Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8005,2,Mod(1,8005)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8005, 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("8005.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8005 = 5 \cdot 1601 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8005.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: | \(63.9202468180\) |
Analytic rank: | \(1\) |
Dimension: | \(127\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 8005.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.69002 | −1.90213 | −0.951065 | − | 0.308992i | \(-0.900008\pi\) | ||||
−0.951065 | + | 0.308992i | \(0.900008\pi\) | |||||||
\(3\) | 2.05113 | 1.18422 | 0.592111 | − | 0.805856i | \(-0.298295\pi\) | ||||
0.592111 | + | 0.805856i | \(0.298295\pi\) | |||||||
\(4\) | 5.23619 | 2.61810 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −5.51758 | −2.25254 | ||||||||
\(7\) | −1.38538 | −0.523625 | −0.261813 | − | 0.965119i | \(-0.584320\pi\) | ||||
−0.261813 | + | 0.965119i | \(0.584320\pi\) | |||||||
\(8\) | −8.70541 | −3.07783 | ||||||||
\(9\) | 1.20715 | 0.402382 | ||||||||
\(10\) | 2.69002 | 0.850658 | ||||||||
\(11\) | 1.93988 | 0.584896 | 0.292448 | − | 0.956281i | \(-0.405530\pi\) | ||||
0.292448 | + | 0.956281i | \(0.405530\pi\) | |||||||
\(12\) | 10.7401 | 3.10041 | ||||||||
\(13\) | 4.32088 | 1.19840 | 0.599198 | − | 0.800601i | \(-0.295486\pi\) | ||||
0.599198 | + | 0.800601i | \(0.295486\pi\) | |||||||
\(14\) | 3.72670 | 0.996003 | ||||||||
\(15\) | −2.05113 | −0.529600 | ||||||||
\(16\) | 12.9453 | 3.23633 | ||||||||
\(17\) | −4.04578 | −0.981245 | −0.490623 | − | 0.871372i | \(-0.663231\pi\) | ||||
−0.490623 | + | 0.871372i | \(0.663231\pi\) | |||||||
\(18\) | −3.24724 | −0.765382 | ||||||||
\(19\) | −4.73138 | −1.08545 | −0.542726 | − | 0.839910i | \(-0.682608\pi\) | ||||
−0.542726 | + | 0.839910i | \(0.682608\pi\) | |||||||
\(20\) | −5.23619 | −1.17085 | ||||||||
\(21\) | −2.84160 | −0.620089 | ||||||||
\(22\) | −5.21831 | −1.11255 | ||||||||
\(23\) | −0.808388 | −0.168561 | −0.0842803 | − | 0.996442i | \(-0.526859\pi\) | ||||
−0.0842803 | + | 0.996442i | \(0.526859\pi\) | |||||||
\(24\) | −17.8560 | −3.64483 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −11.6232 | −2.27951 | ||||||||
\(27\) | −3.67738 | −0.707713 | ||||||||
\(28\) | −7.25413 | −1.37090 | ||||||||
\(29\) | −2.23470 | −0.414974 | −0.207487 | − | 0.978238i | \(-0.566528\pi\) | ||||
−0.207487 | + | 0.978238i | \(0.566528\pi\) | |||||||
\(30\) | 5.51758 | 1.00737 | ||||||||
\(31\) | 0.820011 | 0.147278 | 0.0736392 | − | 0.997285i | \(-0.476539\pi\) | ||||
0.0736392 | + | 0.997285i | \(0.476539\pi\) | |||||||
\(32\) | −17.4123 | −3.07809 | ||||||||
\(33\) | 3.97895 | 0.692647 | ||||||||
\(34\) | 10.8832 | 1.86646 | ||||||||
\(35\) | 1.38538 | 0.234172 | ||||||||
\(36\) | 6.32084 | 1.05347 | ||||||||
\(37\) | 3.61583 | 0.594439 | 0.297220 | − | 0.954809i | \(-0.403941\pi\) | ||||
0.297220 | + | 0.954809i | \(0.403941\pi\) | |||||||
\(38\) | 12.7275 | 2.06467 | ||||||||
\(39\) | 8.86270 | 1.41917 | ||||||||
\(40\) | 8.70541 | 1.37645 | ||||||||
\(41\) | 5.58513 | 0.872250 | 0.436125 | − | 0.899886i | \(-0.356351\pi\) | ||||
0.436125 | + | 0.899886i | \(0.356351\pi\) | |||||||
\(42\) | 7.64396 | 1.17949 | ||||||||
\(43\) | 12.1612 | 1.85457 | 0.927283 | − | 0.374361i | \(-0.122138\pi\) | ||||
0.927283 | + | 0.374361i | \(0.122138\pi\) | |||||||
\(44\) | 10.1576 | 1.53131 | ||||||||
\(45\) | −1.20715 | −0.179951 | ||||||||
\(46\) | 2.17458 | 0.320624 | ||||||||
\(47\) | 6.91380 | 1.00848 | 0.504241 | − | 0.863563i | \(-0.331772\pi\) | ||||
0.504241 | + | 0.863563i | \(0.331772\pi\) | |||||||
\(48\) | 26.5526 | 3.83254 | ||||||||
\(49\) | −5.08072 | −0.725816 | ||||||||
\(50\) | −2.69002 | −0.380426 | ||||||||
\(51\) | −8.29843 | −1.16201 | ||||||||
\(52\) | 22.6250 | 3.13752 | ||||||||
\(53\) | −12.2952 | −1.68888 | −0.844439 | − | 0.535652i | \(-0.820066\pi\) | ||||
−0.844439 | + | 0.535652i | \(0.820066\pi\) | |||||||
\(54\) | 9.89222 | 1.34616 | ||||||||
\(55\) | −1.93988 | −0.261573 | ||||||||
\(56\) | 12.0603 | 1.61163 | ||||||||
\(57\) | −9.70468 | −1.28542 | ||||||||
\(58\) | 6.01139 | 0.789334 | ||||||||
\(59\) | −7.26412 | −0.945709 | −0.472854 | − | 0.881141i | \(-0.656776\pi\) | ||||
−0.472854 | + | 0.881141i | \(0.656776\pi\) | |||||||
\(60\) | −10.7401 | −1.38654 | ||||||||
\(61\) | −1.38258 | −0.177021 | −0.0885103 | − | 0.996075i | \(-0.528211\pi\) | ||||
−0.0885103 | + | 0.996075i | \(0.528211\pi\) | |||||||
\(62\) | −2.20584 | −0.280142 | ||||||||
\(63\) | −1.67236 | −0.210697 | ||||||||
\(64\) | 20.9488 | 2.61860 | ||||||||
\(65\) | −4.32088 | −0.535939 | ||||||||
\(66\) | −10.7035 | −1.31750 | ||||||||
\(67\) | 14.3222 | 1.74974 | 0.874869 | − | 0.484359i | \(-0.160947\pi\) | ||||
0.874869 | + | 0.484359i | \(0.160947\pi\) | |||||||
\(68\) | −21.1845 | −2.56899 | ||||||||
\(69\) | −1.65811 | −0.199613 | ||||||||
\(70\) | −3.72670 | −0.445426 | ||||||||
\(71\) | −2.52449 | −0.299602 | −0.149801 | − | 0.988716i | \(-0.547863\pi\) | ||||
−0.149801 | + | 0.988716i | \(0.547863\pi\) | |||||||
\(72\) | −10.5087 | −1.23846 | ||||||||
\(73\) | 4.31419 | 0.504938 | 0.252469 | − | 0.967605i | \(-0.418757\pi\) | ||||
0.252469 | + | 0.967605i | \(0.418757\pi\) | |||||||
\(74\) | −9.72666 | −1.13070 | ||||||||
\(75\) | 2.05113 | 0.236844 | ||||||||
\(76\) | −24.7744 | −2.84182 | ||||||||
\(77\) | −2.68748 | −0.306266 | ||||||||
\(78\) | −23.8408 | −2.69944 | ||||||||
\(79\) | −9.69374 | −1.09063 | −0.545315 | − | 0.838231i | \(-0.683590\pi\) | ||||
−0.545315 | + | 0.838231i | \(0.683590\pi\) | |||||||
\(80\) | −12.9453 | −1.44733 | ||||||||
\(81\) | −11.1642 | −1.24047 | ||||||||
\(82\) | −15.0241 | −1.65913 | ||||||||
\(83\) | −7.24012 | −0.794706 | −0.397353 | − | 0.917666i | \(-0.630071\pi\) | ||||
−0.397353 | + | 0.917666i | \(0.630071\pi\) | |||||||
\(84\) | −14.8792 | −1.62345 | ||||||||
\(85\) | 4.04578 | 0.438826 | ||||||||
\(86\) | −32.7138 | −3.52762 | ||||||||
\(87\) | −4.58367 | −0.491421 | ||||||||
\(88\) | −16.8875 | −1.80021 | ||||||||
\(89\) | −6.26494 | −0.664083 | −0.332041 | − | 0.943265i | \(-0.607737\pi\) | ||||
−0.332041 | + | 0.943265i | \(0.607737\pi\) | |||||||
\(90\) | 3.24724 | 0.342289 | ||||||||
\(91\) | −5.98607 | −0.627511 | ||||||||
\(92\) | −4.23287 | −0.441308 | ||||||||
\(93\) | 1.68195 | 0.174410 | ||||||||
\(94\) | −18.5982 | −1.91826 | ||||||||
\(95\) | 4.73138 | 0.485429 | ||||||||
\(96\) | −35.7150 | −3.64515 | ||||||||
\(97\) | −11.5587 | −1.17361 | −0.586803 | − | 0.809730i | \(-0.699614\pi\) | ||||
−0.586803 | + | 0.809730i | \(0.699614\pi\) | |||||||
\(98\) | 13.6672 | 1.38060 | ||||||||
\(99\) | 2.34172 | 0.235351 | ||||||||
\(100\) | 5.23619 | 0.523619 | ||||||||
\(101\) | 9.86474 | 0.981578 | 0.490789 | − | 0.871278i | \(-0.336709\pi\) | ||||
0.490789 | + | 0.871278i | \(0.336709\pi\) | |||||||
\(102\) | 22.3229 | 2.21030 | ||||||||
\(103\) | 16.2715 | 1.60328 | 0.801639 | − | 0.597808i | \(-0.203962\pi\) | ||||
0.801639 | + | 0.597808i | \(0.203962\pi\) | |||||||
\(104\) | −37.6151 | −3.68846 | ||||||||
\(105\) | 2.84160 | 0.277312 | ||||||||
