | −3.03701 | −0.339548 | ||||||||
\(81\) | −5.45912 | −0.606569 | ||||||||
\(82\) | 4.39673 | 0.485538 | ||||||||
\(83\) | −15.3279 | −1.68246 | −0.841230 | − | 0.540677i | \(-0.818168\pi\) | ||||
−0.841230 | + | 0.540677i | \(0.818168\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.200557 | 0.0217534 | ||||||||
\(86\) | −0.0475887 | −0.00513162 | ||||||||
\(87\) | 6.30347 | 0.675803 | ||||||||
\(88\) | −6.69352 | −0.713531 | ||||||||
\(89\) | −0.0211515 | −0.00224205 | −0.00112103 | − | 0.999999i | \(-0.500357\pi\) | ||||
−0.00112103 | + | 0.999999i | \(0.500357\pi\) | |||||||
\(90\) | 0.919206 | 0.0968928 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.08629 | −0.113254 | ||||||||
\(93\) | 7.40922 | 0.768300 | ||||||||
\(94\) | −4.30051 | −0.443563 | ||||||||
\(95\) | −2.53963 | −0.260561 | ||||||||
\(96\) | −5.20405 | −0.531136 | ||||||||
\(97\) | 6.81907 | 0.692372 | 0.346186 | − | 0.938166i | \(-0.387477\pi\) | ||||
0.346186 | + | 0.938166i | \(0.387477\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.77656 | 0.279054 | ||||||||
\(100\) | −3.04612 | −0.304612 | ||||||||
\(101\) | −18.6740 | −1.85813 | −0.929066 | − | 0.369915i | \(-0.879387\pi\) | ||||
−0.929066 | + | 0.369915i | \(0.879387\pi\) | |||||||
\(102\) | 0.761249 | 0.0753749 | ||||||||
\(103\) | 16.2419 | 1.60036 | 0.800181 | − | 0.599758i | \(-0.204737\pi\) | ||||
0.800181 | + | 0.599758i | \(0.204737\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.56906 | 0.832301 | ||||||||
\(107\) | −14.7351 | −1.42449 | −0.712246 | − | 0.701930i | \(-0.752322\pi\) | ||||
−0.712246 | + | 0.701930i | \(0.752322\pi\) | |||||||
\(108\) | 3.73205 | 0.359116 | ||||||||
\(109\) | 3.20868 | 0.307336 | 0.153668 | − | 0.988123i | \(-0.450891\pi\) | ||||
0.153668 | + | 0.988123i | \(0.450891\pi\) | |||||||
\(110\) | 3.10639 | 0.296183 | ||||||||
\(111\) | 14.7120 | 1.39640 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.8675 | 1.30455 | 0.652273 | − | 0.757985i | \(-0.273816\pi\) | ||||
0.652273 | + | 0.757985i | \(0.273816\pi\) | |||||||
\(114\) | −9.63963 | −0.902834 | ||||||||
\(115\) | −1.02292 | −0.0953879 | ||||||||
\(116\) | −2.87646 | −0.267073 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 23.8611 | 2.19659 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.96581 | −0.179453 | ||||||||
\(121\) | −1.61683 | −0.146985 | ||||||||
\(122\) | 12.6670 | 1.14681 | ||||||||
\(123\) | 3.90042 | 0.351689 | ||||||||
\(124\) | −3.38105 | −0.303627 | ||||||||
\(125\) | −5.97718 | −0.534615 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.71753 | −0.152406 | −0.0762030 | − | 0.997092i | \(-0.524280\pi\) | ||||
−0.0762030 | + | 0.997092i | \(0.524280\pi\) | |||||||
\(128\) | −13.5591 | −1.19847 | ||||||||
\(129\) | −0.0422167 | −0.00371698 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.9464 | 1.04376 | 0.521881 | − | 0.853018i | \(-0.325231\pi\) | ||||
0.521881 | + | 0.853018i | \(0.325231\pi\) | |||||||
\(132\) | 2.92646 | 0.254716 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −17.4590 | −1.50823 | ||||||||
\(135\) | 3.51432 | 0.302465 | ||||||||
\(136\) | 0.704853 | 0.0604407 | ||||||||
\(137\) | 9.25173 | 0.790428 | 0.395214 | − | 0.918589i | \(-0.370670\pi\) | ||||
0.395214 | + | 0.918589i | \(0.370670\pi\) | |||||||
\(138\) | −3.88268 | −0.330516 | ||||||||
\(139\) | −7.68373 | −0.651725 | −0.325863 | − | 0.945417i | \(-0.605655\pi\) | ||||
−0.325863 | + | 0.945417i | \(0.605655\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.81506 | −0.321286 | ||||||||
\(142\) | −1.15263 | −0.0967264 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 4.42751 | 0.368959 | ||||||||
\(145\) | −2.70865 | −0.224941 | ||||||||
\(146\) | −22.3165 | −1.84693 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.71354 | −0.551849 | ||||||||
\(149\) | 11.2644 | 0.922816 | 0.461408 | − | 0.887188i | \(-0.347344\pi\) | ||||
0.461408 | + | 0.887188i | \(0.347344\pi\) | |||||||
\(150\) | −10.8876 | −0.888966 | ||||||||
\(151\) | 11.3802 | 0.926111 | 0.463056 | − | 0.886329i | \(-0.346753\pi\) | ||||
0.463056 | + | 0.886329i | \(0.346753\pi\) | |||||||
\(152\) | −8.92550 | −0.723954 | ||||||||
\(153\) | −0.292382 | −0.0236377 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.18380 | −0.255729 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.9387 | −1.75090 | −0.875448 | − | 0.483312i | \(-0.839434\pi\) | ||||
−0.875448 | + | 0.483312i | \(0.839434\pi\) | |||||||
\(158\) | 12.2232 | 0.972426 | ||||||||
\(159\) | 7.60176 | 0.602859 | ||||||||
\(160\) | 2.23622 | 0.176789 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 8.90401 | 0.699565 | ||||||||
\(163\) | −16.5999 | −1.30021 | −0.650104 | − | 0.759846i | \(-0.725274\pi\) | ||||
−0.650104 | + | 0.759846i | \(0.725274\pi\) | |||||||
\(164\) | −1.77988 | −0.138985 | ||||||||
\(165\) | 2.75573 | 0.214533 | ||||||||
\(166\) | 25.0004 | 1.94041 | ||||||||
\(167\) | 3.48459 | 0.269645 | 0.134823 | − | 0.990870i | \(-0.456954\pi\) | ||||
0.134823 | + | 0.990870i | \(0.456954\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −0.327115 | −0.0250886 | ||||||||
\(171\) | 3.70241 | 0.283131 | ||||||||
\(172\) | 0.0192648 | 0.00146892 | ||||||||
\(173\) | 1.41713 | 0.107743 | 0.0538714 | − | 0.998548i | \(-0.482844\pi\) | ||||
0.0538714 | + | 0.998548i | \(0.482844\pi\) | |||||||
\(174\) | −10.2812 | −0.779414 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 14.9624 | 1.12784 | ||||||||
\(177\) | 21.1676 | 1.59105 | ||||||||
\(178\) | 0.0344988 | 0.00258579 | ||||||||
\(179\) | −21.0463 | −1.57308 | −0.786539 | − | 0.617541i | \(-0.788129\pi\) | ||||
−0.786539 | + | 0.617541i | \(0.788129\pi\) | |||||||
\(180\) | −0.372111 | −0.0277355 | ||||||||
\(181\) | −20.7908 | −1.54537 | −0.772685 | − | 0.634789i | \(-0.781087\pi\) | ||||
−0.772685 | + | 0.634789i | \(0.781087\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.2371 | 0.830670 | ||||||||
\(184\) | −3.59504 | −0.265030 | ||||||||
\(185\) | −6.32188 | −0.464794 | ||||||||
\(186\) | −12.0847 | −0.886093 | ||||||||
\(187\) | −0.988085 | −0.0722559 | ||||||||
\(188\) | 1.74092 | 0.126970 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.14223 | 0.300509 | ||||||||
