Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8027,2,Mod(1,8027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8027, 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("8027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8027 = 23 \cdot 349 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8027.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: | \(64.0959177025\) |
Analytic rank: | \(1\) |
Dimension: | \(149\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 8027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.55845 | −1.80910 | −0.904548 | − | 0.426372i | \(-0.859792\pi\) | ||||
−0.904548 | + | 0.426372i | \(0.859792\pi\) | |||||||
\(3\) | −2.16736 | −1.25132 | −0.625662 | − | 0.780095i | \(-0.715171\pi\) | ||||
−0.625662 | + | 0.780095i | \(0.715171\pi\) | |||||||
\(4\) | 4.54566 | 2.27283 | ||||||||
\(5\) | 2.09071 | 0.934994 | 0.467497 | − | 0.883995i | \(-0.345156\pi\) | ||||
0.467497 | + | 0.883995i | \(0.345156\pi\) | |||||||
\(6\) | 5.54507 | 2.26376 | ||||||||
\(7\) | −1.08828 | −0.411332 | −0.205666 | − | 0.978622i | \(-0.565936\pi\) | ||||
−0.205666 | + | 0.978622i | \(0.565936\pi\) | |||||||
\(8\) | −6.51294 | −2.30267 | ||||||||
\(9\) | 1.69743 | 0.565810 | ||||||||
\(10\) | −5.34897 | −1.69149 | ||||||||
\(11\) | −0.572630 | −0.172654 | −0.0863272 | − | 0.996267i | \(-0.527513\pi\) | ||||
−0.0863272 | + | 0.996267i | \(0.527513\pi\) | |||||||
\(12\) | −9.85206 | −2.84404 | ||||||||
\(13\) | 6.70474 | 1.85956 | 0.929780 | − | 0.368116i | \(-0.119997\pi\) | ||||
0.929780 | + | 0.368116i | \(0.119997\pi\) | |||||||
\(14\) | 2.78431 | 0.744139 | ||||||||
\(15\) | −4.53131 | −1.16998 | ||||||||
\(16\) | 7.57170 | 1.89292 | ||||||||
\(17\) | 4.32748 | 1.04957 | 0.524784 | − | 0.851236i | \(-0.324146\pi\) | ||||
0.524784 | + | 0.851236i | \(0.324146\pi\) | |||||||
\(18\) | −4.34279 | −1.02360 | ||||||||
\(19\) | 7.81314 | 1.79246 | 0.896229 | − | 0.443592i | \(-0.146296\pi\) | ||||
0.896229 | + | 0.443592i | \(0.146296\pi\) | |||||||
\(20\) | 9.50365 | 2.12508 | ||||||||
\(21\) | 2.35870 | 0.514709 | ||||||||
\(22\) | 1.46504 | 0.312348 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 14.1158 | 2.88139 | ||||||||
\(25\) | −0.628931 | −0.125786 | ||||||||
\(26\) | −17.1537 | −3.36412 | ||||||||
\(27\) | 2.82313 | 0.543312 | ||||||||
\(28\) | −4.94696 | −0.934888 | ||||||||
\(29\) | 0.377519 | 0.0701036 | 0.0350518 | − | 0.999385i | \(-0.488840\pi\) | ||||
0.0350518 | + | 0.999385i | \(0.488840\pi\) | |||||||
\(30\) | 11.5931 | 2.11661 | ||||||||
\(31\) | 2.85397 | 0.512587 | 0.256294 | − | 0.966599i | \(-0.417499\pi\) | ||||
0.256294 | + | 0.966599i | \(0.417499\pi\) | |||||||
\(32\) | −6.34592 | −1.12181 | ||||||||
\(33\) | 1.24109 | 0.216046 | ||||||||
\(34\) | −11.0716 | −1.89877 | ||||||||
\(35\) | −2.27528 | −0.384593 | ||||||||
\(36\) | 7.71594 | 1.28599 | ||||||||
\(37\) | −10.7375 | −1.76523 | −0.882615 | − | 0.470097i | \(-0.844219\pi\) | ||||
−0.882615 | + | 0.470097i | \(0.844219\pi\) | |||||||
\(38\) | −19.9895 | −3.24273 | ||||||||
\(39\) | −14.5315 | −2.32691 | ||||||||
\(40\) | −13.6167 | −2.15298 | ||||||||
\(41\) | 1.13241 | 0.176853 | 0.0884264 | − | 0.996083i | \(-0.471816\pi\) | ||||
0.0884264 | + | 0.996083i | \(0.471816\pi\) | |||||||
\(42\) | −6.03460 | −0.931159 | ||||||||
\(43\) | −11.9714 | −1.82562 | −0.912809 | − | 0.408387i | \(-0.866091\pi\) | ||||
−0.912809 | + | 0.408387i | \(0.866091\pi\) | |||||||
\(44\) | −2.60298 | −0.392414 | ||||||||
\(45\) | 3.54883 | 0.529029 | ||||||||
\(46\) | 2.55845 | 0.377223 | ||||||||
\(47\) | 5.19986 | 0.758478 | 0.379239 | − | 0.925299i | \(-0.376186\pi\) | ||||
0.379239 | + | 0.925299i | \(0.376186\pi\) | |||||||
\(48\) | −16.4106 | −2.36866 | ||||||||
\(49\) | −5.81564 | −0.830806 | ||||||||
\(50\) | 1.60909 | 0.227559 | ||||||||
\(51\) | −9.37918 | −1.31335 | ||||||||
\(52\) | 30.4774 | 4.22646 | ||||||||
\(53\) | −12.3033 | −1.68999 | −0.844994 | − | 0.534776i | \(-0.820396\pi\) | ||||
−0.844994 | + | 0.534776i | \(0.820396\pi\) | |||||||
\(54\) | −7.22284 | −0.982904 | ||||||||
\(55\) | −1.19720 | −0.161431 | ||||||||
\(56\) | 7.08792 | 0.947163 | ||||||||
\(57\) | −16.9339 | −2.24294 | ||||||||
\(58\) | −0.965864 | −0.126824 | ||||||||
\(59\) | 11.8731 | 1.54575 | 0.772875 | − | 0.634558i | \(-0.218818\pi\) | ||||
0.772875 | + | 0.634558i | \(0.218818\pi\) | |||||||
\(60\) | −20.5978 | −2.65916 | ||||||||
\(61\) | −4.91632 | −0.629471 | −0.314735 | − | 0.949179i | \(-0.601916\pi\) | ||||
−0.314735 | + | 0.949179i | \(0.601916\pi\) | |||||||
\(62\) | −7.30172 | −0.927320 | ||||||||
\(63\) | −1.84728 | −0.232736 | ||||||||
\(64\) | 1.09232 | 0.136540 | ||||||||
\(65\) | 14.0177 | 1.73868 | ||||||||
\(66\) | −3.17527 | −0.390849 | ||||||||
\(67\) | 9.03085 | 1.10329 | 0.551647 | − | 0.834078i | \(-0.314000\pi\) | ||||
0.551647 | + | 0.834078i | \(0.314000\pi\) | |||||||
\(68\) | 19.6712 | 2.38549 | ||||||||
\(69\) | 2.16736 | 0.260919 | ||||||||
\(70\) | 5.82120 | 0.695766 | ||||||||
\(71\) | −3.28754 | −0.390159 | −0.195079 | − | 0.980787i | \(-0.562496\pi\) | ||||
−0.195079 | + | 0.980787i | \(0.562496\pi\) | |||||||
\(72\) | −11.0553 | −1.30287 | ||||||||
\(73\) | −10.7068 | −1.25313 | −0.626566 | − | 0.779368i | \(-0.715540\pi\) | ||||
−0.626566 | + | 0.779368i | \(0.715540\pi\) | |||||||
\(74\) | 27.4713 | 3.19347 | ||||||||
\(75\) | 1.36312 | 0.157399 | ||||||||
\(76\) | 35.5159 | 4.07395 | ||||||||
\(77\) | 0.623183 | 0.0710183 | ||||||||
\(78\) | 37.1782 | 4.20960 | ||||||||
\(79\) | −2.73419 | −0.307620 | −0.153810 | − | 0.988100i | \(-0.549154\pi\) | ||||
−0.153810 | + | 0.988100i | \(0.549154\pi\) | |||||||
\(80\) | 15.8302 | 1.76987 | ||||||||
\(81\) | −11.2110 | −1.24567 | ||||||||
\(82\) | −2.89721 | −0.319944 | ||||||||
\(83\) | −5.15394 | −0.565718 | −0.282859 | − | 0.959161i | \(-0.591283\pi\) | ||||
−0.282859 | + | 0.959161i | \(0.591283\pi\) | |||||||
\(84\) | 10.7218 | 1.16985 | ||||||||
\(85\) | 9.04750 | 0.981339 | ||||||||
\(86\) | 30.6281 | 3.30272 | ||||||||
\(87\) | −0.818219 | −0.0877223 | ||||||||
\(88\) | 3.72950 | 0.397566 | ||||||||
\(89\) | 8.87297 | 0.940533 | 0.470267 | − | 0.882524i | \(-0.344158\pi\) | ||||
0.470267 | + | 0.882524i | \(0.344158\pi\) | |||||||
\(90\) | −9.07951 | −0.957064 | ||||||||
\(91\) | −7.29665 | −0.764897 | ||||||||
\(92\) | −4.54566 | −0.473918 | ||||||||
\(93\) | −6.18556 | −0.641413 | ||||||||
\(94\) | −13.3036 | −1.37216 | ||||||||
\(95\) | 16.3350 | 1.67594 | ||||||||
\(96\) | 13.7539 | 1.40375 | ||||||||
\(97\) | −3.08901 | −0.313642 | −0.156821 | − | 0.987627i | \(-0.550125\pi\) | ||||
−0.156821 | + | 0.987627i | \(0.550125\pi\) | |||||||
\(98\) | 14.8790 | 1.50301 | ||||||||
\(99\) | −0.971999 | −0.0976895 | ||||||||
\(100\) | −2.85891 | −0.285891 | ||||||||
\(101\) | −3.85148 | −0.383237 | −0.191618 | − | 0.981470i | \(-0.561374\pi\) | ||||
−0.191618 | + | 0.981470i | \(0.561374\pi\) | |||||||
\(102\) | 23.9962 | 2.37597 | ||||||||
\(103\) | −14.9638 | −1.47443 | −0.737215 | − | 0.675658i | \(-0.763860\pi\) | ||||
−0.737215 | + | 0.675658i | \(0.763860\pi\) | |||||||
\(104\) | −43.6675 | −4.28195 | ||||||||
\(105\) | 4.93135 | 0.481250 | ||||||||