\(106\) | 33.0744 | 3.21247 | ||||||||
\(107\) | 19.6177 | 1.89652 | 0.948260 | − | 0.317496i | \(-0.102842\pi\) | ||||
0.948260 | + | 0.317496i | \(0.102842\pi\) | |||||||
\(108\) | −19.2555 | −1.85286 | ||||||||
\(109\) | −6.65940 | −0.637855 | −0.318928 | − | 0.947779i | \(-0.603323\pi\) | ||||
−0.318928 | + | 0.947779i | \(0.603323\pi\) | |||||||
\(110\) | 5.21831 | 0.497547 | ||||||||
\(111\) | 7.41655 | 0.703948 | ||||||||
\(112\) | −17.9342 | −1.69463 | ||||||||
\(113\) | −3.63673 | −0.342115 | −0.171057 | − | 0.985261i | \(-0.554718\pi\) | ||||
−0.171057 | + | 0.985261i | \(0.554718\pi\) | |||||||
\(114\) | 26.1058 | 2.44503 | ||||||||
\(115\) | 0.808388 | 0.0753826 | ||||||||
\(116\) | −11.7013 | −1.08644 | ||||||||
\(117\) | 5.21593 | 0.482213 | ||||||||
\(118\) | 19.5406 | 1.79886 | ||||||||
\(119\) | 5.60495 | 0.513805 | ||||||||
\(120\) | 17.8560 | 1.63002 | ||||||||
\(121\) | −7.23686 | −0.657897 | ||||||||
\(122\) | 3.71915 | 0.336716 | ||||||||
\(123\) | 11.4558 | 1.03294 | ||||||||
\(124\) | 4.29374 | 0.385589 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 4.49867 | 0.400773 | ||||||||
\(127\) | −15.1846 | −1.34741 | −0.673707 | − | 0.738999i | \(-0.735299\pi\) | ||||
−0.673707 | + | 0.738999i | \(0.735299\pi\) | |||||||
\(128\) | −21.5280 | −1.90282 | ||||||||
\(129\) | 24.9442 | 2.19622 | ||||||||
\(130\) | 11.6232 | 1.01943 | ||||||||
\(131\) | 4.53262 | 0.396017 | 0.198008 | − | 0.980200i | \(-0.436553\pi\) | ||||
0.198008 | + | 0.980200i | \(0.436553\pi\) | |||||||
\(132\) | 20.8346 | 1.81342 | ||||||||
\(133\) | 6.55477 | 0.568370 | ||||||||
\(134\) | −38.5270 | −3.32823 | ||||||||
\(135\) | 3.67738 | 0.316499 | ||||||||
\(136\) | 35.2202 | 3.02010 | ||||||||
\(137\) | −7.45963 | −0.637319 | −0.318659 | − | 0.947869i | \(-0.603233\pi\) | ||||
−0.318659 | + | 0.947869i | \(0.603233\pi\) | |||||||
\(138\) | 4.46035 | 0.379690 | ||||||||
\(139\) | 10.7698 | 0.913483 | 0.456742 | − | 0.889599i | \(-0.349016\pi\) | ||||
0.456742 | + | 0.889599i | \(0.349016\pi\) | |||||||
\(140\) | 7.25413 | 0.613086 | ||||||||
\(141\) | 14.1811 | 1.19427 | ||||||||
\(142\) | 6.79092 | 0.569881 | ||||||||
\(143\) | 8.38199 | 0.700938 | ||||||||
\(144\) | 15.6269 | 1.30224 | ||||||||
\(145\) | 2.23470 | 0.185582 | ||||||||
\(146\) | −11.6052 | −0.960457 | ||||||||
\(147\) | −10.4212 | −0.859528 | ||||||||
\(148\) | 18.9332 | 1.55630 | ||||||||
\(149\) | −11.6884 | −0.957553 | −0.478776 | − | 0.877937i | \(-0.658920\pi\) | ||||
−0.478776 | + | 0.877937i | \(0.658920\pi\) | |||||||
\(150\) | −5.51758 | −0.450509 | ||||||||
\(151\) | 7.71664 | 0.627971 | 0.313986 | − | 0.949428i | \(-0.398336\pi\) | ||||
0.313986 | + | 0.949428i | \(0.398336\pi\) | |||||||
\(152\) | 41.1886 | 3.34084 | ||||||||
\(153\) | −4.88384 | −0.394835 | ||||||||
\(154\) | 7.22936 | 0.582558 | ||||||||
\(155\) | −0.820011 | −0.0658649 | ||||||||
\(156\) | 46.4068 | 3.71552 | ||||||||
\(157\) | −9.51429 | −0.759323 | −0.379662 | − | 0.925125i | \(-0.623960\pi\) | ||||
−0.379662 | + | 0.925125i | \(0.623960\pi\) | |||||||
\(158\) | 26.0763 | 2.07452 | ||||||||
\(159\) | −25.2191 | −2.00001 | ||||||||
\(160\) | 17.4123 | 1.37657 | ||||||||
\(161\) | 1.11993 | 0.0882626 | ||||||||
\(162\) | 30.0320 | 2.35954 | ||||||||
\(163\) | −12.5666 | −0.984291 | −0.492146 | − | 0.870513i | \(-0.663787\pi\) | ||||
−0.492146 | + | 0.870513i | \(0.663787\pi\) | |||||||
\(164\) | 29.2448 | 2.28364 | ||||||||
\(165\) | −3.97895 | −0.309761 | ||||||||
\(166\) | 19.4760 | 1.51163 | ||||||||
\(167\) | −0.0227980 | −0.00176416 | −0.000882080 | − | 1.00000i | \(-0.500281\pi\) | ||||
−0.000882080 | 1.00000i | \(0.500281\pi\) | ||||||||
\(168\) | 24.7373 | 1.90853 | ||||||||
\(169\) | 5.67001 | 0.436155 | ||||||||
\(170\) | −10.8832 | −0.834704 | ||||||||
\(171\) | −5.71146 | −0.436766 | ||||||||
\(172\) | 63.6784 | 4.85543 | ||||||||
\(173\) | −16.3209 | −1.24086 | −0.620428 | − | 0.784263i | \(-0.713041\pi\) | ||||
−0.620428 | + | 0.784263i | \(0.713041\pi\) | |||||||
\(174\) | 12.3302 | 0.934747 | ||||||||
\(175\) | −1.38538 | −0.104725 | ||||||||
\(176\) | 25.1124 | 1.89292 | ||||||||
\(177\) | −14.8997 | −1.11993 | ||||||||
\(178\) | 16.8528 | 1.26317 | ||||||||
\(179\) | −10.1311 | −0.757238 | −0.378619 | − | 0.925553i | \(-0.623601\pi\) | ||||
−0.378619 | + | 0.925553i | \(0.623601\pi\) | |||||||
\(180\) | −6.32084 | −0.471128 | ||||||||
\(181\) | −9.58351 | −0.712337 | −0.356168 | − | 0.934422i | \(-0.615917\pi\) | ||||
−0.356168 | + | 0.934422i | \(0.615917\pi\) | |||||||
\(182\) | 16.1026 | 1.19361 | ||||||||
\(183\) | −2.83585 | −0.209632 | ||||||||
\(184\) | 7.03735 | 0.518800 | ||||||||
\(185\) | −3.61583 | −0.265841 | ||||||||
\(186\) | −4.52448 | −0.331751 | ||||||||
\(187\) | −7.84833 | −0.573926 | ||||||||
\(188\) | 36.2020 | 2.64030 | ||||||||
\(189\) | 5.09458 | 0.370576 | ||||||||
\(190\) | −12.7275 | −0.923349 | ||||||||
\(191\) | −19.6684 | −1.42316 | −0.711578 | − | 0.702607i | \(-0.752019\pi\) | ||||
−0.711578 | + | 0.702607i | \(0.752019\pi\) | |||||||
\(192\) | 42.9688 | 3.10100 | ||||||||
\(193\) | −6.06207 | −0.436357 | −0.218179 | − | 0.975909i | \(-0.570012\pi\) | ||||
−0.218179 | + | 0.975909i | \(0.570012\pi\) | |||||||
\(194\) | 31.0930 | 2.23235 | ||||||||
\(195\) | −8.86270 | −0.634671 | ||||||||
\(196\) | −26.6036 | −1.90026 | ||||||||
\(197\) | −3.67433 | −0.261785 | −0.130893 | − | 0.991397i | \(-0.541784\pi\) | ||||
−0.130893 | + | 0.991397i | \(0.541784\pi\) | |||||||
\(198\) | −6.29926 | −0.447669 | ||||||||
\(199\) | −8.24821 | −0.584700 | −0.292350 | − | 0.956311i | \(-0.594437\pi\) | ||||
−0.292350 | + | 0.956311i | \(0.594437\pi\) | |||||||
\(200\) | −8.70541 | −0.615566 | ||||||||
\(201\) | 29.3768 | 2.07208 | ||||||||
\(202\) | −26.5363 | −1.86709 | ||||||||
\(203\) | 3.09592 | 0.217291 | ||||||||
\(204\) | −43.4522 | −3.04226 | ||||||||
\(205\) | −5.58513 | −0.390082 | ||||||||
\(206\) | −43.7706 | −3.04964 | ||||||||
\(207\) | −0.975842 | −0.0678257 | ||||||||
\(208\) | 55.9352 | 3.87841 | ||||||||
\(209\) | −9.17831 | −0.634877 | ||||||||
\(210\) | −7.64396 | −0.527483 | ||||||||
\(211\) | −11.2412 | −0.773876 | −0.386938 | − | 0.922106i | \(-0.626467\pi\) | ||||
−0.386938 | + | 0.922106i | \(0.626467\pi\) | |||||||
\(212\) | −64.3801 | −4.42165 | ||||||||
\(213\) | −5.17806 | −0.354795 | ||||||||
\(214\) | −52.7721 | −3.60742 | ||||||||
\(215\) | −12.1612 | −0.829387 | ||||||||
\(216\) | 32.0131 | 2.17822 | ||||||||
\(217\) | −1.13603 | −0.0771187 | ||||||||
\(218\) | 17.9139 | 1.21328 | ||||||||
\(219\) | 8.84898 | 0.597959 | ||||||||
\(220\) | −10.1576 | −0.684825 | ||||||||
\(221\) | −17.4813 | −1.17592 | ||||||||
\(222\) | −19.9507 | −1.33900 | ||||||||
\(223\) | 20.7832 | 1.39175 | 0.695874 | − | 0.718164i | \(-0.255017\pi\) | ||||
0.695874 | + | 0.718164i | \(0.255017\pi\) | |||||||
\(224\) | 24.1227 | 1.61177 | ||||||||
\(225\) | 1.20715 | 0.0804763 | ||||||||
\(226\) | 9.78287 | 0.650747 | ||||||||
\(227\) | −8.26868 | −0.548812 | −0.274406 | − | 0.961614i | \(-0.588481\pi\) | ||||
−0.274406 | + | 0.961614i | \(0.588481\pi\) | |||||||
\(228\) | −50.8156 | −3.36534 | ||||||||
\(229\) | 8.19504 | 0.541544 | 0.270772 | − | 0.962644i | \(-0.412721\pi\) | ||||
