Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8020,2,Mod(1,8020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8020, 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("8020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8020 = 2^{2} \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8020.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0400224211\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8020.1 |
$q$-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 | 0 | ||||||||
\(3\) | 0.732051 | 0.422650 | 0.211325 | − | 0.977416i | \(-0.432222\pi\) | ||||
0.211325 | + | 0.977416i | \(0.432222\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.46410 | 1.30931 | 0.654654 | − | 0.755929i | \(-0.272814\pi\) | ||||
0.654654 | + | 0.755929i | \(0.272814\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.46410 | −0.821367 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.46410 | −1.04447 | −0.522233 | − | 0.852803i | \(-0.674901\pi\) | ||||
−0.522233 | + | 0.852803i | \(0.674901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.26795 | −0.906366 | −0.453183 | − | 0.891417i | \(-0.649712\pi\) | ||||
−0.453183 | + | 0.891417i | \(0.649712\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.732051 | −0.189015 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.732051 | −0.177548 | −0.0887742 | − | 0.996052i | \(-0.528295\pi\) | ||||
−0.0887742 | + | 0.996052i | \(0.528295\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.92820 | −1.58944 | −0.794719 | − | 0.606977i | \(-0.792382\pi\) | ||||
−0.794719 | + | 0.606977i | \(0.792382\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.53590 | 0.553378 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.19615 | −0.457929 | −0.228965 | − | 0.973435i | \(-0.573534\pi\) | ||||
−0.228965 | + | 0.973435i | \(0.573534\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.00000 | −0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.46410 | −0.271877 | −0.135938 | − | 0.990717i | \(-0.543405\pi\) | ||||
−0.135938 | + | 0.990717i | \(0.543405\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.46410 | 0.262960 | 0.131480 | − | 0.991319i | \(-0.458027\pi\) | ||||
0.131480 | + | 0.991319i | \(0.458027\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.53590 | −0.441443 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.46410 | −0.585540 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.1962 | 1.67624 | 0.838119 | − | 0.545488i | \(-0.183656\pi\) | ||||
0.838119 | + | 0.545488i | \(0.183656\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.39230 | −0.383075 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.39230 | 1.31066 | 0.655329 | − | 0.755344i | \(-0.272530\pi\) | ||||
0.655329 | + | 0.755344i | \(0.272530\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00000 | −0.304997 | −0.152499 | − | 0.988304i | \(-0.548732\pi\) | ||||
−0.152499 | + | 0.988304i | \(0.548732\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.46410 | 0.367327 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.92820 | 0.718852 | 0.359426 | − | 0.933174i | \(-0.382972\pi\) | ||||
0.359426 | + | 0.933174i | \(0.382972\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000 | 0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.535898 | −0.0750408 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.80385 | 0.247778 | 0.123889 | − | 0.992296i | \(-0.460463\pi\) | ||||
0.123889 | + | 0.992296i | \(0.460463\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.46410 | 0.467099 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.07180 | −0.671776 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.00000 | −1.04151 | −0.520756 | − | 0.853706i | \(-0.674350\pi\) | ||||
−0.520756 | + | 0.853706i | \(0.674350\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.92820 | −0.630992 | −0.315496 | − | 0.948927i | \(-0.602171\pi\) | ||||
−0.315496 | + | 0.948927i | \(0.602171\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.53590 | −1.07542 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.26795 | 0.405339 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.19615 | 0.268303 | 0.134151 | − | 0.990961i | \(-0.457169\pi\) | ||||
0.134151 | + | 0.990961i | \(0.457169\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.60770 | −0.193544 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.46410 | 1.12318 | 0.561591 | − | 0.827415i | \(-0.310189\pi\) | ||||
0.561591 | + | 0.827415i | \(0.310189\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.9282 | 1.51313 | 0.756566 | − | 0.653917i | \(-0.226876\pi\) | ||||
0.756566 | + | 0.653917i | \(0.226876\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.732051 | 0.0845299 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.0000 | −1.36753 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.46410 | 0.496011 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.8564 | 1.30141 | 0.650705 | − | 0.759331i | \(-0.274474\pi\) | ||||
0.650705 | + | 0.759331i | \(0.274474\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.732051 | 0.0794021 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.07180 | −0.114909 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.8564 | 1.25678 | 0.628388 | − | 0.777900i | \(-0.283715\pi\) | ||||
0.628388 | + | 0.777900i | \(0.283715\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.3205 | −1.18671 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.07180 | 0.111140 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.92820 | 0.710819 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.26795 | 0.737948 | 0.368974 | − | 0.929440i | \(-0.379709\pi\) | ||||
0.368974 | + | 0.929440i | \(0.379709\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.53590 | 0.857890 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.9282 | 1.68442 | 0.842210 | − | 0.539150i | \(-0.181255\pi\) | ||||
0.842210 | + | 0.539150i | \(0.181255\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.3923 | 1.02398 | 0.511992 | − | 0.858990i | \(-0.328908\pi\) | ||||
0.511992 | + | 0.858990i | \(0.328908\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.53590 | −0.247478 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.5885 | 1.79701 | 0.898507 | − | 0.438959i | \(-0.144653\pi\) | ||||