\(106\) | 31.4773 | 3.05735 | ||||||||
\(107\) | 3.30099 | 0.319118 | 0.159559 | − | 0.987188i | \(-0.448993\pi\) | ||||
0.159559 | + | 0.987188i | \(0.448993\pi\) | |||||||
\(108\) | 12.8330 | 1.23486 | ||||||||
\(109\) | −12.7781 | −1.22392 | −0.611959 | − | 0.790890i | \(-0.709618\pi\) | ||||
−0.611959 | + | 0.790890i | \(0.709618\pi\) | |||||||
\(110\) | 3.06298 | 0.292044 | ||||||||
\(111\) | 23.2719 | 2.20887 | ||||||||
\(112\) | −8.24014 | −0.778620 | ||||||||
\(113\) | −15.1681 | −1.42690 | −0.713449 | − | 0.700707i | \(-0.752868\pi\) | ||||
−0.713449 | + | 0.700707i | \(0.752868\pi\) | |||||||
\(114\) | 43.3244 | 4.05770 | ||||||||
\(115\) | −2.09071 | −0.194960 | ||||||||
\(116\) | 1.71607 | 0.159334 | ||||||||
\(117\) | 11.3808 | 1.05216 | ||||||||
\(118\) | −30.3768 | −2.79641 | ||||||||
\(119\) | −4.70952 | −0.431721 | ||||||||
\(120\) | 29.5121 | 2.69408 | ||||||||
\(121\) | −10.6721 | −0.970190 | ||||||||
\(122\) | 12.5782 | 1.13877 | ||||||||
\(123\) | −2.45434 | −0.221300 | ||||||||
\(124\) | 12.9732 | 1.16502 | ||||||||
\(125\) | −11.7685 | −1.05260 | ||||||||
\(126\) | 4.72618 | 0.421041 | ||||||||
\(127\) | −0.0914164 | −0.00811190 | −0.00405595 | − | 0.999992i | \(-0.501291\pi\) | ||||
−0.00405595 | + | 0.999992i | \(0.501291\pi\) | |||||||
\(128\) | 9.89720 | 0.874797 | ||||||||
\(129\) | 25.9462 | 2.28444 | ||||||||
\(130\) | −35.8635 | −3.14543 | ||||||||
\(131\) | −12.4632 | −1.08892 | −0.544459 | − | 0.838787i | \(-0.683265\pi\) | ||||
−0.544459 | + | 0.838787i | \(0.683265\pi\) | |||||||
\(132\) | 5.64158 | 0.491037 | ||||||||
\(133\) | −8.50291 | −0.737296 | ||||||||
\(134\) | −23.1050 | −1.99597 | ||||||||
\(135\) | 5.90235 | 0.507994 | ||||||||
\(136\) | −28.1846 | −2.41681 | ||||||||
\(137\) | −12.0257 | −1.02743 | −0.513714 | − | 0.857962i | \(-0.671731\pi\) | ||||
−0.513714 | + | 0.857962i | \(0.671731\pi\) | |||||||
\(138\) | −5.54507 | −0.472027 | ||||||||
\(139\) | −19.9830 | −1.69494 | −0.847470 | − | 0.530843i | \(-0.821875\pi\) | ||||
−0.847470 | + | 0.530843i | \(0.821875\pi\) | |||||||
\(140\) | −10.3427 | −0.874114 | ||||||||
\(141\) | −11.2700 | −0.949101 | ||||||||
\(142\) | 8.41099 | 0.705835 | ||||||||
\(143\) | −3.83933 | −0.321061 | ||||||||
\(144\) | 12.8524 | 1.07103 | ||||||||
\(145\) | 0.789284 | 0.0655465 | ||||||||
\(146\) | 27.3927 | 2.26704 | ||||||||
\(147\) | 12.6046 | 1.03961 | ||||||||
\(148\) | −48.8089 | −4.01206 | ||||||||
\(149\) | −18.5822 | −1.52231 | −0.761155 | − | 0.648570i | \(-0.775368\pi\) | ||||
−0.761155 | + | 0.648570i | \(0.775368\pi\) | |||||||
\(150\) | −3.48747 | −0.284750 | ||||||||
\(151\) | −5.46717 | −0.444912 | −0.222456 | − | 0.974943i | \(-0.571407\pi\) | ||||
−0.222456 | + | 0.974943i | \(0.571407\pi\) | |||||||
\(152\) | −50.8865 | −4.12744 | ||||||||
\(153\) | 7.34559 | 0.593856 | ||||||||
\(154\) | −1.59438 | −0.128479 | ||||||||
\(155\) | 5.96682 | 0.479266 | ||||||||
\(156\) | −66.0555 | −5.28867 | ||||||||
\(157\) | 10.4416 | 0.833333 | 0.416666 | − | 0.909059i | \(-0.363198\pi\) | ||||
0.416666 | + | 0.909059i | \(0.363198\pi\) | |||||||
\(158\) | 6.99528 | 0.556514 | ||||||||
\(159\) | 26.6656 | 2.11472 | ||||||||
\(160\) | −13.2675 | −1.04889 | ||||||||
\(161\) | 1.08828 | 0.0857687 | ||||||||
\(162\) | 28.6828 | 2.25354 | ||||||||
\(163\) | −10.9470 | −0.857437 | −0.428719 | − | 0.903438i | \(-0.641035\pi\) | ||||
−0.428719 | + | 0.903438i | \(0.641035\pi\) | |||||||
\(164\) | 5.14755 | 0.401956 | ||||||||
\(165\) | 2.59476 | 0.202002 | ||||||||
\(166\) | 13.1861 | 1.02344 | ||||||||
\(167\) | 8.40690 | 0.650546 | 0.325273 | − | 0.945620i | \(-0.394544\pi\) | ||||
0.325273 | + | 0.945620i | \(0.394544\pi\) | |||||||
\(168\) | −15.3620 | −1.18521 | ||||||||
\(169\) | 31.9535 | 2.45796 | ||||||||
\(170\) | −23.1476 | −1.77534 | ||||||||
\(171\) | 13.2623 | 1.01419 | ||||||||
\(172\) | −54.4178 | −4.14932 | ||||||||
\(173\) | 8.06123 | 0.612884 | 0.306442 | − | 0.951889i | \(-0.400861\pi\) | ||||
0.306442 | + | 0.951889i | \(0.400861\pi\) | |||||||
\(174\) | 2.09337 | 0.158698 | ||||||||
\(175\) | 0.684455 | 0.0517399 | ||||||||
\(176\) | −4.33578 | −0.326822 | ||||||||
\(177\) | −25.7333 | −1.93423 | ||||||||
\(178\) | −22.7010 | −1.70151 | ||||||||
\(179\) | 18.0151 | 1.34651 | 0.673255 | − | 0.739410i | \(-0.264896\pi\) | ||||
0.673255 | + | 0.739410i | \(0.264896\pi\) | |||||||
\(180\) | 16.1318 | 1.20239 | ||||||||
\(181\) | −10.1670 | −0.755708 | −0.377854 | − | 0.925865i | \(-0.623338\pi\) | ||||
−0.377854 | + | 0.925865i | \(0.623338\pi\) | |||||||
\(182\) | 18.6681 | 1.38377 | ||||||||
\(183\) | 10.6554 | 0.787671 | ||||||||
\(184\) | 6.51294 | 0.480140 | ||||||||
\(185\) | −22.4489 | −1.65048 | ||||||||
\(186\) | 15.8254 | 1.16038 | ||||||||
\(187\) | −2.47804 | −0.181212 | ||||||||
\(188\) | 23.6368 | 1.72389 | ||||||||
\(189\) | −3.07237 | −0.223482 | ||||||||
\(190\) | −41.7923 | −3.03193 | ||||||||
\(191\) | −18.0265 | −1.30435 | −0.652176 | − | 0.758067i | \(-0.726144\pi\) | ||||
−0.652176 | + | 0.758067i | \(0.726144\pi\) | |||||||
\(192\) | −2.36744 | −0.170855 | ||||||||
\(193\) | −17.4815 | −1.25835 | −0.629174 | − | 0.777264i | \(-0.716607\pi\) | ||||
−0.629174 | + | 0.777264i | \(0.716607\pi\) | |||||||
\(194\) | 7.90308 | 0.567408 | ||||||||
\(195\) | −30.3813 | −2.17565 | ||||||||
\(196\) | −26.4359 | −1.88828 | ||||||||
\(197\) | 2.27470 | 0.162066 | 0.0810330 | − | 0.996711i | \(-0.474178\pi\) | ||||
0.0810330 | + | 0.996711i | \(0.474178\pi\) | |||||||
\(198\) | 2.48681 | 0.176730 | ||||||||
\(199\) | 16.5889 | 1.17596 | 0.587978 | − | 0.808877i | \(-0.299924\pi\) | ||||
0.587978 | + | 0.808877i | \(0.299924\pi\) | |||||||
\(200\) | 4.09619 | 0.289644 | ||||||||
\(201\) | −19.5731 | −1.38058 | ||||||||
\(202\) | 9.85381 | 0.693312 | ||||||||
\(203\) | −0.410848 | −0.0288359 | ||||||||
\(204\) | −42.6346 | −2.98502 | ||||||||
\(205\) | 2.36754 | 0.165356 | ||||||||
\(206\) | 38.2842 | 2.66739 | ||||||||
\(207\) | −1.69743 | −0.117980 | ||||||||
\(208\) | 50.7662 | 3.52000 | ||||||||
\(209\) | −4.47404 | −0.309476 | ||||||||
\(210\) | −12.6166 | −0.870628 | ||||||||
\(211\) | 0.486380 | 0.0334838 | 0.0167419 | − | 0.999860i | \(-0.494671\pi\) | ||||
0.0167419 | + | 0.999860i | \(0.494671\pi\) | |||||||
\(212\) | −55.9266 | −3.84105 | ||||||||
\(213\) | 7.12526 | 0.488215 | ||||||||
\(214\) | −8.44540 | −0.577316 | ||||||||
\(215\) | −25.0287 | −1.70694 | ||||||||
\(216\) | −18.3869 | −1.25107 | ||||||||
\(217\) | −3.10592 | −0.210844 | ||||||||
\(218\) | 32.6920 | 2.21418 | ||||||||
\(219\) | 23.2054 | 1.56807 | ||||||||
\(220\) | −5.44208 | −0.366905 | ||||||||
\(221\) | 29.0146 | 1.95173 | ||||||||
\(222\) | −59.5400 | −3.99606 | ||||||||
\(223\) | −13.9279 | −0.932683 | −0.466342 | − | 0.884605i | \(-0.654428\pi\) | ||||
−0.466342 | + | 0.884605i | \(0.654428\pi\) | |||||||
\(224\) | 6.90615 | 0.461437 | ||||||||
\(225\) | −1.06757 | −0.0711711 | ||||||||
\(226\) | 38.8069 | 2.58140 | ||||||||
\(227\) | −4.44523 | −0.295040 | −0.147520 | − | 0.989059i | \(-0.547129\pi\) | ||||
−0.147520 | + | 0.989059i | \(0.547129\pi\) | |||||||
\(228\) | −76.9755 | −5.09783 | ||||||||
