Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8002,2,Mod(1,8002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8002 = 2 \cdot 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8002.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: | \(63.8962916974\) |
Analytic rank: | \(1\) |
Dimension: | \(69\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 8002.1 |
$q$-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 | ||||||||
\(3\) | −3.04857 | −1.76009 | −0.880046 | − | 0.474889i | \(-0.842488\pi\) | ||||
−0.880046 | + | 0.474889i | \(0.842488\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.106661 | −0.0477001 | −0.0238500 | − | 0.999716i | \(-0.507592\pi\) | ||||
−0.0238500 | + | 0.999716i | \(0.507592\pi\) | |||||||
\(6\) | −3.04857 | −1.24457 | ||||||||
\(7\) | −0.613952 | −0.232052 | −0.116026 | − | 0.993246i | \(-0.537016\pi\) | ||||
−0.116026 | + | 0.993246i | \(0.537016\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 6.29376 | 2.09792 | ||||||||
\(10\) | −0.106661 | −0.0337291 | ||||||||
\(11\) | 4.91299 | 1.48132 | 0.740662 | − | 0.671878i | \(-0.234512\pi\) | ||||
0.740662 | + | 0.671878i | \(0.234512\pi\) | |||||||
\(12\) | −3.04857 | −0.880046 | ||||||||
\(13\) | −1.74319 | −0.483474 | −0.241737 | − | 0.970342i | \(-0.577717\pi\) | ||||
−0.241737 | + | 0.970342i | \(0.577717\pi\) | |||||||
\(14\) | −0.613952 | −0.164086 | ||||||||
\(15\) | 0.325162 | 0.0839565 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.753248 | 0.182689 | 0.0913447 | − | 0.995819i | \(-0.470883\pi\) | ||||
0.0913447 | + | 0.995819i | \(0.470883\pi\) | |||||||
\(18\) | 6.29376 | 1.48345 | ||||||||
\(19\) | 0.918851 | 0.210799 | 0.105399 | − | 0.994430i | \(-0.466388\pi\) | ||||
0.105399 | + | 0.994430i | \(0.466388\pi\) | |||||||
\(20\) | −0.106661 | −0.0238500 | ||||||||
\(21\) | 1.87168 | 0.408433 | ||||||||
\(22\) | 4.91299 | 1.04745 | ||||||||
\(23\) | −3.35738 | −0.700062 | −0.350031 | − | 0.936738i | \(-0.613829\pi\) | ||||
−0.350031 | + | 0.936738i | \(0.613829\pi\) | |||||||
\(24\) | −3.04857 | −0.622286 | ||||||||
\(25\) | −4.98862 | −0.997725 | ||||||||
\(26\) | −1.74319 | −0.341868 | ||||||||
\(27\) | −10.0413 | −1.93244 | ||||||||
\(28\) | −0.613952 | −0.116026 | ||||||||
\(29\) | 3.52490 | 0.654558 | 0.327279 | − | 0.944928i | \(-0.393868\pi\) | ||||
0.327279 | + | 0.944928i | \(0.393868\pi\) | |||||||
\(30\) | 0.325162 | 0.0593662 | ||||||||
\(31\) | −6.13162 | −1.10127 | −0.550636 | − | 0.834746i | \(-0.685615\pi\) | ||||
−0.550636 | + | 0.834746i | \(0.685615\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −14.9776 | −2.60726 | ||||||||
\(34\) | 0.753248 | 0.129181 | ||||||||
\(35\) | 0.0654846 | 0.0110689 | ||||||||
\(36\) | 6.29376 | 1.04896 | ||||||||
\(37\) | −1.78363 | −0.293227 | −0.146613 | − | 0.989194i | \(-0.546837\pi\) | ||||
−0.146613 | + | 0.989194i | \(0.546837\pi\) | |||||||
\(38\) | 0.918851 | 0.149057 | ||||||||
\(39\) | 5.31423 | 0.850958 | ||||||||
\(40\) | −0.106661 | −0.0168645 | ||||||||
\(41\) | −9.94633 | −1.55336 | −0.776678 | − | 0.629898i | \(-0.783097\pi\) | ||||
−0.776678 | + | 0.629898i | \(0.783097\pi\) | |||||||
\(42\) | 1.87168 | 0.288806 | ||||||||
\(43\) | 5.22747 | 0.797181 | 0.398591 | − | 0.917129i | \(-0.369499\pi\) | ||||
0.398591 | + | 0.917129i | \(0.369499\pi\) | |||||||
\(44\) | 4.91299 | 0.740662 | ||||||||
\(45\) | −0.671297 | −0.100071 | ||||||||
\(46\) | −3.35738 | −0.495018 | ||||||||
\(47\) | −8.14368 | −1.18788 | −0.593939 | − | 0.804510i | \(-0.702428\pi\) | ||||
−0.593939 | + | 0.804510i | \(0.702428\pi\) | |||||||
\(48\) | −3.04857 | −0.440023 | ||||||||
\(49\) | −6.62306 | −0.946152 | ||||||||
\(50\) | −4.98862 | −0.705498 | ||||||||
\(51\) | −2.29633 | −0.321550 | ||||||||
\(52\) | −1.74319 | −0.241737 | ||||||||
\(53\) | 6.17368 | 0.848020 | 0.424010 | − | 0.905658i | \(-0.360622\pi\) | ||||
0.424010 | + | 0.905658i | \(0.360622\pi\) | |||||||
\(54\) | −10.0413 | −1.36644 | ||||||||
\(55\) | −0.524023 | −0.0706593 | ||||||||
\(56\) | −0.613952 | −0.0820428 | ||||||||
\(57\) | −2.80118 | −0.371025 | ||||||||
\(58\) | 3.52490 | 0.462842 | ||||||||
\(59\) | 8.55876 | 1.11426 | 0.557128 | − | 0.830427i | \(-0.311903\pi\) | ||||
0.557128 | + | 0.830427i | \(0.311903\pi\) | |||||||
\(60\) | 0.325162 | 0.0419783 | ||||||||
\(61\) | −3.22483 | −0.412898 | −0.206449 | − | 0.978457i | \(-0.566191\pi\) | ||||
−0.206449 | + | 0.978457i | \(0.566191\pi\) | |||||||
\(62\) | −6.13162 | −0.778717 | ||||||||
\(63\) | −3.86407 | −0.486827 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.185930 | 0.0230617 | ||||||||
\(66\) | −14.9776 | −1.84361 | ||||||||
\(67\) | −4.18508 | −0.511288 | −0.255644 | − | 0.966771i | \(-0.582288\pi\) | ||||
−0.255644 | + | 0.966771i | \(0.582288\pi\) | |||||||
\(68\) | 0.753248 | 0.0913447 | ||||||||
\(69\) | 10.2352 | 1.23217 | ||||||||
\(70\) | 0.0654846 | 0.00782690 | ||||||||
\(71\) | −0.630097 | −0.0747788 | −0.0373894 | − | 0.999301i | \(-0.511904\pi\) | ||||
−0.0373894 | + | 0.999301i | \(0.511904\pi\) | |||||||
\(72\) | 6.29376 | 0.741727 | ||||||||
\(73\) | −0.360837 | −0.0422328 | −0.0211164 | − | 0.999777i | \(-0.506722\pi\) | ||||
−0.0211164 | + | 0.999777i | \(0.506722\pi\) | |||||||
\(74\) | −1.78363 | −0.207343 | ||||||||
\(75\) | 15.2082 | 1.75609 | ||||||||
\(76\) | 0.918851 | 0.105399 | ||||||||
\(77\) | −3.01634 | −0.343744 | ||||||||
\(78\) | 5.31423 | 0.601718 | ||||||||
\(79\) | 14.1602 | 1.59315 | 0.796574 | − | 0.604541i | \(-0.206643\pi\) | ||||
0.796574 | + | 0.604541i | \(0.206643\pi\) | |||||||
\(80\) | −0.106661 | −0.0119250 | ||||||||
\(81\) | 11.7302 | 1.30335 | ||||||||
\(82\) | −9.94633 | −1.09839 | ||||||||
\(83\) | 4.38774 | 0.481617 | 0.240808 | − | 0.970573i | \(-0.422587\pi\) | ||||
0.240808 | + | 0.970573i | \(0.422587\pi\) | |||||||
\(84\) | 1.87168 | 0.204216 | ||||||||
\(85\) | −0.0803419 | −0.00871430 | ||||||||
\(86\) | 5.22747 | 0.563692 | ||||||||
\(87\) | −10.7459 | −1.15208 | ||||||||
\(88\) | 4.91299 | 0.523727 | ||||||||
\(89\) | 15.2114 | 1.61241 | 0.806205 | − | 0.591637i | \(-0.201518\pi\) | ||||
0.806205 | + | 0.591637i | \(0.201518\pi\) | |||||||
\(90\) | −0.671297 | −0.0707609 | ||||||||
\(91\) | 1.07024 | 0.112191 | ||||||||
\(92\) | −3.35738 | −0.350031 | ||||||||
\(93\) | 18.6927 | 1.93834 | ||||||||
\(94\) | −8.14368 | −0.839957 | ||||||||
\(95\) | −0.0980052 | −0.0100551 | ||||||||
\(96\) | −3.04857 | −0.311143 | ||||||||
\(97\) | −2.30536 | −0.234074 | −0.117037 | − | 0.993128i | \(-0.537340\pi\) | ||||
−0.117037 | + | 0.993128i | \(0.537340\pi\) | |||||||
\(98\) | −6.62306 | −0.669030 | ||||||||
\(99\) | 30.9212 | 3.10770 | ||||||||
\(100\) | −4.98862 | −0.498862 | ||||||||
\(101\) | 6.36247 | 0.633090 | 0.316545 | − | 0.948578i | \(-0.397477\pi\) | ||||
0.316545 | + | 0.948578i | \(0.397477\pi\) | |||||||
\(102\) | −2.29633 | −0.227370 | ||||||||
\(103\) | −0.453725 | −0.0447069 | −0.0223534 | − | 0.999750i | \(-0.507116\pi\) | ||||
−0.0223534 | + | 0.999750i | \(0.507116\pi\) | |||||||
\(104\) | −1.74319 | −0.170934 | ||||||||
\(105\) | −0.199634 | −0.0194823 | ||||||||
\(106\) | 6.17368 | 0.599640 | ||||||||
\(107\) | −6.75717 | −0.653241 | −0.326620 | − | 0.945156i | \(-0.605910\pi\) | ||||