0.898507 | + | 0.438959i | \(0.144653\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.3205 | −1.85057 | −0.925285 | − | 0.379274i | \(-0.876174\pi\) | ||||
−0.925285 | + | 0.379274i | \(0.876174\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.46410 | 0.708461 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.53590 | 0.802990 | 0.401495 | − | 0.915861i | \(-0.368491\pi\) | ||||
0.401495 | + | 0.915861i | \(0.368491\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.19615 | 0.204792 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.05256 | 0.744459 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.53590 | −0.232465 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.14359 | 0.553949 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.26795 | 0.644926 | 0.322463 | − | 0.946582i | \(-0.395489\pi\) | ||||
0.322463 | + | 0.946582i | \(0.395489\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.46410 | −0.128907 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.4641 | 1.17636 | 0.588182 | − | 0.808729i | \(-0.299844\pi\) | ||||
0.588182 | + | 0.808729i | \(0.299844\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −24.0000 | −2.08106 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.00000 | 0.344265 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.66025 | 0.654460 | 0.327230 | − | 0.944945i | \(-0.393885\pi\) | ||||
0.327230 | + | 0.944945i | \(0.393885\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.92820 | −0.248367 | −0.124183 | − | 0.992259i | \(-0.539631\pi\) | ||||
−0.124183 | + | 0.992259i | \(0.539631\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.60770 | 0.303823 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.3205 | 0.946668 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.46410 | 0.121587 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.66025 | 0.301893 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.9282 | −1.38681 | −0.693406 | − | 0.720547i | \(-0.743891\pi\) | ||||
−0.693406 | + | 0.720547i | \(0.743891\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.53590 | 0.694642 | 0.347321 | − | 0.937746i | \(-0.387092\pi\) | ||||
0.347321 | + | 0.937746i | \(0.387092\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.80385 | 0.145832 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.46410 | −0.117599 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.73205 | 0.377659 | 0.188829 | − | 0.982010i | \(-0.439531\pi\) | ||||
0.188829 | + | 0.982010i | \(0.439531\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.32051 | 0.104723 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.60770 | −0.599570 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.80385 | −0.141288 | −0.0706441 | − | 0.997502i | \(-0.522505\pi\) | ||||
−0.0706441 | + | 0.997502i | \(0.522505\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.53590 | 0.197419 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.80385 | 0.139586 | 0.0697930 | − | 0.997561i | \(-0.477766\pi\) | ||||
0.0697930 | + | 0.997561i | \(0.477766\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.32051 | −0.178501 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 17.0718 | 1.30551 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.535898 | −0.0407436 | −0.0203718 | − | 0.999792i | \(-0.506485\pi\) | ||||
−0.0203718 | + | 0.999792i | \(0.506485\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.46410 | 0.261861 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.85641 | −0.440194 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.32051 | 0.696647 | 0.348324 | − | 0.937374i | \(-0.386751\pi\) | ||||
0.348324 | + | 0.937374i | \(0.386751\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.60770 | −0.266688 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.1962 | −0.749636 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.53590 | 0.185443 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.8564 | −1.00791 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.39230 | −0.317816 | −0.158908 | − | 0.987293i | \(-0.550797\pi\) | ||||
−0.158908 | + | 0.987293i | \(0.550797\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.19615 | −0.446009 | −0.223004 | − | 0.974817i | \(-0.571586\pi\) | ||||
−0.223004 | + | 0.974817i | \(0.571586\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.39230 | 0.171317 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.46410 | −0.246807 | −0.123404 | − | 0.992357i | \(-0.539381\pi\) | ||||
−0.123404 | + | 0.992357i | \(0.539381\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.7846 | −1.75693 | −0.878467 | − | 0.477803i | \(-0.841433\pi\) | ||||
−0.878467 | + | 0.477803i | \(0.841433\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.60770 | 0.113398 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.07180 | −0.355970 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.39230 | −0.586144 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.41154 | 0.376128 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 24.0000 | 1.66011 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.4641 | −1.20228 | −0.601139 | − | 0.799144i | \(-0.705286\pi\) | ||||
−0.601139 | + | 0.799144i | \(0.705286\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.92820 | 0.474713 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.00000 | 0.136399 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.07180 | 0.344296 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.46410 | 0.639525 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.39230 | 0.160924 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.3205 | 0.892007 | 0.446004 | − | 0.895031i | \(-0.352847\pi\) | ||||
0.446004 | + | 0.895031i | \(0.352847\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.46410 | −0.164273 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.8038 | −0.916194 | −0.458097 | − | 0.888902i | \(-0.651469\pi\) | ||||
−0.458097 | + | 0.888902i | \(0.651469\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.9282 | 1.38297 | 0.691487 | − | 0.722389i | \(-0.256956\pi\) | ||||
0.691487 | + | 0.722389i | \(0.256956\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.78461 | −0.577985 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 26.1962 | 1.71617 | 0.858084 | − | 0.513510i | \(-0.171655\pi\) | ||||