\(191\) | 5.77056 | 0.417543 | 0.208772 | − | 0.977964i | \(-0.433053\pi\) | ||||
0.208772 | + | 0.977964i | \(0.433053\pi\) | |||||||
\(192\) | −5.64721 | −0.407553 | ||||||||
\(193\) | −9.09061 | −0.654356 | −0.327178 | − | 0.944963i | \(-0.606098\pi\) | ||||
−0.327178 | + | 0.944963i | \(0.606098\pi\) | |||||||
\(194\) | −11.1221 | −0.798523 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.6642 | 1.61475 | 0.807377 | − | 0.590036i | \(-0.200886\pi\) | ||||
0.807377 | + | 0.590036i | \(0.200886\pi\) | |||||||
\(198\) | −4.52866 | −0.321838 | ||||||||
\(199\) | 6.32121 | 0.448099 | 0.224049 | − | 0.974578i | \(-0.428072\pi\) | ||||
0.224049 | + | 0.974578i | \(0.428072\pi\) | |||||||
\(200\) | −10.0810 | −0.712833 | ||||||||
\(201\) | −15.4882 | −1.09245 | ||||||||
\(202\) | 30.4579 | 2.14301 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.308168 | −0.0215760 | ||||||||
\(205\) | −1.67604 | −0.117060 | ||||||||
\(206\) | −26.4911 | −1.84572 | ||||||||
\(207\) | 1.49127 | 0.103650 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.5120 | 0.865475 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.2077 | 0.909259 | 0.454629 | − | 0.890681i | \(-0.349772\pi\) | ||||
0.454629 | + | 0.890681i | \(0.349772\pi\) | |||||||
\(212\) | −3.46891 | −0.238246 | ||||||||
\(213\) | −1.02252 | −0.0700617 | ||||||||
\(214\) | 24.0334 | 1.64289 | ||||||||
\(215\) | 0.0181409 | 0.00123720 | ||||||||
\(216\) | 12.3510 | 0.840381 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −5.23346 | −0.354455 | ||||||||
\(219\) | −19.7974 | −1.33778 | ||||||||
\(220\) | −1.25752 | −0.0847822 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −23.9958 | −1.61049 | ||||||||
\(223\) | 14.9324 | 0.999949 | 0.499975 | − | 0.866040i | \(-0.333343\pi\) | ||||
0.499975 | + | 0.866040i | \(0.333343\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.18172 | 0.278781 | ||||||||
\(226\) | −22.6184 | −1.50455 | ||||||||
\(227\) | 16.6916 | 1.10786 | 0.553931 | − | 0.832563i | \(-0.313127\pi\) | ||||
0.553931 | + | 0.832563i | \(0.313127\pi\) | |||||||
\(228\) | 3.90230 | 0.258436 | ||||||||
\(229\) | −15.0896 | −0.997147 | −0.498573 | − | 0.866848i | \(-0.666143\pi\) | ||||
−0.498573 | + | 0.866848i | \(0.666143\pi\) | |||||||
\(230\) | 1.66842 | 0.110012 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.51951 | −0.624987 | ||||||||
\(233\) | 10.7315 | 0.703047 | 0.351523 | − | 0.936179i | \(-0.385664\pi\) | ||||
0.351523 | + | 0.936179i | \(0.385664\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.63936 | 0.106940 | ||||||||
\(236\) | −9.65939 | −0.628773 | ||||||||
\(237\) | 10.8434 | 0.704356 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.60488 | 0.168496 | 0.0842479 | − | 0.996445i | \(-0.473151\pi\) | ||||
0.0842479 | + | 0.996445i | \(0.473151\pi\) | |||||||
\(240\) | 4.39430 | 0.283651 | ||||||||
\(241\) | −22.4531 | −1.44633 | −0.723165 | − | 0.690675i | \(-0.757313\pi\) | ||||
−0.723165 | + | 0.690675i | \(0.757313\pi\) | |||||||
\(242\) | 2.63710 | 0.169519 | ||||||||
\(243\) | −9.05794 | −0.581067 | ||||||||
\(244\) | −5.12782 | −0.328275 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.36172 | −0.405608 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −11.1894 | −0.710529 | ||||||||
\(249\) | 22.1783 | 1.40549 | ||||||||
\(250\) | 9.74898 | 0.616579 | ||||||||
\(251\) | −19.8520 | −1.25305 | −0.626524 | − | 0.779402i | \(-0.715523\pi\) | ||||
−0.626524 | + | 0.779402i | \(0.715523\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.03963 | 0.316839 | ||||||||
\(254\) | 2.80135 | 0.175772 | ||||||||
\(255\) | −0.290189 | −0.0181724 | ||||||||
\(256\) | 14.3095 | 0.894343 | ||||||||
\(257\) | −4.30542 | −0.268564 | −0.134282 | − | 0.990943i | \(-0.542873\pi\) | ||||
−0.134282 | + | 0.990943i | \(0.542873\pi\) | |||||||
\(258\) | 0.0688569 | 0.00428685 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.94882 | 0.244426 | ||||||||
\(262\) | −19.4850 | −1.20379 | ||||||||
\(263\) | −21.2519 | −1.31045 | −0.655224 | − | 0.755434i | \(-0.727426\pi\) | ||||
−0.655224 | + | 0.755434i | \(0.727426\pi\) | |||||||
\(264\) | 9.68498 | 0.596069 | ||||||||
\(265\) | −3.26654 | −0.200662 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.0306045 | 0.00187296 | ||||||||
\(268\) | 7.06773 | 0.431730 | ||||||||
\(269\) | −30.8114 | −1.87860 | −0.939302 | − | 0.343090i | \(-0.888526\pi\) | ||||
−0.939302 | + | 0.343090i | \(0.888526\pi\) | |||||||
\(270\) | −5.73198 | −0.348837 | ||||||||
\(271\) | 0.666306 | 0.0404752 | 0.0202376 | − | 0.999795i | \(-0.493558\pi\) | ||||
0.0202376 | + | 0.999795i | \(0.493558\pi\) | |||||||
\(272\) | −1.57560 | −0.0955350 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.0899 | −0.911613 | ||||||||
\(275\) | 14.1318 | 0.852181 | ||||||||
\(276\) | 1.57178 | 0.0946100 | ||||||||
\(277\) | −15.4086 | −0.925815 | −0.462907 | − | 0.886407i | \(-0.653194\pi\) | ||||
−0.462907 | + | 0.886407i | \(0.653194\pi\) | |||||||
\(278\) | 12.5324 | 0.751645 | ||||||||
\(279\) | 4.64152 | 0.277880 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.6079 | −0.871436 | −0.435718 | − | 0.900083i | \(-0.643505\pi\) | ||||
−0.435718 | + | 0.900083i | \(0.643505\pi\) | |||||||
\(282\) | 6.22249 | 0.370544 | ||||||||
\(283\) | −1.10196 | −0.0655045 | −0.0327523 | − | 0.999464i | \(-0.510427\pi\) | ||||
−0.0327523 | + | 0.999464i | \(0.510427\pi\) | |||||||
\(284\) | 0.466605 | 0.0276879 | ||||||||
\(285\) | 3.67464 | 0.217667 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −3.26009 | −0.192102 | ||||||||
\(289\) | −16.8960 | −0.993879 | ||||||||
\(290\) | 4.41790 | 0.259428 | ||||||||
\(291\) | −9.86665 | −0.578393 | ||||||||
\(292\) | 9.03415 | 0.528683 | ||||||||
\(293\) | 12.1452 | 0.709529 | 0.354764 | − | 0.934956i | \(-0.384561\pi\) | ||||
0.354764 | + | 0.934956i | \(0.384561\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.09588 | −0.529582 | ||||||||
\(296\) | −22.2181 | −1.29140 | ||||||||
\(297\) | −17.3140 | −1.00466 | ||||||||
\(298\) | −18.3726 | −1.06430 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 4.40748 | 0.254466 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −18.5616 | −1.06810 | ||||||||
\(303\) | 27.0198 | 1.55224 | ||||||||
\(304\) | 19.9517 | 1.14431 | ||||||||
