Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6019,2,Mod(1,6019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6019, 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("6019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6019 = 13 \cdot 463 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6019.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: | \(48.0619569766\) |
Analytic rank: | \(1\) |
Dimension: | \(108\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 6019.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.61467 | −1.84885 | −0.924425 | − | 0.381364i | \(-0.875454\pi\) | ||||
−0.924425 | + | 0.381364i | \(0.875454\pi\) | |||||||
\(3\) | 0.516414 | 0.298152 | 0.149076 | − | 0.988826i | \(-0.452370\pi\) | ||||
0.149076 | + | 0.988826i | \(0.452370\pi\) | |||||||
\(4\) | 4.83649 | 2.41825 | ||||||||
\(5\) | −3.96792 | −1.77451 | −0.887253 | − | 0.461283i | \(-0.847389\pi\) | ||||
−0.887253 | + | 0.461283i | \(0.847389\pi\) | |||||||
\(6\) | −1.35025 | −0.551238 | ||||||||
\(7\) | 3.66433 | 1.38499 | 0.692494 | − | 0.721424i | \(-0.256512\pi\) | ||||
0.692494 | + | 0.721424i | \(0.256512\pi\) | |||||||
\(8\) | −7.41648 | −2.62212 | ||||||||
\(9\) | −2.73332 | −0.911105 | ||||||||
\(10\) | 10.3748 | 3.28079 | ||||||||
\(11\) | −4.05913 | −1.22387 | −0.611937 | − | 0.790907i | \(-0.709609\pi\) | ||||
−0.611937 | + | 0.790907i | \(0.709609\pi\) | |||||||
\(12\) | 2.49763 | 0.721004 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −9.58102 | −2.56063 | ||||||||
\(15\) | −2.04909 | −0.529072 | ||||||||
\(16\) | 9.71866 | 2.42966 | ||||||||
\(17\) | 6.83477 | 1.65768 | 0.828838 | − | 0.559489i | \(-0.189002\pi\) | ||||
0.828838 | + | 0.559489i | \(0.189002\pi\) | |||||||
\(18\) | 7.14672 | 1.68450 | ||||||||
\(19\) | 5.65862 | 1.29818 | 0.649088 | − | 0.760713i | \(-0.275151\pi\) | ||||
0.649088 | + | 0.760713i | \(0.275151\pi\) | |||||||
\(20\) | −19.1908 | −4.29119 | ||||||||
\(21\) | 1.89231 | 0.412937 | ||||||||
\(22\) | 10.6133 | 2.26276 | ||||||||
\(23\) | −4.75842 | −0.992199 | −0.496099 | − | 0.868266i | \(-0.665235\pi\) | ||||
−0.496099 | + | 0.868266i | \(0.665235\pi\) | |||||||
\(24\) | −3.82998 | −0.781791 | ||||||||
\(25\) | 10.7444 | 2.14887 | ||||||||
\(26\) | 2.61467 | 0.512779 | ||||||||
\(27\) | −2.96077 | −0.569800 | ||||||||
\(28\) | 17.7225 | 3.34924 | ||||||||
\(29\) | 2.57174 | 0.477559 | 0.238780 | − | 0.971074i | \(-0.423253\pi\) | ||||
0.238780 | + | 0.971074i | \(0.423253\pi\) | |||||||
\(30\) | 5.35769 | 0.978175 | ||||||||
\(31\) | −3.95962 | −0.711169 | −0.355584 | − | 0.934644i | \(-0.615718\pi\) | ||||
−0.355584 | + | 0.934644i | \(0.615718\pi\) | |||||||
\(32\) | −10.5781 | −1.86996 | ||||||||
\(33\) | −2.09619 | −0.364900 | ||||||||
\(34\) | −17.8707 | −3.06479 | ||||||||
\(35\) | −14.5398 | −2.45767 | ||||||||
\(36\) | −13.2197 | −2.20328 | ||||||||
\(37\) | −7.21708 | −1.18648 | −0.593240 | − | 0.805026i | \(-0.702151\pi\) | ||||
−0.593240 | + | 0.805026i | \(0.702151\pi\) | |||||||
\(38\) | −14.7954 | −2.40013 | ||||||||
\(39\) | −0.516414 | −0.0826925 | ||||||||
\(40\) | 29.4280 | 4.65297 | ||||||||
\(41\) | −9.50552 | −1.48451 | −0.742256 | − | 0.670116i | \(-0.766244\pi\) | ||||
−0.742256 | + | 0.670116i | \(0.766244\pi\) | |||||||
\(42\) | −4.94777 | −0.763458 | ||||||||
\(43\) | −5.45391 | −0.831714 | −0.415857 | − | 0.909430i | \(-0.636518\pi\) | ||||
−0.415857 | + | 0.909430i | \(0.636518\pi\) | |||||||
\(44\) | −19.6319 | −2.95963 | ||||||||
\(45\) | 10.8456 | 1.61676 | ||||||||
\(46\) | 12.4417 | 1.83443 | ||||||||
\(47\) | 9.77351 | 1.42561 | 0.712806 | − | 0.701361i | \(-0.247424\pi\) | ||||
0.712806 | + | 0.701361i | \(0.247424\pi\) | |||||||
\(48\) | 5.01885 | 0.724409 | ||||||||
\(49\) | 6.42734 | 0.918192 | ||||||||
\(50\) | −28.0929 | −3.97294 | ||||||||
\(51\) | 3.52957 | 0.494239 | ||||||||
\(52\) | −4.83649 | −0.670700 | ||||||||
\(53\) | 2.55531 | 0.350999 | 0.175500 | − | 0.984479i | \(-0.443846\pi\) | ||||
0.175500 | + | 0.984479i | \(0.443846\pi\) | |||||||
\(54\) | 7.74142 | 1.05347 | ||||||||
\(55\) | 16.1063 | 2.17177 | ||||||||
\(56\) | −27.1765 | −3.63161 | ||||||||
\(57\) | 2.92219 | 0.387054 | ||||||||
\(58\) | −6.72423 | −0.882935 | ||||||||
\(59\) | 1.66855 | 0.217227 | 0.108614 | − | 0.994084i | \(-0.465359\pi\) | ||||
0.108614 | + | 0.994084i | \(0.465359\pi\) | |||||||
\(60\) | −9.91039 | −1.27943 | ||||||||
\(61\) | 6.44218 | 0.824837 | 0.412418 | − | 0.910995i | \(-0.364684\pi\) | ||||
0.412418 | + | 0.910995i | \(0.364684\pi\) | |||||||
\(62\) | 10.3531 | 1.31484 | ||||||||
\(63\) | −10.0158 | −1.26187 | ||||||||
\(64\) | 8.22091 | 1.02761 | ||||||||
\(65\) | 3.96792 | 0.492159 | ||||||||
\(66\) | 5.48085 | 0.674646 | ||||||||
\(67\) | −12.3003 | −1.50272 | −0.751362 | − | 0.659890i | \(-0.770603\pi\) | ||||
−0.751362 | + | 0.659890i | \(0.770603\pi\) | |||||||
\(68\) | 33.0563 | 4.00867 | ||||||||
\(69\) | −2.45732 | −0.295826 | ||||||||
\(70\) | 38.0167 | 4.54386 | ||||||||
\(71\) | 11.6516 | 1.38279 | 0.691397 | − | 0.722475i | \(-0.256996\pi\) | ||||
0.691397 | + | 0.722475i | \(0.256996\pi\) | |||||||
\(72\) | 20.2716 | 2.38903 | ||||||||
\(73\) | 9.66772 | 1.13152 | 0.565761 | − | 0.824570i | \(-0.308583\pi\) | ||||
0.565761 | + | 0.824570i | \(0.308583\pi\) | |||||||
\(74\) | 18.8703 | 2.19362 | ||||||||
\(75\) | 5.54854 | 0.640690 | ||||||||
\(76\) | 27.3678 | 3.13931 | ||||||||
\(77\) | −14.8740 | −1.69505 | ||||||||
\(78\) | 1.35025 | 0.152886 | ||||||||
\(79\) | 17.0304 | 1.91606 | 0.958032 | − | 0.286661i | \(-0.0925453\pi\) | ||||
0.958032 | + | 0.286661i | \(0.0925453\pi\) | |||||||
\(80\) | −38.5628 | −4.31145 | ||||||||
\(81\) | 6.67097 | 0.741219 | ||||||||
\(82\) | 24.8538 | 2.74464 | ||||||||
\(83\) | −5.34508 | −0.586699 | −0.293350 | − | 0.956005i | \(-0.594770\pi\) | ||||
−0.293350 | + | 0.956005i | \(0.594770\pi\) | |||||||
\(84\) | 9.15216 | 0.998583 | ||||||||
\(85\) | −27.1198 | −2.94156 | ||||||||
\(86\) | 14.2602 | 1.53771 | ||||||||
\(87\) | 1.32808 | 0.142385 | ||||||||
\(88\) | 30.1044 | 3.20914 | ||||||||
\(89\) | 1.55773 | 0.165119 | 0.0825597 | − | 0.996586i | \(-0.473690\pi\) | ||||
0.0825597 | + | 0.996586i | \(0.473690\pi\) | |||||||
\(90\) | −28.3576 | −2.98915 | ||||||||
\(91\) | −3.66433 | −0.384127 | ||||||||
\(92\) | −23.0140 | −2.39938 | ||||||||
\(93\) | −2.04480 | −0.212036 | ||||||||
\(94\) | −25.5545 | −2.63574 | ||||||||
\(95\) | −22.4529 | −2.30362 | ||||||||
\(96\) | −5.46268 | −0.557533 | ||||||||
\(97\) | −8.63999 | −0.877258 | −0.438629 | − | 0.898668i | \(-0.644536\pi\) | ||||
−0.438629 | + | 0.898668i | \(0.644536\pi\) | |||||||
\(98\) | −16.8054 | −1.69760 | ||||||||
\(99\) | 11.0949 | 1.11508 | ||||||||
\(100\) | 51.9649 | 5.19649 | ||||||||
\(101\) | 2.63471 | 0.262163 | 0.131082 | − | 0.991372i | \(-0.458155\pi\) | ||||
0.131082 | + | 0.991372i | \(0.458155\pi\) | |||||||
\(102\) | −9.22867 | −0.913774 | ||||||||
\(103\) | −4.04364 | −0.398432 | −0.199216 | − | 0.979956i | \(-0.563839\pi\) | ||||
−0.199216 | + | 0.979956i | \(0.563839\pi\) | |||||||
\(104\) | 7.41648 | 0.727246 | ||||||||
\(105\) | −7.50854 | −0.732759 | ||||||||