0.858084 | + | 0.513510i | \(0.171655\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.92820 | −0.321481 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.5359 | −1.32836 | −0.664178 | − | 0.747574i | \(-0.731218\pi\) | ||||
−0.664178 | + | 0.747574i | \(0.731218\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.8564 | −0.763738 | −0.381869 | − | 0.924216i | \(-0.624719\pi\) | ||||
−0.381869 | + | 0.924216i | \(0.624719\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.2679 | 0.979439 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.00000 | −0.319438 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 22.6410 | 1.44061 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.67949 | 0.550040 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.32051 | −0.462066 | −0.231033 | − | 0.972946i | \(-0.574211\pi\) | ||||
−0.231033 | + | 0.972946i | \(0.574211\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.60770 | 0.478292 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.535898 | 0.0335593 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.535898 | 0.0334284 | 0.0167142 | − | 0.999860i | \(-0.494679\pi\) | ||||
0.0167142 | + | 0.999860i | \(0.494679\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 35.3205 | 2.19471 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.60770 | 0.223311 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.928203 | 0.0572355 | 0.0286177 | − | 0.999590i | \(-0.490889\pi\) | ||||
0.0286177 | + | 0.999590i | \(0.490889\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.80385 | −0.110809 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.67949 | 0.531176 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.46410 | −0.211210 | −0.105605 | − | 0.994408i | \(-0.533678\pi\) | ||||
−0.105605 | + | 0.994408i | \(0.533678\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.3923 | −1.23874 | −0.619372 | − | 0.785098i | \(-0.712613\pi\) | ||||
−0.619372 | + | 0.785098i | \(0.712613\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.28719 | −0.501563 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.46410 | −0.208893 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.1962 | −1.33364 | −0.666819 | − | 0.745220i | \(-0.732344\pi\) | ||||
−0.666819 | + | 0.745220i | \(0.732344\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.60770 | −0.215987 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.143594 | 0.00856607 | 0.00428304 | − | 0.999991i | \(-0.498637\pi\) | ||||
0.00428304 | + | 0.999991i | \(0.498637\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.6603 | 0.693130 | 0.346565 | − | 0.938026i | \(-0.387348\pi\) | ||||
0.346565 | + | 0.938026i | \(0.387348\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.07180 | 0.300427 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 29.0718 | 1.71605 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4641 | −0.968477 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.32051 | 0.311894 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.19615 | −0.361983 | −0.180992 | − | 0.983485i | \(-0.557931\pi\) | ||||
−0.180992 | + | 0.983485i | \(0.557931\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.00000 | 0.465778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.8564 | 0.804030 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.17691 | 0.415052 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.92820 | −0.399335 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.3923 | 0.711919 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.92820 | 0.282188 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.92820 | 0.509559 | 0.254780 | − | 0.966999i | \(-0.417997\pi\) | ||||
0.254780 | + | 0.966999i | \(0.417997\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.60770 | 0.432787 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.92820 | −0.392862 | −0.196431 | − | 0.980518i | \(-0.562935\pi\) | ||||
−0.196431 | + | 0.980518i | \(0.562935\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.3923 | −1.49178 | −0.745891 | − | 0.666068i | \(-0.767976\pi\) | ||||
−0.745891 | + | 0.666068i | \(0.767976\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.53590 | 0.480943 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −30.5885 | −1.71802 | −0.859009 | − | 0.511960i | \(-0.828920\pi\) | ||||
−0.859009 | + | 0.511960i | \(0.828920\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.07180 | 0.283966 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.6077 | 0.759507 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.07180 | 0.282202 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.26795 | −0.181273 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.1436 | −0.782143 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 17.0718 | 0.941199 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.60770 | −0.308227 | −0.154113 | − | 0.988053i | \(-0.549252\pi\) | ||||
−0.154113 | + | 0.988053i | \(0.549252\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −25.1244 | −1.37681 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.19615 | −0.119989 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.7128 | −1.18277 | −0.591386 | − | 0.806389i | \(-0.701419\pi\) | ||||
−0.591386 | + | 0.806389i | \(0.701419\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.24871 | 0.339383 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.07180 | −0.274653 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.92820 | −0.374088 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.60770 | 0.0865554 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.05256 | 0.432284 | 0.216142 | − | 0.976362i | \(-0.430653\pi\) | ||||
0.216142 | + | 0.976362i | \(0.430653\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.535898 | −0.0286860 | −0.0143430 | − | 0.999897i | \(-0.504566\pi\) | ||||
−0.0143430 | + | 0.999897i | \(0.504566\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.0718 | 0.697721 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.73205 | 0.251862 | 0.125931 | − | 0.992039i | \(-0.459808\pi\) | ||||
0.125931 | + | 0.992039i | \(0.459808\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.46410 | −0.502302 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.85641 | −0.0982514 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.92820 | −0.365657 | −0.182828 | − | 0.983145i | \(-0.558525\pi\) | ||||
