Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8042,2,Mod(1,8042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8042, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8042 = 2 \cdot 4021 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8042.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: | \(64.2156933055\) |
Analytic rank: | \(1\) |
Dimension: | \(67\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 8042.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.50743 | −0.870318 | −0.435159 | − | 0.900354i | \(-0.643308\pi\) | ||||
−0.435159 | + | 0.900354i | \(0.643308\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.46037 | −1.10031 | −0.550155 | − | 0.835063i | \(-0.685431\pi\) | ||||
−0.550155 | + | 0.835063i | \(0.685431\pi\) | |||||||
\(6\) | −1.50743 | −0.615407 | ||||||||
\(7\) | −5.08447 | −1.92175 | −0.960875 | − | 0.276984i | \(-0.910665\pi\) | ||||
−0.960875 | + | 0.276984i | \(0.910665\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.727642 | −0.242547 | ||||||||
\(10\) | −2.46037 | −0.778037 | ||||||||
\(11\) | 6.13957 | 1.85115 | 0.925575 | − | 0.378564i | \(-0.123582\pi\) | ||||
0.925575 | + | 0.378564i | \(0.123582\pi\) | |||||||
\(12\) | −1.50743 | −0.435159 | ||||||||
\(13\) | −1.35250 | −0.375117 | −0.187558 | − | 0.982253i | \(-0.560057\pi\) | ||||
−0.187558 | + | 0.982253i | \(0.560057\pi\) | |||||||
\(14\) | −5.08447 | −1.35888 | ||||||||
\(15\) | 3.70884 | 0.957619 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.01670 | 1.70180 | 0.850900 | − | 0.525328i | \(-0.176057\pi\) | ||||
0.850900 | + | 0.525328i | \(0.176057\pi\) | |||||||
\(18\) | −0.727642 | −0.171507 | ||||||||
\(19\) | −5.54184 | −1.27138 | −0.635692 | − | 0.771943i | \(-0.719285\pi\) | ||||
−0.635692 | + | 0.771943i | \(0.719285\pi\) | |||||||
\(20\) | −2.46037 | −0.550155 | ||||||||
\(21\) | 7.66450 | 1.67253 | ||||||||
\(22\) | 6.13957 | 1.30896 | ||||||||
\(23\) | −8.72989 | −1.82031 | −0.910154 | − | 0.414269i | \(-0.864037\pi\) | ||||
−0.910154 | + | 0.414269i | \(0.864037\pi\) | |||||||
\(24\) | −1.50743 | −0.307704 | ||||||||
\(25\) | 1.05341 | 0.210682 | ||||||||
\(26\) | −1.35250 | −0.265248 | ||||||||
\(27\) | 5.61918 | 1.08141 | ||||||||
\(28\) | −5.08447 | −0.960875 | ||||||||
\(29\) | 3.89589 | 0.723448 | 0.361724 | − | 0.932285i | \(-0.382188\pi\) | ||||
0.361724 | + | 0.932285i | \(0.382188\pi\) | |||||||
\(30\) | 3.70884 | 0.677139 | ||||||||
\(31\) | 2.99382 | 0.537706 | 0.268853 | − | 0.963181i | \(-0.413355\pi\) | ||||
0.268853 | + | 0.963181i | \(0.413355\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −9.25500 | −1.61109 | ||||||||
\(34\) | 7.01670 | 1.20335 | ||||||||
\(35\) | 12.5097 | 2.11452 | ||||||||
\(36\) | −0.727642 | −0.121274 | ||||||||
\(37\) | 2.45803 | 0.404097 | 0.202049 | − | 0.979376i | \(-0.435240\pi\) | ||||
0.202049 | + | 0.979376i | \(0.435240\pi\) | |||||||
\(38\) | −5.54184 | −0.899005 | ||||||||
\(39\) | 2.03881 | 0.326471 | ||||||||
\(40\) | −2.46037 | −0.389018 | ||||||||
\(41\) | 3.56872 | 0.557341 | 0.278670 | − | 0.960387i | \(-0.410106\pi\) | ||||
0.278670 | + | 0.960387i | \(0.410106\pi\) | |||||||
\(42\) | 7.66450 | 1.18266 | ||||||||
\(43\) | 2.60394 | 0.397097 | 0.198549 | − | 0.980091i | \(-0.436377\pi\) | ||||
0.198549 | + | 0.980091i | \(0.436377\pi\) | |||||||
\(44\) | 6.13957 | 0.925575 | ||||||||
\(45\) | 1.79027 | 0.266877 | ||||||||
\(46\) | −8.72989 | −1.28715 | ||||||||
\(47\) | 7.26088 | 1.05911 | 0.529554 | − | 0.848276i | \(-0.322359\pi\) | ||||
0.529554 | + | 0.848276i | \(0.322359\pi\) | |||||||
\(48\) | −1.50743 | −0.217579 | ||||||||
\(49\) | 18.8518 | 2.69312 | ||||||||
\(50\) | 1.05341 | 0.148975 | ||||||||
\(51\) | −10.5772 | −1.48111 | ||||||||
\(52\) | −1.35250 | −0.187558 | ||||||||
\(53\) | −11.4355 | −1.57079 | −0.785395 | − | 0.618995i | \(-0.787540\pi\) | ||||
−0.785395 | + | 0.618995i | \(0.787540\pi\) | |||||||
\(54\) | 5.61918 | 0.764673 | ||||||||
\(55\) | −15.1056 | −2.03684 | ||||||||
\(56\) | −5.08447 | −0.679441 | ||||||||
\(57\) | 8.35395 | 1.10651 | ||||||||
\(58\) | 3.89589 | 0.511555 | ||||||||
\(59\) | 7.78393 | 1.01338 | 0.506691 | − | 0.862128i | \(-0.330869\pi\) | ||||
0.506691 | + | 0.862128i | \(0.330869\pi\) | |||||||
\(60\) | 3.70884 | 0.478810 | ||||||||
\(61\) | 0.118205 | 0.0151346 | 0.00756729 | − | 0.999971i | \(-0.497591\pi\) | ||||
0.00756729 | + | 0.999971i | \(0.497591\pi\) | |||||||
\(62\) | 2.99382 | 0.380216 | ||||||||
\(63\) | 3.69968 | 0.466115 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.32765 | 0.412745 | ||||||||
\(66\) | −9.25500 | −1.13921 | ||||||||
\(67\) | 3.26379 | 0.398735 | 0.199367 | − | 0.979925i | \(-0.436111\pi\) | ||||
0.199367 | + | 0.979925i | \(0.436111\pi\) | |||||||
\(68\) | 7.01670 | 0.850900 | ||||||||
\(69\) | 13.1597 | 1.58425 | ||||||||
\(70\) | 12.5097 | 1.49519 | ||||||||
\(71\) | 12.1343 | 1.44008 | 0.720039 | − | 0.693934i | \(-0.244124\pi\) | ||||
0.720039 | + | 0.693934i | \(0.244124\pi\) | |||||||
\(72\) | −0.727642 | −0.0857535 | ||||||||
\(73\) | −7.86733 | −0.920801 | −0.460401 | − | 0.887711i | \(-0.652294\pi\) | ||||
−0.460401 | + | 0.887711i | \(0.652294\pi\) | |||||||
\(74\) | 2.45803 | 0.285740 | ||||||||
\(75\) | −1.58795 | −0.183361 | ||||||||
\(76\) | −5.54184 | −0.635692 | ||||||||
\(77\) | −31.2165 | −3.55745 | ||||||||
\(78\) | 2.03881 | 0.230850 | ||||||||
\(79\) | −13.3791 | −1.50527 | −0.752633 | − | 0.658440i | \(-0.771217\pi\) | ||||
−0.752633 | + | 0.658440i | \(0.771217\pi\) | |||||||
\(80\) | −2.46037 | −0.275078 | ||||||||
\(81\) | −6.28761 | −0.698623 | ||||||||
\(82\) | 3.56872 | 0.394100 | ||||||||
\(83\) | 11.8911 | 1.30522 | 0.652611 | − | 0.757693i | \(-0.273673\pi\) | ||||
0.652611 | + | 0.757693i | \(0.273673\pi\) | |||||||
\(84\) | 7.66450 | 0.836266 | ||||||||
\(85\) | −17.2637 | −1.87251 | ||||||||
\(86\) | 2.60394 | 0.280790 | ||||||||
\(87\) | −5.87279 | −0.629629 | ||||||||
\(88\) | 6.13957 | 0.654480 | ||||||||
\(89\) | −17.2789 | −1.83156 | −0.915779 | − | 0.401681i | \(-0.868426\pi\) | ||||
−0.915779 | + | 0.401681i | \(0.868426\pi\) | |||||||
\(90\) | 1.79027 | 0.188711 | ||||||||
\(91\) | 6.87676 | 0.720880 | ||||||||
\(92\) | −8.72989 | −0.910154 | ||||||||
\(93\) | −4.51299 | −0.467975 | ||||||||
\(94\) | 7.26088 | 0.748903 | ||||||||
\(95\) | 13.6350 | 1.39892 | ||||||||
\(96\) | −1.50743 | −0.153852 | ||||||||
\(97\) | 7.57290 | 0.768912 | 0.384456 | − | 0.923143i | \(-0.374389\pi\) | ||||
0.384456 | + | 0.923143i | \(0.374389\pi\) | |||||||
\(98\) | 18.8518 | 1.90432 | ||||||||
\(99\) | −4.46741 | −0.448992 | ||||||||
\(100\) | 1.05341 | 0.105341 | ||||||||
\(101\) | −16.5960 | −1.65136 | −0.825680 | − | 0.564139i | \(-0.809208\pi\) | ||||
−0.825680 | + | 0.564139i | \(0.809208\pi\) | |||||||
\(102\) | −10.5772 | −1.04730 | ||||||||
\(103\) | 10.9796 | 1.08186 | 0.540928 | − | 0.841069i | \(-0.318073\pi\) | ||||
0.540928 | + | 0.841069i | \(0.318073\pi\) | |||||||
\(104\) | −1.35250 | −0.132624 | ||||||||
\(105\) | −18.8575 | −1.84030 | ||||||||
\(106\) | −11.4355 | −1.11072 | ||||||||
\(107\) | −6.36100 | −0.614941 | −0.307471 | − | 0.951558i | \(-0.599483\pi\) | ||||