0.270772 | + | 0.962644i | \(0.412721\pi\) | |||||||
\(230\) | −2.17458 | −0.143387 | ||||||||
\(231\) | −5.51237 | −0.362687 | ||||||||
\(232\) | 19.4540 | 1.27722 | ||||||||
\(233\) | 21.8603 | 1.43212 | 0.716058 | − | 0.698041i | \(-0.245945\pi\) | ||||
0.716058 | + | 0.698041i | \(0.245945\pi\) | |||||||
\(234\) | −14.0309 | −0.917231 | ||||||||
\(235\) | −6.91380 | −0.451006 | ||||||||
\(236\) | −38.0364 | −2.47596 | ||||||||
\(237\) | −19.8831 | −1.29155 | ||||||||
\(238\) | −15.0774 | −0.977323 | ||||||||
\(239\) | −20.2126 | −1.30744 | −0.653721 | − | 0.756736i | \(-0.726793\pi\) | ||||
−0.653721 | + | 0.756736i | \(0.726793\pi\) | |||||||
\(240\) | −26.5526 | −1.71396 | ||||||||
\(241\) | −9.00590 | −0.580121 | −0.290060 | − | 0.957008i | \(-0.593675\pi\) | ||||
−0.290060 | + | 0.957008i | \(0.593675\pi\) | |||||||
\(242\) | 19.4673 | 1.25140 | ||||||||
\(243\) | −11.8672 | −0.761280 | ||||||||
\(244\) | −7.23943 | −0.463457 | ||||||||
\(245\) | 5.08072 | 0.324595 | ||||||||
\(246\) | −30.8164 | −1.96478 | ||||||||
\(247\) | −20.4437 | −1.30080 | ||||||||
\(248\) | −7.13854 | −0.453297 | ||||||||
\(249\) | −14.8504 | −0.941109 | ||||||||
\(250\) | 2.69002 | 0.170132 | ||||||||
\(251\) | 6.34335 | 0.400389 | 0.200194 | − | 0.979756i | \(-0.435843\pi\) | ||||
0.200194 | + | 0.979756i | \(0.435843\pi\) | |||||||
\(252\) | −8.75679 | −0.551626 | ||||||||
\(253\) | −1.56818 | −0.0985904 | ||||||||
\(254\) | 40.8468 | 2.56296 | ||||||||
\(255\) | 8.29843 | 0.519668 | ||||||||
\(256\) | 16.0130 | 1.00082 | ||||||||
\(257\) | −18.9673 | −1.18315 | −0.591573 | − | 0.806252i | \(-0.701493\pi\) | ||||
−0.591573 | + | 0.806252i | \(0.701493\pi\) | |||||||
\(258\) | −67.1004 | −4.17749 | ||||||||
\(259\) | −5.00931 | −0.311264 | ||||||||
\(260\) | −22.6250 | −1.40314 | ||||||||
\(261\) | −2.69761 | −0.166978 | ||||||||
\(262\) | −12.1928 | −0.753275 | ||||||||
\(263\) | 14.8471 | 0.915513 | 0.457756 | − | 0.889078i | \(-0.348653\pi\) | ||||
0.457756 | + | 0.889078i | \(0.348653\pi\) | |||||||
\(264\) | −34.6384 | −2.13185 | ||||||||
\(265\) | 12.2952 | 0.755289 | ||||||||
\(266\) | −17.6324 | −1.08111 | ||||||||
\(267\) | −12.8502 | −0.786421 | ||||||||
\(268\) | 74.9939 | 4.58098 | ||||||||
\(269\) | 5.04501 | 0.307599 | 0.153800 | − | 0.988102i | \(-0.450849\pi\) | ||||
0.153800 | + | 0.988102i | \(0.450849\pi\) | |||||||
\(270\) | −9.89222 | −0.602022 | ||||||||
\(271\) | 15.0955 | 0.916986 | 0.458493 | − | 0.888698i | \(-0.348389\pi\) | ||||
0.458493 | + | 0.888698i | \(0.348389\pi\) | |||||||
\(272\) | −52.3739 | −3.17563 | ||||||||
\(273\) | −12.2782 | −0.743112 | ||||||||
\(274\) | 20.0665 | 1.21226 | ||||||||
\(275\) | 1.93988 | 0.116979 | ||||||||
\(276\) | −8.68219 | −0.522606 | ||||||||
\(277\) | 3.27710 | 0.196902 | 0.0984509 | − | 0.995142i | \(-0.468611\pi\) | ||||
0.0984509 | + | 0.995142i | \(0.468611\pi\) | |||||||
\(278\) | −28.9710 | −1.73756 | ||||||||
\(279\) | 0.989872 | 0.0592621 | ||||||||
\(280\) | −12.0603 | −0.720742 | ||||||||
\(281\) | 20.9460 | 1.24954 | 0.624768 | − | 0.780811i | \(-0.285194\pi\) | ||||
0.624768 | + | 0.780811i | \(0.285194\pi\) | |||||||
\(282\) | −38.1474 | −2.27165 | ||||||||
\(283\) | −7.20354 | −0.428206 | −0.214103 | − | 0.976811i | \(-0.568683\pi\) | ||||
−0.214103 | + | 0.976811i | \(0.568683\pi\) | |||||||
\(284\) | −13.2187 | −0.784386 | ||||||||
\(285\) | 9.70468 | 0.574856 | ||||||||
\(286\) | −22.5477 | −1.33327 | ||||||||
\(287\) | −7.73754 | −0.456732 | ||||||||
\(288\) | −21.0192 | −1.23857 | ||||||||
\(289\) | −0.631684 | −0.0371579 | ||||||||
\(290\) | −6.01139 | −0.353001 | ||||||||
\(291\) | −23.7084 | −1.38981 | ||||||||
\(292\) | 22.5899 | 1.32198 | ||||||||
\(293\) | 27.7493 | 1.62113 | 0.810564 | − | 0.585650i | \(-0.199161\pi\) | ||||
0.810564 | + | 0.585650i | \(0.199161\pi\) | |||||||
\(294\) | 28.0333 | 1.63493 | ||||||||
\(295\) | 7.26412 | 0.422934 | ||||||||
\(296\) | −31.4773 | −1.82958 | ||||||||
\(297\) | −7.13369 | −0.413938 | ||||||||
\(298\) | 31.4421 | 1.82139 | ||||||||
\(299\) | −3.49295 | −0.202002 | ||||||||
\(300\) | 10.7401 | 0.620081 | ||||||||
\(301\) | −16.8479 | −0.971098 | ||||||||
\(302\) | −20.7579 | −1.19448 | ||||||||
\(303\) | 20.2339 | 1.16241 | ||||||||
\(304\) | −61.2492 | −3.51288 | ||||||||
\(305\) | 1.38258 | 0.0791661 | ||||||||
\(306\) | 13.1376 | 0.751027 | ||||||||
\(307\) | 10.3046 | 0.588113 | 0.294057 | − | 0.955788i | \(-0.404995\pi\) | ||||
0.294057 | + | 0.955788i | \(0.404995\pi\) | |||||||
\(308\) | −14.0721 | −0.801835 | ||||||||
\(309\) | 33.3750 | 1.89864 | ||||||||
\(310\) | 2.20584 | 0.125284 | ||||||||
\(311\) | −15.3433 | −0.870038 | −0.435019 | − | 0.900421i | \(-0.643258\pi\) | ||||
−0.435019 | + | 0.900421i | \(0.643258\pi\) | |||||||
\(312\) | −77.1535 | −4.36795 | ||||||||
\(313\) | 10.1903 | 0.575988 | 0.287994 | − | 0.957632i | \(-0.407012\pi\) | ||||
0.287994 | + | 0.957632i | \(0.407012\pi\) | |||||||
\(314\) | 25.5936 | 1.44433 | ||||||||
\(315\) | 1.67236 | 0.0942267 | ||||||||
\(316\) | −50.7583 | −2.85538 | ||||||||
\(317\) | −13.4241 | −0.753970 | −0.376985 | − | 0.926219i | \(-0.623039\pi\) | ||||
−0.376985 | + | 0.926219i | \(0.623039\pi\) | |||||||
\(318\) | 67.8399 | 3.80427 | ||||||||
\(319\) | −4.33506 | −0.242717 | ||||||||
\(320\) | −20.9488 | −1.17107 | ||||||||
\(321\) | 40.2386 | 2.24590 | ||||||||
\(322\) | −3.01262 | −0.167887 | ||||||||
\(323\) | 19.1421 | 1.06509 | ||||||||
\(324\) | −58.4581 | −3.24767 | ||||||||
\(325\) | 4.32088 | 0.239679 | ||||||||
\(326\) | 33.8043 | 1.87225 | ||||||||
\(327\) | −13.6593 | −0.755362 | ||||||||
\(328\) | −48.6208 | −2.68464 | ||||||||
\(329\) | −9.57826 | −0.528066 | ||||||||
\(330\) | 10.7035 | 0.589206 | ||||||||
\(331\) | −13.8946 | −0.763717 | −0.381859 | − | 0.924221i | \(-0.624716\pi\) | ||||
−0.381859 | + | 0.924221i | \(0.624716\pi\) | |||||||
\(332\) | −37.9107 | −2.08062 | ||||||||
\(333\) | 4.36484 | 0.239192 | ||||||||
\(334\) | 0.0613269 | 0.00335566 | ||||||||
\(335\) | −14.3222 | −0.782507 | ||||||||
\(336\) | −36.7855 | −2.00681 | ||||||||
\(337\) | −28.0910 | −1.53022 | −0.765108 | − | 0.643902i | \(-0.777314\pi\) | ||||
−0.765108 | + | 0.643902i | \(0.777314\pi\) | |||||||
\(338\) | −15.2524 | −0.829623 | ||||||||
\(339\) | −7.45941 | −0.405140 | ||||||||
\(340\) | 21.1845 | 1.14889 | ||||||||
\(341\) | 1.59072 | 0.0861425 | ||||||||
\(342\) | 15.3639 | 0.830786 | ||||||||
\(343\) | 16.7364 | 0.903681 | ||||||||
\(344\) | −105.868 | −5.70804 | ||||||||
\(345\) | 1.65811 | 0.0892697 | ||||||||
\(346\) | 43.9035 | 2.36027 | ||||||||
\(347\) | −15.3942 | −0.826404 | −0.413202 | − | 0.910639i | \(-0.635590\pi\) | ||||
−0.413202 | + | 0.910639i | \(0.635590\pi\) | |||||||
\(348\) | −24.0010 | −1.28659 | ||||||||
\(349\) | 30.3553 | 1.62488 | 0.812440 | − | 0.583045i | \(-0.198139\pi\) | ||||
0.812440 | + | 0.583045i | \(0.198139\pi\) | |||||||
\(350\) | 3.72670 | 0.199201 | ||||||||
\(351\) | −15.8895 | −0.848121 | ||||||||
\(352\) | −33.7778 | −1.80036 | ||||||||
\(353\) | −24.0981 | −1.28261 | −0.641306 | − | 0.767285i | \(-0.721607\pi\) | ||||
−0.641306 | + | 0.767285i | \(0.721607\pi\) | |||||||