−0.182828 | + | 0.983145i | \(0.558525\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 29.0000 | 1.52632 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.732051 | 0.0384227 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.9282 | −0.676693 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.2679 | 1.21458 | 0.607289 | − | 0.794481i | \(-0.292257\pi\) | ||||
0.607289 | + | 0.794481i | \(0.292257\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −20.6795 | −1.07653 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.24871 | 0.324417 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.7128 | 1.53847 | 0.769236 | − | 0.638965i | \(-0.220637\pi\) | ||||
0.769236 | + | 0.638965i | \(0.220637\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.732051 | −0.0378029 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.78461 | 0.246420 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.535898 | −0.0275273 | −0.0137636 | − | 0.999905i | \(-0.504381\pi\) | ||||
−0.0137636 | + | 0.999905i | \(0.504381\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.32051 | 0.272578 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.7846 | −0.755458 | −0.377729 | − | 0.925916i | \(-0.623295\pi\) | ||||
−0.377729 | + | 0.925916i | \(0.623295\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.0000 | 0.611577 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.92820 | 0.250515 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.39230 | 0.121295 | 0.0606473 | − | 0.998159i | \(-0.480683\pi\) | ||||
0.0606473 | + | 0.998159i | \(0.480683\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.60770 | 0.0813046 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.85641 | 0.497190 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.46410 | 0.374613 | 0.187306 | − | 0.982302i | \(-0.440024\pi\) | ||||
0.187306 | + | 0.982302i | \(0.440024\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −17.5692 | −0.879561 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.00000 | −0.0499376 | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.78461 | −0.238338 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.46410 | −0.221823 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −35.3205 | −1.75077 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.39230 | 0.217185 | 0.108593 | − | 0.994086i | \(-0.465366\pi\) | ||||
0.108593 | + | 0.994086i | \(0.465366\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.60770 | 0.276607 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −27.7128 | −1.36366 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.8564 | −0.582008 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.14359 | −0.104972 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −33.3205 | −1.62781 | −0.813907 | − | 0.580996i | \(-0.802663\pi\) | ||||
−0.813907 | + | 0.580996i | \(0.802663\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.53590 | 0.318540 | 0.159270 | − | 0.987235i | \(-0.449086\pi\) | ||||
0.159270 | + | 0.987235i | \(0.449086\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.1436 | −0.590442 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.732051 | −0.0355097 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.0718 | −0.826162 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.28719 | 0.400109 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 32.3923 | 1.56028 | 0.780141 | − | 0.625603i | \(-0.215147\pi\) | ||||
0.780141 | + | 0.625603i | \(0.215147\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.3923 | 1.26833 | 0.634167 | − | 0.773196i | \(-0.281343\pi\) | ||||
0.634167 | + | 0.773196i | \(0.281343\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.07180 | 0.0513887 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.2154 | 0.727851 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −40.7846 | −1.94654 | −0.973272 | − | 0.229657i | \(-0.926240\pi\) | ||||
−0.973272 | + | 0.229657i | \(0.926240\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.3205 | −0.586691 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.80385 | 0.275749 | 0.137875 | − | 0.990450i | \(-0.455973\pi\) | ||||
0.137875 | + | 0.990450i | \(0.455973\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.8564 | −0.562048 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.3923 | −0.586136 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.67949 | 0.126453 | 0.0632265 | − | 0.997999i | \(-0.479861\pi\) | ||||
0.0632265 | + | 0.997999i | \(0.479861\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29.0718 | −1.36894 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.24871 | 0.293590 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.3205 | 0.530714 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.3205 | 1.55867 | 0.779334 | − | 0.626609i | \(-0.215558\pi\) | ||||
0.779334 | + | 0.626609i | \(0.215558\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.92820 | 0.136677 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.0000 | 0.465746 | 0.232873 | − | 0.972507i | \(-0.425187\pi\) | ||||
0.232873 | + | 0.972507i | \(0.425187\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.5885 | 0.677983 | 0.338992 | − | 0.940789i | \(-0.389914\pi\) | ||||
0.338992 | + | 0.940789i | \(0.389914\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.07180 | −0.0497034 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.1244 | 0.977519 | 0.488759 | − | 0.872419i | \(-0.337450\pi\) | ||||
0.488759 | + | 0.872419i | \(0.337450\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.60770 | 0.351291 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.46410 | 0.159617 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.92820 | 0.318559 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.92820 | −0.317888 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.44486 | −0.203516 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.7846 | 0.766908 | 0.383454 | − | 0.923560i | \(-0.374734\pi\) | ||||
0.383454 | + | 0.923560i | \(0.374734\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −33.3205 | −1.51928 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.56922 | −0.253408 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.26795 | −0.330021 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.8564 | 0.718522 | 0.359261 | − | 0.933237i | \(-0.383029\pi\) | ||||