\(229\) | 20.0929 | 1.32777 | 0.663887 | − | 0.747833i | \(-0.268906\pi\) | ||||
0.663887 | + | 0.747833i | \(0.268906\pi\) | |||||||
\(230\) | 5.34897 | 0.352701 | ||||||||
\(231\) | −1.35066 | −0.0888668 | ||||||||
\(232\) | −2.45876 | −0.161426 | ||||||||
\(233\) | 21.3391 | 1.39797 | 0.698986 | − | 0.715136i | \(-0.253635\pi\) | ||||
0.698986 | + | 0.715136i | \(0.253635\pi\) | |||||||
\(234\) | −29.1172 | −1.90345 | ||||||||
\(235\) | 10.8714 | 0.709172 | ||||||||
\(236\) | 53.9712 | 3.51323 | ||||||||
\(237\) | 5.92595 | 0.384932 | ||||||||
\(238\) | 12.0491 | 0.781025 | ||||||||
\(239\) | 17.5715 | 1.13661 | 0.568303 | − | 0.822819i | \(-0.307600\pi\) | ||||
0.568303 | + | 0.822819i | \(0.307600\pi\) | |||||||
\(240\) | −34.3097 | −2.21468 | ||||||||
\(241\) | −0.237506 | −0.0152991 | −0.00764957 | − | 0.999971i | \(-0.502435\pi\) | ||||
−0.00764957 | + | 0.999971i | \(0.502435\pi\) | |||||||
\(242\) | 27.3040 | 1.75517 | ||||||||
\(243\) | 15.8289 | 1.01542 | ||||||||
\(244\) | −22.3479 | −1.43068 | ||||||||
\(245\) | −12.1588 | −0.776798 | ||||||||
\(246\) | 6.27929 | 0.400353 | ||||||||
\(247\) | 52.3851 | 3.33318 | ||||||||
\(248\) | −18.5877 | −1.18032 | ||||||||
\(249\) | 11.1704 | 0.707896 | ||||||||
\(250\) | 30.1090 | 1.90426 | ||||||||
\(251\) | 4.70249 | 0.296819 | 0.148409 | − | 0.988926i | \(-0.452585\pi\) | ||||
0.148409 | + | 0.988926i | \(0.452585\pi\) | |||||||
\(252\) | −8.39712 | −0.528969 | ||||||||
\(253\) | 0.572630 | 0.0360009 | ||||||||
\(254\) | 0.233884 | 0.0146752 | ||||||||
\(255\) | −19.6092 | −1.22797 | ||||||||
\(256\) | −27.5061 | −1.71913 | ||||||||
\(257\) | 4.32883 | 0.270025 | 0.135012 | − | 0.990844i | \(-0.456893\pi\) | ||||
0.135012 | + | 0.990844i | \(0.456893\pi\) | |||||||
\(258\) | −66.3821 | −4.13277 | ||||||||
\(259\) | 11.6854 | 0.726095 | ||||||||
\(260\) | 63.7195 | 3.95172 | ||||||||
\(261\) | 0.640813 | 0.0396653 | ||||||||
\(262\) | 31.8866 | 1.96996 | ||||||||
\(263\) | −7.77504 | −0.479429 | −0.239715 | − | 0.970843i | \(-0.577054\pi\) | ||||
−0.239715 | + | 0.970843i | \(0.577054\pi\) | |||||||
\(264\) | −8.08315 | −0.497484 | ||||||||
\(265\) | −25.7226 | −1.58013 | ||||||||
\(266\) | 21.7543 | 1.33384 | ||||||||
\(267\) | −19.2309 | −1.17691 | ||||||||
\(268\) | 41.0512 | 2.50760 | ||||||||
\(269\) | −30.9948 | −1.88978 | −0.944892 | − | 0.327383i | \(-0.893833\pi\) | ||||
−0.944892 | + | 0.327383i | \(0.893833\pi\) | |||||||
\(270\) | −15.1009 | −0.919009 | ||||||||
\(271\) | 14.8952 | 0.904821 | 0.452410 | − | 0.891810i | \(-0.350564\pi\) | ||||
0.452410 | + | 0.891810i | \(0.350564\pi\) | |||||||
\(272\) | 32.7663 | 1.98675 | ||||||||
\(273\) | 15.8144 | 0.957133 | ||||||||
\(274\) | 30.7672 | 1.85872 | ||||||||
\(275\) | 0.360145 | 0.0217175 | ||||||||
\(276\) | 9.85206 | 0.593024 | ||||||||
\(277\) | −15.2531 | −0.916468 | −0.458234 | − | 0.888832i | \(-0.651518\pi\) | ||||
−0.458234 | + | 0.888832i | \(0.651518\pi\) | |||||||
\(278\) | 51.1256 | 3.06631 | ||||||||
\(279\) | 4.84441 | 0.290027 | ||||||||
\(280\) | 14.8188 | 0.885591 | ||||||||
\(281\) | 7.74032 | 0.461749 | 0.230874 | − | 0.972984i | \(-0.425841\pi\) | ||||
0.230874 | + | 0.972984i | \(0.425841\pi\) | |||||||
\(282\) | 28.8336 | 1.71702 | ||||||||
\(283\) | −27.5054 | −1.63503 | −0.817513 | − | 0.575910i | \(-0.804648\pi\) | ||||
−0.817513 | + | 0.575910i | \(0.804648\pi\) | |||||||
\(284\) | −14.9440 | −0.886764 | ||||||||
\(285\) | −35.4038 | −2.09714 | ||||||||
\(286\) | 9.82273 | 0.580830 | ||||||||
\(287\) | −1.23238 | −0.0727453 | ||||||||
\(288\) | −10.7717 | −0.634731 | ||||||||
\(289\) | 1.72706 | 0.101592 | ||||||||
\(290\) | −2.01934 | −0.118580 | ||||||||
\(291\) | 6.69499 | 0.392467 | ||||||||
\(292\) | −48.6693 | −2.84816 | ||||||||
\(293\) | −12.0116 | −0.701726 | −0.350863 | − | 0.936427i | \(-0.614112\pi\) | ||||
−0.350863 | + | 0.936427i | \(0.614112\pi\) | |||||||
\(294\) | −32.2481 | −1.88075 | ||||||||
\(295\) | 24.8233 | 1.44527 | ||||||||
\(296\) | 69.9325 | 4.06474 | ||||||||
\(297\) | −1.61661 | −0.0938052 | ||||||||
\(298\) | 47.5415 | 2.75401 | ||||||||
\(299\) | −6.70474 | −0.387745 | ||||||||
\(300\) | 6.19627 | 0.357742 | ||||||||
\(301\) | 13.0282 | 0.750935 | ||||||||
\(302\) | 13.9875 | 0.804888 | ||||||||
\(303\) | 8.34753 | 0.479553 | ||||||||
\(304\) | 59.1587 | 3.39299 | ||||||||
\(305\) | −10.2786 | −0.588551 | ||||||||
\(306\) | −18.7933 | −1.07434 | ||||||||
\(307\) | −8.23444 | −0.469965 | −0.234982 | − | 0.972000i | \(-0.575503\pi\) | ||||
−0.234982 | + | 0.972000i | \(0.575503\pi\) | |||||||
\(308\) | 2.83278 | 0.161412 | ||||||||
\(309\) | 32.4320 | 1.84499 | ||||||||
\(310\) | −15.2658 | −0.867039 | ||||||||
\(311\) | −6.20525 | −0.351868 | −0.175934 | − | 0.984402i | \(-0.556294\pi\) | ||||
−0.175934 | + | 0.984402i | \(0.556294\pi\) | |||||||
\(312\) | 94.6431 | 5.35811 | ||||||||
\(313\) | −11.6970 | −0.661153 | −0.330576 | − | 0.943779i | \(-0.607243\pi\) | ||||
−0.330576 | + | 0.943779i | \(0.607243\pi\) | |||||||
\(314\) | −26.7144 | −1.50758 | ||||||||
\(315\) | −3.86213 | −0.217607 | ||||||||
\(316\) | −12.4287 | −0.699168 | ||||||||
\(317\) | 9.01989 | 0.506608 | 0.253304 | − | 0.967387i | \(-0.418483\pi\) | ||||
0.253304 | + | 0.967387i | \(0.418483\pi\) | |||||||
\(318\) | −68.2226 | −3.82573 | ||||||||
\(319\) | −0.216179 | −0.0121037 | ||||||||
\(320\) | 2.28372 | 0.127664 | ||||||||
\(321\) | −7.15441 | −0.399320 | ||||||||
\(322\) | −2.78431 | −0.155164 | ||||||||
\(323\) | 33.8112 | 1.88131 | ||||||||
\(324\) | −50.9615 | −2.83119 | ||||||||
\(325\) | −4.21682 | −0.233907 | ||||||||
\(326\) | 28.0074 | 1.55119 | ||||||||
\(327\) | 27.6946 | 1.53152 | ||||||||
\(328\) | −7.37532 | −0.407234 | ||||||||
\(329\) | −5.65892 | −0.311986 | ||||||||
\(330\) | −6.63857 | −0.365441 | ||||||||
\(331\) | 27.3403 | 1.50276 | 0.751379 | − | 0.659871i | \(-0.229389\pi\) | ||||
0.751379 | + | 0.659871i | \(0.229389\pi\) | |||||||
\(332\) | −23.4280 | −1.28578 | ||||||||
\(333\) | −18.2261 | −0.998784 | ||||||||
\(334\) | −21.5086 | −1.17690 | ||||||||
\(335\) | 18.8809 | 1.03157 | ||||||||
\(336\) | 17.8593 | 0.974306 | ||||||||
\(337\) | −33.8605 | −1.84450 | −0.922250 | − | 0.386595i | \(-0.873651\pi\) | ||||
−0.922250 | + | 0.386595i | \(0.873651\pi\) | |||||||
\(338\) | −81.7514 | −4.44669 | ||||||||
\(339\) | 32.8747 | 1.78551 | ||||||||
\(340\) | 41.1269 | 2.23042 | ||||||||
\(341\) | −1.63427 | −0.0885005 | ||||||||
\(342\) | −33.9308 | −1.83477 | ||||||||
\(343\) | 13.9470 | 0.753069 | ||||||||
\(344\) | 77.9688 | 4.20380 | ||||||||
\(345\) | 4.53131 | 0.243958 | ||||||||
\(346\) | −20.6242 | −1.10877 | ||||||||
\(347\) | 1.64263 | 0.0881809 | 0.0440904 | − | 0.999028i | \(-0.485961\pi\) | ||||
0.0440904 | + | 0.999028i | \(0.485961\pi\) | |||||||
\(348\) | −3.71934 | −0.199378 | ||||||||
\(349\) | −1.00000 | −0.0535288 | ||||||||
\(350\) | −1.75114 | −0.0936025 | ||||||||
\(351\) | 18.9284 | 1.01032 | ||||||||
\(352\) | 3.63386 | 0.193685 | ||||||||
\(353\) | 2.92348 | 0.155601 | 0.0778004 | − | 0.996969i | \(-0.475210\pi\) | ||||
0.0778004 | + | 0.996969i | \(0.475210\pi\) | |||||||
\(354\) | 65.8373 | 3.49921 | ||||||||
\(355\) | −6.87328 | −0.364796 | ||||||||