\(305\) | −4.82867 | −0.276489 | ||||||||
\(306\) | 0.476886 | 0.0272617 | ||||||||
\(307\) | −21.4221 | −1.22262 | −0.611312 | − | 0.791390i | \(-0.709358\pi\) | ||||
−0.611312 | + | 0.791390i | \(0.709358\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −23.5007 | −1.33691 | ||||||||
\(310\) | 5.19289 | 0.294936 | ||||||||
\(311\) | −12.6808 | −0.719062 | −0.359531 | − | 0.933133i | \(-0.617063\pi\) | ||||
−0.359531 | + | 0.933133i | \(0.617063\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.7396 | 1.22879 | 0.614397 | − | 0.788997i | \(-0.289399\pi\) | ||||
0.614397 | + | 0.788997i | \(0.289399\pi\) | |||||||
\(314\) | 35.7827 | 2.01934 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.94818 | −0.278357 | ||||||||
\(317\) | 12.3285 | 0.692436 | 0.346218 | − | 0.938154i | \(-0.387466\pi\) | ||||
0.346218 | + | 0.938154i | \(0.387466\pi\) | |||||||
\(318\) | −12.3987 | −0.695287 | ||||||||
\(319\) | 13.3447 | 0.747162 | ||||||||
\(320\) | 2.42665 | 0.135654 | ||||||||
\(321\) | 21.3204 | 1.18999 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.31757 | −0.0733113 | ||||||||
\(324\) | −3.60451 | −0.200250 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 27.0751 | 1.49955 | ||||||||
\(327\) | −4.64270 | −0.256742 | ||||||||
\(328\) | −5.89042 | −0.325244 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.49469 | −0.247425 | ||||||||
\(331\) | 13.3730 | 0.735048 | 0.367524 | − | 0.930014i | \(-0.380206\pi\) | ||||
0.367524 | + | 0.930014i | \(0.380206\pi\) | |||||||
\(332\) | −10.1206 | −0.555441 | ||||||||
\(333\) | 9.21637 | 0.505054 | ||||||||
\(334\) | −5.68348 | −0.310986 | ||||||||
\(335\) | 6.65540 | 0.363624 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.7393 | −1.56553 | −0.782766 | − | 0.622316i | \(-0.786192\pi\) | ||||
−0.782766 | + | 0.622316i | \(0.786192\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −20.0652 | −1.08979 | ||||||||
\(340\) | 0.132422 | 0.00718160 | ||||||||
\(341\) | 15.6857 | 0.849427 | ||||||||
\(342\) | −6.03876 | −0.326539 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.0637558 | 0.00343748 | ||||||||
\(345\) | 1.48008 | 0.0796850 | ||||||||
\(346\) | −2.31140 | −0.124261 | ||||||||
\(347\) | 13.9206 | 0.747296 | 0.373648 | − | 0.927571i | \(-0.378107\pi\) | ||||
0.373648 | + | 0.927571i | \(0.378107\pi\) | |||||||
\(348\) | 4.16201 | 0.223107 | ||||||||
\(349\) | −2.65542 | −0.142141 | −0.0710707 | − | 0.997471i | \(-0.522642\pi\) | ||||
−0.0710707 | + | 0.997471i | \(0.522642\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −11.0172 | −0.587220 | ||||||||
\(353\) | 9.17164 | 0.488157 | 0.244079 | − | 0.969755i | \(-0.421514\pi\) | ||||
0.244079 | + | 0.969755i | \(0.421514\pi\) | |||||||
\(354\) | −34.5250 | −1.83498 | ||||||||
\(355\) | 0.439384 | 0.0233201 | ||||||||
\(356\) | −0.0139657 | −0.000740182 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 34.3273 | 1.81425 | ||||||||
\(359\) | −6.08926 | −0.321379 | −0.160689 | − | 0.987005i | \(-0.551372\pi\) | ||||
−0.160689 | + | 0.987005i | \(0.551372\pi\) | |||||||
\(360\) | −1.23149 | −0.0649050 | ||||||||
\(361\) | −2.31577 | −0.121883 | ||||||||
\(362\) | 33.9106 | 1.78230 | ||||||||
\(363\) | 2.33942 | 0.122788 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.50711 | 0.445282 | ||||||||
\(366\) | −18.3281 | −0.958025 | ||||||||
\(367\) | 2.83281 | 0.147871 | 0.0739357 | − | 0.997263i | \(-0.476444\pi\) | ||||
0.0739357 | + | 0.997263i | \(0.476444\pi\) | |||||||
\(368\) | 8.03622 | 0.418917 | ||||||||
\(369\) | 2.44342 | 0.127200 | ||||||||
\(370\) | 10.3112 | 0.536054 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.89210 | 0.253644 | ||||||||
\(373\) | 10.2417 | 0.530296 | 0.265148 | − | 0.964208i | \(-0.414579\pi\) | ||||
0.265148 | + | 0.964208i | \(0.414579\pi\) | |||||||
\(374\) | 1.61160 | 0.0833338 | ||||||||
\(375\) | 8.64849 | 0.446606 | ||||||||
\(376\) | 5.76151 | 0.297127 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.5731 | 0.645834 | 0.322917 | − | 0.946427i | \(-0.395336\pi\) | ||||
0.322917 | + | 0.946427i | \(0.395336\pi\) | |||||||
\(380\) | −1.67685 | −0.0860206 | ||||||||
\(381\) | 2.48512 | 0.127317 | ||||||||
\(382\) | −9.41198 | −0.481559 | ||||||||
\(383\) | −21.2569 | −1.08618 | −0.543088 | − | 0.839676i | \(-0.682745\pi\) | ||||
−0.543088 | + | 0.839676i | \(0.682745\pi\) | |||||||
\(384\) | 19.6189 | 1.00117 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.8271 | 0.754679 | ||||||||
\(387\) | −0.0264467 | −0.00134436 | ||||||||
\(388\) | 4.50245 | 0.228577 | ||||||||
\(389\) | 14.3161 | 0.725853 | 0.362926 | − | 0.931818i | \(-0.381778\pi\) | ||||
0.362926 | + | 0.931818i | \(0.381778\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.530693 | −0.0268383 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.2855 | −0.871937 | ||||||||
\(394\) | −36.9660 | −1.86232 | ||||||||
\(395\) | −4.65951 | −0.234445 | ||||||||
\(396\) | 1.83328 | 0.0921260 | ||||||||
\(397\) | −25.9730 | −1.30355 | −0.651773 | − | 0.758414i | \(-0.725974\pi\) | ||||
−0.651773 | + | 0.758414i | \(0.725974\pi\) | |||||||
\(398\) | −10.3101 | −0.516799 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 22.5347 | 1.12673 | ||||||||
\(401\) | 25.8931 | 1.29304 | 0.646519 | − | 0.762898i | \(-0.276224\pi\) | ||||
0.646519 | + | 0.762898i | \(0.276224\pi\) | |||||||
\(402\) | 25.2618 | 1.25994 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −12.3299 | −0.613437 | ||||||||
\(405\) | −3.39422 | −0.168660 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 31.1461 | 1.54385 | ||||||||
\(408\) | −1.01987 | −0.0504909 | ||||||||
\(409\) | −7.88925 | −0.390098 | −0.195049 | − | 0.980793i | \(-0.562487\pi\) | ||||
−0.195049 | + | 0.980793i | \(0.562487\pi\) | |||||||
\(410\) | 2.73368 | 0.135007 | ||||||||
\(411\) | −13.3865 | −0.660307 | ||||||||
\(412\) | 10.7241 | 0.528338 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.43231 | −0.119542 | ||||||||
\(415\) | −9.53020 | −0.467819 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.1177 | 0.544438 | ||||||||
\(418\) | −20.4076 | −0.998166 | ||||||||
\(419\) | −8.88956 | −0.434283 | −0.217142 | − | 0.976140i | \(-0.569673\pi\) | ||||