0.359261 | + | 0.933237i | \(0.383029\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.32051 | −0.0597154 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 37.8564 | 1.70844 | 0.854218 | − | 0.519915i | \(-0.174036\pi\) | ||||
0.854218 | + | 0.519915i | \(0.174036\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.07180 | 0.0482713 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.53590 | −0.383660 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 32.7846 | 1.47059 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.07180 | 0.0479802 | 0.0239901 | − | 0.999712i | \(-0.492363\pi\) | ||||
0.0239901 | + | 0.999712i | \(0.492363\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.32051 | 0.0589959 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.8564 | 1.42041 | 0.710203 | − | 0.703996i | \(-0.248603\pi\) | ||||
0.710203 | + | 0.703996i | \(0.248603\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.9282 | −0.753295 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.69873 | −0.0754432 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.3923 | 1.16982 | 0.584909 | − | 0.811099i | \(-0.301130\pi\) | ||||
0.584909 | + | 0.811099i | \(0.301130\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 44.7846 | 1.98115 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 27.7128 | 1.22355 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.3923 | −0.457940 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.0718 | −0.750817 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.392305 | −0.0172203 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.8564 | −0.869925 | −0.434962 | − | 0.900449i | \(-0.643238\pi\) | ||||
−0.434962 | + | 0.900449i | \(0.643238\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.58846 | −0.113185 | −0.0565927 | − | 0.998397i | \(-0.518024\pi\) | ||||
−0.0565927 | + | 0.998397i | \(0.518024\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.53590 | 0.110676 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.07180 | −0.0466882 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.1769 | −0.790301 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19.7128 | 0.855463 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −27.4256 | −1.18794 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.5885 | −0.803649 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.82309 | 0.294438 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −17.3205 | −0.746047 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.7128 | 1.27745 | 0.638727 | − | 0.769434i | \(-0.279461\pi\) | ||||
0.638727 | + | 0.769434i | \(0.279461\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.32051 | −0.314153 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.3205 | 0.827600 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.60770 | −0.0687401 | −0.0343700 | − | 0.999409i | \(-0.510942\pi\) | ||||
−0.0343700 | + | 0.999409i | \(0.510942\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.1436 | 0.518276 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.1436 | 0.432132 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.46410 | −0.316833 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 42.0000 | 1.77960 | 0.889799 | − | 0.456354i | \(-0.150845\pi\) | ||||
0.889799 | + | 0.456354i | \(0.150845\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.53590 | 0.276439 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.85641 | 0.0783775 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.39230 | 0.100824 | 0.0504118 | − | 0.998729i | \(-0.483947\pi\) | ||||
0.0504118 | + | 0.998729i | \(0.483947\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.53590 | −0.359108 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 15.4641 | 0.649431 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 40.2487 | 1.68731 | 0.843657 | − | 0.536883i | \(-0.180398\pi\) | ||||
0.843657 | + | 0.536883i | \(0.180398\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.32051 | −0.306354 | −0.153177 | − | 0.988199i | \(-0.548950\pi\) | ||||
−0.153177 | + | 0.988199i | \(0.548950\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.21539 | −0.134325 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.19615 | −0.0915859 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.3205 | 0.721062 | 0.360531 | − | 0.932747i | \(-0.382595\pi\) | ||||
0.360531 | + | 0.932747i | \(0.382595\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.53590 | −0.188506 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 41.0718 | 1.70395 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.24871 | −0.258795 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.05256 | −0.332932 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.1769 | −1.12171 | −0.560856 | − | 0.827914i | \(-0.689528\pi\) | ||||
−0.560856 | + | 0.827914i | \(0.689528\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.1436 | −0.417959 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.53590 | −0.104313 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.12436 | −0.374692 | −0.187346 | − | 0.982294i | \(-0.559989\pi\) | ||||
−0.187346 | + | 0.982294i | \(0.559989\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.53590 | 0.103962 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.1436 | −0.742568 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 43.1769 | 1.76416 | 0.882080 | − | 0.471099i | \(-0.156142\pi\) | ||||
0.882080 | + | 0.471099i | \(0.156142\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.0000 | 0.571072 | 0.285536 | − | 0.958368i | \(-0.407828\pi\) | ||||
0.285536 | + | 0.958368i | \(0.407828\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.41154 | −0.220375 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.71281 | −0.394231 | −0.197115 | − | 0.980380i | \(-0.563157\pi\) | ||||
−0.197115 | + | 0.980380i | \(0.563157\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.71281 | −0.150451 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.1051 | −0.651543 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.3397 | 1.14463 | 0.572316 | − | 0.820033i | \(-0.306045\pi\) | ||||