\(354\) | 40.0804 | 2.13025 | ||||||||
\(355\) | 2.52449 | 0.133986 | ||||||||
\(356\) | −32.8044 | −1.73863 | ||||||||
\(357\) | 11.4965 | 0.608459 | ||||||||
\(358\) | 27.2530 | 1.44036 | ||||||||
\(359\) | −36.3442 | −1.91817 | −0.959086 | − | 0.283113i | \(-0.908633\pi\) | ||||
−0.959086 | + | 0.283113i | \(0.908633\pi\) | |||||||
\(360\) | 10.5087 | 0.553857 | ||||||||
\(361\) | 3.38592 | 0.178206 | ||||||||
\(362\) | 25.7798 | 1.35496 | ||||||||
\(363\) | −14.8438 | −0.779096 | ||||||||
\(364\) | −31.3442 | −1.64288 | ||||||||
\(365\) | −4.31419 | −0.225815 | ||||||||
\(366\) | 7.62847 | 0.398747 | ||||||||
\(367\) | −18.3927 | −0.960090 | −0.480045 | − | 0.877244i | \(-0.659380\pi\) | ||||
−0.480045 | + | 0.877244i | \(0.659380\pi\) | |||||||
\(368\) | −10.4648 | −0.545518 | ||||||||
\(369\) | 6.74206 | 0.350978 | ||||||||
\(370\) | 9.72666 | 0.505665 | ||||||||
\(371\) | 17.0336 | 0.884340 | ||||||||
\(372\) | 8.80702 | 0.456623 | ||||||||
\(373\) | −14.1950 | −0.734987 | −0.367493 | − | 0.930026i | \(-0.619784\pi\) | ||||
−0.367493 | + | 0.930026i | \(0.619784\pi\) | |||||||
\(374\) | 21.1121 | 1.09168 | ||||||||
\(375\) | −2.05113 | −0.105920 | ||||||||
\(376\) | −60.1875 | −3.10393 | ||||||||
\(377\) | −9.65589 | −0.497303 | ||||||||
\(378\) | −13.7045 | −0.704884 | ||||||||
\(379\) | 16.5377 | 0.849482 | 0.424741 | − | 0.905315i | \(-0.360365\pi\) | ||||
0.424741 | + | 0.905315i | \(0.360365\pi\) | |||||||
\(380\) | 24.7744 | 1.27090 | ||||||||
\(381\) | −31.1456 | −1.59564 | ||||||||
\(382\) | 52.9083 | 2.70703 | ||||||||
\(383\) | −23.1431 | −1.18256 | −0.591279 | − | 0.806467i | \(-0.701377\pi\) | ||||
−0.591279 | + | 0.806467i | \(0.701377\pi\) | |||||||
\(384\) | −44.1567 | −2.25336 | ||||||||
\(385\) | 2.68748 | 0.136967 | ||||||||
\(386\) | 16.3071 | 0.830008 | ||||||||
\(387\) | 14.6803 | 0.746243 | ||||||||
\(388\) | −60.5235 | −3.07261 | ||||||||
\(389\) | −14.7277 | −0.746722 | −0.373361 | − | 0.927686i | \(-0.621795\pi\) | ||||
−0.373361 | + | 0.927686i | \(0.621795\pi\) | |||||||
\(390\) | 23.8408 | 1.20723 | ||||||||
\(391\) | 3.27056 | 0.165399 | ||||||||
\(392\) | 44.2297 | 2.23394 | ||||||||
\(393\) | 9.29700 | 0.468972 | ||||||||
\(394\) | 9.88402 | 0.497950 | ||||||||
\(395\) | 9.69374 | 0.487745 | ||||||||
\(396\) | 12.2617 | 0.616173 | ||||||||
\(397\) | −12.3576 | −0.620209 | −0.310104 | − | 0.950703i | \(-0.600364\pi\) | ||||
−0.310104 | + | 0.950703i | \(0.600364\pi\) | |||||||
\(398\) | 22.1878 | 1.11217 | ||||||||
\(399\) | 13.4447 | 0.673077 | ||||||||
\(400\) | 12.9453 | 0.647266 | ||||||||
\(401\) | −17.7148 | −0.884635 | −0.442317 | − | 0.896859i | \(-0.645843\pi\) | ||||
−0.442317 | + | 0.896859i | \(0.645843\pi\) | |||||||
\(402\) | −79.0241 | −3.94136 | ||||||||
\(403\) | 3.54317 | 0.176498 | ||||||||
\(404\) | 51.6537 | 2.56987 | ||||||||
\(405\) | 11.1642 | 0.554755 | ||||||||
\(406\) | −8.32807 | −0.413315 | ||||||||
\(407\) | 7.01429 | 0.347685 | ||||||||
\(408\) | 72.2412 | 3.57647 | ||||||||
\(409\) | −28.8978 | −1.42890 | −0.714451 | − | 0.699685i | \(-0.753324\pi\) | ||||
−0.714451 | + | 0.699685i | \(0.753324\pi\) | |||||||
\(410\) | 15.0241 | 0.741987 | ||||||||
\(411\) | −15.3007 | −0.754727 | ||||||||
\(412\) | 85.2007 | 4.19754 | ||||||||
\(413\) | 10.0636 | 0.495197 | ||||||||
\(414\) | 2.62503 | 0.129013 | ||||||||
\(415\) | 7.24012 | 0.355403 | ||||||||
\(416\) | −75.2366 | −3.68878 | ||||||||
\(417\) | 22.0903 | 1.08177 | ||||||||
\(418\) | 24.6898 | 1.20762 | ||||||||
\(419\) | −25.9768 | −1.26905 | −0.634524 | − | 0.772903i | \(-0.718804\pi\) | ||||
−0.634524 | + | 0.772903i | \(0.718804\pi\) | |||||||
\(420\) | 14.8792 | 0.726030 | ||||||||
\(421\) | −1.28000 | −0.0623836 | −0.0311918 | − | 0.999513i | \(-0.509930\pi\) | ||||
−0.0311918 | + | 0.999513i | \(0.509930\pi\) | |||||||
\(422\) | 30.2390 | 1.47201 | ||||||||
\(423\) | 8.34596 | 0.405794 | ||||||||
\(424\) | 107.035 | 5.19808 | ||||||||
\(425\) | −4.04578 | −0.196249 | ||||||||
\(426\) | 13.9291 | 0.674866 | ||||||||
\(427\) | 1.91540 | 0.0926925 | ||||||||
\(428\) | 102.722 | 4.96527 | ||||||||
\(429\) | 17.1926 | 0.830066 | ||||||||
\(430\) | 32.7138 | 1.57760 | ||||||||
\(431\) | −13.7996 | −0.664705 | −0.332352 | − | 0.943155i | \(-0.607842\pi\) | ||||
−0.332352 | + | 0.943155i | \(0.607842\pi\) | |||||||
\(432\) | −47.6049 | −2.29039 | ||||||||
\(433\) | 25.2891 | 1.21532 | 0.607658 | − | 0.794199i | \(-0.292109\pi\) | ||||
0.607658 | + | 0.794199i | \(0.292109\pi\) | |||||||
\(434\) | 3.05594 | 0.146690 | ||||||||
\(435\) | 4.58367 | 0.219770 | ||||||||
\(436\) | −34.8699 | −1.66997 | ||||||||
\(437\) | 3.82479 | 0.182964 | ||||||||
\(438\) | −23.8039 | −1.13739 | ||||||||
\(439\) | 32.8565 | 1.56815 | 0.784077 | − | 0.620663i | \(-0.213137\pi\) | ||||
0.784077 | + | 0.620663i | \(0.213137\pi\) | |||||||
\(440\) | 16.8875 | 0.805078 | ||||||||
\(441\) | −6.13316 | −0.292055 | ||||||||
\(442\) | 47.0251 | 2.23675 | ||||||||
\(443\) | −1.52897 | −0.0726437 | −0.0363219 | − | 0.999340i | \(-0.511564\pi\) | ||||
−0.0363219 | + | 0.999340i | \(0.511564\pi\) | |||||||
\(444\) | 38.8345 | 1.84300 | ||||||||
\(445\) | 6.26494 | 0.296987 | ||||||||
\(446\) | −55.9072 | −2.64728 | ||||||||
\(447\) | −23.9745 | −1.13396 | ||||||||
\(448\) | −29.0221 | −1.37117 | ||||||||
\(449\) | 10.2547 | 0.483950 | 0.241975 | − | 0.970282i | \(-0.422205\pi\) | ||||
0.241975 | + | 0.970282i | \(0.422205\pi\) | |||||||
\(450\) | −3.24724 | −0.153076 | ||||||||
\(451\) | 10.8345 | 0.510176 | ||||||||
\(452\) | −19.0426 | −0.895689 | ||||||||
\(453\) | 15.8279 | 0.743658 | ||||||||
\(454\) | 22.2429 | 1.04391 | ||||||||
\(455\) | 5.98607 | 0.280631 | ||||||||
\(456\) | 84.4833 | 3.95629 | ||||||||
\(457\) | −13.4329 | −0.628363 | −0.314182 | − | 0.949363i | \(-0.601730\pi\) | ||||
−0.314182 | + | 0.949363i | \(0.601730\pi\) | |||||||
\(458\) | −22.0448 | −1.03009 | ||||||||
\(459\) | 14.8779 | 0.694440 | ||||||||
\(460\) | 4.23287 | 0.197359 | ||||||||
\(461\) | 7.91296 | 0.368543 | 0.184272 | − | 0.982875i | \(-0.441007\pi\) | ||||
0.184272 | + | 0.982875i | \(0.441007\pi\) | |||||||
\(462\) | 14.8284 | 0.689878 | ||||||||
\(463\) | 38.0903 | 1.77021 | 0.885103 | − | 0.465395i | \(-0.154088\pi\) | ||||
0.885103 | + | 0.465395i | \(0.154088\pi\) | |||||||
\(464\) | −28.9290 | −1.34299 | ||||||||
\(465\) | −1.68195 | −0.0779986 | ||||||||
\(466\) | −58.8046 | −2.72407 | ||||||||
\(467\) | 2.19222 | 0.101444 | 0.0507220 | − | 0.998713i | \(-0.483848\pi\) | ||||
0.0507220 | + | 0.998713i | \(0.483848\pi\) | |||||||
\(468\) | 27.3116 | 1.26248 | ||||||||
\(469\) | −19.8418 | −0.916208 | ||||||||
\(470\) | 18.5982 | 0.857873 | ||||||||
\(471\) | −19.5151 | −0.899207 | ||||||||
\(472\) | 63.2372 | 2.91073 | ||||||||
\(473\) | 23.5913 | 1.08473 | ||||||||
\(474\) | 53.4860 | 2.45669 | ||||||||
\(475\) | −4.73138 | −0.217090 | ||||||||
\(476\) | 29.3486 | 1.34519 | ||||||||
\(477\) | −14.8421 | −0.679574 | ||||||||
\(478\) | 54.3722 | 2.48692 | ||||||||
\(479\) | 1.42175 | 0.0649615 | 0.0324807 | − | 0.999472i | \(-0.489659\pi\) | ||||
0.0324807 | + | 0.999472i | \(0.489659\pi\) | |||||||
\(480\) | 35.7150 | 1.63016 | ||||||||