−0.217142 | + | 0.976140i | \(0.569673\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.1179 | −0.883014 | −0.441507 | − | 0.897258i | \(-0.645556\pi\) | ||||
−0.441507 | + | 0.897258i | \(0.645556\pi\) | |||||||
\(422\) | −21.5423 | −1.04866 | ||||||||
\(423\) | −2.38995 | −0.116203 | ||||||||
\(424\) | −11.4802 | −0.557528 | ||||||||
\(425\) | −1.48814 | −0.0721852 | ||||||||
\(426\) | 1.66776 | 0.0808032 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −9.72916 | −0.470277 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.0295884 | −0.00142688 | ||||||||
\(431\) | 14.0264 | 0.675627 | 0.337814 | − | 0.941213i | \(-0.390313\pi\) | ||||
0.337814 | + | 0.941213i | \(0.390313\pi\) | |||||||
\(432\) | −27.6090 | −1.32834 | ||||||||
\(433\) | −18.1108 | −0.870349 | −0.435174 | − | 0.900346i | \(-0.643313\pi\) | ||||
−0.435174 | + | 0.900346i | \(0.643313\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.91920 | 0.187911 | ||||||||
\(436\) | 2.11860 | 0.101463 | ||||||||
\(437\) | 6.72012 | 0.321467 | ||||||||
\(438\) | 32.2902 | 1.54289 | ||||||||
\(439\) | −31.6624 | −1.51116 | −0.755581 | − | 0.655055i | \(-0.772645\pi\) | ||||
−0.755581 | + | 0.655055i | \(0.772645\pi\) | |||||||
\(440\) | −4.16171 | −0.198402 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.52503 | −0.167479 | −0.0837396 | − | 0.996488i | \(-0.526686\pi\) | ||||
−0.0837396 | + | 0.996488i | \(0.526686\pi\) | |||||||
\(444\) | 9.71395 | 0.461004 | ||||||||
\(445\) | −0.0131510 | −0.000623417 0 | ||||||||
\(446\) | −24.3553 | −1.15326 | ||||||||
\(447\) | −16.2987 | −0.770902 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.96156 | −0.281343 | −0.140672 | − | 0.990056i | \(-0.544926\pi\) | ||||
−0.140672 | + | 0.990056i | \(0.544926\pi\) | |||||||
\(450\) | −6.82053 | −0.321523 | ||||||||
\(451\) | 8.25737 | 0.388824 | ||||||||
\(452\) | 9.15633 | 0.430678 | ||||||||
\(453\) | −16.4663 | −0.773654 | ||||||||
\(454\) | −27.2246 | −1.27771 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 12.9145 | 0.604776 | ||||||||
\(457\) | 27.0351 | 1.26465 | 0.632325 | − | 0.774703i | \(-0.282101\pi\) | ||||
0.632325 | + | 0.774703i | \(0.282101\pi\) | |||||||
\(458\) | 24.6116 | 1.15002 | ||||||||
\(459\) | 1.82324 | 0.0851014 | ||||||||
\(460\) | −0.675407 | −0.0314910 | ||||||||
\(461\) | 27.0280 | 1.25882 | 0.629409 | − | 0.777074i | \(-0.283297\pi\) | ||||
0.629409 | + | 0.777074i | \(0.283297\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.1949 | −0.892063 | −0.446032 | − | 0.895017i | \(-0.647163\pi\) | ||||
−0.446032 | + | 0.895017i | \(0.647163\pi\) | |||||||
\(464\) | 21.2796 | 0.987880 | ||||||||
\(465\) | 4.60670 | 0.213631 | ||||||||
\(466\) | −17.5035 | −0.810835 | ||||||||
\(467\) | −18.7331 | −0.866863 | −0.433432 | − | 0.901186i | \(-0.642697\pi\) | ||||
−0.433432 | + | 0.901186i | \(0.642697\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2.67385 | −0.123336 | ||||||||
\(471\) | 31.7435 | 1.46266 | ||||||||
\(472\) | −31.9673 | −1.47141 | ||||||||
\(473\) | −0.0893748 | −0.00410946 | ||||||||
\(474\) | −17.6860 | −0.812344 | ||||||||
\(475\) | 18.8441 | 0.864629 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.76214 | 0.218043 | ||||||||
\(478\) | −4.24865 | −0.194329 | ||||||||
\(479\) | 34.7686 | 1.58862 | 0.794308 | − | 0.607515i | \(-0.207833\pi\) | ||||
0.794308 | + | 0.607515i | \(0.207833\pi\) | |||||||
\(480\) | −3.23564 | −0.147686 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 36.6217 | 1.66807 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.06755 | −0.0485249 | ||||||||
\(485\) | 4.23978 | 0.192518 | ||||||||
\(486\) | 14.7738 | 0.670153 | ||||||||
\(487\) | 25.0825 | 1.13660 | 0.568299 | − | 0.822822i | \(-0.307602\pi\) | ||||
0.568299 | + | 0.822822i | \(0.307602\pi\) | |||||||
\(488\) | −16.9703 | −0.768209 | ||||||||
\(489\) | 24.0188 | 1.08617 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.6116 | −0.569156 | −0.284578 | − | 0.958653i | \(-0.591853\pi\) | ||||
−0.284578 | + | 0.958653i | \(0.591853\pi\) | |||||||
\(492\) | 2.57534 | 0.116105 | ||||||||
\(493\) | −1.40525 | −0.0632894 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.72633 | 0.0775929 | ||||||||
\(496\) | 25.0124 | 1.12309 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −36.1736 | −1.62098 | ||||||||
\(499\) | 21.8571 | 0.978457 | 0.489229 | − | 0.872156i | \(-0.337278\pi\) | ||||
0.489229 | + | 0.872156i | \(0.337278\pi\) | |||||||
\(500\) | −3.94656 | −0.176496 | ||||||||
\(501\) | −5.04191 | −0.225256 | ||||||||
\(502\) | 32.3793 | 1.44516 | ||||||||
\(503\) | 37.0022 | 1.64985 | 0.824923 | − | 0.565246i | \(-0.191219\pi\) | ||||
0.824923 | + | 0.565246i | \(0.191219\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.6106 | −0.516665 | ||||||||
\(506\) | −8.21981 | −0.365415 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.13404 | −0.0503147 | ||||||||
\(509\) | 1.79789 | 0.0796901 | 0.0398450 | − | 0.999206i | \(-0.487314\pi\) | ||||
0.0398450 | + | 0.999206i | \(0.487314\pi\) | |||||||
\(510\) | 0.473309 | 0.0209585 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 3.77891 | 0.167006 | ||||||||
\(513\) | −23.0875 | −1.01934 | ||||||||
\(514\) | 7.02228 | 0.309739 | ||||||||
\(515\) | 10.0985 | 0.444991 | ||||||||
\(516\) | −0.0278746 | −0.00122711 | ||||||||
\(517\) | −8.07665 | −0.355211 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.05048 | −0.0900061 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.06094 | −0.353156 | −0.176578 | − | 0.984287i | \(-0.556503\pi\) | ||||
−0.176578 | + | 0.984287i | \(0.556503\pi\) | |||||||
\(522\) | −6.44066 | −0.281900 | ||||||||
\(523\) | 10.4616 | 0.457455 | 0.228727 | − | 0.973490i | \(-0.426544\pi\) | ||||
0.228727 | + | 0.973490i | \(0.426544\pi\) | |||||||
\(524\) | 7.88788 | 0.344584 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 34.6626 | 1.51136 | ||||||||
\(527\) | −1.65176 | −0.0719519 | ||||||||
\(528\) | −21.6494 | −0.942171 | ||||||||
\(529\) | −20.2932 | −0.882315 | ||||||||
\(530\) | 5.32784 | 0.231427 | ||||||||
\(531\) | 13.2605 | 0.575455 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −0.0499169 | −0.00216012 | ||||||||
\(535\) | −9.16157 | −0.396089 | ||||||||
\(536\) | 23.3903 | 1.01031 | ||||||||