−0.326620 | + | 0.945156i | \(0.605910\pi\) | |||||||
\(108\) | −10.0413 | −0.966220 | ||||||||
\(109\) | 8.33265 | 0.798123 | 0.399061 | − | 0.916924i | \(-0.369336\pi\) | ||||
0.399061 | + | 0.916924i | \(0.369336\pi\) | |||||||
\(110\) | −0.524023 | −0.0499636 | ||||||||
\(111\) | 5.43751 | 0.516106 | ||||||||
\(112\) | −0.613952 | −0.0580130 | ||||||||
\(113\) | −10.8912 | −1.02456 | −0.512280 | − | 0.858819i | \(-0.671199\pi\) | ||||
−0.512280 | + | 0.858819i | \(0.671199\pi\) | |||||||
\(114\) | −2.80118 | −0.262354 | ||||||||
\(115\) | 0.358100 | 0.0333930 | ||||||||
\(116\) | 3.52490 | 0.327279 | ||||||||
\(117\) | −10.9712 | −1.01429 | ||||||||
\(118\) | 8.55876 | 0.787897 | ||||||||
\(119\) | −0.462458 | −0.0423935 | ||||||||
\(120\) | 0.325162 | 0.0296831 | ||||||||
\(121\) | 13.1375 | 1.19432 | ||||||||
\(122\) | −3.22483 | −0.291963 | ||||||||
\(123\) | 30.3221 | 2.73405 | ||||||||
\(124\) | −6.13162 | −0.550636 | ||||||||
\(125\) | 1.06539 | 0.0952917 | ||||||||
\(126\) | −3.86407 | −0.344239 | ||||||||
\(127\) | −14.0274 | −1.24473 | −0.622365 | − | 0.782727i | \(-0.713828\pi\) | ||||
−0.622365 | + | 0.782727i | \(0.713828\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −15.9363 | −1.40311 | ||||||||
\(130\) | 0.185930 | 0.0163071 | ||||||||
\(131\) | −8.60225 | −0.751582 | −0.375791 | − | 0.926704i | \(-0.622629\pi\) | ||||
−0.375791 | + | 0.926704i | \(0.622629\pi\) | |||||||
\(132\) | −14.9776 | −1.30363 | ||||||||
\(133\) | −0.564130 | −0.0489163 | ||||||||
\(134\) | −4.18508 | −0.361536 | ||||||||
\(135\) | 1.07101 | 0.0921776 | ||||||||
\(136\) | 0.753248 | 0.0645905 | ||||||||
\(137\) | 4.23540 | 0.361854 | 0.180927 | − | 0.983496i | \(-0.442090\pi\) | ||||
0.180927 | + | 0.983496i | \(0.442090\pi\) | |||||||
\(138\) | 10.2352 | 0.871277 | ||||||||
\(139\) | −17.6617 | −1.49804 | −0.749022 | − | 0.662545i | \(-0.769476\pi\) | ||||
−0.749022 | + | 0.662545i | \(0.769476\pi\) | |||||||
\(140\) | 0.0654846 | 0.00553446 | ||||||||
\(141\) | 24.8266 | 2.09077 | ||||||||
\(142\) | −0.630097 | −0.0528766 | ||||||||
\(143\) | −8.56428 | −0.716181 | ||||||||
\(144\) | 6.29376 | 0.524480 | ||||||||
\(145\) | −0.375968 | −0.0312225 | ||||||||
\(146\) | −0.360837 | −0.0298631 | ||||||||
\(147\) | 20.1909 | 1.66531 | ||||||||
\(148\) | −1.78363 | −0.146613 | ||||||||
\(149\) | 3.34112 | 0.273715 | 0.136857 | − | 0.990591i | \(-0.456300\pi\) | ||||
0.136857 | + | 0.990591i | \(0.456300\pi\) | |||||||
\(150\) | 15.2082 | 1.24174 | ||||||||
\(151\) | −1.53758 | −0.125127 | −0.0625633 | − | 0.998041i | \(-0.519928\pi\) | ||||
−0.0625633 | + | 0.998041i | \(0.519928\pi\) | |||||||
\(152\) | 0.918851 | 0.0745286 | ||||||||
\(153\) | 4.74076 | 0.383268 | ||||||||
\(154\) | −3.01634 | −0.243064 | ||||||||
\(155\) | 0.654003 | 0.0525308 | ||||||||
\(156\) | 5.31423 | 0.425479 | ||||||||
\(157\) | −15.2523 | −1.21726 | −0.608631 | − | 0.793453i | \(-0.708281\pi\) | ||||
−0.608631 | + | 0.793453i | \(0.708281\pi\) | |||||||
\(158\) | 14.1602 | 1.12653 | ||||||||
\(159\) | −18.8209 | −1.49259 | ||||||||
\(160\) | −0.106661 | −0.00843226 | ||||||||
\(161\) | 2.06127 | 0.162451 | ||||||||
\(162\) | 11.7302 | 0.921608 | ||||||||
\(163\) | −14.5705 | −1.14125 | −0.570624 | − | 0.821212i | \(-0.693298\pi\) | ||||
−0.570624 | + | 0.821212i | \(0.693298\pi\) | |||||||
\(164\) | −9.94633 | −0.776678 | ||||||||
\(165\) | 1.59752 | 0.124367 | ||||||||
\(166\) | 4.38774 | 0.340555 | ||||||||
\(167\) | 5.47291 | 0.423506 | 0.211753 | − | 0.977323i | \(-0.432083\pi\) | ||||
0.211753 | + | 0.977323i | \(0.432083\pi\) | |||||||
\(168\) | 1.87168 | 0.144403 | ||||||||
\(169\) | −9.96129 | −0.766253 | ||||||||
\(170\) | −0.0803419 | −0.00616194 | ||||||||
\(171\) | 5.78303 | 0.442239 | ||||||||
\(172\) | 5.22747 | 0.398591 | ||||||||
\(173\) | −19.7961 | −1.50507 | −0.752535 | − | 0.658552i | \(-0.771169\pi\) | ||||
−0.752535 | + | 0.658552i | \(0.771169\pi\) | |||||||
\(174\) | −10.7459 | −0.814645 | ||||||||
\(175\) | 3.06278 | 0.231524 | ||||||||
\(176\) | 4.91299 | 0.370331 | ||||||||
\(177\) | −26.0919 | −1.96119 | ||||||||
\(178\) | 15.2114 | 1.14015 | ||||||||
\(179\) | −4.91078 | −0.367049 | −0.183524 | − | 0.983015i | \(-0.558751\pi\) | ||||
−0.183524 | + | 0.983015i | \(0.558751\pi\) | |||||||
\(180\) | −0.671297 | −0.0500355 | ||||||||
\(181\) | −3.08931 | −0.229626 | −0.114813 | − | 0.993387i | \(-0.536627\pi\) | ||||
−0.114813 | + | 0.993387i | \(0.536627\pi\) | |||||||
\(182\) | 1.07024 | 0.0793311 | ||||||||
\(183\) | 9.83113 | 0.726738 | ||||||||
\(184\) | −3.35738 | −0.247509 | ||||||||
\(185\) | 0.190243 | 0.0139869 | ||||||||
\(186\) | 18.6927 | 1.37061 | ||||||||
\(187\) | 3.70070 | 0.270622 | ||||||||
\(188\) | −8.14368 | −0.593939 | ||||||||
\(189\) | 6.16485 | 0.448427 | ||||||||
\(190\) | −0.0980052 | −0.00711004 | ||||||||
\(191\) | 11.5369 | 0.834778 | 0.417389 | − | 0.908728i | \(-0.362945\pi\) | ||||
0.417389 | + | 0.908728i | \(0.362945\pi\) | |||||||
\(192\) | −3.04857 | −0.220011 | ||||||||
\(193\) | −17.7635 | −1.27864 | −0.639322 | − | 0.768939i | \(-0.720785\pi\) | ||||
−0.639322 | + | 0.768939i | \(0.720785\pi\) | |||||||
\(194\) | −2.30536 | −0.165515 | ||||||||
\(195\) | −0.566819 | −0.0405908 | ||||||||
\(196\) | −6.62306 | −0.473076 | ||||||||
\(197\) | 14.5005 | 1.03312 | 0.516559 | − | 0.856251i | \(-0.327213\pi\) | ||||
0.516559 | + | 0.856251i | \(0.327213\pi\) | |||||||
\(198\) | 30.9212 | 2.19747 | ||||||||
\(199\) | −4.28047 | −0.303435 | −0.151717 | − | 0.988424i | \(-0.548480\pi\) | ||||
−0.151717 | + | 0.988424i | \(0.548480\pi\) | |||||||
\(200\) | −4.98862 | −0.352749 | ||||||||
\(201\) | 12.7585 | 0.899914 | ||||||||
\(202\) | 6.36247 | 0.447662 | ||||||||
\(203\) | −2.16412 | −0.151892 | ||||||||
\(204\) | −2.29633 | −0.160775 | ||||||||
\(205\) | 1.06088 | 0.0740952 | ||||||||
\(206\) | −0.453725 | −0.0316125 | ||||||||
\(207\) | −21.1305 | −1.46867 | ||||||||
\(208\) | −1.74319 | −0.120868 | ||||||||
\(209\) | 4.51431 | 0.312261 | ||||||||
\(210\) | −0.199634 | −0.0137761 | ||||||||
\(211\) | 5.93973 | 0.408908 | 0.204454 | − | 0.978876i | \(-0.434458\pi\) | ||||
0.204454 | + | 0.978876i | \(0.434458\pi\) | |||||||
\(212\) | 6.17368 | 0.424010 | ||||||||
\(213\) | 1.92089 | 0.131618 | ||||||||
\(214\) | −6.75717 | −0.461911 | ||||||||
\(215\) | −0.557565 | −0.0380256 | ||||||||
\(216\) | −10.0413 | −0.683221 | ||||||||
\(217\) | 3.76452 | 0.255553 | ||||||||
\(218\) | 8.33265 | 0.564358 | ||||||||
\(219\) | 1.10004 | 0.0743335 | ||||||||
\(220\) | −0.524023 | −0.0353296 | ||||||||
\(221\) | −1.31305 | −0.0883255 | ||||||||
\(222\) | 5.43751 | 0.364942 | ||||||||
\(223\) | 18.8388 | 1.26154 | 0.630770 | − | 0.775970i | \(-0.282739\pi\) | ||||
0.630770 | + | 0.775970i | \(0.282739\pi\) | |||||||
\(224\) | −0.613952 | −0.0410214 | ||||||||
\(225\) | −31.3972 | −2.09315 | ||||||||
\(226\) | −10.8912 | −0.724473 | ||||||||
\(227\) | 15.4741 | 1.02705 | 0.513525 | − | 0.858074i | \(-0.328339\pi\) | ||||
0.513525 | + | 0.858074i | \(0.328339\pi\) | |||||||
\(228\) | −2.80118 | −0.185513 | ||||||||
\(229\) | −3.49682 | −0.231076 | −0.115538 | − | 0.993303i | \(-0.536859\pi\) | ||||
−0.115538 | + | 0.993303i | \(0.536859\pi\) | |||||||
\(230\) | 0.358100 | 0.0236124 | ||||||||