−0.307471 | + | 0.951558i | \(0.599483\pi\) | |||||||
\(108\) | 5.61918 | 0.540705 | ||||||||
\(109\) | 10.6018 | 1.01547 | 0.507735 | − | 0.861513i | \(-0.330483\pi\) | ||||
0.507735 | + | 0.861513i | \(0.330483\pi\) | |||||||
\(110\) | −15.1056 | −1.44026 | ||||||||
\(111\) | −3.70531 | −0.351693 | ||||||||
\(112\) | −5.08447 | −0.480437 | ||||||||
\(113\) | −8.58785 | −0.807877 | −0.403939 | − | 0.914786i | \(-0.632359\pi\) | ||||
−0.403939 | + | 0.914786i | \(0.632359\pi\) | |||||||
\(114\) | 8.35395 | 0.782420 | ||||||||
\(115\) | 21.4788 | 2.00290 | ||||||||
\(116\) | 3.89589 | 0.361724 | ||||||||
\(117\) | 0.984138 | 0.0909836 | ||||||||
\(118\) | 7.78393 | 0.716569 | ||||||||
\(119\) | −35.6762 | −3.27043 | ||||||||
\(120\) | 3.70884 | 0.338570 | ||||||||
\(121\) | 26.6943 | 2.42676 | ||||||||
\(122\) | 0.118205 | 0.0107018 | ||||||||
\(123\) | −5.37962 | −0.485064 | ||||||||
\(124\) | 2.99382 | 0.268853 | ||||||||
\(125\) | 9.71006 | 0.868494 | ||||||||
\(126\) | 3.69968 | 0.329593 | ||||||||
\(127\) | 9.54416 | 0.846907 | 0.423454 | − | 0.905918i | \(-0.360818\pi\) | ||||
0.423454 | + | 0.905918i | \(0.360818\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −3.92527 | −0.345601 | ||||||||
\(130\) | 3.32765 | 0.291855 | ||||||||
\(131\) | −1.83025 | −0.159909 | −0.0799547 | − | 0.996799i | \(-0.525478\pi\) | ||||
−0.0799547 | + | 0.996799i | \(0.525478\pi\) | |||||||
\(132\) | −9.25500 | −0.805544 | ||||||||
\(133\) | 28.1773 | 2.44328 | ||||||||
\(134\) | 3.26379 | 0.281948 | ||||||||
\(135\) | −13.8252 | −1.18989 | ||||||||
\(136\) | 7.01670 | 0.601677 | ||||||||
\(137\) | −4.67347 | −0.399281 | −0.199641 | − | 0.979869i | \(-0.563978\pi\) | ||||
−0.199641 | + | 0.979869i | \(0.563978\pi\) | |||||||
\(138\) | 13.1597 | 1.12023 | ||||||||
\(139\) | −19.8711 | −1.68545 | −0.842723 | − | 0.538347i | \(-0.819049\pi\) | ||||
−0.842723 | + | 0.538347i | \(0.819049\pi\) | |||||||
\(140\) | 12.5097 | 1.05726 | ||||||||
\(141\) | −10.9453 | −0.921761 | ||||||||
\(142\) | 12.1343 | 1.01829 | ||||||||
\(143\) | −8.30378 | −0.694397 | ||||||||
\(144\) | −0.727642 | −0.0606369 | ||||||||
\(145\) | −9.58531 | −0.796017 | ||||||||
\(146\) | −7.86733 | −0.651105 | ||||||||
\(147\) | −28.4179 | −2.34387 | ||||||||
\(148\) | 2.45803 | 0.202049 | ||||||||
\(149\) | −14.5346 | −1.19072 | −0.595362 | − | 0.803458i | \(-0.702991\pi\) | ||||
−0.595362 | + | 0.803458i | \(0.702991\pi\) | |||||||
\(150\) | −1.58795 | −0.129656 | ||||||||
\(151\) | −4.73484 | −0.385316 | −0.192658 | − | 0.981266i | \(-0.561711\pi\) | ||||
−0.192658 | + | 0.981266i | \(0.561711\pi\) | |||||||
\(152\) | −5.54184 | −0.449502 | ||||||||
\(153\) | −5.10565 | −0.412767 | ||||||||
\(154\) | −31.2165 | −2.51549 | ||||||||
\(155\) | −7.36590 | −0.591644 | ||||||||
\(156\) | 2.03881 | 0.163235 | ||||||||
\(157\) | 6.50607 | 0.519241 | 0.259620 | − | 0.965711i | \(-0.416403\pi\) | ||||
0.259620 | + | 0.965711i | \(0.416403\pi\) | |||||||
\(158\) | −13.3791 | −1.06438 | ||||||||
\(159\) | 17.2383 | 1.36709 | ||||||||
\(160\) | −2.46037 | −0.194509 | ||||||||
\(161\) | 44.3869 | 3.49818 | ||||||||
\(162\) | −6.28761 | −0.494001 | ||||||||
\(163\) | 6.56285 | 0.514042 | 0.257021 | − | 0.966406i | \(-0.417259\pi\) | ||||
0.257021 | + | 0.966406i | \(0.417259\pi\) | |||||||
\(164\) | 3.56872 | 0.278670 | ||||||||
\(165\) | 22.7707 | 1.77270 | ||||||||
\(166\) | 11.8911 | 0.922932 | ||||||||
\(167\) | −11.0561 | −0.855550 | −0.427775 | − | 0.903885i | \(-0.640702\pi\) | ||||
−0.427775 | + | 0.903885i | \(0.640702\pi\) | |||||||
\(168\) | 7.66450 | 0.591329 | ||||||||
\(169\) | −11.1707 | −0.859287 | ||||||||
\(170\) | −17.2637 | −1.32406 | ||||||||
\(171\) | 4.03247 | 0.308371 | ||||||||
\(172\) | 2.60394 | 0.198549 | ||||||||
\(173\) | −4.68551 | −0.356233 | −0.178116 | − | 0.984009i | \(-0.557000\pi\) | ||||
−0.178116 | + | 0.984009i | \(0.557000\pi\) | |||||||
\(174\) | −5.87279 | −0.445215 | ||||||||
\(175\) | −5.35604 | −0.404879 | ||||||||
\(176\) | 6.13957 | 0.462787 | ||||||||
\(177\) | −11.7338 | −0.881964 | ||||||||
\(178\) | −17.2789 | −1.29511 | ||||||||
\(179\) | 9.67377 | 0.723051 | 0.361526 | − | 0.932362i | \(-0.382256\pi\) | ||||
0.361526 | + | 0.932362i | \(0.382256\pi\) | |||||||
\(180\) | 1.79027 | 0.133439 | ||||||||
\(181\) | −12.8673 | −0.956421 | −0.478211 | − | 0.878245i | \(-0.658714\pi\) | ||||
−0.478211 | + | 0.878245i | \(0.658714\pi\) | |||||||
\(182\) | 6.87676 | 0.509739 | ||||||||
\(183\) | −0.178186 | −0.0131719 | ||||||||
\(184\) | −8.72989 | −0.643576 | ||||||||
\(185\) | −6.04765 | −0.444632 | ||||||||
\(186\) | −4.51299 | −0.330908 | ||||||||
\(187\) | 43.0795 | 3.15029 | ||||||||
\(188\) | 7.26088 | 0.529554 | ||||||||
\(189\) | −28.5705 | −2.07820 | ||||||||
\(190\) | 13.6350 | 0.989184 | ||||||||
\(191\) | −2.18137 | −0.157838 | −0.0789192 | − | 0.996881i | \(-0.525147\pi\) | ||||
−0.0789192 | + | 0.996881i | \(0.525147\pi\) | |||||||
\(192\) | −1.50743 | −0.108790 | ||||||||
\(193\) | −10.4373 | −0.751293 | −0.375647 | − | 0.926763i | \(-0.622579\pi\) | ||||
−0.375647 | + | 0.926763i | \(0.622579\pi\) | |||||||
\(194\) | 7.57290 | 0.543703 | ||||||||
\(195\) | −5.01622 | −0.359219 | ||||||||
\(196\) | 18.8518 | 1.34656 | ||||||||
\(197\) | 6.26423 | 0.446308 | 0.223154 | − | 0.974783i | \(-0.428365\pi\) | ||||
0.223154 | + | 0.974783i | \(0.428365\pi\) | |||||||
\(198\) | −4.46741 | −0.317485 | ||||||||
\(199\) | 4.27957 | 0.303370 | 0.151685 | − | 0.988429i | \(-0.451530\pi\) | ||||
0.151685 | + | 0.988429i | \(0.451530\pi\) | |||||||
\(200\) | 1.05341 | 0.0744875 | ||||||||
\(201\) | −4.91994 | −0.347026 | ||||||||
\(202\) | −16.5960 | −1.16769 | ||||||||
\(203\) | −19.8085 | −1.39029 | ||||||||
\(204\) | −10.5772 | −0.740553 | ||||||||
\(205\) | −8.78037 | −0.613248 | ||||||||
\(206\) | 10.9796 | 0.764987 | ||||||||
\(207\) | 6.35224 | 0.441511 | ||||||||
\(208\) | −1.35250 | −0.0937792 | ||||||||
\(209\) | −34.0245 | −2.35352 | ||||||||
\(210\) | −18.8575 | −1.30129 | ||||||||
\(211\) | −9.24903 | −0.636730 | −0.318365 | − | 0.947968i | \(-0.603134\pi\) | ||||
−0.318365 | + | 0.947968i | \(0.603134\pi\) | |||||||
\(212\) | −11.4355 | −0.785395 | ||||||||
\(213\) | −18.2917 | −1.25333 | ||||||||
\(214\) | −6.36100 | −0.434829 | ||||||||
\(215\) | −6.40665 | −0.436930 | ||||||||
\(216\) | 5.61918 | 0.382336 | ||||||||
\(217\) | −15.2220 | −1.03334 | ||||||||
\(218\) | 10.6018 | 0.718046 | ||||||||
\(219\) | 11.8595 | 0.801390 | ||||||||
\(220\) | −15.1056 | −1.01842 | ||||||||
\(221\) | −9.49010 | −0.638373 | ||||||||
\(222\) | −3.70531 | −0.248684 | ||||||||
\(223\) | 18.5235 | 1.24042 | 0.620212 | − | 0.784434i | \(-0.287047\pi\) | ||||
0.620212 | + | 0.784434i | \(0.287047\pi\) | |||||||
\(224\) | −5.08447 | −0.339720 | ||||||||
\(225\) | −0.766507 | −0.0511005 | ||||||||
\(226\) | −8.58785 | −0.571256 | ||||||||
\(227\) | −14.0148 | −0.930193 | −0.465096 | − | 0.885260i | \(-0.653980\pi\) | ||||
−0.465096 | + | 0.885260i | \(0.653980\pi\) | |||||||
\(228\) | 8.35395 | 0.553254 | ||||||||
\(229\) | −19.3989 | −1.28191 | −0.640956 | − | 0.767577i | \(-0.721462\pi\) | ||||
−0.640956 | + | 0.767577i | \(0.721462\pi\) | |||||||
\(230\) | 21.4788 | 1.41627 | ||||||||