\(537\) | 30.4524 | 1.31412 | ||||||||
\(538\) | 50.2545 | 2.16662 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.32041 | 0.0998546 | ||||||||
\(541\) | −16.9634 | −0.729314 | −0.364657 | − | 0.931142i | \(-0.618814\pi\) | ||||
−0.364657 | + | 0.931142i | \(0.618814\pi\) | |||||||
\(542\) | −1.08677 | −0.0466806 | ||||||||
\(543\) | 30.0827 | 1.29097 | ||||||||
\(544\) | 1.16016 | 0.0497413 | ||||||||
\(545\) | 1.99500 | 0.0854566 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 45.3373 | 1.93848 | 0.969242 | − | 0.246110i | \(-0.0791525\pi\) | ||||
0.969242 | + | 0.246110i | \(0.0791525\pi\) | |||||||
\(548\) | 6.10866 | 0.260949 | ||||||||
\(549\) | 7.03950 | 0.300438 | ||||||||
\(550\) | −23.0495 | −0.982833 | ||||||||
\(551\) | 17.7946 | 0.758076 | ||||||||
\(552\) | 5.20173 | 0.221400 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 25.1320 | 1.06776 | ||||||||
\(555\) | 9.14725 | 0.388279 | ||||||||
\(556\) | −5.07335 | −0.215158 | ||||||||
\(557\) | 25.1006 | 1.06355 | 0.531774 | − | 0.846886i | \(-0.321526\pi\) | ||||
0.531774 | + | 0.846886i | \(0.321526\pi\) | |||||||
\(558\) | −7.57047 | −0.320484 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.42968 | 0.0603611 | ||||||||
\(562\) | 23.8260 | 1.00504 | ||||||||
\(563\) | 22.9222 | 0.966054 | 0.483027 | − | 0.875605i | \(-0.339537\pi\) | ||||
0.483027 | + | 0.875605i | \(0.339537\pi\) | |||||||
\(564\) | −2.51898 | −0.106068 | ||||||||
\(565\) | 8.62216 | 0.362737 | ||||||||
\(566\) | 1.79733 | 0.0755474 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.54421 | 0.0647935 | ||||||||
\(569\) | 8.46758 | 0.354979 | 0.177490 | − | 0.984123i | \(-0.443202\pi\) | ||||
0.177490 | + | 0.984123i | \(0.443202\pi\) | |||||||
\(570\) | −5.99347 | −0.251039 | ||||||||
\(571\) | −37.4312 | −1.56645 | −0.783224 | − | 0.621739i | \(-0.786426\pi\) | ||||
−0.783224 | + | 0.621739i | \(0.786426\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.34953 | −0.348807 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.59010 | 0.316529 | ||||||||
\(576\) | −3.53771 | −0.147404 | ||||||||
\(577\) | −16.9867 | −0.707165 | −0.353582 | − | 0.935403i | \(-0.615037\pi\) | ||||
−0.353582 | + | 0.935403i | \(0.615037\pi\) | |||||||
\(578\) | 27.5579 | 1.14626 | ||||||||
\(579\) | 13.1534 | 0.546636 | ||||||||
\(580\) | −1.78845 | −0.0742613 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 16.0928 | 0.667070 | ||||||||
\(583\) | 16.0933 | 0.666516 | ||||||||
\(584\) | 29.8981 | 1.23719 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −19.8092 | −0.818310 | ||||||||
\(587\) | −20.3458 | −0.839761 | −0.419881 | − | 0.907579i | \(-0.637928\pi\) | ||||
−0.419881 | + | 0.907579i | \(0.637928\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.9161 | 0.861834 | ||||||||
\(590\) | 14.8357 | 0.610775 | ||||||||
\(591\) | −32.7932 | −1.34893 | ||||||||
\(592\) | 49.6656 | 2.04124 | ||||||||
\(593\) | −24.0395 | −0.987183 | −0.493591 | − | 0.869694i | \(-0.664316\pi\) | ||||
−0.493591 | + | 0.869694i | \(0.664316\pi\) | |||||||
\(594\) | 28.2398 | 1.15869 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.43758 | 0.304655 | ||||||||
\(597\) | −9.14628 | −0.374332 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 34.8604 | 1.42436 | 0.712178 | − | 0.701999i | \(-0.247709\pi\) | ||||
0.712178 | + | 0.701999i | \(0.247709\pi\) | |||||||
\(600\) | 14.5864 | 0.595486 | ||||||||
\(601\) | 1.10866 | 0.0452230 | 0.0226115 | − | 0.999744i | \(-0.492802\pi\) | ||||
0.0226115 | + | 0.999744i | \(0.492802\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.70260 | −0.395121 | ||||||||
\(604\) | 7.51406 | 0.305743 | ||||||||
\(605\) | −1.00527 | −0.0408700 | ||||||||
\(606\) | −44.0701 | −1.79023 | ||||||||
\(607\) | −2.68151 | −0.108839 | −0.0544196 | − | 0.998518i | \(-0.517331\pi\) | ||||
−0.0544196 | + | 0.998518i | \(0.517331\pi\) | |||||||
\(608\) | −14.6910 | −0.595797 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.87573 | 0.318879 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −0.193052 | −0.00780366 | ||||||||
\(613\) | 11.9915 | 0.484332 | 0.242166 | − | 0.970235i | \(-0.422142\pi\) | ||||
0.242166 | + | 0.970235i | \(0.422142\pi\) | |||||||
\(614\) | 34.9402 | 1.41007 | ||||||||
\(615\) | 2.42510 | 0.0977893 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.9660 | −0.964834 | −0.482417 | − | 0.875942i | \(-0.660241\pi\) | ||||
−0.482417 | + | 0.875942i | \(0.660241\pi\) | |||||||
\(618\) | 38.3305 | 1.54188 | ||||||||
\(619\) | 8.67800 | 0.348798 | 0.174399 | − | 0.984675i | \(-0.444202\pi\) | ||||
0.174399 | + | 0.984675i | \(0.444202\pi\) | |||||||
\(620\) | −2.10218 | −0.0844255 | ||||||||
\(621\) | −9.29925 | −0.373166 | ||||||||
\(622\) | 20.6828 | 0.829305 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.3508 | 0.774032 | ||||||||
\(626\) | −35.4580 | −1.41719 | ||||||||
\(627\) | −18.1039 | −0.723000 | ||||||||
\(628\) | −14.4855 | −0.578034 | ||||||||
\(629\) | −3.27980 | −0.130774 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.2789 | −0.847098 | −0.423549 | − | 0.905873i | \(-0.639216\pi\) | ||||
−0.423549 | + | 0.905873i | \(0.639216\pi\) | |||||||
\(632\) | −16.3758 | −0.651393 | ||||||||
\(633\) | −19.1105 | −0.759576 | ||||||||
\(634\) | −20.1082 | −0.798597 | ||||||||
\(635\) | −1.06788 | −0.0423775 | ||||||||
\(636\) | 5.01924 | 0.199026 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −21.7657 | −0.861713 | ||||||||
\(639\) | −0.640557 | −0.0253400 | ||||||||
\(640\) | −8.43040 | −0.333241 | ||||||||
\(641\) | 23.7425 | 0.937772 | 0.468886 | − | 0.883259i | \(-0.344656\pi\) | ||||
0.468886 | + | 0.883259i | \(0.344656\pi\) | |||||||
\(642\) | −34.7744 | −1.37244 | ||||||||
\(643\) | 0.0581552 | 0.00229342 | 0.00114671 | − | 0.999999i | \(-0.499635\pi\) | ||||
0.00114671 | + | 0.999999i | \(0.499635\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.0262484 | −0.00103353 | ||||||||
\(646\) | 2.14900 | 0.0845511 | ||||||||
\(647\) | 37.9906 | 1.49356 | 0.746782 | − | 0.665069i | \(-0.231598\pi\) | ||||
0.746782 | + | 0.665069i | \(0.231598\pi\) | |||||||
\(648\) | −11.9289 | −0.468613 | ||||||||
\(649\) | 44.8127 | 1.75905 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.9605 | −0.429246 | ||||||||