\(356\) | 40.3335 | 2.13767 | ||||||||
\(357\) | 10.2072 | 0.540222 | ||||||||
\(358\) | −46.0906 | −2.43597 | ||||||||
\(359\) | −17.8603 | −0.942631 | −0.471316 | − | 0.881965i | \(-0.656221\pi\) | ||||
−0.471316 | + | 0.881965i | \(0.656221\pi\) | |||||||
\(360\) | −23.1133 | −1.21818 | ||||||||
\(361\) | 42.0452 | 2.21291 | ||||||||
\(362\) | 26.0118 | 1.36715 | ||||||||
\(363\) | 23.1302 | 1.21402 | ||||||||
\(364\) | −33.1681 | −1.73848 | ||||||||
\(365\) | −22.3848 | −1.17167 | ||||||||
\(366\) | −27.2613 | −1.42497 | ||||||||
\(367\) | −18.0746 | −0.943489 | −0.471744 | − | 0.881735i | \(-0.656375\pi\) | ||||
−0.471744 | + | 0.881735i | \(0.656375\pi\) | |||||||
\(368\) | −7.57170 | −0.394702 | ||||||||
\(369\) | 1.92219 | 0.100065 | ||||||||
\(370\) | 57.4344 | 2.98587 | ||||||||
\(371\) | 13.3895 | 0.695146 | ||||||||
\(372\) | −28.1174 | −1.45782 | ||||||||
\(373\) | −33.4792 | −1.73349 | −0.866745 | − | 0.498752i | \(-0.833792\pi\) | ||||
−0.866745 | + | 0.498752i | \(0.833792\pi\) | |||||||
\(374\) | 6.33994 | 0.327831 | ||||||||
\(375\) | 25.5064 | 1.31715 | ||||||||
\(376\) | −33.8664 | −1.74653 | ||||||||
\(377\) | 2.53117 | 0.130362 | ||||||||
\(378\) | 7.86049 | 0.404300 | ||||||||
\(379\) | 32.9058 | 1.69026 | 0.845130 | − | 0.534561i | \(-0.179523\pi\) | ||||
0.845130 | + | 0.534561i | \(0.179523\pi\) | |||||||
\(380\) | 74.2534 | 3.80912 | ||||||||
\(381\) | 0.198132 | 0.0101506 | ||||||||
\(382\) | 46.1199 | 2.35970 | ||||||||
\(383\) | −32.9753 | −1.68496 | −0.842479 | − | 0.538730i | \(-0.818904\pi\) | ||||
−0.842479 | + | 0.538730i | \(0.818904\pi\) | |||||||
\(384\) | −21.4508 | −1.09465 | ||||||||
\(385\) | 1.30289 | 0.0664017 | ||||||||
\(386\) | 44.7256 | 2.27647 | ||||||||
\(387\) | −20.3206 | −1.03295 | ||||||||
\(388\) | −14.0416 | −0.712854 | ||||||||
\(389\) | 27.3377 | 1.38608 | 0.693038 | − | 0.720901i | \(-0.256272\pi\) | ||||
0.693038 | + | 0.720901i | \(0.256272\pi\) | |||||||
\(390\) | 77.7289 | 3.93596 | ||||||||
\(391\) | −4.32748 | −0.218850 | ||||||||
\(392\) | 37.8769 | 1.91307 | ||||||||
\(393\) | 27.0123 | 1.36259 | ||||||||
\(394\) | −5.81971 | −0.293193 | ||||||||
\(395\) | −5.71639 | −0.287623 | ||||||||
\(396\) | −4.41837 | −0.222032 | ||||||||
\(397\) | −2.63299 | −0.132146 | −0.0660730 | − | 0.997815i | \(-0.521047\pi\) | ||||
−0.0660730 | + | 0.997815i | \(0.521047\pi\) | |||||||
\(398\) | −42.4418 | −2.12742 | ||||||||
\(399\) | 18.4288 | 0.922595 | ||||||||
\(400\) | −4.76208 | −0.238104 | ||||||||
\(401\) | −7.71959 | −0.385498 | −0.192749 | − | 0.981248i | \(-0.561740\pi\) | ||||
−0.192749 | + | 0.981248i | \(0.561740\pi\) | |||||||
\(402\) | 50.0767 | 2.49760 | ||||||||
\(403\) | 19.1351 | 0.953187 | ||||||||
\(404\) | −17.5075 | −0.871031 | ||||||||
\(405\) | −23.4390 | −1.16469 | ||||||||
\(406\) | 1.05113 | 0.0521669 | ||||||||
\(407\) | 6.14859 | 0.304775 | ||||||||
\(408\) | 61.0860 | 3.02421 | ||||||||
\(409\) | 6.19025 | 0.306088 | 0.153044 | − | 0.988219i | \(-0.451092\pi\) | ||||
0.153044 | + | 0.988219i | \(0.451092\pi\) | |||||||
\(410\) | −6.05723 | −0.299146 | ||||||||
\(411\) | 26.0640 | 1.28564 | ||||||||
\(412\) | −68.0205 | −3.35113 | ||||||||
\(413\) | −12.9213 | −0.635817 | ||||||||
\(414\) | 4.34279 | 0.213436 | ||||||||
\(415\) | −10.7754 | −0.528943 | ||||||||
\(416\) | −42.5477 | −2.08607 | ||||||||
\(417\) | 43.3104 | 2.12092 | ||||||||
\(418\) | 11.4466 | 0.559871 | ||||||||
\(419\) | 0.119648 | 0.00584518 | 0.00292259 | − | 0.999996i | \(-0.499070\pi\) | ||||
0.00292259 | + | 0.999996i | \(0.499070\pi\) | |||||||
\(420\) | 22.4162 | 1.09380 | ||||||||
\(421\) | 35.3432 | 1.72252 | 0.861260 | − | 0.508165i | \(-0.169676\pi\) | ||||
0.861260 | + | 0.508165i | \(0.169676\pi\) | |||||||
\(422\) | −1.24438 | −0.0605753 | ||||||||
\(423\) | 8.82640 | 0.429154 | ||||||||
\(424\) | 80.1306 | 3.89149 | ||||||||
\(425\) | −2.72169 | −0.132021 | ||||||||
\(426\) | −18.2296 | −0.883227 | ||||||||
\(427\) | 5.35035 | 0.258922 | ||||||||
\(428\) | 15.0052 | 0.725302 | ||||||||
\(429\) | 8.32120 | 0.401751 | ||||||||
\(430\) | 64.0346 | 3.08802 | ||||||||
\(431\) | −35.4439 | −1.70727 | −0.853636 | − | 0.520870i | \(-0.825608\pi\) | ||||
−0.853636 | + | 0.520870i | \(0.825608\pi\) | |||||||
\(432\) | 21.3759 | 1.02845 | ||||||||
\(433\) | −31.0338 | −1.49139 | −0.745694 | − | 0.666289i | \(-0.767882\pi\) | ||||
−0.745694 | + | 0.666289i | \(0.767882\pi\) | |||||||
\(434\) | 7.94634 | 0.381437 | ||||||||
\(435\) | −1.71066 | −0.0820198 | ||||||||
\(436\) | −58.0848 | −2.78176 | ||||||||
\(437\) | −7.81314 | −0.373753 | ||||||||
\(438\) | −59.3698 | −2.83680 | ||||||||
\(439\) | 12.8352 | 0.612590 | 0.306295 | − | 0.951937i | \(-0.400911\pi\) | ||||
0.306295 | + | 0.951937i | \(0.400911\pi\) | |||||||
\(440\) | 7.79731 | 0.371722 | ||||||||
\(441\) | −9.87164 | −0.470078 | ||||||||
\(442\) | −74.2324 | −3.53087 | ||||||||
\(443\) | 40.8922 | 1.94285 | 0.971424 | − | 0.237351i | \(-0.0762791\pi\) | ||||
0.971424 | + | 0.237351i | \(0.0762791\pi\) | |||||||
\(444\) | 105.786 | 5.02039 | ||||||||
\(445\) | 18.5508 | 0.879393 | ||||||||
\(446\) | 35.6339 | 1.68731 | ||||||||
\(447\) | 40.2742 | 1.90490 | ||||||||
\(448\) | −1.18875 | −0.0561631 | ||||||||
\(449\) | −15.8681 | −0.748863 | −0.374432 | − | 0.927255i | \(-0.622162\pi\) | ||||
−0.374432 | + | 0.927255i | \(0.622162\pi\) | |||||||
\(450\) | 2.73131 | 0.128755 | ||||||||
\(451\) | −0.648452 | −0.0305344 | ||||||||
\(452\) | −68.9492 | −3.24310 | ||||||||
\(453\) | 11.8493 | 0.556728 | ||||||||
\(454\) | 11.3729 | 0.533756 | ||||||||
\(455\) | −15.2552 | −0.715174 | ||||||||
\(456\) | 110.289 | 5.16476 | ||||||||
\(457\) | −6.44894 | −0.301669 | −0.150834 | − | 0.988559i | \(-0.548196\pi\) | ||||
−0.150834 | + | 0.988559i | \(0.548196\pi\) | |||||||
\(458\) | −51.4065 | −2.40207 | ||||||||
\(459\) | 12.2170 | 0.570243 | ||||||||
\(460\) | −9.50365 | −0.443110 | ||||||||
\(461\) | 26.6938 | 1.24326 | 0.621628 | − | 0.783313i | \(-0.286472\pi\) | ||||
0.621628 | + | 0.783313i | \(0.286472\pi\) | |||||||
\(462\) | 3.45559 | 0.160769 | ||||||||
\(463\) | 24.0380 | 1.11714 | 0.558570 | − | 0.829457i | \(-0.311350\pi\) | ||||
0.558570 | + | 0.829457i | \(0.311350\pi\) | |||||||
\(464\) | 2.85846 | 0.132701 | ||||||||
\(465\) | −12.9322 | −0.599717 | ||||||||
\(466\) | −54.5950 | −2.52906 | ||||||||
\(467\) | −3.66311 | −0.169509 | −0.0847543 | − | 0.996402i | \(-0.527011\pi\) | ||||
−0.0847543 | + | 0.996402i | \(0.527011\pi\) | |||||||
\(468\) | 51.7333 | 2.39137 | ||||||||
\(469\) | −9.82812 | −0.453820 | ||||||||
\(470\) | −27.8139 | −1.28296 | ||||||||
\(471\) | −22.6307 | −1.04277 | ||||||||
\(472\) | −77.3290 | −3.55935 | ||||||||
\(473\) | 6.85517 | 0.315201 | ||||||||
\(474\) | −15.1612 | −0.696379 | ||||||||
\(475\) | −4.91393 | −0.225467 | ||||||||
\(476\) | −21.4079 | −0.981228 | ||||||||
\(477\) | −20.8840 | −0.956212 | ||||||||
\(478\) | −44.9558 | −2.05623 | ||||||||
\(479\) | 34.5023 | 1.57645 | 0.788224 | − | 0.615388i | \(-0.211001\pi\) | ||||
0.788224 | + | 0.615388i | \(0.211001\pi\) | |||||||
\(480\) | 28.7553 | 1.31250 | ||||||||
\(481\) | −71.9919 | −3.28255 | ||||||||
