Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, 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("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.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: | \(64.0240523407\) |
Analytic rank: | \(0\) |
Dimension: | \(47\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-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 | ||||||||
\(3\) | −2.00763 | −1.15911 | −0.579554 | − | 0.814934i | \(-0.696773\pi\) | ||||
−0.579554 | + | 0.814934i | \(0.696773\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.79399 | −0.802295 | −0.401147 | − | 0.916013i | \(-0.631389\pi\) | ||||
−0.401147 | + | 0.916013i | \(0.631389\pi\) | |||||||
\(6\) | −2.00763 | −0.819614 | ||||||||
\(7\) | −2.43862 | −0.921710 | −0.460855 | − | 0.887475i | \(-0.652457\pi\) | ||||
−0.460855 | + | 0.887475i | \(0.652457\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.03060 | 0.343533 | ||||||||
\(10\) | −1.79399 | −0.567308 | ||||||||
\(11\) | −1.56812 | −0.472807 | −0.236403 | − | 0.971655i | \(-0.575969\pi\) | ||||
−0.236403 | + | 0.971655i | \(0.575969\pi\) | |||||||
\(12\) | −2.00763 | −0.579554 | ||||||||
\(13\) | −4.34066 | −1.20388 | −0.601941 | − | 0.798541i | \(-0.705606\pi\) | ||||
−0.601941 | + | 0.798541i | \(0.705606\pi\) | |||||||
\(14\) | −2.43862 | −0.651747 | ||||||||
\(15\) | 3.60167 | 0.929947 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.98642 | −0.724313 | −0.362157 | − | 0.932117i | \(-0.617959\pi\) | ||||
−0.362157 | + | 0.932117i | \(0.617959\pi\) | |||||||
\(18\) | 1.03060 | 0.242914 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −1.79399 | −0.401147 | ||||||||
\(21\) | 4.89585 | 1.06836 | ||||||||
\(22\) | −1.56812 | −0.334325 | ||||||||
\(23\) | 1.92268 | 0.400906 | 0.200453 | − | 0.979703i | \(-0.435759\pi\) | ||||
0.200453 | + | 0.979703i | \(0.435759\pi\) | |||||||
\(24\) | −2.00763 | −0.409807 | ||||||||
\(25\) | −1.78161 | −0.356323 | ||||||||
\(26\) | −4.34066 | −0.851273 | ||||||||
\(27\) | 3.95384 | 0.760917 | ||||||||
\(28\) | −2.43862 | −0.460855 | ||||||||
\(29\) | 0.562491 | 0.104452 | 0.0522260 | − | 0.998635i | \(-0.483368\pi\) | ||||
0.0522260 | + | 0.998635i | \(0.483368\pi\) | |||||||
\(30\) | 3.60167 | 0.657572 | ||||||||
\(31\) | −4.85429 | −0.871856 | −0.435928 | − | 0.899982i | \(-0.643580\pi\) | ||||
−0.435928 | + | 0.899982i | \(0.643580\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.14822 | 0.548034 | ||||||||
\(34\) | −2.98642 | −0.512167 | ||||||||
\(35\) | 4.37484 | 0.739483 | ||||||||
\(36\) | 1.03060 | 0.171766 | ||||||||
\(37\) | −3.93975 | −0.647691 | −0.323846 | − | 0.946110i | \(-0.604976\pi\) | ||||
−0.323846 | + | 0.946110i | \(0.604976\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 8.71445 | 1.39543 | ||||||||
\(40\) | −1.79399 | −0.283654 | ||||||||
\(41\) | −11.0744 | −1.72954 | −0.864768 | − | 0.502172i | \(-0.832534\pi\) | ||||
−0.864768 | + | 0.502172i | \(0.832534\pi\) | |||||||
\(42\) | 4.89585 | 0.755446 | ||||||||
\(43\) | −8.43678 | −1.28660 | −0.643298 | − | 0.765616i | \(-0.722434\pi\) | ||||
−0.643298 | + | 0.765616i | \(0.722434\pi\) | |||||||
\(44\) | −1.56812 | −0.236403 | ||||||||
\(45\) | −1.84888 | −0.275615 | ||||||||
\(46\) | 1.92268 | 0.283484 | ||||||||
\(47\) | −6.03573 | −0.880401 | −0.440201 | − | 0.897899i | \(-0.645093\pi\) | ||||
−0.440201 | + | 0.897899i | \(0.645093\pi\) | |||||||
\(48\) | −2.00763 | −0.289777 | ||||||||
\(49\) | −1.05316 | −0.150451 | ||||||||
\(50\) | −1.78161 | −0.251958 | ||||||||
\(51\) | 5.99564 | 0.839558 | ||||||||
\(52\) | −4.34066 | −0.601941 | ||||||||
\(53\) | −4.46382 | −0.613153 | −0.306577 | − | 0.951846i | \(-0.599184\pi\) | ||||
−0.306577 | + | 0.951846i | \(0.599184\pi\) | |||||||
\(54\) | 3.95384 | 0.538049 | ||||||||
\(55\) | 2.81319 | 0.379331 | ||||||||
\(56\) | −2.43862 | −0.325874 | ||||||||
\(57\) | 2.00763 | 0.265918 | ||||||||
\(58\) | 0.562491 | 0.0738587 | ||||||||
\(59\) | 14.3798 | 1.87209 | 0.936043 | − | 0.351886i | \(-0.114459\pi\) | ||||
0.936043 | + | 0.351886i | \(0.114459\pi\) | |||||||
\(60\) | 3.60167 | 0.464974 | ||||||||
\(61\) | −12.9806 | −1.66200 | −0.830998 | − | 0.556275i | \(-0.812230\pi\) | ||||
−0.830998 | + | 0.556275i | \(0.812230\pi\) | |||||||
\(62\) | −4.85429 | −0.616495 | ||||||||
\(63\) | −2.51323 | −0.316638 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 7.78708 | 0.965868 | ||||||||
\(66\) | 3.14822 | 0.387519 | ||||||||
\(67\) | −15.9394 | −1.94731 | −0.973656 | − | 0.228020i | \(-0.926775\pi\) | ||||
−0.973656 | + | 0.228020i | \(0.926775\pi\) | |||||||
\(68\) | −2.98642 | −0.362157 | ||||||||
\(69\) | −3.86004 | −0.464694 | ||||||||
\(70\) | 4.37484 | 0.522894 | ||||||||
\(71\) | 8.05400 | 0.955834 | 0.477917 | − | 0.878405i | \(-0.341392\pi\) | ||||
0.477917 | + | 0.878405i | \(0.341392\pi\) | |||||||
\(72\) | 1.03060 | 0.121457 | ||||||||
\(73\) | 2.43690 | 0.285217 | 0.142609 | − | 0.989779i | \(-0.454451\pi\) | ||||
0.142609 | + | 0.989779i | \(0.454451\pi\) | |||||||
\(74\) | −3.93975 | −0.457987 | ||||||||
\(75\) | 3.57683 | 0.413017 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 3.82405 | 0.435791 | ||||||||
\(78\) | 8.71445 | 0.986718 | ||||||||
\(79\) | −2.99978 | −0.337502 | −0.168751 | − | 0.985659i | \(-0.553973\pi\) | ||||
−0.168751 | + | 0.985659i | \(0.553973\pi\) | |||||||
\(80\) | −1.79399 | −0.200574 | ||||||||
\(81\) | −11.0297 | −1.22552 | ||||||||
\(82\) | −11.0744 | −1.22297 | ||||||||
\(83\) | 9.69270 | 1.06391 | 0.531956 | − | 0.846772i | \(-0.321457\pi\) | ||||
0.531956 | + | 0.846772i | \(0.321457\pi\) | |||||||
\(84\) | 4.89585 | 0.534181 | ||||||||
\(85\) | 5.35760 | 0.581113 | ||||||||
\(86\) | −8.43678 | −0.909761 | ||||||||
\(87\) | −1.12928 | −0.121071 | ||||||||
\(88\) | −1.56812 | −0.167162 | ||||||||
\(89\) | −11.2633 | −1.19390 | −0.596951 | − | 0.802277i | \(-0.703621\pi\) | ||||
−0.596951 | + | 0.802277i | \(0.703621\pi\) | |||||||
\(90\) | −1.84888 | −0.194889 | ||||||||
\(91\) | 10.5852 | 1.10963 | ||||||||
\(92\) | 1.92268 | 0.200453 | ||||||||
\(93\) | 9.74564 | 1.01058 | ||||||||
\(94\) | −6.03573 | −0.622538 | ||||||||
\(95\) | 1.79399 | 0.184059 | ||||||||
\(96\) | −2.00763 | −0.204903 | ||||||||
\(97\) | 3.44243 | 0.349526 | 0.174763 | − | 0.984611i | \(-0.444084\pi\) | ||||
0.174763 | + | 0.984611i | \(0.444084\pi\) | |||||||
\(98\) | −1.05316 | −0.106385 | ||||||||
\(99\) | −1.61610 | −0.162425 | ||||||||
\(100\) | −1.78161 | −0.178161 | ||||||||
\(101\) | 15.0221 | 1.49475 | 0.747376 | − | 0.664402i | \(-0.231314\pi\) | ||||
0.747376 | + | 0.664402i | \(0.231314\pi\) | |||||||
\(102\) | 5.99564 | 0.593657 | ||||||||
\(103\) | 1.88560 | 0.185793 | 0.0928967 | − | 0.995676i | \(-0.470387\pi\) | ||||
0.0928967 | + | 0.995676i | \(0.470387\pi\) | |||||||
\(104\) | −4.34066 | −0.425636 | ||||||||
\(105\) | −8.78309 | −0.857141 | ||||||||
\(106\) | −4.46382 | −0.433565 | ||||||||
\(107\) | −15.1780 | −1.46731 | −0.733655 | − | 0.679522i | \(-0.762187\pi\) | ||||
−0.733655 | + | 0.679522i | \(0.762187\pi\) | |||||||
\(108\) | 3.95384 | 0.380458 | ||||||||
\(109\) | −6.18520 | −0.592434 | −0.296217 | − | 0.955121i | \(-0.595725\pi\) | ||||