\(231\) | 47.0568 | 3.09611 | ||||||||
\(232\) | 3.89589 | 0.255777 | ||||||||
\(233\) | −16.1292 | −1.05666 | −0.528330 | − | 0.849039i | \(-0.677182\pi\) | ||||
−0.528330 | + | 0.849039i | \(0.677182\pi\) | |||||||
\(234\) | 0.984138 | 0.0643351 | ||||||||
\(235\) | −17.8644 | −1.16535 | ||||||||
\(236\) | 7.78393 | 0.506691 | ||||||||
\(237\) | 20.1681 | 1.31006 | ||||||||
\(238\) | −35.6762 | −2.31254 | ||||||||
\(239\) | −16.9585 | −1.09695 | −0.548476 | − | 0.836167i | \(-0.684792\pi\) | ||||
−0.548476 | + | 0.836167i | \(0.684792\pi\) | |||||||
\(240\) | 3.70884 | 0.239405 | ||||||||
\(241\) | 27.3400 | 1.76113 | 0.880564 | − | 0.473928i | \(-0.157164\pi\) | ||||
0.880564 | + | 0.473928i | \(0.157164\pi\) | |||||||
\(242\) | 26.6943 | 1.71598 | ||||||||
\(243\) | −7.37937 | −0.473387 | ||||||||
\(244\) | 0.118205 | 0.00756729 | ||||||||
\(245\) | −46.3825 | −2.96327 | ||||||||
\(246\) | −5.37962 | −0.342992 | ||||||||
\(247\) | 7.49535 | 0.476918 | ||||||||
\(248\) | 2.99382 | 0.190108 | ||||||||
\(249\) | −17.9251 | −1.13596 | ||||||||
\(250\) | 9.71006 | 0.614118 | ||||||||
\(251\) | 13.0250 | 0.822131 | 0.411065 | − | 0.911606i | \(-0.365157\pi\) | ||||
0.411065 | + | 0.911606i | \(0.365157\pi\) | |||||||
\(252\) | 3.69968 | 0.233058 | ||||||||
\(253\) | −53.5978 | −3.36966 | ||||||||
\(254\) | 9.54416 | 0.598854 | ||||||||
\(255\) | 26.0238 | 1.62968 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.52106 | −0.219638 | −0.109819 | − | 0.993952i | \(-0.535027\pi\) | ||||
−0.109819 | + | 0.993952i | \(0.535027\pi\) | |||||||
\(258\) | −3.92527 | −0.244377 | ||||||||
\(259\) | −12.4978 | −0.776573 | ||||||||
\(260\) | 3.32765 | 0.206372 | ||||||||
\(261\) | −2.83481 | −0.175470 | ||||||||
\(262\) | −1.83025 | −0.113073 | ||||||||
\(263\) | −14.7974 | −0.912449 | −0.456225 | − | 0.889865i | \(-0.650799\pi\) | ||||
−0.456225 | + | 0.889865i | \(0.650799\pi\) | |||||||
\(264\) | −9.25500 | −0.569606 | ||||||||
\(265\) | 28.1356 | 1.72836 | ||||||||
\(266\) | 28.1773 | 1.72766 | ||||||||
\(267\) | 26.0468 | 1.59404 | ||||||||
\(268\) | 3.26379 | 0.199367 | ||||||||
\(269\) | 7.83519 | 0.477720 | 0.238860 | − | 0.971054i | \(-0.423226\pi\) | ||||
0.238860 | + | 0.971054i | \(0.423226\pi\) | |||||||
\(270\) | −13.8252 | −0.841377 | ||||||||
\(271\) | 0.261639 | 0.0158934 | 0.00794672 | − | 0.999968i | \(-0.497470\pi\) | ||||
0.00794672 | + | 0.999968i | \(0.497470\pi\) | |||||||
\(272\) | 7.01670 | 0.425450 | ||||||||
\(273\) | −10.3663 | −0.627395 | ||||||||
\(274\) | −4.67347 | −0.282335 | ||||||||
\(275\) | 6.46750 | 0.390005 | ||||||||
\(276\) | 13.1597 | 0.792123 | ||||||||
\(277\) | −20.2781 | −1.21839 | −0.609196 | − | 0.793020i | \(-0.708508\pi\) | ||||
−0.609196 | + | 0.793020i | \(0.708508\pi\) | |||||||
\(278\) | −19.8711 | −1.19179 | ||||||||
\(279\) | −2.17843 | −0.130419 | ||||||||
\(280\) | 12.5097 | 0.747596 | ||||||||
\(281\) | 27.0775 | 1.61531 | 0.807653 | − | 0.589658i | \(-0.200737\pi\) | ||||
0.807653 | + | 0.589658i | \(0.200737\pi\) | |||||||
\(282\) | −10.9453 | −0.651783 | ||||||||
\(283\) | 11.3312 | 0.673568 | 0.336784 | − | 0.941582i | \(-0.390661\pi\) | ||||
0.336784 | + | 0.941582i | \(0.390661\pi\) | |||||||
\(284\) | 12.1343 | 0.720039 | ||||||||
\(285\) | −20.5538 | −1.21750 | ||||||||
\(286\) | −8.30378 | −0.491013 | ||||||||
\(287\) | −18.1451 | −1.07107 | ||||||||
\(288\) | −0.727642 | −0.0428767 | ||||||||
\(289\) | 32.2341 | 1.89612 | ||||||||
\(290\) | −9.58531 | −0.562869 | ||||||||
\(291\) | −11.4157 | −0.669198 | ||||||||
\(292\) | −7.86733 | −0.460401 | ||||||||
\(293\) | −23.4273 | −1.36864 | −0.684319 | − | 0.729183i | \(-0.739900\pi\) | ||||
−0.684319 | + | 0.729183i | \(0.739900\pi\) | |||||||
\(294\) | −28.4179 | −1.65737 | ||||||||
\(295\) | −19.1513 | −1.11503 | ||||||||
\(296\) | 2.45803 | 0.142870 | ||||||||
\(297\) | 34.4993 | 2.00185 | ||||||||
\(298\) | −14.5346 | −0.841969 | ||||||||
\(299\) | 11.8072 | 0.682828 | ||||||||
\(300\) | −1.58795 | −0.0916803 | ||||||||
\(301\) | −13.2397 | −0.763121 | ||||||||
\(302\) | −4.73484 | −0.272460 | ||||||||
\(303\) | 25.0173 | 1.43721 | ||||||||
\(304\) | −5.54184 | −0.317846 | ||||||||
\(305\) | −0.290827 | −0.0166527 | ||||||||
\(306\) | −5.10565 | −0.291870 | ||||||||
\(307\) | −12.2086 | −0.696779 | −0.348390 | − | 0.937350i | \(-0.613271\pi\) | ||||
−0.348390 | + | 0.937350i | \(0.613271\pi\) | |||||||
\(308\) | −31.2165 | −1.77872 | ||||||||
\(309\) | −16.5511 | −0.941557 | ||||||||
\(310\) | −7.36590 | −0.418355 | ||||||||
\(311\) | −0.714648 | −0.0405240 | −0.0202620 | − | 0.999795i | \(-0.506450\pi\) | ||||
−0.0202620 | + | 0.999795i | \(0.506450\pi\) | |||||||
\(312\) | 2.03881 | 0.115425 | ||||||||
\(313\) | −19.5181 | −1.10323 | −0.551614 | − | 0.834100i | \(-0.685988\pi\) | ||||
−0.551614 | + | 0.834100i | \(0.685988\pi\) | |||||||
\(314\) | 6.50607 | 0.367159 | ||||||||
\(315\) | −9.10256 | −0.512871 | ||||||||
\(316\) | −13.3791 | −0.752633 | ||||||||
\(317\) | −20.8123 | −1.16894 | −0.584468 | − | 0.811417i | \(-0.698697\pi\) | ||||
−0.584468 | + | 0.811417i | \(0.698697\pi\) | |||||||
\(318\) | 17.2383 | 0.966676 | ||||||||
\(319\) | 23.9191 | 1.33921 | ||||||||
\(320\) | −2.46037 | −0.137539 | ||||||||
\(321\) | 9.58879 | 0.535194 | ||||||||
\(322\) | 44.3869 | 2.47358 | ||||||||
\(323\) | −38.8854 | −2.16364 | ||||||||
\(324\) | −6.28761 | −0.349312 | ||||||||
\(325\) | −1.42474 | −0.0790305 | ||||||||
\(326\) | 6.56285 | 0.363483 | ||||||||
\(327\) | −15.9815 | −0.883782 | ||||||||
\(328\) | 3.56872 | 0.197050 | ||||||||
\(329\) | −36.9177 | −2.03534 | ||||||||
\(330\) | 22.7707 | 1.25349 | ||||||||
\(331\) | −24.3169 | −1.33658 | −0.668289 | − | 0.743902i | \(-0.732973\pi\) | ||||
−0.668289 | + | 0.743902i | \(0.732973\pi\) | |||||||
\(332\) | 11.8911 | 0.652611 | ||||||||
\(333\) | −1.78856 | −0.0980127 | ||||||||
\(334\) | −11.0561 | −0.604965 | ||||||||
\(335\) | −8.03012 | −0.438732 | ||||||||
\(336\) | 7.66450 | 0.418133 | ||||||||
\(337\) | −17.2938 | −0.942056 | −0.471028 | − | 0.882118i | \(-0.656117\pi\) | ||||
−0.471028 | + | 0.882118i | \(0.656117\pi\) | |||||||
\(338\) | −11.1707 | −0.607608 | ||||||||
\(339\) | 12.9456 | 0.703110 | ||||||||
\(340\) | −17.2637 | −0.936253 | ||||||||
\(341\) | 18.3808 | 0.995375 | ||||||||
\(342\) | 4.03247 | 0.218051 | ||||||||
\(343\) | −60.2603 | −3.25375 | ||||||||
\(344\) | 2.60394 | 0.140395 | ||||||||
\(345\) | −32.3778 | −1.74316 | ||||||||
\(346\) | −4.68551 | −0.251895 | ||||||||
\(347\) | −29.9903 | −1.60996 | −0.804982 | − | 0.593299i | \(-0.797825\pi\) | ||||
−0.804982 | + | 0.593299i | \(0.797825\pi\) | |||||||
\(348\) | −5.87279 | −0.314815 | ||||||||
\(349\) | 1.14031 | 0.0610395 | 0.0305197 | − | 0.999534i | \(-0.490284\pi\) | ||||
0.0305197 | + | 0.999534i | \(0.490284\pi\) | |||||||
\(350\) | −5.35604 | −0.286292 | ||||||||
\(351\) | −7.59995 | −0.405655 | ||||||||
\(352\) | 6.13957 | 0.327240 | ||||||||
\(353\) | 4.30092 | 0.228915 | 0.114457 | − | 0.993428i | \(-0.463487\pi\) | ||||
0.114457 | + | 0.993428i | \(0.463487\pi\) | |||||||
\(354\) | −11.7338 | −0.623643 | ||||||||
\(355\) | −29.8549 | −1.58453 | ||||||||