\(482\) | 0.607648 | 0.0276776 | ||||||||
\(483\) | −2.35870 | −0.107324 | ||||||||
\(484\) | −48.5117 | −2.20508 | ||||||||
\(485\) | −6.45823 | −0.293253 | ||||||||
\(486\) | −40.4973 | −1.83700 | ||||||||
\(487\) | −38.9746 | −1.76611 | −0.883054 | − | 0.469272i | \(-0.844516\pi\) | ||||
−0.883054 | + | 0.469272i | \(0.844516\pi\) | |||||||
\(488\) | 32.0197 | 1.44946 | ||||||||
\(489\) | 23.7261 | 1.07293 | ||||||||
\(490\) | 31.1077 | 1.40530 | ||||||||
\(491\) | 30.1341 | 1.35993 | 0.679966 | − | 0.733244i | \(-0.261994\pi\) | ||||
0.679966 | + | 0.733244i | \(0.261994\pi\) | |||||||
\(492\) | −11.1566 | −0.502977 | ||||||||
\(493\) | 1.63371 | 0.0735785 | ||||||||
\(494\) | −134.025 | −6.03005 | ||||||||
\(495\) | −2.03217 | −0.0913391 | ||||||||
\(496\) | 21.6094 | 0.970289 | ||||||||
\(497\) | 3.57777 | 0.160485 | ||||||||
\(498\) | −28.5789 | −1.28065 | ||||||||
\(499\) | −6.41075 | −0.286985 | −0.143492 | − | 0.989651i | \(-0.545833\pi\) | ||||
−0.143492 | + | 0.989651i | \(0.545833\pi\) | |||||||
\(500\) | −53.4954 | −2.39239 | ||||||||
\(501\) | −18.2207 | −0.814043 | ||||||||
\(502\) | −12.0311 | −0.536973 | ||||||||
\(503\) | −8.29640 | −0.369918 | −0.184959 | − | 0.982746i | \(-0.559215\pi\) | ||||
−0.184959 | + | 0.982746i | \(0.559215\pi\) | |||||||
\(504\) | 12.0312 | 0.535914 | ||||||||
\(505\) | −8.05233 | −0.358324 | ||||||||
\(506\) | −1.46504 | −0.0651291 | ||||||||
\(507\) | −69.2546 | −3.07571 | ||||||||
\(508\) | −0.415548 | −0.0184370 | ||||||||
\(509\) | −1.52084 | −0.0674099 | −0.0337050 | − | 0.999432i | \(-0.510731\pi\) | ||||
−0.0337050 | + | 0.999432i | \(0.510731\pi\) | |||||||
\(510\) | 50.1690 | 2.22152 | ||||||||
\(511\) | 11.6520 | 0.515454 | ||||||||
\(512\) | 50.5786 | 2.23528 | ||||||||
\(513\) | 22.0575 | 0.973864 | ||||||||
\(514\) | −11.0751 | −0.488501 | ||||||||
\(515\) | −31.2850 | −1.37858 | ||||||||
\(516\) | 117.943 | 5.19214 | ||||||||
\(517\) | −2.97760 | −0.130955 | ||||||||
\(518\) | −29.8965 | −1.31358 | ||||||||
\(519\) | −17.4715 | −0.766916 | ||||||||
\(520\) | −91.2961 | −4.00360 | ||||||||
\(521\) | −2.10526 | −0.0922333 | −0.0461166 | − | 0.998936i | \(-0.514685\pi\) | ||||
−0.0461166 | + | 0.998936i | \(0.514685\pi\) | |||||||
\(522\) | −1.63949 | −0.0717584 | ||||||||
\(523\) | 27.1481 | 1.18710 | 0.593552 | − | 0.804796i | \(-0.297725\pi\) | ||||
0.593552 | + | 0.804796i | \(0.297725\pi\) | |||||||
\(524\) | −56.6537 | −2.47493 | ||||||||
\(525\) | −1.48346 | −0.0647434 | ||||||||
\(526\) | 19.8920 | 0.867334 | ||||||||
\(527\) | 12.3505 | 0.537995 | ||||||||
\(528\) | 9.39717 | 0.408959 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 65.8100 | 2.85860 | ||||||||
\(531\) | 20.1538 | 0.874601 | ||||||||
\(532\) | −38.6513 | −1.67575 | ||||||||
\(533\) | 7.59252 | 0.328868 | ||||||||
\(534\) | 49.2012 | 2.12915 | ||||||||
\(535\) | 6.90141 | 0.298374 | ||||||||
\(536\) | −58.8174 | −2.54052 | ||||||||
\(537\) | −39.0451 | −1.68492 | ||||||||
\(538\) | 79.2985 | 3.41880 | ||||||||
\(539\) | 3.33021 | 0.143442 | ||||||||
\(540\) | 26.8301 | 1.15458 | ||||||||
\(541\) | 13.6886 | 0.588519 | 0.294259 | − | 0.955726i | \(-0.404927\pi\) | ||||
0.294259 | + | 0.955726i | \(0.404927\pi\) | |||||||
\(542\) | −38.1087 | −1.63691 | ||||||||
\(543\) | 22.0355 | 0.945635 | ||||||||
\(544\) | −27.4618 | −1.17742 | ||||||||
\(545\) | −26.7152 | −1.14436 | ||||||||
\(546\) | −40.4604 | −1.73155 | ||||||||
\(547\) | 18.2783 | 0.781522 | 0.390761 | − | 0.920492i | \(-0.372212\pi\) | ||||
0.390761 | + | 0.920492i | \(0.372212\pi\) | |||||||
\(548\) | −54.6649 | −2.33517 | ||||||||
\(549\) | −8.34511 | −0.356161 | ||||||||
\(550\) | −0.921412 | −0.0392891 | ||||||||
\(551\) | 2.94961 | 0.125658 | ||||||||
\(552\) | −14.1158 | −0.600810 | ||||||||
\(553\) | 2.97557 | 0.126534 | ||||||||
\(554\) | 39.0242 | 1.65798 | ||||||||
\(555\) | 48.6548 | 2.06528 | ||||||||
\(556\) | −90.8361 | −3.85231 | ||||||||
\(557\) | −27.5191 | −1.16602 | −0.583010 | − | 0.812465i | \(-0.698125\pi\) | ||||
−0.583010 | + | 0.812465i | \(0.698125\pi\) | |||||||
\(558\) | −12.3942 | −0.524687 | ||||||||
\(559\) | −80.2649 | −3.39485 | ||||||||
\(560\) | −17.2278 | −0.728005 | ||||||||
\(561\) | 5.37080 | 0.226755 | ||||||||
\(562\) | −19.8032 | −0.835348 | ||||||||
\(563\) | 2.09577 | 0.0883262 | 0.0441631 | − | 0.999024i | \(-0.485938\pi\) | ||||
0.0441631 | + | 0.999024i | \(0.485938\pi\) | |||||||
\(564\) | −51.2294 | −2.15714 | ||||||||
\(565\) | −31.7122 | −1.33414 | ||||||||
\(566\) | 70.3712 | 2.95792 | ||||||||
\(567\) | 12.2008 | 0.512384 | ||||||||
\(568\) | 21.4115 | 0.898407 | ||||||||
\(569\) | −14.4176 | −0.604417 | −0.302208 | − | 0.953242i | \(-0.597724\pi\) | ||||
−0.302208 | + | 0.953242i | \(0.597724\pi\) | |||||||
\(570\) | 90.5788 | 3.79393 | ||||||||
\(571\) | −16.6303 | −0.695954 | −0.347977 | − | 0.937503i | \(-0.613131\pi\) | ||||
−0.347977 | + | 0.937503i | \(0.613131\pi\) | |||||||
\(572\) | −17.4523 | −0.729717 | ||||||||
\(573\) | 39.0699 | 1.63217 | ||||||||
\(574\) | 3.15299 | 0.131603 | ||||||||
\(575\) | 0.628931 | 0.0262282 | ||||||||
\(576\) | 1.85413 | 0.0772554 | ||||||||
\(577\) | 44.5377 | 1.85413 | 0.927064 | − | 0.374904i | \(-0.122324\pi\) | ||||
0.927064 | + | 0.374904i | \(0.122324\pi\) | |||||||
\(578\) | −4.41860 | −0.183790 | ||||||||
\(579\) | 37.8887 | 1.57460 | ||||||||
\(580\) | 3.58781 | 0.148976 | ||||||||
\(581\) | 5.60894 | 0.232698 | ||||||||
\(582\) | −17.1288 | −0.710011 | ||||||||
\(583\) | 7.04523 | 0.291784 | ||||||||
\(584\) | 69.7325 | 2.88555 | ||||||||
\(585\) | 23.7940 | 0.983761 | ||||||||
\(586\) | 30.7311 | 1.26949 | ||||||||
\(587\) | 39.7683 | 1.64142 | 0.820708 | − | 0.571348i | \(-0.193579\pi\) | ||||
0.820708 | + | 0.571348i | \(0.193579\pi\) | |||||||
\(588\) | 57.2960 | 2.36285 | ||||||||
\(589\) | 22.2984 | 0.918791 | ||||||||
\(590\) | −63.5091 | −2.61463 | ||||||||
\(591\) | −4.93009 | −0.202797 | ||||||||
\(592\) | −81.3008 | −3.34144 | ||||||||
\(593\) | 33.6019 | 1.37987 | 0.689933 | − | 0.723874i | \(-0.257640\pi\) | ||||
0.689933 | + | 0.723874i | \(0.257640\pi\) | |||||||
\(594\) | 4.13601 | 0.169703 | ||||||||
\(595\) | −9.84624 | −0.403656 | ||||||||
\(596\) | −84.4682 | −3.45995 | ||||||||
\(597\) | −35.9540 | −1.47150 | ||||||||
\(598\) | 17.1537 | 0.701468 | ||||||||
\(599\) | −17.6751 | −0.722186 | −0.361093 | − | 0.932530i | \(-0.617596\pi\) | ||||
−0.361093 | + | 0.932530i | \(0.617596\pi\) | |||||||
\(600\) | −8.87790 | −0.362439 | ||||||||
\(601\) | −4.34564 | −0.177262 | −0.0886311 | − | 0.996065i | \(-0.528249\pi\) | ||||
−0.0886311 | + | 0.996065i | \(0.528249\pi\) | |||||||
\(602\) | −33.3321 | −1.35851 | ||||||||
\(603\) | 15.3292 | 0.624255 | ||||||||
\(604\) | −24.8519 | −1.01121 | ||||||||
\(605\) | −22.3123 | −0.907122 | ||||||||
\(606\) | −21.3567 | −0.867557 | ||||||||
\(607\) | −17.5745 | −0.713329 | −0.356664 | − | 0.934233i | \(-0.616086\pi\) | ||||
−0.356664 | + | 0.934233i | \(0.616086\pi\) | |||||||
\(608\) | −49.5816 | −2.01080 | ||||||||
\(609\) | 0.890453 | 0.0360830 | ||||||||
\(610\) | 26.2973 | 1.06475 | ||||||||
\(611\) | 34.8637 | 1.41044 | ||||||||
\(612\) | 33.3905 | 1.34973 | ||||||||