\(106\) | −6.68130 | −0.648945 | ||||||||
\(107\) | 6.85131 | 0.662342 | 0.331171 | − | 0.943571i | \(-0.392556\pi\) | ||||
0.331171 | + | 0.943571i | \(0.392556\pi\) | |||||||
\(108\) | −14.3197 | −1.37792 | ||||||||
\(109\) | −8.75770 | −0.838835 | −0.419418 | − | 0.907793i | \(-0.637766\pi\) | ||||
−0.419418 | + | 0.907793i | \(0.637766\pi\) | |||||||
\(110\) | −42.1126 | −4.01528 | ||||||||
\(111\) | −3.72700 | −0.353751 | ||||||||
\(112\) | 35.6124 | 3.36506 | ||||||||
\(113\) | 5.02085 | 0.472322 | 0.236161 | − | 0.971714i | \(-0.424111\pi\) | ||||
0.236161 | + | 0.971714i | \(0.424111\pi\) | |||||||
\(114\) | −7.64056 | −0.715604 | ||||||||
\(115\) | 18.8810 | 1.76066 | ||||||||
\(116\) | 12.4382 | 1.15486 | ||||||||
\(117\) | 2.73332 | 0.252695 | ||||||||
\(118\) | −4.36272 | −0.401620 | ||||||||
\(119\) | 25.0449 | 2.29586 | ||||||||
\(120\) | 15.1970 | 1.38729 | ||||||||
\(121\) | 5.47652 | 0.497866 | ||||||||
\(122\) | −16.8442 | −1.52500 | ||||||||
\(123\) | −4.90879 | −0.442610 | ||||||||
\(124\) | −19.1507 | −1.71978 | ||||||||
\(125\) | −22.7931 | −2.03868 | ||||||||
\(126\) | 26.1880 | 2.33301 | ||||||||
\(127\) | 11.8635 | 1.05272 | 0.526359 | − | 0.850262i | \(-0.323557\pi\) | ||||
0.526359 | + | 0.850262i | \(0.323557\pi\) | |||||||
\(128\) | −0.338753 | −0.0299419 | ||||||||
\(129\) | −2.81648 | −0.247977 | ||||||||
\(130\) | −10.3748 | −0.909929 | ||||||||
\(131\) | −16.0397 | −1.40140 | −0.700699 | − | 0.713457i | \(-0.747129\pi\) | ||||
−0.700699 | + | 0.713457i | \(0.747129\pi\) | |||||||
\(132\) | −10.1382 | −0.882418 | ||||||||
\(133\) | 20.7351 | 1.79796 | ||||||||
\(134\) | 32.1613 | 2.77831 | ||||||||
\(135\) | 11.7481 | 1.01111 | ||||||||
\(136\) | −50.6900 | −4.34663 | ||||||||
\(137\) | −11.3458 | −0.969334 | −0.484667 | − | 0.874699i | \(-0.661059\pi\) | ||||
−0.484667 | + | 0.874699i | \(0.661059\pi\) | |||||||
\(138\) | 6.42506 | 0.546938 | ||||||||
\(139\) | 6.10627 | 0.517927 | 0.258963 | − | 0.965887i | \(-0.416619\pi\) | ||||
0.258963 | + | 0.965887i | \(0.416619\pi\) | |||||||
\(140\) | −70.3214 | −5.94325 | ||||||||
\(141\) | 5.04718 | 0.425049 | ||||||||
\(142\) | −30.4651 | −2.55658 | ||||||||
\(143\) | 4.05913 | 0.339441 | ||||||||
\(144\) | −26.5642 | −2.21368 | ||||||||
\(145\) | −10.2044 | −0.847432 | ||||||||
\(146\) | −25.2779 | −2.09201 | ||||||||
\(147\) | 3.31917 | 0.273761 | ||||||||
\(148\) | −34.9053 | −2.86920 | ||||||||
\(149\) | 3.37099 | 0.276162 | 0.138081 | − | 0.990421i | \(-0.455907\pi\) | ||||
0.138081 | + | 0.990421i | \(0.455907\pi\) | |||||||
\(150\) | −14.5076 | −1.18454 | ||||||||
\(151\) | −5.03260 | −0.409547 | −0.204773 | − | 0.978809i | \(-0.565646\pi\) | ||||
−0.204773 | + | 0.978809i | \(0.565646\pi\) | |||||||
\(152\) | −41.9670 | −3.40397 | ||||||||
\(153\) | −18.6816 | −1.51032 | ||||||||
\(154\) | 38.8906 | 3.13389 | ||||||||
\(155\) | 15.7114 | 1.26197 | ||||||||
\(156\) | −2.49763 | −0.199971 | ||||||||
\(157\) | −0.156318 | −0.0124755 | −0.00623775 | − | 0.999981i | \(-0.501986\pi\) | ||||
−0.00623775 | + | 0.999981i | \(0.501986\pi\) | |||||||
\(158\) | −44.5287 | −3.54251 | ||||||||
\(159\) | 1.31960 | 0.104651 | ||||||||
\(160\) | 41.9730 | 3.31826 | ||||||||
\(161\) | −17.4364 | −1.37418 | ||||||||
\(162\) | −17.4424 | −1.37040 | ||||||||
\(163\) | 16.1465 | 1.26469 | 0.632347 | − | 0.774685i | \(-0.282092\pi\) | ||||
0.632347 | + | 0.774685i | \(0.282092\pi\) | |||||||
\(164\) | −45.9733 | −3.58991 | ||||||||
\(165\) | 8.31751 | 0.647517 | ||||||||
\(166\) | 13.9756 | 1.08472 | ||||||||
\(167\) | 17.1965 | 1.33071 | 0.665354 | − | 0.746528i | \(-0.268281\pi\) | ||||
0.665354 | + | 0.746528i | \(0.268281\pi\) | |||||||
\(168\) | −14.0343 | −1.08277 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 70.9093 | 5.43849 | ||||||||
\(171\) | −15.4668 | −1.18277 | ||||||||
\(172\) | −26.3778 | −2.01129 | ||||||||
\(173\) | 6.29881 | 0.478890 | 0.239445 | − | 0.970910i | \(-0.423035\pi\) | ||||
0.239445 | + | 0.970910i | \(0.423035\pi\) | |||||||
\(174\) | −3.47249 | −0.263249 | ||||||||
\(175\) | 39.3709 | 2.97616 | ||||||||
\(176\) | −39.4493 | −2.97360 | ||||||||
\(177\) | 0.861665 | 0.0647667 | ||||||||
\(178\) | −4.07295 | −0.305281 | ||||||||
\(179\) | −16.7790 | −1.25412 | −0.627062 | − | 0.778969i | \(-0.715743\pi\) | ||||
−0.627062 | + | 0.778969i | \(0.715743\pi\) | |||||||
\(180\) | 52.4545 | 3.90973 | ||||||||
\(181\) | −12.8676 | −0.956438 | −0.478219 | − | 0.878241i | \(-0.658717\pi\) | ||||
−0.478219 | + | 0.878241i | \(0.658717\pi\) | |||||||
\(182\) | 9.58102 | 0.710192 | ||||||||
\(183\) | 3.32683 | 0.245927 | ||||||||
\(184\) | 35.2907 | 2.60167 | ||||||||
\(185\) | 28.6367 | 2.10542 | ||||||||
\(186\) | 5.34648 | 0.392023 | ||||||||
\(187\) | −27.7432 | −2.02879 | ||||||||
\(188\) | 47.2695 | 3.44748 | ||||||||
\(189\) | −10.8492 | −0.789166 | ||||||||
\(190\) | 58.7069 | 4.25905 | ||||||||
\(191\) | 1.64260 | 0.118854 | 0.0594272 | − | 0.998233i | \(-0.481073\pi\) | ||||
0.0594272 | + | 0.998233i | \(0.481073\pi\) | |||||||
\(192\) | 4.24540 | 0.306385 | ||||||||
\(193\) | −10.0442 | −0.722999 | −0.361499 | − | 0.932372i | \(-0.617735\pi\) | ||||
−0.361499 | + | 0.932372i | \(0.617735\pi\) | |||||||
\(194\) | 22.5907 | 1.62192 | ||||||||
\(195\) | 2.04909 | 0.146738 | ||||||||
\(196\) | 31.0858 | 2.22041 | ||||||||
\(197\) | −5.42575 | −0.386569 | −0.193284 | − | 0.981143i | \(-0.561914\pi\) | ||||
−0.193284 | + | 0.981143i | \(0.561914\pi\) | |||||||
\(198\) | −29.0094 | −2.06161 | ||||||||
\(199\) | 20.1230 | 1.42648 | 0.713239 | − | 0.700921i | \(-0.247227\pi\) | ||||
0.713239 | + | 0.700921i | \(0.247227\pi\) | |||||||
\(200\) | −79.6853 | −5.63460 | ||||||||
\(201\) | −6.35206 | −0.448040 | ||||||||
\(202\) | −6.88889 | −0.484701 | ||||||||
\(203\) | 9.42370 | 0.661414 | ||||||||
\(204\) | 17.0708 | 1.19519 | ||||||||
\(205\) | 37.7171 | 2.63428 | ||||||||
\(206\) | 10.5728 | 0.736640 | ||||||||
\(207\) | 13.0063 | 0.903998 | ||||||||
\(208\) | −9.71866 | −0.673868 | ||||||||
\(209\) | −22.9691 | −1.58880 | ||||||||
\(210\) | 19.6323 | 1.35476 | ||||||||
\(211\) | −5.86848 | −0.404003 | −0.202001 | − | 0.979385i | \(-0.564745\pi\) | ||||
−0.202001 | + | 0.979385i | \(0.564745\pi\) | |||||||
\(212\) | 12.3587 | 0.848802 | ||||||||
\(213\) | 6.01707 | 0.412283 | ||||||||
\(214\) | −17.9139 | −1.22457 | ||||||||
\(215\) | 21.6407 | 1.47588 | ||||||||
\(216\) | 21.9585 | 1.49408 | ||||||||
\(217\) | −14.5094 | −0.984960 | ||||||||
\(218\) | 22.8985 | 1.55088 | ||||||||
\(219\) | 4.99255 | 0.337365 | ||||||||
\(220\) | 77.8978 | 5.25187 | ||||||||
\(221\) | −6.83477 | −0.459757 | ||||||||
\(222\) | 9.74487 | 0.654033 | ||||||||
\(223\) | −13.8753 | −0.929161 | −0.464581 | − | 0.885531i | \(-0.653795\pi\) | ||||
−0.464581 | + | 0.885531i | \(0.653795\pi\) | |||||||
\(224\) | −38.7617 | −2.58987 | ||||||||
\(225\) | −29.3677 | −1.95785 | ||||||||
\(226\) | −13.1279 | −0.873253 | ||||||||
\(227\) | −1.13422 | −0.0752811 | −0.0376405 | − | 0.999291i | \(-0.511984\pi\) | ||||
−0.0376405 | + | 0.999291i | \(0.511984\pi\) | |||||||
\(228\) | 14.1331 | 0.935990 | ||||||||
\(229\) | 6.71154 | 0.443511 | 0.221756 | − | 0.975102i | \(-0.428821\pi\) | ||||