\(356\) | −17.2789 | −0.915779 | ||||||||
\(357\) | 53.7795 | 2.84631 | ||||||||
\(358\) | 9.67377 | 0.511275 | ||||||||
\(359\) | 6.62605 | 0.349710 | 0.174855 | − | 0.984594i | \(-0.444054\pi\) | ||||
0.174855 | + | 0.984594i | \(0.444054\pi\) | |||||||
\(360\) | 1.79027 | 0.0943554 | ||||||||
\(361\) | 11.7120 | 0.616419 | ||||||||
\(362\) | −12.8673 | −0.676292 | ||||||||
\(363\) | −40.2399 | −2.11205 | ||||||||
\(364\) | 6.87676 | 0.360440 | ||||||||
\(365\) | 19.3565 | 1.01317 | ||||||||
\(366\) | −0.178186 | −0.00931393 | ||||||||
\(367\) | −4.25410 | −0.222062 | −0.111031 | − | 0.993817i | \(-0.535415\pi\) | ||||
−0.111031 | + | 0.993817i | \(0.535415\pi\) | |||||||
\(368\) | −8.72989 | −0.455077 | ||||||||
\(369\) | −2.59675 | −0.135182 | ||||||||
\(370\) | −6.04765 | −0.314402 | ||||||||
\(371\) | 58.1436 | 3.01866 | ||||||||
\(372\) | −4.51299 | −0.233988 | ||||||||
\(373\) | −11.8018 | −0.611075 | −0.305537 | − | 0.952180i | \(-0.598836\pi\) | ||||
−0.305537 | + | 0.952180i | \(0.598836\pi\) | |||||||
\(374\) | 43.0795 | 2.22759 | ||||||||
\(375\) | −14.6373 | −0.755866 | ||||||||
\(376\) | 7.26088 | 0.374452 | ||||||||
\(377\) | −5.26920 | −0.271377 | ||||||||
\(378\) | −28.5705 | −1.46951 | ||||||||
\(379\) | 20.1557 | 1.03533 | 0.517665 | − | 0.855584i | \(-0.326801\pi\) | ||||
0.517665 | + | 0.855584i | \(0.326801\pi\) | |||||||
\(380\) | 13.6350 | 0.699459 | ||||||||
\(381\) | −14.3872 | −0.737078 | ||||||||
\(382\) | −2.18137 | −0.111609 | ||||||||
\(383\) | −19.1024 | −0.976086 | −0.488043 | − | 0.872820i | \(-0.662289\pi\) | ||||
−0.488043 | + | 0.872820i | \(0.662289\pi\) | |||||||
\(384\) | −1.50743 | −0.0769259 | ||||||||
\(385\) | 76.8040 | 3.91429 | ||||||||
\(386\) | −10.4373 | −0.531244 | ||||||||
\(387\) | −1.89474 | −0.0963149 | ||||||||
\(388\) | 7.57290 | 0.384456 | ||||||||
\(389\) | −9.81847 | −0.497816 | −0.248908 | − | 0.968527i | \(-0.580072\pi\) | ||||
−0.248908 | + | 0.968527i | \(0.580072\pi\) | |||||||
\(390\) | −5.01622 | −0.254006 | ||||||||
\(391\) | −61.2550 | −3.09780 | ||||||||
\(392\) | 18.8518 | 0.952162 | ||||||||
\(393\) | 2.75897 | 0.139172 | ||||||||
\(394\) | 6.26423 | 0.315588 | ||||||||
\(395\) | 32.9175 | 1.65626 | ||||||||
\(396\) | −4.46741 | −0.224496 | ||||||||
\(397\) | 8.71093 | 0.437189 | 0.218594 | − | 0.975816i | \(-0.429853\pi\) | ||||
0.218594 | + | 0.975816i | \(0.429853\pi\) | |||||||
\(398\) | 4.27957 | 0.214515 | ||||||||
\(399\) | −42.4754 | −2.12643 | ||||||||
\(400\) | 1.05341 | 0.0526706 | ||||||||
\(401\) | 38.9361 | 1.94438 | 0.972188 | − | 0.234203i | \(-0.0752481\pi\) | ||||
0.972188 | + | 0.234203i | \(0.0752481\pi\) | |||||||
\(402\) | −4.91994 | −0.245384 | ||||||||
\(403\) | −4.04915 | −0.201703 | ||||||||
\(404\) | −16.5960 | −0.825680 | ||||||||
\(405\) | 15.4698 | 0.768702 | ||||||||
\(406\) | −19.8085 | −0.983080 | ||||||||
\(407\) | 15.0912 | 0.748044 | ||||||||
\(408\) | −10.5772 | −0.523650 | ||||||||
\(409\) | 19.9201 | 0.984983 | 0.492492 | − | 0.870317i | \(-0.336086\pi\) | ||||
0.492492 | + | 0.870317i | \(0.336086\pi\) | |||||||
\(410\) | −8.78037 | −0.433632 | ||||||||
\(411\) | 7.04495 | 0.347502 | ||||||||
\(412\) | 10.9796 | 0.540928 | ||||||||
\(413\) | −39.5772 | −1.94747 | ||||||||
\(414\) | 6.35224 | 0.312196 | ||||||||
\(415\) | −29.2566 | −1.43615 | ||||||||
\(416\) | −1.35250 | −0.0663119 | ||||||||
\(417\) | 29.9544 | 1.46687 | ||||||||
\(418\) | −34.0245 | −1.66419 | ||||||||
\(419\) | 38.0867 | 1.86066 | 0.930328 | − | 0.366730i | \(-0.119523\pi\) | ||||
0.930328 | + | 0.366730i | \(0.119523\pi\) | |||||||
\(420\) | −18.8575 | −0.920152 | ||||||||
\(421\) | −3.33316 | −0.162448 | −0.0812240 | − | 0.996696i | \(-0.525883\pi\) | ||||
−0.0812240 | + | 0.996696i | \(0.525883\pi\) | |||||||
\(422\) | −9.24903 | −0.450236 | ||||||||
\(423\) | −5.28333 | −0.256884 | ||||||||
\(424\) | −11.4355 | −0.555358 | ||||||||
\(425\) | 7.39147 | 0.358539 | ||||||||
\(426\) | −18.2917 | −0.886235 | ||||||||
\(427\) | −0.601009 | −0.0290849 | ||||||||
\(428\) | −6.36100 | −0.307471 | ||||||||
\(429\) | 12.5174 | 0.604346 | ||||||||
\(430\) | −6.40665 | −0.308956 | ||||||||
\(431\) | 2.96161 | 0.142656 | 0.0713280 | − | 0.997453i | \(-0.477276\pi\) | ||||
0.0713280 | + | 0.997453i | \(0.477276\pi\) | |||||||
\(432\) | 5.61918 | 0.270353 | ||||||||
\(433\) | 31.2183 | 1.50026 | 0.750128 | − | 0.661292i | \(-0.229992\pi\) | ||||
0.750128 | + | 0.661292i | \(0.229992\pi\) | |||||||
\(434\) | −15.2220 | −0.730679 | ||||||||
\(435\) | 14.4492 | 0.692788 | ||||||||
\(436\) | 10.6018 | 0.507735 | ||||||||
\(437\) | 48.3797 | 2.31431 | ||||||||
\(438\) | 11.8595 | 0.566668 | ||||||||
\(439\) | 22.0650 | 1.05310 | 0.526552 | − | 0.850143i | \(-0.323485\pi\) | ||||
0.526552 | + | 0.850143i | \(0.323485\pi\) | |||||||
\(440\) | −15.1056 | −0.720131 | ||||||||
\(441\) | −13.7174 | −0.653209 | ||||||||
\(442\) | −9.49010 | −0.451398 | ||||||||
\(443\) | −32.3480 | −1.53690 | −0.768451 | − | 0.639909i | \(-0.778972\pi\) | ||||
−0.768451 | + | 0.639909i | \(0.778972\pi\) | |||||||
\(444\) | −3.70531 | −0.175846 | ||||||||
\(445\) | 42.5124 | 2.01528 | ||||||||
\(446\) | 18.5235 | 0.877112 | ||||||||
\(447\) | 21.9100 | 1.03631 | ||||||||
\(448\) | −5.08447 | −0.240219 | ||||||||
\(449\) | −19.5080 | −0.920639 | −0.460319 | − | 0.887753i | \(-0.652265\pi\) | ||||
−0.460319 | + | 0.887753i | \(0.652265\pi\) | |||||||
\(450\) | −0.766507 | −0.0361335 | ||||||||
\(451\) | 21.9104 | 1.03172 | ||||||||
\(452\) | −8.58785 | −0.403939 | ||||||||
\(453\) | 7.13747 | 0.335347 | ||||||||
\(454\) | −14.0148 | −0.657746 | ||||||||
\(455\) | −16.9194 | −0.793192 | ||||||||
\(456\) | 8.35395 | 0.391210 | ||||||||
\(457\) | −37.6584 | −1.76158 | −0.880792 | − | 0.473503i | \(-0.842989\pi\) | ||||
−0.880792 | + | 0.473503i | \(0.842989\pi\) | |||||||
\(458\) | −19.3989 | −0.906449 | ||||||||
\(459\) | 39.4281 | 1.84034 | ||||||||
\(460\) | 21.4788 | 1.00145 | ||||||||
\(461\) | 8.88393 | 0.413766 | 0.206883 | − | 0.978366i | \(-0.433668\pi\) | ||||
0.206883 | + | 0.978366i | \(0.433668\pi\) | |||||||
\(462\) | 47.0568 | 2.18928 | ||||||||
\(463\) | −3.30357 | −0.153530 | −0.0767650 | − | 0.997049i | \(-0.524459\pi\) | ||||
−0.0767650 | + | 0.997049i | \(0.524459\pi\) | |||||||
\(464\) | 3.89589 | 0.180862 | ||||||||
\(465\) | 11.1036 | 0.514918 | ||||||||
\(466\) | −16.1292 | −0.747171 | ||||||||
\(467\) | 6.17430 | 0.285713 | 0.142856 | − | 0.989743i | \(-0.454371\pi\) | ||||
0.142856 | + | 0.989743i | \(0.454371\pi\) | |||||||
\(468\) | 0.984138 | 0.0454918 | ||||||||
\(469\) | −16.5946 | −0.766268 | ||||||||
\(470\) | −17.8644 | −0.824026 | ||||||||
\(471\) | −9.80747 | −0.451904 | ||||||||
\(472\) | 7.78393 | 0.358285 | ||||||||
\(473\) | 15.9871 | 0.735087 | ||||||||
\(474\) | 20.1681 | 0.926352 | ||||||||
\(475\) | −5.83784 | −0.267858 | ||||||||
\(476\) | −35.6762 | −1.63522 | ||||||||
\(477\) | 8.32097 | 0.380991 | ||||||||
\(478\) | −16.9585 | −0.775662 | ||||||||
\(479\) | −33.6049 | −1.53545 | −0.767724 | − | 0.640781i | \(-0.778611\pi\) | ||||
−0.767724 | + | 0.640781i | \(0.778611\pi\) | |||||||
\(480\) | 3.70884 | 0.169285 | ||||||||
\(481\) | −3.32449 | −0.151584 | ||||||||