\(231\) | 9.19553 | 0.605021 | ||||||||
\(232\) | 3.52490 | 0.231421 | ||||||||
\(233\) | −25.8327 | −1.69236 | −0.846179 | − | 0.532899i | \(-0.821103\pi\) | ||||
−0.846179 | + | 0.532899i | \(0.821103\pi\) | |||||||
\(234\) | −10.9712 | −0.717211 | ||||||||
\(235\) | 0.868611 | 0.0566619 | ||||||||
\(236\) | 8.55876 | 0.557128 | ||||||||
\(237\) | −43.1684 | −2.80409 | ||||||||
\(238\) | −0.462458 | −0.0299767 | ||||||||
\(239\) | 12.5745 | 0.813380 | 0.406690 | − | 0.913566i | \(-0.366683\pi\) | ||||
0.406690 | + | 0.913566i | \(0.366683\pi\) | |||||||
\(240\) | 0.325162 | 0.0209891 | ||||||||
\(241\) | 6.89941 | 0.444430 | 0.222215 | − | 0.974998i | \(-0.428671\pi\) | ||||
0.222215 | + | 0.974998i | \(0.428671\pi\) | |||||||
\(242\) | 13.1375 | 0.844511 | ||||||||
\(243\) | −5.63640 | −0.361575 | ||||||||
\(244\) | −3.22483 | −0.206449 | ||||||||
\(245\) | 0.706420 | 0.0451315 | ||||||||
\(246\) | 30.3221 | 1.93326 | ||||||||
\(247\) | −1.60173 | −0.101916 | ||||||||
\(248\) | −6.13162 | −0.389358 | ||||||||
\(249\) | −13.3763 | −0.847689 | ||||||||
\(250\) | 1.06539 | 0.0673814 | ||||||||
\(251\) | 7.65888 | 0.483424 | 0.241712 | − | 0.970348i | \(-0.422291\pi\) | ||||
0.241712 | + | 0.970348i | \(0.422291\pi\) | |||||||
\(252\) | −3.86407 | −0.243414 | ||||||||
\(253\) | −16.4948 | −1.03702 | ||||||||
\(254\) | −14.0274 | −0.880157 | ||||||||
\(255\) | 0.244928 | 0.0153380 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −1.00875 | −0.0629243 | −0.0314621 | − | 0.999505i | \(-0.510016\pi\) | ||||
−0.0314621 | + | 0.999505i | \(0.510016\pi\) | |||||||
\(258\) | −15.9363 | −0.992150 | ||||||||
\(259\) | 1.09506 | 0.0680439 | ||||||||
\(260\) | 0.185930 | 0.0115309 | ||||||||
\(261\) | 22.1849 | 1.37321 | ||||||||
\(262\) | −8.60225 | −0.531449 | ||||||||
\(263\) | 23.2435 | 1.43326 | 0.716628 | − | 0.697455i | \(-0.245684\pi\) | ||||
0.716628 | + | 0.697455i | \(0.245684\pi\) | |||||||
\(264\) | −14.9776 | −0.921807 | ||||||||
\(265\) | −0.658488 | −0.0404506 | ||||||||
\(266\) | −0.564130 | −0.0345891 | ||||||||
\(267\) | −46.3731 | −2.83799 | ||||||||
\(268\) | −4.18508 | −0.255644 | ||||||||
\(269\) | −26.2817 | −1.60243 | −0.801213 | − | 0.598380i | \(-0.795811\pi\) | ||||
−0.801213 | + | 0.598380i | \(0.795811\pi\) | |||||||
\(270\) | 1.07101 | 0.0651794 | ||||||||
\(271\) | −15.6701 | −0.951888 | −0.475944 | − | 0.879475i | \(-0.657894\pi\) | ||||
−0.475944 | + | 0.879475i | \(0.657894\pi\) | |||||||
\(272\) | 0.753248 | 0.0456724 | ||||||||
\(273\) | −3.26268 | −0.197467 | ||||||||
\(274\) | 4.23540 | 0.255870 | ||||||||
\(275\) | −24.5091 | −1.47795 | ||||||||
\(276\) | 10.2352 | 0.616086 | ||||||||
\(277\) | −11.5647 | −0.694856 | −0.347428 | − | 0.937707i | \(-0.612945\pi\) | ||||
−0.347428 | + | 0.937707i | \(0.612945\pi\) | |||||||
\(278\) | −17.6617 | −1.05928 | ||||||||
\(279\) | −38.5910 | −2.31038 | ||||||||
\(280\) | 0.0654846 | 0.00391345 | ||||||||
\(281\) | −14.1091 | −0.841678 | −0.420839 | − | 0.907135i | \(-0.638264\pi\) | ||||
−0.420839 | + | 0.907135i | \(0.638264\pi\) | |||||||
\(282\) | 24.8266 | 1.47840 | ||||||||
\(283\) | −16.8451 | −1.00134 | −0.500668 | − | 0.865639i | \(-0.666912\pi\) | ||||
−0.500668 | + | 0.865639i | \(0.666912\pi\) | |||||||
\(284\) | −0.630097 | −0.0373894 | ||||||||
\(285\) | 0.298775 | 0.0176979 | ||||||||
\(286\) | −8.56428 | −0.506416 | ||||||||
\(287\) | 6.10657 | 0.360460 | ||||||||
\(288\) | 6.29376 | 0.370863 | ||||||||
\(289\) | −16.4326 | −0.966625 | ||||||||
\(290\) | −0.375968 | −0.0220776 | ||||||||
\(291\) | 7.02805 | 0.411992 | ||||||||
\(292\) | −0.360837 | −0.0211164 | ||||||||
\(293\) | −0.226701 | −0.0132440 | −0.00662201 | − | 0.999978i | \(-0.502108\pi\) | ||||
−0.00662201 | + | 0.999978i | \(0.502108\pi\) | |||||||
\(294\) | 20.1909 | 1.17755 | ||||||||
\(295\) | −0.912882 | −0.0531501 | ||||||||
\(296\) | −1.78363 | −0.103671 | ||||||||
\(297\) | −49.3326 | −2.86257 | ||||||||
\(298\) | 3.34112 | 0.193546 | ||||||||
\(299\) | 5.85254 | 0.338461 | ||||||||
\(300\) | 15.2082 | 0.878043 | ||||||||
\(301\) | −3.20942 | −0.184988 | ||||||||
\(302\) | −1.53758 | −0.0884779 | ||||||||
\(303\) | −19.3964 | −1.11430 | ||||||||
\(304\) | 0.918851 | 0.0526997 | ||||||||
\(305\) | 0.343963 | 0.0196953 | ||||||||
\(306\) | 4.74076 | 0.271011 | ||||||||
\(307\) | −13.6595 | −0.779588 | −0.389794 | − | 0.920902i | \(-0.627454\pi\) | ||||
−0.389794 | + | 0.920902i | \(0.627454\pi\) | |||||||
\(308\) | −3.01634 | −0.171872 | ||||||||
\(309\) | 1.38321 | 0.0786882 | ||||||||
\(310\) | 0.654003 | 0.0371449 | ||||||||
\(311\) | −12.3045 | −0.697726 | −0.348863 | − | 0.937174i | \(-0.613432\pi\) | ||||
−0.348863 | + | 0.937174i | \(0.613432\pi\) | |||||||
\(312\) | 5.31423 | 0.300859 | ||||||||
\(313\) | 25.9209 | 1.46513 | 0.732567 | − | 0.680695i | \(-0.238322\pi\) | ||||
0.732567 | + | 0.680695i | \(0.238322\pi\) | |||||||
\(314\) | −15.2523 | −0.860735 | ||||||||
\(315\) | 0.412144 | 0.0232217 | ||||||||
\(316\) | 14.1602 | 0.796574 | ||||||||
\(317\) | −18.2940 | −1.02750 | −0.513748 | − | 0.857941i | \(-0.671743\pi\) | ||||
−0.513748 | + | 0.857941i | \(0.671743\pi\) | |||||||
\(318\) | −18.8209 | −1.05542 | ||||||||
\(319\) | 17.3178 | 0.969612 | ||||||||
\(320\) | −0.106661 | −0.00596251 | ||||||||
\(321\) | 20.5997 | 1.14976 | ||||||||
\(322\) | 2.06127 | 0.114870 | ||||||||
\(323\) | 0.692122 | 0.0385107 | ||||||||
\(324\) | 11.7302 | 0.651675 | ||||||||
\(325\) | 8.69611 | 0.482374 | ||||||||
\(326\) | −14.5705 | −0.806984 | ||||||||
\(327\) | −25.4026 | −1.40477 | ||||||||
\(328\) | −9.94633 | −0.549194 | ||||||||
\(329\) | 4.99983 | 0.275650 | ||||||||
\(330\) | 1.59752 | 0.0879406 | ||||||||
\(331\) | 14.0821 | 0.774024 | 0.387012 | − | 0.922075i | \(-0.373507\pi\) | ||||
0.387012 | + | 0.922075i | \(0.373507\pi\) | |||||||
\(332\) | 4.38774 | 0.240808 | ||||||||
\(333\) | −11.2257 | −0.615167 | ||||||||
\(334\) | 5.47291 | 0.299464 | ||||||||
\(335\) | 0.446383 | 0.0243885 | ||||||||
\(336\) | 1.87168 | 0.102108 | ||||||||
\(337\) | −1.41883 | −0.0772888 | −0.0386444 | − | 0.999253i | \(-0.512304\pi\) | ||||
−0.0386444 | + | 0.999253i | \(0.512304\pi\) | |||||||
\(338\) | −9.96129 | −0.541823 | ||||||||
\(339\) | 33.2026 | 1.80332 | ||||||||
\(340\) | −0.0803419 | −0.00435715 | ||||||||
\(341\) | −30.1246 | −1.63134 | ||||||||
\(342\) | 5.78303 | 0.312710 | ||||||||
\(343\) | 8.36391 | 0.451609 | ||||||||
\(344\) | 5.22747 | 0.281846 | ||||||||
\(345\) | −1.09169 | −0.0587747 | ||||||||
\(346\) | −19.7961 | −1.06425 | ||||||||
\(347\) | 32.7399 | 1.75757 | 0.878784 | − | 0.477220i | \(-0.158355\pi\) | ||||
0.878784 | + | 0.477220i | \(0.158355\pi\) | |||||||
\(348\) | −10.7459 | −0.576041 | ||||||||
\(349\) | −22.3611 | −1.19696 | −0.598482 | − | 0.801137i | \(-0.704229\pi\) | ||||
−0.598482 | + | 0.801137i | \(0.704229\pi\) | |||||||
\(350\) | 3.06278 | 0.163712 | ||||||||
\(351\) | 17.5038 | 0.934284 | ||||||||
\(352\) | 4.91299 | 0.261863 | ||||||||
\(353\) | −29.4548 | −1.56772 | −0.783860 | − | 0.620937i | \(-0.786752\pi\) | ||||
−0.783860 | + | 0.620937i | \(0.786752\pi\) | |||||||
\(354\) | −26.0919 | −1.38677 | ||||||||
\(355\) | 0.0672066 | 0.00356696 | ||||||||