0.572316 | + | 0.820033i | \(0.306045\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.14359 | −0.247734 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.1962 | 0.732550 | 0.366275 | − | 0.930507i | \(-0.380633\pi\) | ||||
0.366275 | + | 0.930507i | \(0.380633\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.3205 | 0.856944 | 0.428472 | − | 0.903555i | \(-0.359052\pi\) | ||||
0.428472 | + | 0.903555i | \(0.359052\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.78461 | 0.352514 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 41.0718 | 1.64551 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 17.5692 | 0.701647 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.46410 | −0.297613 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.1051 | −1.59656 | −0.798280 | − | 0.602287i | \(-0.794256\pi\) | ||||
−0.798280 | + | 0.602287i | \(0.794256\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.7846 | −0.508143 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.26795 | −0.288420 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.3397 | −0.647404 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −23.3205 | −0.922545 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.85641 | 0.152319 | 0.0761594 | − | 0.997096i | \(-0.475734\pi\) | ||||
0.0761594 | + | 0.997096i | \(0.475734\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −32.9282 | −1.29856 | −0.649281 | − | 0.760549i | \(-0.724930\pi\) | ||||
−0.649281 | + | 0.760549i | \(0.724930\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.46410 | 0.0576489 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.3397 | 0.485125 | 0.242563 | − | 0.970136i | \(-0.422012\pi\) | ||||
0.242563 | + | 0.970136i | \(0.422012\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.7128 | 1.08782 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.71281 | 0.145517 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.24871 | −0.166265 | −0.0831325 | − | 0.996539i | \(-0.526492\pi\) | ||||
−0.0831325 | + | 0.996539i | \(0.526492\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.4641 | −0.526086 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −31.8564 | −1.24284 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.92820 | −0.269884 | −0.134942 | − | 0.990853i | \(-0.543085\pi\) | ||||
−0.134942 | + | 0.990853i | \(0.543085\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.85641 | −0.149997 | −0.0749984 | − | 0.997184i | \(-0.523895\pi\) | ||||
−0.0749984 | + | 0.997184i | \(0.523895\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.75129 | 0.0680144 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 24.0000 | 0.930680 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.21539 | 0.124500 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.75129 | 0.377007 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.0718 | 0.659049 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.4449 | −0.788092 | −0.394046 | − | 0.919091i | \(-0.628925\pi\) | ||||
−0.394046 | + | 0.919091i | \(0.628925\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.00000 | −0.153960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.3923 | −0.860606 | −0.430303 | − | 0.902684i | \(-0.641593\pi\) | ||||
−0.430303 | + | 0.902684i | \(0.641593\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25.1769 | 0.966201 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.1051 | −0.387229 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.3397 | −0.472167 | −0.236084 | − | 0.971733i | \(-0.575864\pi\) | ||||
−0.236084 | + | 0.971733i | \(0.575864\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.66025 | −0.292683 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.3205 | 0.584514 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.89488 | −0.224577 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.0000 | −0.608669 | −0.304334 | − | 0.952565i | \(-0.598434\pi\) | ||||
−0.304334 | + | 0.952565i | \(0.598434\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 29.5692 | 1.12324 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.92820 | 0.111073 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.14359 | −0.232705 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.1769 | 0.725338 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.9282 | −0.941525 | −0.470763 | − | 0.882260i | \(-0.656021\pi\) | ||||
−0.470763 | + | 0.882260i | \(0.656021\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −70.6410 | −2.66428 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.60770 | −0.135874 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 58.6410 | 2.20542 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 42.7846 | 1.60681 | 0.803405 | − | 0.595433i | \(-0.203020\pi\) | ||||
0.803405 | + | 0.595433i | \(0.203020\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.21539 | −0.120417 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.3205 | −0.423363 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.0333 | −0.561430 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −48.2487 | −1.79937 | −0.899687 | − | 0.436536i | \(-0.856205\pi\) | ||||
−0.899687 | + | 0.436536i | \(0.856205\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 36.0000 | 1.34071 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.67949 | −0.322794 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.46410 | −0.0543754 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.2679 | 0.862960 | 0.431480 | − | 0.902122i | \(-0.357991\pi\) | ||||
0.431480 | + | 0.902122i | \(0.357991\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.21539 | −0.0820515 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.46410 | 0.0541518 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.4641 | −0.718923 | −0.359461 | − | 0.933160i | \(-0.617040\pi\) | ||||
−0.359461 | + | 0.933160i | \(0.617040\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.66025 | −0.135011 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.60770 | −0.280233 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27.4641 | −1.01028 | −0.505142 | − | 0.863036i | \(-0.668560\pi\) | ||||
−0.505142 | + | 0.863036i | \(0.668560\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.5744 | 0.608875 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.9808 | 0.549591 | 0.274795 | − | 0.961503i | \(-0.411390\pi\) | ||||