\(482\) | 27.3400 | 1.24530 | ||||||||
\(483\) | −66.9103 | −3.04452 | ||||||||
\(484\) | 26.6943 | 1.21338 | ||||||||
\(485\) | −18.6321 | −0.846042 | ||||||||
\(486\) | −7.37937 | −0.334735 | ||||||||
\(487\) | 6.50466 | 0.294754 | 0.147377 | − | 0.989080i | \(-0.452917\pi\) | ||||
0.147377 | + | 0.989080i | \(0.452917\pi\) | |||||||
\(488\) | 0.118205 | 0.00535088 | ||||||||
\(489\) | −9.89306 | −0.447380 | ||||||||
\(490\) | −46.3825 | −2.09535 | ||||||||
\(491\) | 37.9220 | 1.71139 | 0.855697 | − | 0.517477i | \(-0.173129\pi\) | ||||
0.855697 | + | 0.517477i | \(0.173129\pi\) | |||||||
\(492\) | −5.37962 | −0.242532 | ||||||||
\(493\) | 27.3363 | 1.23116 | ||||||||
\(494\) | 7.49535 | 0.337232 | ||||||||
\(495\) | 10.9915 | 0.494030 | ||||||||
\(496\) | 2.99382 | 0.134427 | ||||||||
\(497\) | −61.6965 | −2.76747 | ||||||||
\(498\) | −17.9251 | −0.803244 | ||||||||
\(499\) | −7.27918 | −0.325861 | −0.162930 | − | 0.986638i | \(-0.552095\pi\) | ||||
−0.162930 | + | 0.986638i | \(0.552095\pi\) | |||||||
\(500\) | 9.71006 | 0.434247 | ||||||||
\(501\) | 16.6664 | 0.744600 | ||||||||
\(502\) | 13.0250 | 0.581334 | ||||||||
\(503\) | −2.71900 | −0.121234 | −0.0606170 | − | 0.998161i | \(-0.519307\pi\) | ||||
−0.0606170 | + | 0.998161i | \(0.519307\pi\) | |||||||
\(504\) | 3.69968 | 0.164797 | ||||||||
\(505\) | 40.8322 | 1.81701 | ||||||||
\(506\) | −53.5978 | −2.38271 | ||||||||
\(507\) | 16.8391 | 0.747853 | ||||||||
\(508\) | 9.54416 | 0.423454 | ||||||||
\(509\) | 0.244700 | 0.0108461 | 0.00542306 | − | 0.999985i | \(-0.498274\pi\) | ||||
0.00542306 | + | 0.999985i | \(0.498274\pi\) | |||||||
\(510\) | 26.0238 | 1.15235 | ||||||||
\(511\) | 40.0012 | 1.76955 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −31.1406 | −1.37489 | ||||||||
\(514\) | −3.52106 | −0.155307 | ||||||||
\(515\) | −27.0139 | −1.19038 | ||||||||
\(516\) | −3.92527 | −0.172800 | ||||||||
\(517\) | 44.5787 | 1.96057 | ||||||||
\(518\) | −12.4978 | −0.549120 | ||||||||
\(519\) | 7.06310 | 0.310036 | ||||||||
\(520\) | 3.32765 | 0.145927 | ||||||||
\(521\) | −10.2034 | −0.447017 | −0.223509 | − | 0.974702i | \(-0.571751\pi\) | ||||
−0.223509 | + | 0.974702i | \(0.571751\pi\) | |||||||
\(522\) | −2.83481 | −0.124076 | ||||||||
\(523\) | −15.7765 | −0.689860 | −0.344930 | − | 0.938628i | \(-0.612097\pi\) | ||||
−0.344930 | + | 0.938628i | \(0.612097\pi\) | |||||||
\(524\) | −1.83025 | −0.0799547 | ||||||||
\(525\) | 8.07388 | 0.352373 | ||||||||
\(526\) | −14.7974 | −0.645199 | ||||||||
\(527\) | 21.0067 | 0.915068 | ||||||||
\(528\) | −9.25500 | −0.402772 | ||||||||
\(529\) | 53.2110 | 2.31352 | ||||||||
\(530\) | 28.1356 | 1.22213 | ||||||||
\(531\) | −5.66392 | −0.245793 | ||||||||
\(532\) | 28.1773 | 1.22164 | ||||||||
\(533\) | −4.82671 | −0.209068 | ||||||||
\(534\) | 26.0468 | 1.12715 | ||||||||
\(535\) | 15.6504 | 0.676626 | ||||||||
\(536\) | 3.26379 | 0.140974 | ||||||||
\(537\) | −14.5826 | −0.629284 | ||||||||
\(538\) | 7.83519 | 0.337799 | ||||||||
\(539\) | 115.742 | 4.98537 | ||||||||
\(540\) | −13.8252 | −0.594944 | ||||||||
\(541\) | 29.0031 | 1.24694 | 0.623470 | − | 0.781847i | \(-0.285722\pi\) | ||||
0.623470 | + | 0.781847i | \(0.285722\pi\) | |||||||
\(542\) | 0.261639 | 0.0112384 | ||||||||
\(543\) | 19.3967 | 0.832390 | ||||||||
\(544\) | 7.01670 | 0.300838 | ||||||||
\(545\) | −26.0844 | −1.11733 | ||||||||
\(546\) | −10.3663 | −0.443635 | ||||||||
\(547\) | −28.7833 | −1.23069 | −0.615343 | − | 0.788260i | \(-0.710982\pi\) | ||||
−0.615343 | + | 0.788260i | \(0.710982\pi\) | |||||||
\(548\) | −4.67347 | −0.199641 | ||||||||
\(549\) | −0.0860108 | −0.00367085 | ||||||||
\(550\) | 6.46750 | 0.275775 | ||||||||
\(551\) | −21.5904 | −0.919780 | ||||||||
\(552\) | 13.1597 | 0.560116 | ||||||||
\(553\) | 68.0256 | 2.89274 | ||||||||
\(554\) | −20.2781 | −0.861533 | ||||||||
\(555\) | 9.11644 | 0.386971 | ||||||||
\(556\) | −19.8711 | −0.842723 | ||||||||
\(557\) | 14.9313 | 0.632658 | 0.316329 | − | 0.948650i | \(-0.397550\pi\) | ||||
0.316329 | + | 0.948650i | \(0.397550\pi\) | |||||||
\(558\) | −2.17843 | −0.0922203 | ||||||||
\(559\) | −3.52184 | −0.148958 | ||||||||
\(560\) | 12.5097 | 0.528630 | ||||||||
\(561\) | −64.9395 | −2.74175 | ||||||||
\(562\) | 27.0775 | 1.14219 | ||||||||
\(563\) | −15.5535 | −0.655503 | −0.327752 | − | 0.944764i | \(-0.606291\pi\) | ||||
−0.327752 | + | 0.944764i | \(0.606291\pi\) | |||||||
\(564\) | −10.9453 | −0.460880 | ||||||||
\(565\) | 21.1293 | 0.888916 | ||||||||
\(566\) | 11.3312 | 0.476284 | ||||||||
\(567\) | 31.9692 | 1.34258 | ||||||||
\(568\) | 12.1343 | 0.509144 | ||||||||
\(569\) | −38.3983 | −1.60974 | −0.804870 | − | 0.593451i | \(-0.797765\pi\) | ||||
−0.804870 | + | 0.593451i | \(0.797765\pi\) | |||||||
\(570\) | −20.5538 | −0.860904 | ||||||||
\(571\) | 9.72038 | 0.406785 | 0.203393 | − | 0.979097i | \(-0.434803\pi\) | ||||
0.203393 | + | 0.979097i | \(0.434803\pi\) | |||||||
\(572\) | −8.30378 | −0.347199 | ||||||||
\(573\) | 3.28827 | 0.137369 | ||||||||
\(574\) | −18.1451 | −0.757361 | ||||||||
\(575\) | −9.19618 | −0.383507 | ||||||||
\(576\) | −0.727642 | −0.0303184 | ||||||||
\(577\) | −34.3480 | −1.42993 | −0.714963 | − | 0.699162i | \(-0.753557\pi\) | ||||
−0.714963 | + | 0.699162i | \(0.753557\pi\) | |||||||
\(578\) | 32.2341 | 1.34076 | ||||||||
\(579\) | 15.7335 | 0.653863 | ||||||||
\(580\) | −9.58531 | −0.398008 | ||||||||
\(581\) | −60.4602 | −2.50831 | ||||||||
\(582\) | −11.4157 | −0.473194 | ||||||||
\(583\) | −70.2092 | −2.90777 | ||||||||
\(584\) | −7.86733 | −0.325552 | ||||||||
\(585\) | −2.42134 | −0.100110 | ||||||||
\(586\) | −23.4273 | −0.967773 | ||||||||
\(587\) | 5.63871 | 0.232734 | 0.116367 | − | 0.993206i | \(-0.462875\pi\) | ||||
0.116367 | + | 0.993206i | \(0.462875\pi\) | |||||||
\(588\) | −28.4179 | −1.17193 | ||||||||
\(589\) | −16.5913 | −0.683631 | ||||||||
\(590\) | −19.1513 | −0.788448 | ||||||||
\(591\) | −9.44292 | −0.388430 | ||||||||
\(592\) | 2.45803 | 0.101024 | ||||||||
\(593\) | −3.03585 | −0.124667 | −0.0623337 | − | 0.998055i | \(-0.519854\pi\) | ||||
−0.0623337 | + | 0.998055i | \(0.519854\pi\) | |||||||
\(594\) | 34.4993 | 1.41552 | ||||||||
\(595\) | 87.7766 | 3.59849 | ||||||||
\(596\) | −14.5346 | −0.595362 | ||||||||
\(597\) | −6.45116 | −0.264029 | ||||||||
\(598\) | 11.8072 | 0.482833 | ||||||||
\(599\) | 21.2626 | 0.868766 | 0.434383 | − | 0.900728i | \(-0.356966\pi\) | ||||
0.434383 | + | 0.900728i | \(0.356966\pi\) | |||||||
\(600\) | −1.58795 | −0.0648278 | ||||||||
\(601\) | 5.08342 | 0.207357 | 0.103678 | − | 0.994611i | \(-0.466939\pi\) | ||||
0.103678 | + | 0.994611i | \(0.466939\pi\) | |||||||
\(602\) | −13.2397 | −0.539608 | ||||||||
\(603\) | −2.37487 | −0.0967121 | ||||||||
\(604\) | −4.73484 | −0.192658 | ||||||||
\(605\) | −65.6778 | −2.67018 | ||||||||
\(606\) | 25.0173 | 1.01626 | ||||||||
\(607\) | −4.64678 | −0.188607 | −0.0943035 | − | 0.995543i | \(-0.530062\pi\) | ||||
−0.0943035 | + | 0.995543i | \(0.530062\pi\) | |||||||
\(608\) | −5.54184 | −0.224751 | ||||||||
\(609\) | 29.8600 | 1.20999 | ||||||||
\(610\) | −0.290827 | −0.0117753 | ||||||||
\(611\) | −9.82037 | −0.397289 | ||||||||