−0.296217 | + | 0.955121i | \(0.595725\pi\) | |||||||
\(110\) | 2.81319 | 0.268227 | ||||||||
\(111\) | 7.90958 | 0.750744 | ||||||||
\(112\) | −2.43862 | −0.230427 | ||||||||
\(113\) | 6.58029 | 0.619022 | 0.309511 | − | 0.950896i | \(-0.399835\pi\) | ||||
0.309511 | + | 0.950896i | \(0.399835\pi\) | |||||||
\(114\) | 2.00763 | 0.188032 | ||||||||
\(115\) | −3.44926 | −0.321645 | ||||||||
\(116\) | 0.562491 | 0.0522260 | ||||||||
\(117\) | −4.47347 | −0.413573 | ||||||||
\(118\) | 14.3798 | 1.32376 | ||||||||
\(119\) | 7.28273 | 0.667607 | ||||||||
\(120\) | 3.60167 | 0.328786 | ||||||||
\(121\) | −8.54099 | −0.776454 | ||||||||
\(122\) | −12.9806 | −1.17521 | ||||||||
\(123\) | 22.2334 | 2.00472 | ||||||||
\(124\) | −4.85429 | −0.435928 | ||||||||
\(125\) | 12.1661 | 1.08817 | ||||||||
\(126\) | −2.51323 | −0.223897 | ||||||||
\(127\) | 5.64488 | 0.500902 | 0.250451 | − | 0.968129i | \(-0.419421\pi\) | ||||
0.250451 | + | 0.968129i | \(0.419421\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 16.9380 | 1.49131 | ||||||||
\(130\) | 7.78708 | 0.682972 | ||||||||
\(131\) | −22.2737 | −1.94606 | −0.973030 | − | 0.230679i | \(-0.925905\pi\) | ||||
−0.973030 | + | 0.230679i | \(0.925905\pi\) | |||||||
\(132\) | 3.14822 | 0.274017 | ||||||||
\(133\) | 2.43862 | 0.211455 | ||||||||
\(134\) | −15.9394 | −1.37696 | ||||||||
\(135\) | −7.09313 | −0.610480 | ||||||||
\(136\) | −2.98642 | −0.256083 | ||||||||
\(137\) | 16.4778 | 1.40780 | 0.703899 | − | 0.710301i | \(-0.251441\pi\) | ||||
0.703899 | + | 0.710301i | \(0.251441\pi\) | |||||||
\(138\) | −3.86004 | −0.328588 | ||||||||
\(139\) | −11.6853 | −0.991134 | −0.495567 | − | 0.868570i | \(-0.665040\pi\) | ||||
−0.495567 | + | 0.868570i | \(0.665040\pi\) | |||||||
\(140\) | 4.37484 | 0.369742 | ||||||||
\(141\) | 12.1175 | 1.02048 | ||||||||
\(142\) | 8.05400 | 0.675877 | ||||||||
\(143\) | 6.80668 | 0.569203 | ||||||||
\(144\) | 1.03060 | 0.0858832 | ||||||||
\(145\) | −1.00910 | −0.0838013 | ||||||||
\(146\) | 2.43690 | 0.201679 | ||||||||
\(147\) | 2.11435 | 0.174389 | ||||||||
\(148\) | −3.93975 | −0.323846 | ||||||||
\(149\) | 8.74140 | 0.716123 | 0.358062 | − | 0.933698i | \(-0.383438\pi\) | ||||
0.358062 | + | 0.933698i | \(0.383438\pi\) | |||||||
\(150\) | 3.57683 | 0.292047 | ||||||||
\(151\) | 1.07980 | 0.0878725 | 0.0439362 | − | 0.999034i | \(-0.486010\pi\) | ||||
0.0439362 | + | 0.999034i | \(0.486010\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −3.07780 | −0.248825 | ||||||||
\(154\) | 3.82405 | 0.308151 | ||||||||
\(155\) | 8.70853 | 0.699486 | ||||||||
\(156\) | 8.71445 | 0.697715 | ||||||||
\(157\) | −2.01582 | −0.160880 | −0.0804402 | − | 0.996759i | \(-0.525633\pi\) | ||||
−0.0804402 | + | 0.996759i | \(0.525633\pi\) | |||||||
\(158\) | −2.99978 | −0.238650 | ||||||||
\(159\) | 8.96173 | 0.710711 | ||||||||
\(160\) | −1.79399 | −0.141827 | ||||||||
\(161\) | −4.68867 | −0.369519 | ||||||||
\(162\) | −11.0297 | −0.866572 | ||||||||
\(163\) | 21.8879 | 1.71439 | 0.857197 | − | 0.514988i | \(-0.172204\pi\) | ||||
0.857197 | + | 0.514988i | \(0.172204\pi\) | |||||||
\(164\) | −11.0744 | −0.864768 | ||||||||
\(165\) | −5.64786 | −0.439685 | ||||||||
\(166\) | 9.69270 | 0.752300 | ||||||||
\(167\) | −4.09048 | −0.316530 | −0.158265 | − | 0.987397i | \(-0.550590\pi\) | ||||
−0.158265 | + | 0.987397i | \(0.550590\pi\) | |||||||
\(168\) | 4.89585 | 0.377723 | ||||||||
\(169\) | 5.84130 | 0.449331 | ||||||||
\(170\) | 5.35760 | 0.410909 | ||||||||
\(171\) | −1.03060 | −0.0788118 | ||||||||
\(172\) | −8.43678 | −0.643298 | ||||||||
\(173\) | 8.61177 | 0.654741 | 0.327370 | − | 0.944896i | \(-0.393838\pi\) | ||||
0.327370 | + | 0.944896i | \(0.393838\pi\) | |||||||
\(174\) | −1.12928 | −0.0856103 | ||||||||
\(175\) | 4.34467 | 0.328426 | ||||||||
\(176\) | −1.56812 | −0.118202 | ||||||||
\(177\) | −28.8693 | −2.16995 | ||||||||
\(178\) | −11.2633 | −0.844217 | ||||||||
\(179\) | 16.8064 | 1.25617 | 0.628085 | − | 0.778145i | \(-0.283839\pi\) | ||||
0.628085 | + | 0.778145i | \(0.283839\pi\) | |||||||
\(180\) | −1.84888 | −0.137807 | ||||||||
\(181\) | 6.55162 | 0.486978 | 0.243489 | − | 0.969904i | \(-0.421708\pi\) | ||||
0.243489 | + | 0.969904i | \(0.421708\pi\) | |||||||
\(182\) | 10.5852 | 0.784627 | ||||||||
\(183\) | 26.0603 | 1.92643 | ||||||||
\(184\) | 1.92268 | 0.141742 | ||||||||
\(185\) | 7.06786 | 0.519639 | ||||||||
\(186\) | 9.74564 | 0.714585 | ||||||||
\(187\) | 4.68307 | 0.342460 | ||||||||
\(188\) | −6.03573 | −0.440201 | ||||||||
\(189\) | −9.64189 | −0.701345 | ||||||||
\(190\) | 1.79399 | 0.130149 | ||||||||
\(191\) | −22.4079 | −1.62138 | −0.810688 | − | 0.585478i | \(-0.800907\pi\) | ||||
−0.810688 | + | 0.585478i | \(0.800907\pi\) | |||||||
\(192\) | −2.00763 | −0.144889 | ||||||||
\(193\) | 21.0583 | 1.51581 | 0.757904 | − | 0.652366i | \(-0.226224\pi\) | ||||
0.757904 | + | 0.652366i | \(0.226224\pi\) | |||||||
\(194\) | 3.44243 | 0.247152 | ||||||||
\(195\) | −15.6336 | −1.11955 | ||||||||
\(196\) | −1.05316 | −0.0752254 | ||||||||
\(197\) | 17.7540 | 1.26492 | 0.632461 | − | 0.774592i | \(-0.282045\pi\) | ||||
0.632461 | + | 0.774592i | \(0.282045\pi\) | |||||||
\(198\) | −1.61610 | −0.114852 | ||||||||
\(199\) | 10.1854 | 0.722023 | 0.361012 | − | 0.932561i | \(-0.382432\pi\) | ||||
0.361012 | + | 0.932561i | \(0.382432\pi\) | |||||||
\(200\) | −1.78161 | −0.125979 | ||||||||
\(201\) | 32.0006 | 2.25715 | ||||||||
\(202\) | 15.0221 | 1.05695 | ||||||||
\(203\) | −1.37170 | −0.0962744 | ||||||||
\(204\) | 5.99564 | 0.419779 | ||||||||
\(205\) | 19.8674 | 1.38760 | ||||||||
\(206\) | 1.88560 | 0.131376 | ||||||||
\(207\) | 1.98151 | 0.137724 | ||||||||
\(208\) | −4.34066 | −0.300970 | ||||||||
\(209\) | 1.56812 | 0.108469 | ||||||||
\(210\) | −8.78309 | −0.606090 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | −4.46382 | −0.306577 | ||||||||
\(213\) | −16.1695 | −1.10792 | ||||||||
\(214\) | −15.1780 | −1.03754 | ||||||||
\(215\) | 15.1355 | 1.03223 | ||||||||
\(216\) | 3.95384 | 0.269025 | ||||||||
\(217\) | 11.8377 | 0.803598 | ||||||||
\(218\) | −6.18520 | −0.418914 | ||||||||
\(219\) | −4.89240 | −0.330598 | ||||||||
\(220\) | 2.81319 | 0.189665 | ||||||||
\(221\) | 12.9630 | 0.871987 | ||||||||
\(222\) | 7.90958 | 0.530856 | ||||||||
\(223\) | −18.5493 | −1.24215 | −0.621076 | − | 0.783750i | \(-0.713304\pi\) | ||||
−0.621076 | + | 0.783750i | \(0.713304\pi\) | |||||||
\(224\) | −2.43862 | −0.162937 | ||||||||
\(225\) | −1.83613 | −0.122409 | ||||||||
\(226\) | 6.58029 | 0.437715 | ||||||||
\(227\) | −17.7495 | −1.17807 | −0.589036 | − | 0.808107i | \(-0.700493\pi\) | ||||
−0.589036 | + | 0.808107i | \(0.700493\pi\) | |||||||
\(228\) | 2.00763 | 0.132959 | ||||||||
\(229\) | −5.45582 | −0.360531 | −0.180265 | − | 0.983618i | \(-0.557696\pi\) | ||||
−0.180265 | + | 0.983618i | \(0.557696\pi\) | |||||||
\(230\) | −3.44926 | −0.227437 | ||||||||
\(231\) | −7.67729 | −0.505129 | ||||||||
\(232\) | 0.562491 | 0.0369294 | ||||||||
\(233\) | 7.59030 | 0.497257 | 0.248629 | − | 0.968599i | \(-0.420020\pi\) | ||||
0.248629 | + | 0.968599i | \(0.420020\pi\) | |||||||