\(653\) | 6.02234 | 0.235672 | 0.117836 | − | 0.993033i | \(-0.462404\pi\) | ||||
0.117836 | + | 0.993033i | \(0.462404\pi\) | |||||||
\(654\) | 7.57240 | 0.296104 | ||||||||
\(655\) | 7.42771 | 0.290225 | ||||||||
\(656\) | 13.1672 | 0.514094 | ||||||||
\(657\) | −12.4021 | −0.483852 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.5808 | 1.19126 | 0.595630 | − | 0.803259i | \(-0.296902\pi\) | ||||
0.595630 | + | 0.803259i | \(0.296902\pi\) | |||||||
\(660\) | 1.81953 | 0.0708253 | ||||||||
\(661\) | 50.2882 | 1.95598 | 0.977992 | − | 0.208640i | \(-0.0669038\pi\) | ||||
0.977992 | + | 0.208640i | \(0.0669038\pi\) | |||||||
\(662\) | −21.8119 | −0.847743 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −33.4937 | −1.29981 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −15.0322 | −0.582487 | ||||||||
\(667\) | 7.16736 | 0.277521 | ||||||||
\(668\) | 2.30078 | 0.0890197 | ||||||||
\(669\) | −21.6060 | −0.835337 | ||||||||
\(670\) | −10.8552 | −0.419373 | ||||||||
\(671\) | 23.7895 | 0.918382 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.0095 | 0.385837 | 0.192918 | − | 0.981215i | \(-0.438205\pi\) | ||||
0.192918 | + | 0.981215i | \(0.438205\pi\) | |||||||
\(674\) | 46.8749 | 1.80555 | ||||||||
\(675\) | −26.0764 | −1.00368 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −40.9889 | −1.57533 | −0.787665 | − | 0.616104i | \(-0.788710\pi\) | ||||
−0.787665 | + | 0.616104i | \(0.788710\pi\) | |||||||
\(678\) | 32.7270 | 1.25687 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.438245 | 0.0168059 | ||||||||
\(681\) | −24.1514 | −0.925485 | ||||||||
\(682\) | −25.5839 | −0.979657 | ||||||||
\(683\) | 26.1325 | 0.999932 | 0.499966 | − | 0.866045i | \(-0.333346\pi\) | ||||
0.499966 | + | 0.866045i | \(0.333346\pi\) | |||||||
\(684\) | 2.44460 | 0.0934717 | ||||||||
\(685\) | 5.75229 | 0.219784 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.8334 | 0.832996 | ||||||||
\(688\) | −0.142517 | −0.00543343 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −2.41407 | −0.0919020 | ||||||||
\(691\) | 34.7107 | 1.32046 | 0.660229 | − | 0.751064i | \(-0.270459\pi\) | ||||
0.660229 | + | 0.751064i | \(0.270459\pi\) | |||||||
\(692\) | 0.935695 | 0.0355698 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −22.7049 | −0.861867 | ||||||||
\(695\) | −4.77738 | −0.181216 | ||||||||
\(696\) | 13.7740 | 0.522101 | ||||||||
\(697\) | −0.869533 | −0.0329359 | ||||||||
\(698\) | 4.33108 | 0.163934 | ||||||||
\(699\) | −15.5277 | −0.587311 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 48.3337 | 1.82554 | 0.912769 | − | 0.408475i | \(-0.133939\pi\) | ||||
0.912769 | + | 0.408475i | \(0.133939\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 41.5319 | 1.56640 | ||||||||
\(704\) | −11.9554 | −0.450587 | ||||||||
\(705\) | −2.37202 | −0.0893355 | ||||||||
\(706\) | −14.9593 | −0.562999 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 13.9764 | 0.525264 | ||||||||
\(709\) | 11.5080 | 0.432191 | 0.216095 | − | 0.976372i | \(-0.430668\pi\) | ||||
0.216095 | + | 0.976372i | \(0.430668\pi\) | |||||||
\(710\) | −0.716650 | −0.0268954 | ||||||||
\(711\) | 6.79288 | 0.254753 | ||||||||
\(712\) | −0.0462189 | −0.00173213 | ||||||||
\(713\) | 8.42466 | 0.315506 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −13.8963 | −0.519330 | ||||||||
\(717\) | −3.76905 | −0.140758 | ||||||||
\(718\) | 9.93179 | 0.370651 | ||||||||
\(719\) | −0.0753591 | −0.00281042 | −0.00140521 | − | 0.999999i | \(-0.500447\pi\) | ||||
−0.00140521 | + | 0.999999i | \(0.500447\pi\) | |||||||
\(720\) | 2.75282 | 0.102591 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 3.77710 | 0.140569 | ||||||||
\(723\) | 32.4878 | 1.20823 | ||||||||
\(724\) | −13.7276 | −0.510183 | ||||||||
\(725\) | 20.0983 | 0.746431 | ||||||||
\(726\) | −3.81568 | −0.141613 | ||||||||
\(727\) | −13.0961 | −0.485708 | −0.242854 | − | 0.970063i | \(-0.578084\pi\) | ||||
−0.242854 | + | 0.970063i | \(0.578084\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.4835 | 1.09198 | ||||||||
\(730\) | −13.8754 | −0.513551 | ||||||||
\(731\) | 0.00941152 | 0.000348098 0 | ||||||||
\(732\) | 7.41955 | 0.274234 | ||||||||
\(733\) | 21.9965 | 0.812459 | 0.406230 | − | 0.913771i | \(-0.366843\pi\) | ||||
0.406230 | + | 0.913771i | \(0.366843\pi\) | |||||||
\(734\) | −4.62041 | −0.170542 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.91727 | −0.218113 | ||||||||
\(737\) | −32.7892 | −1.20781 | ||||||||
\(738\) | −3.98531 | −0.146701 | ||||||||
\(739\) | −40.4642 | −1.48850 | −0.744249 | − | 0.667902i | \(-0.767193\pi\) | ||||
−0.744249 | + | 0.667902i | \(0.767193\pi\) | |||||||
\(740\) | −4.17416 | −0.153445 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.3064 | −0.488165 | −0.244083 | − | 0.969754i | \(-0.578487\pi\) | ||||
−0.244083 | + | 0.969754i | \(0.578487\pi\) | |||||||
\(744\) | 16.1902 | 0.593561 | ||||||||
\(745\) | 7.00368 | 0.256595 | ||||||||
\(746\) | −16.7046 | −0.611599 | ||||||||
\(747\) | 13.8936 | 0.508341 | ||||||||
\(748\) | −0.652405 | −0.0238543 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −14.1060 | −0.515078 | ||||||||
\(751\) | 49.9077 | 1.82116 | 0.910580 | − | 0.413334i | \(-0.135636\pi\) | ||||
0.910580 | + | 0.413334i | \(0.135636\pi\) | |||||||
\(752\) | −12.8791 | −0.469651 | ||||||||
\(753\) | 28.7243 | 1.04677 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.07570 | 0.257511 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.0788 | −0.366319 | −0.183160 | − | 0.983083i | \(-0.558632\pi\) | ||||
−0.183160 | + | 0.983083i | \(0.558632\pi\) | |||||||
\(758\) | −20.5071 | −0.744851 | ||||||||
\(759\) | −7.29194 | −0.264681 | ||||||||
\(760\) | −5.54946 | −0.201300 | ||||||||
\(761\) | −28.2853 | −1.02534 | −0.512671 | − | 0.858585i | \(-0.671344\pi\) | ||||
−0.512671 | + | 0.858585i | \(0.671344\pi\) | |||||||
\(762\) | −4.05332 | −0.146836 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 3.81014 | 0.137846 | ||||||||
\(765\) | −0.181790 | −0.00657262 | ||||||||
\(766\) | 34.6707 | 1.25270 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −20.7047 | −0.747116 | ||||||||
\(769\) | 21.7382 | 0.783901 | 0.391950 | − | 0.919986i | \(-0.371800\pi\) | ||||