\(612\) | −5.10565 | −0.206383 | ||||||||
\(613\) | 32.1653 | 1.29914 | 0.649572 | − | 0.760300i | \(-0.274948\pi\) | ||||
0.649572 | + | 0.760300i | \(0.274948\pi\) | |||||||
\(614\) | −12.2086 | −0.492697 | ||||||||
\(615\) | 13.2358 | 0.533720 | ||||||||
\(616\) | −31.2165 | −1.25775 | ||||||||
\(617\) | −10.3097 | −0.415051 | −0.207526 | − | 0.978230i | \(-0.566541\pi\) | ||||
−0.207526 | + | 0.978230i | \(0.566541\pi\) | |||||||
\(618\) | −16.5511 | −0.665782 | ||||||||
\(619\) | 15.1097 | 0.607309 | 0.303655 | − | 0.952782i | \(-0.401793\pi\) | ||||
0.303655 | + | 0.952782i | \(0.401793\pi\) | |||||||
\(620\) | −7.36590 | −0.295822 | ||||||||
\(621\) | −49.0548 | −1.96850 | ||||||||
\(622\) | −0.714648 | −0.0286548 | ||||||||
\(623\) | 87.8540 | 3.51980 | ||||||||
\(624\) | 2.03881 | 0.0816177 | ||||||||
\(625\) | −29.1574 | −1.16630 | ||||||||
\(626\) | −19.5181 | −0.780100 | ||||||||
\(627\) | 51.2897 | 2.04831 | ||||||||
\(628\) | 6.50607 | 0.259620 | ||||||||
\(629\) | 17.2472 | 0.687692 | ||||||||
\(630\) | −9.10256 | −0.362655 | ||||||||
\(631\) | −5.16314 | −0.205541 | −0.102771 | − | 0.994705i | \(-0.532771\pi\) | ||||
−0.102771 | + | 0.994705i | \(0.532771\pi\) | |||||||
\(632\) | −13.3791 | −0.532192 | ||||||||
\(633\) | 13.9423 | 0.554157 | ||||||||
\(634\) | −20.8123 | −0.826562 | ||||||||
\(635\) | −23.4821 | −0.931861 | ||||||||
\(636\) | 17.2383 | 0.683543 | ||||||||
\(637\) | −25.4972 | −1.01023 | ||||||||
\(638\) | 23.9191 | 0.946965 | ||||||||
\(639\) | −8.82944 | −0.349287 | ||||||||
\(640\) | −2.46037 | −0.0972546 | ||||||||
\(641\) | 25.3859 | 1.00268 | 0.501342 | − | 0.865249i | \(-0.332840\pi\) | ||||
0.501342 | + | 0.865249i | \(0.332840\pi\) | |||||||
\(642\) | 9.58879 | 0.378439 | ||||||||
\(643\) | −41.7951 | −1.64824 | −0.824120 | − | 0.566416i | \(-0.808330\pi\) | ||||
−0.824120 | + | 0.566416i | \(0.808330\pi\) | |||||||
\(644\) | 44.3869 | 1.74909 | ||||||||
\(645\) | 9.65761 | 0.380268 | ||||||||
\(646\) | −38.8854 | −1.52993 | ||||||||
\(647\) | −22.1478 | −0.870720 | −0.435360 | − | 0.900256i | \(-0.643379\pi\) | ||||
−0.435360 | + | 0.900256i | \(0.643379\pi\) | |||||||
\(648\) | −6.28761 | −0.247001 | ||||||||
\(649\) | 47.7900 | 1.87592 | ||||||||
\(650\) | −1.42474 | −0.0558830 | ||||||||
\(651\) | 22.9462 | 0.899331 | ||||||||
\(652\) | 6.56285 | 0.257021 | ||||||||
\(653\) | −17.4592 | −0.683230 | −0.341615 | − | 0.939840i | \(-0.610974\pi\) | ||||
−0.341615 | + | 0.939840i | \(0.610974\pi\) | |||||||
\(654\) | −15.9815 | −0.624928 | ||||||||
\(655\) | 4.50308 | 0.175950 | ||||||||
\(656\) | 3.56872 | 0.139335 | ||||||||
\(657\) | 5.72460 | 0.223338 | ||||||||
\(658\) | −36.9177 | −1.43920 | ||||||||
\(659\) | −31.5496 | −1.22900 | −0.614499 | − | 0.788918i | \(-0.710642\pi\) | ||||
−0.614499 | + | 0.788918i | \(0.710642\pi\) | |||||||
\(660\) | 22.7707 | 0.886348 | ||||||||
\(661\) | 25.0337 | 0.973699 | 0.486850 | − | 0.873486i | \(-0.338146\pi\) | ||||
0.486850 | + | 0.873486i | \(0.338146\pi\) | |||||||
\(662\) | −24.3169 | −0.945104 | ||||||||
\(663\) | 14.3057 | 0.555588 | ||||||||
\(664\) | 11.8911 | 0.461466 | ||||||||
\(665\) | −69.3266 | −2.68837 | ||||||||
\(666\) | −1.78856 | −0.0693055 | ||||||||
\(667\) | −34.0107 | −1.31690 | ||||||||
\(668\) | −11.0561 | −0.427775 | ||||||||
\(669\) | −27.9229 | −1.07956 | ||||||||
\(670\) | −8.03012 | −0.310230 | ||||||||
\(671\) | 0.725727 | 0.0280164 | ||||||||
\(672\) | 7.66450 | 0.295665 | ||||||||
\(673\) | −5.97534 | −0.230333 | −0.115166 | − | 0.993346i | \(-0.536740\pi\) | ||||
−0.115166 | + | 0.993346i | \(0.536740\pi\) | |||||||
\(674\) | −17.2938 | −0.666134 | ||||||||
\(675\) | 5.91931 | 0.227834 | ||||||||
\(676\) | −11.1707 | −0.429644 | ||||||||
\(677\) | 22.5056 | 0.864961 | 0.432481 | − | 0.901643i | \(-0.357638\pi\) | ||||
0.432481 | + | 0.901643i | \(0.357638\pi\) | |||||||
\(678\) | 12.9456 | 0.497174 | ||||||||
\(679\) | −38.5042 | −1.47766 | ||||||||
\(680\) | −17.2637 | −0.662031 | ||||||||
\(681\) | 21.1263 | 0.809563 | ||||||||
\(682\) | 18.3808 | 0.703836 | ||||||||
\(683\) | 3.34161 | 0.127863 | 0.0639315 | − | 0.997954i | \(-0.479636\pi\) | ||||
0.0639315 | + | 0.997954i | \(0.479636\pi\) | |||||||
\(684\) | 4.03247 | 0.154186 | ||||||||
\(685\) | 11.4985 | 0.439333 | ||||||||
\(686\) | −60.2603 | −2.30075 | ||||||||
\(687\) | 29.2425 | 1.11567 | ||||||||
\(688\) | 2.60394 | 0.0992743 | ||||||||
\(689\) | 15.4666 | 0.589230 | ||||||||
\(690\) | −32.3778 | −1.23260 | ||||||||
\(691\) | 32.4859 | 1.23582 | 0.617911 | − | 0.786248i | \(-0.287979\pi\) | ||||
0.617911 | + | 0.786248i | \(0.287979\pi\) | |||||||
\(692\) | −4.68551 | −0.178116 | ||||||||
\(693\) | 22.7144 | 0.862849 | ||||||||
\(694\) | −29.9903 | −1.13842 | ||||||||
\(695\) | 48.8903 | 1.85451 | ||||||||
\(696\) | −5.87279 | −0.222608 | ||||||||
\(697\) | 25.0407 | 0.948482 | ||||||||
\(698\) | 1.14031 | 0.0431614 | ||||||||
\(699\) | 24.3137 | 0.919630 | ||||||||
\(700\) | −5.35604 | −0.202439 | ||||||||
\(701\) | −29.6259 | −1.11895 | −0.559477 | − | 0.828846i | \(-0.688998\pi\) | ||||
−0.559477 | + | 0.828846i | \(0.688998\pi\) | |||||||
\(702\) | −7.59995 | −0.286842 | ||||||||
\(703\) | −13.6220 | −0.513763 | ||||||||
\(704\) | 6.13957 | 0.231394 | ||||||||
\(705\) | 26.9295 | 1.01422 | ||||||||
\(706\) | 4.30092 | 0.161867 | ||||||||
\(707\) | 84.3817 | 3.17350 | ||||||||
\(708\) | −11.7338 | −0.440982 | ||||||||
\(709\) | −29.5063 | −1.10813 | −0.554066 | − | 0.832472i | \(-0.686925\pi\) | ||||
−0.554066 | + | 0.832472i | \(0.686925\pi\) | |||||||
\(710\) | −29.8549 | −1.12043 | ||||||||
\(711\) | 9.73520 | 0.365098 | ||||||||
\(712\) | −17.2789 | −0.647554 | ||||||||
\(713\) | −26.1357 | −0.978791 | ||||||||
\(714\) | 53.7795 | 2.01265 | ||||||||
\(715\) | 20.4304 | 0.764052 | ||||||||
\(716\) | 9.67377 | 0.361526 | ||||||||
\(717\) | 25.5638 | 0.954696 | ||||||||
\(718\) | 6.62605 | 0.247282 | ||||||||
\(719\) | 50.6198 | 1.88780 | 0.943901 | − | 0.330229i | \(-0.107126\pi\) | ||||
0.943901 | + | 0.330229i | \(0.107126\pi\) | |||||||
\(720\) | 1.79027 | 0.0667193 | ||||||||
\(721\) | −55.8256 | −2.07905 | ||||||||
\(722\) | 11.7120 | 0.435874 | ||||||||
\(723\) | −41.2133 | −1.53274 | ||||||||
\(724\) | −12.8673 | −0.478211 | ||||||||
\(725\) | 4.10397 | 0.152418 | ||||||||
\(726\) | −40.2399 | −1.49344 | ||||||||
\(727\) | 42.2365 | 1.56647 | 0.783233 | − | 0.621729i | \(-0.213569\pi\) | ||||
0.783233 | + | 0.621729i | \(0.213569\pi\) | |||||||
\(728\) | 6.87676 | 0.254870 | ||||||||
\(729\) | 29.9867 | 1.11062 | ||||||||
\(730\) | 19.3565 | 0.716417 | ||||||||
\(731\) | 18.2711 | 0.675780 | ||||||||
\(732\) | −0.178186 | −0.00658595 | ||||||||
\(733\) | 10.9034 | 0.402725 | 0.201363 | − | 0.979517i | \(-0.435463\pi\) | ||||
0.201363 | + | 0.979517i | \(0.435463\pi\) | |||||||
\(734\) | −4.25410 | −0.157022 | ||||||||
\(735\) | 69.9185 | 2.57898 | ||||||||
\(736\) | −8.72989 | −0.321788 | ||||||||
\(737\) | 20.0382 | 0.738118 | ||||||||
\(738\) | −2.59675 | −0.0955878 | ||||||||
\(739\) | 48.4140 | 1.78094 | 0.890468 | − | 0.455045i | \(-0.150377\pi\) | ||||
0.890468 | + | 0.455045i | \(0.150377\pi\) | |||||||
\(740\) | −6.04765 | −0.222316 | ||||||||
\(741\) | −11.2987 | −0.415070 | ||||||||
\(742\) | 58.1436 | 2.13452 | ||||||||
\(743\) | 34.4891 | 1.26528 | 0.632641 | − | 0.774445i | \(-0.281971\pi\) | ||||
0.632641 | + | 0.774445i | \(0.281971\pi\) | |||||||
\(744\) | −4.51299 | −0.165454 | ||||||||
\(745\) | 35.7606 | 1.31017 | ||||||||
\(746\) | −11.8018 | −0.432095 | ||||||||
\(747\) | −8.65250 | −0.316578 | ||||||||
\(748\) | 43.0795 | 1.57514 | ||||||||
\(749\) | 32.3423 | 1.18176 | ||||||||
\(750\) | −14.6373 | −0.534478 | ||||||||
\(751\) | 23.9765 | 0.874916 | 0.437458 | − | 0.899239i | \(-0.355879\pi\) | ||||
0.437458 | + | 0.899239i | \(0.355879\pi\) | |||||||
\(752\) | 7.26088 | 0.264777 | ||||||||
\(753\) | −19.6343 | −0.715515 | ||||||||
\(754\) | −5.26920 | −0.191893 | ||||||||
\(755\) | 11.6495 | 0.423967 | ||||||||
\(756\) | −28.5705 | −1.03910 | ||||||||
\(757\) | −21.5509 | −0.783279 | −0.391640 | − | 0.920119i | \(-0.628092\pi\) | ||||
−0.391640 | + | 0.920119i | \(0.628092\pi\) | |||||||
\(758\) | 20.1557 | 0.732089 | ||||||||
\(759\) | 80.7951 | 2.93268 | ||||||||
\(760\) | 13.6350 | 0.494592 | ||||||||
\(761\) | 12.6620 | 0.458997 | 0.229499 | − | 0.973309i | \(-0.426291\pi\) | ||||
0.229499 | + | 0.973309i | \(0.426291\pi\) | |||||||
\(762\) | −14.3872 | −0.521193 | ||||||||
\(763\) | −53.9046 | −1.95148 | ||||||||
\(764\) | −2.18137 | −0.0789192 | ||||||||
\(765\) | 12.5618 | 0.454172 | ||||||||
\(766\) | −19.1024 | −0.690197 | ||||||||
\(767\) | −10.5278 | −0.380137 | ||||||||
\(768\) | −1.50743 | −0.0543948 | ||||||||
\(769\) | −19.7506 | −0.712223 | −0.356112 | − | 0.934443i | \(-0.615898\pi\) | ||||
−0.356112 | + | 0.934443i | \(0.615898\pi\) | |||||||
\(770\) | 76.8040 | 2.76782 | ||||||||
\(771\) | 5.30777 | 0.191155 | ||||||||
\(772\) | −10.4373 | −0.375647 | ||||||||
\(773\) | 5.20107 | 0.187070 | 0.0935348 | − | 0.995616i | \(-0.470183\pi\) | ||||
0.0935348 | + | 0.995616i | \(0.470183\pi\) | |||||||
\(774\) | −1.89474 | −0.0681049 | ||||||||
\(775\) | 3.15373 | 0.113285 | ||||||||
\(776\) | 7.57290 | 0.271851 | ||||||||
\(777\) | 18.8396 | 0.675865 | ||||||||
\(778\) | −9.81847 | −0.352009 | ||||||||
\(779\) | −19.7773 | −0.708595 | ||||||||
\(780\) | −5.01622 | −0.179610 | ||||||||
\(781\) | 74.4995 | 2.66580 | ||||||||
\(782\) | −61.2550 | −2.19048 | ||||||||
\(783\) | 21.8917 | 0.782344 | ||||||||
\(784\) | 18.8518 | 0.673280 | ||||||||
\(785\) | −16.0073 | −0.571326 | ||||||||
\(786\) | 2.75897 | 0.0984094 | ||||||||
\(787\) | −22.0891 | −0.787390 | −0.393695 | − | 0.919241i | \(-0.628803\pi\) | ||||
−0.393695 | + | 0.919241i | \(0.628803\pi\) | |||||||
\(788\) | 6.26423 | 0.223154 | ||||||||
\(789\) | 22.3062 | 0.794120 | ||||||||
\(790\) | 32.9175 | 1.17115 | ||||||||
\(791\) | 43.6647 | 1.55254 | ||||||||
\(792\) | −4.46741 | −0.158742 | ||||||||
\(793\) | −0.159872 | −0.00567724 | ||||||||
\(794\) | 8.71093 | 0.309139 | ||||||||
\(795\) | −42.4126 | −1.50422 | ||||||||
\(796\) | 4.27957 | 0.151685 | ||||||||
\(797\) | −13.7660 | −0.487617 | −0.243809 | − | 0.969823i | \(-0.578397\pi\) | ||||
−0.243809 | + | 0.969823i | \(0.578397\pi\) | |||||||
\(798\) | −42.4754 | −1.50361 | ||||||||
\(799\) | 50.9474 | 1.80239 | ||||||||
\(800\) | 1.05341 | 0.0372437 | ||||||||
\(801\) | 12.5729 | 0.444240 | ||||||||
\(802\) | 38.9361 | 1.37488 | ||||||||
\(803\) | −48.3020 | −1.70454 | ||||||||
\(804\) | −4.91994 | −0.173513 | ||||||||
\(805\) | −109.208 | −3.84908 | ||||||||
\(806\) | −4.04915 | −0.142625 | ||||||||
\(807\) | −11.8110 | −0.415768 | ||||||||
\(808\) | −16.5960 | −0.583844 | ||||||||
\(809\) | 9.91473 | 0.348583 | 0.174292 | − | 0.984694i | \(-0.444236\pi\) | ||||
0.174292 | + | 0.984694i | \(0.444236\pi\) | |||||||
\(810\) | 15.4698 | 0.543555 | ||||||||
\(811\) | −25.0294 | −0.878902 | −0.439451 | − | 0.898267i | \(-0.644827\pi\) | ||||
−0.439451 | + | 0.898267i | \(0.644827\pi\) | |||||||
\(812\) | −19.8085 | −0.695143 | ||||||||
\(813\) | −0.394403 | −0.0138323 | ||||||||
\(814\) | 15.0912 | 0.528947 | ||||||||
\(815\) | −16.1470 | −0.565606 | ||||||||
\(816\) | −10.5772 | −0.370276 | ||||||||
\(817\) | −14.4306 | −0.504863 | ||||||||
\(818\) | 19.9201 | 0.696488 | ||||||||
\(819\) | −5.00382 | −0.174848 | ||||||||
\(820\) | −8.78037 | −0.306624 | ||||||||
\(821\) | −14.8924 | −0.519749 | −0.259874 | − | 0.965642i | \(-0.583681\pi\) | ||||
−0.259874 | + | 0.965642i | \(0.583681\pi\) | |||||||
\(822\) | 7.04495 | 0.245721 | ||||||||
\(823\) | 8.84132 | 0.308189 | 0.154094 | − | 0.988056i | \(-0.450754\pi\) | ||||
0.154094 | + | 0.988056i | \(0.450754\pi\) | |||||||
\(824\) | 10.9796 | 0.382494 | ||||||||
\(825\) | −9.74932 | −0.339428 | ||||||||
\(826\) | −39.5772 | −1.37707 | ||||||||
\(827\) | 19.6624 | 0.683728 | 0.341864 | − | 0.939749i | \(-0.388942\pi\) | ||||
0.341864 | + | 0.939749i | \(0.388942\pi\) | |||||||
\(828\) | 6.35224 | 0.220756 | ||||||||
\(829\) | 9.24352 | 0.321041 | 0.160520 | − | 0.987033i | \(-0.448683\pi\) | ||||
0.160520 | + | 0.987033i | \(0.448683\pi\) | |||||||
\(830\) | −29.2566 | −1.01551 | ||||||||
\(831\) | 30.5679 | 1.06039 | ||||||||
\(832\) | −1.35250 | −0.0468896 | ||||||||
\(833\) | 132.278 | 4.58315 | ||||||||
\(834\) | 29.9544 | 1.03724 | ||||||||
\(835\) | 27.2022 | 0.941370 | ||||||||
\(836\) | −34.0245 | −1.17676 | ||||||||
\(837\) | 16.8228 | 0.581481 | ||||||||
\(838\) | 38.0867 | 1.31568 | ||||||||
\(839\) | 47.2432 | 1.63101 | 0.815507 | − | 0.578747i | \(-0.196458\pi\) | ||||
0.815507 | + | 0.578747i | \(0.196458\pi\) | |||||||
\(840\) | −18.8575 | −0.650646 | ||||||||
\(841\) | −13.8221 | −0.476623 | ||||||||
\(842\) | −3.33316 | −0.114868 | ||||||||
\(843\) | −40.8175 | −1.40583 | ||||||||
\(844\) | −9.24903 | −0.318365 | ||||||||
\(845\) | 27.4841 | 0.945483 | ||||||||
\(846\) | −5.28333 | −0.181644 | ||||||||
\(847\) | −135.726 | −4.66362 | ||||||||
\(848\) | −11.4355 | −0.392697 | ||||||||
\(849\) | −17.0810 | −0.586218 | ||||||||
\(850\) | 7.39147 | 0.253525 | ||||||||
\(851\) | −21.4583 | −0.735582 | ||||||||
\(852\) | −18.2917 | −0.626663 | ||||||||
\(853\) | −45.7390 | −1.56607 | −0.783036 | − | 0.621976i | \(-0.786330\pi\) | ||||
−0.783036 | + | 0.621976i | \(0.786330\pi\) | |||||||
\(854\) | −0.601009 | −0.0205661 | ||||||||
\(855\) | −9.92137 | −0.339304 | ||||||||
\(856\) | −6.36100 | −0.217415 | ||||||||
\(857\) | −5.43679 | −0.185717 | −0.0928585 | − | 0.995679i | \(-0.529600\pi\) | ||||
−0.0928585 | + | 0.995679i | \(0.529600\pi\) | |||||||
\(858\) | 12.5174 | 0.427337 | ||||||||
\(859\) | 41.9422 | 1.43105 | 0.715525 | − | 0.698587i | \(-0.246188\pi\) | ||||
0.715525 | + | 0.698587i | \(0.246188\pi\) | |||||||
\(860\) | −6.40665 | −0.218465 | ||||||||
\(861\) | 27.3525 | 0.932171 | ||||||||
\(862\) | 2.96161 | 0.100873 | ||||||||
\(863\) | −14.5329 | −0.494704 | −0.247352 | − | 0.968926i | \(-0.579560\pi\) | ||||
−0.247352 | + | 0.968926i | \(0.579560\pi\) | |||||||
\(864\) | 5.61918 | 0.191168 | ||||||||
\(865\) | 11.5281 | 0.391967 | ||||||||
\(866\) | 31.2183 | 1.06084 | ||||||||
\(867\) | −48.5907 | −1.65023 | ||||||||
\(868\) | −15.2220 | −0.516668 | ||||||||
\(869\) | −82.1419 | −2.78647 | ||||||||
\(870\) | 14.4492 | 0.489875 | ||||||||
\(871\) | −4.41428 | −0.149572 | ||||||||
\(872\) | 10.6018 | 0.359023 | ||||||||
\(873\) | −5.51036 | −0.186498 | ||||||||
\(874\) | 48.3797 | 1.63647 | ||||||||
\(875\) | −49.3705 | −1.66903 | ||||||||
\(876\) | 11.8595 | 0.400695 | ||||||||
\(877\) | −14.2458 | −0.481045 | −0.240523 | − | 0.970644i | \(-0.577319\pi\) | ||||
−0.240523 | + | 0.970644i | \(0.577319\pi\) | |||||||
\(878\) | 22.0650 | 0.744657 | ||||||||
\(879\) | 35.3151 | 1.19115 | ||||||||
\(880\) | −15.1056 | −0.509210 | ||||||||
\(881\) | −22.1206 | −0.745262 | −0.372631 | − | 0.927980i | \(-0.621544\pi\) | ||||
−0.372631 | + | 0.927980i | \(0.621544\pi\) | |||||||
\(882\) | −13.7174 | −0.461889 | ||||||||
\(883\) | 46.1779 | 1.55401 | 0.777005 | − | 0.629495i | \(-0.216738\pi\) | ||||
0.777005 | + | 0.629495i | \(0.216738\pi\) | |||||||
\(884\) | −9.49010 | −0.319187 | ||||||||
\(885\) | 28.8694 | 0.970434 | ||||||||
\(886\) | −32.3480 | −1.08675 | ||||||||
\(887\) | −13.9149 | −0.467216 | −0.233608 | − | 0.972331i | \(-0.575053\pi\) | ||||
−0.233608 | + | 0.972331i | \(0.575053\pi\) | |||||||
\(888\) | −3.70531 | −0.124342 | ||||||||
\(889\) | −48.5270 | −1.62754 | ||||||||
\(890\) | 42.5124 | 1.42502 | ||||||||
\(891\) | −38.6032 | −1.29326 | ||||||||
\(892\) | 18.5235 | 0.620212 | ||||||||
\(893\) | −40.2386 | −1.34653 | ||||||||
\(894\) | 21.9100 | 0.732780 | ||||||||
\(895\) | −23.8010 | −0.795581 | ||||||||
\(896\) | −5.08447 | −0.169860 | ||||||||
\(897\) | −17.7986 | −0.594277 | ||||||||
\(898\) | −19.5080 | −0.650990 | ||||||||
\(899\) | 11.6636 | 0.389002 | ||||||||
\(900\) | −0.766507 | −0.0255502 | ||||||||
\(901\) | −80.2396 | −2.67317 | ||||||||
\(902\) | 21.9104 | 0.729537 | ||||||||
\(903\) | 19.9579 | 0.664158 | ||||||||
\(904\) | −8.58785 | −0.285628 | ||||||||
\(905\) | 31.6584 | 1.05236 | ||||||||
\(906\) | 7.13747 | 0.237126 | ||||||||
\(907\) | 47.8753 | 1.58967 | 0.794837 | − | 0.606823i | \(-0.207556\pi\) | ||||
0.794837 | + | 0.606823i | \(0.207556\pi\) | |||||||
\(908\) | −14.0148 | −0.465096 | ||||||||
\(909\) | 12.0759 | 0.400533 | ||||||||
\(910\) | −16.9194 | −0.560871 | ||||||||
\(911\) | −48.5759 | −1.60939 | −0.804695 | − | 0.593688i | \(-0.797671\pi\) | ||||
−0.804695 | + | 0.593688i | \(0.797671\pi\) | |||||||
\(912\) | 8.35395 | 0.276627 | ||||||||
\(913\) | 73.0065 | 2.41616 | ||||||||
\(914\) | −37.6584 | −1.24563 | ||||||||
\(915\) | 0.438403 | 0.0144932 | ||||||||
\(916\) | −19.3989 | −0.640956 | ||||||||
\(917\) | 9.30583 | 0.307306 | ||||||||
\(918\) | 39.4281 | 1.30132 | ||||||||
\(919\) | −52.4784 | −1.73110 | −0.865551 | − | 0.500821i | \(-0.833031\pi\) | ||||
−0.865551 | + | 0.500821i | \(0.833031\pi\) | |||||||
\(920\) | 21.4788 | 0.708134 | ||||||||
\(921\) | 18.4036 | 0.606419 | ||||||||
\(922\) | 8.88393 | 0.292577 | ||||||||
\(923\) | −16.4117 | −0.540197 | ||||||||
\(924\) | 47.0568 | 1.54805 | ||||||||
\(925\) | 2.58932 | 0.0851362 | ||||||||
\(926\) | −3.30357 | −0.108562 | ||||||||
\(927\) | −7.98924 | −0.262401 | ||||||||
\(928\) | 3.89589 | 0.127889 | ||||||||
\(929\) | −47.5590 | −1.56036 | −0.780181 | − | 0.625554i | \(-0.784873\pi\) | ||||
−0.780181 | + | 0.625554i | \(0.784873\pi\) | |||||||
\(930\) | 11.1036 | 0.364102 | ||||||||
\(931\) | −104.474 | −3.42399 | ||||||||
\(932\) | −16.1292 | −0.528330 | ||||||||
\(933\) | 1.07729 | 0.0352687 | ||||||||
\(934\) | 6.17430 | 0.202029 | ||||||||
\(935\) | −105.991 | −3.46629 | ||||||||
\(936\) | 0.984138 | 0.0321676 | ||||||||
\(937\) | −3.73233 | −0.121930 | −0.0609649 | − | 0.998140i | \(-0.519418\pi\) | ||||
−0.0609649 | + | 0.998140i | \(0.519418\pi\) | |||||||
\(938\) | −16.5946 | −0.541834 | ||||||||
\(939\) | 29.4222 | 0.960158 | ||||||||
\(940\) | −17.8644 | −0.582674 | ||||||||
\(941\) | 25.0433 | 0.816389 | 0.408194 | − | 0.912895i | \(-0.366159\pi\) | ||||
0.408194 | + | 0.912895i | \(0.366159\pi\) | |||||||
\(942\) | −9.80747 | −0.319545 | ||||||||
\(943\) | −31.1546 | −1.01453 | ||||||||
\(944\) | 7.78393 | 0.253345 | ||||||||
\(945\) | 70.2940 | 2.28666 | ||||||||
\(946\) | 15.9871 | 0.519785 | ||||||||
\(947\) | −12.3962 | −0.402821 | −0.201410 | − | 0.979507i | \(-0.564552\pi\) | ||||
−0.201410 | + | 0.979507i | \(0.564552\pi\) | |||||||
\(948\) | 20.1681 | 0.655030 | ||||||||
\(949\) | 10.6406 | 0.345408 | ||||||||
\(950\) | −5.83784 | −0.189404 | ||||||||
\(951\) | 31.3732 | 1.01734 | ||||||||
\(952\) | −35.6762 | −1.15627 | ||||||||
\(953\) | 15.8362 | 0.512986 | 0.256493 | − | 0.966546i | \(-0.417433\pi\) | ||||
0.256493 | + | 0.966546i | \(0.417433\pi\) | |||||||
\(954\) | 8.32097 | 0.269401 | ||||||||
\(955\) | 5.36697 | 0.173671 | ||||||||
\(956\) | −16.9585 | −0.548476 | ||||||||
\(957\) | −36.0564 | −1.16554 | ||||||||
\(958\) | −33.6049 | −1.08573 | ||||||||
\(959\) | 23.7621 | 0.767319 | ||||||||
\(960\) | 3.70884 | 0.119702 | ||||||||
\(961\) | −22.0370 | −0.710872 | ||||||||
\(962\) | −3.32449 | −0.107186 | ||||||||
\(963\) | 4.62853 | 0.149152 | ||||||||
\(964\) | 27.3400 | 0.880564 | ||||||||
\(965\) | 25.6796 | 0.826655 | ||||||||
\(966\) | −66.9103 | −2.15280 | ||||||||
\(967\) | −59.3223 | −1.90768 | −0.953838 | − | 0.300321i | \(-0.902906\pi\) | ||||
−0.953838 | + | 0.300321i | \(0.902906\pi\) | |||||||
\(968\) | 26.6943 | 0.857988 | ||||||||
\(969\) | 58.6172 | 1.88306 | ||||||||
\(970\) | −18.6321 | −0.598242 | ||||||||
\(971\) | 41.5975 | 1.33493 | 0.667464 | − | 0.744642i | \(-0.267380\pi\) | ||||
0.667464 | + | 0.744642i | \(0.267380\pi\) | |||||||
\(972\) | −7.37937 | −0.236693 | ||||||||
\(973\) | 101.034 | 3.23900 | ||||||||
\(974\) | 6.50466 | 0.208423 | ||||||||
\(975\) | 2.14771 | 0.0687816 | ||||||||
\(976\) | 0.118205 | 0.00378365 | ||||||||
\(977\) | −23.5074 | −0.752069 | −0.376034 | − | 0.926606i | \(-0.622713\pi\) | ||||
−0.376034 | + | 0.926606i | \(0.622713\pi\) | |||||||
\(978\) | −9.89306 | −0.316345 | ||||||||
\(979\) | −106.085 | −3.39049 | ||||||||
\(980\) | −46.3825 | −1.48163 | ||||||||
\(981\) | −7.71433 | −0.246300 | ||||||||
\(982\) | 37.9220 | 1.21014 | ||||||||
\(983\) | 49.6256 | 1.58281 | 0.791406 | − | 0.611291i | \(-0.209350\pi\) | ||||
0.791406 | + | 0.611291i | \(0.209350\pi\) | |||||||
\(984\) | −5.37962 | −0.171496 | ||||||||
\(985\) | −15.4123 | −0.491077 | ||||||||
\(986\) | 27.3363 | 0.870564 | ||||||||
\(987\) | 55.6511 | 1.77139 | ||||||||
\(988\) | 7.49535 | 0.238459 | ||||||||
\(989\) | −22.7321 | −0.722840 | ||||||||
\(990\) | 10.9915 | 0.349332 | ||||||||
\(991\) | 61.1688 | 1.94309 | 0.971545 | − | 0.236853i | \(-0.0761161\pi\) | ||||
0.971545 | + | 0.236853i | \(0.0761161\pi\) | |||||||
\(992\) | 2.99382 | 0.0950539 | ||||||||
\(993\) | 36.6561 | 1.16325 | ||||||||
\(994\) | −61.6965 | −1.95690 | ||||||||
\(995\) | −10.5293 | −0.333801 | ||||||||
\(996\) | −17.9251 | −0.567979 | ||||||||
\(997\) | 8.88082 | 0.281258 | 0.140629 | − | 0.990062i | \(-0.455087\pi\) | ||||
0.140629 | + | 0.990062i | \(0.455087\pi\) | |||||||
\(998\) | −7.27918 | −0.230418 | ||||||||
\(999\) | 13.8121 | 0.436995 |
(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 | 8042.2.a.a.1.20 | ✓ | 67 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8042.2.a.a.1.20 | ✓ | 67 | 1.1 | even | 1 | trivial |