\(356\) | 15.2114 | 0.806205 | ||||||||
\(357\) | 1.40984 | 0.0746164 | ||||||||
\(358\) | −4.91078 | −0.259543 | ||||||||
\(359\) | 19.3394 | 1.02070 | 0.510348 | − | 0.859968i | \(-0.329517\pi\) | ||||
0.510348 | + | 0.859968i | \(0.329517\pi\) | |||||||
\(360\) | −0.671297 | −0.0353804 | ||||||||
\(361\) | −18.1557 | −0.955564 | ||||||||
\(362\) | −3.08931 | −0.162370 | ||||||||
\(363\) | −40.0506 | −2.10211 | ||||||||
\(364\) | 1.07024 | 0.0560956 | ||||||||
\(365\) | 0.0384871 | 0.00201451 | ||||||||
\(366\) | 9.83113 | 0.513881 | ||||||||
\(367\) | −27.7582 | −1.44897 | −0.724483 | − | 0.689293i | \(-0.757921\pi\) | ||||
−0.724483 | + | 0.689293i | \(0.757921\pi\) | |||||||
\(368\) | −3.35738 | −0.175015 | ||||||||
\(369\) | −62.5998 | −3.25882 | ||||||||
\(370\) | 0.190243 | 0.00989026 | ||||||||
\(371\) | −3.79034 | −0.196785 | ||||||||
\(372\) | 18.6927 | 0.969169 | ||||||||
\(373\) | −11.2325 | −0.581598 | −0.290799 | − | 0.956784i | \(-0.593921\pi\) | ||||
−0.290799 | + | 0.956784i | \(0.593921\pi\) | |||||||
\(374\) | 3.70070 | 0.191359 | ||||||||
\(375\) | −3.24792 | −0.167722 | ||||||||
\(376\) | −8.14368 | −0.419978 | ||||||||
\(377\) | −6.14457 | −0.316462 | ||||||||
\(378\) | 6.16485 | 0.317086 | ||||||||
\(379\) | 24.1984 | 1.24299 | 0.621495 | − | 0.783418i | \(-0.286526\pi\) | ||||
0.621495 | + | 0.783418i | \(0.286526\pi\) | |||||||
\(380\) | −0.0980052 | −0.00502756 | ||||||||
\(381\) | 42.7634 | 2.19084 | ||||||||
\(382\) | 11.5369 | 0.590277 | ||||||||
\(383\) | 20.6939 | 1.05741 | 0.528704 | − | 0.848806i | \(-0.322678\pi\) | ||||
0.528704 | + | 0.848806i | \(0.322678\pi\) | |||||||
\(384\) | −3.04857 | −0.155572 | ||||||||
\(385\) | 0.321725 | 0.0163966 | ||||||||
\(386\) | −17.7635 | −0.904138 | ||||||||
\(387\) | 32.9004 | 1.67242 | ||||||||
\(388\) | −2.30536 | −0.117037 | ||||||||
\(389\) | −25.5726 | −1.29658 | −0.648290 | − | 0.761394i | \(-0.724516\pi\) | ||||
−0.648290 | + | 0.761394i | \(0.724516\pi\) | |||||||
\(390\) | −0.566819 | −0.0287020 | ||||||||
\(391\) | −2.52894 | −0.127894 | ||||||||
\(392\) | −6.62306 | −0.334515 | ||||||||
\(393\) | 26.2245 | 1.32285 | ||||||||
\(394\) | 14.5005 | 0.730525 | ||||||||
\(395\) | −1.51034 | −0.0759933 | ||||||||
\(396\) | 30.9212 | 1.55385 | ||||||||
\(397\) | −8.57870 | −0.430553 | −0.215276 | − | 0.976553i | \(-0.569065\pi\) | ||||
−0.215276 | + | 0.976553i | \(0.569065\pi\) | |||||||
\(398\) | −4.28047 | −0.214561 | ||||||||
\(399\) | 1.71979 | 0.0860972 | ||||||||
\(400\) | −4.98862 | −0.249431 | ||||||||
\(401\) | 15.1107 | 0.754591 | 0.377295 | − | 0.926093i | \(-0.376854\pi\) | ||||
0.377295 | + | 0.926093i | \(0.376854\pi\) | |||||||
\(402\) | 12.7585 | 0.636335 | ||||||||
\(403\) | 10.6886 | 0.532436 | ||||||||
\(404\) | 6.36247 | 0.316545 | ||||||||
\(405\) | −1.25115 | −0.0621699 | ||||||||
\(406\) | −2.16412 | −0.107404 | ||||||||
\(407\) | −8.76296 | −0.434364 | ||||||||
\(408\) | −2.29633 | −0.113685 | ||||||||
\(409\) | 34.2678 | 1.69443 | 0.847216 | − | 0.531248i | \(-0.178277\pi\) | ||||
0.847216 | + | 0.531248i | \(0.178277\pi\) | |||||||
\(410\) | 1.06088 | 0.0523932 | ||||||||
\(411\) | −12.9119 | −0.636897 | ||||||||
\(412\) | −0.453725 | −0.0223534 | ||||||||
\(413\) | −5.25467 | −0.258565 | ||||||||
\(414\) | −21.1305 | −1.03851 | ||||||||
\(415\) | −0.467999 | −0.0229732 | ||||||||
\(416\) | −1.74319 | −0.0854669 | ||||||||
\(417\) | 53.8428 | 2.63669 | ||||||||
\(418\) | 4.51431 | 0.220802 | ||||||||
\(419\) | 7.49890 | 0.366345 | 0.183173 | − | 0.983081i | \(-0.441363\pi\) | ||||
0.183173 | + | 0.983081i | \(0.441363\pi\) | |||||||
\(420\) | −0.199634 | −0.00974115 | ||||||||
\(421\) | −26.4786 | −1.29049 | −0.645244 | − | 0.763977i | \(-0.723244\pi\) | ||||
−0.645244 | + | 0.763977i | \(0.723244\pi\) | |||||||
\(422\) | 5.93973 | 0.289141 | ||||||||
\(423\) | −51.2544 | −2.49207 | ||||||||
\(424\) | 6.17368 | 0.299820 | ||||||||
\(425\) | −3.75767 | −0.182274 | ||||||||
\(426\) | 1.92089 | 0.0930676 | ||||||||
\(427\) | 1.97989 | 0.0958138 | ||||||||
\(428\) | −6.75717 | −0.326620 | ||||||||
\(429\) | 26.1088 | 1.26054 | ||||||||
\(430\) | −0.557565 | −0.0268882 | ||||||||
\(431\) | −18.4406 | −0.888253 | −0.444126 | − | 0.895964i | \(-0.646486\pi\) | ||||
−0.444126 | + | 0.895964i | \(0.646486\pi\) | |||||||
\(432\) | −10.0413 | −0.483110 | ||||||||
\(433\) | −39.7443 | −1.90999 | −0.954994 | − | 0.296626i | \(-0.904138\pi\) | ||||
−0.954994 | + | 0.296626i | \(0.904138\pi\) | |||||||
\(434\) | 3.76452 | 0.180703 | ||||||||
\(435\) | 1.14616 | 0.0549544 | ||||||||
\(436\) | 8.33265 | 0.399061 | ||||||||
\(437\) | −3.08493 | −0.147572 | ||||||||
\(438\) | 1.10004 | 0.0525617 | ||||||||
\(439\) | −18.3908 | −0.877747 | −0.438873 | − | 0.898549i | \(-0.644622\pi\) | ||||
−0.438873 | + | 0.898549i | \(0.644622\pi\) | |||||||
\(440\) | −0.524023 | −0.0249818 | ||||||||
\(441\) | −41.6840 | −1.98495 | ||||||||
\(442\) | −1.31305 | −0.0624556 | ||||||||
\(443\) | 40.0120 | 1.90103 | 0.950513 | − | 0.310685i | \(-0.100558\pi\) | ||||
0.950513 | + | 0.310685i | \(0.100558\pi\) | |||||||
\(444\) | 5.43751 | 0.258053 | ||||||||
\(445\) | −1.62246 | −0.0769121 | ||||||||
\(446\) | 18.8388 | 0.892044 | ||||||||
\(447\) | −10.1856 | −0.481763 | ||||||||
\(448\) | −0.613952 | −0.0290065 | ||||||||
\(449\) | −14.8628 | −0.701419 | −0.350709 | − | 0.936484i | \(-0.614060\pi\) | ||||
−0.350709 | + | 0.936484i | \(0.614060\pi\) | |||||||
\(450\) | −31.3972 | −1.48008 | ||||||||
\(451\) | −48.8662 | −2.30102 | ||||||||
\(452\) | −10.8912 | −0.512280 | ||||||||
\(453\) | 4.68742 | 0.220234 | ||||||||
\(454\) | 15.4741 | 0.726235 | ||||||||
\(455\) | −0.114152 | −0.00535153 | ||||||||
\(456\) | −2.80118 | −0.131177 | ||||||||
\(457\) | −7.18478 | −0.336090 | −0.168045 | − | 0.985779i | \(-0.553745\pi\) | ||||
−0.168045 | + | 0.985779i | \(0.553745\pi\) | |||||||
\(458\) | −3.49682 | −0.163396 | ||||||||
\(459\) | −7.56355 | −0.353036 | ||||||||
\(460\) | 0.358100 | 0.0166965 | ||||||||
\(461\) | −1.75478 | −0.0817284 | −0.0408642 | − | 0.999165i | \(-0.513011\pi\) | ||||
−0.0408642 | + | 0.999165i | \(0.513011\pi\) | |||||||
\(462\) | 9.19553 | 0.427815 | ||||||||
\(463\) | 32.2241 | 1.49758 | 0.748791 | − | 0.662806i | \(-0.230634\pi\) | ||||
0.748791 | + | 0.662806i | \(0.230634\pi\) | |||||||
\(464\) | 3.52490 | 0.163639 | ||||||||
\(465\) | −1.99377 | −0.0924589 | ||||||||
\(466\) | −25.8327 | −1.19668 | ||||||||
\(467\) | −32.6604 | −1.51134 | −0.755671 | − | 0.654952i | \(-0.772689\pi\) | ||||
−0.755671 | + | 0.654952i | \(0.772689\pi\) | |||||||
\(468\) | −10.9712 | −0.507145 | ||||||||
\(469\) | 2.56944 | 0.118646 | ||||||||
\(470\) | 0.868611 | 0.0400660 | ||||||||
\(471\) | 46.4975 | 2.14249 | ||||||||
\(472\) | 8.55876 | 0.393949 | ||||||||
\(473\) | 25.6825 | 1.18088 | ||||||||
\(474\) | −43.1684 | −1.98279 | ||||||||
\(475\) | −4.58380 | −0.210319 | ||||||||
\(476\) | −0.462458 | −0.0211967 | ||||||||
\(477\) | 38.8557 | 1.77908 | ||||||||
\(478\) | 12.5745 | 0.575146 | ||||||||
\(479\) | 38.1370 | 1.74252 | 0.871261 | − | 0.490820i | \(-0.163303\pi\) | ||||
0.871261 | + | 0.490820i | \(0.163303\pi\) | |||||||
\(480\) | 0.325162 | 0.0148416 | ||||||||
\(481\) | 3.10920 | 0.141767 | ||||||||