\(481\) | 15.6236 | 0.712374 | ||||||||
\(482\) | 24.2260 | 1.10347 | ||||||||
\(483\) | 2.29712 | 0.104522 | ||||||||
\(484\) | −37.8936 | −1.72244 | ||||||||
\(485\) | 11.5587 | 0.524853 | ||||||||
\(486\) | 31.9229 | 1.44805 | ||||||||
\(487\) | −13.7825 | −0.624546 | −0.312273 | − | 0.949992i | \(-0.601090\pi\) | ||||
−0.312273 | + | 0.949992i | \(0.601090\pi\) | |||||||
\(488\) | 12.0359 | 0.544839 | ||||||||
\(489\) | −25.7757 | −1.16562 | ||||||||
\(490\) | −13.6672 | −0.617422 | ||||||||
\(491\) | −24.7229 | −1.11573 | −0.557866 | − | 0.829931i | \(-0.688380\pi\) | ||||
−0.557866 | + | 0.829931i | \(0.688380\pi\) | |||||||
\(492\) | 59.9850 | 2.70433 | ||||||||
\(493\) | 9.04111 | 0.407191 | ||||||||
\(494\) | 54.9939 | 2.47429 | ||||||||
\(495\) | −2.34172 | −0.105252 | ||||||||
\(496\) | 10.6153 | 0.476642 | ||||||||
\(497\) | 3.49738 | 0.156879 | ||||||||
\(498\) | 39.9479 | 1.79011 | ||||||||
\(499\) | 30.2450 | 1.35395 | 0.676977 | − | 0.736005i | \(-0.263290\pi\) | ||||
0.676977 | + | 0.736005i | \(0.263290\pi\) | |||||||
\(500\) | −5.23619 | −0.234170 | ||||||||
\(501\) | −0.0467616 | −0.00208916 | ||||||||
\(502\) | −17.0637 | −0.761592 | ||||||||
\(503\) | 14.4914 | 0.646138 | 0.323069 | − | 0.946375i | \(-0.395285\pi\) | ||||
0.323069 | + | 0.946375i | \(0.395285\pi\) | |||||||
\(504\) | 14.5586 | 0.648490 | ||||||||
\(505\) | −9.86474 | −0.438975 | ||||||||
\(506\) | 4.21842 | 0.187532 | ||||||||
\(507\) | 11.6299 | 0.516504 | ||||||||
\(508\) | −79.5094 | −3.52766 | ||||||||
\(509\) | −14.3250 | −0.634944 | −0.317472 | − | 0.948268i | \(-0.602834\pi\) | ||||
−0.317472 | + | 0.948268i | \(0.602834\pi\) | |||||||
\(510\) | −22.3229 | −0.988475 | ||||||||
\(511\) | −5.97681 | −0.264398 | ||||||||
\(512\) | −0.0193966 | −0.000857216 0 | ||||||||
\(513\) | 17.3991 | 0.768188 | ||||||||
\(514\) | 51.0223 | 2.25050 | ||||||||
\(515\) | −16.2715 | −0.717008 | ||||||||
\(516\) | 130.613 | 5.74991 | ||||||||
\(517\) | 13.4119 | 0.589857 | ||||||||
\(518\) | 13.4751 | 0.592064 | ||||||||
\(519\) | −33.4764 | −1.46945 | ||||||||
\(520\) | 37.6151 | 1.64953 | ||||||||
\(521\) | −28.4226 | −1.24522 | −0.622609 | − | 0.782533i | \(-0.713927\pi\) | ||||
−0.622609 | + | 0.782533i | \(0.713927\pi\) | |||||||
\(522\) | 7.25662 | 0.317614 | ||||||||
\(523\) | −6.98975 | −0.305640 | −0.152820 | − | 0.988254i | \(-0.548836\pi\) | ||||
−0.152820 | + | 0.988254i | \(0.548836\pi\) | |||||||
\(524\) | 23.7337 | 1.03681 | ||||||||
\(525\) | −2.84160 | −0.124018 | ||||||||
\(526\) | −39.9390 | −1.74142 | ||||||||
\(527\) | −3.31758 | −0.144516 | ||||||||
\(528\) | 51.5088 | 2.24163 | ||||||||
\(529\) | −22.3465 | −0.971587 | ||||||||
\(530\) | −33.0744 | −1.43666 | ||||||||
\(531\) | −8.76885 | −0.380536 | ||||||||
\(532\) | 34.3220 | 1.48805 | ||||||||
\(533\) | 24.1327 | 1.04530 | ||||||||
\(534\) | 34.5673 | 1.49587 | ||||||||
\(535\) | −19.6177 | −0.848149 | ||||||||
\(536\) | −124.681 | −5.38539 | ||||||||
\(537\) | −20.7803 | −0.896737 | ||||||||
\(538\) | −13.5712 | −0.585094 | ||||||||
\(539\) | −9.85598 | −0.424527 | ||||||||
\(540\) | 19.2555 | 0.828624 | ||||||||
\(541\) | −10.6041 | −0.455905 | −0.227952 | − | 0.973672i | \(-0.573203\pi\) | ||||
−0.227952 | + | 0.973672i | \(0.573203\pi\) | |||||||
\(542\) | −40.6071 | −1.74423 | ||||||||
\(543\) | −19.6571 | −0.843565 | ||||||||
\(544\) | 70.4464 | 3.02036 | ||||||||
\(545\) | 6.65940 | 0.285257 | ||||||||
\(546\) | 33.0286 | 1.41350 | ||||||||
\(547\) | −12.9955 | −0.555646 | −0.277823 | − | 0.960632i | \(-0.589613\pi\) | ||||
−0.277823 | + | 0.960632i | \(0.589613\pi\) | |||||||
\(548\) | −39.0600 | −1.66856 | ||||||||
\(549\) | −1.66897 | −0.0712299 | ||||||||
\(550\) | −5.21831 | −0.222510 | ||||||||
\(551\) | 10.5732 | 0.450434 | ||||||||
\(552\) | 14.4345 | 0.614375 | ||||||||
\(553\) | 13.4295 | 0.571082 | ||||||||
\(554\) | −8.81545 | −0.374533 | ||||||||
\(555\) | −7.41655 | −0.314815 | ||||||||
\(556\) | 56.3928 | 2.39159 | ||||||||
\(557\) | 38.5264 | 1.63242 | 0.816208 | − | 0.577758i | \(-0.196072\pi\) | ||||
0.816208 | + | 0.577758i | \(0.196072\pi\) | |||||||
\(558\) | −2.66277 | −0.112724 | ||||||||
\(559\) | 52.5471 | 2.22251 | ||||||||
\(560\) | 17.9342 | 0.757860 | ||||||||
\(561\) | −16.0980 | −0.679656 | ||||||||
\(562\) | −56.3452 | −2.37678 | ||||||||
\(563\) | −33.0366 | −1.39233 | −0.696164 | − | 0.717883i | \(-0.745111\pi\) | ||||
−0.696164 | + | 0.717883i | \(0.745111\pi\) | |||||||
\(564\) | 74.2551 | 3.12670 | ||||||||
\(565\) | 3.63673 | 0.152998 | ||||||||
\(566\) | 19.3776 | 0.814503 | ||||||||
\(567\) | 15.4667 | 0.649542 | ||||||||
\(568\) | 21.9767 | 0.922123 | ||||||||
\(569\) | 19.0304 | 0.797796 | 0.398898 | − | 0.916995i | \(-0.369393\pi\) | ||||
0.398898 | + | 0.916995i | \(0.369393\pi\) | |||||||
\(570\) | −26.1058 | −1.09345 | ||||||||
\(571\) | −10.8712 | −0.454945 | −0.227472 | − | 0.973785i | \(-0.573046\pi\) | ||||
−0.227472 | + | 0.973785i | \(0.573046\pi\) | |||||||
\(572\) | 43.8897 | 1.83512 | ||||||||
\(573\) | −40.3425 | −1.68533 | ||||||||
\(574\) | 20.8141 | 0.868764 | ||||||||
\(575\) | −0.808388 | −0.0337121 | ||||||||
\(576\) | 25.2882 | 1.05368 | ||||||||
\(577\) | 17.3881 | 0.723877 | 0.361938 | − | 0.932202i | \(-0.382115\pi\) | ||||
0.361938 | + | 0.932202i | \(0.382115\pi\) | |||||||
\(578\) | 1.69924 | 0.0706791 | ||||||||
\(579\) | −12.4341 | −0.516744 | ||||||||
\(580\) | 11.7013 | 0.485872 | ||||||||
\(581\) | 10.0303 | 0.416128 | ||||||||
\(582\) | 63.7760 | 2.64360 | ||||||||
\(583\) | −23.8513 | −0.987818 | ||||||||
\(584\) | −37.5568 | −1.55411 | ||||||||
\(585\) | −5.21593 | −0.215652 | ||||||||
\(586\) | −74.6460 | −3.08360 | ||||||||
\(587\) | 21.0663 | 0.869501 | 0.434750 | − | 0.900551i | \(-0.356837\pi\) | ||||
0.434750 | + | 0.900551i | \(0.356837\pi\) | |||||||
\(588\) | −54.5675 | −2.25033 | ||||||||
\(589\) | −3.87978 | −0.159864 | ||||||||
\(590\) | −19.5406 | −0.804475 | ||||||||
\(591\) | −7.53654 | −0.310012 | ||||||||
\(592\) | 46.8082 | 1.92380 | ||||||||
\(593\) | 35.0428 | 1.43904 | 0.719518 | − | 0.694473i | \(-0.244363\pi\) | ||||
0.719518 | + | 0.694473i | \(0.244363\pi\) | |||||||
\(594\) | 19.1897 | 0.787364 | ||||||||
\(595\) | −5.60495 | −0.229781 | ||||||||
\(596\) | −61.2028 | −2.50697 | ||||||||
\(597\) | −16.9182 | −0.692414 | ||||||||
\(598\) | 9.39609 | 0.384235 | ||||||||
\(599\) | −35.8561 | −1.46504 | −0.732520 | − | 0.680746i | \(-0.761656\pi\) | ||||
−0.732520 | + | 0.680746i | \(0.761656\pi\) | |||||||
\(600\) | −17.8560 | −0.728966 | ||||||||
\(601\) | −7.41619 | −0.302513 | −0.151256 | − | 0.988495i | \(-0.548332\pi\) | ||||
−0.151256 | + | 0.988495i | \(0.548332\pi\) | |||||||
\(602\) | 45.3212 | 1.84715 | ||||||||
\(603\) | 17.2890 | 0.704063 | ||||||||
\(604\) | 40.4058 | 1.64409 | ||||||||
\(605\) | 7.23686 | 0.294220 | ||||||||
\(606\) | −54.4295 | −2.21105 | ||||||||
\(607\) | −3.82881 | −0.155407 | −0.0777034 | − | 0.996977i | \(-0.524759\pi\) | ||||
−0.0777034 | + | 0.996977i | \(0.524759\pi\) | |||||||
\(608\) | 82.3843 | 3.34112 | ||||||||
\(609\) | 6.35014 | 0.257321 | ||||||||
\(610\) | −3.71915 | −0.150584 | ||||||||
\(611\) | 29.8737 | 1.20856 | ||||||||