\(613\) | −6.27729 | −0.253538 | −0.126769 | − | 0.991932i | \(-0.540461\pi\) | ||||
−0.126769 | + | 0.991932i | \(0.540461\pi\) | |||||||
\(614\) | 21.0674 | 0.850211 | ||||||||
\(615\) | −5.13131 | −0.206914 | ||||||||
\(616\) | −4.05875 | −0.163532 | ||||||||
\(617\) | 27.3866 | 1.10254 | 0.551272 | − | 0.834326i | \(-0.314143\pi\) | ||||
0.551272 | + | 0.834326i | \(0.314143\pi\) | |||||||
\(618\) | −82.9755 | −3.33776 | ||||||||
\(619\) | 17.5376 | 0.704897 | 0.352449 | − | 0.935831i | \(-0.385349\pi\) | ||||
0.352449 | + | 0.935831i | \(0.385349\pi\) | |||||||
\(620\) | 27.1231 | 1.08929 | ||||||||
\(621\) | −2.82313 | −0.113288 | ||||||||
\(622\) | 15.8758 | 0.636562 | ||||||||
\(623\) | −9.65630 | −0.386871 | ||||||||
\(624\) | −110.028 | −4.40466 | ||||||||
\(625\) | −21.4598 | −0.858392 | ||||||||
\(626\) | 29.9261 | 1.19609 | ||||||||
\(627\) | 9.69683 | 0.387254 | ||||||||
\(628\) | 47.4641 | 1.89402 | ||||||||
\(629\) | −46.4662 | −1.85273 | ||||||||
\(630\) | 9.88107 | 0.393671 | ||||||||
\(631\) | 47.8209 | 1.90372 | 0.951859 | − | 0.306535i | \(-0.0991695\pi\) | ||||
0.951859 | + | 0.306535i | \(0.0991695\pi\) | |||||||
\(632\) | 17.8076 | 0.708348 | ||||||||
\(633\) | −1.05416 | −0.0418990 | ||||||||
\(634\) | −23.0769 | −0.916502 | ||||||||
\(635\) | −0.191125 | −0.00758458 | ||||||||
\(636\) | 121.213 | 4.80640 | ||||||||
\(637\) | −38.9923 | −1.54493 | ||||||||
\(638\) | 0.553083 | 0.0218967 | ||||||||
\(639\) | −5.58036 | −0.220756 | ||||||||
\(640\) | 20.6922 | 0.817930 | ||||||||
\(641\) | −10.1589 | −0.401251 | −0.200626 | − | 0.979668i | \(-0.564297\pi\) | ||||
−0.200626 | + | 0.979668i | \(0.564297\pi\) | |||||||
\(642\) | 18.3042 | 0.722409 | ||||||||
\(643\) | 16.9046 | 0.666651 | 0.333326 | − | 0.942812i | \(-0.391829\pi\) | ||||
0.333326 | + | 0.942812i | \(0.391829\pi\) | |||||||
\(644\) | 4.94696 | 0.194938 | ||||||||
\(645\) | 54.2460 | 2.13594 | ||||||||
\(646\) | −86.5042 | −3.40346 | ||||||||
\(647\) | 15.7257 | 0.618242 | 0.309121 | − | 0.951023i | \(-0.399965\pi\) | ||||
0.309121 | + | 0.951023i | \(0.399965\pi\) | |||||||
\(648\) | 73.0167 | 2.86837 | ||||||||
\(649\) | −6.79891 | −0.266880 | ||||||||
\(650\) | 10.7885 | 0.423160 | ||||||||
\(651\) | 6.73164 | 0.263834 | ||||||||
\(652\) | −49.7614 | −1.94881 | ||||||||
\(653\) | −32.5049 | −1.27202 | −0.636008 | − | 0.771683i | \(-0.719415\pi\) | ||||
−0.636008 | + | 0.771683i | \(0.719415\pi\) | |||||||
\(654\) | −70.8553 | −2.77066 | ||||||||
\(655\) | −26.0570 | −1.01813 | ||||||||
\(656\) | 8.57427 | 0.334769 | ||||||||
\(657\) | −18.1740 | −0.709035 | ||||||||
\(658\) | 14.4781 | 0.564413 | ||||||||
\(659\) | −12.7285 | −0.495833 | −0.247917 | − | 0.968781i | \(-0.579746\pi\) | ||||
−0.247917 | + | 0.968781i | \(0.579746\pi\) | |||||||
\(660\) | 11.7949 | 0.459116 | ||||||||
\(661\) | −15.7884 | −0.614097 | −0.307048 | − | 0.951694i | \(-0.599341\pi\) | ||||
−0.307048 | + | 0.951694i | \(0.599341\pi\) | |||||||
\(662\) | −69.9487 | −2.71863 | ||||||||
\(663\) | −62.8850 | −2.44225 | ||||||||
\(664\) | 33.5673 | 1.30266 | ||||||||
\(665\) | −17.7771 | −0.689367 | ||||||||
\(666\) | 46.6305 | 1.80690 | ||||||||
\(667\) | −0.377519 | −0.0146176 | ||||||||
\(668\) | 38.2149 | 1.47858 | ||||||||
\(669\) | 30.1868 | 1.16709 | ||||||||
\(670\) | −48.3058 | −1.86622 | ||||||||
\(671\) | 2.81523 | 0.108681 | ||||||||
\(672\) | −14.9681 | −0.577407 | ||||||||
\(673\) | −14.1982 | −0.547299 | −0.273649 | − | 0.961830i | \(-0.588231\pi\) | ||||
−0.273649 | + | 0.961830i | \(0.588231\pi\) | |||||||
\(674\) | 86.6304 | 3.33688 | ||||||||
\(675\) | −1.77556 | −0.0683412 | ||||||||
\(676\) | 145.250 | 5.58653 | ||||||||
\(677\) | −3.23792 | −0.124443 | −0.0622216 | − | 0.998062i | \(-0.519819\pi\) | ||||
−0.0622216 | + | 0.998062i | \(0.519819\pi\) | |||||||
\(678\) | −84.1083 | −3.23016 | ||||||||
\(679\) | 3.36172 | 0.129011 | ||||||||
\(680\) | −58.9258 | −2.25970 | ||||||||
\(681\) | 9.63439 | 0.369190 | ||||||||
\(682\) | 4.18118 | 0.160106 | ||||||||
\(683\) | −10.9123 | −0.417547 | −0.208774 | − | 0.977964i | \(-0.566947\pi\) | ||||
−0.208774 | + | 0.977964i | \(0.566947\pi\) | |||||||
\(684\) | 60.2857 | 2.30508 | ||||||||
\(685\) | −25.1423 | −0.960638 | ||||||||
\(686\) | −35.6828 | −1.36237 | ||||||||
\(687\) | −43.5484 | −1.66147 | ||||||||
\(688\) | −90.6436 | −3.45576 | ||||||||
\(689\) | −82.4904 | −3.14263 | ||||||||
\(690\) | −11.5931 | −0.441343 | ||||||||
\(691\) | 26.7202 | 1.01648 | 0.508242 | − | 0.861214i | \(-0.330296\pi\) | ||||
0.508242 | + | 0.861214i | \(0.330296\pi\) | |||||||
\(692\) | 36.6436 | 1.39298 | ||||||||
\(693\) | 1.05781 | 0.0401828 | ||||||||
\(694\) | −4.20258 | −0.159528 | ||||||||
\(695\) | −41.7788 | −1.58476 | ||||||||
\(696\) | 5.32901 | 0.201996 | ||||||||
\(697\) | 4.90048 | 0.185619 | ||||||||
\(698\) | 2.55845 | 0.0968387 | ||||||||
\(699\) | −46.2494 | −1.74931 | ||||||||
\(700\) | 3.11130 | 0.117596 | ||||||||
\(701\) | 11.4647 | 0.433018 | 0.216509 | − | 0.976281i | \(-0.430533\pi\) | ||||
0.216509 | + | 0.976281i | \(0.430533\pi\) | |||||||
\(702\) | −48.4273 | −1.82777 | ||||||||
\(703\) | −83.8934 | −3.16410 | ||||||||
\(704\) | −0.625493 | −0.0235741 | ||||||||
\(705\) | −23.5622 | −0.887404 | ||||||||
\(706\) | −7.47956 | −0.281497 | ||||||||
\(707\) | 4.19150 | 0.157638 | ||||||||
\(708\) | −116.975 | −4.39618 | ||||||||
\(709\) | 32.2851 | 1.21249 | 0.606247 | − | 0.795277i | \(-0.292674\pi\) | ||||
0.606247 | + | 0.795277i | \(0.292674\pi\) | |||||||
\(710\) | 17.5849 | 0.659951 | ||||||||
\(711\) | −4.64109 | −0.174054 | ||||||||
\(712\) | −57.7891 | −2.16574 | ||||||||
\(713\) | −2.85397 | −0.106882 | ||||||||
\(714\) | −26.1146 | −0.977314 | ||||||||
\(715\) | −8.02693 | −0.300190 | ||||||||
\(716\) | 81.8904 | 3.06039 | ||||||||
\(717\) | −38.0837 | −1.42226 | ||||||||
\(718\) | 45.6947 | 1.70531 | ||||||||
\(719\) | −35.0346 | −1.30657 | −0.653285 | − | 0.757112i | \(-0.726609\pi\) | ||||
−0.653285 | + | 0.757112i | \(0.726609\pi\) | |||||||
\(720\) | 26.8707 | 1.00141 | ||||||||
\(721\) | 16.2849 | 0.606481 | ||||||||
\(722\) | −107.570 | −4.00336 | ||||||||
\(723\) | 0.514761 | 0.0191442 | ||||||||
\(724\) | −46.2157 | −1.71759 | ||||||||
\(725\) | −0.237434 | −0.00881807 | ||||||||
\(726\) | −59.1775 | −2.19628 | ||||||||
\(727\) | −34.0891 | −1.26430 | −0.632148 | − | 0.774848i | \(-0.717827\pi\) | ||||
−0.632148 | + | 0.774848i | \(0.717827\pi\) | |||||||
\(728\) | 47.5226 | 1.76131 | ||||||||
\(729\) | −0.673720 | −0.0249526 | ||||||||
\(730\) | 57.2702 | 2.11967 | ||||||||
\(731\) | −51.8059 | −1.91611 | ||||||||
\(732\) | 48.4359 | 1.79024 | ||||||||
\(733\) | 49.8656 | 1.84183 | 0.920914 | − | 0.389765i | \(-0.127444\pi\) | ||||
0.920914 | + | 0.389765i | \(0.127444\pi\) | |||||||
\(734\) | 46.2430 | 1.70686 | ||||||||
\(735\) | 26.3525 | 0.972026 | ||||||||
\(736\) | 6.34592 | 0.233914 | ||||||||
\(737\) | −5.17134 | −0.190489 | ||||||||
\(738\) | −4.91782 | −0.181027 | ||||||||
\(739\) | −6.61721 | −0.243418 | −0.121709 | − | 0.992566i | \(-0.538837\pi\) | ||||
−0.121709 | + | 0.992566i | \(0.538837\pi\) | |||||||
\(740\) | −102.045 | −3.75126 | ||||||||
\(741\) | −113.537 | −4.17089 | ||||||||
\(742\) | −34.2563 | −1.25759 | ||||||||
\(743\) | 43.9946 | 1.61401 | 0.807003 | − | 0.590547i | \(-0.201088\pi\) | ||||
0.807003 | + | 0.590547i | \(0.201088\pi\) | |||||||
\(744\) | 40.2861 | 1.47696 | ||||||||
\(745\) | −38.8499 | −1.42335 | ||||||||
\(746\) | 85.6549 | 3.13605 | ||||||||
\(747\) | −8.74844 | −0.320089 | ||||||||
\(748\) | −11.2643 | −0.411865 | ||||||||
\(749\) | −3.59241 | −0.131264 | ||||||||
\(750\) | −65.2569 | −2.38285 | ||||||||
\(751\) | −30.3461 | −1.10734 | −0.553672 | − | 0.832735i | \(-0.686774\pi\) | ||||
−0.553672 | + | 0.832735i | \(0.686774\pi\) | |||||||
\(752\) | 39.3718 | 1.43574 | ||||||||
\(753\) | −10.1920 | −0.371416 | ||||||||
\(754\) | −6.47587 | −0.235837 | ||||||||
\(755\) | −11.4303 | −0.415990 | ||||||||
\(756\) | −13.9659 | −0.507936 | ||||||||
\(757\) | −22.1165 | −0.803839 | −0.401919 | − | 0.915675i | \(-0.631657\pi\) | ||||
−0.401919 | + | 0.915675i | \(0.631657\pi\) | |||||||
\(758\) | −84.1879 | −3.05784 | ||||||||
\(759\) | −1.24109 | −0.0450488 | ||||||||
\(760\) | −106.389 | −3.85913 | ||||||||
\(761\) | 50.4559 | 1.82902 | 0.914512 | − | 0.404559i | \(-0.132575\pi\) | ||||
0.914512 | + | 0.404559i | \(0.132575\pi\) | |||||||
\(762\) | −0.506910 | −0.0183634 | ||||||||
\(763\) | 13.9062 | 0.503437 | ||||||||
\(764\) | −81.9424 | −2.96457 | ||||||||
\(765\) | 15.3575 | 0.555251 | ||||||||
\(766\) | 84.3655 | 3.04825 | ||||||||
\(767\) | 79.6062 | 2.87441 | ||||||||
\(768\) | 59.6155 | 2.15119 | ||||||||
\(769\) | −40.6203 | −1.46481 | −0.732403 | − | 0.680871i | \(-0.761601\pi\) | ||||
−0.732403 | + | 0.680871i | \(0.761601\pi\) | |||||||
\(770\) | −3.33339 | −0.120127 | ||||||||
\(771\) | −9.38211 | −0.337888 | ||||||||
\(772\) | −79.4651 | −2.86001 | ||||||||
\(773\) | −0.554639 | −0.0199490 | −0.00997448 | − | 0.999950i | \(-0.503175\pi\) | ||||
−0.00997448 | + | 0.999950i | \(0.503175\pi\) | |||||||
\(774\) | 51.9891 | 1.86871 | ||||||||
\(775\) | −1.79495 | −0.0644764 | ||||||||
\(776\) | 20.1185 | 0.722214 | ||||||||
\(777\) | −25.3264 | −0.908580 | ||||||||
\(778\) | −69.9421 | −2.50755 | ||||||||
\(779\) | 8.84769 | 0.317001 | ||||||||
\(780\) | −138.103 | −4.94487 | ||||||||
\(781\) | 1.88254 | 0.0673626 | ||||||||
\(782\) | 11.0716 | 0.395921 | ||||||||
\(783\) | 1.06579 | 0.0380881 | ||||||||
\(784\) | −44.0343 | −1.57265 | ||||||||
\(785\) | 21.8304 | 0.779161 | ||||||||
\(786\) | −69.1095 | −2.46506 | ||||||||
\(787\) | −39.8718 | −1.42128 | −0.710638 | − | 0.703558i | \(-0.751593\pi\) | ||||
−0.710638 | + | 0.703558i | \(0.751593\pi\) | |||||||
\(788\) | 10.3400 | 0.368348 | ||||||||
\(789\) | 16.8513 | 0.599921 | ||||||||
\(790\) | 14.6251 | 0.520338 | ||||||||
\(791\) | 16.5072 | 0.586929 | ||||||||
\(792\) | 6.33057 | 0.224947 | ||||||||
\(793\) | −32.9627 | −1.17054 | ||||||||
\(794\) | 6.73637 | 0.239065 | ||||||||
\(795\) | 55.7501 | 1.97725 | ||||||||
\(796\) | 75.4075 | 2.67275 | ||||||||
\(797\) | −23.7275 | −0.840471 | −0.420235 | − | 0.907415i | \(-0.638052\pi\) | ||||
−0.420235 | + | 0.907415i | \(0.638052\pi\) | |||||||
\(798\) | −47.1492 | −1.66906 | ||||||||
\(799\) | 22.5023 | 0.796074 | ||||||||
\(800\) | 3.99115 | 0.141108 | ||||||||
\(801\) | 15.0612 | 0.532163 | ||||||||
\(802\) | 19.7502 | 0.697403 | ||||||||
\(803\) | 6.13101 | 0.216359 | ||||||||
\(804\) | −88.9725 | −3.13782 | ||||||||
\(805\) | 2.27528 | 0.0801932 | ||||||||
\(806\) | −48.9561 | −1.72441 | ||||||||
\(807\) | 67.1767 | 2.36473 | ||||||||
\(808\) | 25.0844 | 0.882468 | ||||||||
\(809\) | −7.46657 | −0.262510 | −0.131255 | − | 0.991349i | \(-0.541901\pi\) | ||||
−0.131255 | + | 0.991349i | \(0.541901\pi\) | |||||||
\(810\) | 59.9675 | 2.10704 | ||||||||
\(811\) | −1.86543 | −0.0655042 | −0.0327521 | − | 0.999464i | \(-0.510427\pi\) | ||||
−0.0327521 | + | 0.999464i | \(0.510427\pi\) | |||||||
\(812\) | −1.86757 | −0.0655390 | ||||||||
\(813\) | −32.2833 | −1.13222 | ||||||||
\(814\) | −15.7309 | −0.551366 | ||||||||
\(815\) | −22.8871 | −0.801699 | ||||||||
\(816\) | −71.0163 | −2.48607 | ||||||||
\(817\) | −93.5341 | −3.27234 | ||||||||
\(818\) | −15.8374 | −0.553743 | ||||||||
\(819\) | −12.3855 | −0.432786 | ||||||||
\(820\) | 10.7620 | 0.375827 | ||||||||
\(821\) | −8.91557 | −0.311156 | −0.155578 | − | 0.987824i | \(-0.549724\pi\) | ||||
−0.155578 | + | 0.987824i | \(0.549724\pi\) | |||||||
\(822\) | −66.6835 | −2.32585 | ||||||||
\(823\) | −29.1497 | −1.01609 | −0.508047 | − | 0.861329i | \(-0.669632\pi\) | ||||
−0.508047 | + | 0.861329i | \(0.669632\pi\) | |||||||
\(824\) | 97.4585 | 3.39513 | ||||||||
\(825\) | −0.780562 | −0.0271757 | ||||||||
\(826\) | 33.0585 | 1.15025 | ||||||||
\(827\) | −26.8507 | −0.933692 | −0.466846 | − | 0.884339i | \(-0.654610\pi\) | ||||
−0.466846 | + | 0.884339i | \(0.654610\pi\) | |||||||
\(828\) | −7.71594 | −0.268147 | ||||||||
\(829\) | 0.0673933 | 0.00234067 | 0.00117033 | − | 0.999999i | \(-0.499627\pi\) | ||||
0.00117033 | + | 0.999999i | \(0.499627\pi\) | |||||||
\(830\) | 27.5683 | 0.956909 | ||||||||
\(831\) | 33.0588 | 1.14680 | ||||||||
\(832\) | 7.32369 | 0.253903 | ||||||||
\(833\) | −25.1671 | −0.871987 | ||||||||
\(834\) | −110.807 | −3.83694 | ||||||||
\(835\) | 17.5764 | 0.608256 | ||||||||
\(836\) | −20.3375 | −0.703385 | ||||||||
\(837\) | 8.05713 | 0.278495 | ||||||||
\(838\) | −0.306113 | −0.0105745 | ||||||||
\(839\) | 6.36028 | 0.219581 | 0.109791 | − | 0.993955i | \(-0.464982\pi\) | ||||
0.109791 | + | 0.993955i | \(0.464982\pi\) | |||||||
\(840\) | −32.1176 | −1.10816 | ||||||||
\(841\) | −28.8575 | −0.995085 | ||||||||
\(842\) | −90.4236 | −3.11620 | ||||||||
\(843\) | −16.7760 | −0.577797 | ||||||||
\(844\) | 2.21092 | 0.0761029 | ||||||||
\(845\) | 66.8055 | 2.29818 | ||||||||
\(846\) | −22.5819 | −0.776381 | ||||||||
\(847\) | 11.6143 | 0.399071 | ||||||||
\(848\) | −93.1568 | −3.19902 | ||||||||
\(849\) | 59.6140 | 2.04595 | ||||||||
\(850\) | 6.96329 | 0.238839 | ||||||||
\(851\) | 10.7375 | 0.368076 | ||||||||
\(852\) | 32.3890 | 1.10963 | ||||||||
\(853\) | −30.8901 | −1.05766 | −0.528829 | − | 0.848728i | \(-0.677369\pi\) | ||||
−0.528829 | + | 0.848728i | \(0.677369\pi\) | |||||||
\(854\) | −13.6886 | −0.468414 | ||||||||
\(855\) | 27.7275 | 0.948262 | ||||||||
\(856\) | −21.4991 | −0.734825 | ||||||||
\(857\) | 1.53183 | 0.0523264 | 0.0261632 | − | 0.999658i | \(-0.491671\pi\) | ||||
0.0261632 | + | 0.999658i | \(0.491671\pi\) | |||||||
\(858\) | −21.2894 | −0.726807 | ||||||||
\(859\) | −44.1394 | −1.50602 | −0.753009 | − | 0.658010i | \(-0.771398\pi\) | ||||
−0.753009 | + | 0.658010i | \(0.771398\pi\) | |||||||
\(860\) | −113.772 | −3.87959 | ||||||||
\(861\) | 2.67101 | 0.0910278 | ||||||||
\(862\) | 90.6814 | 3.08862 | ||||||||
\(863\) | 1.34221 | 0.0456894 | 0.0228447 | − | 0.999739i | \(-0.492728\pi\) | ||||
0.0228447 | + | 0.999739i | \(0.492728\pi\) | |||||||
\(864\) | −17.9154 | −0.609493 | ||||||||
\(865\) | 16.8537 | 0.573043 | ||||||||
\(866\) | 79.3983 | 2.69806 | ||||||||
\(867\) | −3.74316 | −0.127124 | ||||||||
\(868\) | −14.1185 | −0.479212 | ||||||||
\(869\) | 1.56568 | 0.0531119 | ||||||||
\(870\) | 4.37663 | 0.148382 | ||||||||
\(871\) | 60.5495 | 2.05164 | ||||||||
\(872\) | 83.2228 | 2.81828 | ||||||||
\(873\) | −5.24338 | −0.177462 | ||||||||
\(874\) | 19.9895 | 0.676156 | ||||||||
\(875\) | 12.8074 | 0.432970 | ||||||||
\(876\) | 105.484 | 3.56396 | ||||||||
\(877\) | 5.95567 | 0.201109 | 0.100554 | − | 0.994932i | \(-0.467938\pi\) | ||||
0.100554 | + | 0.994932i | \(0.467938\pi\) | |||||||
\(878\) | −32.8382 | −1.10824 | ||||||||
\(879\) | 26.0334 | 0.878086 | ||||||||
\(880\) | −9.06485 | −0.305576 | ||||||||
\(881\) | 40.3518 | 1.35949 | 0.679743 | − | 0.733451i | \(-0.262091\pi\) | ||||
0.679743 | + | 0.733451i | \(0.262091\pi\) | |||||||
\(882\) | 25.2561 | 0.850417 | ||||||||
\(883\) | 16.4008 | 0.551929 | 0.275965 | − | 0.961168i | \(-0.411003\pi\) | ||||
0.275965 | + | 0.961168i | \(0.411003\pi\) | |||||||
\(884\) | 131.890 | 4.43596 | ||||||||
\(885\) | −53.8009 | −1.80850 | ||||||||
\(886\) | −104.621 | −3.51480 | ||||||||
\(887\) | 52.0897 | 1.74900 | 0.874500 | − | 0.485025i | \(-0.161190\pi\) | ||||
0.874500 | + | 0.485025i | \(0.161190\pi\) | |||||||
\(888\) | −151.568 | −5.08631 | ||||||||
\(889\) | 0.0994869 | 0.00333668 | ||||||||
\(890\) | −47.4613 | −1.59091 | ||||||||
\(891\) | 6.41976 | 0.215070 | ||||||||
\(892\) | −63.3116 | −2.11983 | ||||||||
\(893\) | 40.6273 | 1.35954 | ||||||||
\(894\) | −103.039 | −3.44615 | ||||||||
\(895\) | 37.6643 | 1.25898 | ||||||||
\(896\) | −10.7710 | −0.359832 | ||||||||
\(897\) | 14.5315 | 0.485194 | ||||||||
\(898\) | 40.5978 | 1.35477 | ||||||||
\(899\) | 1.07743 | 0.0359342 | ||||||||
\(900\) | −4.85279 | −0.161760 | ||||||||
\(901\) | −53.2422 | −1.77376 | ||||||||
\(902\) | 1.65903 | 0.0552397 | ||||||||
\(903\) | −28.2368 | −0.939663 | ||||||||
\(904\) | 98.7891 | 3.28568 | ||||||||
\(905\) | −21.2563 | −0.706582 | ||||||||
\(906\) | −30.3158 | −1.00718 | ||||||||
\(907\) | 0.548629 | 0.0182169 | 0.00910847 | − | 0.999959i | \(-0.497101\pi\) | ||||
0.00910847 | + | 0.999959i | \(0.497101\pi\) | |||||||
\(908\) | −20.2065 | −0.670576 | ||||||||
\(909\) | −6.53762 | −0.216839 | ||||||||
\(910\) | 39.0296 | 1.29382 | ||||||||
\(911\) | −11.7488 | −0.389254 | −0.194627 | − | 0.980877i | \(-0.562350\pi\) | ||||
−0.194627 | + | 0.980877i | \(0.562350\pi\) | |||||||
\(912\) | −128.218 | −4.24572 | ||||||||
\(913\) | 2.95130 | 0.0976737 | ||||||||
\(914\) | 16.4993 | 0.545748 | ||||||||
\(915\) | 22.2774 | 0.736468 | ||||||||
\(916\) | 91.3353 | 3.01780 | ||||||||
\(917\) | 13.5635 | 0.447907 | ||||||||
\(918\) | −31.2567 | −1.03162 | ||||||||
\(919\) | −48.0176 | −1.58395 | −0.791977 | − | 0.610550i | \(-0.790948\pi\) | ||||
−0.791977 | + | 0.610550i | \(0.790948\pi\) | |||||||
\(920\) | 13.6167 | 0.448928 | ||||||||
\(921\) | 17.8470 | 0.588078 | ||||||||
\(922\) | −68.2948 | −2.24917 | ||||||||
\(923\) | −22.0421 | −0.725523 | ||||||||
\(924\) | −6.13963 | −0.201979 | ||||||||
\(925\) | 6.75313 | 0.222042 | ||||||||
\(926\) | −61.5000 | −2.02101 | ||||||||
\(927\) | −25.4001 | −0.834247 | ||||||||
\(928\) | −2.39571 | −0.0786430 | ||||||||
\(929\) | 1.46111 | 0.0479376 | 0.0239688 | − | 0.999713i | \(-0.492370\pi\) | ||||
0.0239688 | + | 0.999713i | \(0.492370\pi\) | |||||||
\(930\) | 33.0864 | 1.08495 | ||||||||
\(931\) | −45.4384 | −1.48918 | ||||||||
\(932\) | 97.0003 | 3.17735 | ||||||||
\(933\) | 13.4490 | 0.440300 | ||||||||
\(934\) | 9.37188 | 0.306657 | ||||||||
\(935\) | −5.18087 | −0.169433 | ||||||||
\(936\) | −74.1226 | −2.42277 | ||||||||
\(937\) | −25.4885 | −0.832674 | −0.416337 | − | 0.909210i | \(-0.636686\pi\) | ||||
−0.416337 | + | 0.909210i | \(0.636686\pi\) | |||||||
\(938\) | 25.1447 | 0.821005 | ||||||||
\(939\) | 25.3515 | 0.827316 | ||||||||
\(940\) | 49.4177 | 1.61183 | ||||||||
\(941\) | −17.7647 | −0.579112 | −0.289556 | − | 0.957161i | \(-0.593508\pi\) | ||||
−0.289556 | + | 0.957161i | \(0.593508\pi\) | |||||||
\(942\) | 57.8995 | 1.88647 | ||||||||
\(943\) | −1.13241 | −0.0368764 | ||||||||
\(944\) | 89.8997 | 2.92599 | ||||||||
\(945\) | −6.42343 | −0.208954 | ||||||||
\(946\) | −17.5386 | −0.570229 | ||||||||
\(947\) | −28.2392 | −0.917650 | −0.458825 | − | 0.888527i | \(-0.651729\pi\) | ||||
−0.458825 | + | 0.888527i | \(0.651729\pi\) | |||||||
\(948\) | 26.9374 | 0.874885 | ||||||||
\(949\) | −71.7861 | −2.33027 | ||||||||
\(950\) | 12.5720 | 0.407891 | ||||||||
\(951\) | −19.5493 | −0.633930 | ||||||||
\(952\) | 30.6728 | 0.994111 | ||||||||
\(953\) | 5.98352 | 0.193825 | 0.0969125 | − | 0.995293i | \(-0.469103\pi\) | ||||
0.0969125 | + | 0.995293i | \(0.469103\pi\) | |||||||
\(954\) | 53.4306 | 1.72988 | ||||||||
\(955\) | −37.6882 | −1.21956 | ||||||||
\(956\) | 79.8740 | 2.58331 | ||||||||
\(957\) | 0.468536 | 0.0151456 | ||||||||
\(958\) | −88.2722 | −2.85195 | ||||||||
\(959\) | 13.0874 | 0.422614 | ||||||||
\(960\) | −4.94963 | −0.159748 | ||||||||
\(961\) | −22.8549 | −0.737254 | ||||||||
\(962\) | 184.188 | 5.93845 | ||||||||
\(963\) | 5.60319 | 0.180560 | ||||||||
\(964\) | −1.07962 | −0.0347723 | ||||||||
\(965\) | −36.5488 | −1.17655 | ||||||||
\(966\) | 6.03460 | 0.194160 | ||||||||
\(967\) | 16.5491 | 0.532182 | 0.266091 | − | 0.963948i | \(-0.414268\pi\) | ||||
0.266091 | + | 0.963948i | \(0.414268\pi\) | |||||||
\(968\) | 69.5067 | 2.23403 | ||||||||
\(969\) | −73.2809 | −2.35412 | ||||||||
\(970\) | 16.5231 | 0.530523 | ||||||||
\(971\) | −29.7739 | −0.955490 | −0.477745 | − | 0.878499i | \(-0.658546\pi\) | ||||
−0.477745 | + | 0.878499i | \(0.658546\pi\) | |||||||
\(972\) | 71.9526 | 2.30788 | ||||||||
\(973\) | 21.7472 | 0.697183 | ||||||||
\(974\) | 99.7145 | 3.19506 | ||||||||
\(975\) | 9.13935 | 0.292693 | ||||||||
\(976\) | −37.2249 | −1.19154 | ||||||||
\(977\) | −16.2033 | −0.518389 | −0.259194 | − | 0.965825i | \(-0.583457\pi\) | ||||
−0.259194 | + | 0.965825i | \(0.583457\pi\) | |||||||
\(978\) | −60.7020 | −1.94104 | ||||||||
\(979\) | −5.08093 | −0.162387 | ||||||||
\(980\) | −55.2698 | −1.76553 | ||||||||
\(981\) | −21.6899 | −0.692504 | ||||||||
\(982\) | −77.0965 | −2.46025 | ||||||||
\(983\) | −37.3227 | −1.19041 | −0.595205 | − | 0.803574i | \(-0.702929\pi\) | ||||
−0.595205 | + | 0.803574i | \(0.702929\pi\) | |||||||
\(984\) | 15.9849 | 0.509581 | ||||||||
\(985\) | 4.75575 | 0.151531 | ||||||||
\(986\) | −4.17976 | −0.133111 | ||||||||
\(987\) | 12.2649 | 0.390396 | ||||||||
\(988\) | 238.125 | 7.57576 | ||||||||
\(989\) | 11.9714 | 0.380668 | ||||||||
\(990\) | 5.19920 | 0.165241 | ||||||||
\(991\) | −35.1627 | −1.11698 | −0.558490 | − | 0.829511i | \(-0.688619\pi\) | ||||
−0.558490 | + | 0.829511i | \(0.688619\pi\) | |||||||
\(992\) | −18.1110 | −0.575026 | ||||||||
\(993\) | −59.2561 | −1.88044 | ||||||||
\(994\) | −9.15353 | −0.290332 | ||||||||
\(995\) | 34.6826 | 1.09951 | ||||||||
\(996\) | 50.7769 | 1.60893 | ||||||||
\(997\) | 3.84743 | 0.121849 | 0.0609247 | − | 0.998142i | \(-0.480595\pi\) | ||||
0.0609247 | + | 0.998142i | \(0.480595\pi\) | |||||||
\(998\) | 16.4016 | 0.519183 | ||||||||
\(999\) | −30.3133 | −0.959071 |
(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 | 8027.2.a.d.1.9 | ✓ | 149 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8027.2.a.d.1.9 | ✓ | 149 | 1.1 | even | 1 | trivial |