\(482\) | 6.89941 | 0.314260 | ||||||||
\(483\) | −6.28392 | −0.285928 | ||||||||
\(484\) | 13.1375 | 0.597159 | ||||||||
\(485\) | 0.245891 | 0.0111654 | ||||||||
\(486\) | −5.63640 | −0.255672 | ||||||||
\(487\) | −11.4672 | −0.519630 | −0.259815 | − | 0.965658i | \(-0.583662\pi\) | ||||
−0.259815 | + | 0.965658i | \(0.583662\pi\) | |||||||
\(488\) | −3.22483 | −0.145981 | ||||||||
\(489\) | 44.4191 | 2.00870 | ||||||||
\(490\) | 0.706420 | 0.0319128 | ||||||||
\(491\) | 4.87300 | 0.219916 | 0.109958 | − | 0.993936i | \(-0.464928\pi\) | ||||
0.109958 | + | 0.993936i | \(0.464928\pi\) | |||||||
\(492\) | 30.3221 | 1.36702 | ||||||||
\(493\) | 2.65513 | 0.119581 | ||||||||
\(494\) | −1.60173 | −0.0720653 | ||||||||
\(495\) | −3.29808 | −0.148238 | ||||||||
\(496\) | −6.13162 | −0.275318 | ||||||||
\(497\) | 0.386850 | 0.0173526 | ||||||||
\(498\) | −13.3763 | −0.599407 | ||||||||
\(499\) | 3.32755 | 0.148962 | 0.0744808 | − | 0.997222i | \(-0.476270\pi\) | ||||
0.0744808 | + | 0.997222i | \(0.476270\pi\) | |||||||
\(500\) | 1.06539 | 0.0476458 | ||||||||
\(501\) | −16.6845 | −0.745409 | ||||||||
\(502\) | 7.65888 | 0.341833 | ||||||||
\(503\) | −25.7827 | −1.14959 | −0.574796 | − | 0.818297i | \(-0.694919\pi\) | ||||
−0.574796 | + | 0.818297i | \(0.694919\pi\) | |||||||
\(504\) | −3.86407 | −0.172119 | ||||||||
\(505\) | −0.678625 | −0.0301984 | ||||||||
\(506\) | −16.4948 | −0.733282 | ||||||||
\(507\) | 30.3677 | 1.34868 | ||||||||
\(508\) | −14.0274 | −0.622365 | ||||||||
\(509\) | −31.7711 | −1.40823 | −0.704114 | − | 0.710087i | \(-0.748656\pi\) | ||||
−0.704114 | + | 0.710087i | \(0.748656\pi\) | |||||||
\(510\) | 0.244928 | 0.0108456 | ||||||||
\(511\) | 0.221537 | 0.00980020 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −9.22641 | −0.407356 | ||||||||
\(514\) | −1.00875 | −0.0444942 | ||||||||
\(515\) | 0.0483947 | 0.00213252 | ||||||||
\(516\) | −15.9363 | −0.701556 | ||||||||
\(517\) | −40.0099 | −1.75963 | ||||||||
\(518\) | 1.09506 | 0.0481143 | ||||||||
\(519\) | 60.3498 | 2.64906 | ||||||||
\(520\) | 0.185930 | 0.00815356 | ||||||||
\(521\) | −3.81114 | −0.166969 | −0.0834845 | − | 0.996509i | \(-0.526605\pi\) | ||||
−0.0834845 | + | 0.996509i | \(0.526605\pi\) | |||||||
\(522\) | 22.1849 | 0.971007 | ||||||||
\(523\) | −38.3840 | −1.67841 | −0.839207 | − | 0.543813i | \(-0.816980\pi\) | ||||
−0.839207 | + | 0.543813i | \(0.816980\pi\) | |||||||
\(524\) | −8.60225 | −0.375791 | ||||||||
\(525\) | −9.33708 | −0.407504 | ||||||||
\(526\) | 23.2435 | 1.01347 | ||||||||
\(527\) | −4.61863 | −0.201191 | ||||||||
\(528\) | −14.9776 | −0.651816 | ||||||||
\(529\) | −11.7280 | −0.509914 | ||||||||
\(530\) | −0.658488 | −0.0286029 | ||||||||
\(531\) | 53.8668 | 2.33762 | ||||||||
\(532\) | −0.564130 | −0.0244582 | ||||||||
\(533\) | 17.3383 | 0.751007 | ||||||||
\(534\) | −46.3731 | −2.00676 | ||||||||
\(535\) | 0.720724 | 0.0311596 | ||||||||
\(536\) | −4.18508 | −0.180768 | ||||||||
\(537\) | 14.9708 | 0.646039 | ||||||||
\(538\) | −26.2817 | −1.13309 | ||||||||
\(539\) | −32.5391 | −1.40156 | ||||||||
\(540\) | 1.07101 | 0.0460888 | ||||||||
\(541\) | −42.5303 | −1.82852 | −0.914259 | − | 0.405130i | \(-0.867226\pi\) | ||||
−0.914259 | + | 0.405130i | \(0.867226\pi\) | |||||||
\(542\) | −15.6701 | −0.673087 | ||||||||
\(543\) | 9.41796 | 0.404163 | ||||||||
\(544\) | 0.753248 | 0.0322952 | ||||||||
\(545\) | −0.888766 | −0.0380705 | ||||||||
\(546\) | −3.26268 | −0.139630 | ||||||||
\(547\) | −20.4653 | −0.875034 | −0.437517 | − | 0.899210i | \(-0.644142\pi\) | ||||
−0.437517 | + | 0.899210i | \(0.644142\pi\) | |||||||
\(548\) | 4.23540 | 0.180927 | ||||||||
\(549\) | −20.2963 | −0.866227 | ||||||||
\(550\) | −24.5091 | −1.04507 | ||||||||
\(551\) | 3.23886 | 0.137980 | ||||||||
\(552\) | 10.2352 | 0.435639 | ||||||||
\(553\) | −8.69370 | −0.369694 | ||||||||
\(554\) | −11.5647 | −0.491337 | ||||||||
\(555\) | −0.579969 | −0.0246183 | ||||||||
\(556\) | −17.6617 | −0.749022 | ||||||||
\(557\) | −10.3026 | −0.436536 | −0.218268 | − | 0.975889i | \(-0.570041\pi\) | ||||
−0.218268 | + | 0.975889i | \(0.570041\pi\) | |||||||
\(558\) | −38.5910 | −1.63369 | ||||||||
\(559\) | −9.11246 | −0.385416 | ||||||||
\(560\) | 0.0654846 | 0.00276723 | ||||||||
\(561\) | −11.2818 | −0.476320 | ||||||||
\(562\) | −14.1091 | −0.595156 | ||||||||
\(563\) | −25.4461 | −1.07243 | −0.536213 | − | 0.844083i | \(-0.680145\pi\) | ||||
−0.536213 | + | 0.844083i | \(0.680145\pi\) | |||||||
\(564\) | 24.8266 | 1.04539 | ||||||||
\(565\) | 1.16166 | 0.0488716 | ||||||||
\(566\) | −16.8451 | −0.708052 | ||||||||
\(567\) | −7.20176 | −0.302445 | ||||||||
\(568\) | −0.630097 | −0.0264383 | ||||||||
\(569\) | −33.3982 | −1.40013 | −0.700063 | − | 0.714081i | \(-0.746845\pi\) | ||||
−0.700063 | + | 0.714081i | \(0.746845\pi\) | |||||||
\(570\) | 0.298775 | 0.0125143 | ||||||||
\(571\) | 9.08209 | 0.380073 | 0.190037 | − | 0.981777i | \(-0.439139\pi\) | ||||
0.190037 | + | 0.981777i | \(0.439139\pi\) | |||||||
\(572\) | −8.56428 | −0.358090 | ||||||||
\(573\) | −35.1709 | −1.46929 | ||||||||
\(574\) | 6.10657 | 0.254883 | ||||||||
\(575\) | 16.7487 | 0.698469 | ||||||||
\(576\) | 6.29376 | 0.262240 | ||||||||
\(577\) | 28.6130 | 1.19117 | 0.595587 | − | 0.803291i | \(-0.296919\pi\) | ||||
0.595587 | + | 0.803291i | \(0.296919\pi\) | |||||||
\(578\) | −16.4326 | −0.683507 | ||||||||
\(579\) | 54.1532 | 2.25053 | ||||||||
\(580\) | −0.375968 | −0.0156112 | ||||||||
\(581\) | −2.69386 | −0.111760 | ||||||||
\(582\) | 7.02805 | 0.291322 | ||||||||
\(583\) | 30.3312 | 1.25619 | ||||||||
\(584\) | −0.360837 | −0.0149315 | ||||||||
\(585\) | 1.17020 | 0.0483817 | ||||||||
\(586\) | −0.226701 | −0.00936494 | ||||||||
\(587\) | −8.28498 | −0.341958 | −0.170979 | − | 0.985275i | \(-0.554693\pi\) | ||||
−0.170979 | + | 0.985275i | \(0.554693\pi\) | |||||||
\(588\) | 20.1909 | 0.832657 | ||||||||
\(589\) | −5.63404 | −0.232147 | ||||||||
\(590\) | −0.912882 | −0.0375828 | ||||||||
\(591\) | −44.2058 | −1.81838 | ||||||||
\(592\) | −1.78363 | −0.0733067 | ||||||||
\(593\) | 8.97125 | 0.368405 | 0.184203 | − | 0.982888i | \(-0.441030\pi\) | ||||
0.184203 | + | 0.982888i | \(0.441030\pi\) | |||||||
\(594\) | −49.3326 | −2.02414 | ||||||||
\(595\) | 0.0493261 | 0.00202217 | ||||||||
\(596\) | 3.34112 | 0.136857 | ||||||||
\(597\) | 13.0493 | 0.534072 | ||||||||
\(598\) | 5.85254 | 0.239328 | ||||||||
\(599\) | −0.162180 | −0.00662648 | −0.00331324 | − | 0.999995i | \(-0.501055\pi\) | ||||
−0.00331324 | + | 0.999995i | \(0.501055\pi\) | |||||||
\(600\) | 15.2082 | 0.620870 | ||||||||
\(601\) | 0.893200 | 0.0364344 | 0.0182172 | − | 0.999834i | \(-0.494201\pi\) | ||||
0.0182172 | + | 0.999834i | \(0.494201\pi\) | |||||||
\(602\) | −3.20942 | −0.130806 | ||||||||
\(603\) | −26.3399 | −1.07264 | ||||||||
\(604\) | −1.53758 | −0.0625633 | ||||||||
\(605\) | −1.40125 | −0.0569691 | ||||||||
\(606\) | −19.3964 | −0.787926 | ||||||||
\(607\) | −33.8680 | −1.37466 | −0.687329 | − | 0.726346i | \(-0.741217\pi\) | ||||
−0.687329 | + | 0.726346i | \(0.741217\pi\) | |||||||
\(608\) | 0.918851 | 0.0372643 | ||||||||
\(609\) | 6.59747 | 0.267343 | ||||||||
\(610\) | 0.343963 | 0.0139267 | ||||||||
\(611\) | 14.1960 | 0.574308 | ||||||||