0.221756 | + | 0.975102i | \(0.428821\pi\) | |||||||
\(230\) | −49.3676 | −3.25520 | ||||||||
\(231\) | −7.68115 | −0.505382 | ||||||||
\(232\) | −19.0732 | −1.25222 | ||||||||
\(233\) | −4.49394 | −0.294408 | −0.147204 | − | 0.989106i | \(-0.547027\pi\) | ||||
−0.147204 | + | 0.989106i | \(0.547027\pi\) | |||||||
\(234\) | −7.14672 | −0.467195 | ||||||||
\(235\) | −38.7804 | −2.52976 | ||||||||
\(236\) | 8.06995 | 0.525309 | ||||||||
\(237\) | 8.79472 | 0.571278 | ||||||||
\(238\) | −65.4841 | −4.24470 | ||||||||
\(239\) | −15.9542 | −1.03199 | −0.515997 | − | 0.856590i | \(-0.672578\pi\) | ||||
−0.515997 | + | 0.856590i | \(0.672578\pi\) | |||||||
\(240\) | −19.9144 | −1.28547 | ||||||||
\(241\) | 24.6518 | 1.58796 | 0.793980 | − | 0.607944i | \(-0.208006\pi\) | ||||
0.793980 | + | 0.607944i | \(0.208006\pi\) | |||||||
\(242\) | −14.3193 | −0.920479 | ||||||||
\(243\) | 12.3273 | 0.790796 | ||||||||
\(244\) | 31.1575 | 1.99466 | ||||||||
\(245\) | −25.5032 | −1.62934 | ||||||||
\(246\) | 12.8348 | 0.818320 | ||||||||
\(247\) | −5.65862 | −0.360049 | ||||||||
\(248\) | 29.3664 | 1.86477 | ||||||||
\(249\) | −2.76028 | −0.174925 | ||||||||
\(250\) | 59.5964 | 3.76921 | ||||||||
\(251\) | 29.1834 | 1.84204 | 0.921019 | − | 0.389518i | \(-0.127358\pi\) | ||||
0.921019 | + | 0.389518i | \(0.127358\pi\) | |||||||
\(252\) | −48.4412 | −3.05151 | ||||||||
\(253\) | 19.3150 | 1.21433 | ||||||||
\(254\) | −31.0192 | −1.94632 | ||||||||
\(255\) | −14.0051 | −0.877030 | ||||||||
\(256\) | −15.5561 | −0.972256 | ||||||||
\(257\) | −28.7805 | −1.79528 | −0.897641 | − | 0.440728i | \(-0.854720\pi\) | ||||
−0.897641 | + | 0.440728i | \(0.854720\pi\) | |||||||
\(258\) | 7.36416 | 0.458472 | ||||||||
\(259\) | −26.4458 | −1.64326 | ||||||||
\(260\) | 19.1908 | 1.19016 | ||||||||
\(261\) | −7.02937 | −0.435107 | ||||||||
\(262\) | 41.9386 | 2.59098 | ||||||||
\(263\) | 22.3088 | 1.37562 | 0.687810 | − | 0.725890i | \(-0.258572\pi\) | ||||
0.687810 | + | 0.725890i | \(0.258572\pi\) | |||||||
\(264\) | 15.5464 | 0.956813 | ||||||||
\(265\) | −10.1393 | −0.622850 | ||||||||
\(266\) | −54.2153 | −3.32415 | ||||||||
\(267\) | 0.804435 | 0.0492306 | ||||||||
\(268\) | −59.4904 | −3.63395 | ||||||||
\(269\) | 10.8353 | 0.660638 | 0.330319 | − | 0.943869i | \(-0.392844\pi\) | ||||
0.330319 | + | 0.943869i | \(0.392844\pi\) | |||||||
\(270\) | −30.7173 | −1.86940 | ||||||||
\(271\) | −32.4903 | −1.97364 | −0.986822 | − | 0.161812i | \(-0.948266\pi\) | ||||
−0.986822 | + | 0.161812i | \(0.948266\pi\) | |||||||
\(272\) | 66.4248 | 4.02760 | ||||||||
\(273\) | −1.89231 | −0.114528 | ||||||||
\(274\) | 29.6654 | 1.79215 | ||||||||
\(275\) | −43.6127 | −2.62994 | ||||||||
\(276\) | −11.8848 | −0.715380 | ||||||||
\(277\) | −30.5687 | −1.83670 | −0.918349 | − | 0.395772i | \(-0.870477\pi\) | ||||
−0.918349 | + | 0.395772i | \(0.870477\pi\) | |||||||
\(278\) | −15.9659 | −0.957569 | ||||||||
\(279\) | 10.8229 | 0.647950 | ||||||||
\(280\) | 107.834 | 6.44431 | ||||||||
\(281\) | 18.5659 | 1.10755 | 0.553774 | − | 0.832667i | \(-0.313187\pi\) | ||||
0.553774 | + | 0.832667i | \(0.313187\pi\) | |||||||
\(282\) | −13.1967 | −0.785852 | ||||||||
\(283\) | −5.44527 | −0.323688 | −0.161844 | − | 0.986816i | \(-0.551744\pi\) | ||||
−0.161844 | + | 0.986816i | \(0.551744\pi\) | |||||||
\(284\) | 56.3530 | 3.34393 | ||||||||
\(285\) | −11.5950 | −0.686829 | ||||||||
\(286\) | −10.6133 | −0.627576 | ||||||||
\(287\) | −34.8314 | −2.05603 | ||||||||
\(288\) | 28.9133 | 1.70373 | ||||||||
\(289\) | 29.7141 | 1.74789 | ||||||||
\(290\) | 26.6812 | 1.56677 | ||||||||
\(291\) | −4.46181 | −0.261556 | ||||||||
\(292\) | 46.7578 | 2.73630 | ||||||||
\(293\) | −2.81750 | −0.164600 | −0.0823000 | − | 0.996608i | \(-0.526227\pi\) | ||||
−0.0823000 | + | 0.996608i | \(0.526227\pi\) | |||||||
\(294\) | −8.67853 | −0.506142 | ||||||||
\(295\) | −6.62068 | −0.385471 | ||||||||
\(296\) | 53.5253 | 3.11109 | ||||||||
\(297\) | 12.0181 | 0.697363 | ||||||||
\(298\) | −8.81401 | −0.510582 | ||||||||
\(299\) | 4.75842 | 0.275186 | ||||||||
\(300\) | 26.8354 | 1.54935 | ||||||||
\(301\) | −19.9850 | −1.15191 | ||||||||
\(302\) | 13.1586 | 0.757191 | ||||||||
\(303\) | 1.36060 | 0.0781645 | ||||||||
\(304\) | 54.9941 | 3.15413 | ||||||||
\(305\) | −25.5620 | −1.46368 | ||||||||
\(306\) | 48.8462 | 2.79235 | ||||||||
\(307\) | −16.7456 | −0.955721 | −0.477860 | − | 0.878436i | \(-0.658588\pi\) | ||||
−0.477860 | + | 0.878436i | \(0.658588\pi\) | |||||||
\(308\) | −71.9380 | −4.09905 | ||||||||
\(309\) | −2.08819 | −0.118793 | ||||||||
\(310\) | −41.0802 | −2.33320 | ||||||||
\(311\) | −29.3352 | −1.66344 | −0.831722 | − | 0.555192i | \(-0.812645\pi\) | ||||
−0.831722 | + | 0.555192i | \(0.812645\pi\) | |||||||
\(312\) | 3.82998 | 0.216830 | ||||||||
\(313\) | 20.3749 | 1.15166 | 0.575830 | − | 0.817570i | \(-0.304679\pi\) | ||||
0.575830 | + | 0.817570i | \(0.304679\pi\) | |||||||
\(314\) | 0.408719 | 0.0230653 | ||||||||
\(315\) | 39.7418 | 2.23920 | ||||||||
\(316\) | 82.3671 | 4.63351 | ||||||||
\(317\) | −2.12437 | −0.119316 | −0.0596582 | − | 0.998219i | \(-0.519001\pi\) | ||||
−0.0596582 | + | 0.998219i | \(0.519001\pi\) | |||||||
\(318\) | −3.45032 | −0.193484 | ||||||||
\(319\) | −10.4390 | −0.584472 | ||||||||
\(320\) | −32.6199 | −1.82351 | ||||||||
\(321\) | 3.53812 | 0.197478 | ||||||||
\(322\) | 45.5905 | 2.54066 | ||||||||
\(323\) | 38.6754 | 2.15195 | ||||||||
\(324\) | 32.2641 | 1.79245 | ||||||||
\(325\) | −10.7444 | −0.595989 | ||||||||
\(326\) | −42.2178 | −2.33823 | ||||||||
\(327\) | −4.52260 | −0.250100 | ||||||||
\(328\) | 70.4975 | 3.89257 | ||||||||
\(329\) | 35.8134 | 1.97446 | ||||||||
\(330\) | −21.7475 | −1.19716 | ||||||||
\(331\) | −6.61479 | −0.363581 | −0.181791 | − | 0.983337i | \(-0.558189\pi\) | ||||
−0.181791 | + | 0.983337i | \(0.558189\pi\) | |||||||
\(332\) | −25.8514 | −1.41878 | ||||||||
\(333\) | 19.7265 | 1.08101 | ||||||||
\(334\) | −44.9632 | −2.46028 | ||||||||
\(335\) | 48.8066 | 2.66659 | ||||||||
\(336\) | 18.3908 | 1.00330 | ||||||||
\(337\) | −11.7420 | −0.639628 | −0.319814 | − | 0.947480i | \(-0.603621\pi\) | ||||
−0.319814 | + | 0.947480i | \(0.603621\pi\) | |||||||
\(338\) | −2.61467 | −0.142219 | ||||||||
\(339\) | 2.59284 | 0.140824 | ||||||||
\(340\) | −131.165 | −7.11340 | ||||||||
\(341\) | 16.0726 | 0.870380 | ||||||||
\(342\) | 40.4405 | 2.18677 | ||||||||
\(343\) | −2.09841 | −0.113303 | ||||||||
\(344\) | 40.4488 | 2.18086 | ||||||||
\(345\) | 9.75042 | 0.524945 | ||||||||
\(346\) | −16.4693 | −0.885395 | ||||||||
\(347\) | −28.2984 | −1.51914 | −0.759568 | − | 0.650428i | \(-0.774590\pi\) | ||||
−0.759568 | + | 0.650428i | \(0.774590\pi\) | |||||||
\(348\) | 6.42325 | 0.344322 | ||||||||
\(349\) | −17.7809 | −0.951788 | −0.475894 | − | 0.879503i | \(-0.657875\pi\) | ||||
−0.475894 | + | 0.879503i | \(0.657875\pi\) | |||||||
\(350\) | −102.942 | −5.50247 | ||||||||
\(351\) | 2.96077 | 0.158034 | ||||||||
\(352\) | 42.9379 | 2.28860 | ||||||||
\(353\) | −13.1955 | −0.702324 | −0.351162 | − | 0.936315i | \(-0.614213\pi\) | ||||
−0.351162 | + | 0.936315i | \(0.614213\pi\) | |||||||