\(612\) | −25.5727 | −1.03372 | ||||||||
\(613\) | −40.0343 | −1.61697 | −0.808485 | − | 0.588517i | \(-0.799712\pi\) | ||||
−0.808485 | + | 0.588517i | \(0.799712\pi\) | |||||||
\(614\) | −27.7195 | −1.11867 | ||||||||
\(615\) | −11.4558 | −0.461944 | ||||||||
\(616\) | 23.3956 | 0.942636 | ||||||||
\(617\) | −13.6021 | −0.547599 | −0.273799 | − | 0.961787i | \(-0.588280\pi\) | ||||
−0.273799 | + | 0.961787i | \(0.588280\pi\) | |||||||
\(618\) | −89.7793 | −3.61145 | ||||||||
\(619\) | 17.5173 | 0.704082 | 0.352041 | − | 0.935985i | \(-0.385488\pi\) | ||||
0.352041 | + | 0.935985i | \(0.385488\pi\) | |||||||
\(620\) | −4.29374 | −0.172441 | ||||||||
\(621\) | 2.97275 | 0.119292 | ||||||||
\(622\) | 41.2737 | 1.65492 | ||||||||
\(623\) | 8.67934 | 0.347730 | ||||||||
\(624\) | 114.731 | 4.59290 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −27.4120 | −1.09560 | ||||||||
\(627\) | −18.8259 | −0.751835 | ||||||||
\(628\) | −49.8187 | −1.98798 | ||||||||
\(629\) | −14.6289 | −0.583291 | ||||||||
\(630\) | −4.49867 | −0.179231 | ||||||||
\(631\) | 10.2056 | 0.406278 | 0.203139 | − | 0.979150i | \(-0.434886\pi\) | ||||
0.203139 | + | 0.979150i | \(0.434886\pi\) | |||||||
\(632\) | 84.3880 | 3.35677 | ||||||||
\(633\) | −23.0572 | −0.916441 | ||||||||
\(634\) | 36.1109 | 1.43415 | ||||||||
\(635\) | 15.1846 | 0.602582 | ||||||||
\(636\) | −132.052 | −5.23621 | ||||||||
\(637\) | −21.9532 | −0.869816 | ||||||||
\(638\) | 11.6614 | 0.461678 | ||||||||
\(639\) | −3.04743 | −0.120554 | ||||||||
\(640\) | 21.5280 | 0.850968 | ||||||||
\(641\) | 33.8750 | 1.33798 | 0.668990 | − | 0.743271i | \(-0.266727\pi\) | ||||
0.668990 | + | 0.743271i | \(0.266727\pi\) | |||||||
\(642\) | −108.243 | −4.27199 | ||||||||
\(643\) | −40.9036 | −1.61308 | −0.806539 | − | 0.591180i | \(-0.798662\pi\) | ||||
−0.806539 | + | 0.591180i | \(0.798662\pi\) | |||||||
\(644\) | 5.86415 | 0.231080 | ||||||||
\(645\) | −24.9442 | −0.982178 | ||||||||
\(646\) | −51.4926 | −2.02595 | ||||||||
\(647\) | 7.99359 | 0.314261 | 0.157130 | − | 0.987578i | \(-0.449776\pi\) | ||||
0.157130 | + | 0.987578i | \(0.449776\pi\) | |||||||
\(648\) | 97.1893 | 3.81796 | ||||||||
\(649\) | −14.0915 | −0.553141 | ||||||||
\(650\) | −11.6232 | −0.455901 | ||||||||
\(651\) | −2.33015 | −0.0913256 | ||||||||
\(652\) | −65.8011 | −2.57697 | ||||||||
\(653\) | −18.6089 | −0.728224 | −0.364112 | − | 0.931355i | \(-0.618628\pi\) | ||||
−0.364112 | + | 0.931355i | \(0.618628\pi\) | |||||||
\(654\) | 36.7438 | 1.43680 | ||||||||
\(655\) | −4.53262 | −0.177104 | ||||||||
\(656\) | 72.3013 | 2.82289 | ||||||||
\(657\) | 5.20785 | 0.203178 | ||||||||
\(658\) | 25.7657 | 1.00445 | ||||||||
\(659\) | −18.3532 | −0.714941 | −0.357470 | − | 0.933924i | \(-0.616361\pi\) | ||||
−0.357470 | + | 0.933924i | \(0.616361\pi\) | |||||||
\(660\) | −20.8346 | −0.810984 | ||||||||
\(661\) | 8.22147 | 0.319778 | 0.159889 | − | 0.987135i | \(-0.448886\pi\) | ||||
0.159889 | + | 0.987135i | \(0.448886\pi\) | |||||||
\(662\) | 37.3768 | 1.45269 | ||||||||
\(663\) | −35.8565 | −1.39255 | ||||||||
\(664\) | 63.0282 | 2.44597 | ||||||||
\(665\) | −6.55477 | −0.254183 | ||||||||
\(666\) | −11.7415 | −0.454973 | ||||||||
\(667\) | 1.80651 | 0.0699482 | ||||||||
\(668\) | −0.119375 | −0.00461874 | ||||||||
\(669\) | 42.6292 | 1.64814 | ||||||||
\(670\) | 38.5270 | 1.48843 | ||||||||
\(671\) | −2.68203 | −0.103539 | ||||||||
\(672\) | 49.4789 | 1.90869 | ||||||||
\(673\) | 45.9897 | 1.77277 | 0.886387 | − | 0.462945i | \(-0.153207\pi\) | ||||
0.886387 | + | 0.462945i | \(0.153207\pi\) | |||||||
\(674\) | 75.5653 | 2.91067 | ||||||||
\(675\) | −3.67738 | −0.141543 | ||||||||
\(676\) | 29.6893 | 1.14190 | ||||||||
\(677\) | −7.63041 | −0.293261 | −0.146630 | − | 0.989191i | \(-0.546843\pi\) | ||||
−0.146630 | + | 0.989191i | \(0.546843\pi\) | |||||||
\(678\) | 20.0660 | 0.770628 | ||||||||
\(679\) | 16.0132 | 0.614530 | ||||||||
\(680\) | −35.2202 | −1.35063 | ||||||||
\(681\) | −16.9602 | −0.649915 | ||||||||
\(682\) | −4.27907 | −0.163854 | ||||||||
\(683\) | −13.7534 | −0.526260 | −0.263130 | − | 0.964760i | \(-0.584755\pi\) | ||||
−0.263130 | + | 0.964760i | \(0.584755\pi\) | |||||||
\(684\) | −29.9063 | −1.14350 | ||||||||
\(685\) | 7.45963 | 0.285018 | ||||||||
\(686\) | −45.0212 | −1.71892 | ||||||||
\(687\) | 16.8091 | 0.641308 | ||||||||
\(688\) | 157.431 | 6.00199 | ||||||||
\(689\) | −53.1262 | −2.02395 | ||||||||
\(690\) | −4.46035 | −0.169803 | ||||||||
\(691\) | 49.5079 | 1.88337 | 0.941685 | − | 0.336497i | \(-0.109242\pi\) | ||||
0.941685 | + | 0.336497i | \(0.109242\pi\) | |||||||
\(692\) | −85.4594 | −3.24868 | ||||||||
\(693\) | −3.24418 | −0.123236 | ||||||||
\(694\) | 41.4107 | 1.57193 | ||||||||
\(695\) | −10.7698 | −0.408522 | ||||||||
\(696\) | 39.9028 | 1.51251 | ||||||||
\(697\) | −22.5962 | −0.855891 | ||||||||
\(698\) | −81.6562 | −3.09073 | ||||||||
\(699\) | 44.8384 | 1.69594 | ||||||||
\(700\) | −7.25413 | −0.274180 | ||||||||
\(701\) | −42.3425 | −1.59925 | −0.799627 | − | 0.600497i | \(-0.794970\pi\) | ||||
−0.799627 | + | 0.600497i | \(0.794970\pi\) | |||||||
\(702\) | 42.7431 | 1.61324 | ||||||||
\(703\) | −17.1079 | −0.645236 | ||||||||
\(704\) | 40.6382 | 1.53161 | ||||||||
\(705\) | −14.1811 | −0.534092 | ||||||||
\(706\) | 64.8243 | 2.43969 | ||||||||
\(707\) | −13.6664 | −0.513979 | ||||||||
\(708\) | −78.0176 | −2.93208 | ||||||||
\(709\) | −0.135807 | −0.00510033 | −0.00255017 | − | 0.999997i | \(-0.500812\pi\) | ||||
−0.00255017 | + | 0.999997i | \(0.500812\pi\) | |||||||
\(710\) | −6.79092 | −0.254859 | ||||||||
\(711\) | −11.7017 | −0.438850 | ||||||||
\(712\) | 54.5389 | 2.04393 | ||||||||
\(713\) | −0.662887 | −0.0248253 | ||||||||
\(714\) | −30.9258 | −1.15737 | ||||||||
\(715\) | −8.38199 | −0.313469 | ||||||||
\(716\) | −53.0486 | −1.98252 | ||||||||
\(717\) | −41.4587 | −1.54830 | ||||||||
\(718\) | 97.7665 | 3.64861 | ||||||||
\(719\) | −32.2138 | −1.20137 | −0.600686 | − | 0.799485i | \(-0.705106\pi\) | ||||
−0.600686 | + | 0.799485i | \(0.705106\pi\) | |||||||
\(720\) | −15.6269 | −0.582380 | ||||||||
\(721\) | −22.5423 | −0.839517 | ||||||||
\(722\) | −9.10819 | −0.338972 | ||||||||
\(723\) | −18.4723 | −0.686992 | ||||||||
\(724\) | −50.1811 | −1.86497 | ||||||||
\(725\) | −2.23470 | −0.0829948 | ||||||||
\(726\) | 39.9300 | 1.48194 | ||||||||
\(727\) | −14.0276 | −0.520253 | −0.260127 | − | 0.965575i | \(-0.583764\pi\) | ||||
−0.260127 | + | 0.965575i | \(0.583764\pi\) | |||||||
\(728\) | 52.1112 | 1.93137 | ||||||||
\(729\) | 9.15155 | 0.338946 | ||||||||
\(730\) | 11.6052 | 0.429529 | ||||||||
\(731\) | −49.2015 | −1.81978 | ||||||||
\(732\) | −14.8490 | −0.548836 | ||||||||
\(733\) | 26.8081 | 0.990179 | 0.495089 | − | 0.868842i | \(-0.335135\pi\) | ||||
0.495089 | + | 0.868842i | \(0.335135\pi\) | |||||||
\(734\) | 49.4766 | 1.82622 | ||||||||
\(735\) | 10.4212 | 0.384393 | ||||||||
\(736\) | 14.0759 | 0.518845 | ||||||||
\(737\) | 27.7834 | 1.02342 | ||||||||
\(738\) | −18.1363 | −0.667605 | ||||||||
\(739\) | 13.2063 | 0.485801 | 0.242901 | − | 0.970051i | \(-0.421901\pi\) | ||||
0.242901 | + | 0.970051i | \(0.421901\pi\) | |||||||