\(612\) | 4.74076 | 0.191634 | ||||||||
\(613\) | 3.60845 | 0.145744 | 0.0728719 | − | 0.997341i | \(-0.476784\pi\) | ||||
0.0728719 | + | 0.997341i | \(0.476784\pi\) | |||||||
\(614\) | −13.6595 | −0.551252 | ||||||||
\(615\) | −3.23417 | −0.130414 | ||||||||
\(616\) | −3.01634 | −0.121532 | ||||||||
\(617\) | 35.4987 | 1.42912 | 0.714562 | − | 0.699573i | \(-0.246626\pi\) | ||||
0.714562 | + | 0.699573i | \(0.246626\pi\) | |||||||
\(618\) | 1.38321 | 0.0556410 | ||||||||
\(619\) | 7.22259 | 0.290300 | 0.145150 | − | 0.989410i | \(-0.453633\pi\) | ||||
0.145150 | + | 0.989410i | \(0.453633\pi\) | |||||||
\(620\) | 0.654003 | 0.0262654 | ||||||||
\(621\) | 33.7123 | 1.35283 | ||||||||
\(622\) | −12.3045 | −0.493367 | ||||||||
\(623\) | −9.33910 | −0.374163 | ||||||||
\(624\) | 5.31423 | 0.212739 | ||||||||
\(625\) | 24.8295 | 0.993179 | ||||||||
\(626\) | 25.9209 | 1.03601 | ||||||||
\(627\) | −13.7622 | −0.549608 | ||||||||
\(628\) | −15.2523 | −0.608631 | ||||||||
\(629\) | −1.34351 | −0.0535694 | ||||||||
\(630\) | 0.412144 | 0.0164202 | ||||||||
\(631\) | 27.5850 | 1.09814 | 0.549071 | − | 0.835775i | \(-0.314982\pi\) | ||||
0.549071 | + | 0.835775i | \(0.314982\pi\) | |||||||
\(632\) | 14.1602 | 0.563263 | ||||||||
\(633\) | −18.1077 | −0.719715 | ||||||||
\(634\) | −18.2940 | −0.726549 | ||||||||
\(635\) | 1.49617 | 0.0593737 | ||||||||
\(636\) | −18.8209 | −0.746296 | ||||||||
\(637\) | 11.5453 | 0.457439 | ||||||||
\(638\) | 17.3178 | 0.685619 | ||||||||
\(639\) | −3.96568 | −0.156880 | ||||||||
\(640\) | −0.106661 | −0.00421613 | ||||||||
\(641\) | −0.286667 | −0.0113227 | −0.00566134 | − | 0.999984i | \(-0.501802\pi\) | ||||
−0.00566134 | + | 0.999984i | \(0.501802\pi\) | |||||||
\(642\) | 20.5997 | 0.813005 | ||||||||
\(643\) | −28.1240 | −1.10910 | −0.554552 | − | 0.832149i | \(-0.687110\pi\) | ||||
−0.554552 | + | 0.832149i | \(0.687110\pi\) | |||||||
\(644\) | 2.06127 | 0.0812254 | ||||||||
\(645\) | 1.69977 | 0.0669286 | ||||||||
\(646\) | 0.692122 | 0.0272312 | ||||||||
\(647\) | −3.07712 | −0.120974 | −0.0604870 | − | 0.998169i | \(-0.519265\pi\) | ||||
−0.0604870 | + | 0.998169i | \(0.519265\pi\) | |||||||
\(648\) | 11.7302 | 0.460804 | ||||||||
\(649\) | 42.0491 | 1.65057 | ||||||||
\(650\) | 8.69611 | 0.341090 | ||||||||
\(651\) | −11.4764 | −0.449796 | ||||||||
\(652\) | −14.5705 | −0.570624 | ||||||||
\(653\) | −21.4278 | −0.838535 | −0.419267 | − | 0.907863i | \(-0.637713\pi\) | ||||
−0.419267 | + | 0.907863i | \(0.637713\pi\) | |||||||
\(654\) | −25.4026 | −0.993322 | ||||||||
\(655\) | 0.917522 | 0.0358505 | ||||||||
\(656\) | −9.94633 | −0.388339 | ||||||||
\(657\) | −2.27102 | −0.0886010 | ||||||||
\(658\) | 4.99983 | 0.194914 | ||||||||
\(659\) | −23.6525 | −0.921372 | −0.460686 | − | 0.887563i | \(-0.652397\pi\) | ||||
−0.460686 | + | 0.887563i | \(0.652397\pi\) | |||||||
\(660\) | 1.59752 | 0.0621834 | ||||||||
\(661\) | −5.78219 | −0.224901 | −0.112451 | − | 0.993657i | \(-0.535870\pi\) | ||||
−0.112451 | + | 0.993657i | \(0.535870\pi\) | |||||||
\(662\) | 14.0821 | 0.547317 | ||||||||
\(663\) | 4.00293 | 0.155461 | ||||||||
\(664\) | 4.38774 | 0.170277 | ||||||||
\(665\) | 0.0601705 | 0.00233331 | ||||||||
\(666\) | −11.2257 | −0.434989 | ||||||||
\(667\) | −11.8344 | −0.458231 | ||||||||
\(668\) | 5.47291 | 0.211753 | ||||||||
\(669\) | −57.4314 | −2.22043 | ||||||||
\(670\) | 0.446383 | 0.0172453 | ||||||||
\(671\) | −15.8436 | −0.611635 | ||||||||
\(672\) | 1.87168 | 0.0722014 | ||||||||
\(673\) | 7.09081 | 0.273331 | 0.136665 | − | 0.990617i | \(-0.456362\pi\) | ||||
0.136665 | + | 0.990617i | \(0.456362\pi\) | |||||||
\(674\) | −1.41883 | −0.0546514 | ||||||||
\(675\) | 50.0920 | 1.92804 | ||||||||
\(676\) | −9.96129 | −0.383127 | ||||||||
\(677\) | 31.3240 | 1.20388 | 0.601940 | − | 0.798541i | \(-0.294394\pi\) | ||||
0.601940 | + | 0.798541i | \(0.294394\pi\) | |||||||
\(678\) | 33.2026 | 1.27514 | ||||||||
\(679\) | 1.41538 | 0.0543174 | ||||||||
\(680\) | −0.0803419 | −0.00308097 | ||||||||
\(681\) | −47.1738 | −1.80770 | ||||||||
\(682\) | −30.1246 | −1.15353 | ||||||||
\(683\) | 37.9091 | 1.45055 | 0.725275 | − | 0.688459i | \(-0.241713\pi\) | ||||
0.725275 | + | 0.688459i | \(0.241713\pi\) | |||||||
\(684\) | 5.78303 | 0.221120 | ||||||||
\(685\) | −0.451750 | −0.0172605 | ||||||||
\(686\) | 8.36391 | 0.319336 | ||||||||
\(687\) | 10.6603 | 0.406715 | ||||||||
\(688\) | 5.22747 | 0.199295 | ||||||||
\(689\) | −10.7619 | −0.409995 | ||||||||
\(690\) | −1.09169 | −0.0415600 | ||||||||
\(691\) | −35.8466 | −1.36367 | −0.681834 | − | 0.731507i | \(-0.738817\pi\) | ||||
−0.681834 | + | 0.731507i | \(0.738817\pi\) | |||||||
\(692\) | −19.7961 | −0.752535 | ||||||||
\(693\) | −18.9841 | −0.721148 | ||||||||
\(694\) | 32.7399 | 1.24279 | ||||||||
\(695\) | 1.88381 | 0.0714568 | ||||||||
\(696\) | −10.7459 | −0.407322 | ||||||||
\(697\) | −7.49205 | −0.283782 | ||||||||
\(698\) | −22.3611 | −0.846381 | ||||||||
\(699\) | 78.7528 | 2.97870 | ||||||||
\(700\) | 3.06278 | 0.115762 | ||||||||
\(701\) | −8.39479 | −0.317067 | −0.158533 | − | 0.987354i | \(-0.550677\pi\) | ||||
−0.158533 | + | 0.987354i | \(0.550677\pi\) | |||||||
\(702\) | 17.5038 | 0.660639 | ||||||||
\(703\) | −1.63889 | −0.0618119 | ||||||||
\(704\) | 4.91299 | 0.185165 | ||||||||
\(705\) | −2.64802 | −0.0997301 | ||||||||
\(706\) | −29.4548 | −1.10855 | ||||||||
\(707\) | −3.90625 | −0.146910 | ||||||||
\(708\) | −26.0919 | −0.980595 | ||||||||
\(709\) | 40.7039 | 1.52867 | 0.764334 | − | 0.644821i | \(-0.223068\pi\) | ||||
0.764334 | + | 0.644821i | \(0.223068\pi\) | |||||||
\(710\) | 0.0672066 | 0.00252222 | ||||||||
\(711\) | 89.1210 | 3.34230 | ||||||||
\(712\) | 15.2114 | 0.570073 | ||||||||
\(713\) | 20.5862 | 0.770958 | ||||||||
\(714\) | 1.40984 | 0.0527618 | ||||||||
\(715\) | 0.913471 | 0.0341619 | ||||||||
\(716\) | −4.91078 | −0.183524 | ||||||||
\(717\) | −38.3344 | −1.43162 | ||||||||
\(718\) | 19.3394 | 0.721741 | ||||||||
\(719\) | −17.9616 | −0.669854 | −0.334927 | − | 0.942244i | \(-0.608712\pi\) | ||||
−0.334927 | + | 0.942244i | \(0.608712\pi\) | |||||||
\(720\) | −0.671297 | −0.0250178 | ||||||||
\(721\) | 0.278566 | 0.0103743 | ||||||||
\(722\) | −18.1557 | −0.675686 | ||||||||
\(723\) | −21.0333 | −0.782237 | ||||||||
\(724\) | −3.08931 | −0.114813 | ||||||||
\(725\) | −17.5844 | −0.653069 | ||||||||
\(726\) | −40.0506 | −1.48642 | ||||||||
\(727\) | 32.8911 | 1.21986 | 0.609932 | − | 0.792454i | \(-0.291197\pi\) | ||||
0.609932 | + | 0.792454i | \(0.291197\pi\) | |||||||
\(728\) | 1.07024 | 0.0396655 | ||||||||
\(729\) | −18.0075 | −0.666945 | ||||||||
\(730\) | 0.0384871 | 0.00142447 | ||||||||
\(731\) | 3.93758 | 0.145637 | ||||||||
\(732\) | 9.83113 | 0.363369 | ||||||||
\(733\) | 9.04047 | 0.333917 | 0.166959 | − | 0.985964i | \(-0.446605\pi\) | ||||
0.166959 | + | 0.985964i | \(0.446605\pi\) | |||||||
\(734\) | −27.7582 | −1.02457 | ||||||||
\(735\) | −2.15357 | −0.0794356 | ||||||||
\(736\) | −3.35738 | −0.123755 | ||||||||
\(737\) | −20.5613 | −0.757383 | ||||||||
\(738\) | −62.5998 | −2.30433 | ||||||||
\(739\) | 16.0773 | 0.591412 | 0.295706 | − | 0.955279i | \(-0.404445\pi\) | ||||
0.295706 | + | 0.955279i | \(0.404445\pi\) | |||||||