0.391950 | + | 0.919986i | \(0.371800\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.22959 | 0.224353 | ||||||||
\(772\) | −6.00228 | −0.216027 | ||||||||
\(773\) | 6.34043 | 0.228050 | 0.114025 | − | 0.993478i | \(-0.463626\pi\) | ||||
0.114025 | + | 0.993478i | \(0.463626\pi\) | |||||||
\(774\) | 0.0431355 | 0.00155047 | ||||||||
\(775\) | 23.6239 | 0.848595 | ||||||||
\(776\) | 14.9006 | 0.534902 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −23.3500 | −0.837137 | ||||||||
\(779\) | 11.0108 | 0.394504 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.16471 | −0.0774596 | ||||||||
\(782\) | 0.865579 | 0.0309530 | ||||||||
\(783\) | −24.6240 | −0.879991 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13.6404 | −0.486848 | ||||||||
\(786\) | 28.1932 | 1.00562 | ||||||||
\(787\) | −7.69793 | −0.274402 | −0.137201 | − | 0.990543i | \(-0.543811\pi\) | ||||
−0.137201 | + | 0.990543i | \(0.543811\pi\) | |||||||
\(788\) | 14.9645 | 0.533089 | ||||||||
\(789\) | 30.7498 | 1.09472 | ||||||||
\(790\) | 7.59981 | 0.270389 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 6.06717 | 0.215587 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 42.3628 | 1.50340 | ||||||||
\(795\) | 4.72642 | 0.167629 | ||||||||
\(796\) | 4.17372 | 0.147934 | ||||||||
\(797\) | −27.1989 | −0.963433 | −0.481716 | − | 0.876327i | \(-0.659986\pi\) | ||||
−0.481716 | + | 0.876327i | \(0.659986\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.850503 | 0.0300886 | ||||||||
\(800\) | −16.5928 | −0.586645 | ||||||||
\(801\) | 0.0191722 | 0.000677417 0 | ||||||||
\(802\) | −42.2325 | −1.49128 | ||||||||
\(803\) | −41.9120 | −1.47904 | ||||||||
\(804\) | −10.2264 | −0.360658 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 44.5816 | 1.56935 | ||||||||
\(808\) | −40.8053 | −1.43553 | ||||||||
\(809\) | 6.55072 | 0.230311 | 0.115156 | − | 0.993347i | \(-0.463263\pi\) | ||||
0.115156 | + | 0.993347i | \(0.463263\pi\) | |||||||
\(810\) | 5.53610 | 0.194519 | ||||||||
\(811\) | −6.35691 | −0.223221 | −0.111611 | − | 0.993752i | \(-0.535601\pi\) | ||||
−0.111611 | + | 0.993752i | \(0.535601\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.964090 | −0.0338121 | ||||||||
\(814\) | −50.8003 | −1.78055 | ||||||||
\(815\) | −10.3211 | −0.361531 | ||||||||
\(816\) | 2.27977 | 0.0798080 | ||||||||
\(817\) | −0.119177 | −0.00416948 | ||||||||
\(818\) | 12.8676 | 0.449906 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.10664 | −0.0386457 | ||||||||
\(821\) | 42.3383 | 1.47762 | 0.738809 | − | 0.673915i | \(-0.235388\pi\) | ||||
0.738809 | + | 0.673915i | \(0.235388\pi\) | |||||||
\(822\) | 21.8338 | 0.761543 | ||||||||
\(823\) | 30.0749 | 1.04835 | 0.524173 | − | 0.851612i | \(-0.324375\pi\) | ||||
0.524173 | + | 0.851612i | \(0.324375\pi\) | |||||||
\(824\) | 35.4908 | 1.23638 | ||||||||
\(825\) | −20.4476 | −0.711894 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.4926 | 0.851693 | 0.425846 | − | 0.904795i | \(-0.359976\pi\) | ||||
0.425846 | + | 0.904795i | \(0.359976\pi\) | |||||||
\(828\) | 0.984644 | 0.0342187 | ||||||||
\(829\) | 56.7272 | 1.97022 | 0.985109 | − | 0.171929i | \(-0.0550001\pi\) | ||||
0.985109 | + | 0.171929i | \(0.0550001\pi\) | |||||||
\(830\) | 15.5441 | 0.539543 | ||||||||
\(831\) | 22.2950 | 0.773406 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −18.1334 | −0.627908 | ||||||||
\(835\) | 2.16655 | 0.0749766 | ||||||||
\(836\) | 8.26135 | 0.285725 | ||||||||
\(837\) | −28.9436 | −1.00044 | ||||||||
\(838\) | 14.4992 | 0.500866 | ||||||||
\(839\) | −30.0186 | −1.03636 | −0.518179 | − | 0.855272i | \(-0.673390\pi\) | ||||
−0.518179 | + | 0.855272i | \(0.673390\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.0211 | −0.345556 | ||||||||
\(842\) | 29.5510 | 1.01839 | ||||||||
\(843\) | 21.1365 | 0.727979 | ||||||||
\(844\) | 8.72071 | 0.300179 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.89809 | 0.134019 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 25.6624 | 0.881252 | ||||||||
\(849\) | 1.59444 | 0.0547211 | ||||||||
\(850\) | 2.42720 | 0.0832523 | ||||||||
\(851\) | 16.7283 | 0.573439 | ||||||||
\(852\) | −0.675139 | −0.0231299 | ||||||||
\(853\) | −30.2869 | −1.03700 | −0.518501 | − | 0.855077i | \(-0.673510\pi\) | ||||
−0.518501 | + | 0.855077i | \(0.673510\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.30199 | 0.0787263 | ||||||||
\(856\) | −32.1982 | −1.10051 | ||||||||
\(857\) | −28.4632 | −0.972283 | −0.486142 | − | 0.873880i | \(-0.661596\pi\) | ||||
−0.486142 | + | 0.873880i | \(0.661596\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 48.9603 | 1.67050 | 0.835251 | − | 0.549868i | \(-0.185322\pi\) | ||||
0.835251 | + | 0.549868i | \(0.185322\pi\) | |||||||
\(860\) | 0.0119779 | 0.000408444 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −22.8775 | −0.779212 | ||||||||
\(863\) | 24.5352 | 0.835187 | 0.417594 | − | 0.908634i | \(-0.362874\pi\) | ||||
0.417594 | + | 0.908634i | \(0.362874\pi\) | |||||||
\(864\) | 20.3292 | 0.691615 | ||||||||
\(865\) | 0.881108 | 0.0299586 | ||||||||
\(866\) | 29.5393 | 1.00379 | ||||||||
\(867\) | 24.4471 | 0.830266 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 22.9560 | 0.778730 | ||||||||
\(870\) | −6.39235 | −0.216721 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 7.01141 | 0.237436 | ||||||||
\(873\) | −6.18098 | −0.209194 | ||||||||
\(874\) | −10.9607 | −0.370753 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −13.0717 | −0.441651 | ||||||||
\(877\) | −45.6733 | −1.54228 | −0.771139 | − | 0.636666i | \(-0.780313\pi\) | ||||
−0.771139 | + | 0.636666i | \(0.780313\pi\) | |||||||
\(878\) | 51.6424 | 1.74285 | ||||||||
\(879\) | −17.5731 | −0.592726 | ||||||||
\(880\) | 9.30294 | 0.313602 | ||||||||
\(881\) | −37.0156 | −1.24709 | −0.623543 | − | 0.781789i | \(-0.714308\pi\) | ||||
−0.623543 | + | 0.781789i | \(0.714308\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.5124 | 0.488381 | 0.244190 | − | 0.969727i | \(-0.421478\pi\) | ||||
0.244190 | + | 0.969727i | \(0.421478\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.1610 | 0.442402 | ||||||||
\(886\) | 5.74944 | 0.193156 | ||||||||
