Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2001,2,Mod(1,2001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2001 = 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2001.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: | \(15.9780654445\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} - 33 x^{18} + 64 x^{17} + 453 x^{16} - 846 x^{15} - 3353 x^{14} + 5985 x^{13} + 14484 x^{12} - 24566 x^{11} - 36791 x^{10} + 59410 x^{9} + 52109 x^{8} + \cdots - 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(0.458217\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.458217 | 0.324008 | 0.162004 | − | 0.986790i | \(-0.448204\pi\) | ||||
0.162004 | + | 0.986790i | \(0.448204\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.79004 | −0.895018 | ||||||||
\(5\) | −0.388274 | −0.173641 | −0.0868206 | − | 0.996224i | \(-0.527671\pi\) | ||||
−0.0868206 | + | 0.996224i | \(0.527671\pi\) | |||||||
\(6\) | 0.458217 | 0.187066 | ||||||||
\(7\) | −4.22376 | −1.59643 | −0.798215 | − | 0.602372i | \(-0.794222\pi\) | ||||
−0.798215 | + | 0.602372i | \(0.794222\pi\) | |||||||
\(8\) | −1.73666 | −0.614002 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.177914 | −0.0562612 | ||||||||
\(11\) | 2.44305 | 0.736607 | 0.368304 | − | 0.929706i | \(-0.379939\pi\) | ||||
0.368304 | + | 0.929706i | \(0.379939\pi\) | |||||||
\(12\) | −1.79004 | −0.516739 | ||||||||
\(13\) | 0.942751 | 0.261472 | 0.130736 | − | 0.991417i | \(-0.458266\pi\) | ||||
0.130736 | + | 0.991417i | \(0.458266\pi\) | |||||||
\(14\) | −1.93540 | −0.517257 | ||||||||
\(15\) | −0.388274 | −0.100252 | ||||||||
\(16\) | 2.78431 | 0.696077 | ||||||||
\(17\) | −2.35495 | −0.571159 | −0.285579 | − | 0.958355i | \(-0.592186\pi\) | ||||
−0.285579 | + | 0.958355i | \(0.592186\pi\) | |||||||
\(18\) | 0.458217 | 0.108003 | ||||||||
\(19\) | 2.89264 | 0.663617 | 0.331809 | − | 0.943347i | \(-0.392341\pi\) | ||||
0.331809 | + | 0.943347i | \(0.392341\pi\) | |||||||
\(20\) | 0.695024 | 0.155412 | ||||||||
\(21\) | −4.22376 | −0.921699 | ||||||||
\(22\) | 1.11945 | 0.238667 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −1.73666 | −0.354494 | ||||||||
\(25\) | −4.84924 | −0.969849 | ||||||||
\(26\) | 0.431985 | 0.0847191 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 7.56068 | 1.42883 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | −0.177914 | −0.0324824 | ||||||||
\(31\) | 7.75420 | 1.39270 | 0.696348 | − | 0.717704i | \(-0.254807\pi\) | ||||
0.696348 | + | 0.717704i | \(0.254807\pi\) | |||||||
\(32\) | 4.74914 | 0.839537 | ||||||||
\(33\) | 2.44305 | 0.425281 | ||||||||
\(34\) | −1.07908 | −0.185060 | ||||||||
\(35\) | 1.63997 | 0.277206 | ||||||||
\(36\) | −1.79004 | −0.298339 | ||||||||
\(37\) | −2.82580 | −0.464559 | −0.232280 | − | 0.972649i | \(-0.574618\pi\) | ||||
−0.232280 | + | 0.972649i | \(0.574618\pi\) | |||||||
\(38\) | 1.32546 | 0.215018 | ||||||||
\(39\) | 0.942751 | 0.150961 | ||||||||
\(40\) | 0.674299 | 0.106616 | ||||||||
\(41\) | 5.25950 | 0.821395 | 0.410698 | − | 0.911772i | \(-0.365285\pi\) | ||||
0.410698 | + | 0.911772i | \(0.365285\pi\) | |||||||
\(42\) | −1.93540 | −0.298638 | ||||||||
\(43\) | −9.79866 | −1.49428 | −0.747141 | − | 0.664665i | \(-0.768574\pi\) | ||||
−0.747141 | + | 0.664665i | \(0.768574\pi\) | |||||||
\(44\) | −4.37315 | −0.659277 | ||||||||
\(45\) | −0.388274 | −0.0578804 | ||||||||
\(46\) | 0.458217 | 0.0675604 | ||||||||
\(47\) | 9.98999 | 1.45719 | 0.728595 | − | 0.684945i | \(-0.240174\pi\) | ||||
0.728595 | + | 0.684945i | \(0.240174\pi\) | |||||||
\(48\) | 2.78431 | 0.401880 | ||||||||
\(49\) | 10.8401 | 1.54859 | ||||||||
\(50\) | −2.22201 | −0.314239 | ||||||||
\(51\) | −2.35495 | −0.329759 | ||||||||
\(52\) | −1.68756 | −0.234022 | ||||||||
\(53\) | 6.00735 | 0.825173 | 0.412586 | − | 0.910918i | \(-0.364625\pi\) | ||||
0.412586 | + | 0.910918i | \(0.364625\pi\) | |||||||
\(54\) | 0.458217 | 0.0623555 | ||||||||
\(55\) | −0.948572 | −0.127905 | ||||||||
\(56\) | 7.33523 | 0.980212 | ||||||||
\(57\) | 2.89264 | 0.383140 | ||||||||
\(58\) | 0.458217 | 0.0601669 | ||||||||
\(59\) | 8.95684 | 1.16608 | 0.583041 | − | 0.812443i | \(-0.301863\pi\) | ||||
0.583041 | + | 0.812443i | \(0.301863\pi\) | |||||||
\(60\) | 0.695024 | 0.0897272 | ||||||||
\(61\) | 8.75196 | 1.12057 | 0.560287 | − | 0.828299i | \(-0.310691\pi\) | ||||
0.560287 | + | 0.828299i | \(0.310691\pi\) | |||||||
\(62\) | 3.55311 | 0.451245 | ||||||||
\(63\) | −4.22376 | −0.532143 | ||||||||
\(64\) | −3.39248 | −0.424060 | ||||||||
\(65\) | −0.366045 | −0.0454023 | ||||||||
\(66\) | 1.11945 | 0.137795 | ||||||||
\(67\) | −8.58964 | −1.04939 | −0.524696 | − | 0.851290i | \(-0.675821\pi\) | ||||
−0.524696 | + | 0.851290i | \(0.675821\pi\) | |||||||
\(68\) | 4.21544 | 0.511197 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0.751464 | 0.0898171 | ||||||||
\(71\) | 6.86529 | 0.814761 | 0.407380 | − | 0.913259i | \(-0.366442\pi\) | ||||
0.407380 | + | 0.913259i | \(0.366442\pi\) | |||||||
\(72\) | −1.73666 | −0.204667 | ||||||||
\(73\) | 12.2145 | 1.42960 | 0.714802 | − | 0.699327i | \(-0.246517\pi\) | ||||
0.714802 | + | 0.699327i | \(0.246517\pi\) | |||||||
\(74\) | −1.29483 | −0.150521 | ||||||||
\(75\) | −4.84924 | −0.559942 | ||||||||
\(76\) | −5.17793 | −0.593950 | ||||||||
\(77\) | −10.3189 | −1.17594 | ||||||||
\(78\) | 0.431985 | 0.0489126 | ||||||||
\(79\) | −7.05107 | −0.793308 | −0.396654 | − | 0.917968i | \(-0.629829\pi\) | ||||
−0.396654 | + | 0.917968i | \(0.629829\pi\) | |||||||
\(80\) | −1.08107 | −0.120868 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.40999 | 0.266139 | ||||||||
\(83\) | 10.9024 | 1.19669 | 0.598345 | − | 0.801238i | \(-0.295825\pi\) | ||||
0.598345 | + | 0.801238i | \(0.295825\pi\) | |||||||
\(84\) | 7.56068 | 0.824938 | ||||||||
\(85\) | 0.914364 | 0.0991767 | ||||||||
\(86\) | −4.48992 | −0.484160 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | −4.24275 | −0.452279 | ||||||||
\(89\) | 8.73399 | 0.925801 | 0.462901 | − | 0.886410i | \(-0.346809\pi\) | ||||
0.462901 | + | 0.886410i | \(0.346809\pi\) | |||||||
\(90\) | −0.177914 | −0.0187537 | ||||||||
\(91\) | −3.98195 | −0.417422 | ||||||||
\(92\) | −1.79004 | −0.186624 | ||||||||
\(93\) | 7.75420 | 0.804074 | ||||||||
\(94\) | 4.57759 | 0.472142 | ||||||||
\(95\) | −1.12314 | −0.115231 | ||||||||
\(96\) | 4.74914 | 0.484707 | ||||||||
\(97\) | 17.6770 | 1.79483 | 0.897413 | − | 0.441192i | \(-0.145444\pi\) | ||||
0.897413 | + | 0.441192i | \(0.145444\pi\) | |||||||
\(98\) | 4.96713 | 0.501756 | ||||||||
\(99\) | 2.44305 | 0.245536 | ||||||||
\(100\) | 8.68033 | 0.868033 | ||||||||
\(101\) | 8.17134 | 0.813078 | 0.406539 | − | 0.913633i | \(-0.366735\pi\) | ||||
0.406539 | + | 0.913633i | \(0.366735\pi\) | |||||||
\(102\) | −1.07908 | −0.106845 | ||||||||
\(103\) | 9.88143 | 0.973646 | 0.486823 | − | 0.873501i | \(-0.338156\pi\) | ||||
0.486823 | + | 0.873501i | \(0.338156\pi\) | |||||||
\(104\) | −1.63724 | −0.160544 | ||||||||
\(105\) | 1.63997 | 0.160045 | ||||||||
\(106\) | 2.75267 | 0.267363 | ||||||||
\(107\) | −10.5569 | −1.02057 | −0.510285 | − | 0.860005i | \(-0.670460\pi\) | ||||
−0.510285 | + | 0.860005i | \(0.670460\pi\) | |||||||
\(108\) | −1.79004 | −0.172246 | ||||||||
\(109\) | 15.2793 | 1.46349 | 0.731745 | − | 0.681578i | \(-0.238706\pi\) | ||||
0.731745 | + | 0.681578i | \(0.238706\pi\) | |||||||
\(110\) | −0.434652 | −0.0414424 | ||||||||
\(111\) | −2.82580 | −0.268213 | ||||||||
\(112\) | −11.7602 | −1.11124 | ||||||||
\(113\) | −11.6224 | −1.09334 | −0.546670 | − | 0.837348i | \(-0.684105\pi\) | ||||
−0.546670 | + | 0.837348i | \(0.684105\pi\) | |||||||
\(114\) | 1.32546 | 0.124140 | ||||||||
\(115\) | −0.388274 | −0.0362067 | ||||||||
\(116\) | −1.79004 | −0.166201 | ||||||||
\(117\) | 0.942751 | 0.0871573 | ||||||||
\(118\) | 4.10418 | 0.377820 | ||||||||
\(119\) | 9.94673 | 0.911815 | ||||||||
\(120\) | 0.674299 | 0.0615548 | ||||||||
\(121\) | −5.03150 | −0.457409 | ||||||||
\(122\) | 4.01030 | 0.363075 | ||||||||
\(123\) | 5.25950 | 0.474233 | ||||||||
\(124\) | −13.8803 | −1.24649 | ||||||||
\(125\) | 3.82420 | 0.342047 | ||||||||
\(126\) | −1.93540 | −0.172419 | ||||||||
\(127\) | −6.93670 | −0.615532 | −0.307766 | − | 0.951462i | \(-0.599581\pi\) | ||||
−0.307766 | + | 0.951462i | \(0.599581\pi\) | |||||||
\(128\) | −11.0528 | −0.976936 | ||||||||
\(129\) | −9.79866 | −0.862724 | ||||||||
\(130\) | −0.167728 | −0.0147107 | ||||||||
\(131\) | −12.5516 | −1.09664 | −0.548319 | − | 0.836270i | \(-0.684732\pi\) | ||||
−0.548319 | + | 0.836270i | \(0.684732\pi\) | |||||||
\(132\) | −4.37315 | −0.380634 | ||||||||
\(133\) | −12.2178 | −1.05942 | ||||||||
\(134\) | −3.93592 | −0.340012 | ||||||||
\(135\) | −0.388274 | −0.0334173 | ||||||||
\(136\) | 4.08974 | 0.350693 | ||||||||
\(137\) | −11.6780 | −0.997716 | −0.498858 | − | 0.866684i | \(-0.666247\pi\) | ||||
−0.498858 | + | 0.866684i | \(0.666247\pi\) | |||||||
\(138\) | 0.458217 | 0.0390060 | ||||||||
\(139\) | −2.41460 | −0.204804 | −0.102402 | − | 0.994743i | \(-0.532653\pi\) | ||||
−0.102402 | + | 0.994743i | \(0.532653\pi\) | |||||||
\(140\) | −2.93561 | −0.248105 | ||||||||
\(141\) | 9.98999 | 0.841309 | ||||||||
\(142\) | 3.14580 | 0.263989 | ||||||||
\(143\) | 2.30319 | 0.192602 | ||||||||
\(144\) | 2.78431 | 0.232026 | ||||||||
\(145\) | −0.388274 | −0.0322444 | ||||||||
\(146\) | 5.59691 | 0.463204 | ||||||||
\(147\) | 10.8401 | 0.894079 | ||||||||
\(148\) | 5.05829 | 0.415789 | ||||||||
\(149\) | −8.54594 | −0.700110 | −0.350055 | − | 0.936729i | \(-0.613837\pi\) | ||||
−0.350055 | + | 0.936729i | \(0.613837\pi\) | |||||||
\(150\) | −2.22201 | −0.181426 | ||||||||
\(151\) | −4.65908 | −0.379150 | −0.189575 | − | 0.981866i | \(-0.560711\pi\) | ||||
−0.189575 | + | 0.981866i | \(0.560711\pi\) | |||||||
\(152\) | −5.02353 | −0.407462 | ||||||||
\(153\) | −2.35495 | −0.190386 | ||||||||
\(154\) | −4.72828 | −0.381015 | ||||||||
\(155\) | −3.01075 | −0.241829 | ||||||||
\(156\) | −1.68756 | −0.135113 | ||||||||
\(157\) | −6.62907 | −0.529057 | −0.264529 | − | 0.964378i | \(-0.585216\pi\) | ||||
−0.264529 | + | 0.964378i | \(0.585216\pi\) | |||||||
\(158\) | −3.23092 | −0.257038 | ||||||||
\(159\) | 6.00735 | 0.476414 | ||||||||
\(160\) | −1.84396 | −0.145778 | ||||||||
\(161\) | −4.22376 | −0.332879 | ||||||||
\(162\) | 0.458217 | 0.0360009 | ||||||||
\(163\) | 7.80982 | 0.611712 | 0.305856 | − | 0.952078i | \(-0.401057\pi\) | ||||
0.305856 | + | 0.952078i | \(0.401057\pi\) | |||||||
\(164\) | −9.41469 | −0.735164 | ||||||||
\(165\) | −0.948572 | −0.0738462 | ||||||||
\(166\) | 4.99566 | 0.387738 | ||||||||
\(167\) | −20.4339 | −1.58122 | −0.790611 | − | 0.612319i | \(-0.790237\pi\) | ||||
−0.790611 | + | 0.612319i | \(0.790237\pi\) | |||||||
\(168\) | 7.33523 | 0.565925 | ||||||||
\(169\) | −12.1112 | −0.931632 | ||||||||
\(170\) | 0.418977 | 0.0321341 | ||||||||
\(171\) | 2.89264 | 0.221206 | ||||||||
\(172\) | 17.5400 | 1.33741 | ||||||||
\(173\) | −11.5310 | −0.876688 | −0.438344 | − | 0.898807i | \(-0.644435\pi\) | ||||
−0.438344 | + | 0.898807i | \(0.644435\pi\) | |||||||
\(174\) | 0.458217 | 0.0347374 | ||||||||
\(175\) | 20.4820 | 1.54830 | ||||||||
\(176\) | 6.80220 | 0.512735 | ||||||||
\(177\) | 8.95684 | 0.673237 | ||||||||
\(178\) | 4.00207 | 0.299968 | ||||||||
\(179\) | −11.3766 | −0.850327 | −0.425163 | − | 0.905117i | \(-0.639783\pi\) | ||||
−0.425163 | + | 0.905117i | \(0.639783\pi\) | |||||||
\(180\) | 0.695024 | 0.0518040 | ||||||||
\(181\) | 0.967738 | 0.0719314 | 0.0359657 | − | 0.999353i | \(-0.488549\pi\) | ||||
0.0359657 | + | 0.999353i | \(0.488549\pi\) | |||||||
\(182\) | −1.82460 | −0.135248 | ||||||||
\(183\) | 8.75196 | 0.646964 | ||||||||
\(184\) | −1.73666 | −0.128028 | ||||||||
\(185\) | 1.09718 | 0.0806666 | ||||||||
\(186\) | 3.55311 | 0.260527 | ||||||||
\(187\) | −5.75325 | −0.420720 | ||||||||
\(188\) | −17.8825 | −1.30421 | ||||||||
\(189\) | −4.22376 | −0.307233 | ||||||||
\(190\) | −0.514640 | −0.0373359 | ||||||||
\(191\) | 11.6319 | 0.841653 | 0.420826 | − | 0.907141i | \(-0.361740\pi\) | ||||
0.420826 | + | 0.907141i | \(0.361740\pi\) | |||||||
\(192\) | −3.39248 | −0.244831 | ||||||||
\(193\) | 15.4098 | 1.10922 | 0.554610 | − | 0.832110i | \(-0.312867\pi\) | ||||
0.554610 | + | 0.832110i | \(0.312867\pi\) | |||||||
\(194\) | 8.09990 | 0.581539 | ||||||||
\(195\) | −0.366045 | −0.0262130 | ||||||||
\(196\) | −19.4042 | −1.38602 | ||||||||
\(197\) | −9.27867 | −0.661078 | −0.330539 | − | 0.943792i | \(-0.607231\pi\) | ||||
−0.330539 | + | 0.943792i | \(0.607231\pi\) | |||||||
\(198\) | 1.11945 | 0.0795557 | ||||||||
\(199\) | 7.73656 | 0.548430 | 0.274215 | − | 0.961668i | \(-0.411582\pi\) | ||||
0.274215 | + | 0.961668i | \(0.411582\pi\) | |||||||
\(200\) | 8.42149 | 0.595489 | ||||||||
\(201\) | −8.58964 | −0.605866 | ||||||||
\(202\) | 3.74425 | 0.263444 | ||||||||
\(203\) | −4.22376 | −0.296450 | ||||||||
\(204\) | 4.21544 | 0.295140 | ||||||||
\(205\) | −2.04212 | −0.142628 | ||||||||
\(206\) | 4.52784 | 0.315470 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 2.62491 | 0.182005 | ||||||||
\(209\) | 7.06687 | 0.488825 | ||||||||
\(210\) | 0.751464 | 0.0518559 | ||||||||
\(211\) | 16.0483 | 1.10481 | 0.552404 | − | 0.833577i | \(-0.313711\pi\) | ||||
0.552404 | + | 0.833577i | \(0.313711\pi\) | |||||||
\(212\) | −10.7534 | −0.738545 | ||||||||
\(213\) | 6.86529 | 0.470402 | ||||||||
\(214\) | −4.83734 | −0.330673 | ||||||||
\(215\) | 3.80456 | 0.259469 | ||||||||
\(216\) | −1.73666 | −0.118165 | ||||||||
\(217\) | −32.7519 | −2.22334 | ||||||||
\(218\) | 7.00123 | 0.474183 | ||||||||
\(219\) | 12.2145 | 0.825382 | ||||||||
\(220\) | 1.69798 | 0.114478 | ||||||||
\(221\) | −2.22013 | −0.149342 | ||||||||
\(222\) | −1.29483 | −0.0869034 | ||||||||
\(223\) | 17.6200 | 1.17992 | 0.589961 | − | 0.807432i | \(-0.299143\pi\) | ||||
0.589961 | + | 0.807432i | \(0.299143\pi\) | |||||||
\(224\) | −20.0592 | −1.34026 | ||||||||
\(225\) | −4.84924 | −0.323283 | ||||||||
\(226\) | −5.32557 | −0.354252 | ||||||||
\(227\) | −6.15492 | −0.408516 | −0.204258 | − | 0.978917i | \(-0.565478\pi\) | ||||
−0.204258 | + | 0.978917i | \(0.565478\pi\) | |||||||
\(228\) | −5.17793 | −0.342917 | ||||||||
\(229\) | 6.76626 | 0.447127 | 0.223563 | − | 0.974689i | \(-0.428231\pi\) | ||||
0.223563 | + | 0.974689i | \(0.428231\pi\) | |||||||
\(230\) | −0.177914 | −0.0117313 | ||||||||
\(231\) | −10.3189 | −0.678931 | ||||||||
\(232\) | −1.73666 | −0.114017 | ||||||||
\(233\) | −12.9500 | −0.848382 | −0.424191 | − | 0.905573i | \(-0.639441\pi\) | ||||
−0.424191 | + | 0.905573i | \(0.639441\pi\) | |||||||
\(234\) | 0.431985 | 0.0282397 | ||||||||
\(235\) | −3.87885 | −0.253028 | ||||||||
\(236\) | −16.0331 | −1.04366 | ||||||||
\(237\) | −7.05107 | −0.458016 | ||||||||
\(238\) | 4.55776 | 0.295436 | ||||||||
\(239\) | 26.2200 | 1.69603 | 0.848016 | − | 0.529970i | \(-0.177797\pi\) | ||||
0.848016 | + | 0.529970i | \(0.177797\pi\) | |||||||
\(240\) | −1.08107 | −0.0697829 | ||||||||
\(241\) | −13.4553 | −0.866733 | −0.433367 | − | 0.901218i | \(-0.642675\pi\) | ||||
−0.433367 | + | 0.901218i | \(0.642675\pi\) | |||||||
\(242\) | −2.30552 | −0.148205 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −15.6663 | −1.00293 | ||||||||
\(245\) | −4.20893 | −0.268899 | ||||||||
\(246\) | 2.40999 | 0.153655 | ||||||||
\(247\) | 2.72704 | 0.173517 | ||||||||
\(248\) | −13.4664 | −0.855118 | ||||||||
\(249\) | 10.9024 | 0.690910 | ||||||||
\(250\) | 1.75231 | 0.110826 | ||||||||
\(251\) | 6.61094 | 0.417279 | 0.208640 | − | 0.977993i | \(-0.433096\pi\) | ||||
0.208640 | + | 0.977993i | \(0.433096\pi\) | |||||||
\(252\) | 7.56068 | 0.476278 | ||||||||
\(253\) | 2.44305 | 0.153593 | ||||||||
\(254\) | −3.17851 | −0.199438 | ||||||||
\(255\) | 0.914364 | 0.0572597 | ||||||||
\(256\) | 1.72039 | 0.107524 | ||||||||
\(257\) | 12.6358 | 0.788198 | 0.394099 | − | 0.919068i | \(-0.371057\pi\) | ||||
0.394099 | + | 0.919068i | \(0.371057\pi\) | |||||||
\(258\) | −4.48992 | −0.279530 | ||||||||
\(259\) | 11.9355 | 0.741637 | ||||||||
\(260\) | 0.655234 | 0.0406359 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | −5.75135 | −0.355320 | ||||||||
\(263\) | −31.2519 | −1.92707 | −0.963537 | − | 0.267575i | \(-0.913778\pi\) | ||||
−0.963537 | + | 0.267575i | \(0.913778\pi\) | |||||||
\(264\) | −4.24275 | −0.261123 | ||||||||
\(265\) | −2.33249 | −0.143284 | ||||||||
\(266\) | −5.59841 | −0.343261 | ||||||||
\(267\) | 8.73399 | 0.534512 | ||||||||
\(268\) | 15.3758 | 0.939225 | ||||||||
\(269\) | −12.8085 | −0.780946 | −0.390473 | − | 0.920614i | \(-0.627688\pi\) | ||||
−0.390473 | + | 0.920614i | \(0.627688\pi\) | |||||||
\(270\) | −0.177914 | −0.0108275 | ||||||||
\(271\) | −5.91426 | −0.359266 | −0.179633 | − | 0.983734i | \(-0.557491\pi\) | ||||
−0.179633 | + | 0.983734i | \(0.557491\pi\) | |||||||
\(272\) | −6.55689 | −0.397570 | ||||||||
\(273\) | −3.98195 | −0.240999 | ||||||||
\(274\) | −5.35105 | −0.323268 | ||||||||
\(275\) | −11.8469 | −0.714398 | ||||||||
\(276\) | −1.79004 | −0.107748 | ||||||||
\(277\) | 11.5359 | 0.693128 | 0.346564 | − | 0.938026i | \(-0.387348\pi\) | ||||
0.346564 | + | 0.938026i | \(0.387348\pi\) | |||||||
\(278\) | −1.10641 | −0.0663583 | ||||||||
\(279\) | 7.75420 | 0.464232 | ||||||||
\(280\) | −2.84808 | −0.170205 | ||||||||
\(281\) | 22.5802 | 1.34702 | 0.673510 | − | 0.739178i | \(-0.264786\pi\) | ||||
0.673510 | + | 0.739178i | \(0.264786\pi\) | |||||||
\(282\) | 4.57759 | 0.272591 | ||||||||
\(283\) | 15.6402 | 0.929716 | 0.464858 | − | 0.885385i | \(-0.346105\pi\) | ||||
0.464858 | + | 0.885385i | \(0.346105\pi\) | |||||||
\(284\) | −12.2891 | −0.729226 | ||||||||
\(285\) | −1.12314 | −0.0665288 | ||||||||
\(286\) | 1.05536 | 0.0624047 | ||||||||
\(287\) | −22.2148 | −1.31130 | ||||||||
\(288\) | 4.74914 | 0.279846 | ||||||||
\(289\) | −11.4542 | −0.673778 | ||||||||
\(290\) | −0.177914 | −0.0104474 | ||||||||
\(291\) | 17.6770 | 1.03624 | ||||||||
\(292\) | −21.8645 | −1.27952 | ||||||||
\(293\) | 5.69213 | 0.332538 | 0.166269 | − | 0.986080i | \(-0.446828\pi\) | ||||
0.166269 | + | 0.986080i | \(0.446828\pi\) | |||||||
\(294\) | 4.96713 | 0.289689 | ||||||||
\(295\) | −3.47770 | −0.202480 | ||||||||
\(296\) | 4.90746 | 0.285240 | ||||||||
\(297\) | 2.44305 | 0.141760 | ||||||||
\(298\) | −3.91590 | −0.226842 | ||||||||
\(299\) | 0.942751 | 0.0545207 | ||||||||
\(300\) | 8.68033 | 0.501159 | ||||||||
\(301\) | 41.3872 | 2.38552 | ||||||||
\(302\) | −2.13487 | −0.122848 | ||||||||
\(303\) | 8.17134 | 0.469431 | ||||||||
\(304\) | 8.05400 | 0.461929 | ||||||||
\(305\) | −3.39815 | −0.194578 | ||||||||
\(306\) | −1.07908 | −0.0616867 | ||||||||
\(307\) | −0.793984 | −0.0453150 | −0.0226575 | − | 0.999743i | \(-0.507213\pi\) | ||||
−0.0226575 | + | 0.999743i | \(0.507213\pi\) | |||||||
\(308\) | 18.4711 | 1.05249 | ||||||||
\(309\) | 9.88143 | 0.562135 | ||||||||
\(310\) | −1.37958 | −0.0783548 | ||||||||
\(311\) | 33.6511 | 1.90818 | 0.954088 | − | 0.299525i | \(-0.0968283\pi\) | ||||
0.954088 | + | 0.299525i | \(0.0968283\pi\) | |||||||
\(312\) | −1.63724 | −0.0926903 | ||||||||
\(313\) | −17.9983 | −1.01732 | −0.508661 | − | 0.860967i | \(-0.669859\pi\) | ||||
−0.508661 | + | 0.860967i | \(0.669859\pi\) | |||||||
\(314\) | −3.03755 | −0.171419 | ||||||||
\(315\) | 1.63997 | 0.0924020 | ||||||||
\(316\) | 12.6217 | 0.710025 | ||||||||
\(317\) | −11.0791 | −0.622266 | −0.311133 | − | 0.950366i | \(-0.600708\pi\) | ||||
−0.311133 | + | 0.950366i | \(0.600708\pi\) | |||||||
\(318\) | 2.75267 | 0.154362 | ||||||||
\(319\) | 2.44305 | 0.136785 | ||||||||
\(320\) | 1.31721 | 0.0736342 | ||||||||
\(321\) | −10.5569 | −0.589227 | ||||||||
\(322\) | −1.93540 | −0.107856 | ||||||||
\(323\) | −6.81202 | −0.379031 | ||||||||
\(324\) | −1.79004 | −0.0994465 | ||||||||
\(325\) | −4.57163 | −0.253588 | ||||||||
\(326\) | 3.57859 | 0.198200 | ||||||||
\(327\) | 15.2793 | 0.844947 | ||||||||
\(328\) | −9.13396 | −0.504338 | ||||||||
\(329\) | −42.1953 | −2.32630 | ||||||||
\(330\) | −0.434652 | −0.0239268 | ||||||||
\(331\) | 32.2908 | 1.77486 | 0.887430 | − | 0.460942i | \(-0.152488\pi\) | ||||
0.887430 | + | 0.460942i | \(0.152488\pi\) | |||||||
\(332\) | −19.5157 | −1.07106 | ||||||||
\(333\) | −2.82580 | −0.154853 | ||||||||
\(334\) | −9.36316 | −0.512329 | ||||||||
\(335\) | 3.33513 | 0.182218 | ||||||||
\(336\) | −11.7602 | −0.641573 | ||||||||
\(337\) | −11.4739 | −0.625023 | −0.312512 | − | 0.949914i | \(-0.601170\pi\) | ||||
−0.312512 | + | 0.949914i | \(0.601170\pi\) | |||||||
\(338\) | −5.54957 | −0.301857 | ||||||||
\(339\) | −11.6224 | −0.631240 | ||||||||
\(340\) | −1.63674 | −0.0887649 | ||||||||
\(341\) | 18.9439 | 1.02587 | ||||||||
\(342\) | 1.32546 | 0.0716726 | ||||||||
\(343\) | −16.2198 | −0.875785 | ||||||||
\(344\) | 17.0169 | 0.917492 | ||||||||
\(345\) | −0.388274 | −0.0209039 | ||||||||
\(346\) | −5.28372 | −0.284054 | ||||||||
\(347\) | 32.4849 | 1.74388 | 0.871940 | − | 0.489613i | \(-0.162862\pi\) | ||||
0.871940 | + | 0.489613i | \(0.162862\pi\) | |||||||
\(348\) | −1.79004 | −0.0959561 | ||||||||
\(349\) | −20.8858 | −1.11799 | −0.558996 | − | 0.829170i | \(-0.688813\pi\) | ||||
−0.558996 | + | 0.829170i | \(0.688813\pi\) | |||||||
\(350\) | 9.38522 | 0.501661 | ||||||||
\(351\) | 0.942751 | 0.0503203 | ||||||||
\(352\) | 11.6024 | 0.618409 | ||||||||
\(353\) | −9.36223 | −0.498301 | −0.249151 | − | 0.968465i | \(-0.580151\pi\) | ||||
−0.249151 | + | 0.968465i | \(0.580151\pi\) | |||||||
\(354\) | 4.10418 | 0.218135 | ||||||||
\(355\) | −2.66561 | −0.141476 | ||||||||
\(356\) | −15.6342 | −0.828609 | ||||||||
\(357\) | 9.94673 | 0.526437 | ||||||||
\(358\) | −5.21295 | −0.275513 | ||||||||
\(359\) | −9.22588 | −0.486923 | −0.243462 | − | 0.969911i | \(-0.578283\pi\) | ||||
−0.243462 | + | 0.969911i | \(0.578283\pi\) | |||||||
\(360\) | 0.674299 | 0.0355387 | ||||||||
\(361\) | −10.6326 | −0.559612 | ||||||||
\(362\) | 0.443434 | 0.0233064 | ||||||||
\(363\) | −5.03150 | −0.264085 | ||||||||
\(364\) | 7.12784 | 0.373600 | ||||||||
\(365\) | −4.74258 | −0.248238 | ||||||||
\(366\) | 4.01030 | 0.209622 | ||||||||
\(367\) | 10.0371 | 0.523933 | 0.261967 | − | 0.965077i | \(-0.415629\pi\) | ||||
0.261967 | + | 0.965077i | \(0.415629\pi\) | |||||||
\(368\) | 2.78431 | 0.145142 | ||||||||
\(369\) | 5.25950 | 0.273798 | ||||||||
\(370\) | 0.502749 | 0.0261367 | ||||||||
\(371\) | −25.3736 | −1.31733 | ||||||||
\(372\) | −13.8803 | −0.719661 | ||||||||
\(373\) | 35.0846 | 1.81661 | 0.908307 | − | 0.418305i | \(-0.137376\pi\) | ||||
0.908307 | + | 0.418305i | \(0.137376\pi\) | |||||||
\(374\) | −2.63624 | −0.136317 | ||||||||
\(375\) | 3.82420 | 0.197481 | ||||||||
\(376\) | −17.3492 | −0.894718 | ||||||||
\(377\) | 0.942751 | 0.0485541 | ||||||||
\(378\) | −1.93540 | −0.0995462 | ||||||||
\(379\) | 22.9740 | 1.18009 | 0.590047 | − | 0.807369i | \(-0.299109\pi\) | ||||
0.590047 | + | 0.807369i | \(0.299109\pi\) | |||||||
\(380\) | 2.01045 | 0.103134 | ||||||||
\(381\) | −6.93670 | −0.355378 | ||||||||
\(382\) | 5.32993 | 0.272703 | ||||||||
\(383\) | 31.6924 | 1.61941 | 0.809703 | − | 0.586839i | \(-0.199628\pi\) | ||||
0.809703 | + | 0.586839i | \(0.199628\pi\) | |||||||
\(384\) | −11.0528 | −0.564034 | ||||||||
\(385\) | 4.00654 | 0.204192 | ||||||||
\(386\) | 7.06103 | 0.359397 | ||||||||
\(387\) | −9.79866 | −0.498094 | ||||||||
\(388\) | −31.6424 | −1.60640 | ||||||||
\(389\) | 8.44436 | 0.428146 | 0.214073 | − | 0.976818i | \(-0.431327\pi\) | ||||
0.214073 | + | 0.976818i | \(0.431327\pi\) | |||||||
\(390\) | −0.167728 | −0.00849325 | ||||||||
\(391\) | −2.35495 | −0.119095 | ||||||||
\(392\) | −18.8256 | −0.950837 | ||||||||
\(393\) | −12.5516 | −0.633144 | ||||||||
\(394\) | −4.25165 | −0.214195 | ||||||||
\(395\) | 2.73774 | 0.137751 | ||||||||
\(396\) | −4.37315 | −0.219759 | ||||||||
\(397\) | −31.7006 | −1.59101 | −0.795503 | − | 0.605950i | \(-0.792793\pi\) | ||||
−0.795503 | + | 0.605950i | \(0.792793\pi\) | |||||||
\(398\) | 3.54502 | 0.177696 | ||||||||
\(399\) | −12.2178 | −0.611656 | ||||||||
\(400\) | −13.5018 | −0.675089 | ||||||||
\(401\) | −14.8420 | −0.741172 | −0.370586 | − | 0.928798i | \(-0.620843\pi\) | ||||
−0.370586 | + | 0.928798i | \(0.620843\pi\) | |||||||
\(402\) | −3.93592 | −0.196306 | ||||||||
\(403\) | 7.31028 | 0.364151 | ||||||||
\(404\) | −14.6270 | −0.727720 | ||||||||
\(405\) | −0.388274 | −0.0192935 | ||||||||
\(406\) | −1.93540 | −0.0960522 | ||||||||
\(407\) | −6.90358 | −0.342198 | ||||||||
\(408\) | 4.08974 | 0.202472 | ||||||||
\(409\) | 26.2358 | 1.29728 | 0.648638 | − | 0.761097i | \(-0.275339\pi\) | ||||
0.648638 | + | 0.761097i | \(0.275339\pi\) | |||||||
\(410\) | −0.935736 | −0.0462127 | ||||||||
\(411\) | −11.6780 | −0.576032 | ||||||||
\(412\) | −17.6881 | −0.871431 | ||||||||
\(413\) | −37.8315 | −1.86157 | ||||||||
\(414\) | 0.458217 | 0.0225201 | ||||||||
\(415\) | −4.23310 | −0.207795 | ||||||||
\(416\) | 4.47725 | 0.219515 | ||||||||
\(417\) | −2.41460 | −0.118244 | ||||||||
\(418\) | 3.23816 | 0.158384 | ||||||||
\(419\) | −30.9185 | −1.51047 | −0.755233 | − | 0.655456i | \(-0.772476\pi\) | ||||
−0.755233 | + | 0.655456i | \(0.772476\pi\) | |||||||
\(420\) | −2.93561 | −0.143243 | ||||||||
\(421\) | 0.992608 | 0.0483767 | 0.0241884 | − | 0.999707i | \(-0.492300\pi\) | ||||
0.0241884 | + | 0.999707i | \(0.492300\pi\) | |||||||
\(422\) | 7.35359 | 0.357967 | ||||||||
\(423\) | 9.98999 | 0.485730 | ||||||||
\(424\) | −10.4327 | −0.506658 | ||||||||
\(425\) | 11.4197 | 0.553937 | ||||||||
\(426\) | 3.14580 | 0.152414 | ||||||||
\(427\) | −36.9662 | −1.78892 | ||||||||
\(428\) | 18.8972 | 0.913429 | ||||||||
\(429\) | 2.30319 | 0.111199 | ||||||||
\(430\) | 1.74332 | 0.0840701 | ||||||||
\(431\) | −18.1930 | −0.876325 | −0.438163 | − | 0.898896i | \(-0.644371\pi\) | ||||
−0.438163 | + | 0.898896i | \(0.644371\pi\) | |||||||
\(432\) | 2.78431 | 0.133960 | ||||||||
\(433\) | 28.0391 | 1.34747 | 0.673737 | − | 0.738971i | \(-0.264688\pi\) | ||||
0.673737 | + | 0.738971i | \(0.264688\pi\) | |||||||
\(434\) | −15.0075 | −0.720382 | ||||||||
\(435\) | −0.388274 | −0.0186163 | ||||||||
\(436\) | −27.3505 | −1.30985 | ||||||||
\(437\) | 2.89264 | 0.138374 | ||||||||
\(438\) | 5.59691 | 0.267431 | ||||||||
\(439\) | 27.0109 | 1.28916 | 0.644579 | − | 0.764538i | \(-0.277033\pi\) | ||||
0.644579 | + | 0.764538i | \(0.277033\pi\) | |||||||
\(440\) | 1.64735 | 0.0785342 | ||||||||
\(441\) | 10.8401 | 0.516197 | ||||||||
\(442\) | −1.01730 | −0.0483881 | ||||||||
\(443\) | 5.22924 | 0.248449 | 0.124224 | − | 0.992254i | \(-0.460356\pi\) | ||||
0.124224 | + | 0.992254i | \(0.460356\pi\) | |||||||
\(444\) | 5.05829 | 0.240056 | ||||||||
\(445\) | −3.39118 | −0.160757 | ||||||||
\(446\) | 8.07378 | 0.382305 | ||||||||
\(447\) | −8.54594 | −0.404209 | ||||||||
\(448\) | 14.3290 | 0.676982 | ||||||||
\(449\) | 16.8352 | 0.794504 | 0.397252 | − | 0.917709i | \(-0.369964\pi\) | ||||
0.397252 | + | 0.917709i | \(0.369964\pi\) | |||||||
\(450\) | −2.22201 | −0.104746 | ||||||||
\(451\) | 12.8492 | 0.605046 | ||||||||
\(452\) | 20.8045 | 0.978560 | ||||||||
\(453\) | −4.65908 | −0.218903 | ||||||||
\(454\) | −2.82029 | −0.132363 | ||||||||
\(455\) | 1.54609 | 0.0724816 | ||||||||
\(456\) | −5.02353 | −0.235249 | ||||||||
\(457\) | −35.7717 | −1.67333 | −0.836666 | − | 0.547714i | \(-0.815498\pi\) | ||||
−0.836666 | + | 0.547714i | \(0.815498\pi\) | |||||||
\(458\) | 3.10042 | 0.144873 | ||||||||
\(459\) | −2.35495 | −0.109920 | ||||||||
\(460\) | 0.695024 | 0.0324057 | ||||||||
\(461\) | −6.40943 | −0.298517 | −0.149259 | − | 0.988798i | \(-0.547689\pi\) | ||||
−0.149259 | + | 0.988798i | \(0.547689\pi\) | |||||||
\(462\) | −4.72828 | −0.219979 | ||||||||
\(463\) | 29.7155 | 1.38100 | 0.690499 | − | 0.723334i | \(-0.257391\pi\) | ||||
0.690499 | + | 0.723334i | \(0.257391\pi\) | |||||||
\(464\) | 2.78431 | 0.129258 | ||||||||
\(465\) | −3.01075 | −0.139620 | ||||||||
\(466\) | −5.93391 | −0.274883 | ||||||||
\(467\) | 9.50195 | 0.439698 | 0.219849 | − | 0.975534i | \(-0.429444\pi\) | ||||
0.219849 | + | 0.975534i | \(0.429444\pi\) | |||||||
\(468\) | −1.68756 | −0.0780074 | ||||||||
\(469\) | 36.2805 | 1.67528 | ||||||||
\(470\) | −1.77736 | −0.0819833 | ||||||||
\(471\) | −6.62907 | −0.305451 | ||||||||
\(472\) | −15.5550 | −0.715976 | ||||||||
\(473\) | −23.9386 | −1.10070 | ||||||||
\(474\) | −3.23092 | −0.148401 | ||||||||
\(475\) | −14.0271 | −0.643608 | ||||||||
\(476\) | −17.8050 | −0.816091 | ||||||||
\(477\) | 6.00735 | 0.275058 | ||||||||
\(478\) | 12.0145 | 0.549529 | ||||||||
\(479\) | 25.7687 | 1.17740 | 0.588700 | − | 0.808351i | \(-0.299640\pi\) | ||||
0.588700 | + | 0.808351i | \(0.299640\pi\) | |||||||
\(480\) | −1.84396 | −0.0841651 | ||||||||
\(481\) | −2.66403 | −0.121469 | ||||||||
\(482\) | −6.16546 | −0.280829 | ||||||||
\(483\) | −4.22376 | −0.192188 | ||||||||
\(484\) | 9.00658 | 0.409390 | ||||||||
\(485\) | −6.86350 | −0.311656 | ||||||||
\(486\) | 0.458217 | 0.0207852 | ||||||||
\(487\) | −25.3632 | −1.14931 | −0.574657 | − | 0.818394i | \(-0.694865\pi\) | ||||
−0.574657 | + | 0.818394i | \(0.694865\pi\) | |||||||
\(488\) | −15.1992 | −0.688035 | ||||||||
\(489\) | 7.80982 | 0.353172 | ||||||||
\(490\) | −1.92861 | −0.0871256 | ||||||||
\(491\) | 33.6058 | 1.51661 | 0.758305 | − | 0.651900i | \(-0.226028\pi\) | ||||
0.758305 | + | 0.651900i | \(0.226028\pi\) | |||||||
\(492\) | −9.41469 | −0.424447 | ||||||||
\(493\) | −2.35495 | −0.106061 | ||||||||
\(494\) | 1.24958 | 0.0562211 | ||||||||
\(495\) | −0.948572 | −0.0426351 | ||||||||
\(496\) | 21.5901 | 0.969423 | ||||||||
\(497\) | −28.9973 | −1.30071 | ||||||||
\(498\) | 4.99566 | 0.223861 | ||||||||
\(499\) | 24.4757 | 1.09568 | 0.547842 | − | 0.836582i | \(-0.315450\pi\) | ||||
0.547842 | + | 0.836582i | \(0.315450\pi\) | |||||||
\(500\) | −6.84546 | −0.306138 | ||||||||
\(501\) | −20.4339 | −0.912918 | ||||||||
\(502\) | 3.02925 | 0.135202 | ||||||||
\(503\) | −2.75225 | −0.122717 | −0.0613584 | − | 0.998116i | \(-0.519543\pi\) | ||||
−0.0613584 | + | 0.998116i | \(0.519543\pi\) | |||||||
\(504\) | 7.33523 | 0.326737 | ||||||||
\(505\) | −3.17271 | −0.141184 | ||||||||
\(506\) | 1.11945 | 0.0497655 | ||||||||
\(507\) | −12.1112 | −0.537878 | ||||||||
\(508\) | 12.4169 | 0.550913 | ||||||||
\(509\) | 22.2953 | 0.988221 | 0.494110 | − | 0.869399i | \(-0.335494\pi\) | ||||
0.494110 | + | 0.869399i | \(0.335494\pi\) | |||||||
\(510\) | 0.418977 | 0.0185526 | ||||||||
\(511\) | −51.5913 | −2.28226 | ||||||||
\(512\) | 22.8938 | 1.01177 | ||||||||
\(513\) | 2.89264 | 0.127713 | ||||||||
\(514\) | 5.78993 | 0.255383 | ||||||||
\(515\) | −3.83670 | −0.169065 | ||||||||
\(516\) | 17.5400 | 0.772154 | ||||||||
\(517\) | 24.4061 | 1.07338 | ||||||||
\(518\) | 5.46906 | 0.240297 | ||||||||
\(519\) | −11.5310 | −0.506156 | ||||||||
\(520\) | 0.635696 | 0.0278771 | ||||||||
\(521\) | −16.4927 | −0.722560 | −0.361280 | − | 0.932457i | \(-0.617660\pi\) | ||||
−0.361280 | + | 0.932457i | \(0.617660\pi\) | |||||||
\(522\) | 0.458217 | 0.0200556 | ||||||||
\(523\) | −38.6999 | −1.69223 | −0.846114 | − | 0.533002i | \(-0.821064\pi\) | ||||
−0.846114 | + | 0.533002i | \(0.821064\pi\) | |||||||
\(524\) | 22.4678 | 0.981511 | ||||||||
\(525\) | 20.4820 | 0.893909 | ||||||||
\(526\) | −14.3202 | −0.624388 | ||||||||
\(527\) | −18.2607 | −0.795450 | ||||||||
\(528\) | 6.80220 | 0.296028 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −1.06879 | −0.0464252 | ||||||||
\(531\) | 8.95684 | 0.388694 | ||||||||
\(532\) | 21.8703 | 0.948199 | ||||||||
\(533\) | 4.95839 | 0.214772 | ||||||||
\(534\) | 4.00207 | 0.173186 | ||||||||
\(535\) | 4.09895 | 0.177213 | ||||||||
\(536\) | 14.9173 | 0.644328 | ||||||||
\(537\) | −11.3766 | −0.490936 | ||||||||
\(538\) | −5.86906 | −0.253033 | ||||||||
\(539\) | 26.4830 | 1.14070 | ||||||||
\(540\) | 0.695024 | 0.0299091 | ||||||||
\(541\) | 27.7527 | 1.19318 | 0.596592 | − | 0.802545i | \(-0.296521\pi\) | ||||
0.596592 | + | 0.802545i | \(0.296521\pi\) | |||||||
\(542\) | −2.71002 | −0.116405 | ||||||||
\(543\) | 0.967738 | 0.0415296 | ||||||||
\(544\) | −11.1840 | −0.479509 | ||||||||
\(545\) | −5.93254 | −0.254122 | ||||||||
\(546\) | −1.82460 | −0.0780856 | ||||||||
\(547\) | 37.3701 | 1.59783 | 0.798914 | − | 0.601445i | \(-0.205408\pi\) | ||||
0.798914 | + | 0.601445i | \(0.205408\pi\) | |||||||
\(548\) | 20.9040 | 0.892974 | ||||||||
\(549\) | 8.75196 | 0.373525 | ||||||||
\(550\) | −5.42848 | −0.231471 | ||||||||
\(551\) | 2.89264 | 0.123231 | ||||||||
\(552\) | −1.73666 | −0.0739172 | ||||||||
\(553\) | 29.7820 | 1.26646 | ||||||||
\(554\) | 5.28597 | 0.224579 | ||||||||
\(555\) | 1.09718 | 0.0465729 | ||||||||
\(556\) | 4.32223 | 0.183303 | ||||||||
\(557\) | −21.0747 | −0.892963 | −0.446482 | − | 0.894793i | \(-0.647323\pi\) | ||||
−0.446482 | + | 0.894793i | \(0.647323\pi\) | |||||||
\(558\) | 3.55311 | 0.150415 | ||||||||
\(559\) | −9.23770 | −0.390713 | ||||||||
\(560\) | 4.56619 | 0.192957 | ||||||||
\(561\) | −5.75325 | −0.242903 | ||||||||
\(562\) | 10.3466 | 0.436446 | ||||||||
\(563\) | −2.78677 | −0.117448 | −0.0587241 | − | 0.998274i | \(-0.518703\pi\) | ||||
−0.0587241 | + | 0.998274i | \(0.518703\pi\) | |||||||
\(564\) | −17.8825 | −0.752987 | ||||||||
\(565\) | 4.51266 | 0.189849 | ||||||||
\(566\) | 7.16663 | 0.301236 | ||||||||
\(567\) | −4.22376 | −0.177381 | ||||||||
\(568\) | −11.9227 | −0.500265 | ||||||||
\(569\) | −29.7476 | −1.24708 | −0.623541 | − | 0.781790i | \(-0.714307\pi\) | ||||
−0.623541 | + | 0.781790i | \(0.714307\pi\) | |||||||
\(570\) | −0.514640 | −0.0215559 | ||||||||
\(571\) | 0.560978 | 0.0234762 | 0.0117381 | − | 0.999931i | \(-0.496264\pi\) | ||||
0.0117381 | + | 0.999931i | \(0.496264\pi\) | |||||||
\(572\) | −4.12279 | −0.172383 | ||||||||
\(573\) | 11.6319 | 0.485929 | ||||||||
\(574\) | −10.1792 | −0.424872 | ||||||||
\(575\) | −4.84924 | −0.202227 | ||||||||
\(576\) | −3.39248 | −0.141353 | ||||||||
\(577\) | −7.83682 | −0.326251 | −0.163126 | − | 0.986605i | \(-0.552158\pi\) | ||||
−0.163126 | + | 0.986605i | \(0.552158\pi\) | |||||||
\(578\) | −5.24852 | −0.218310 | ||||||||
\(579\) | 15.4098 | 0.640409 | ||||||||
\(580\) | 0.695024 | 0.0288593 | ||||||||
\(581\) | −46.0490 | −1.91043 | ||||||||
\(582\) | 8.09990 | 0.335751 | ||||||||
\(583\) | 14.6763 | 0.607829 | ||||||||
\(584\) | −21.2125 | −0.877780 | ||||||||
\(585\) | −0.366045 | −0.0151341 | ||||||||
\(586\) | 2.60823 | 0.107745 | ||||||||
\(587\) | 3.76713 | 0.155486 | 0.0777431 | − | 0.996973i | \(-0.475229\pi\) | ||||
0.0777431 | + | 0.996973i | \(0.475229\pi\) | |||||||
\(588\) | −19.4042 | −0.800217 | ||||||||
\(589\) | 22.4301 | 0.924217 | ||||||||
\(590\) | −1.59354 | −0.0656052 | ||||||||
\(591\) | −9.27867 | −0.381674 | ||||||||
\(592\) | −7.86790 | −0.323369 | ||||||||
\(593\) | −35.5044 | −1.45799 | −0.728995 | − | 0.684519i | \(-0.760012\pi\) | ||||
−0.728995 | + | 0.684519i | \(0.760012\pi\) | |||||||
\(594\) | 1.11945 | 0.0459315 | ||||||||
\(595\) | −3.86205 | −0.158329 | ||||||||
\(596\) | 15.2975 | 0.626612 | ||||||||
\(597\) | 7.73656 | 0.316636 | ||||||||
\(598\) | 0.431985 | 0.0176652 | ||||||||
\(599\) | −27.5676 | −1.12638 | −0.563191 | − | 0.826327i | \(-0.690427\pi\) | ||||
−0.563191 | + | 0.826327i | \(0.690427\pi\) | |||||||
\(600\) | 8.42149 | 0.343806 | ||||||||
\(601\) | 12.8048 | 0.522318 | 0.261159 | − | 0.965296i | \(-0.415895\pi\) | ||||
0.261159 | + | 0.965296i | \(0.415895\pi\) | |||||||
\(602\) | 18.9643 | 0.772928 | ||||||||
\(603\) | −8.58964 | −0.349797 | ||||||||
\(604\) | 8.33992 | 0.339347 | ||||||||
\(605\) | 1.95360 | 0.0794251 | ||||||||
\(606\) | 3.74425 | 0.152100 | ||||||||
\(607\) | 12.8523 | 0.521661 | 0.260830 | − | 0.965385i | \(-0.416004\pi\) | ||||
0.260830 | + | 0.965385i | \(0.416004\pi\) | |||||||
\(608\) | 13.7375 | 0.557131 | ||||||||
\(609\) | −4.22376 | −0.171155 | ||||||||
\(610\) | −1.55709 | −0.0630449 | ||||||||
\(611\) | 9.41807 | 0.381014 | ||||||||
\(612\) | 4.21544 | 0.170399 | ||||||||
\(613\) | −5.06650 | −0.204634 | −0.102317 | − | 0.994752i | \(-0.532626\pi\) | ||||
−0.102317 | + | 0.994752i | \(0.532626\pi\) | |||||||
\(614\) | −0.363817 | −0.0146825 | ||||||||
\(615\) | −2.04212 | −0.0823464 | ||||||||
\(616\) | 17.9203 | 0.722031 | ||||||||
\(617\) | −38.5316 | −1.55122 | −0.775612 | − | 0.631210i | \(-0.782559\pi\) | ||||
−0.775612 | + | 0.631210i | \(0.782559\pi\) | |||||||
\(618\) | 4.52784 | 0.182136 | ||||||||
\(619\) | 3.18784 | 0.128130 | 0.0640650 | − | 0.997946i | \(-0.479593\pi\) | ||||
0.0640650 | + | 0.997946i | \(0.479593\pi\) | |||||||
\(620\) | 5.38936 | 0.216442 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 15.4195 | 0.618265 | ||||||||
\(623\) | −36.8903 | −1.47798 | ||||||||
\(624\) | 2.62491 | 0.105080 | ||||||||
\(625\) | 22.7614 | 0.910455 | ||||||||
\(626\) | −8.24711 | −0.329621 | ||||||||
\(627\) | 7.06687 | 0.282224 | ||||||||
\(628\) | 11.8663 | 0.473516 | ||||||||
\(629\) | 6.65462 | 0.265337 | ||||||||
\(630\) | 0.751464 | 0.0299390 | ||||||||
\(631\) | −10.3307 | −0.411259 | −0.205630 | − | 0.978630i | \(-0.565924\pi\) | ||||
−0.205630 | + | 0.978630i | \(0.565924\pi\) | |||||||
\(632\) | 12.2453 | 0.487092 | ||||||||
\(633\) | 16.0483 | 0.637861 | ||||||||
\(634\) | −5.07665 | −0.201619 | ||||||||
\(635\) | 2.69334 | 0.106882 | ||||||||
\(636\) | −10.7534 | −0.426399 | ||||||||
\(637\) | 10.2195 | 0.404913 | ||||||||
\(638\) | 1.11945 | 0.0443194 | ||||||||
\(639\) | 6.86529 | 0.271587 | ||||||||
\(640\) | 4.29150 | 0.169636 | ||||||||
\(641\) | −47.7506 | −1.88603 | −0.943017 | − | 0.332745i | \(-0.892025\pi\) | ||||
−0.943017 | + | 0.332745i | \(0.892025\pi\) | |||||||
\(642\) | −4.83734 | −0.190914 | ||||||||
\(643\) | −9.36074 | −0.369152 | −0.184576 | − | 0.982818i | \(-0.559091\pi\) | ||||
−0.184576 | + | 0.982818i | \(0.559091\pi\) | |||||||
\(644\) | 7.56068 | 0.297933 | ||||||||
\(645\) | 3.80456 | 0.149804 | ||||||||
\(646\) | −3.12138 | −0.122809 | ||||||||
\(647\) | −5.62914 | −0.221304 | −0.110652 | − | 0.993859i | \(-0.535294\pi\) | ||||
−0.110652 | + | 0.993859i | \(0.535294\pi\) | |||||||
\(648\) | −1.73666 | −0.0682225 | ||||||||
\(649\) | 21.8820 | 0.858944 | ||||||||
\(650\) | −2.09480 | −0.0821647 | ||||||||
\(651\) | −32.7519 | −1.28365 | ||||||||
\(652\) | −13.9799 | −0.547494 | ||||||||
\(653\) | 34.3700 | 1.34500 | 0.672501 | − | 0.740096i | \(-0.265220\pi\) | ||||
0.672501 | + | 0.740096i | \(0.265220\pi\) | |||||||
\(654\) | 7.00123 | 0.273770 | ||||||||
\(655\) | 4.87345 | 0.190421 | ||||||||
\(656\) | 14.6440 | 0.571754 | ||||||||
\(657\) | 12.2145 | 0.476535 | ||||||||
\(658\) | −19.3346 | −0.753742 | ||||||||
\(659\) | −5.00171 | −0.194839 | −0.0974195 | − | 0.995243i | \(-0.531059\pi\) | ||||
−0.0974195 | + | 0.995243i | \(0.531059\pi\) | |||||||
\(660\) | 1.69798 | 0.0660937 | ||||||||
\(661\) | −2.29622 | −0.0893124 | −0.0446562 | − | 0.999002i | \(-0.514219\pi\) | ||||
−0.0446562 | + | 0.999002i | \(0.514219\pi\) | |||||||
\(662\) | 14.7962 | 0.575070 | ||||||||
\(663\) | −2.22013 | −0.0862226 | ||||||||
\(664\) | −18.9337 | −0.734771 | ||||||||
\(665\) | 4.74385 | 0.183959 | ||||||||
\(666\) | −1.29483 | −0.0501737 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 36.5774 | 1.41522 | ||||||||
\(669\) | 17.6200 | 0.681228 | ||||||||
\(670\) | 1.52821 | 0.0590400 | ||||||||
\(671\) | 21.3815 | 0.825423 | ||||||||
\(672\) | −20.0592 | −0.773801 | ||||||||
\(673\) | −29.0415 | −1.11947 | −0.559735 | − | 0.828672i | \(-0.689097\pi\) | ||||
−0.559735 | + | 0.828672i | \(0.689097\pi\) | |||||||
\(674\) | −5.25754 | −0.202513 | ||||||||
\(675\) | −4.84924 | −0.186647 | ||||||||
\(676\) | 21.6795 | 0.833828 | ||||||||
\(677\) | 31.2273 | 1.20016 | 0.600081 | − | 0.799939i | \(-0.295135\pi\) | ||||
0.600081 | + | 0.799939i | \(0.295135\pi\) | |||||||
\(678\) | −5.32557 | −0.204527 | ||||||||
\(679\) | −74.6633 | −2.86531 | ||||||||
\(680\) | −1.58794 | −0.0608947 | ||||||||
\(681\) | −6.15492 | −0.235857 | ||||||||
\(682\) | 8.68043 | 0.332391 | ||||||||
\(683\) | −8.11445 | −0.310491 | −0.155245 | − | 0.987876i | \(-0.549617\pi\) | ||||
−0.155245 | + | 0.987876i | \(0.549617\pi\) | |||||||
\(684\) | −5.17793 | −0.197983 | ||||||||
\(685\) | 4.53425 | 0.173245 | ||||||||
\(686\) | −7.43218 | −0.283762 | ||||||||
\(687\) | 6.76626 | 0.258149 | ||||||||
\(688\) | −27.2825 | −1.04013 | ||||||||
\(689\) | 5.66343 | 0.215760 | ||||||||
\(690\) | −0.177914 | −0.00677306 | ||||||||
\(691\) | −33.6303 | −1.27936 | −0.639679 | − | 0.768643i | \(-0.720933\pi\) | ||||
−0.639679 | + | 0.768643i | \(0.720933\pi\) | |||||||
\(692\) | 20.6410 | 0.784652 | ||||||||
\(693\) | −10.3189 | −0.391981 | ||||||||
\(694\) | 14.8851 | 0.565032 | ||||||||
\(695\) | 0.937527 | 0.0355624 | ||||||||
\(696\) | −1.73666 | −0.0658279 | ||||||||
\(697\) | −12.3858 | −0.469147 | ||||||||
\(698\) | −9.57024 | −0.362239 | ||||||||
\(699\) | −12.9500 | −0.489813 | ||||||||
\(700\) | −36.6636 | −1.38575 | ||||||||
\(701\) | 18.4301 | 0.696095 | 0.348047 | − | 0.937477i | \(-0.386845\pi\) | ||||
0.348047 | + | 0.937477i | \(0.386845\pi\) | |||||||
\(702\) | 0.431985 | 0.0163042 | ||||||||
\(703\) | −8.17404 | −0.308290 | ||||||||
\(704\) | −8.28799 | −0.312365 | ||||||||
\(705\) | −3.87885 | −0.146086 | ||||||||
\(706\) | −4.28993 | −0.161454 | ||||||||
\(707\) | −34.5137 | −1.29802 | ||||||||
\(708\) | −16.0331 | −0.602560 | ||||||||
\(709\) | 22.8313 | 0.857449 | 0.428724 | − | 0.903435i | \(-0.358963\pi\) | ||||
0.428724 | + | 0.903435i | \(0.358963\pi\) | |||||||
\(710\) | −1.22143 | −0.0458394 | ||||||||
\(711\) | −7.05107 | −0.264436 | ||||||||
\(712\) | −15.1680 | −0.568444 | ||||||||
\(713\) | 7.75420 | 0.290397 | ||||||||
\(714\) | 4.55776 | 0.170570 | ||||||||
\(715\) | −0.894267 | −0.0334437 | ||||||||
\(716\) | 20.3645 | 0.761058 | ||||||||
\(717\) | 26.2200 | 0.979205 | ||||||||
\(718\) | −4.22746 | −0.157767 | ||||||||
\(719\) | −14.3474 | −0.535067 | −0.267533 | − | 0.963549i | \(-0.586209\pi\) | ||||
−0.267533 | + | 0.963549i | \(0.586209\pi\) | |||||||
\(720\) | −1.08107 | −0.0402892 | ||||||||
\(721\) | −41.7367 | −1.55436 | ||||||||
\(722\) | −4.87205 | −0.181319 | ||||||||
\(723\) | −13.4553 | −0.500409 | ||||||||
\(724\) | −1.73229 | −0.0643800 | ||||||||
\(725\) | −4.84924 | −0.180096 | ||||||||
\(726\) | −2.30552 | −0.0855659 | ||||||||
\(727\) | 27.7841 | 1.03046 | 0.515228 | − | 0.857053i | \(-0.327707\pi\) | ||||
0.515228 | + | 0.857053i | \(0.327707\pi\) | |||||||
\(728\) | 6.91529 | 0.256298 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −2.17313 | −0.0804313 | ||||||||
\(731\) | 23.0753 | 0.853472 | ||||||||
\(732\) | −15.6663 | −0.579044 | ||||||||
\(733\) | 50.8399 | 1.87782 | 0.938908 | − | 0.344169i | \(-0.111839\pi\) | ||||
0.938908 | + | 0.344169i | \(0.111839\pi\) | |||||||
\(734\) | 4.59918 | 0.169759 | ||||||||
\(735\) | −4.20893 | −0.155249 | ||||||||
\(736\) | 4.74914 | 0.175056 | ||||||||
\(737\) | −20.9849 | −0.772989 | ||||||||
\(738\) | 2.40999 | 0.0887130 | ||||||||
\(739\) | 22.0471 | 0.811016 | 0.405508 | − | 0.914091i | \(-0.367095\pi\) | ||||
0.405508 | + | 0.914091i | \(0.367095\pi\) | |||||||
\(740\) | −1.96400 | −0.0721981 | ||||||||
\(741\) | 2.72704 | 0.100180 | ||||||||
\(742\) | −11.6266 | −0.426826 | ||||||||
\(743\) | 11.4104 | 0.418607 | 0.209304 | − | 0.977851i | \(-0.432880\pi\) | ||||
0.209304 | + | 0.977851i | \(0.432880\pi\) | |||||||
\(744\) | −13.4664 | −0.493703 | ||||||||
\(745\) | 3.31816 | 0.121568 | ||||||||
\(746\) | 16.0764 | 0.588598 | ||||||||
\(747\) | 10.9024 | 0.398897 | ||||||||
\(748\) | 10.2985 | 0.376552 | ||||||||
\(749\) | 44.5896 | 1.62927 | ||||||||
\(750\) | 1.75231 | 0.0639855 | ||||||||
\(751\) | −6.41232 | −0.233989 | −0.116994 | − | 0.993133i | \(-0.537326\pi\) | ||||
−0.116994 | + | 0.993133i | \(0.537326\pi\) | |||||||
\(752\) | 27.8152 | 1.01432 | ||||||||
\(753\) | 6.61094 | 0.240916 | ||||||||
\(754\) | 0.431985 | 0.0157319 | ||||||||
\(755\) | 1.80900 | 0.0658361 | ||||||||
\(756\) | 7.56068 | 0.274979 | ||||||||
\(757\) | 29.1131 | 1.05813 | 0.529066 | − | 0.848581i | \(-0.322542\pi\) | ||||
0.529066 | + | 0.848581i | \(0.322542\pi\) | |||||||
\(758\) | 10.5271 | 0.382360 | ||||||||
\(759\) | 2.44305 | 0.0886771 | ||||||||
\(760\) | 1.95051 | 0.0707523 | ||||||||
\(761\) | −38.8881 | −1.40969 | −0.704846 | − | 0.709360i | \(-0.748984\pi\) | ||||
−0.704846 | + | 0.709360i | \(0.748984\pi\) | |||||||
\(762\) | −3.17851 | −0.115145 | ||||||||
\(763\) | −64.5360 | −2.33636 | ||||||||
\(764\) | −20.8215 | −0.753295 | ||||||||
\(765\) | 0.914364 | 0.0330589 | ||||||||
\(766\) | 14.5220 | 0.524702 | ||||||||
\(767\) | 8.44407 | 0.304898 | ||||||||
\(768\) | 1.72039 | 0.0620791 | ||||||||
\(769\) | 15.3319 | 0.552882 | 0.276441 | − | 0.961031i | \(-0.410845\pi\) | ||||
0.276441 | + | 0.961031i | \(0.410845\pi\) | |||||||
\(770\) | 1.83586 | 0.0661600 | ||||||||
\(771\) | 12.6358 | 0.455066 | ||||||||
\(772\) | −27.5841 | −0.992773 | ||||||||
\(773\) | 22.8383 | 0.821438 | 0.410719 | − | 0.911762i | \(-0.365278\pi\) | ||||
0.410719 | + | 0.911762i | \(0.365278\pi\) | |||||||
\(774\) | −4.48992 | −0.161387 | ||||||||
\(775\) | −37.6020 | −1.35070 | ||||||||
\(776\) | −30.6989 | −1.10203 | ||||||||
\(777\) | 11.9355 | 0.428184 | ||||||||
\(778\) | 3.86935 | 0.138723 | ||||||||
\(779\) | 15.2138 | 0.545092 | ||||||||
\(780\) | 0.655234 | 0.0234611 | ||||||||
\(781\) | 16.7723 | 0.600159 | ||||||||
\(782\) | −1.07908 | −0.0385877 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | 30.1822 | 1.07794 | ||||||||
\(785\) | 2.57389 | 0.0918662 | ||||||||
\(786\) | −5.75135 | −0.205144 | ||||||||
\(787\) | −29.6186 | −1.05579 | −0.527895 | − | 0.849310i | \(-0.677018\pi\) | ||||
−0.527895 | + | 0.849310i | \(0.677018\pi\) | |||||||
\(788\) | 16.6092 | 0.591677 | ||||||||
\(789\) | −31.2519 | −1.11260 | ||||||||
\(790\) | 1.25448 | 0.0446325 | ||||||||
\(791\) | 49.0901 | 1.74544 | ||||||||
\(792\) | −4.24275 | −0.150760 | ||||||||
\(793\) | 8.25092 | 0.292999 | ||||||||
\(794\) | −14.5257 | −0.515499 | ||||||||
\(795\) | −2.33249 | −0.0827251 | ||||||||
\(796\) | −13.8487 | −0.490855 | ||||||||
\(797\) | −45.8911 | −1.62554 | −0.812772 | − | 0.582581i | \(-0.802043\pi\) | ||||
−0.812772 | + | 0.582581i | \(0.802043\pi\) | |||||||
\(798\) | −5.59841 | −0.198182 | ||||||||
\(799\) | −23.5259 | −0.832287 | ||||||||
\(800\) | −23.0297 | −0.814224 | ||||||||
\(801\) | 8.73399 | 0.308600 | ||||||||
\(802\) | −6.80084 | −0.240146 | ||||||||
\(803\) | 29.8408 | 1.05306 | ||||||||
\(804\) | 15.3758 | 0.542262 | ||||||||
\(805\) | 1.63997 | 0.0578015 | ||||||||
\(806\) | 3.34970 | 0.117988 | ||||||||
\(807\) | −12.8085 | −0.450879 | ||||||||
\(808\) | −14.1908 | −0.499232 | ||||||||
\(809\) | −19.1118 | −0.671934 | −0.335967 | − | 0.941874i | \(-0.609063\pi\) | ||||
−0.335967 | + | 0.941874i | \(0.609063\pi\) | |||||||
\(810\) | −0.177914 | −0.00625125 | ||||||||
\(811\) | −33.0111 | −1.15918 | −0.579588 | − | 0.814910i | \(-0.696786\pi\) | ||||
−0.579588 | + | 0.814910i | \(0.696786\pi\) | |||||||
\(812\) | 7.56068 | 0.265328 | ||||||||
\(813\) | −5.91426 | −0.207422 | ||||||||
\(814\) | −3.16334 | −0.110875 | ||||||||
\(815\) | −3.03234 | −0.106218 | ||||||||
\(816\) | −6.55689 | −0.229537 | ||||||||
\(817\) | −28.3440 | −0.991632 | ||||||||
\(818\) | 12.0217 | 0.420328 | ||||||||
\(819\) | −3.98195 | −0.139141 | ||||||||
\(820\) | 3.65548 | 0.127655 | ||||||||
\(821\) | −46.4488 | −1.62107 | −0.810537 | − | 0.585688i | \(-0.800825\pi\) | ||||
−0.810537 | + | 0.585688i | \(0.800825\pi\) | |||||||
\(822\) | −5.35105 | −0.186639 | ||||||||
\(823\) | 56.9950 | 1.98672 | 0.993361 | − | 0.115041i | \(-0.0366999\pi\) | ||||
0.993361 | + | 0.115041i | \(0.0366999\pi\) | |||||||
\(824\) | −17.1607 | −0.597821 | ||||||||
\(825\) | −11.8469 | −0.412458 | ||||||||
\(826\) | −17.3351 | −0.603164 | ||||||||
\(827\) | −4.61165 | −0.160363 | −0.0801814 | − | 0.996780i | \(-0.525550\pi\) | ||||
−0.0801814 | + | 0.996780i | \(0.525550\pi\) | |||||||
\(828\) | −1.79004 | −0.0622081 | ||||||||
\(829\) | −22.8183 | −0.792514 | −0.396257 | − | 0.918140i | \(-0.629691\pi\) | ||||
−0.396257 | + | 0.918140i | \(0.629691\pi\) | |||||||
\(830\) | −1.93968 | −0.0673273 | ||||||||
\(831\) | 11.5359 | 0.400178 | ||||||||
\(832\) | −3.19826 | −0.110880 | ||||||||
\(833\) | −25.5279 | −0.884490 | ||||||||
\(834\) | −1.10641 | −0.0383120 | ||||||||
\(835\) | 7.93393 | 0.274565 | ||||||||
\(836\) | −12.6500 | −0.437508 | ||||||||
\(837\) | 7.75420 | 0.268025 | ||||||||
\(838\) | −14.1674 | −0.489404 | ||||||||
\(839\) | −11.8899 | −0.410484 | −0.205242 | − | 0.978711i | \(-0.565798\pi\) | ||||
−0.205242 | + | 0.978711i | \(0.565798\pi\) | |||||||
\(840\) | −2.84808 | −0.0982680 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0.454830 | 0.0156745 | ||||||||
\(843\) | 22.5802 | 0.777702 | ||||||||
\(844\) | −28.7270 | −0.988823 | ||||||||
\(845\) | 4.70247 | 0.161770 | ||||||||
\(846\) | 4.57759 | 0.157381 | ||||||||
\(847\) | 21.2519 | 0.730222 | ||||||||
\(848\) | 16.7263 | 0.574384 | ||||||||
\(849\) | 15.6402 | 0.536772 | ||||||||
\(850\) | 5.23271 | 0.179480 | ||||||||
\(851\) | −2.82580 | −0.0968673 | ||||||||
\(852\) | −12.2891 | −0.421019 | ||||||||
\(853\) | −46.1976 | −1.58178 | −0.790888 | − | 0.611961i | \(-0.790381\pi\) | ||||
−0.790888 | + | 0.611961i | \(0.790381\pi\) | |||||||
\(854\) | −16.9385 | −0.579625 | ||||||||
\(855\) | −1.12314 | −0.0384104 | ||||||||
\(856\) | 18.3337 | 0.626632 | ||||||||
\(857\) | 19.4331 | 0.663822 | 0.331911 | − | 0.943311i | \(-0.392307\pi\) | ||||
0.331911 | + | 0.943311i | \(0.392307\pi\) | |||||||
\(858\) | 1.05536 | 0.0360294 | ||||||||
\(859\) | −12.5294 | −0.427497 | −0.213748 | − | 0.976889i | \(-0.568567\pi\) | ||||
−0.213748 | + | 0.976889i | \(0.568567\pi\) | |||||||
\(860\) | −6.81031 | −0.232230 | ||||||||
\(861\) | −22.2148 | −0.757080 | ||||||||
\(862\) | −8.33634 | −0.283937 | ||||||||
\(863\) | 26.0144 | 0.885542 | 0.442771 | − | 0.896635i | \(-0.353996\pi\) | ||||
0.442771 | + | 0.896635i | \(0.353996\pi\) | |||||||
\(864\) | 4.74914 | 0.161569 | ||||||||
\(865\) | 4.47719 | 0.152229 | ||||||||
\(866\) | 12.8480 | 0.436593 | ||||||||
\(867\) | −11.4542 | −0.389006 | ||||||||
\(868\) | 58.6271 | 1.98993 | ||||||||
\(869\) | −17.2261 | −0.584356 | ||||||||
\(870\) | −0.177914 | −0.00603184 | ||||||||
\(871\) | −8.09789 | −0.274386 | ||||||||
\(872\) | −26.5349 | −0.898586 | ||||||||
\(873\) | 17.6770 | 0.598275 | ||||||||
\(874\) | 1.32546 | 0.0448343 | ||||||||
\(875\) | −16.1525 | −0.546054 | ||||||||
\(876\) | −21.8645 | −0.738733 | ||||||||
\(877\) | −16.6305 | −0.561572 | −0.280786 | − | 0.959770i | \(-0.590595\pi\) | ||||
−0.280786 | + | 0.959770i | \(0.590595\pi\) | |||||||
\(878\) | 12.3768 | 0.417698 | ||||||||
\(879\) | 5.69213 | 0.191991 | ||||||||
\(880\) | −2.64111 | −0.0890320 | ||||||||
\(881\) | −14.0882 | −0.474643 | −0.237321 | − | 0.971431i | \(-0.576269\pi\) | ||||
−0.237321 | + | 0.971431i | \(0.576269\pi\) | |||||||
\(882\) | 4.96713 | 0.167252 | ||||||||
\(883\) | 4.22567 | 0.142205 | 0.0711025 | − | 0.997469i | \(-0.477348\pi\) | ||||
0.0711025 | + | 0.997469i | \(0.477348\pi\) | |||||||
\(884\) | 3.97411 | 0.133664 | ||||||||
\(885\) | −3.47770 | −0.116902 | ||||||||
\(886\) | 2.39613 | 0.0804996 | ||||||||
\(887\) | 43.9960 | 1.47724 | 0.738620 | − | 0.674122i | \(-0.235478\pi\) | ||||
0.738620 | + | 0.674122i | \(0.235478\pi\) | |||||||
\(888\) | 4.90746 | 0.164684 | ||||||||
\(889\) | 29.2989 | 0.982655 | ||||||||
\(890\) | −1.55390 | −0.0520867 | ||||||||
\(891\) | 2.44305 | 0.0818453 | ||||||||
\(892\) | −31.5404 | −1.05605 | ||||||||
\(893\) | 28.8975 | 0.967017 | ||||||||
\(894\) | −3.91590 | −0.130967 | ||||||||
\(895\) | 4.41723 | 0.147652 | ||||||||
\(896\) | 46.6842 | 1.55961 | ||||||||
\(897\) | 0.942751 | 0.0314775 | ||||||||
\(898\) | 7.71420 | 0.257426 | ||||||||
\(899\) | 7.75420 | 0.258617 | ||||||||
\(900\) | 8.68033 | 0.289344 | ||||||||
\(901\) | −14.1470 | −0.471305 | ||||||||
\(902\) | 5.88773 | 0.196040 | ||||||||
\(903\) | 41.3872 | 1.37728 | ||||||||
\(904\) | 20.1841 | 0.671313 | ||||||||
\(905\) | −0.375747 | −0.0124903 | ||||||||
\(906\) | −2.13487 | −0.0709263 | ||||||||
\(907\) | −2.60868 | −0.0866198 | −0.0433099 | − | 0.999062i | \(-0.513790\pi\) | ||||
−0.0433099 | + | 0.999062i | \(0.513790\pi\) | |||||||
\(908\) | 11.0175 | 0.365630 | ||||||||
\(909\) | 8.17134 | 0.271026 | ||||||||
\(910\) | 0.708443 | 0.0234847 | ||||||||
\(911\) | 34.0968 | 1.12968 | 0.564839 | − | 0.825201i | \(-0.308938\pi\) | ||||
0.564839 | + | 0.825201i | \(0.308938\pi\) | |||||||
\(912\) | 8.05400 | 0.266695 | ||||||||
\(913\) | 26.6351 | 0.881492 | ||||||||
\(914\) | −16.3912 | −0.542174 | ||||||||
\(915\) | −3.39815 | −0.112340 | ||||||||
\(916\) | −12.1119 | −0.400187 | ||||||||
\(917\) | 53.0149 | 1.75070 | ||||||||
\(918\) | −1.07908 | −0.0356149 | ||||||||
\(919\) | −7.53835 | −0.248667 | −0.124334 | − | 0.992240i | \(-0.539679\pi\) | ||||
−0.124334 | + | 0.992240i | \(0.539679\pi\) | |||||||
\(920\) | 0.674299 | 0.0222310 | ||||||||
\(921\) | −0.793984 | −0.0261626 | ||||||||
\(922\) | −2.93691 | −0.0967221 | ||||||||
\(923\) | 6.47226 | 0.213037 | ||||||||
\(924\) | 18.4711 | 0.607656 | ||||||||
\(925\) | 13.7030 | 0.450552 | ||||||||
\(926\) | 13.6162 | 0.447455 | ||||||||
\(927\) | 9.88143 | 0.324549 | ||||||||
\(928\) | 4.74914 | 0.155898 | ||||||||
\(929\) | −26.2779 | −0.862150 | −0.431075 | − | 0.902316i | \(-0.641866\pi\) | ||||
−0.431075 | + | 0.902316i | \(0.641866\pi\) | |||||||
\(930\) | −1.37958 | −0.0452382 | ||||||||
\(931\) | 31.3566 | 1.02767 | ||||||||
\(932\) | 23.1810 | 0.759317 | ||||||||
\(933\) | 33.6511 | 1.10169 | ||||||||
\(934\) | 4.35396 | 0.142466 | ||||||||
\(935\) | 2.23384 | 0.0730543 | ||||||||
\(936\) | −1.63724 | −0.0535148 | ||||||||
\(937\) | 27.9872 | 0.914302 | 0.457151 | − | 0.889389i | \(-0.348870\pi\) | ||||
0.457151 | + | 0.889389i | \(0.348870\pi\) | |||||||
\(938\) | 16.6244 | 0.542805 | ||||||||
\(939\) | −17.9983 | −0.587351 | ||||||||
\(940\) | 6.94328 | 0.226465 | ||||||||
\(941\) | −10.4294 | −0.339989 | −0.169994 | − | 0.985445i | \(-0.554375\pi\) | ||||
−0.169994 | + | 0.985445i | \(0.554375\pi\) | |||||||
\(942\) | −3.03755 | −0.0989689 | ||||||||
\(943\) | 5.25950 | 0.171273 | ||||||||
\(944\) | 24.9386 | 0.811682 | ||||||||
\(945\) | 1.63997 | 0.0533483 | ||||||||
\(946\) | −10.9691 | −0.356636 | ||||||||
\(947\) | 48.0799 | 1.56239 | 0.781193 | − | 0.624290i | \(-0.214612\pi\) | ||||
0.781193 | + | 0.624290i | \(0.214612\pi\) | |||||||
\(948\) | 12.6217 | 0.409933 | ||||||||
\(949\) | 11.5153 | 0.373801 | ||||||||
\(950\) | −6.42747 | −0.208535 | ||||||||
\(951\) | −11.0791 | −0.359265 | ||||||||
\(952\) | −17.2741 | −0.559856 | ||||||||
\(953\) | −46.2541 | −1.49832 | −0.749159 | − | 0.662390i | \(-0.769542\pi\) | ||||
−0.749159 | + | 0.662390i | \(0.769542\pi\) | |||||||
\(954\) | 2.75267 | 0.0891210 | ||||||||
\(955\) | −4.51635 | −0.146146 | ||||||||
\(956\) | −46.9348 | −1.51798 | ||||||||
\(957\) | 2.44305 | 0.0789726 | ||||||||
\(958\) | 11.8076 | 0.381488 | ||||||||
\(959\) | 49.3249 | 1.59278 | ||||||||
\(960\) | 1.31721 | 0.0425127 | ||||||||
\(961\) | 29.1277 | 0.939603 | ||||||||
\(962\) | −1.22070 | −0.0393571 | ||||||||
\(963\) | −10.5569 | −0.340190 | ||||||||
\(964\) | 24.0855 | 0.775742 | ||||||||
\(965\) | −5.98321 | −0.192606 | ||||||||
\(966\) | −1.93540 | −0.0622704 | ||||||||
\(967\) | 39.2454 | 1.26205 | 0.631023 | − | 0.775764i | \(-0.282635\pi\) | ||||
0.631023 | + | 0.775764i | \(0.282635\pi\) | |||||||
\(968\) | 8.73801 | 0.280850 | ||||||||
\(969\) | −6.81202 | −0.218833 | ||||||||
\(970\) | −3.14497 | −0.100979 | ||||||||
\(971\) | −18.5745 | −0.596085 | −0.298042 | − | 0.954553i | \(-0.596334\pi\) | ||||
−0.298042 | + | 0.954553i | \(0.596334\pi\) | |||||||
\(972\) | −1.79004 | −0.0574155 | ||||||||
\(973\) | 10.1987 | 0.326956 | ||||||||
\(974\) | −11.6218 | −0.372388 | ||||||||
\(975\) | −4.57163 | −0.146409 | ||||||||
\(976\) | 24.3681 | 0.780005 | ||||||||
\(977\) | 9.33171 | 0.298548 | 0.149274 | − | 0.988796i | \(-0.452306\pi\) | ||||
0.149274 | + | 0.988796i | \(0.452306\pi\) | |||||||
\(978\) | 3.57859 | 0.114431 | ||||||||
\(979\) | 21.3376 | 0.681952 | ||||||||
\(980\) | 7.53415 | 0.240670 | ||||||||
\(981\) | 15.2793 | 0.487830 | ||||||||
\(982\) | 15.3988 | 0.491395 | ||||||||
\(983\) | −32.6070 | −1.04000 | −0.520001 | − | 0.854166i | \(-0.674068\pi\) | ||||
−0.520001 | + | 0.854166i | \(0.674068\pi\) | |||||||
\(984\) | −9.13396 | −0.291180 | ||||||||
\(985\) | 3.60266 | 0.114790 | ||||||||
\(986\) | −1.07908 | −0.0343648 | ||||||||
\(987\) | −42.1953 | −1.34309 | ||||||||
\(988\) | −4.88150 | −0.155301 | ||||||||
\(989\) | −9.79866 | −0.311579 | ||||||||
\(990\) | −0.434652 | −0.0138141 | ||||||||
\(991\) | −10.6210 | −0.337388 | −0.168694 | − | 0.985668i | \(-0.553955\pi\) | ||||
−0.168694 | + | 0.985668i | \(0.553955\pi\) | |||||||
\(992\) | 36.8258 | 1.16922 | ||||||||
\(993\) | 32.2908 | 1.02472 | ||||||||
\(994\) | −13.2871 | −0.421441 | ||||||||
\(995\) | −3.00390 | −0.0952300 | ||||||||
\(996\) | −19.5157 | −0.618377 | ||||||||
\(997\) | 48.5845 | 1.53869 | 0.769343 | − | 0.638836i | \(-0.220584\pi\) | ||||
0.769343 | + | 0.638836i | \(0.220584\pi\) | |||||||
\(998\) | 11.2152 | 0.355011 | ||||||||
\(999\) | −2.82580 | −0.0894045 |
(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 | 2001.2.a.o.1.11 | ✓ | 20 | |
3.2 | odd | 2 | 6003.2.a.s.1.10 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.o.1.11 | ✓ | 20 | 1.1 | even | 1 | trivial | |
6003.2.a.s.1.10 | 20 | 3.2 | odd | 2 |