\(740\) | 0.190243 | 0.00699347 | ||||||||
\(741\) | 4.88298 | 0.179381 | ||||||||
\(742\) | −3.79034 | −0.139148 | ||||||||
\(743\) | 24.2251 | 0.888734 | 0.444367 | − | 0.895845i | \(-0.353429\pi\) | ||||
0.444367 | + | 0.895845i | \(0.353429\pi\) | |||||||
\(744\) | 18.6927 | 0.685306 | ||||||||
\(745\) | −0.356366 | −0.0130562 | ||||||||
\(746\) | −11.2325 | −0.411252 | ||||||||
\(747\) | 27.6154 | 1.01039 | ||||||||
\(748\) | 3.70070 | 0.135311 | ||||||||
\(749\) | 4.14858 | 0.151586 | ||||||||
\(750\) | −3.24792 | −0.118597 | ||||||||
\(751\) | 9.64049 | 0.351787 | 0.175893 | − | 0.984409i | \(-0.443719\pi\) | ||||
0.175893 | + | 0.984409i | \(0.443719\pi\) | |||||||
\(752\) | −8.14368 | −0.296970 | ||||||||
\(753\) | −23.3486 | −0.850871 | ||||||||
\(754\) | −6.14457 | −0.223772 | ||||||||
\(755\) | 0.163999 | 0.00596855 | ||||||||
\(756\) | 6.16485 | 0.224214 | ||||||||
\(757\) | −8.34692 | −0.303374 | −0.151687 | − | 0.988429i | \(-0.548471\pi\) | ||||
−0.151687 | + | 0.988429i | \(0.548471\pi\) | |||||||
\(758\) | 24.1984 | 0.878926 | ||||||||
\(759\) | 50.2854 | 1.82525 | ||||||||
\(760\) | −0.0980052 | −0.00355502 | ||||||||
\(761\) | 11.4700 | 0.415786 | 0.207893 | − | 0.978152i | \(-0.433339\pi\) | ||||
0.207893 | + | 0.978152i | \(0.433339\pi\) | |||||||
\(762\) | 42.7634 | 1.54916 | ||||||||
\(763\) | −5.11585 | −0.185206 | ||||||||
\(764\) | 11.5369 | 0.417389 | ||||||||
\(765\) | −0.505653 | −0.0182819 | ||||||||
\(766\) | 20.6939 | 0.747701 | ||||||||
\(767\) | −14.9195 | −0.538713 | ||||||||
\(768\) | −3.04857 | −0.110006 | ||||||||
\(769\) | 0.0609674 | 0.00219854 | 0.00109927 | − | 0.999999i | \(-0.499650\pi\) | ||||
0.00109927 | + | 0.999999i | \(0.499650\pi\) | |||||||
\(770\) | 0.321725 | 0.0115942 | ||||||||
\(771\) | 3.07525 | 0.110752 | ||||||||
\(772\) | −17.7635 | −0.639322 | ||||||||
\(773\) | −7.77696 | −0.279718 | −0.139859 | − | 0.990171i | \(-0.544665\pi\) | ||||
−0.139859 | + | 0.990171i | \(0.544665\pi\) | |||||||
\(774\) | 32.9004 | 1.18258 | ||||||||
\(775\) | 30.5884 | 1.09877 | ||||||||
\(776\) | −2.30536 | −0.0827577 | ||||||||
\(777\) | −3.33837 | −0.119764 | ||||||||
\(778\) | −25.5726 | −0.916820 | ||||||||
\(779\) | −9.13919 | −0.327445 | ||||||||
\(780\) | −0.566819 | −0.0202954 | ||||||||
\(781\) | −3.09566 | −0.110772 | ||||||||
\(782\) | −2.52894 | −0.0904346 | ||||||||
\(783\) | −35.3944 | −1.26489 | ||||||||
\(784\) | −6.62306 | −0.236538 | ||||||||
\(785\) | 1.62682 | 0.0580636 | ||||||||
\(786\) | 26.2245 | 0.935398 | ||||||||
\(787\) | −23.7962 | −0.848242 | −0.424121 | − | 0.905606i | \(-0.639417\pi\) | ||||
−0.424121 | + | 0.905606i | \(0.639417\pi\) | |||||||
\(788\) | 14.5005 | 0.516559 | ||||||||
\(789\) | −70.8594 | −2.52266 | ||||||||
\(790\) | −1.51034 | −0.0537354 | ||||||||
\(791\) | 6.68669 | 0.237751 | ||||||||
\(792\) | 30.9212 | 1.09874 | ||||||||
\(793\) | 5.62150 | 0.199625 | ||||||||
\(794\) | −8.57870 | −0.304447 | ||||||||
\(795\) | 2.00745 | 0.0711968 | ||||||||
\(796\) | −4.28047 | −0.151717 | ||||||||
\(797\) | −9.40157 | −0.333021 | −0.166510 | − | 0.986040i | \(-0.553250\pi\) | ||||
−0.166510 | + | 0.986040i | \(0.553250\pi\) | |||||||
\(798\) | 1.71979 | 0.0608799 | ||||||||
\(799\) | −6.13421 | −0.217013 | ||||||||
\(800\) | −4.98862 | −0.176374 | ||||||||
\(801\) | 95.7372 | 3.38271 | ||||||||
\(802\) | 15.1107 | 0.533576 | ||||||||
\(803\) | −1.77279 | −0.0625604 | ||||||||
\(804\) | 12.7585 | 0.449957 | ||||||||
\(805\) | −0.219856 | −0.00774892 | ||||||||
\(806\) | 10.6886 | 0.376489 | ||||||||
\(807\) | 80.1216 | 2.82041 | ||||||||
\(808\) | 6.36247 | 0.223831 | ||||||||
\(809\) | 12.5746 | 0.442099 | 0.221049 | − | 0.975263i | \(-0.429052\pi\) | ||||
0.221049 | + | 0.975263i | \(0.429052\pi\) | |||||||
\(810\) | −1.25115 | −0.0439608 | ||||||||
\(811\) | 44.3058 | 1.55579 | 0.777894 | − | 0.628396i | \(-0.216288\pi\) | ||||
0.777894 | + | 0.628396i | \(0.216288\pi\) | |||||||
\(812\) | −2.16412 | −0.0759458 | ||||||||
\(813\) | 47.7712 | 1.67541 | ||||||||
\(814\) | −8.76296 | −0.307142 | ||||||||
\(815\) | 1.55410 | 0.0544376 | ||||||||
\(816\) | −2.29633 | −0.0803875 | ||||||||
\(817\) | 4.80326 | 0.168045 | ||||||||
\(818\) | 34.2678 | 1.19815 | ||||||||
\(819\) | 6.73580 | 0.235368 | ||||||||
\(820\) | 1.06088 | 0.0370476 | ||||||||
\(821\) | 22.7577 | 0.794249 | 0.397125 | − | 0.917765i | \(-0.370008\pi\) | ||||
0.397125 | + | 0.917765i | \(0.370008\pi\) | |||||||
\(822\) | −12.9119 | −0.450354 | ||||||||
\(823\) | −52.9089 | −1.84429 | −0.922144 | − | 0.386846i | \(-0.873564\pi\) | ||||
−0.922144 | + | 0.386846i | \(0.873564\pi\) | |||||||
\(824\) | −0.453725 | −0.0158063 | ||||||||
\(825\) | 74.7176 | 2.60133 | ||||||||
\(826\) | −5.25467 | −0.182833 | ||||||||
\(827\) | −39.8726 | −1.38651 | −0.693253 | − | 0.720695i | \(-0.743823\pi\) | ||||
−0.693253 | + | 0.720695i | \(0.743823\pi\) | |||||||
\(828\) | −21.1305 | −0.734337 | ||||||||
\(829\) | 18.1965 | 0.631990 | 0.315995 | − | 0.948761i | \(-0.397662\pi\) | ||||
0.315995 | + | 0.948761i | \(0.397662\pi\) | |||||||
\(830\) | −0.467999 | −0.0162445 | ||||||||
\(831\) | 35.2558 | 1.22301 | ||||||||
\(832\) | −1.74319 | −0.0604342 | ||||||||
\(833\) | −4.98881 | −0.172852 | ||||||||
\(834\) | 53.8428 | 1.86442 | ||||||||
\(835\) | −0.583744 | −0.0202013 | ||||||||
\(836\) | 4.51431 | 0.156131 | ||||||||
\(837\) | 61.5692 | 2.12814 | ||||||||
\(838\) | 7.49890 | 0.259045 | ||||||||
\(839\) | 18.5130 | 0.639141 | 0.319570 | − | 0.947563i | \(-0.396461\pi\) | ||||
0.319570 | + | 0.947563i | \(0.396461\pi\) | |||||||
\(840\) | −0.199634 | −0.00688803 | ||||||||
\(841\) | −16.5751 | −0.571554 | ||||||||
\(842\) | −26.4786 | −0.912512 | ||||||||
\(843\) | 43.0125 | 1.48143 | ||||||||
\(844\) | 5.93973 | 0.204454 | ||||||||
\(845\) | 1.06248 | 0.0365503 | ||||||||
\(846\) | −51.2544 | −1.76216 | ||||||||
\(847\) | −8.06580 | −0.277144 | ||||||||
\(848\) | 6.17368 | 0.212005 | ||||||||
\(849\) | 51.3534 | 1.76244 | ||||||||
\(850\) | −3.75767 | −0.128887 | ||||||||
\(851\) | 5.98832 | 0.205277 | ||||||||
\(852\) | 1.92089 | 0.0658088 | ||||||||
\(853\) | 27.4700 | 0.940553 | 0.470277 | − | 0.882519i | \(-0.344154\pi\) | ||||
0.470277 | + | 0.882519i | \(0.344154\pi\) | |||||||
\(854\) | 1.97989 | 0.0677506 | ||||||||
\(855\) | −0.616821 | −0.0210948 | ||||||||
\(856\) | −6.75717 | −0.230955 | ||||||||
\(857\) | 47.0770 | 1.60812 | 0.804059 | − | 0.594549i | \(-0.202669\pi\) | ||||
0.804059 | + | 0.594549i | \(0.202669\pi\) | |||||||
\(858\) | 26.1088 | 0.891339 | ||||||||
\(859\) | −21.4307 | −0.731205 | −0.365602 | − | 0.930771i | \(-0.619137\pi\) | ||||
−0.365602 | + | 0.930771i | \(0.619137\pi\) | |||||||
\(860\) | −0.557565 | −0.0190128 | ||||||||
\(861\) | −18.6163 | −0.634442 | ||||||||
\(862\) | −18.4406 | −0.628090 | ||||||||
\(863\) | −8.84649 | −0.301138 | −0.150569 | − | 0.988600i | \(-0.548111\pi\) | ||||
−0.150569 | + | 0.988600i | \(0.548111\pi\) | |||||||
\(864\) | −10.0413 | −0.341610 | ||||||||
\(865\) | 2.11147 | 0.0717920 | ||||||||
\(866\) | −39.7443 | −1.35056 | ||||||||
\(867\) | 50.0959 | 1.70135 | ||||||||
\(868\) | 3.76452 | 0.127776 | ||||||||
\(869\) | 69.5690 | 2.35997 | ||||||||
\(870\) | 1.14616 | 0.0388586 | ||||||||