\(887\) | −2.47725 | −0.0831779 | −0.0415890 | − | 0.999135i | \(-0.513242\pi\) | ||||
−0.0415890 | + | 0.999135i | \(0.513242\pi\) | |||||||
\(888\) | 32.1479 | 1.07881 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.0214497 | 0.000718996 0 | ||||||||
\(891\) | 16.7224 | 0.560220 | ||||||||
\(892\) | 9.85947 | 0.330120 | ||||||||
\(893\) | −10.7699 | −0.360399 | ||||||||
\(894\) | 26.5837 | 0.889093 | ||||||||
\(895\) | −13.0856 | −0.437404 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.72351 | 0.324478 | ||||||||
\(899\) | 22.3081 | 0.744018 | ||||||||
\(900\) | 2.76108 | 0.0920358 | ||||||||
\(901\) | −1.69469 | −0.0564582 | ||||||||
\(902\) | −13.4681 | −0.448437 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 30.3025 | 1.00784 | ||||||||
\(905\) | −12.9268 | −0.429700 | ||||||||
\(906\) | 26.8571 | 0.892267 | ||||||||
\(907\) | 48.5987 | 1.61369 | 0.806847 | − | 0.590760i | \(-0.201172\pi\) | ||||
0.806847 | + | 0.590760i | \(0.201172\pi\) | |||||||
\(908\) | 11.0210 | 0.365745 | ||||||||
\(909\) | 16.9266 | 0.561419 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.13289 | 0.0706658 | 0.0353329 | − | 0.999376i | \(-0.488751\pi\) | ||||
0.0353329 | + | 0.999376i | \(0.488751\pi\) | |||||||
\(912\) | −28.8686 | −0.955933 | ||||||||
\(913\) | 46.9525 | 1.55390 | ||||||||
\(914\) | −44.0952 | −1.45854 | ||||||||
\(915\) | 6.98670 | 0.230973 | ||||||||
\(916\) | −9.96323 | −0.329194 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −2.97376 | −0.0981488 | ||||||||
\(919\) | −57.8351 | −1.90780 | −0.953902 | − | 0.300118i | \(-0.902974\pi\) | ||||
−0.953902 | + | 0.300118i | \(0.902974\pi\) | |||||||
\(920\) | −2.23523 | −0.0736932 | ||||||||
\(921\) | 30.9960 | 1.02135 | ||||||||
\(922\) | −44.0836 | −1.45182 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 46.9085 | 1.54234 | ||||||||
\(926\) | 31.3076 | 1.02883 | ||||||||
\(927\) | −14.7221 | −0.483536 | ||||||||
\(928\) | −15.6687 | −0.514350 | ||||||||
\(929\) | −40.3415 | −1.32356 | −0.661781 | − | 0.749697i | \(-0.730199\pi\) | ||||
−0.661781 | + | 0.749697i | \(0.730199\pi\) | |||||||
\(930\) | −7.51369 | −0.246384 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 7.08575 | 0.232101 | ||||||||
\(933\) | 18.3481 | 0.600689 | ||||||||
\(934\) | 30.5543 | 0.999767 | ||||||||
\(935\) | −0.614345 | −0.0200912 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.6687 | −1.26325 | −0.631625 | − | 0.775274i | \(-0.717612\pi\) | ||||
−0.631625 | + | 0.775274i | \(0.717612\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −31.4554 | −1.02651 | ||||||||
\(940\) | 1.08242 | 0.0353048 | ||||||||
\(941\) | −24.9826 | −0.814410 | −0.407205 | − | 0.913337i | \(-0.633497\pi\) | ||||
−0.407205 | + | 0.913337i | \(0.633497\pi\) | |||||||
\(942\) | −51.7747 | −1.68691 | ||||||||
\(943\) | 4.43497 | 0.144423 | ||||||||
\(944\) | 71.4586 | 2.32578 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.145773 | 0.00473950 | ||||||||
\(947\) | 47.3287 | 1.53798 | 0.768988 | − | 0.639264i | \(-0.220761\pi\) | ||||
0.768988 | + | 0.639264i | \(0.220761\pi\) | |||||||
\(948\) | 7.15961 | 0.232533 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −30.7354 | −0.997189 | ||||||||
\(951\) | −17.8383 | −0.578446 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15.7277 | −0.509469 | −0.254735 | − | 0.967011i | \(-0.581988\pi\) | ||||
−0.254735 | + | 0.967011i | \(0.581988\pi\) | |||||||
\(954\) | −7.76721 | −0.251473 | ||||||||
\(955\) | 3.58786 | 0.116101 | ||||||||
\(956\) | 1.71993 | 0.0556265 | ||||||||
\(957\) | −19.3088 | −0.624164 | ||||||||
\(958\) | −56.7087 | −1.83218 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.51117 | −0.113323 | ||||||||
\(961\) | −4.77857 | −0.154147 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.3562 | 0.430398 | ||||||||
\(964\) | −14.8251 | −0.477486 | ||||||||
\(965\) | −5.65211 | −0.181948 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.3906 | 1.04161 | 0.520806 | − | 0.853675i | \(-0.325632\pi\) | ||||
0.520806 | + | 0.853675i | \(0.325632\pi\) | |||||||
\(968\) | −3.53300 | −0.113555 | ||||||||
\(969\) | 1.90641 | 0.0612428 | ||||||||
\(970\) | −6.91522 | −0.222034 | ||||||||
\(971\) | 34.5508 | 1.10879 | 0.554395 | − | 0.832254i | \(-0.312950\pi\) | ||||
0.554395 | + | 0.832254i | \(0.312950\pi\) | |||||||
\(972\) | −5.98071 | −0.191831 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −40.9105 | −1.31086 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 37.9348 | 1.21426 | ||||||||
\(977\) | −53.0833 | −1.69828 | −0.849142 | − | 0.528165i | \(-0.822880\pi\) | ||||
−0.849142 | + | 0.528165i | \(0.822880\pi\) | |||||||
\(978\) | −39.1754 | −1.25269 | ||||||||
\(979\) | 0.0647911 | 0.00207073 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.90842 | −0.0928588 | ||||||||
\(982\) | 20.5700 | 0.656416 | ||||||||
\(983\) | −18.1042 | −0.577434 | −0.288717 | − | 0.957414i | \(-0.593229\pi\) | ||||
−0.288717 | + | 0.957414i | \(0.593229\pi\) | |||||||
\(984\) | 8.52297 | 0.271702 | ||||||||
\(985\) | 14.0915 | 0.448993 | ||||||||
\(986\) | 2.29202 | 0.0729927 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.0480026 | −0.00152639 | ||||||||
\(990\) | −2.81571 | −0.0894891 | ||||||||
\(991\) | 28.2373 | 0.896986 | 0.448493 | − | 0.893786i | \(-0.351961\pi\) | ||||
0.448493 | + | 0.893786i | \(0.351961\pi\) | |||||||
\(992\) | −18.4173 | −0.584749 | ||||||||
\(993\) | −19.3497 | −0.614044 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.93023 | 0.124597 | ||||||||
\(996\) | 14.6437 | 0.464004 | ||||||||
\(997\) | 13.2773 | 0.420496 | 0.210248 | − | 0.977648i | \(-0.432573\pi\) | ||||
0.210248 | + | 0.977648i | \(0.432573\pi\) | |||||||
\(998\) | −35.6496 | −1.12847 | ||||||||
\(999\) | −57.4714 | −1.81832 |
(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.cz.1.7 | yes | 36 | |
7.6 | odd | 2 | inner | 8281.2.a.cz.1.8 | yes | 36 | |
13.12 | even | 2 | 8281.2.a.cy.1.29 | ✓ | 36 | ||
91.90 | odd | 2 | 8281.2.a.cy.1.30 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8281.2.a.cy.1.29 | ✓ | 36 | 13.12 | even | 2 | ||
8281.2.a.cy.1.30 | yes | 36 | 91.90 | odd | 2 | ||
8281.2.a.cz.1.7 | yes | 36 | 1.1 | even | 1 | trivial | |
8281.2.a.cz.1.8 | yes | 36 | 7.6 | odd | 2 | inner |