\(354\) | −2.25297 | −0.119744 | ||||||||
\(355\) | −46.2327 | −2.45377 | ||||||||
\(356\) | 7.53396 | 0.399299 | ||||||||
\(357\) | 12.9335 | 0.684516 | ||||||||
\(358\) | 43.8716 | 2.31869 | ||||||||
\(359\) | −27.6771 | −1.46074 | −0.730372 | − | 0.683050i | \(-0.760653\pi\) | ||||
−0.730372 | + | 0.683050i | \(0.760653\pi\) | |||||||
\(360\) | −80.4359 | −4.23935 | ||||||||
\(361\) | 13.0199 | 0.685260 | ||||||||
\(362\) | 33.6444 | 1.76831 | ||||||||
\(363\) | 2.82815 | 0.148440 | ||||||||
\(364\) | −17.7225 | −0.928912 | ||||||||
\(365\) | −38.3607 | −2.00789 | ||||||||
\(366\) | −8.69857 | −0.454681 | ||||||||
\(367\) | −4.14855 | −0.216552 | −0.108276 | − | 0.994121i | \(-0.534533\pi\) | ||||
−0.108276 | + | 0.994121i | \(0.534533\pi\) | |||||||
\(368\) | −46.2454 | −2.41071 | ||||||||
\(369\) | 25.9816 | 1.35255 | ||||||||
\(370\) | −74.8756 | −3.89260 | ||||||||
\(371\) | 9.36352 | 0.486130 | ||||||||
\(372\) | −9.88968 | −0.512756 | ||||||||
\(373\) | 20.9763 | 1.08611 | 0.543057 | − | 0.839696i | \(-0.317267\pi\) | ||||
0.543057 | + | 0.839696i | \(0.317267\pi\) | |||||||
\(374\) | 72.5393 | 3.75092 | ||||||||
\(375\) | −11.7707 | −0.607835 | ||||||||
\(376\) | −72.4850 | −3.73813 | ||||||||
\(377\) | −2.57174 | −0.132451 | ||||||||
\(378\) | 28.3672 | 1.45905 | ||||||||
\(379\) | −0.158477 | −0.00814039 | −0.00407020 | − | 0.999992i | \(-0.501296\pi\) | ||||
−0.00407020 | + | 0.999992i | \(0.501296\pi\) | |||||||
\(380\) | −108.593 | −5.57072 | ||||||||
\(381\) | 6.12650 | 0.313870 | ||||||||
\(382\) | −4.29486 | −0.219744 | ||||||||
\(383\) | −1.59774 | −0.0816405 | −0.0408203 | − | 0.999167i | \(-0.512997\pi\) | ||||
−0.0408203 | + | 0.999167i | \(0.512997\pi\) | |||||||
\(384\) | −0.174937 | −0.00892722 | ||||||||
\(385\) | 59.0188 | 3.00788 | ||||||||
\(386\) | 26.2623 | 1.33672 | ||||||||
\(387\) | 14.9073 | 0.757779 | ||||||||
\(388\) | −41.7872 | −2.12142 | ||||||||
\(389\) | −21.5650 | −1.09339 | −0.546694 | − | 0.837333i | \(-0.684114\pi\) | ||||
−0.546694 | + | 0.837333i | \(0.684114\pi\) | |||||||
\(390\) | −5.35769 | −0.271297 | ||||||||
\(391\) | −32.5227 | −1.64474 | ||||||||
\(392\) | −47.6683 | −2.40761 | ||||||||
\(393\) | −8.28315 | −0.417830 | ||||||||
\(394\) | 14.1865 | 0.714707 | ||||||||
\(395\) | −67.5750 | −3.40007 | ||||||||
\(396\) | 53.6603 | 2.69653 | ||||||||
\(397\) | −12.3672 | −0.620691 | −0.310345 | − | 0.950624i | \(-0.600445\pi\) | ||||
−0.310345 | + | 0.950624i | \(0.600445\pi\) | |||||||
\(398\) | −52.6149 | −2.63734 | ||||||||
\(399\) | 10.7079 | 0.536065 | ||||||||
\(400\) | 104.421 | 5.22103 | ||||||||
\(401\) | 27.7093 | 1.38374 | 0.691869 | − | 0.722023i | \(-0.256788\pi\) | ||||
0.691869 | + | 0.722023i | \(0.256788\pi\) | |||||||
\(402\) | 16.6085 | 0.828359 | ||||||||
\(403\) | 3.95962 | 0.197243 | ||||||||
\(404\) | 12.7427 | 0.633975 | ||||||||
\(405\) | −26.4698 | −1.31530 | ||||||||
\(406\) | −24.6398 | −1.22285 | ||||||||
\(407\) | 29.2950 | 1.45210 | ||||||||
\(408\) | −26.1770 | −1.29596 | ||||||||
\(409\) | −3.32364 | −0.164344 | −0.0821718 | − | 0.996618i | \(-0.526186\pi\) | ||||
−0.0821718 | + | 0.996618i | \(0.526186\pi\) | |||||||
\(410\) | −98.6177 | −4.87038 | ||||||||
\(411\) | −5.85911 | −0.289009 | ||||||||
\(412\) | −19.5570 | −0.963505 | ||||||||
\(413\) | 6.11414 | 0.300857 | ||||||||
\(414\) | −34.0071 | −1.67136 | ||||||||
\(415\) | 21.2088 | 1.04110 | ||||||||
\(416\) | 10.5781 | 0.518634 | ||||||||
\(417\) | 3.15336 | 0.154421 | ||||||||
\(418\) | 60.0564 | 2.93746 | ||||||||
\(419\) | 20.8682 | 1.01948 | 0.509738 | − | 0.860329i | \(-0.329742\pi\) | ||||
0.509738 | + | 0.860329i | \(0.329742\pi\) | |||||||
\(420\) | −36.3150 | −1.77199 | ||||||||
\(421\) | −17.3042 | −0.843355 | −0.421677 | − | 0.906746i | \(-0.638559\pi\) | ||||
−0.421677 | + | 0.906746i | \(0.638559\pi\) | |||||||
\(422\) | 15.3441 | 0.746940 | ||||||||
\(423\) | −26.7141 | −1.29888 | ||||||||
\(424\) | −18.9514 | −0.920363 | ||||||||
\(425\) | 73.4352 | 3.56213 | ||||||||
\(426\) | −15.7326 | −0.762248 | ||||||||
\(427\) | 23.6063 | 1.14239 | ||||||||
\(428\) | 33.1363 | 1.60170 | ||||||||
\(429\) | 2.09619 | 0.101205 | ||||||||
\(430\) | −56.5832 | −2.72868 | ||||||||
\(431\) | 17.8907 | 0.861765 | 0.430883 | − | 0.902408i | \(-0.358202\pi\) | ||||
0.430883 | + | 0.902408i | \(0.358202\pi\) | |||||||
\(432\) | −28.7747 | −1.38442 | ||||||||
\(433\) | 5.75906 | 0.276763 | 0.138381 | − | 0.990379i | \(-0.455810\pi\) | ||||
0.138381 | + | 0.990379i | \(0.455810\pi\) | |||||||
\(434\) | 37.9372 | 1.82104 | ||||||||
\(435\) | −5.26971 | −0.252663 | ||||||||
\(436\) | −42.3565 | −2.02851 | ||||||||
\(437\) | −26.9261 | −1.28805 | ||||||||
\(438\) | −13.0539 | −0.623738 | ||||||||
\(439\) | 4.41924 | 0.210919 | 0.105460 | − | 0.994424i | \(-0.466369\pi\) | ||||
0.105460 | + | 0.994424i | \(0.466369\pi\) | |||||||
\(440\) | −119.452 | −5.69465 | ||||||||
\(441\) | −17.5680 | −0.836570 | ||||||||
\(442\) | 17.8707 | 0.850021 | ||||||||
\(443\) | 34.4181 | 1.63525 | 0.817627 | − | 0.575748i | \(-0.195289\pi\) | ||||
0.817627 | + | 0.575748i | \(0.195289\pi\) | |||||||
\(444\) | −18.0256 | −0.855457 | ||||||||
\(445\) | −6.18095 | −0.293005 | ||||||||
\(446\) | 36.2794 | 1.71788 | ||||||||
\(447\) | 1.74083 | 0.0823383 | ||||||||
\(448\) | 30.1242 | 1.42323 | ||||||||
\(449\) | 8.81167 | 0.415848 | 0.207924 | − | 0.978145i | \(-0.433329\pi\) | ||||
0.207924 | + | 0.978145i | \(0.433329\pi\) | |||||||
\(450\) | 76.7868 | 3.61977 | ||||||||
\(451\) | 38.5841 | 1.81686 | ||||||||
\(452\) | 24.2833 | 1.14219 | ||||||||
\(453\) | −2.59890 | −0.122107 | ||||||||
\(454\) | 2.96562 | 0.139183 | ||||||||
\(455\) | 14.5398 | 0.681635 | ||||||||
\(456\) | −21.6724 | −1.01490 | ||||||||
\(457\) | 22.7634 | 1.06483 | 0.532413 | − | 0.846485i | \(-0.321285\pi\) | ||||
0.532413 | + | 0.846485i | \(0.321285\pi\) | |||||||
\(458\) | −17.5485 | −0.819985 | ||||||||
\(459\) | −20.2362 | −0.944543 | ||||||||
\(460\) | 91.3178 | 4.25771 | ||||||||
\(461\) | −29.0577 | −1.35335 | −0.676675 | − | 0.736282i | \(-0.736580\pi\) | ||||
−0.676675 | + | 0.736282i | \(0.736580\pi\) | |||||||
\(462\) | 20.0837 | 0.934376 | ||||||||
\(463\) | −1.00000 | −0.0464739 | ||||||||
\(464\) | 24.9938 | 1.16031 | ||||||||
\(465\) | 8.11361 | 0.376260 | ||||||||
\(466\) | 11.7502 | 0.544316 | ||||||||
\(467\) | −30.8878 | −1.42932 | −0.714658 | − | 0.699474i | \(-0.753418\pi\) | ||||
−0.714658 | + | 0.699474i | \(0.753418\pi\) | |||||||
\(468\) | 13.2197 | 0.611079 | ||||||||
\(469\) | −45.0725 | −2.08125 | ||||||||
\(470\) | 101.398 | 4.67714 | ||||||||
\(471\) | −0.0807246 | −0.00371960 | ||||||||
\(472\) | −12.3748 | −0.569596 | ||||||||
\(473\) | 22.1381 | 1.01791 | ||||||||
\(474\) | −22.9953 | −1.05621 | ||||||||
\(475\) | 60.7982 | 2.78961 | ||||||||
\(476\) | 121.129 | 5.55196 | ||||||||
\(477\) | −6.98448 | −0.319797 | ||||||||
\(478\) | 41.7150 | 1.90800 | ||||||||
\(479\) | −28.7693 | −1.31450 | −0.657251 | − | 0.753672i | \(-0.728281\pi\) | ||||
−0.657251 | + | 0.753672i | \(0.728281\pi\) | |||||||
\(480\) | 21.6755 | 0.989345 | ||||||||
\(481\) | 7.21708 | 0.329070 | ||||||||