\(871\) | 7.29538 | 0.247195 | ||||||||
\(872\) | 8.33265 | 0.282179 | ||||||||
\(873\) | −14.5094 | −0.491069 | ||||||||
\(874\) | −3.08493 | −0.104349 | ||||||||
\(875\) | −0.654101 | −0.0221126 | ||||||||
\(876\) | 1.10004 | 0.0371667 | ||||||||
\(877\) | 41.9319 | 1.41594 | 0.707970 | − | 0.706243i | \(-0.249611\pi\) | ||||
0.707970 | + | 0.706243i | \(0.249611\pi\) | |||||||
\(878\) | −18.3908 | −0.620661 | ||||||||
\(879\) | 0.691114 | 0.0233107 | ||||||||
\(880\) | −0.524023 | −0.0176648 | ||||||||
\(881\) | 3.22506 | 0.108655 | 0.0543275 | − | 0.998523i | \(-0.482699\pi\) | ||||
0.0543275 | + | 0.998523i | \(0.482699\pi\) | |||||||
\(882\) | −41.6840 | −1.40357 | ||||||||
\(883\) | −14.5819 | −0.490720 | −0.245360 | − | 0.969432i | \(-0.578906\pi\) | ||||
−0.245360 | + | 0.969432i | \(0.578906\pi\) | |||||||
\(884\) | −1.31305 | −0.0441628 | ||||||||
\(885\) | 2.78298 | 0.0935490 | ||||||||
\(886\) | 40.0120 | 1.34423 | ||||||||
\(887\) | 9.12280 | 0.306314 | 0.153157 | − | 0.988202i | \(-0.451056\pi\) | ||||
0.153157 | + | 0.988202i | \(0.451056\pi\) | |||||||
\(888\) | 5.43751 | 0.182471 | ||||||||
\(889\) | 8.61215 | 0.288842 | ||||||||
\(890\) | −1.62246 | −0.0543851 | ||||||||
\(891\) | 57.6302 | 1.93068 | ||||||||
\(892\) | 18.8388 | 0.630770 | ||||||||
\(893\) | −7.48283 | −0.250403 | ||||||||
\(894\) | −10.1856 | −0.340658 | ||||||||
\(895\) | 0.523787 | 0.0175083 | ||||||||
\(896\) | −0.613952 | −0.0205107 | ||||||||
\(897\) | −17.8419 | −0.595723 | ||||||||
\(898\) | −14.8628 | −0.495978 | ||||||||
\(899\) | −21.6134 | −0.720846 | ||||||||
\(900\) | −31.3972 | −1.04657 | ||||||||
\(901\) | 4.65031 | 0.154924 | ||||||||
\(902\) | −48.8662 | −1.62707 | ||||||||
\(903\) | 9.78412 | 0.325595 | ||||||||
\(904\) | −10.8912 | −0.362237 | ||||||||
\(905\) | 0.329507 | 0.0109532 | ||||||||
\(906\) | 4.68742 | 0.155729 | ||||||||
\(907\) | −31.5625 | −1.04802 | −0.524008 | − | 0.851714i | \(-0.675564\pi\) | ||||
−0.524008 | + | 0.851714i | \(0.675564\pi\) | |||||||
\(908\) | 15.4741 | 0.513525 | ||||||||
\(909\) | 40.0439 | 1.32817 | ||||||||
\(910\) | −0.114152 | −0.00378410 | ||||||||
\(911\) | 11.1509 | 0.369447 | 0.184723 | − | 0.982791i | \(-0.440861\pi\) | ||||
0.184723 | + | 0.982791i | \(0.440861\pi\) | |||||||
\(912\) | −2.80118 | −0.0927563 | ||||||||
\(913\) | 21.5569 | 0.713430 | ||||||||
\(914\) | −7.18478 | −0.237651 | ||||||||
\(915\) | −1.04859 | −0.0346655 | ||||||||
\(916\) | −3.49682 | −0.115538 | ||||||||
\(917\) | 5.28137 | 0.174406 | ||||||||
\(918\) | −7.56355 | −0.249635 | ||||||||
\(919\) | −6.67855 | −0.220305 | −0.110153 | − | 0.993915i | \(-0.535134\pi\) | ||||
−0.110153 | + | 0.993915i | \(0.535134\pi\) | |||||||
\(920\) | 0.358100 | 0.0118062 | ||||||||
\(921\) | 41.6419 | 1.37215 | ||||||||
\(922\) | −1.75478 | −0.0577907 | ||||||||
\(923\) | 1.09838 | 0.0361536 | ||||||||
\(924\) | 9.19553 | 0.302511 | ||||||||
\(925\) | 8.89785 | 0.292560 | ||||||||
\(926\) | 32.2241 | 1.05895 | ||||||||
\(927\) | −2.85564 | −0.0937915 | ||||||||
\(928\) | 3.52490 | 0.115711 | ||||||||
\(929\) | 3.01293 | 0.0988510 | 0.0494255 | − | 0.998778i | \(-0.484261\pi\) | ||||
0.0494255 | + | 0.998778i | \(0.484261\pi\) | |||||||
\(930\) | −1.99377 | −0.0653783 | ||||||||
\(931\) | −6.08560 | −0.199448 | ||||||||
\(932\) | −25.8327 | −0.846179 | ||||||||
\(933\) | 37.5112 | 1.22806 | ||||||||
\(934\) | −32.6604 | −1.06868 | ||||||||
\(935\) | −0.394719 | −0.0129087 | ||||||||
\(936\) | −10.9712 | −0.358605 | ||||||||
\(937\) | −23.5473 | −0.769256 | −0.384628 | − | 0.923072i | \(-0.625670\pi\) | ||||
−0.384628 | + | 0.923072i | \(0.625670\pi\) | |||||||
\(938\) | 2.56944 | 0.0838951 | ||||||||
\(939\) | −79.0215 | −2.57877 | ||||||||
\(940\) | 0.868611 | 0.0283310 | ||||||||
\(941\) | 27.4812 | 0.895861 | 0.447930 | − | 0.894068i | \(-0.352161\pi\) | ||||
0.447930 | + | 0.894068i | \(0.352161\pi\) | |||||||
\(942\) | 46.4975 | 1.51497 | ||||||||
\(943\) | 33.3936 | 1.08744 | ||||||||
\(944\) | 8.55876 | 0.278564 | ||||||||
\(945\) | −0.657547 | −0.0213900 | ||||||||
\(946\) | 25.6825 | 0.835011 | ||||||||
\(947\) | −2.64385 | −0.0859136 | −0.0429568 | − | 0.999077i | \(-0.513678\pi\) | ||||
−0.0429568 | + | 0.999077i | \(0.513678\pi\) | |||||||
\(948\) | −43.1684 | −1.40204 | ||||||||
\(949\) | 0.629007 | 0.0204184 | ||||||||
\(950\) | −4.58380 | −0.148718 | ||||||||
\(951\) | 55.7706 | 1.80849 | ||||||||
\(952\) | −0.462458 | −0.0149884 | ||||||||
\(953\) | −48.5720 | −1.57340 | −0.786701 | − | 0.617334i | \(-0.788213\pi\) | ||||
−0.786701 | + | 0.617334i | \(0.788213\pi\) | |||||||
\(954\) | 38.8557 | 1.25800 | ||||||||
\(955\) | −1.23053 | −0.0398190 | ||||||||
\(956\) | 12.5745 | 0.406690 | ||||||||
\(957\) | −52.7945 | −1.70661 | ||||||||
\(958\) | 38.1370 | 1.23215 | ||||||||
\(959\) | −2.60033 | −0.0839691 | ||||||||
\(960\) | 0.325162 | 0.0104946 | ||||||||
\(961\) | 6.59679 | 0.212800 | ||||||||
\(962\) | 3.10920 | 0.100245 | ||||||||
\(963\) | −42.5280 | −1.37045 | ||||||||
\(964\) | 6.89941 | 0.222215 | ||||||||
\(965\) | 1.89467 | 0.0609914 | ||||||||
\(966\) | −6.28392 | −0.202182 | ||||||||
\(967\) | 25.1306 | 0.808147 | 0.404074 | − | 0.914727i | \(-0.367594\pi\) | ||||
0.404074 | + | 0.914727i | \(0.367594\pi\) | |||||||
\(968\) | 13.1375 | 0.422255 | ||||||||
\(969\) | −2.10998 | −0.0677824 | ||||||||
\(970\) | 0.245891 | 0.00789510 | ||||||||
\(971\) | −3.99028 | −0.128054 | −0.0640272 | − | 0.997948i | \(-0.520394\pi\) | ||||
−0.0640272 | + | 0.997948i | \(0.520394\pi\) | |||||||
\(972\) | −5.63640 | −0.180788 | ||||||||
\(973\) | 10.8434 | 0.347624 | ||||||||
\(974\) | −11.4672 | −0.367434 | ||||||||
\(975\) | −26.5107 | −0.849022 | ||||||||
\(976\) | −3.22483 | −0.103224 | ||||||||
\(977\) | −33.5520 | −1.07342 | −0.536712 | − | 0.843766i | \(-0.680334\pi\) | ||||
−0.536712 | + | 0.843766i | \(0.680334\pi\) | |||||||
\(978\) | 44.4191 | 1.42036 | ||||||||
\(979\) | 74.7337 | 2.38850 | ||||||||
\(980\) | 0.706420 | 0.0225658 | ||||||||
\(981\) | 52.4437 | 1.67440 | ||||||||
\(982\) | 4.87300 | 0.155504 | ||||||||
\(983\) | −27.3889 | −0.873571 | −0.436786 | − | 0.899566i | \(-0.643883\pi\) | ||||
−0.436786 | + | 0.899566i | \(0.643883\pi\) | |||||||
\(984\) | 30.3221 | 0.966632 | ||||||||
\(985\) | −1.54663 | −0.0492799 | ||||||||
\(986\) | 2.65513 | 0.0845564 | ||||||||
\(987\) | −15.2423 | −0.485169 | ||||||||
\(988\) | −1.60173 | −0.0509578 | ||||||||
\(989\) | −17.5506 | −0.558076 | ||||||||
\(990\) | −3.29808 | −0.104820 | ||||||||
\(991\) | 23.5918 | 0.749418 | 0.374709 | − | 0.927142i | \(-0.377743\pi\) | ||||
0.374709 | + | 0.927142i | \(0.377743\pi\) | |||||||
\(992\) | −6.13162 | −0.194679 | ||||||||
\(993\) | −42.9303 | −1.36235 | ||||||||
\(994\) | 0.386850 | 0.0122701 | ||||||||
\(995\) | 0.456558 | 0.0144739 | ||||||||
\(996\) | −13.3763 | −0.423845 | ||||||||
\(997\) | −52.7751 | −1.67140 | −0.835702 | − | 0.549184i | \(-0.814939\pi\) | ||||
−0.835702 | + | 0.549184i | \(0.814939\pi\) | |||||||
\(998\) | 3.32755 | 0.105332 | ||||||||
\(999\) | 17.9099 | 0.566643 |
(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 | 8002.2.a.d.1.5 | ✓ | 69 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8002.2.a.d.1.5 | ✓ | 69 | 1.1 | even | 1 | trivial |