0.274795 | + | 0.961503i | \(0.411390\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.9282 | 0.620201 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −29.2154 | −1.06894 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 64.3923 | 2.35284 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.0000 | −0.437886 | −0.218943 | − | 0.975738i | \(-0.570261\pi\) | ||||
−0.218943 | + | 0.975738i | \(0.570261\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.35898 | −0.195292 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.53590 | −0.310653 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.3205 | −0.920290 | −0.460145 | − | 0.887844i | \(-0.652202\pi\) | ||||
−0.460145 | + | 0.887844i | \(0.652202\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.56922 | 0.202150 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.46410 | 0.343073 | 0.171537 | − | 0.985178i | \(-0.445127\pi\) | ||||
0.171537 | + | 0.985178i | \(0.445127\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −66.9282 | −2.42296 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.80385 | −0.0652182 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 26.1436 | 0.943990 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.1051 | 1.08562 | 0.542809 | − | 0.839856i | \(-0.317361\pi\) | ||||
0.542809 | + | 0.839856i | \(0.317361\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.392305 | 0.0141285 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.78461 | −0.100155 | −0.0500777 | − | 0.998745i | \(-0.515947\pi\) | ||||
−0.0500777 | + | 0.998745i | \(0.515947\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.46410 | 0.0525921 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 25.8564 | 0.927593 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −58.1436 | −2.08321 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.7846 | −1.17313 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.85641 | 0.209291 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.73205 | −0.168894 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 44.7321 | 1.59453 | 0.797263 | − | 0.603632i | \(-0.206281\pi\) | ||||
0.797263 | + | 0.603632i | \(0.206281\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.679492 | 0.0241906 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 29.5692 | 1.05136 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.1051 | 0.571910 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.32051 | −0.0468336 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −34.3923 | −1.21824 | −0.609119 | − | 0.793079i | \(-0.708477\pi\) | ||||
−0.609119 | + | 0.793079i | \(0.708477\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.60770 | −0.127631 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −29.2154 | −1.03228 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −44.7846 | −1.58041 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.60770 | 0.268136 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.53590 | −0.0892679 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.7846 | 0.941697 | 0.470848 | − | 0.882214i | \(-0.343948\pi\) | ||||
0.470848 | + | 0.882214i | \(0.343948\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.9282 | 0.664659 | 0.332330 | − | 0.943163i | \(-0.392165\pi\) | ||||
0.332330 | + | 0.943163i | \(0.392165\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14.9282 | −0.523555 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.80385 | 0.0631860 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.8564 | 0.484774 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 27.8949 | 0.974726 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 47.5692 | 1.66018 | 0.830089 | − | 0.557632i | \(-0.188290\pi\) | ||||
0.830089 | + | 0.557632i | \(0.188290\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.94744 | −0.137599 | −0.0687996 | − | 0.997631i | \(-0.521917\pi\) | ||||
−0.0687996 | + | 0.997631i | \(0.521917\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.53590 | −0.0882886 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 52.2487 | 1.81687 | 0.908433 | − | 0.418031i | \(-0.137280\pi\) | ||||
0.908433 | + | 0.418031i | \(0.137280\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 50.1051 | 1.74022 | 0.870111 | − | 0.492855i | \(-0.164047\pi\) | ||||
0.870111 | + | 0.492855i | \(0.164047\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.2487 | −0.563662 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.66025 | −0.126820 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.80385 | −0.0624247 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.85641 | −0.202427 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22.1436 | 0.764482 | 0.382241 | − | 0.924063i | \(-0.375152\pi\) | ||||
0.382241 | + | 0.924063i | \(0.375152\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.8564 | −0.926083 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.105118 | 0.00362045 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.32051 | 0.0798279 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.46410 | 0.119028 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.53590 | 0.292951 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22.3923 | −0.767598 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.9282 | 0.716568 | 0.358284 | − | 0.933613i | \(-0.383362\pi\) | ||||
0.358284 | + | 0.933613i | \(0.383362\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −17.0718 | −0.583843 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.75129 | 0.264779 | 0.132389 | − | 0.991198i | \(-0.457735\pi\) | ||||
0.132389 | + | 0.991198i | \(0.457735\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.2487 | 1.50975 | 0.754873 | − | 0.655871i | \(-0.227698\pi\) | ||||
0.754873 | + | 0.655871i | \(0.227698\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 21.2820 | 0.725290 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29.8038 | 1.01453 | 0.507267 | − | 0.861789i | \(-0.330656\pi\) | ||||
0.507267 | + | 0.861789i | \(0.330656\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.535898 | 0.0182211 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.0526 | −0.409326 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.17691 | −0.243180 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −17.9090 | −0.606127 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.46410 | −0.117108 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −57.5167 | −1.94220 | −0.971100 | − | 0.238674i | \(-0.923287\pi\) | ||||