\(482\) | −64.4562 | −2.93590 | ||||||||
\(483\) | −9.00442 | −0.409715 | ||||||||
\(484\) | 26.4871 | 1.20396 | ||||||||
\(485\) | 34.2827 | 1.55670 | ||||||||
\(486\) | −32.2318 | −1.46206 | ||||||||
\(487\) | 8.93341 | 0.404811 | 0.202406 | − | 0.979302i | \(-0.435124\pi\) | ||||
0.202406 | + | 0.979302i | \(0.435124\pi\) | |||||||
\(488\) | −47.7783 | −2.16282 | ||||||||
\(489\) | 8.33830 | 0.377071 | ||||||||
\(490\) | 66.6823 | 3.01240 | ||||||||
\(491\) | −26.5992 | −1.20041 | −0.600203 | − | 0.799847i | \(-0.704914\pi\) | ||||
−0.600203 | + | 0.799847i | \(0.704914\pi\) | |||||||
\(492\) | −23.7413 | −1.07034 | ||||||||
\(493\) | 17.5772 | 0.791638 | ||||||||
\(494\) | 14.7954 | 0.665677 | ||||||||
\(495\) | −44.0235 | −1.97871 | ||||||||
\(496\) | −38.4822 | −1.72790 | ||||||||
\(497\) | 42.6954 | 1.91515 | ||||||||
\(498\) | 7.21721 | 0.323411 | ||||||||
\(499\) | −11.8209 | −0.529178 | −0.264589 | − | 0.964361i | \(-0.585236\pi\) | ||||
−0.264589 | + | 0.964361i | \(0.585236\pi\) | |||||||
\(500\) | −110.239 | −4.93002 | ||||||||
\(501\) | 8.88054 | 0.396753 | ||||||||
\(502\) | −76.3048 | −3.40565 | ||||||||
\(503\) | −36.4015 | −1.62306 | −0.811531 | − | 0.584309i | \(-0.801366\pi\) | ||||
−0.811531 | + | 0.584309i | \(0.801366\pi\) | |||||||
\(504\) | 74.2819 | 3.30878 | ||||||||
\(505\) | −10.4543 | −0.465210 | ||||||||
\(506\) | −50.5024 | −2.24511 | ||||||||
\(507\) | 0.516414 | 0.0229348 | ||||||||
\(508\) | 57.3778 | 2.54573 | ||||||||
\(509\) | 12.5810 | 0.557642 | 0.278821 | − | 0.960343i | \(-0.410056\pi\) | ||||
0.278821 | + | 0.960343i | \(0.410056\pi\) | |||||||
\(510\) | 36.6186 | 1.62150 | ||||||||
\(511\) | 35.4258 | 1.56714 | ||||||||
\(512\) | 41.3515 | 1.82750 | ||||||||
\(513\) | −16.7538 | −0.739700 | ||||||||
\(514\) | 75.2516 | 3.31920 | ||||||||
\(515\) | 16.0448 | 0.707019 | ||||||||
\(516\) | −13.6219 | −0.599669 | ||||||||
\(517\) | −39.6719 | −1.74477 | ||||||||
\(518\) | 69.1469 | 3.03814 | ||||||||
\(519\) | 3.25280 | 0.142782 | ||||||||
\(520\) | −29.4280 | −1.29050 | ||||||||
\(521\) | 22.4443 | 0.983303 | 0.491651 | − | 0.870792i | \(-0.336393\pi\) | ||||
0.491651 | + | 0.870792i | \(0.336393\pi\) | |||||||
\(522\) | 18.3795 | 0.804447 | ||||||||
\(523\) | −17.0484 | −0.745476 | −0.372738 | − | 0.927937i | \(-0.621581\pi\) | ||||
−0.372738 | + | 0.927937i | \(0.621581\pi\) | |||||||
\(524\) | −77.5761 | −3.38893 | ||||||||
\(525\) | 20.3317 | 0.887348 | ||||||||
\(526\) | −58.3302 | −2.54332 | ||||||||
\(527\) | −27.0631 | −1.17889 | ||||||||
\(528\) | −20.3722 | −0.886585 | ||||||||
\(529\) | −0.357457 | −0.0155416 | ||||||||
\(530\) | 26.5108 | 1.15156 | ||||||||
\(531\) | −4.56069 | −0.197917 | ||||||||
\(532\) | 100.285 | 4.34790 | ||||||||
\(533\) | 9.50552 | 0.411730 | ||||||||
\(534\) | −2.10333 | −0.0910201 | ||||||||
\(535\) | −27.1854 | −1.17533 | ||||||||
\(536\) | 91.2251 | 3.94032 | ||||||||
\(537\) | −8.66494 | −0.373920 | ||||||||
\(538\) | −28.3306 | −1.22142 | ||||||||
\(539\) | −26.0894 | −1.12375 | ||||||||
\(540\) | 56.8194 | 2.44512 | ||||||||
\(541\) | −27.9361 | −1.20107 | −0.600534 | − | 0.799599i | \(-0.705045\pi\) | ||||
−0.600534 | + | 0.799599i | \(0.705045\pi\) | |||||||
\(542\) | 84.9513 | 3.64897 | ||||||||
\(543\) | −6.64499 | −0.285164 | ||||||||
\(544\) | −72.2989 | −3.09979 | ||||||||
\(545\) | 34.7498 | 1.48852 | ||||||||
\(546\) | 4.94777 | 0.211745 | ||||||||
\(547\) | 26.0637 | 1.11440 | 0.557201 | − | 0.830378i | \(-0.311875\pi\) | ||||
0.557201 | + | 0.830378i | \(0.311875\pi\) | |||||||
\(548\) | −54.8737 | −2.34409 | ||||||||
\(549\) | −17.6085 | −0.751513 | ||||||||
\(550\) | 114.033 | 4.86237 | ||||||||
\(551\) | 14.5525 | 0.619956 | ||||||||
\(552\) | 18.2246 | 0.775692 | ||||||||
\(553\) | 62.4049 | 2.65373 | ||||||||
\(554\) | 79.9271 | 3.39578 | ||||||||
\(555\) | 14.7884 | 0.627734 | ||||||||
\(556\) | 29.5329 | 1.25247 | ||||||||
\(557\) | 40.3163 | 1.70826 | 0.854128 | − | 0.520063i | \(-0.174092\pi\) | ||||
0.854128 | + | 0.520063i | \(0.174092\pi\) | |||||||
\(558\) | −28.2983 | −1.19796 | ||||||||
\(559\) | 5.45391 | 0.230676 | ||||||||
\(560\) | −141.307 | −5.97131 | ||||||||
\(561\) | −14.3270 | −0.604886 | ||||||||
\(562\) | −48.5437 | −2.04769 | ||||||||
\(563\) | −14.1869 | −0.597906 | −0.298953 | − | 0.954268i | \(-0.596637\pi\) | ||||
−0.298953 | + | 0.954268i | \(0.596637\pi\) | |||||||
\(564\) | 24.4106 | 1.02787 | ||||||||
\(565\) | −19.9223 | −0.838138 | ||||||||
\(566\) | 14.2376 | 0.598450 | ||||||||
\(567\) | 24.4446 | 1.02658 | ||||||||
\(568\) | −86.4140 | −3.62585 | ||||||||
\(569\) | 3.21884 | 0.134941 | 0.0674704 | − | 0.997721i | \(-0.478507\pi\) | ||||
0.0674704 | + | 0.997721i | \(0.478507\pi\) | |||||||
\(570\) | 30.3171 | 1.26984 | ||||||||
\(571\) | −19.3074 | −0.807991 | −0.403996 | − | 0.914761i | \(-0.632379\pi\) | ||||
−0.403996 | + | 0.914761i | \(0.632379\pi\) | |||||||
\(572\) | 19.6319 | 0.820852 | ||||||||
\(573\) | 0.848263 | 0.0354367 | ||||||||
\(574\) | 91.0725 | 3.80129 | ||||||||
\(575\) | −51.1261 | −2.13211 | ||||||||
\(576\) | −22.4703 | −0.936265 | ||||||||
\(577\) | −33.3699 | −1.38921 | −0.694603 | − | 0.719393i | \(-0.744420\pi\) | ||||
−0.694603 | + | 0.719393i | \(0.744420\pi\) | |||||||
\(578\) | −77.6926 | −3.23159 | ||||||||
\(579\) | −5.18698 | −0.215563 | ||||||||
\(580\) | −49.3536 | −2.04930 | ||||||||
\(581\) | −19.5862 | −0.812571 | ||||||||
\(582\) | 11.6662 | 0.483578 | ||||||||
\(583\) | −10.3723 | −0.429579 | ||||||||
\(584\) | −71.7005 | −2.96699 | ||||||||
\(585\) | −10.8456 | −0.448409 | ||||||||
\(586\) | 7.36682 | 0.304321 | ||||||||
\(587\) | −15.6739 | −0.646932 | −0.323466 | − | 0.946240i | \(-0.604848\pi\) | ||||
−0.323466 | + | 0.946240i | \(0.604848\pi\) | |||||||
\(588\) | 16.0531 | 0.662020 | ||||||||
\(589\) | −22.4060 | −0.923222 | ||||||||
\(590\) | 17.3109 | 0.712678 | ||||||||
\(591\) | −2.80193 | −0.115256 | ||||||||
\(592\) | −70.1403 | −2.88275 | ||||||||
\(593\) | −18.7228 | −0.768853 | −0.384427 | − | 0.923156i | \(-0.625601\pi\) | ||||
−0.384427 | + | 0.923156i | \(0.625601\pi\) | |||||||
\(594\) | −31.4234 | −1.28932 | ||||||||
\(595\) | −99.3760 | −4.07402 | ||||||||
\(596\) | 16.3037 | 0.667828 | ||||||||
\(597\) | 10.3918 | 0.425307 | ||||||||
\(598\) | −12.4417 | −0.508778 | ||||||||
\(599\) | 21.6083 | 0.882891 | 0.441446 | − | 0.897288i | \(-0.354466\pi\) | ||||
0.441446 | + | 0.897288i | \(0.354466\pi\) | |||||||
\(600\) | −41.1506 | −1.67997 | ||||||||
\(601\) | −23.6929 | −0.966453 | −0.483226 | − | 0.875495i | \(-0.660535\pi\) | ||||
−0.483226 | + | 0.875495i | \(0.660535\pi\) | |||||||
\(602\) | 52.2540 | 2.12972 | ||||||||
\(603\) | 33.6207 | 1.36914 | ||||||||
\(604\) | −24.3401 | −0.990385 | ||||||||
\(605\) | −21.7304 | −0.883465 | ||||||||
\(606\) | −3.55752 | −0.144514 | ||||||||
\(607\) | −5.78819 | −0.234935 | −0.117468 | − | 0.993077i | \(-0.537478\pi\) | ||||
−0.117468 | + | 0.993077i | \(0.537478\pi\) | |||||||
\(608\) | −59.8574 | −2.42754 | ||||||||
\(609\) | 4.86653 | 0.197202 | ||||||||
\(610\) | 66.8362 | 2.70612 | ||||||||
\(611\) | −9.77351 | −0.395394 | ||||||||
\(612\) | −90.3534 | −3.65232 | ||||||||
\(613\) | −0.444274 | −0.0179441 | −0.00897204 | − | 0.999960i | \(-0.502856\pi\) | ||||
−0.00897204 | + | 0.999960i | \(0.502856\pi\) | |||||||
\(614\) | 43.7841 | 1.76698 | ||||||||
\(615\) | 19.4776 | 0.785414 | ||||||||
\(616\) | 110.313 | 4.44463 | ||||||||
\(617\) | 34.8303 | 1.40221 | 0.701107 | − | 0.713056i | \(-0.252690\pi\) | ||||
0.701107 | + | 0.713056i | \(0.252690\pi\) | |||||||
\(618\) | 5.45993 | 0.219631 | ||||||||
\(619\) | −0.879306 | −0.0353423 | −0.0176711 | − | 0.999844i | \(-0.505625\pi\) | ||||
−0.0176711 | + | 0.999844i | \(0.505625\pi\) | |||||||
\(620\) | 75.9882 | 3.05176 | ||||||||
\(621\) | 14.0886 | 0.565355 | ||||||||
\(622\) | 76.7017 | 3.07546 | ||||||||
\(623\) | 5.70805 | 0.228688 | ||||||||
\(624\) | −5.01885 | −0.200915 | ||||||||
\(625\) | 36.7193 | 1.46877 | ||||||||
\(626\) | −53.2737 | −2.12924 | ||||||||
\(627\) | −11.8615 | −0.473705 | ||||||||
\(628\) | −0.756028 | −0.0301688 | ||||||||
\(629\) | −49.3271 | −1.96680 | ||||||||
\(630\) | −103.912 | −4.13994 | ||||||||
\(631\) | −29.6761 | −1.18139 | −0.590693 | − | 0.806897i | \(-0.701145\pi\) | ||||
−0.590693 | + | 0.806897i | \(0.701145\pi\) | |||||||
\(632\) | −126.305 | −5.02415 | ||||||||
\(633\) | −3.03056 | −0.120454 | ||||||||
\(634\) | 5.55452 | 0.220598 | ||||||||
\(635\) | −47.0735 | −1.86805 | ||||||||
\(636\) | 6.38223 | 0.253072 | ||||||||
\(637\) | −6.42734 | −0.254661 | ||||||||
\(638\) | 27.2945 | 1.08060 | ||||||||
\(639\) | −31.8476 | −1.25987 | ||||||||
\(640\) | 1.34414 | 0.0531320 | ||||||||
\(641\) | −7.53264 | −0.297521 | −0.148761 | − | 0.988873i | \(-0.547528\pi\) | ||||
−0.148761 | + | 0.988873i | \(0.547528\pi\) | |||||||
\(642\) | −9.25100 | −0.365108 | ||||||||
\(643\) | 10.4189 | 0.410883 | 0.205441 | − | 0.978669i | \(-0.434137\pi\) | ||||
0.205441 | + | 0.978669i | \(0.434137\pi\) | |||||||
\(644\) | −84.3311 | −3.32311 | ||||||||
\(645\) | 11.1755 | 0.440037 | ||||||||
\(646\) | −101.123 | −3.97864 | ||||||||
\(647\) | −3.41329 | −0.134190 | −0.0670952 | − | 0.997747i | \(-0.521373\pi\) | ||||
−0.0670952 | + | 0.997747i | \(0.521373\pi\) | |||||||
\(648\) | −49.4751 | −1.94357 | ||||||||
\(649\) | −6.77287 | −0.265859 | ||||||||
\(650\) | 28.0929 | 1.10189 | ||||||||
\(651\) | −7.49285 | −0.293668 | ||||||||
\(652\) | 78.0925 | 3.05834 | ||||||||
\(653\) | 14.4692 | 0.566223 | 0.283112 | − | 0.959087i | \(-0.408633\pi\) | ||||
0.283112 | + | 0.959087i | \(0.408633\pi\) | |||||||
\(654\) | 11.8251 | 0.462398 | ||||||||
\(655\) | 63.6443 | 2.48679 | ||||||||
\(656\) | −92.3809 | −3.60687 | ||||||||
\(657\) | −26.4249 | −1.03094 | ||||||||
\(658\) | −93.6401 | −3.65047 | ||||||||
\(659\) | −40.9706 | −1.59599 | −0.797995 | − | 0.602664i | \(-0.794106\pi\) | ||||
−0.797995 | + | 0.602664i | \(0.794106\pi\) | |||||||
\(660\) | 40.2276 | 1.56586 | ||||||||
\(661\) | −37.2666 | −1.44950 | −0.724751 | − | 0.689010i | \(-0.758045\pi\) | ||||
−0.724751 | + | 0.689010i | \(0.758045\pi\) | |||||||
\(662\) | 17.2955 | 0.672207 | ||||||||
\(663\) | −3.52957 | −0.137077 | ||||||||
\(664\) | 39.6417 | 1.53840 | ||||||||
\(665\) | −82.2750 | −3.19049 | ||||||||
\(666\) | −51.5784 | −1.99862 | ||||||||
\(667\) | −12.2374 | −0.473834 | ||||||||
\(668\) | 83.1709 | 3.21798 | ||||||||
\(669\) | −7.16542 | −0.277031 | ||||||||
\(670\) | −127.613 | −4.93013 | ||||||||
\(671\) | −26.1496 | −1.00950 | ||||||||
\(672\) | −20.0171 | −0.772176 | ||||||||
\(673\) | −23.2471 | −0.896108 | −0.448054 | − | 0.894007i | \(-0.647883\pi\) | ||||
−0.448054 | + | 0.894007i | \(0.647883\pi\) | |||||||
\(674\) | 30.7015 | 1.18258 | ||||||||
\(675\) | −31.8115 | −1.22443 | ||||||||
\(676\) | 4.83649 | 0.186019 | ||||||||
\(677\) | −22.3348 | −0.858395 | −0.429198 | − | 0.903211i | \(-0.641204\pi\) | ||||
−0.429198 | + | 0.903211i | \(0.641204\pi\) | |||||||
\(678\) | −6.77942 | −0.260362 | ||||||||
\(679\) | −31.6598 | −1.21499 | ||||||||
\(680\) | 201.133 | 7.71312 | ||||||||
\(681\) | −0.585729 | −0.0224452 | ||||||||
\(682\) | −42.0245 | −1.60920 | ||||||||
\(683\) | −20.3051 | −0.776952 | −0.388476 | − | 0.921459i | \(-0.626998\pi\) | ||||
−0.388476 | + | 0.921459i | \(0.626998\pi\) | |||||||
\(684\) | −74.8050 | −2.86024 | ||||||||
\(685\) | 45.0190 | 1.72009 | ||||||||
\(686\) | 5.48663 | 0.209481 | ||||||||
\(687\) | 3.46594 | 0.132234 | ||||||||
\(688\) | −53.0047 | −2.02079 | ||||||||
\(689\) | −2.55531 | −0.0973497 | ||||||||
\(690\) | −25.4941 | −0.970544 | ||||||||
\(691\) | 13.9532 | 0.530806 | 0.265403 | − | 0.964138i | \(-0.414495\pi\) | ||||
0.265403 | + | 0.964138i | \(0.414495\pi\) | |||||||
\(692\) | 30.4641 | 1.15807 | ||||||||
\(693\) | 40.6554 | 1.54437 | ||||||||
\(694\) | 73.9909 | 2.80866 | ||||||||
\(695\) | −24.2292 | −0.919064 | ||||||||
\(696\) | −9.84968 | −0.373351 | ||||||||
\(697\) | −64.9681 | −2.46084 | ||||||||
\(698\) | 46.4911 | 1.75971 | ||||||||
\(699\) | −2.32073 | −0.0877782 | ||||||||
\(700\) | 190.417 | 7.19708 | ||||||||
\(701\) | −43.1435 | −1.62951 | −0.814753 | − | 0.579808i | \(-0.803128\pi\) | ||||
−0.814753 | + | 0.579808i | \(0.803128\pi\) | |||||||
\(702\) | −7.74142 | −0.292181 | ||||||||
\(703\) | −40.8387 | −1.54026 | ||||||||
\(704\) | −33.3697 | −1.25767 | ||||||||
\(705\) | −20.0268 | −0.754252 | ||||||||
\(706\) | 34.5018 | 1.29849 | ||||||||
\(707\) | 9.65445 | 0.363093 | ||||||||
\(708\) | 4.16744 | 0.156622 | ||||||||
\(709\) | −19.8621 | −0.745936 | −0.372968 | − | 0.927844i | \(-0.621660\pi\) | ||||
−0.372968 | + | 0.927844i | \(0.621660\pi\) | |||||||
\(710\) | 120.883 | 4.53666 | ||||||||
\(711\) | −46.5493 | −1.74574 | ||||||||
\(712\) | −11.5529 | −0.432963 | ||||||||
\(713\) | 18.8415 | 0.705621 | ||||||||
\(714\) | −33.8169 | −1.26557 | ||||||||
\(715\) | −16.1063 | −0.602341 | ||||||||
\(716\) | −81.1517 | −3.03278 | ||||||||
\(717\) | −8.23900 | −0.307691 | ||||||||
\(718\) | 72.3666 | 2.70070 | ||||||||
\(719\) | −47.3389 | −1.76544 | −0.882722 | − | 0.469896i | \(-0.844291\pi\) | ||||
−0.882722 | + | 0.469896i | \(0.844291\pi\) | |||||||
\(720\) | 105.404 | 3.92819 | ||||||||
\(721\) | −14.8172 | −0.551823 | ||||||||
\(722\) | −34.0428 | −1.26694 | ||||||||
\(723\) | 12.7305 | 0.473453 | ||||||||
\(724\) | −62.2338 | −2.31290 | ||||||||
\(725\) | 27.6316 | 1.02621 | ||||||||
\(726\) | −7.39469 | −0.274443 | ||||||||
\(727\) | −22.3110 | −0.827468 | −0.413734 | − | 0.910398i | \(-0.635776\pi\) | ||||
−0.413734 | + | 0.910398i | \(0.635776\pi\) | |||||||
\(728\) | 27.1765 | 1.00723 | ||||||||
\(729\) | −13.6469 | −0.505441 | ||||||||
\(730\) | 100.301 | 3.71229 | ||||||||
\(731\) | −37.2763 | −1.37871 | ||||||||
\(732\) | 16.0902 | 0.594711 | ||||||||
\(733\) | −15.5210 | −0.573282 | −0.286641 | − | 0.958038i | \(-0.592539\pi\) | ||||
−0.286641 | + | 0.958038i | \(0.592539\pi\) | |||||||
\(734\) | 10.8471 | 0.400373 | ||||||||
\(735\) | −13.1702 | −0.485790 | ||||||||
\(736\) | 50.3350 | 1.85537 | ||||||||
\(737\) | 49.9286 | 1.83914 | ||||||||
\(738\) | −67.9332 | −2.50066 | ||||||||
\(739\) | 51.9562 | 1.91124 | 0.955619 | − | 0.294604i | \(-0.0951879\pi\) | ||||
0.955619 | + | 0.294604i | \(0.0951879\pi\) | |||||||
\(740\) | 138.501 | 5.09141 | ||||||||
\(741\) | −2.92219 | −0.107349 | ||||||||
\(742\) | −24.4825 | −0.898781 | ||||||||
\(743\) | −42.2515 | −1.55006 | −0.775029 | − | 0.631925i | \(-0.782265\pi\) | ||||
−0.775029 | + | 0.631925i | \(0.782265\pi\) | |||||||
\(744\) | 15.1653 | 0.555985 | ||||||||
\(745\) | −13.3758 | −0.490051 | ||||||||
\(746\) | −54.8462 | −2.00806 | ||||||||
\(747\) | 14.6098 | 0.534545 | ||||||||
\(748\) | −134.180 | −4.90610 | ||||||||
\(749\) | 25.1055 | 0.917335 | ||||||||
\(750\) | 30.7764 | 1.12380 | ||||||||
\(751\) | −45.8553 | −1.67328 | −0.836642 | − | 0.547750i | \(-0.815485\pi\) | ||||
−0.836642 | + | 0.547750i | \(0.815485\pi\) | |||||||
\(752\) | 94.9853 | 3.46376 | ||||||||
\(753\) | 15.0707 | 0.549207 | ||||||||
\(754\) | 6.72423 | 0.244882 | ||||||||
\(755\) | 19.9689 | 0.726743 | ||||||||
\(756\) | −52.4722 | −1.90840 | ||||||||
\(757\) | 22.9495 | 0.834115 | 0.417057 | − | 0.908880i | \(-0.363061\pi\) | ||||
0.417057 | + | 0.908880i | \(0.363061\pi\) | |||||||
\(758\) | 0.414364 | 0.0150504 | ||||||||
\(759\) | 9.97456 | 0.362053 | ||||||||
\(760\) | 166.522 | 6.04037 | ||||||||
\(761\) | −16.2527 | −0.589162 | −0.294581 | − | 0.955627i | \(-0.595180\pi\) | ||||
−0.294581 | + | 0.955627i | \(0.595180\pi\) | |||||||
\(762\) | −16.0188 | −0.580298 | ||||||||
\(763\) | −32.0911 | −1.16178 | ||||||||
\(764\) | 7.94443 | 0.287419 | ||||||||
\(765\) | 74.1270 | 2.68007 | ||||||||
\(766\) | 4.17755 | 0.150941 | ||||||||
\(767\) | −1.66855 | −0.0602480 | ||||||||
\(768\) | −8.03339 | −0.289880 | ||||||||
\(769\) | −27.4349 | −0.989327 | −0.494663 | − | 0.869085i | \(-0.664709\pi\) | ||||
−0.494663 | + | 0.869085i | \(0.664709\pi\) | |||||||
\(770\) | −154.315 | −5.56111 | ||||||||
\(771\) | −14.8627 | −0.535267 | ||||||||
\(772\) | −48.5788 | −1.74839 | ||||||||
\(773\) | −1.99609 | −0.0717944 | −0.0358972 | − | 0.999355i | \(-0.511429\pi\) | ||||
−0.0358972 | + | 0.999355i | \(0.511429\pi\) | |||||||
\(774\) | −38.9776 | −1.40102 | ||||||||
\(775\) | −42.5435 | −1.52821 | ||||||||
\(776\) | 64.0783 | 2.30028 | ||||||||
\(777\) | −13.6570 | −0.489941 | ||||||||
\(778\) | 56.3852 | 2.02151 | ||||||||
\(779\) | −53.7881 | −1.92716 | ||||||||
\(780\) | 9.91039 | 0.354849 | ||||||||
\(781\) | −47.2954 | −1.69236 | ||||||||
\(782\) | 85.0361 | 3.04088 | ||||||||
\(783\) | −7.61431 | −0.272113 | ||||||||
\(784\) | 62.4651 | 2.23090 | ||||||||
\(785\) | 0.620255 | 0.0221378 | ||||||||
\(786\) | 21.6577 | 0.772504 | ||||||||
\(787\) | −17.9730 | −0.640669 | −0.320334 | − | 0.947305i | \(-0.603795\pi\) | ||||
−0.320334 | + | 0.947305i | \(0.603795\pi\) | |||||||
\(788\) | −26.2416 | −0.934818 | ||||||||
\(789\) | 11.5206 | 0.410144 | ||||||||
\(790\) | 176.686 | 6.28621 | ||||||||
\(791\) | 18.3981 | 0.654161 | ||||||||
\(792\) | −82.2850 | −2.92387 | ||||||||
\(793\) | −6.44218 | −0.228768 | ||||||||
\(794\) | 32.3361 | 1.14756 | ||||||||
\(795\) | −5.23606 | −0.185704 | ||||||||
\(796\) | 97.3245 | 3.44957 | ||||||||
\(797\) | 52.9183 | 1.87446 | 0.937231 | − | 0.348709i | \(-0.113380\pi\) | ||||
0.937231 | + | 0.348709i | \(0.113380\pi\) | |||||||
\(798\) | −27.9976 | −0.991103 | ||||||||
\(799\) | 66.7997 | 2.36320 | ||||||||
\(800\) | −113.655 | −4.01830 | ||||||||
\(801\) | −4.25778 | −0.150441 | ||||||||
\(802\) | −72.4507 | −2.55832 | ||||||||
\(803\) | −39.2425 | −1.38484 | ||||||||
\(804\) | −30.7217 | −1.08347 | ||||||||
\(805\) | 69.1863 | 2.43850 | ||||||||
\(806\) | −10.3531 | −0.364672 | ||||||||
\(807\) | 5.59549 | 0.196971 | ||||||||
\(808\) | −19.5403 | −0.687424 | ||||||||
\(809\) | −15.8035 | −0.555622 | −0.277811 | − | 0.960636i | \(-0.589609\pi\) | ||||
−0.277811 | + | 0.960636i | \(0.589609\pi\) | |||||||
\(810\) | 69.2098 | 2.43179 | ||||||||
\(811\) | 38.7452 | 1.36053 | 0.680263 | − | 0.732968i | \(-0.261865\pi\) | ||||
0.680263 | + | 0.732968i | \(0.261865\pi\) | |||||||
\(812\) | 45.5776 | 1.59946 | ||||||||
\(813\) | −16.7784 | −0.588446 | ||||||||
\(814\) | −76.5968 | −2.68472 | ||||||||
\(815\) | −64.0681 | −2.24421 | ||||||||
\(816\) | 34.3027 | 1.20084 | ||||||||
\(817\) | −30.8616 | −1.07971 | ||||||||
\(818\) | 8.69022 | 0.303847 | ||||||||
\(819\) | 10.0158 | 0.349980 | ||||||||
\(820\) | 182.418 | 6.37032 | ||||||||
\(821\) | −46.5438 | −1.62439 | −0.812194 | − | 0.583387i | \(-0.801727\pi\) | ||||
−0.812194 | + | 0.583387i | \(0.801727\pi\) | |||||||
\(822\) | 15.3196 | 0.534334 | ||||||||
\(823\) | −33.7574 | −1.17671 | −0.588355 | − | 0.808603i | \(-0.700224\pi\) | ||||
−0.588355 | + | 0.808603i | \(0.700224\pi\) | |||||||
\(824\) | 29.9896 | 1.04474 | ||||||||
\(825\) | −22.5222 | −0.784123 | ||||||||
\(826\) | −15.9864 | −0.556240 | ||||||||
\(827\) | −19.1147 | −0.664682 | −0.332341 | − | 0.943159i | \(-0.607838\pi\) | ||||
−0.332341 | + | 0.943159i | \(0.607838\pi\) | |||||||
\(828\) | 62.9047 | 2.18609 | ||||||||
\(829\) | 42.3630 | 1.47133 | 0.735664 | − | 0.677347i | \(-0.236870\pi\) | ||||
0.735664 | + | 0.677347i | \(0.236870\pi\) | |||||||
\(830\) | −55.4541 | −1.92484 | ||||||||
\(831\) | −15.7861 | −0.547615 | ||||||||
\(832\) | −8.22091 | −0.285009 | ||||||||
\(833\) | 43.9294 | 1.52206 | ||||||||
\(834\) | −8.24500 | −0.285501 | ||||||||
\(835\) | −68.2344 | −2.36135 | ||||||||
\(836\) | −111.090 | −3.84211 | ||||||||
\(837\) | 11.7235 | 0.405224 | ||||||||
\(838\) | −54.5633 | −1.88486 | ||||||||
\(839\) | −12.1013 | −0.417782 | −0.208891 | − | 0.977939i | \(-0.566985\pi\) | ||||
−0.208891 | + | 0.977939i | \(0.566985\pi\) | |||||||
\(840\) | 55.6870 | 1.92138 | ||||||||
\(841\) | −22.3862 | −0.771937 | ||||||||
\(842\) | 45.2447 | 1.55924 | ||||||||
\(843\) | 9.58770 | 0.330218 | ||||||||
\(844\) | −28.3828 | −0.976977 | ||||||||
\(845\) | −3.96792 | −0.136500 | ||||||||
\(846\) | 69.8485 | 2.40144 | ||||||||
\(847\) | 20.0678 | 0.689538 | ||||||||
\(848\) | 24.8342 | 0.852810 | ||||||||
\(849\) | −2.81202 | −0.0965082 | ||||||||
\(850\) | −192.009 | −6.58584 | ||||||||
\(851\) | 34.3419 | 1.17722 | ||||||||
\(852\) | 29.1015 | 0.997000 | ||||||||
\(853\) | 20.1866 | 0.691175 | 0.345587 | − | 0.938387i | \(-0.387680\pi\) | ||||
0.345587 | + | 0.938387i | \(0.387680\pi\) | |||||||
\(854\) | −61.7226 | −2.11210 | ||||||||
\(855\) | 61.3709 | 2.09884 | ||||||||
\(856\) | −50.8126 | −1.73674 | ||||||||
\(857\) | 50.6130 | 1.72891 | 0.864454 | − | 0.502712i | \(-0.167664\pi\) | ||||
0.864454 | + | 0.502712i | \(0.167664\pi\) | |||||||
\(858\) | −5.48085 | −0.187113 | ||||||||
\(859\) | −9.30923 | −0.317627 | −0.158813 | − | 0.987309i | \(-0.550767\pi\) | ||||
−0.158813 | + | 0.987309i | \(0.550767\pi\) | |||||||
\(860\) | 104.665 | 3.56904 | ||||||||
\(861\) | −17.9874 | −0.613010 | ||||||||
\(862\) | −46.7783 | −1.59327 | ||||||||
\(863\) | 40.5687 | 1.38097 | 0.690487 | − | 0.723345i | \(-0.257396\pi\) | ||||
0.690487 | + | 0.723345i | \(0.257396\pi\) | |||||||
\(864\) | 31.3193 | 1.06550 | ||||||||
\(865\) | −24.9932 | −0.849793 | ||||||||
\(866\) | −15.0580 | −0.511693 | ||||||||
\(867\) | 15.3448 | 0.521137 | ||||||||
\(868\) | −70.1744 | −2.38187 | ||||||||
\(869\) | −69.1284 | −2.34502 | ||||||||
\(870\) | 13.7785 | 0.467137 | ||||||||
\(871\) | 12.3003 | 0.416781 | ||||||||
\(872\) | 64.9513 | 2.19953 | ||||||||
\(873\) | 23.6158 | 0.799274 | ||||||||
\(874\) | 70.4027 | 2.38141 | ||||||||
\(875\) | −83.5215 | −2.82354 | ||||||||
\(876\) | 24.1464 | 0.815832 | ||||||||
\(877\) | 35.6136 | 1.20259 | 0.601293 | − | 0.799028i | \(-0.294652\pi\) | ||||
0.601293 | + | 0.799028i | \(0.294652\pi\) | |||||||
\(878\) | −11.5549 | −0.389958 | ||||||||
\(879\) | −1.45500 | −0.0490758 | ||||||||
\(880\) | 156.531 | 5.27667 | ||||||||
\(881\) | −29.6146 | −0.997741 | −0.498871 | − | 0.866676i | \(-0.666252\pi\) | ||||
−0.498871 | + | 0.866676i | \(0.666252\pi\) | |||||||
\(882\) | 45.9344 | 1.54669 | ||||||||
\(883\) | 45.8761 | 1.54385 | 0.771927 | − | 0.635712i | \(-0.219293\pi\) | ||||
0.771927 | + | 0.635712i | \(0.219293\pi\) | |||||||
\(884\) | −33.0563 | −1.11180 | ||||||||
\(885\) | −3.41901 | −0.114929 | ||||||||
\(886\) | −89.9920 | −3.02334 | ||||||||
\(887\) | −10.4274 | −0.350117 | −0.175059 | − | 0.984558i | \(-0.556011\pi\) | ||||
−0.175059 | + | 0.984558i | \(0.556011\pi\) | |||||||
\(888\) | 27.6412 | 0.927579 | ||||||||
\(889\) | 43.4719 | 1.45800 | ||||||||
\(890\) | 16.1611 | 0.541723 | ||||||||
\(891\) | −27.0783 | −0.907157 | ||||||||
\(892\) | −67.1079 | −2.24694 | ||||||||
\(893\) | 55.3045 | 1.85070 | ||||||||
\(894\) | −4.55168 | −0.152231 | ||||||||
\(895\) | 66.5778 | 2.22545 | ||||||||
\(896\) | −1.24131 | −0.0414691 | ||||||||
\(897\) | 2.45732 | 0.0820474 | ||||||||
\(898\) | −23.0396 | −0.768841 | ||||||||
\(899\) | −10.1831 | −0.339625 | ||||||||
\(900\) | −142.037 | −4.73455 | ||||||||
\(901\) | 17.4650 | 0.581843 | ||||||||
\(902\) | −100.885 | −3.35909 | ||||||||
\(903\) | −10.3205 | −0.343445 | ||||||||
\(904\) | −37.2371 | −1.23849 | ||||||||
\(905\) | 51.0574 | 1.69720 | ||||||||
\(906\) | 6.79527 | 0.225758 | ||||||||
\(907\) | 21.2084 | 0.704213 | 0.352107 | − | 0.935960i | \(-0.385465\pi\) | ||||
0.352107 | + | 0.935960i | \(0.385465\pi\) | |||||||
\(908\) | −5.48566 | −0.182048 | ||||||||
\(909\) | −7.20149 | −0.238858 | ||||||||
\(910\) | −38.0167 | −1.26024 | ||||||||
\(911\) | 6.90102 | 0.228641 | 0.114320 | − | 0.993444i | \(-0.463531\pi\) | ||||
0.114320 | + | 0.993444i | \(0.463531\pi\) | |||||||
\(912\) | 28.3998 | 0.940410 | ||||||||
\(913\) | 21.6964 | 0.718045 | ||||||||
\(914\) | −59.5187 | −1.96870 | ||||||||
\(915\) | −13.2006 | −0.436398 | ||||||||
\(916\) | 32.4603 | 1.07252 | ||||||||
\(917\) | −58.7750 | −1.94092 | ||||||||
\(918\) | 52.9109 | 1.74632 | ||||||||
\(919\) | 28.6539 | 0.945204 | 0.472602 | − | 0.881276i | \(-0.343315\pi\) | ||||
0.472602 | + | 0.881276i | \(0.343315\pi\) | |||||||
\(920\) | −140.031 | −4.61667 | ||||||||
\(921\) | −8.64766 | −0.284950 | ||||||||
\(922\) | 75.9761 | 2.50214 | ||||||||
\(923\) | −11.6516 | −0.383518 | ||||||||
\(924\) | −37.1498 | −1.22214 | ||||||||
\(925\) | −77.5428 | −2.54959 | ||||||||
\(926\) | 2.61467 | 0.0859233 | ||||||||
\(927\) | 11.0525 | 0.363013 | ||||||||
\(928\) | −27.2041 | −0.893017 | ||||||||
\(929\) | −29.6861 | −0.973969 | −0.486984 | − | 0.873411i | \(-0.661903\pi\) | ||||
−0.486984 | + | 0.873411i | \(0.661903\pi\) | |||||||
\(930\) | −21.2144 | −0.695648 | ||||||||
\(931\) | 36.3699 | 1.19197 | ||||||||
\(932\) | −21.7349 | −0.711950 | ||||||||
\(933\) | −15.1491 | −0.495959 | ||||||||
\(934\) | 80.7613 | 2.64259 | ||||||||
\(935\) | 110.083 | 3.60009 | ||||||||
\(936\) | −20.2716 | −0.662598 | ||||||||
\(937\) | −18.2151 | −0.595062 | −0.297531 | − | 0.954712i | \(-0.596163\pi\) | ||||
−0.297531 | + | 0.954712i | \(0.596163\pi\) | |||||||
\(938\) | 117.850 | 3.84793 | ||||||||
\(939\) | 10.5219 | 0.343369 | ||||||||
\(940\) | −187.561 | −6.11757 | ||||||||
\(941\) | 27.0873 | 0.883020 | 0.441510 | − | 0.897256i | \(-0.354443\pi\) | ||||
0.441510 | + | 0.897256i | \(0.354443\pi\) | |||||||
\(942\) | 0.211068 | 0.00687697 | ||||||||
\(943\) | 45.2312 | 1.47293 | ||||||||
\(944\) | 16.2161 | 0.527789 | ||||||||
\(945\) | 43.0489 | 1.40038 | ||||||||
\(946\) | −57.8839 | −1.88197 | ||||||||
\(947\) | 34.7395 | 1.12888 | 0.564441 | − | 0.825474i | \(-0.309092\pi\) | ||||
0.564441 | + | 0.825474i | \(0.309092\pi\) | |||||||
\(948\) | 42.5356 | 1.38149 | ||||||||
\(949\) | −9.66772 | −0.313828 | ||||||||
\(950\) | −158.967 | −5.15757 | ||||||||
\(951\) | −1.09705 | −0.0355744 | ||||||||
\(952\) | −185.745 | −6.02003 | ||||||||
\(953\) | 48.4186 | 1.56843 | 0.784215 | − | 0.620489i | \(-0.213066\pi\) | ||||
0.784215 | + | 0.620489i | \(0.213066\pi\) | |||||||
\(954\) | 18.2621 | 0.591257 | ||||||||
\(955\) | −6.51770 | −0.210908 | ||||||||
\(956\) | −77.1625 | −2.49561 | ||||||||
\(957\) | −5.39085 | −0.174261 | ||||||||
\(958\) | 75.2221 | 2.43032 | ||||||||
\(959\) | −41.5747 | −1.34252 | ||||||||
\(960\) | −16.8454 | −0.543682 | ||||||||
\(961\) | −15.3214 | −0.494239 | ||||||||
\(962\) | −18.8703 | −0.608402 | ||||||||
\(963\) | −18.7268 | −0.603463 | ||||||||
\(964\) | 119.228 | 3.84007 | ||||||||
\(965\) | 39.8546 | 1.28297 | ||||||||
\(966\) | 23.5436 | 0.757502 | ||||||||
\(967\) | 26.8726 | 0.864166 | 0.432083 | − | 0.901834i | \(-0.357779\pi\) | ||||
0.432083 | + | 0.901834i | \(0.357779\pi\) | |||||||
\(968\) | −40.6165 | −1.30546 | ||||||||
\(969\) | 19.9725 | 0.641609 | ||||||||
\(970\) | −89.6380 | −2.87810 | ||||||||
\(971\) | 50.6696 | 1.62607 | 0.813033 | − | 0.582217i | \(-0.197815\pi\) | ||||
0.813033 | + | 0.582217i | \(0.197815\pi\) | |||||||
\(972\) | 59.6208 | 1.91234 | ||||||||
\(973\) | 22.3754 | 0.717322 | ||||||||
\(974\) | −23.3579 | −0.748435 | ||||||||
\(975\) | −5.54854 | −0.177695 | ||||||||
\(976\) | 62.6093 | 2.00408 | ||||||||
\(977\) | −51.9373 | −1.66162 | −0.830811 | − | 0.556555i | \(-0.812123\pi\) | ||||
−0.830811 | + | 0.556555i | \(0.812123\pi\) | |||||||
\(978\) | −21.8019 | −0.697147 | ||||||||
\(979\) | −6.32304 | −0.202085 | ||||||||
\(980\) | −123.346 | −3.94014 | ||||||||
\(981\) | 23.9376 | 0.764267 | ||||||||
\(982\) | 69.5482 | 2.21937 | ||||||||
\(983\) | −46.3978 | −1.47986 | −0.739929 | − | 0.672685i | \(-0.765141\pi\) | ||||
−0.739929 | + | 0.672685i | \(0.765141\pi\) | |||||||
\(984\) | 36.4059 | 1.16058 | ||||||||
\(985\) | 21.5289 | 0.685968 | ||||||||
\(986\) | −45.9586 | −1.46362 | ||||||||
\(987\) | 18.4945 | 0.588688 | ||||||||
\(988\) | −27.3678 | −0.870687 | ||||||||
\(989\) | 25.9520 | 0.825226 | ||||||||
\(990\) | 115.107 | 3.65834 | ||||||||
\(991\) | −37.9464 | −1.20541 | −0.602703 | − | 0.797965i | \(-0.705910\pi\) | ||||
−0.602703 | + | 0.797965i | \(0.705910\pi\) | |||||||
\(992\) | 41.8853 | 1.32986 | ||||||||
\(993\) | −3.41597 | −0.108403 | ||||||||
\(994\) | −111.634 | −3.54083 | ||||||||
\(995\) | −79.8462 | −2.53129 | ||||||||
\(996\) | −13.3501 | −0.423013 | ||||||||
\(997\) | −45.8252 | −1.45130 | −0.725649 | − | 0.688065i | \(-0.758461\pi\) | ||||
−0.725649 | + | 0.688065i | \(0.758461\pi\) | |||||||
\(998\) | 30.9078 | 0.978370 | ||||||||
\(999\) | 21.3681 | 0.676056 |
(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 | 6019.2.a.c.1.6 | ✓ | 108 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6019.2.a.c.1.6 | ✓ | 108 | 1.1 | even | 1 | trivial |