\(740\) | −18.9332 | −0.695998 | ||||||||
\(741\) | −41.9328 | −1.54044 | ||||||||
\(742\) | −45.8206 | −1.68213 | ||||||||
\(743\) | 17.8277 | 0.654034 | 0.327017 | − | 0.945019i | \(-0.393957\pi\) | ||||
0.327017 | + | 0.945019i | \(0.393957\pi\) | |||||||
\(744\) | −14.6421 | −0.536805 | ||||||||
\(745\) | 11.6884 | 0.428231 | ||||||||
\(746\) | 38.1847 | 1.39804 | ||||||||
\(747\) | −8.73987 | −0.319775 | ||||||||
\(748\) | −41.0953 | −1.50259 | ||||||||
\(749\) | −27.1781 | −0.993066 | ||||||||
\(750\) | 5.51758 | 0.201474 | ||||||||
\(751\) | −47.5220 | −1.73410 | −0.867051 | − | 0.498220i | \(-0.833987\pi\) | ||||
−0.867051 | + | 0.498220i | \(0.833987\pi\) | |||||||
\(752\) | 89.5014 | 3.26378 | ||||||||
\(753\) | 13.0111 | 0.474149 | ||||||||
\(754\) | 25.9745 | 0.945935 | ||||||||
\(755\) | −7.71664 | −0.280837 | ||||||||
\(756\) | 26.6762 | 0.970205 | ||||||||
\(757\) | 51.7824 | 1.88206 | 0.941032 | − | 0.338317i | \(-0.109858\pi\) | ||||
0.941032 | + | 0.338317i | \(0.109858\pi\) | |||||||
\(758\) | −44.4866 | −1.61583 | ||||||||
\(759\) | −3.21654 | −0.116753 | ||||||||
\(760\) | −41.1886 | −1.49407 | ||||||||
\(761\) | −38.8146 | −1.40703 | −0.703514 | − | 0.710681i | \(-0.748387\pi\) | ||||
−0.703514 | + | 0.710681i | \(0.748387\pi\) | |||||||
\(762\) | 83.7822 | 3.03511 | ||||||||
\(763\) | 9.22582 | 0.333997 | ||||||||
\(764\) | −102.988 | −3.72596 | ||||||||
\(765\) | 4.88384 | 0.176576 | ||||||||
\(766\) | 62.2554 | 2.24938 | ||||||||
\(767\) | −31.3874 | −1.13333 | ||||||||
\(768\) | 32.8449 | 1.18519 | ||||||||
\(769\) | −8.51187 | −0.306946 | −0.153473 | − | 0.988153i | \(-0.549046\pi\) | ||||
−0.153473 | + | 0.988153i | \(0.549046\pi\) | |||||||
\(770\) | −7.22936 | −0.260528 | ||||||||
\(771\) | −38.9044 | −1.40111 | ||||||||
\(772\) | −31.7422 | −1.14243 | ||||||||
\(773\) | −41.2723 | −1.48446 | −0.742230 | − | 0.670145i | \(-0.766232\pi\) | ||||
−0.742230 | + | 0.670145i | \(0.766232\pi\) | |||||||
\(774\) | −39.4904 | −1.41945 | ||||||||
\(775\) | 0.820011 | 0.0294557 | ||||||||
\(776\) | 100.623 | 3.61216 | ||||||||
\(777\) | −10.2748 | −0.368605 | ||||||||
\(778\) | 39.6177 | 1.42036 | ||||||||
\(779\) | −26.4253 | −0.946786 | ||||||||
\(780\) | −46.4068 | −1.66163 | ||||||||
\(781\) | −4.89721 | −0.175236 | ||||||||
\(782\) | −8.79786 | −0.314611 | ||||||||
\(783\) | 8.21786 | 0.293682 | ||||||||
\(784\) | −65.7715 | −2.34898 | ||||||||
\(785\) | 9.51429 | 0.339580 | ||||||||
\(786\) | −25.0091 | −0.892045 | ||||||||
\(787\) | −22.3318 | −0.796043 | −0.398021 | − | 0.917376i | \(-0.630303\pi\) | ||||
−0.398021 | + | 0.917376i | \(0.630303\pi\) | |||||||
\(788\) | −19.2395 | −0.685379 | ||||||||
\(789\) | 30.4534 | 1.08417 | ||||||||
\(790\) | −26.0763 | −0.927754 | ||||||||
\(791\) | 5.03826 | 0.179140 | ||||||||
\(792\) | −20.3856 | −0.724372 | ||||||||
\(793\) | −5.97394 | −0.212141 | ||||||||
\(794\) | 33.2421 | 1.17972 | ||||||||
\(795\) | 25.2191 | 0.894430 | ||||||||
\(796\) | −43.1892 | −1.53080 | ||||||||
\(797\) | 43.9194 | 1.55571 | 0.777853 | − | 0.628446i | \(-0.216309\pi\) | ||||
0.777853 | + | 0.628446i | \(0.216309\pi\) | |||||||
\(798\) | −36.1665 | −1.28028 | ||||||||
\(799\) | −27.9717 | −0.989567 | ||||||||
\(800\) | −17.4123 | −0.615619 | ||||||||
\(801\) | −7.56269 | −0.267215 | ||||||||
\(802\) | 47.6531 | 1.68269 | ||||||||
\(803\) | 8.36902 | 0.295336 | ||||||||
\(804\) | 153.823 | 5.42490 | ||||||||
\(805\) | −1.11993 | −0.0394722 | ||||||||
\(806\) | −9.53119 | −0.335722 | ||||||||
\(807\) | 10.3480 | 0.364266 | ||||||||
\(808\) | −85.8766 | −3.02113 | ||||||||
\(809\) | −23.2165 | −0.816250 | −0.408125 | − | 0.912926i | \(-0.633817\pi\) | ||||
−0.408125 | + | 0.912926i | \(0.633817\pi\) | |||||||
\(810\) | −30.0320 | −1.05522 | ||||||||
\(811\) | 35.9361 | 1.26189 | 0.630944 | − | 0.775829i | \(-0.282668\pi\) | ||||
0.630944 | + | 0.775829i | \(0.282668\pi\) | |||||||
\(812\) | 16.2108 | 0.568888 | ||||||||
\(813\) | 30.9629 | 1.08592 | ||||||||
\(814\) | −18.8686 | −0.661342 | ||||||||
\(815\) | 12.5666 | 0.440188 | ||||||||
\(816\) | −107.426 | −3.76066 | ||||||||
\(817\) | −57.5392 | −2.01304 | ||||||||
\(818\) | 77.7355 | 2.71796 | ||||||||
\(819\) | −7.22606 | −0.252499 | ||||||||
\(820\) | −29.2448 | −1.02127 | ||||||||
\(821\) | 29.5182 | 1.03019 | 0.515096 | − | 0.857133i | \(-0.327756\pi\) | ||||
0.515096 | + | 0.857133i | \(0.327756\pi\) | |||||||
\(822\) | 41.1591 | 1.43559 | ||||||||
\(823\) | 13.5509 | 0.472354 | 0.236177 | − | 0.971710i | \(-0.424106\pi\) | ||||
0.236177 | + | 0.971710i | \(0.424106\pi\) | |||||||
\(824\) | −141.650 | −4.93462 | ||||||||
\(825\) | 3.97895 | 0.138529 | ||||||||
\(826\) | −27.0712 | −0.941929 | ||||||||
\(827\) | −11.5228 | −0.400687 | −0.200343 | − | 0.979726i | \(-0.564206\pi\) | ||||
−0.200343 | + | 0.979726i | \(0.564206\pi\) | |||||||
\(828\) | −5.10969 | −0.177574 | ||||||||
\(829\) | −17.3718 | −0.603346 | −0.301673 | − | 0.953411i | \(-0.597545\pi\) | ||||
−0.301673 | + | 0.953411i | \(0.597545\pi\) | |||||||
\(830\) | −19.4760 | −0.676023 | ||||||||
\(831\) | 6.72177 | 0.233175 | ||||||||
\(832\) | 90.5173 | 3.13812 | ||||||||
\(833\) | 20.5554 | 0.712204 | ||||||||
\(834\) | −59.4233 | −2.05766 | ||||||||
\(835\) | 0.0227980 | 0.000788956 0 | ||||||||
\(836\) | −48.0594 | −1.66217 | ||||||||
\(837\) | −3.01549 | −0.104231 | ||||||||
\(838\) | 69.8780 | 2.41390 | ||||||||
\(839\) | −38.7242 | −1.33691 | −0.668454 | − | 0.743754i | \(-0.733043\pi\) | ||||
−0.668454 | + | 0.743754i | \(0.733043\pi\) | |||||||
\(840\) | −24.7373 | −0.853519 | ||||||||
\(841\) | −24.0061 | −0.827797 | ||||||||
\(842\) | 3.44324 | 0.118662 | ||||||||
\(843\) | 42.9631 | 1.47973 | ||||||||
\(844\) | −58.8611 | −2.02608 | ||||||||
\(845\) | −5.67001 | −0.195054 | ||||||||
\(846\) | −22.4508 | −0.771873 | ||||||||
\(847\) | 10.0258 | 0.344491 | ||||||||
\(848\) | −159.166 | −5.46577 | ||||||||
\(849\) | −14.7754 | −0.507091 | ||||||||
\(850\) | 10.8832 | 0.373291 | ||||||||
\(851\) | −2.92300 | −0.100199 | ||||||||
\(852\) | −27.1133 | −0.928888 | ||||||||
\(853\) | 37.1221 | 1.27104 | 0.635518 | − | 0.772086i | \(-0.280786\pi\) | ||||
0.635518 | + | 0.772086i | \(0.280786\pi\) | |||||||
\(854\) | −5.15245 | −0.176313 | ||||||||
\(855\) | 5.71146 | 0.195328 | ||||||||
\(856\) | −170.781 | −5.83716 | ||||||||
\(857\) | 19.9468 | 0.681369 | 0.340684 | − | 0.940178i | \(-0.389341\pi\) | ||||
0.340684 | + | 0.940178i | \(0.389341\pi\) | |||||||
\(858\) | −46.2483 | −1.57889 | ||||||||
\(859\) | 16.5871 | 0.565945 | 0.282973 | − | 0.959128i | \(-0.408679\pi\) | ||||
0.282973 | + | 0.959128i | \(0.408679\pi\) | |||||||
\(860\) | −63.6784 | −2.17142 | ||||||||
\(861\) | −15.8707 | −0.540873 | ||||||||
\(862\) | 37.1213 | 1.26435 | ||||||||
\(863\) | 39.3992 | 1.34117 | 0.670583 | − | 0.741835i | \(-0.266044\pi\) | ||||
0.670583 | + | 0.741835i | \(0.266044\pi\) | |||||||
\(864\) | 64.0318 | 2.17841 | ||||||||
\(865\) | 16.3209 | 0.554928 | ||||||||
\(866\) | −68.0280 | −2.31169 | ||||||||
\(867\) | −1.29567 | −0.0440032 | ||||||||
\(868\) | −5.94847 | −0.201904 | ||||||||
\(869\) | −18.8047 | −0.637906 | ||||||||
\(870\) | −12.3302 | −0.418032 | ||||||||
\(871\) | 61.8846 | 2.09688 | ||||||||
\(872\) | 57.9728 | 1.96321 | ||||||||
\(873\) | −13.9530 | −0.472238 | ||||||||
\(874\) | −10.2887 | −0.348022 | ||||||||
\(875\) | 1.38538 | 0.0468345 | ||||||||
\(876\) | 46.3350 | 1.56551 | ||||||||
\(877\) | −51.7055 | −1.74597 | −0.872985 | − | 0.487747i | \(-0.837819\pi\) | ||||
−0.872985 | + | 0.487747i | \(0.837819\pi\) | |||||||
\(878\) | −88.3845 | −2.98283 | ||||||||
\(879\) | 56.9174 | 1.91978 | ||||||||
\(880\) | −25.1124 | −0.846539 | ||||||||
\(881\) | 52.2590 | 1.76065 | 0.880325 | − | 0.474371i | \(-0.157324\pi\) | ||||
0.880325 | + | 0.474371i | \(0.157324\pi\) | |||||||
\(882\) | 16.4983 | 0.555527 | ||||||||
\(883\) | −47.0199 | −1.58235 | −0.791173 | − | 0.611593i | \(-0.790529\pi\) | ||||
−0.791173 | + | 0.611593i | \(0.790529\pi\) | |||||||
\(884\) | −91.5356 | −3.07867 | ||||||||
\(885\) | 14.8997 | 0.500847 | ||||||||
\(886\) | 4.11296 | 0.138178 | ||||||||
\(887\) | −6.17592 | −0.207367 | −0.103684 | − | 0.994610i | \(-0.533063\pi\) | ||||
−0.103684 | + | 0.994610i | \(0.533063\pi\) | |||||||
\(888\) | −64.5642 | −2.16663 | ||||||||
\(889\) | 21.0365 | 0.705540 | ||||||||
\(890\) | −16.8528 | −0.564907 | ||||||||
\(891\) | −21.6573 | −0.725546 | ||||||||
\(892\) | 108.825 | 3.64373 | ||||||||
\(893\) | −32.7118 | −1.09466 | ||||||||
\(894\) | 64.4918 | 2.15693 | ||||||||
\(895\) | 10.1311 | 0.338647 | ||||||||
\(896\) | 29.8245 | 0.996366 | ||||||||
\(897\) | −7.16450 | −0.239216 | ||||||||
\(898\) | −27.5854 | −0.920536 | ||||||||
\(899\) | −1.83248 | −0.0611167 | ||||||||
\(900\) | 6.32084 | 0.210695 | ||||||||
\(901\) | 49.7437 | 1.65720 | ||||||||
\(902\) | −29.1449 | −0.970420 | ||||||||
\(903\) | −34.5573 | −1.15000 | ||||||||
\(904\) | 31.6592 | 1.05297 | ||||||||
\(905\) | 9.58351 | 0.318567 | ||||||||
\(906\) | −42.5772 | −1.41453 | ||||||||
\(907\) | −20.4371 | −0.678601 | −0.339301 | − | 0.940678i | \(-0.610190\pi\) | ||||
−0.339301 | + | 0.940678i | \(0.610190\pi\) | |||||||
\(908\) | −43.2964 | −1.43684 | ||||||||
\(909\) | 11.9082 | 0.394969 | ||||||||
\(910\) | −16.1026 | −0.533797 | ||||||||
\(911\) | −25.5361 | −0.846048 | −0.423024 | − | 0.906119i | \(-0.639031\pi\) | ||||
−0.423024 | + | 0.906119i | \(0.639031\pi\) | |||||||
\(912\) | −125.630 | −4.16003 | ||||||||
\(913\) | −14.0450 | −0.464821 | ||||||||
\(914\) | 36.1347 | 1.19523 | ||||||||
\(915\) | 2.83585 | 0.0937502 | ||||||||
\(916\) | 42.9108 | 1.41781 | ||||||||
\(917\) | −6.27941 | −0.207364 | ||||||||
\(918\) | −40.0217 | −1.32091 | ||||||||
\(919\) | 6.96133 | 0.229633 | 0.114817 | − | 0.993387i | \(-0.463372\pi\) | ||||
0.114817 | + | 0.993387i | \(0.463372\pi\) | |||||||
\(920\) | −7.03735 | −0.232015 | ||||||||
\(921\) | 21.1361 | 0.696457 | ||||||||
\(922\) | −21.2860 | −0.701017 | ||||||||
\(923\) | −10.9080 | −0.359042 | ||||||||
\(924\) | −28.8638 | −0.949551 | ||||||||
\(925\) | 3.61583 | 0.118888 | ||||||||
\(926\) | −102.464 | −3.36716 | ||||||||
\(927\) | 19.6421 | 0.645130 | ||||||||
\(928\) | 38.9114 | 1.27733 | ||||||||
\(929\) | 20.0553 | 0.657994 | 0.328997 | − | 0.944331i | \(-0.393289\pi\) | ||||
0.328997 | + | 0.944331i | \(0.393289\pi\) | |||||||
\(930\) | 4.52448 | 0.148363 | ||||||||
\(931\) | 24.0388 | 0.787839 | ||||||||
\(932\) | 114.465 | 3.74942 | ||||||||
\(933\) | −31.4711 | −1.03032 | ||||||||
\(934\) | −5.89712 | −0.192960 | ||||||||
\(935\) | 7.84833 | 0.256668 | ||||||||
\(936\) | −45.4068 | −1.48417 | ||||||||
\(937\) | 8.45554 | 0.276230 | 0.138115 | − | 0.990416i | \(-0.455896\pi\) | ||||
0.138115 | + | 0.990416i | \(0.455896\pi\) | |||||||
\(938\) | 53.3747 | 1.74275 | ||||||||
\(939\) | 20.9016 | 0.682097 | ||||||||
\(940\) | −36.2020 | −1.18078 | ||||||||
\(941\) | 31.6188 | 1.03074 | 0.515372 | − | 0.856966i | \(-0.327654\pi\) | ||||
0.515372 | + | 0.856966i | \(0.327654\pi\) | |||||||
\(942\) | 52.4959 | 1.71041 | ||||||||
\(943\) | −4.51495 | −0.147027 | ||||||||
\(944\) | −94.0365 | −3.06063 | ||||||||
\(945\) | −5.09458 | −0.165727 | ||||||||
\(946\) | −63.4610 | −2.06329 | ||||||||
\(947\) | 37.7937 | 1.22813 | 0.614065 | − | 0.789256i | \(-0.289533\pi\) | ||||
0.614065 | + | 0.789256i | \(0.289533\pi\) | |||||||
\(948\) | −104.112 | −3.38140 | ||||||||
\(949\) | 18.6411 | 0.605116 | ||||||||
\(950\) | 12.7275 | 0.412934 | ||||||||
\(951\) | −27.5345 | −0.892868 | ||||||||
\(952\) | −48.7934 | −1.58140 | ||||||||
\(953\) | 21.5020 | 0.696518 | 0.348259 | − | 0.937398i | \(-0.386773\pi\) | ||||
0.348259 | + | 0.937398i | \(0.386773\pi\) | |||||||
\(954\) | 39.9255 | 1.29264 | ||||||||
\(955\) | 19.6684 | 0.636455 | ||||||||
\(956\) | −105.837 | −3.42301 | ||||||||
\(957\) | −8.89178 | −0.287430 | ||||||||
\(958\) | −3.82453 | −0.123565 | ||||||||
\(959\) | 10.3344 | 0.333716 | ||||||||
\(960\) | −42.9688 | −1.38681 | ||||||||
\(961\) | −30.3276 | −0.978309 | ||||||||
\(962\) | −42.0277 | −1.35503 | ||||||||
\(963\) | 23.6815 | 0.763125 | ||||||||
\(964\) | −47.1566 | −1.51881 | ||||||||
\(965\) | 6.06207 | 0.195145 | ||||||||
\(966\) | −6.17929 | −0.198815 | ||||||||
\(967\) | 9.19873 | 0.295811 | 0.147906 | − | 0.989001i | \(-0.452747\pi\) | ||||
0.147906 | + | 0.989001i | \(0.452747\pi\) | |||||||
\(968\) | 62.9999 | 2.02489 | ||||||||
\(969\) | 39.2630 | 1.26131 | ||||||||
\(970\) | −31.0930 | −0.998338 | ||||||||
\(971\) | 45.4270 | 1.45782 | 0.728912 | − | 0.684608i | \(-0.240027\pi\) | ||||
0.728912 | + | 0.684608i | \(0.240027\pi\) | |||||||
\(972\) | −62.1388 | −1.99310 | ||||||||
\(973\) | −14.9203 | −0.478323 | ||||||||
\(974\) | 37.0753 | 1.18797 | ||||||||
\(975\) | 8.86270 | 0.283834 | ||||||||
\(976\) | −17.8979 | −0.572898 | ||||||||
\(977\) | −12.5457 | −0.401374 | −0.200687 | − | 0.979655i | \(-0.564317\pi\) | ||||
−0.200687 | + | 0.979655i | \(0.564317\pi\) | |||||||
\(978\) | 69.3372 | 2.21716 | ||||||||
\(979\) | −12.1532 | −0.388419 | ||||||||
\(980\) | 26.6036 | 0.849821 | ||||||||
\(981\) | −8.03886 | −0.256661 | ||||||||
\(982\) | 66.5052 | 2.12226 | ||||||||
\(983\) | 36.1055 | 1.15159 | 0.575794 | − | 0.817595i | \(-0.304693\pi\) | ||||
0.575794 | + | 0.817595i | \(0.304693\pi\) | |||||||
\(984\) | −99.7278 | −3.17921 | ||||||||
\(985\) | 3.67433 | 0.117074 | ||||||||
\(986\) | −24.3207 | −0.774530 | ||||||||
\(987\) | −19.6463 | −0.625348 | ||||||||
\(988\) | −107.047 | −3.40563 | ||||||||
\(989\) | −9.83097 | −0.312607 | ||||||||
\(990\) | 6.29926 | 0.200204 | ||||||||
\(991\) | −61.7828 | −1.96259 | −0.981297 | − | 0.192499i | \(-0.938341\pi\) | ||||
−0.981297 | + | 0.192499i | \(0.938341\pi\) | |||||||
\(992\) | −14.2783 | −0.453336 | ||||||||
\(993\) | −28.4997 | −0.904411 | ||||||||
\(994\) | −9.40802 | −0.298404 | ||||||||
\(995\) | 8.24821 | 0.261486 | ||||||||
\(996\) | −77.7598 | −2.46391 | ||||||||
\(997\) | −25.8134 | −0.817519 | −0.408759 | − | 0.912642i | \(-0.634038\pi\) | ||||
−0.408759 | + | 0.912642i | \(0.634038\pi\) | |||||||
\(998\) | −81.3596 | −2.57539 | ||||||||
\(999\) | −13.2968 | −0.420692 |
(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 | 8005.2.a.f.1.4 | ✓ | 127 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8005.2.a.f.1.4 | ✓ | 127 | 1.1 | even | 1 | trivial |