\(234\) | −4.47347 | −0.292440 | ||||||||
\(235\) | 10.8280 | 0.706341 | ||||||||
\(236\) | 14.3798 | 0.936043 | ||||||||
\(237\) | 6.02247 | 0.391201 | ||||||||
\(238\) | 7.28273 | 0.472069 | ||||||||
\(239\) | −21.3228 | −1.37926 | −0.689630 | − | 0.724162i | \(-0.742227\pi\) | ||||
−0.689630 | + | 0.724162i | \(0.742227\pi\) | |||||||
\(240\) | 3.60167 | 0.232487 | ||||||||
\(241\) | 0.738320 | 0.0475594 | 0.0237797 | − | 0.999717i | \(-0.492430\pi\) | ||||
0.0237797 | + | 0.999717i | \(0.492430\pi\) | |||||||
\(242\) | −8.54099 | −0.549036 | ||||||||
\(243\) | 10.2820 | 0.659592 | ||||||||
\(244\) | −12.9806 | −0.830998 | ||||||||
\(245\) | 1.88935 | 0.120706 | ||||||||
\(246\) | 22.2334 | 1.41755 | ||||||||
\(247\) | 4.34066 | 0.276189 | ||||||||
\(248\) | −4.85429 | −0.308248 | ||||||||
\(249\) | −19.4594 | −1.23319 | ||||||||
\(250\) | 12.1661 | 0.769453 | ||||||||
\(251\) | −27.1705 | −1.71499 | −0.857494 | − | 0.514494i | \(-0.827980\pi\) | ||||
−0.857494 | + | 0.514494i | \(0.827980\pi\) | |||||||
\(252\) | −2.51323 | −0.158319 | ||||||||
\(253\) | −3.01500 | −0.189551 | ||||||||
\(254\) | 5.64488 | 0.354191 | ||||||||
\(255\) | −10.7561 | −0.673573 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.47591 | 0.216821 | 0.108411 | − | 0.994106i | \(-0.465424\pi\) | ||||
0.108411 | + | 0.994106i | \(0.465424\pi\) | |||||||
\(258\) | 16.9380 | 1.05451 | ||||||||
\(259\) | 9.60754 | 0.596983 | ||||||||
\(260\) | 7.78708 | 0.482934 | ||||||||
\(261\) | 0.579702 | 0.0358827 | ||||||||
\(262\) | −22.2737 | −1.37607 | ||||||||
\(263\) | 15.5129 | 0.956569 | 0.478285 | − | 0.878205i | \(-0.341259\pi\) | ||||
0.478285 | + | 0.878205i | \(0.341259\pi\) | |||||||
\(264\) | 3.14822 | 0.193759 | ||||||||
\(265\) | 8.00804 | 0.491930 | ||||||||
\(266\) | 2.43862 | 0.149521 | ||||||||
\(267\) | 22.6125 | 1.38386 | ||||||||
\(268\) | −15.9394 | −0.973656 | ||||||||
\(269\) | −6.93004 | −0.422532 | −0.211266 | − | 0.977429i | \(-0.567759\pi\) | ||||
−0.211266 | + | 0.977429i | \(0.567759\pi\) | |||||||
\(270\) | −7.09313 | −0.431674 | ||||||||
\(271\) | 14.8948 | 0.904793 | 0.452397 | − | 0.891817i | \(-0.350569\pi\) | ||||
0.452397 | + | 0.891817i | \(0.350569\pi\) | |||||||
\(272\) | −2.98642 | −0.181078 | ||||||||
\(273\) | −21.2512 | −1.28618 | ||||||||
\(274\) | 16.4778 | 0.995463 | ||||||||
\(275\) | 2.79379 | 0.168472 | ||||||||
\(276\) | −3.86004 | −0.232347 | ||||||||
\(277\) | 21.9705 | 1.32008 | 0.660040 | − | 0.751230i | \(-0.270539\pi\) | ||||
0.660040 | + | 0.751230i | \(0.270539\pi\) | |||||||
\(278\) | −11.6853 | −0.700838 | ||||||||
\(279\) | −5.00282 | −0.299511 | ||||||||
\(280\) | 4.37484 | 0.261447 | ||||||||
\(281\) | 4.45825 | 0.265957 | 0.132979 | − | 0.991119i | \(-0.457546\pi\) | ||||
0.132979 | + | 0.991119i | \(0.457546\pi\) | |||||||
\(282\) | 12.1175 | 0.721589 | ||||||||
\(283\) | −5.52346 | −0.328335 | −0.164168 | − | 0.986432i | \(-0.552494\pi\) | ||||
−0.164168 | + | 0.986432i | \(0.552494\pi\) | |||||||
\(284\) | 8.05400 | 0.477917 | ||||||||
\(285\) | −3.60167 | −0.213344 | ||||||||
\(286\) | 6.80668 | 0.402488 | ||||||||
\(287\) | 27.0063 | 1.59413 | ||||||||
\(288\) | 1.03060 | 0.0607286 | ||||||||
\(289\) | −8.08130 | −0.475370 | ||||||||
\(290\) | −1.00910 | −0.0592565 | ||||||||
\(291\) | −6.91115 | −0.405139 | ||||||||
\(292\) | 2.43690 | 0.142609 | ||||||||
\(293\) | −19.8393 | −1.15903 | −0.579513 | − | 0.814963i | \(-0.696757\pi\) | ||||
−0.579513 | + | 0.814963i | \(0.696757\pi\) | |||||||
\(294\) | 2.11435 | 0.123312 | ||||||||
\(295\) | −25.7971 | −1.50197 | ||||||||
\(296\) | −3.93975 | −0.228993 | ||||||||
\(297\) | −6.20011 | −0.359767 | ||||||||
\(298\) | 8.74140 | 0.506376 | ||||||||
\(299\) | −8.34569 | −0.482644 | ||||||||
\(300\) | 3.57683 | 0.206508 | ||||||||
\(301\) | 20.5741 | 1.18587 | ||||||||
\(302\) | 1.07980 | 0.0621352 | ||||||||
\(303\) | −30.1588 | −1.73258 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 23.2870 | 1.33341 | ||||||||
\(306\) | −3.07780 | −0.175946 | ||||||||
\(307\) | 4.65577 | 0.265719 | 0.132859 | − | 0.991135i | \(-0.457584\pi\) | ||||
0.132859 | + | 0.991135i | \(0.457584\pi\) | |||||||
\(308\) | 3.82405 | 0.217895 | ||||||||
\(309\) | −3.78559 | −0.215355 | ||||||||
\(310\) | 8.70853 | 0.494611 | ||||||||
\(311\) | −24.6145 | −1.39576 | −0.697879 | − | 0.716215i | \(-0.745873\pi\) | ||||
−0.697879 | + | 0.716215i | \(0.745873\pi\) | |||||||
\(312\) | 8.71445 | 0.493359 | ||||||||
\(313\) | 3.34650 | 0.189155 | 0.0945777 | − | 0.995517i | \(-0.469850\pi\) | ||||
0.0945777 | + | 0.995517i | \(0.469850\pi\) | |||||||
\(314\) | −2.01582 | −0.113760 | ||||||||
\(315\) | 4.50870 | 0.254037 | ||||||||
\(316\) | −2.99978 | −0.168751 | ||||||||
\(317\) | 5.15681 | 0.289636 | 0.144818 | − | 0.989458i | \(-0.453740\pi\) | ||||
0.144818 | + | 0.989458i | \(0.453740\pi\) | |||||||
\(318\) | 8.96173 | 0.502549 | ||||||||
\(319\) | −0.882055 | −0.0493856 | ||||||||
\(320\) | −1.79399 | −0.100287 | ||||||||
\(321\) | 30.4718 | 1.70077 | ||||||||
\(322\) | −4.68867 | −0.261290 | ||||||||
\(323\) | 2.98642 | 0.166169 | ||||||||
\(324\) | −11.0297 | −0.612759 | ||||||||
\(325\) | 7.73337 | 0.428970 | ||||||||
\(326\) | 21.8879 | 1.21226 | ||||||||
\(327\) | 12.4176 | 0.686696 | ||||||||
\(328\) | −11.0744 | −0.611483 | ||||||||
\(329\) | 14.7188 | 0.811474 | ||||||||
\(330\) | −5.64786 | −0.310904 | ||||||||
\(331\) | −25.8264 | −1.41955 | −0.709774 | − | 0.704430i | \(-0.751203\pi\) | ||||
−0.709774 | + | 0.704430i | \(0.751203\pi\) | |||||||
\(332\) | 9.69270 | 0.531956 | ||||||||
\(333\) | −4.06030 | −0.222503 | ||||||||
\(334\) | −4.09048 | −0.223821 | ||||||||
\(335\) | 28.5951 | 1.56232 | ||||||||
\(336\) | 4.89585 | 0.267090 | ||||||||
\(337\) | 19.1488 | 1.04310 | 0.521550 | − | 0.853221i | \(-0.325354\pi\) | ||||
0.521550 | + | 0.853221i | \(0.325354\pi\) | |||||||
\(338\) | 5.84130 | 0.317725 | ||||||||
\(339\) | −13.2108 | −0.717514 | ||||||||
\(340\) | 5.35760 | 0.290556 | ||||||||
\(341\) | 7.61212 | 0.412219 | ||||||||
\(342\) | −1.03060 | −0.0557284 | ||||||||
\(343\) | 19.6385 | 1.06038 | ||||||||
\(344\) | −8.43678 | −0.454881 | ||||||||
\(345\) | 6.92485 | 0.372822 | ||||||||
\(346\) | 8.61177 | 0.462972 | ||||||||
\(347\) | 17.9943 | 0.965984 | 0.482992 | − | 0.875625i | \(-0.339550\pi\) | ||||
0.482992 | + | 0.875625i | \(0.339550\pi\) | |||||||
\(348\) | −1.12928 | −0.0605356 | ||||||||
\(349\) | −13.2057 | −0.706884 | −0.353442 | − | 0.935456i | \(-0.614989\pi\) | ||||
−0.353442 | + | 0.935456i | \(0.614989\pi\) | |||||||
\(350\) | 4.34467 | 0.232232 | ||||||||
\(351\) | −17.1623 | −0.916054 | ||||||||
\(352\) | −1.56812 | −0.0835812 | ||||||||
\(353\) | −30.3089 | −1.61318 | −0.806591 | − | 0.591110i | \(-0.798690\pi\) | ||||
−0.806591 | + | 0.591110i | \(0.798690\pi\) | |||||||
\(354\) | −28.8693 | −1.53439 | ||||||||
\(355\) | −14.4488 | −0.766861 | ||||||||
\(356\) | −11.2633 | −0.596951 | ||||||||
\(357\) | −14.6211 | −0.773829 | ||||||||
\(358\) | 16.8064 | 0.888246 | ||||||||
\(359\) | 21.6062 | 1.14033 | 0.570165 | − | 0.821530i | \(-0.306879\pi\) | ||||
0.570165 | + | 0.821530i | \(0.306879\pi\) | |||||||
\(360\) | −1.84888 | −0.0974445 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 6.55162 | 0.344346 | ||||||||
\(363\) | 17.1472 | 0.899994 | ||||||||
\(364\) | 10.5852 | 0.554815 | ||||||||
\(365\) | −4.37176 | −0.228829 | ||||||||
\(366\) | 26.0603 | 1.36219 | ||||||||
\(367\) | −9.98272 | −0.521094 | −0.260547 | − | 0.965461i | \(-0.583903\pi\) | ||||
−0.260547 | + | 0.965461i | \(0.583903\pi\) | |||||||
\(368\) | 1.92268 | 0.100227 | ||||||||
\(369\) | −11.4133 | −0.594152 | ||||||||
\(370\) | 7.06786 | 0.367441 | ||||||||
\(371\) | 10.8855 | 0.565149 | ||||||||
\(372\) | 9.74564 | 0.505288 | ||||||||
\(373\) | −27.0164 | −1.39885 | −0.699427 | − | 0.714704i | \(-0.746561\pi\) | ||||
−0.699427 | + | 0.714704i | \(0.746561\pi\) | |||||||
\(374\) | 4.68307 | 0.242156 | ||||||||
\(375\) | −24.4251 | −1.26131 | ||||||||
\(376\) | −6.03573 | −0.311269 | ||||||||
\(377\) | −2.44158 | −0.125748 | ||||||||
\(378\) | −9.64189 | −0.495926 | ||||||||
\(379\) | 0.972204 | 0.0499388 | 0.0249694 | − | 0.999688i | \(-0.492051\pi\) | ||||
0.0249694 | + | 0.999688i | \(0.492051\pi\) | |||||||
\(380\) | 1.79399 | 0.0920295 | ||||||||
\(381\) | −11.3329 | −0.580600 | ||||||||
\(382\) | −22.4079 | −1.14649 | ||||||||
\(383\) | −18.3603 | −0.938167 | −0.469084 | − | 0.883154i | \(-0.655416\pi\) | ||||
−0.469084 | + | 0.883154i | \(0.655416\pi\) | |||||||
\(384\) | −2.00763 | −0.102452 | ||||||||
\(385\) | −6.86029 | −0.349633 | ||||||||
\(386\) | 21.0583 | 1.07184 | ||||||||
\(387\) | −8.69493 | −0.441988 | ||||||||
\(388\) | 3.44243 | 0.174763 | ||||||||
\(389\) | 17.7954 | 0.902264 | 0.451132 | − | 0.892457i | \(-0.351020\pi\) | ||||
0.451132 | + | 0.892457i | \(0.351020\pi\) | |||||||
\(390\) | −15.6336 | −0.791639 | ||||||||
\(391\) | −5.74193 | −0.290382 | ||||||||
\(392\) | −1.05316 | −0.0531924 | ||||||||
\(393\) | 44.7174 | 2.25569 | ||||||||
\(394\) | 17.7540 | 0.894435 | ||||||||
\(395\) | 5.38157 | 0.270776 | ||||||||
\(396\) | −1.61610 | −0.0812123 | ||||||||
\(397\) | 34.8852 | 1.75084 | 0.875420 | − | 0.483364i | \(-0.160585\pi\) | ||||
0.875420 | + | 0.483364i | \(0.160585\pi\) | |||||||
\(398\) | 10.1854 | 0.510547 | ||||||||
\(399\) | −4.89585 | −0.245099 | ||||||||
\(400\) | −1.78161 | −0.0890807 | ||||||||
\(401\) | 11.6845 | 0.583494 | 0.291747 | − | 0.956496i | \(-0.405764\pi\) | ||||
0.291747 | + | 0.956496i | \(0.405764\pi\) | |||||||
\(402\) | 32.0006 | 1.59604 | ||||||||
\(403\) | 21.0708 | 1.04961 | ||||||||
\(404\) | 15.0221 | 0.747376 | ||||||||
\(405\) | 19.7871 | 0.983227 | ||||||||
\(406\) | −1.37170 | −0.0680763 | ||||||||
\(407\) | 6.17801 | 0.306233 | ||||||||
\(408\) | 5.99564 | 0.296828 | ||||||||
\(409\) | −16.5589 | −0.818783 | −0.409391 | − | 0.912359i | \(-0.634259\pi\) | ||||
−0.409391 | + | 0.912359i | \(0.634259\pi\) | |||||||
\(410\) | 19.8674 | 0.981180 | ||||||||
\(411\) | −33.0815 | −1.63179 | ||||||||
\(412\) | 1.88560 | 0.0928967 | ||||||||
\(413\) | −35.0667 | −1.72552 | ||||||||
\(414\) | 1.98151 | 0.0973859 | ||||||||
\(415\) | −17.3886 | −0.853571 | ||||||||
\(416\) | −4.34066 | −0.212818 | ||||||||
\(417\) | 23.4598 | 1.14883 | ||||||||
\(418\) | 1.56812 | 0.0766994 | ||||||||
\(419\) | 7.52769 | 0.367751 | 0.183876 | − | 0.982949i | \(-0.441136\pi\) | ||||
0.183876 | + | 0.982949i | \(0.441136\pi\) | |||||||
\(420\) | −8.78309 | −0.428571 | ||||||||
\(421\) | −3.34379 | −0.162967 | −0.0814833 | − | 0.996675i | \(-0.525966\pi\) | ||||
−0.0814833 | + | 0.996675i | \(0.525966\pi\) | |||||||
\(422\) | −1.00000 | −0.0486792 | ||||||||
\(423\) | −6.22041 | −0.302447 | ||||||||
\(424\) | −4.46382 | −0.216782 | ||||||||
\(425\) | 5.32065 | 0.258089 | ||||||||
\(426\) | −16.1695 | −0.783414 | ||||||||
\(427\) | 31.6547 | 1.53188 | ||||||||
\(428\) | −15.1780 | −0.733655 | ||||||||
\(429\) | −13.6653 | −0.659769 | ||||||||
\(430\) | 15.1355 | 0.729897 | ||||||||
\(431\) | −36.7080 | −1.76816 | −0.884080 | − | 0.467335i | \(-0.845214\pi\) | ||||
−0.884080 | + | 0.467335i | \(0.845214\pi\) | |||||||
\(432\) | 3.95384 | 0.190229 | ||||||||
\(433\) | 35.4441 | 1.70333 | 0.851667 | − | 0.524084i | \(-0.175592\pi\) | ||||
0.851667 | + | 0.524084i | \(0.175592\pi\) | |||||||
\(434\) | 11.8377 | 0.568230 | ||||||||
\(435\) | 2.02591 | 0.0971348 | ||||||||
\(436\) | −6.18520 | −0.296217 | ||||||||
\(437\) | −1.92268 | −0.0919742 | ||||||||
\(438\) | −4.89240 | −0.233768 | ||||||||
\(439\) | 25.0169 | 1.19399 | 0.596995 | − | 0.802245i | \(-0.296361\pi\) | ||||
0.596995 | + | 0.802245i | \(0.296361\pi\) | |||||||
\(440\) | 2.81319 | 0.134114 | ||||||||
\(441\) | −1.08538 | −0.0516848 | ||||||||
\(442\) | 12.9630 | 0.616588 | ||||||||
\(443\) | 20.7863 | 0.987587 | 0.493794 | − | 0.869579i | \(-0.335610\pi\) | ||||
0.493794 | + | 0.869579i | \(0.335610\pi\) | |||||||
\(444\) | 7.90958 | 0.375372 | ||||||||
\(445\) | 20.2061 | 0.957862 | ||||||||
\(446\) | −18.5493 | −0.878335 | ||||||||
\(447\) | −17.5495 | −0.830065 | ||||||||
\(448\) | −2.43862 | −0.115214 | ||||||||
\(449\) | −2.12952 | −0.100498 | −0.0502492 | − | 0.998737i | \(-0.516002\pi\) | ||||
−0.0502492 | + | 0.998737i | \(0.516002\pi\) | |||||||
\(450\) | −1.83613 | −0.0865559 | ||||||||
\(451\) | 17.3661 | 0.817736 | ||||||||
\(452\) | 6.58029 | 0.309511 | ||||||||
\(453\) | −2.16783 | −0.101854 | ||||||||
\(454\) | −17.7495 | −0.833023 | ||||||||
\(455\) | −18.9897 | −0.890250 | ||||||||
\(456\) | 2.00763 | 0.0940161 | ||||||||
\(457\) | 8.37829 | 0.391920 | 0.195960 | − | 0.980612i | \(-0.437218\pi\) | ||||
0.195960 | + | 0.980612i | \(0.437218\pi\) | |||||||
\(458\) | −5.45582 | −0.254934 | ||||||||
\(459\) | −11.8078 | −0.551142 | ||||||||
\(460\) | −3.44926 | −0.160823 | ||||||||
\(461\) | −26.4321 | −1.23106 | −0.615532 | − | 0.788112i | \(-0.711059\pi\) | ||||
−0.615532 | + | 0.788112i | \(0.711059\pi\) | |||||||
\(462\) | −7.67729 | −0.357180 | ||||||||
\(463\) | 7.76656 | 0.360943 | 0.180471 | − | 0.983580i | \(-0.442238\pi\) | ||||
0.180471 | + | 0.983580i | \(0.442238\pi\) | |||||||
\(464\) | 0.562491 | 0.0261130 | ||||||||
\(465\) | −17.4835 | −0.810780 | ||||||||
\(466\) | 7.59030 | 0.351614 | ||||||||
\(467\) | 8.58514 | 0.397273 | 0.198636 | − | 0.980073i | \(-0.436349\pi\) | ||||
0.198636 | + | 0.980073i | \(0.436349\pi\) | |||||||
\(468\) | −4.47347 | −0.206786 | ||||||||
\(469\) | 38.8702 | 1.79486 | ||||||||
\(470\) | 10.8280 | 0.499459 | ||||||||
\(471\) | 4.04704 | 0.186478 | ||||||||
\(472\) | 14.3798 | 0.661882 | ||||||||
\(473\) | 13.2299 | 0.608312 | ||||||||
\(474\) | 6.02247 | 0.276621 | ||||||||
\(475\) | 1.78161 | 0.0817460 | ||||||||
\(476\) | 7.28273 | 0.333803 | ||||||||
\(477\) | −4.60041 | −0.210638 | ||||||||
\(478\) | −21.3228 | −0.975284 | ||||||||
\(479\) | −26.8403 | −1.22636 | −0.613182 | − | 0.789942i | \(-0.710111\pi\) | ||||
−0.613182 | + | 0.789942i | \(0.710111\pi\) | |||||||
\(480\) | 3.60167 | 0.164393 | ||||||||
\(481\) | 17.1011 | 0.779743 | ||||||||
\(482\) | 0.738320 | 0.0336296 | ||||||||
\(483\) | 9.41315 | 0.428313 | ||||||||
\(484\) | −8.54099 | −0.388227 | ||||||||
\(485\) | −6.17567 | −0.280423 | ||||||||
\(486\) | 10.2820 | 0.466402 | ||||||||
\(487\) | −2.04309 | −0.0925810 | −0.0462905 | − | 0.998928i | \(-0.514740\pi\) | ||||
−0.0462905 | + | 0.998928i | \(0.514740\pi\) | |||||||
\(488\) | −12.9806 | −0.587605 | ||||||||
\(489\) | −43.9430 | −1.98717 | ||||||||
\(490\) | 1.88935 | 0.0853520 | ||||||||
\(491\) | 27.0638 | 1.22137 | 0.610685 | − | 0.791873i | \(-0.290894\pi\) | ||||
0.610685 | + | 0.791873i | \(0.290894\pi\) | |||||||
\(492\) | 22.2334 | 1.00236 | ||||||||
\(493\) | −1.67983 | −0.0756560 | ||||||||
\(494\) | 4.34066 | 0.195295 | ||||||||
\(495\) | 2.89927 | 0.130312 | ||||||||
\(496\) | −4.85429 | −0.217964 | ||||||||
\(497\) | −19.6406 | −0.881001 | ||||||||
\(498\) | −19.4594 | −0.871997 | ||||||||
\(499\) | −15.2351 | −0.682015 | −0.341008 | − | 0.940061i | \(-0.610768\pi\) | ||||
−0.341008 | + | 0.940061i | \(0.610768\pi\) | |||||||
\(500\) | 12.1661 | 0.544085 | ||||||||
\(501\) | 8.21218 | 0.366893 | ||||||||
\(502\) | −27.1705 | −1.21268 | ||||||||
\(503\) | −39.1190 | −1.74423 | −0.872115 | − | 0.489302i | \(-0.837252\pi\) | ||||
−0.872115 | + | 0.489302i | \(0.837252\pi\) | |||||||
\(504\) | −2.51323 | −0.111948 | ||||||||
\(505\) | −26.9494 | −1.19923 | ||||||||
\(506\) | −3.01500 | −0.134033 | ||||||||
\(507\) | −11.7272 | −0.520823 | ||||||||
\(508\) | 5.64488 | 0.250451 | ||||||||
\(509\) | 19.3701 | 0.858564 | 0.429282 | − | 0.903171i | \(-0.358767\pi\) | ||||
0.429282 | + | 0.903171i | \(0.358767\pi\) | |||||||
\(510\) | −10.7561 | −0.476288 | ||||||||
\(511\) | −5.94266 | −0.262888 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −3.95384 | −0.174566 | ||||||||
\(514\) | 3.47591 | 0.153316 | ||||||||
\(515\) | −3.38274 | −0.149061 | ||||||||
\(516\) | 16.9380 | 0.745653 | ||||||||
\(517\) | 9.46476 | 0.416260 | ||||||||
\(518\) | 9.60754 | 0.422131 | ||||||||
\(519\) | −17.2893 | −0.758916 | ||||||||
\(520\) | 7.78708 | 0.341486 | ||||||||
\(521\) | 11.8930 | 0.521042 | 0.260521 | − | 0.965468i | \(-0.416106\pi\) | ||||
0.260521 | + | 0.965468i | \(0.416106\pi\) | |||||||
\(522\) | 0.579702 | 0.0253729 | ||||||||
\(523\) | 14.1575 | 0.619066 | 0.309533 | − | 0.950889i | \(-0.399827\pi\) | ||||
0.309533 | + | 0.950889i | \(0.399827\pi\) | |||||||
\(524\) | −22.2737 | −0.973030 | ||||||||
\(525\) | −8.72251 | −0.380682 | ||||||||
\(526\) | 15.5129 | 0.676397 | ||||||||
\(527\) | 14.4969 | 0.631497 | ||||||||
\(528\) | 3.14822 | 0.137009 | ||||||||
\(529\) | −19.3033 | −0.839274 | ||||||||
\(530\) | 8.00804 | 0.347847 | ||||||||
\(531\) | 14.8198 | 0.643123 | ||||||||
\(532\) | 2.43862 | 0.105727 | ||||||||
\(533\) | 48.0703 | 2.08216 | ||||||||
\(534\) | 22.6125 | 0.978539 | ||||||||
\(535\) | 27.2291 | 1.17721 | ||||||||
\(536\) | −15.9394 | −0.688479 | ||||||||
\(537\) | −33.7411 | −1.45604 | ||||||||
\(538\) | −6.93004 | −0.298775 | ||||||||
\(539\) | 1.65148 | 0.0711342 | ||||||||
\(540\) | −7.09313 | −0.305240 | ||||||||
\(541\) | −0.952493 | −0.0409509 | −0.0204754 | − | 0.999790i | \(-0.506518\pi\) | ||||
−0.0204754 | + | 0.999790i | \(0.506518\pi\) | |||||||
\(542\) | 14.8948 | 0.639786 | ||||||||
\(543\) | −13.1533 | −0.564461 | ||||||||
\(544\) | −2.98642 | −0.128042 | ||||||||
\(545\) | 11.0962 | 0.475307 | ||||||||
\(546\) | −21.2512 | −0.909467 | ||||||||
\(547\) | 4.26440 | 0.182333 | 0.0911664 | − | 0.995836i | \(-0.470941\pi\) | ||||
0.0911664 | + | 0.995836i | \(0.470941\pi\) | |||||||
\(548\) | 16.4778 | 0.703899 | ||||||||
\(549\) | −13.3778 | −0.570950 | ||||||||
\(550\) | 2.79379 | 0.119128 | ||||||||
\(551\) | −0.562491 | −0.0239629 | ||||||||
\(552\) | −3.86004 | −0.164294 | ||||||||
\(553\) | 7.31531 | 0.311079 | ||||||||
\(554\) | 21.9705 | 0.933438 | ||||||||
\(555\) | −14.1897 | −0.602318 | ||||||||
\(556\) | −11.6853 | −0.495567 | ||||||||
\(557\) | 43.2644 | 1.83317 | 0.916586 | − | 0.399837i | \(-0.130933\pi\) | ||||
0.916586 | + | 0.399837i | \(0.130933\pi\) | |||||||
\(558\) | −5.00282 | −0.211786 | ||||||||
\(559\) | 36.6212 | 1.54891 | ||||||||
\(560\) | 4.37484 | 0.184871 | ||||||||
\(561\) | −9.40190 | −0.396949 | ||||||||
\(562\) | 4.45825 | 0.188060 | ||||||||
\(563\) | −5.26828 | −0.222032 | −0.111016 | − | 0.993819i | \(-0.535410\pi\) | ||||
−0.111016 | + | 0.993819i | \(0.535410\pi\) | |||||||
\(564\) | 12.1175 | 0.510240 | ||||||||
\(565\) | −11.8050 | −0.496638 | ||||||||
\(566\) | −5.52346 | −0.232168 | ||||||||
\(567\) | 26.8971 | 1.12957 | ||||||||
\(568\) | 8.05400 | 0.337938 | ||||||||
\(569\) | −25.8701 | −1.08453 | −0.542265 | − | 0.840207i | \(-0.682433\pi\) | ||||
−0.542265 | + | 0.840207i | \(0.682433\pi\) | |||||||
\(570\) | −3.60167 | −0.150857 | ||||||||
\(571\) | 22.2409 | 0.930753 | 0.465377 | − | 0.885113i | \(-0.345919\pi\) | ||||
0.465377 | + | 0.885113i | \(0.345919\pi\) | |||||||
\(572\) | 6.80668 | 0.284602 | ||||||||
\(573\) | 44.9868 | 1.87935 | ||||||||
\(574\) | 27.0063 | 1.12722 | ||||||||
\(575\) | −3.42547 | −0.142852 | ||||||||
\(576\) | 1.03060 | 0.0429416 | ||||||||
\(577\) | −13.5623 | −0.564606 | −0.282303 | − | 0.959325i | \(-0.591098\pi\) | ||||
−0.282303 | + | 0.959325i | \(0.591098\pi\) | |||||||
\(578\) | −8.08130 | −0.336138 | ||||||||
\(579\) | −42.2773 | −1.75699 | ||||||||
\(580\) | −1.00910 | −0.0419007 | ||||||||
\(581\) | −23.6368 | −0.980618 | ||||||||
\(582\) | −6.91115 | −0.286476 | ||||||||
\(583\) | 6.99982 | 0.289903 | ||||||||
\(584\) | 2.43690 | 0.100840 | ||||||||
\(585\) | 8.02535 | 0.331807 | ||||||||
\(586\) | −19.8393 | −0.819555 | ||||||||
\(587\) | −23.9666 | −0.989208 | −0.494604 | − | 0.869118i | \(-0.664687\pi\) | ||||
−0.494604 | + | 0.869118i | \(0.664687\pi\) | |||||||
\(588\) | 2.11435 | 0.0871945 | ||||||||
\(589\) | 4.85429 | 0.200017 | ||||||||
\(590\) | −25.7971 | −1.06205 | ||||||||
\(591\) | −35.6436 | −1.46618 | ||||||||
\(592\) | −3.93975 | −0.161923 | ||||||||
\(593\) | 45.1261 | 1.85311 | 0.926553 | − | 0.376164i | \(-0.122757\pi\) | ||||
0.926553 | + | 0.376164i | \(0.122757\pi\) | |||||||
\(594\) | −6.20011 | −0.254393 | ||||||||
\(595\) | −13.0651 | −0.535617 | ||||||||
\(596\) | 8.74140 | 0.358062 | ||||||||
\(597\) | −20.4485 | −0.836903 | ||||||||
\(598\) | −8.34569 | −0.341281 | ||||||||
\(599\) | 42.9732 | 1.75584 | 0.877918 | − | 0.478810i | \(-0.158932\pi\) | ||||
0.877918 | + | 0.478810i | \(0.158932\pi\) | |||||||
\(600\) | 3.57683 | 0.146023 | ||||||||
\(601\) | −17.6388 | −0.719501 | −0.359751 | − | 0.933049i | \(-0.617138\pi\) | ||||
−0.359751 | + | 0.933049i | \(0.617138\pi\) | |||||||
\(602\) | 20.5741 | 0.838536 | ||||||||
\(603\) | −16.4272 | −0.668966 | ||||||||
\(604\) | 1.07980 | 0.0439362 | ||||||||
\(605\) | 15.3224 | 0.622945 | ||||||||
\(606\) | −30.1588 | −1.22512 | ||||||||
\(607\) | −24.9758 | −1.01374 | −0.506868 | − | 0.862024i | \(-0.669197\pi\) | ||||
−0.506868 | + | 0.862024i | \(0.669197\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 2.75387 | 0.111593 | ||||||||
\(610\) | 23.2870 | 0.942864 | ||||||||
\(611\) | 26.1990 | 1.05990 | ||||||||
\(612\) | −3.07780 | −0.124413 | ||||||||
\(613\) | −41.6642 | −1.68280 | −0.841401 | − | 0.540411i | \(-0.818269\pi\) | ||||
−0.841401 | + | 0.540411i | \(0.818269\pi\) | |||||||
\(614\) | 4.65577 | 0.187891 | ||||||||
\(615\) | −39.8864 | −1.60838 | ||||||||
\(616\) | 3.82405 | 0.154075 | ||||||||
\(617\) | −24.4712 | −0.985173 | −0.492587 | − | 0.870263i | \(-0.663949\pi\) | ||||
−0.492587 | + | 0.870263i | \(0.663949\pi\) | |||||||
\(618\) | −3.78559 | −0.152279 | ||||||||
\(619\) | −2.64664 | −0.106377 | −0.0531887 | − | 0.998584i | \(-0.516938\pi\) | ||||
−0.0531887 | + | 0.998584i | \(0.516938\pi\) | |||||||
\(620\) | 8.70853 | 0.349743 | ||||||||
\(621\) | 7.60197 | 0.305056 | ||||||||
\(622\) | −24.6145 | −0.986950 | ||||||||
\(623\) | 27.4667 | 1.10043 | ||||||||
\(624\) | 8.71445 | 0.348857 | ||||||||
\(625\) | −12.9178 | −0.516711 | ||||||||
\(626\) | 3.34650 | 0.133753 | ||||||||
\(627\) | −3.14822 | −0.125728 | ||||||||
\(628\) | −2.01582 | −0.0804402 | ||||||||
\(629\) | 11.7658 | 0.469131 | ||||||||
\(630\) | 4.50870 | 0.179631 | ||||||||
\(631\) | 7.39706 | 0.294472 | 0.147236 | − | 0.989101i | \(-0.452962\pi\) | ||||
0.147236 | + | 0.989101i | \(0.452962\pi\) | |||||||
\(632\) | −2.99978 | −0.119325 | ||||||||
\(633\) | 2.00763 | 0.0797963 | ||||||||
\(634\) | 5.15681 | 0.204803 | ||||||||
\(635\) | −10.1268 | −0.401871 | ||||||||
\(636\) | 8.96173 | 0.355356 | ||||||||
\(637\) | 4.57139 | 0.181125 | ||||||||
\(638\) | −0.882055 | −0.0349209 | ||||||||
\(639\) | 8.30044 | 0.328360 | ||||||||
\(640\) | −1.79399 | −0.0709135 | ||||||||
\(641\) | 40.8577 | 1.61378 | 0.806892 | − | 0.590700i | \(-0.201148\pi\) | ||||
0.806892 | + | 0.590700i | \(0.201148\pi\) | |||||||
\(642\) | 30.4718 | 1.20263 | ||||||||
\(643\) | 21.0525 | 0.830230 | 0.415115 | − | 0.909769i | \(-0.363741\pi\) | ||||
0.415115 | + | 0.909769i | \(0.363741\pi\) | |||||||
\(644\) | −4.68867 | −0.184760 | ||||||||
\(645\) | −30.3865 | −1.19647 | ||||||||
\(646\) | 2.98642 | 0.117499 | ||||||||
\(647\) | −11.4788 | −0.451277 | −0.225638 | − | 0.974211i | \(-0.572447\pi\) | ||||
−0.225638 | + | 0.974211i | \(0.572447\pi\) | |||||||
\(648\) | −11.0297 | −0.433286 | ||||||||
\(649\) | −22.5492 | −0.885135 | ||||||||
\(650\) | 7.73337 | 0.303328 | ||||||||
\(651\) | −23.7659 | −0.931458 | ||||||||
\(652\) | 21.8879 | 0.857197 | ||||||||
\(653\) | 31.3640 | 1.22737 | 0.613685 | − | 0.789551i | \(-0.289687\pi\) | ||||
0.613685 | + | 0.789551i | \(0.289687\pi\) | |||||||
\(654\) | 12.4176 | 0.485567 | ||||||||
\(655\) | 39.9587 | 1.56131 | ||||||||
\(656\) | −11.0744 | −0.432384 | ||||||||
\(657\) | 2.51146 | 0.0979815 | ||||||||
\(658\) | 14.7188 | 0.573799 | ||||||||
\(659\) | 2.78257 | 0.108393 | 0.0541967 | − | 0.998530i | \(-0.482740\pi\) | ||||
0.0541967 | + | 0.998530i | \(0.482740\pi\) | |||||||
\(660\) | −5.64786 | −0.219843 | ||||||||
\(661\) | 39.1029 | 1.52093 | 0.760464 | − | 0.649380i | \(-0.224972\pi\) | ||||
0.760464 | + | 0.649380i | \(0.224972\pi\) | |||||||
\(662\) | −25.8264 | −1.00377 | ||||||||
\(663\) | −26.0250 | −1.01073 | ||||||||
\(664\) | 9.69270 | 0.376150 | ||||||||
\(665\) | −4.37484 | −0.169649 | ||||||||
\(666\) | −4.06030 | −0.157333 | ||||||||
\(667\) | 1.08149 | 0.0418755 | ||||||||
\(668\) | −4.09048 | −0.158265 | ||||||||
\(669\) | 37.2402 | 1.43979 | ||||||||
\(670\) | 28.5951 | 1.10473 | ||||||||
\(671\) | 20.3552 | 0.785803 | ||||||||
\(672\) | 4.89585 | 0.188861 | ||||||||
\(673\) | −47.2618 | −1.82181 | −0.910905 | − | 0.412616i | \(-0.864615\pi\) | ||||
−0.910905 | + | 0.412616i | \(0.864615\pi\) | |||||||
\(674\) | 19.1488 | 0.737583 | ||||||||
\(675\) | −7.04422 | −0.271132 | ||||||||
\(676\) | 5.84130 | 0.224665 | ||||||||
\(677\) | −37.7782 | −1.45194 | −0.725968 | − | 0.687729i | \(-0.758608\pi\) | ||||
−0.725968 | + | 0.687729i | \(0.758608\pi\) | |||||||
\(678\) | −13.2108 | −0.507359 | ||||||||
\(679\) | −8.39477 | −0.322162 | ||||||||
\(680\) | 5.35760 | 0.205454 | ||||||||
\(681\) | 35.6344 | 1.36551 | ||||||||
\(682\) | 7.61212 | 0.291483 | ||||||||
\(683\) | 14.2962 | 0.547029 | 0.273515 | − | 0.961868i | \(-0.411814\pi\) | ||||
0.273515 | + | 0.961868i | \(0.411814\pi\) | |||||||
\(684\) | −1.03060 | −0.0394059 | ||||||||
\(685\) | −29.5610 | −1.12947 | ||||||||
\(686\) | 19.6385 | 0.749803 | ||||||||
\(687\) | 10.9533 | 0.417894 | ||||||||
\(688\) | −8.43678 | −0.321649 | ||||||||
\(689\) | 19.3759 | 0.738164 | ||||||||
\(690\) | 6.92485 | 0.263625 | ||||||||
\(691\) | 38.5441 | 1.46629 | 0.733144 | − | 0.680073i | \(-0.238052\pi\) | ||||
0.733144 | + | 0.680073i | \(0.238052\pi\) | |||||||
\(692\) | 8.61177 | 0.327370 | ||||||||
\(693\) | 3.94106 | 0.149708 | ||||||||
\(694\) | 17.9943 | 0.683054 | ||||||||
\(695\) | 20.9633 | 0.795182 | ||||||||
\(696\) | −1.12928 | −0.0428051 | ||||||||
\(697\) | 33.0729 | 1.25273 | ||||||||
\(698\) | −13.2057 | −0.499842 | ||||||||
\(699\) | −15.2386 | −0.576375 | ||||||||
\(700\) | 4.34467 | 0.164213 | ||||||||
\(701\) | −24.8451 | −0.938387 | −0.469194 | − | 0.883095i | \(-0.655455\pi\) | ||||
−0.469194 | + | 0.883095i | \(0.655455\pi\) | |||||||
\(702\) | −17.1623 | −0.647748 | ||||||||
\(703\) | 3.93975 | 0.148591 | ||||||||
\(704\) | −1.56812 | −0.0591009 | ||||||||
\(705\) | −21.7387 | −0.818726 | ||||||||
\(706\) | −30.3089 | −1.14069 | ||||||||
\(707\) | −36.6330 | −1.37773 | ||||||||
\(708\) | −28.8693 | −1.08498 | ||||||||
\(709\) | −12.8176 | −0.481376 | −0.240688 | − | 0.970603i | \(-0.577373\pi\) | ||||
−0.240688 | + | 0.970603i | \(0.577373\pi\) | |||||||
\(710\) | −14.4488 | −0.542252 | ||||||||
\(711\) | −3.09157 | −0.115943 | ||||||||
\(712\) | −11.2633 | −0.422108 | ||||||||
\(713\) | −9.33324 | −0.349533 | ||||||||
\(714\) | −14.6211 | −0.547179 | ||||||||
\(715\) | −12.2111 | −0.456669 | ||||||||
\(716\) | 16.8064 | 0.628085 | ||||||||
\(717\) | 42.8085 | 1.59871 | ||||||||
\(718\) | 21.6062 | 0.806336 | ||||||||
\(719\) | −20.0904 | −0.749245 | −0.374623 | − | 0.927177i | \(-0.622228\pi\) | ||||
−0.374623 | + | 0.927177i | \(0.622228\pi\) | |||||||
\(720\) | −1.84888 | −0.0689036 | ||||||||
\(721\) | −4.59825 | −0.171248 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −1.48228 | −0.0551265 | ||||||||
\(724\) | 6.55162 | 0.243489 | ||||||||
\(725\) | −1.00214 | −0.0372186 | ||||||||
\(726\) | 17.1472 | 0.636392 | ||||||||
\(727\) | −7.51975 | −0.278892 | −0.139446 | − | 0.990230i | \(-0.544532\pi\) | ||||
−0.139446 | + | 0.990230i | \(0.544532\pi\) | |||||||
\(728\) | 10.5852 | 0.392313 | ||||||||
\(729\) | 12.4465 | 0.460980 | ||||||||
\(730\) | −4.37176 | −0.161806 | ||||||||
\(731\) | 25.1958 | 0.931899 | ||||||||
\(732\) | 26.0603 | 0.963217 | ||||||||
\(733\) | 17.4972 | 0.646274 | 0.323137 | − | 0.946352i | \(-0.395263\pi\) | ||||
0.323137 | + | 0.946352i | \(0.395263\pi\) | |||||||
\(734\) | −9.98272 | −0.368469 | ||||||||
\(735\) | −3.79312 | −0.139911 | ||||||||
\(736\) | 1.92268 | 0.0708709 | ||||||||
\(737\) | 24.9950 | 0.920703 | ||||||||
\(738\) | −11.4133 | −0.420129 | ||||||||
\(739\) | −27.4871 | −1.01113 | −0.505565 | − | 0.862789i | \(-0.668716\pi\) | ||||
−0.505565 | + | 0.862789i | \(0.668716\pi\) | |||||||
\(740\) | 7.06786 | 0.259820 | ||||||||
\(741\) | −8.71445 | −0.320133 | ||||||||
\(742\) | 10.8855 | 0.399621 | ||||||||
\(743\) | −44.5321 | −1.63373 | −0.816863 | − | 0.576832i | \(-0.804289\pi\) | ||||
−0.816863 | + | 0.576832i | \(0.804289\pi\) | |||||||
\(744\) | 9.74564 | 0.357292 | ||||||||
\(745\) | −15.6820 | −0.574542 | ||||||||
\(746\) | −27.0164 | −0.989139 | ||||||||
\(747\) | 9.98928 | 0.365489 | ||||||||
\(748\) | 4.68307 | 0.171230 | ||||||||
\(749\) | 37.0132 | 1.35243 | ||||||||
\(750\) | −24.4251 | −0.891880 | ||||||||
\(751\) | 25.6955 | 0.937644 | 0.468822 | − | 0.883293i | \(-0.344679\pi\) | ||||
0.468822 | + | 0.883293i | \(0.344679\pi\) | |||||||
\(752\) | −6.03573 | −0.220100 | ||||||||
\(753\) | 54.5485 | 1.98786 | ||||||||
\(754\) | −2.44158 | −0.0889171 | ||||||||
\(755\) | −1.93714 | −0.0704996 | ||||||||
\(756\) | −9.64189 | −0.350672 | ||||||||
\(757\) | 18.4588 | 0.670895 | 0.335447 | − | 0.942059i | \(-0.391113\pi\) | ||||
0.335447 | + | 0.942059i | \(0.391113\pi\) | |||||||
\(758\) | 0.972204 | 0.0353120 | ||||||||
\(759\) | 6.05301 | 0.219710 | ||||||||
\(760\) | 1.79399 | 0.0650747 | ||||||||
\(761\) | 18.1033 | 0.656243 | 0.328121 | − | 0.944636i | \(-0.393584\pi\) | ||||
0.328121 | + | 0.944636i | \(0.393584\pi\) | |||||||
\(762\) | −11.3329 | −0.410546 | ||||||||
\(763\) | 15.0833 | 0.546053 | ||||||||
\(764\) | −22.4079 | −0.810688 | ||||||||
\(765\) | 5.52153 | 0.199631 | ||||||||
\(766\) | −18.3603 | −0.663385 | ||||||||
\(767\) | −62.4176 | −2.25377 | ||||||||
\(768\) | −2.00763 | −0.0724443 | ||||||||
\(769\) | −45.5260 | −1.64171 | −0.820855 | − | 0.571137i | \(-0.806503\pi\) | ||||
−0.820855 | + | 0.571137i | \(0.806503\pi\) | |||||||
\(770\) | −6.86029 | −0.247228 | ||||||||
\(771\) | −6.97836 | −0.251320 | ||||||||
\(772\) | 21.0583 | 0.757904 | ||||||||
\(773\) | −22.0175 | −0.791913 | −0.395956 | − | 0.918269i | \(-0.629587\pi\) | ||||
−0.395956 | + | 0.918269i | \(0.629587\pi\) | |||||||
\(774\) | −8.69493 | −0.312533 | ||||||||
\(775\) | 8.64847 | 0.310662 | ||||||||
\(776\) | 3.44243 | 0.123576 | ||||||||
\(777\) | −19.2884 | −0.691969 | ||||||||
\(778\) | 17.7954 | 0.637997 | ||||||||
\(779\) | 11.0744 | 0.396783 | ||||||||
\(780\) | −15.6336 | −0.559773 | ||||||||
\(781\) | −12.6297 | −0.451925 | ||||||||
\(782\) | −5.74193 | −0.205331 | ||||||||
\(783\) | 2.22400 | 0.0794793 | ||||||||
\(784\) | −1.05316 | −0.0376127 | ||||||||
\(785\) | 3.61636 | 0.129073 | ||||||||
\(786\) | 44.7174 | 1.59502 | ||||||||
\(787\) | −28.0918 | −1.00137 | −0.500683 | − | 0.865631i | \(-0.666918\pi\) | ||||
−0.500683 | + | 0.865631i | \(0.666918\pi\) | |||||||
\(788\) | 17.7540 | 0.632461 | ||||||||
\(789\) | −31.1443 | −1.10877 | ||||||||
\(790\) | 5.38157 | 0.191468 | ||||||||
\(791\) | −16.0468 | −0.570559 | ||||||||
\(792\) | −1.61610 | −0.0574258 | ||||||||
\(793\) | 56.3444 | 2.00085 | ||||||||
\(794\) | 34.8852 | 1.23803 | ||||||||
\(795\) | −16.0772 | −0.570200 | ||||||||
\(796\) | 10.1854 | 0.361012 | ||||||||
\(797\) | −9.55800 | −0.338562 | −0.169281 | − | 0.985568i | \(-0.554144\pi\) | ||||
−0.169281 | + | 0.985568i | \(0.554144\pi\) | |||||||
\(798\) | −4.89585 | −0.173311 | ||||||||
\(799\) | 18.0252 | 0.637686 | ||||||||
\(800\) | −1.78161 | −0.0629896 | ||||||||
\(801\) | −11.6079 | −0.410145 | ||||||||
\(802\) | 11.6845 | 0.412592 | ||||||||
\(803\) | −3.82136 | −0.134853 | ||||||||
\(804\) | 32.0006 | 1.12857 | ||||||||
\(805\) | 8.41142 | 0.296463 | ||||||||
\(806\) | 21.0708 | 0.742187 | ||||||||
\(807\) | 13.9130 | 0.489760 | ||||||||
\(808\) | 15.0221 | 0.528474 | ||||||||
\(809\) | 3.15214 | 0.110823 | 0.0554116 | − | 0.998464i | \(-0.482353\pi\) | ||||
0.0554116 | + | 0.998464i | \(0.482353\pi\) | |||||||
\(810\) | 19.7871 | 0.695246 | ||||||||
\(811\) | −42.8175 | −1.50353 | −0.751763 | − | 0.659433i | \(-0.770796\pi\) | ||||
−0.751763 | + | 0.659433i | \(0.770796\pi\) | |||||||
\(812\) | −1.37170 | −0.0481372 | ||||||||
\(813\) | −29.9033 | −1.04875 | ||||||||
\(814\) | 6.17801 | 0.216539 | ||||||||
\(815\) | −39.2666 | −1.37545 | ||||||||
\(816\) | 5.99564 | 0.209889 | ||||||||
\(817\) | 8.43678 | 0.295165 | ||||||||
\(818\) | −16.5589 | −0.578967 | ||||||||
\(819\) | 10.9091 | 0.381194 | ||||||||
\(820\) | 19.8674 | 0.693799 | ||||||||
\(821\) | −5.54040 | −0.193361 | −0.0966807 | − | 0.995315i | \(-0.530823\pi\) | ||||
−0.0966807 | + | 0.995315i | \(0.530823\pi\) | |||||||
\(822\) | −33.0815 | −1.15385 | ||||||||
\(823\) | −10.4057 | −0.362718 | −0.181359 | − | 0.983417i | \(-0.558050\pi\) | ||||
−0.181359 | + | 0.983417i | \(0.558050\pi\) | |||||||
\(824\) | 1.88560 | 0.0656879 | ||||||||
\(825\) | −5.60891 | −0.195277 | ||||||||
\(826\) | −35.0667 | −1.22013 | ||||||||
\(827\) | −55.2056 | −1.91969 | −0.959843 | − | 0.280538i | \(-0.909487\pi\) | ||||
−0.959843 | + | 0.280538i | \(0.909487\pi\) | |||||||
\(828\) | 1.98151 | 0.0688622 | ||||||||
\(829\) | −43.3892 | −1.50697 | −0.753484 | − | 0.657466i | \(-0.771628\pi\) | ||||
−0.753484 | + | 0.657466i | \(0.771628\pi\) | |||||||
\(830\) | −17.3886 | −0.603566 | ||||||||
\(831\) | −44.1088 | −1.53012 | ||||||||
\(832\) | −4.34066 | −0.150485 | ||||||||
\(833\) | 3.14517 | 0.108974 | ||||||||
\(834\) | 23.4598 | 0.812347 | ||||||||
\(835\) | 7.33826 | 0.253951 | ||||||||
\(836\) | 1.56812 | 0.0542347 | ||||||||
\(837\) | −19.1931 | −0.663410 | ||||||||
\(838\) | 7.52769 | 0.260040 | ||||||||
\(839\) | −43.8812 | −1.51495 | −0.757474 | − | 0.652865i | \(-0.773567\pi\) | ||||
−0.757474 | + | 0.652865i | \(0.773567\pi\) | |||||||
\(840\) | −8.78309 | −0.303045 | ||||||||
\(841\) | −28.6836 | −0.989090 | ||||||||
\(842\) | −3.34379 | −0.115235 | ||||||||
\(843\) | −8.95055 | −0.308273 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | −10.4792 | −0.360496 | ||||||||
\(846\) | −6.22041 | −0.213862 | ||||||||
\(847\) | 20.8282 | 0.715665 | ||||||||
\(848\) | −4.46382 | −0.153288 | ||||||||
\(849\) | 11.0891 | 0.380576 | ||||||||
\(850\) | 5.32065 | 0.182497 | ||||||||
\(851\) | −7.57488 | −0.259663 | ||||||||
\(852\) | −16.1695 | −0.553958 | ||||||||
\(853\) | −6.94606 | −0.237829 | −0.118914 | − | 0.992905i | \(-0.537941\pi\) | ||||
−0.118914 | + | 0.992905i | \(0.537941\pi\) | |||||||
\(854\) | 31.6547 | 1.08320 | ||||||||
\(855\) | 1.84888 | 0.0632303 | ||||||||
\(856\) | −15.1780 | −0.518772 | ||||||||
\(857\) | −3.03688 | −0.103738 | −0.0518690 | − | 0.998654i | \(-0.516518\pi\) | ||||
−0.0518690 | + | 0.998654i | \(0.516518\pi\) | |||||||
\(858\) | −13.6653 | −0.466527 | ||||||||
\(859\) | −12.6581 | −0.431889 | −0.215945 | − | 0.976406i | \(-0.569283\pi\) | ||||
−0.215945 | + | 0.976406i | \(0.569283\pi\) | |||||||
\(860\) | 15.1355 | 0.516115 | ||||||||
\(861\) | −54.2187 | −1.84777 | ||||||||
\(862\) | −36.7080 | −1.25028 | ||||||||
\(863\) | −14.4476 | −0.491803 | −0.245902 | − | 0.969295i | \(-0.579084\pi\) | ||||
−0.245902 | + | 0.969295i | \(0.579084\pi\) | |||||||
\(864\) | 3.95384 | 0.134512 | ||||||||
\(865\) | −15.4494 | −0.525295 | ||||||||
\(866\) | 35.4441 | 1.20444 | ||||||||
\(867\) | 16.2243 | 0.551006 | ||||||||
\(868\) | 11.8377 | 0.401799 | ||||||||
\(869\) | 4.70403 | 0.159573 | ||||||||
\(870\) | 2.02591 | 0.0686847 | ||||||||
\(871\) | 69.1877 | 2.34433 | ||||||||
\(872\) | −6.18520 | −0.209457 | ||||||||
\(873\) | 3.54776 | 0.120074 | ||||||||
\(874\) | −1.92268 | −0.0650356 | ||||||||
\(875\) | −29.6685 | −1.00298 | ||||||||
\(876\) | −4.89240 | −0.165299 | ||||||||
\(877\) | 21.0284 | 0.710080 | 0.355040 | − | 0.934851i | \(-0.384467\pi\) | ||||
0.355040 | + | 0.934851i | \(0.384467\pi\) | |||||||
\(878\) | 25.0169 | 0.844278 | ||||||||
\(879\) | 39.8301 | 1.34344 | ||||||||
\(880\) | 2.81319 | 0.0948326 | ||||||||
\(881\) | −43.6644 | −1.47109 | −0.735546 | − | 0.677474i | \(-0.763074\pi\) | ||||
−0.735546 | + | 0.677474i | \(0.763074\pi\) | |||||||
\(882\) | −1.08538 | −0.0365467 | ||||||||
\(883\) | −17.7562 | −0.597543 | −0.298771 | − | 0.954325i | \(-0.596577\pi\) | ||||
−0.298771 | + | 0.954325i | \(0.596577\pi\) | |||||||
\(884\) | 12.9630 | 0.435994 | ||||||||
\(885\) | 51.7912 | 1.74094 | ||||||||
\(886\) | 20.7863 | 0.698330 | ||||||||
\(887\) | −37.3649 | −1.25459 | −0.627295 | − | 0.778782i | \(-0.715838\pi\) | ||||
−0.627295 | + | 0.778782i | \(0.715838\pi\) | |||||||
\(888\) | 7.90958 | 0.265428 | ||||||||
\(889\) | −13.7657 | −0.461687 | ||||||||
\(890\) | 20.2061 | 0.677311 | ||||||||
\(891\) | 17.2959 | 0.579433 | ||||||||
\(892\) | −18.5493 | −0.621076 | ||||||||
\(893\) | 6.03573 | 0.201978 | ||||||||
\(894\) | −17.5495 | −0.586944 | ||||||||
\(895\) | −30.1505 | −1.00782 | ||||||||
\(896\) | −2.43862 | −0.0814684 | ||||||||
\(897\) | 16.7551 | 0.559437 | ||||||||
\(898\) | −2.12952 | −0.0710631 | ||||||||
\(899\) | −2.73049 | −0.0910671 | ||||||||
\(900\) | −1.83613 | −0.0612043 | ||||||||
\(901\) | 13.3309 | 0.444115 | ||||||||
\(902\) | 17.3661 | 0.578227 | ||||||||
\(903\) | −41.3052 | −1.37455 | ||||||||
\(904\) | 6.58029 | 0.218857 | ||||||||
\(905\) | −11.7535 | −0.390700 | ||||||||
\(906\) | −2.16783 | −0.0720215 | ||||||||
\(907\) | −35.1732 | −1.16791 | −0.583953 | − | 0.811787i | \(-0.698495\pi\) | ||||
−0.583953 | + | 0.811787i | \(0.698495\pi\) | |||||||
\(908\) | −17.7495 | −0.589036 | ||||||||
\(909\) | 15.4817 | 0.513496 | ||||||||
\(910\) | −18.9897 | −0.629502 | ||||||||
\(911\) | −38.8799 | −1.28815 | −0.644075 | − | 0.764962i | \(-0.722758\pi\) | ||||
−0.644075 | + | 0.764962i | \(0.722758\pi\) | |||||||
\(912\) | 2.00763 | 0.0664794 | ||||||||
\(913\) | −15.1993 | −0.503025 | ||||||||
\(914\) | 8.37829 | 0.277129 | ||||||||
\(915\) | −46.7519 | −1.54557 | ||||||||
\(916\) | −5.45582 | −0.180265 | ||||||||
\(917\) | 54.3169 | 1.79370 | ||||||||
\(918\) | −11.8078 | −0.389716 | ||||||||
\(919\) | 10.4829 | 0.345798 | 0.172899 | − | 0.984940i | \(-0.444687\pi\) | ||||
0.172899 | + | 0.984940i | \(0.444687\pi\) | |||||||
\(920\) | −3.44926 | −0.113719 | ||||||||
\(921\) | −9.34708 | −0.307997 | ||||||||
\(922\) | −26.4321 | −0.870493 | ||||||||
\(923\) | −34.9596 | −1.15071 | ||||||||
\(924\) | −7.67729 | −0.252564 | ||||||||
\(925\) | 7.01912 | 0.230787 | ||||||||
\(926\) | 7.76656 | 0.255225 | ||||||||
\(927\) | 1.94329 | 0.0638261 | ||||||||
\(928\) | 0.562491 | 0.0184647 | ||||||||
\(929\) | −21.2402 | −0.696869 | −0.348434 | − | 0.937333i | \(-0.613287\pi\) | ||||
−0.348434 | + | 0.937333i | \(0.613287\pi\) | |||||||
\(930\) | −17.4835 | −0.573308 | ||||||||
\(931\) | 1.05316 | 0.0345158 | ||||||||
\(932\) | 7.59030 | 0.248629 | ||||||||
\(933\) | 49.4169 | 1.61784 | ||||||||
\(934\) | 8.58514 | 0.280914 | ||||||||
\(935\) | −8.40137 | −0.274754 | ||||||||
\(936\) | −4.47347 | −0.146220 | ||||||||
\(937\) | −24.8936 | −0.813239 | −0.406620 | − | 0.913598i | \(-0.633293\pi\) | ||||
−0.406620 | + | 0.913598i | \(0.633293\pi\) | |||||||
\(938\) | 38.8702 | 1.26916 | ||||||||
\(939\) | −6.71855 | −0.219252 | ||||||||
\(940\) | 10.8280 | 0.353171 | ||||||||
\(941\) | 8.16223 | 0.266081 | 0.133041 | − | 0.991111i | \(-0.457526\pi\) | ||||
0.133041 | + | 0.991111i | \(0.457526\pi\) | |||||||
\(942\) | 4.04704 | 0.131860 | ||||||||
\(943\) | −21.2926 | −0.693382 | ||||||||
\(944\) | 14.3798 | 0.468021 | ||||||||
\(945\) | 17.2974 | 0.562685 | ||||||||
\(946\) | 13.2299 | 0.430141 | ||||||||
\(947\) | 44.4251 | 1.44362 | 0.721811 | − | 0.692090i | \(-0.243310\pi\) | ||||
0.721811 | + | 0.692090i | \(0.243310\pi\) | |||||||
\(948\) | 6.02247 | 0.195601 | ||||||||
\(949\) | −10.5777 | −0.343368 | ||||||||
\(950\) | 1.78161 | 0.0578032 | ||||||||
\(951\) | −10.3530 | −0.335719 | ||||||||
\(952\) | 7.28273 | 0.236035 | ||||||||
\(953\) | 8.42769 | 0.273000 | 0.136500 | − | 0.990640i | \(-0.456415\pi\) | ||||
0.136500 | + | 0.990640i | \(0.456415\pi\) | |||||||
\(954\) | −4.60041 | −0.148944 | ||||||||
\(955\) | 40.1994 | 1.30082 | ||||||||
\(956\) | −21.3228 | −0.689630 | ||||||||
\(957\) | 1.77084 | 0.0572433 | ||||||||
\(958\) | −26.8403 | −0.867170 | ||||||||
\(959\) | −40.1831 | −1.29758 | ||||||||
\(960\) | 3.60167 | 0.116243 | ||||||||
\(961\) | −7.43588 | −0.239867 | ||||||||
\(962\) | 17.1011 | 0.551362 | ||||||||
\(963\) | −15.6424 | −0.504069 | ||||||||
\(964\) | 0.738320 | 0.0237797 | ||||||||
\(965\) | −37.7783 | −1.21613 | ||||||||
\(966\) | 9.41315 | 0.302863 | ||||||||
\(967\) | 17.6656 | 0.568086 | 0.284043 | − | 0.958812i | \(-0.408324\pi\) | ||||
0.284043 | + | 0.958812i | \(0.408324\pi\) | |||||||
\(968\) | −8.54099 | −0.274518 | ||||||||
\(969\) | −5.99564 | −0.192608 | ||||||||
\(970\) | −6.17567 | −0.198289 | ||||||||
\(971\) | 52.1695 | 1.67420 | 0.837099 | − | 0.547051i | \(-0.184250\pi\) | ||||
0.837099 | + | 0.547051i | \(0.184250\pi\) | |||||||
\(972\) | 10.2820 | 0.329796 | ||||||||
\(973\) | 28.4960 | 0.913538 | ||||||||
\(974\) | −2.04309 | −0.0654647 | ||||||||
\(975\) | −15.5258 | −0.497223 | ||||||||
\(976\) | −12.9806 | −0.415499 | ||||||||
\(977\) | −22.8120 | −0.729819 | −0.364909 | − | 0.931043i | \(-0.618900\pi\) | ||||
−0.364909 | + | 0.931043i | \(0.618900\pi\) | |||||||
\(978\) | −43.9430 | −1.40514 | ||||||||
\(979\) | 17.6622 | 0.564485 | ||||||||
\(980\) | 1.88935 | 0.0603530 | ||||||||
\(981\) | −6.37445 | −0.203521 | ||||||||
\(982\) | 27.0638 | 0.863640 | ||||||||
\(983\) | −14.4751 | −0.461682 | −0.230841 | − | 0.972991i | \(-0.574148\pi\) | ||||
−0.230841 | + | 0.972991i | \(0.574148\pi\) | |||||||
\(984\) | 22.2334 | 0.708775 | ||||||||
\(985\) | −31.8505 | −1.01484 | ||||||||
\(986\) | −1.67983 | −0.0534968 | ||||||||
\(987\) | −29.5500 | −0.940587 | ||||||||
\(988\) | 4.34066 | 0.138095 | ||||||||
\(989\) | −16.2212 | −0.515805 | ||||||||
\(990\) | 2.89927 | 0.0921448 | ||||||||
\(991\) | −29.6521 | −0.941929 | −0.470964 | − | 0.882152i | \(-0.656094\pi\) | ||||
−0.470964 | + | 0.882152i | \(0.656094\pi\) | |||||||
\(992\) | −4.85429 | −0.154124 | ||||||||
\(993\) | 51.8500 | 1.64541 | ||||||||
\(994\) | −19.6406 | −0.622962 | ||||||||
\(995\) | −18.2724 | −0.579275 | ||||||||
\(996\) | −19.4594 | −0.616595 | ||||||||
\(997\) | −21.5565 | −0.682700 | −0.341350 | − | 0.939936i | \(-0.610884\pi\) | ||||
−0.341350 | + | 0.939936i | \(0.610884\pi\) | |||||||
\(998\) | −15.2351 | −0.482257 | ||||||||
\(999\) | −15.5771 | −0.492839 |
(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 | 8018.2.a.j.1.10 | ✓ | 47 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.j.1.10 | ✓ | 47 | 1.1 | even | 1 | trivial |