−0.971100 | + | 0.238674i | \(0.923287\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.53590 | −0.152992 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.7128 | −0.866287 | −0.433143 | − | 0.901325i | \(-0.642596\pi\) | ||||
−0.433143 | + | 0.901325i | \(0.642596\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.7128 | −0.596084 | −0.298042 | − | 0.954553i | \(-0.596333\pi\) | ||||
−0.298042 | + | 0.954553i | \(0.596333\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.85641 | 0.196861 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32.4449 | 1.08939 | 0.544696 | − | 0.838634i | \(-0.316645\pi\) | ||||
0.544696 | + | 0.838634i | \(0.316645\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 25.1769 | 0.844407 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.4641 | −0.518067 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −34.1436 | −1.14257 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.32051 | −0.311550 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.25387 | 0.175421 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.14359 | −0.0714928 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.32051 | −0.0439925 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.07180 | −0.168779 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.0000 | 0.332411 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.7321 | −0.821214 | −0.410607 | − | 0.911812i | \(-0.634683\pi\) | ||||
−0.410607 | + | 0.911812i | \(0.634683\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −41.7128 | −1.38353 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.7128 | 0.785641 | 0.392820 | − | 0.919615i | \(-0.371499\pi\) | ||||
0.392820 | + | 0.919615i | \(0.371499\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −41.0718 | −1.35928 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.60770 | 0.119267 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 46.6410 | 1.54022 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.784610 | 0.0258819 | 0.0129409 | − | 0.999916i | \(-0.495881\pi\) | ||||
0.0129409 | + | 0.999916i | \(0.495881\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.53590 | 0.215365 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −30.9282 | −1.01801 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.1962 | 0.335247 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −25.6077 | −0.841067 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.46410 | −0.244889 | −0.122445 | − | 0.992475i | \(-0.539073\pi\) | ||||
−0.122445 | + | 0.992475i | \(0.539073\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −34.6410 | −1.13531 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.07180 | −0.166043 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.53590 | −0.0829327 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.3731 | −1.02491 | −0.512457 | − | 0.858713i | \(-0.671264\pi\) | ||||
−0.512457 | + | 0.858713i | \(0.671264\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.3205 | −0.630501 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.7128 | 1.22940 | 0.614701 | − | 0.788760i | \(-0.289277\pi\) | ||||
0.614701 | + | 0.788760i | \(0.289277\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.4308 | −0.600189 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.8564 | 0.450749 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.6410 | 0.670743 | 0.335371 | − | 0.942086i | \(-0.391138\pi\) | ||||
0.335371 | + | 0.942086i | \(0.391138\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −42.2487 | −1.37145 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.3923 | −0.726120 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.3923 | −0.336640 | −0.168320 | − | 0.985732i | \(-0.553834\pi\) | ||||
−0.168320 | + | 0.985732i | \(0.553834\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.39230 | 0.142132 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.71281 | 0.120018 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 26.5359 | 0.856889 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.8564 | −0.930852 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −45.8038 | −1.47601 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.19615 | 0.199461 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36.4449 | −1.17199 | −0.585994 | − | 0.810315i | \(-0.699296\pi\) | ||||
−0.585994 | + | 0.810315i | \(0.699296\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.71281 | 0.119273 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.0000 | −0.513464 | −0.256732 | − | 0.966483i | \(-0.582646\pi\) | ||||
−0.256732 | + | 0.966483i | \(0.582646\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.1436 | −0.325189 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.39230 | −0.0766151 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.53590 | −0.145116 | −0.0725581 | − | 0.997364i | \(-0.523116\pi\) | ||||
−0.0725581 | + | 0.997364i | \(0.523116\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −41.0718 | −1.31266 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 47.6077 | 1.52000 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −35.1769 | −1.12197 | −0.560985 | − | 0.827826i | \(-0.689577\pi\) | ||||
−0.560985 | + | 0.827826i | \(0.689577\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.46410 | 0.110375 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12.4974 | 0.397797 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.39230 | 0.139667 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.3923 | 0.647783 | 0.323891 | − | 0.946094i | \(-0.395009\pi\) | ||||
0.323891 | + | 0.946094i | \(0.395009\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.10512 | −0.130272 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.7846 | 0.785725 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.9282 | 1.04285 | 0.521423 | − | 0.853298i | \(-0.325401\pi\) | ||||
0.521423 | + | 0.853298i | \(0.325401\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −40.7846 | −1.29037 |
(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 | 8020.2.a.b.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8020.2.a.b.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial |