Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2850,2,Mod(1,2850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2850, 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("2850.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2850.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: | \(22.7573645761\) |
Analytic rank: | \(1\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2850.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −2.73205 | −1.03262 | −0.516309 | − | 0.856402i | \(-0.672694\pi\) | ||||
−0.516309 | + | 0.856402i | \(0.672694\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.19615 | 1.56670 | 0.783349 | − | 0.621582i | \(-0.213510\pi\) | ||||
0.783349 | + | 0.621582i | \(0.213510\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −4.73205 | −1.31243 | −0.656217 | − | 0.754572i | \(-0.727845\pi\) | ||||
−0.656217 | + | 0.754572i | \(0.727845\pi\) | |||||||
\(14\) | 2.73205 | 0.730171 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.73205 | 0.662620 | 0.331310 | − | 0.943522i | \(-0.392509\pi\) | ||||
0.331310 | + | 0.943522i | \(0.392509\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.73205 | −0.596182 | ||||||||
\(22\) | −5.19615 | −1.10782 | ||||||||
\(23\) | −8.46410 | −1.76489 | −0.882444 | − | 0.470418i | \(-0.844103\pi\) | ||||
−0.882444 | + | 0.470418i | \(0.844103\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.73205 | 0.928032 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.73205 | −0.516309 | ||||||||
\(29\) | −9.19615 | −1.70768 | −0.853841 | − | 0.520533i | \(-0.825733\pi\) | ||||
−0.853841 | + | 0.520533i | \(0.825733\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.92820 | −1.06474 | −0.532368 | − | 0.846513i | \(-0.678698\pi\) | ||||
−0.532368 | + | 0.846513i | \(0.678698\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 5.19615 | 0.904534 | ||||||||
\(34\) | −2.73205 | −0.468543 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 8.92820 | 1.46779 | 0.733894 | − | 0.679264i | \(-0.237701\pi\) | ||||
0.733894 | + | 0.679264i | \(0.237701\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | −4.73205 | −0.757735 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 2.73205 | 0.421565 | ||||||||
\(43\) | −8.73205 | −1.33163 | −0.665813 | − | 0.746119i | \(-0.731915\pi\) | ||||
−0.665813 | + | 0.746119i | \(0.731915\pi\) | |||||||
\(44\) | 5.19615 | 0.783349 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.46410 | 1.24796 | ||||||||
\(47\) | 3.46410 | 0.505291 | 0.252646 | − | 0.967559i | \(-0.418699\pi\) | ||||
0.252646 | + | 0.967559i | \(0.418699\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0.464102 | 0.0663002 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.73205 | 0.382564 | ||||||||
\(52\) | −4.73205 | −0.656217 | ||||||||
\(53\) | 4.66025 | 0.640135 | 0.320068 | − | 0.947395i | \(-0.396294\pi\) | ||||
0.320068 | + | 0.947395i | \(0.396294\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.73205 | 0.365086 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | 9.19615 | 1.20751 | ||||||||
\(59\) | 2.19615 | 0.285915 | 0.142957 | − | 0.989729i | \(-0.454339\pi\) | ||||
0.142957 | + | 0.989729i | \(0.454339\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.26795 | 1.05860 | 0.529301 | − | 0.848434i | \(-0.322454\pi\) | ||||
0.529301 | + | 0.848434i | \(0.322454\pi\) | |||||||
\(62\) | 5.92820 | 0.752883 | ||||||||
\(63\) | −2.73205 | −0.344206 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.19615 | −0.639602 | ||||||||
\(67\) | 5.19615 | 0.634811 | 0.317406 | − | 0.948290i | \(-0.397188\pi\) | ||||
0.317406 | + | 0.948290i | \(0.397188\pi\) | |||||||
\(68\) | 2.73205 | 0.331310 | ||||||||
\(69\) | −8.46410 | −1.01896 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.1962 | −1.21006 | −0.605030 | − | 0.796202i | \(-0.706839\pi\) | ||||
−0.605030 | + | 0.796202i | \(0.706839\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −14.4641 | −1.69290 | −0.846448 | − | 0.532472i | \(-0.821263\pi\) | ||||
−0.846448 | + | 0.532472i | \(0.821263\pi\) | |||||||
\(74\) | −8.92820 | −1.03788 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −14.1962 | −1.61780 | ||||||||
\(78\) | 4.73205 | 0.535799 | ||||||||
\(79\) | 5.92820 | 0.666975 | 0.333487 | − | 0.942755i | \(-0.391775\pi\) | ||||
0.333487 | + | 0.942755i | \(0.391775\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −16.6603 | −1.82870 | −0.914350 | − | 0.404924i | \(-0.867298\pi\) | ||||
−0.914350 | + | 0.404924i | \(0.867298\pi\) | |||||||
\(84\) | −2.73205 | −0.298091 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.73205 | 0.941601 | ||||||||
\(87\) | −9.19615 | −0.985931 | ||||||||
\(88\) | −5.19615 | −0.553912 | ||||||||
\(89\) | 3.92820 | 0.416389 | 0.208194 | − | 0.978087i | \(-0.433241\pi\) | ||||
0.208194 | + | 0.978087i | \(0.433241\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.9282 | 1.35524 | ||||||||
\(92\) | −8.46410 | −0.882444 | ||||||||
\(93\) | −5.92820 | −0.614726 | ||||||||
\(94\) | −3.46410 | −0.357295 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −17.1244 | −1.73871 | −0.869357 | − | 0.494184i | \(-0.835467\pi\) | ||||
−0.869357 | + | 0.494184i | \(0.835467\pi\) | |||||||
\(98\) | −0.464102 | −0.0468813 | ||||||||
\(99\) | 5.19615 | 0.522233 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.6603 | −1.16024 | −0.580119 | − | 0.814532i | \(-0.696994\pi\) | ||||
−0.580119 | + | 0.814532i | \(0.696994\pi\) | |||||||
\(102\) | −2.73205 | −0.270513 | ||||||||
\(103\) | 14.8564 | 1.46385 | 0.731923 | − | 0.681388i | \(-0.238623\pi\) | ||||
0.731923 | + | 0.681388i | \(0.238623\pi\) | |||||||
\(104\) | 4.73205 | 0.464016 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.66025 | −0.452644 | ||||||||
\(107\) | −4.19615 | −0.405657 | −0.202829 | − | 0.979214i | \(-0.565013\pi\) | ||||
−0.202829 | + | 0.979214i | \(0.565013\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −10.3923 | −0.995402 | −0.497701 | − | 0.867349i | \(-0.665822\pi\) | ||||
−0.497701 | + | 0.867349i | \(0.665822\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.92820 | 0.847428 | ||||||||
\(112\) | −2.73205 | −0.258155 | ||||||||
\(113\) | 14.3205 | 1.34716 | 0.673580 | − | 0.739114i | \(-0.264756\pi\) | ||||
0.673580 | + | 0.739114i | \(0.264756\pi\) | |||||||
\(114\) | −1.00000 | −0.0936586 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −9.19615 | −0.853841 | ||||||||
\(117\) | −4.73205 | −0.437478 | ||||||||
\(118\) | −2.19615 | −0.202172 | ||||||||
\(119\) | −7.46410 | −0.684233 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.0000 | 1.45455 | ||||||||
\(122\) | −8.26795 | −0.748545 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.92820 | −0.532368 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.73205 | 0.243390 | ||||||||
\(127\) | 9.39230 | 0.833432 | 0.416716 | − | 0.909037i | \(-0.363181\pi\) | ||||
0.416716 | + | 0.909037i | \(0.363181\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −8.73205 | −0.768814 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.1962 | −0.978212 | −0.489106 | − | 0.872224i | \(-0.662677\pi\) | ||||
−0.489106 | + | 0.872224i | \(0.662677\pi\) | |||||||
\(132\) | 5.19615 | 0.452267 | ||||||||
\(133\) | −2.73205 | −0.236899 | ||||||||
\(134\) | −5.19615 | −0.448879 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.73205 | −0.234271 | ||||||||
\(137\) | −16.3923 | −1.40049 | −0.700245 | − | 0.713903i | \(-0.746926\pi\) | ||||
−0.700245 | + | 0.713903i | \(0.746926\pi\) | |||||||
\(138\) | 8.46410 | 0.720512 | ||||||||
\(139\) | −3.80385 | −0.322638 | −0.161319 | − | 0.986902i | \(-0.551575\pi\) | ||||
−0.161319 | + | 0.986902i | \(0.551575\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.46410 | 0.291730 | ||||||||
\(142\) | 10.1962 | 0.855642 | ||||||||
\(143\) | −24.5885 | −2.05619 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 14.4641 | 1.19706 | ||||||||
\(147\) | 0.464102 | 0.0382785 | ||||||||
\(148\) | 8.92820 | 0.733894 | ||||||||
\(149\) | −21.8564 | −1.79055 | −0.895273 | − | 0.445517i | \(-0.853020\pi\) | ||||
−0.895273 | + | 0.445517i | \(0.853020\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.3923 | 0.845714 | 0.422857 | − | 0.906196i | \(-0.361027\pi\) | ||||
0.422857 | + | 0.906196i | \(0.361027\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 2.73205 | 0.220873 | ||||||||
\(154\) | 14.1962 | 1.14396 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.73205 | −0.378867 | ||||||||
\(157\) | −21.8564 | −1.74433 | −0.872166 | − | 0.489211i | \(-0.837285\pi\) | ||||
−0.872166 | + | 0.489211i | \(0.837285\pi\) | |||||||
\(158\) | −5.92820 | −0.471623 | ||||||||
\(159\) | 4.66025 | 0.369582 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 23.1244 | 1.82245 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 10.0000 | 0.783260 | 0.391630 | − | 0.920123i | \(-0.371911\pi\) | ||||
0.391630 | + | 0.920123i | \(0.371911\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16.6603 | 1.29309 | ||||||||
\(167\) | −2.00000 | −0.154765 | −0.0773823 | − | 0.997001i | \(-0.524656\pi\) | ||||
−0.0773823 | + | 0.997001i | \(0.524656\pi\) | |||||||
\(168\) | 2.73205 | 0.210782 | ||||||||
\(169\) | 9.39230 | 0.722485 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | −8.73205 | −0.665813 | ||||||||
\(173\) | −22.6603 | −1.72283 | −0.861414 | − | 0.507904i | \(-0.830420\pi\) | ||||
−0.861414 | + | 0.507904i | \(0.830420\pi\) | |||||||
\(174\) | 9.19615 | 0.697159 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.19615 | 0.391675 | ||||||||
\(177\) | 2.19615 | 0.165073 | ||||||||
\(178\) | −3.92820 | −0.294431 | ||||||||
\(179\) | −9.85641 | −0.736702 | −0.368351 | − | 0.929687i | \(-0.620078\pi\) | ||||
−0.368351 | + | 0.929687i | \(0.620078\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.2679 | 1.43218 | 0.716088 | − | 0.698010i | \(-0.245931\pi\) | ||||
0.716088 | + | 0.698010i | \(0.245931\pi\) | |||||||
\(182\) | −12.9282 | −0.958302 | ||||||||
\(183\) | 8.26795 | 0.611184 | ||||||||
\(184\) | 8.46410 | 0.623982 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.92820 | 0.434677 | ||||||||
\(187\) | 14.1962 | 1.03813 | ||||||||
\(188\) | 3.46410 | 0.252646 | ||||||||
\(189\) | −2.73205 | −0.198727 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.4641 | −1.77016 | −0.885080 | − | 0.465439i | \(-0.845897\pi\) | ||||
−0.885080 | + | 0.465439i | \(0.845897\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 10.1962 | 0.733935 | 0.366968 | − | 0.930234i | \(-0.380396\pi\) | ||||
0.366968 | + | 0.930234i | \(0.380396\pi\) | |||||||
\(194\) | 17.1244 | 1.22946 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.464102 | 0.0331501 | ||||||||
\(197\) | −0.339746 | −0.0242059 | −0.0121029 | − | 0.999927i | \(-0.503853\pi\) | ||||
−0.0121029 | + | 0.999927i | \(0.503853\pi\) | |||||||
\(198\) | −5.19615 | −0.369274 | ||||||||
\(199\) | 3.07180 | 0.217754 | 0.108877 | − | 0.994055i | \(-0.465275\pi\) | ||||
0.108877 | + | 0.994055i | \(0.465275\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.19615 | 0.366508 | ||||||||
\(202\) | 11.6603 | 0.820413 | ||||||||
\(203\) | 25.1244 | 1.76338 | ||||||||
\(204\) | 2.73205 | 0.191282 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −14.8564 | −1.03509 | ||||||||
\(207\) | −8.46410 | −0.588296 | ||||||||
\(208\) | −4.73205 | −0.328109 | ||||||||
\(209\) | 5.19615 | 0.359425 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.19615 | 0.495404 | 0.247702 | − | 0.968836i | \(-0.420325\pi\) | ||||
0.247702 | + | 0.968836i | \(0.420325\pi\) | |||||||
\(212\) | 4.66025 | 0.320068 | ||||||||
\(213\) | −10.1962 | −0.698629 | ||||||||
\(214\) | 4.19615 | 0.286843 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 16.1962 | 1.09947 | ||||||||
\(218\) | 10.3923 | 0.703856 | ||||||||
\(219\) | −14.4641 | −0.977393 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.9282 | −0.869645 | ||||||||
\(222\) | −8.92820 | −0.599222 | ||||||||
\(223\) | −17.9282 | −1.20056 | −0.600281 | − | 0.799789i | \(-0.704944\pi\) | ||||
−0.600281 | + | 0.799789i | \(0.704944\pi\) | |||||||
\(224\) | 2.73205 | 0.182543 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.3205 | −0.952586 | ||||||||
\(227\) | −2.00000 | −0.132745 | −0.0663723 | − | 0.997795i | \(-0.521143\pi\) | ||||
−0.0663723 | + | 0.997795i | \(0.521143\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | 5.19615 | 0.343371 | 0.171686 | − | 0.985152i | \(-0.445079\pi\) | ||||
0.171686 | + | 0.985152i | \(0.445079\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.1962 | −0.934038 | ||||||||
\(232\) | 9.19615 | 0.603757 | ||||||||
\(233\) | 17.6603 | 1.15696 | 0.578481 | − | 0.815696i | \(-0.303646\pi\) | ||||
0.578481 | + | 0.815696i | \(0.303646\pi\) | |||||||
\(234\) | 4.73205 | 0.309344 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.19615 | 0.142957 | ||||||||
\(237\) | 5.92820 | 0.385078 | ||||||||
\(238\) | 7.46410 | 0.483826 | ||||||||
\(239\) | −7.07180 | −0.457437 | −0.228718 | − | 0.973493i | \(-0.573453\pi\) | ||||
−0.228718 | + | 0.973493i | \(0.573453\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.80385 | 0.502690 | 0.251345 | − | 0.967898i | \(-0.419127\pi\) | ||||
0.251345 | + | 0.967898i | \(0.419127\pi\) | |||||||
\(242\) | −16.0000 | −1.02852 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 8.26795 | 0.529301 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.73205 | −0.301093 | ||||||||
\(248\) | 5.92820 | 0.376441 | ||||||||
\(249\) | −16.6603 | −1.05580 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.46410 | 0.218652 | 0.109326 | − | 0.994006i | \(-0.465131\pi\) | ||||
0.109326 | + | 0.994006i | \(0.465131\pi\) | |||||||
\(252\) | −2.73205 | −0.172103 | ||||||||
\(253\) | −43.9808 | −2.76505 | ||||||||
\(254\) | −9.39230 | −0.589326 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.9282 | 0.993574 | 0.496787 | − | 0.867872i | \(-0.334513\pi\) | ||||
0.496787 | + | 0.867872i | \(0.334513\pi\) | |||||||
\(258\) | 8.73205 | 0.543634 | ||||||||
\(259\) | −24.3923 | −1.51566 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.19615 | −0.569228 | ||||||||
\(262\) | 11.1962 | 0.691701 | ||||||||
\(263\) | −12.4641 | −0.768569 | −0.384285 | − | 0.923215i | \(-0.625552\pi\) | ||||
−0.384285 | + | 0.923215i | \(0.625552\pi\) | |||||||
\(264\) | −5.19615 | −0.319801 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.73205 | 0.167513 | ||||||||
\(267\) | 3.92820 | 0.240402 | ||||||||
\(268\) | 5.19615 | 0.317406 | ||||||||
\(269\) | 15.4641 | 0.942863 | 0.471431 | − | 0.881903i | \(-0.343737\pi\) | ||||
0.471431 | + | 0.881903i | \(0.343737\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.1244 | −1.52620 | −0.763098 | − | 0.646283i | \(-0.776323\pi\) | ||||
−0.763098 | + | 0.646283i | \(0.776323\pi\) | |||||||
\(272\) | 2.73205 | 0.165655 | ||||||||
\(273\) | 12.9282 | 0.782450 | ||||||||
\(274\) | 16.3923 | 0.990295 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −8.46410 | −0.509479 | ||||||||
\(277\) | 24.5167 | 1.47306 | 0.736532 | − | 0.676403i | \(-0.236462\pi\) | ||||
0.736532 | + | 0.676403i | \(0.236462\pi\) | |||||||
\(278\) | 3.80385 | 0.228140 | ||||||||
\(279\) | −5.92820 | −0.354912 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.0000 | −0.656205 | −0.328102 | − | 0.944642i | \(-0.606409\pi\) | ||||
−0.328102 | + | 0.944642i | \(0.606409\pi\) | |||||||
\(282\) | −3.46410 | −0.206284 | ||||||||
\(283\) | 4.00000 | 0.237775 | 0.118888 | − | 0.992908i | \(-0.462067\pi\) | ||||
0.118888 | + | 0.992908i | \(0.462067\pi\) | |||||||
\(284\) | −10.1962 | −0.605030 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 24.5885 | 1.45395 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −9.53590 | −0.560935 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17.1244 | −1.00385 | ||||||||
\(292\) | −14.4641 | −0.846448 | ||||||||
\(293\) | 26.6603 | 1.55751 | 0.778754 | − | 0.627329i | \(-0.215852\pi\) | ||||
0.778754 | + | 0.627329i | \(0.215852\pi\) | |||||||
\(294\) | −0.464102 | −0.0270670 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8.92820 | −0.518941 | ||||||||
\(297\) | 5.19615 | 0.301511 | ||||||||
\(298\) | 21.8564 | 1.26611 | ||||||||
\(299\) | 40.0526 | 2.31630 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.8564 | 1.37506 | ||||||||
\(302\) | −10.3923 | −0.598010 | ||||||||
\(303\) | −11.6603 | −0.669864 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.73205 | −0.156181 | ||||||||
\(307\) | −4.66025 | −0.265975 | −0.132987 | − | 0.991118i | \(-0.542457\pi\) | ||||
−0.132987 | + | 0.991118i | \(0.542457\pi\) | |||||||
\(308\) | −14.1962 | −0.808901 | ||||||||
\(309\) | 14.8564 | 0.845151 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.4641 | −0.876889 | −0.438444 | − | 0.898758i | \(-0.644470\pi\) | ||||
−0.438444 | + | 0.898758i | \(0.644470\pi\) | |||||||
\(312\) | 4.73205 | 0.267900 | ||||||||
\(313\) | 4.85641 | 0.274500 | 0.137250 | − | 0.990536i | \(-0.456174\pi\) | ||||
0.137250 | + | 0.990536i | \(0.456174\pi\) | |||||||
\(314\) | 21.8564 | 1.23343 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.92820 | 0.333487 | ||||||||
\(317\) | −23.0526 | −1.29476 | −0.647380 | − | 0.762167i | \(-0.724135\pi\) | ||||
−0.647380 | + | 0.762167i | \(0.724135\pi\) | |||||||
\(318\) | −4.66025 | −0.261334 | ||||||||
\(319\) | −47.7846 | −2.67542 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.19615 | −0.234206 | ||||||||
\(322\) | −23.1244 | −1.28867 | ||||||||
\(323\) | 2.73205 | 0.152015 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −10.0000 | −0.553849 | ||||||||
\(327\) | −10.3923 | −0.574696 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.46410 | −0.521773 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.1962 | 1.05512 | 0.527558 | − | 0.849519i | \(-0.323108\pi\) | ||||
0.527558 | + | 0.849519i | \(0.323108\pi\) | |||||||
\(332\) | −16.6603 | −0.914350 | ||||||||
\(333\) | 8.92820 | 0.489263 | ||||||||
\(334\) | 2.00000 | 0.109435 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.73205 | −0.149046 | ||||||||
\(337\) | −15.3205 | −0.834561 | −0.417281 | − | 0.908778i | \(-0.637017\pi\) | ||||
−0.417281 | + | 0.908778i | \(0.637017\pi\) | |||||||
\(338\) | −9.39230 | −0.510874 | ||||||||
\(339\) | 14.3205 | 0.777783 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −30.8038 | −1.66812 | ||||||||
\(342\) | −1.00000 | −0.0540738 | ||||||||
\(343\) | 17.8564 | 0.964155 | ||||||||
\(344\) | 8.73205 | 0.470801 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 22.6603 | 1.21822 | ||||||||
\(347\) | −1.07180 | −0.0575371 | −0.0287685 | − | 0.999586i | \(-0.509159\pi\) | ||||
−0.0287685 | + | 0.999586i | \(0.509159\pi\) | |||||||
\(348\) | −9.19615 | −0.492966 | ||||||||
\(349\) | −13.5885 | −0.727373 | −0.363687 | − | 0.931521i | \(-0.618482\pi\) | ||||
−0.363687 | + | 0.931521i | \(0.618482\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.73205 | −0.252578 | ||||||||
\(352\) | −5.19615 | −0.276956 | ||||||||
\(353\) | 3.41154 | 0.181578 | 0.0907890 | − | 0.995870i | \(-0.471061\pi\) | ||||
0.0907890 | + | 0.995870i | \(0.471061\pi\) | |||||||
\(354\) | −2.19615 | −0.116724 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.92820 | 0.208194 | ||||||||
\(357\) | −7.46410 | −0.395042 | ||||||||
\(358\) | 9.85641 | 0.520927 | ||||||||
\(359\) | 19.8564 | 1.04798 | 0.523991 | − | 0.851724i | \(-0.324443\pi\) | ||||
0.523991 | + | 0.851724i | \(0.324443\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −19.2679 | −1.01270 | ||||||||
\(363\) | 16.0000 | 0.839782 | ||||||||
\(364\) | 12.9282 | 0.677622 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −8.26795 | −0.432173 | ||||||||
\(367\) | −29.5167 | −1.54076 | −0.770379 | − | 0.637587i | \(-0.779933\pi\) | ||||
−0.770379 | + | 0.637587i | \(0.779933\pi\) | |||||||
\(368\) | −8.46410 | −0.441222 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.7321 | −0.661015 | ||||||||
\(372\) | −5.92820 | −0.307363 | ||||||||
\(373\) | −27.6603 | −1.43219 | −0.716097 | − | 0.698001i | \(-0.754073\pi\) | ||||
−0.716097 | + | 0.698001i | \(0.754073\pi\) | |||||||
\(374\) | −14.1962 | −0.734066 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.46410 | −0.178647 | ||||||||
\(377\) | 43.5167 | 2.24122 | ||||||||
\(378\) | 2.73205 | 0.140522 | ||||||||
\(379\) | −29.1769 | −1.49872 | −0.749359 | − | 0.662164i | \(-0.769638\pi\) | ||||
−0.749359 | + | 0.662164i | \(0.769638\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.39230 | 0.481182 | ||||||||
\(382\) | 24.4641 | 1.25169 | ||||||||
\(383\) | −4.05256 | −0.207076 | −0.103538 | − | 0.994625i | \(-0.533016\pi\) | ||||
−0.103538 | + | 0.994625i | \(0.533016\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.1962 | −0.518970 | ||||||||
\(387\) | −8.73205 | −0.443875 | ||||||||
\(388\) | −17.1244 | −0.869357 | ||||||||
\(389\) | 12.9282 | 0.655486 | 0.327743 | − | 0.944767i | \(-0.393712\pi\) | ||||
0.327743 | + | 0.944767i | \(0.393712\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23.1244 | −1.16945 | ||||||||
\(392\) | −0.464102 | −0.0234407 | ||||||||
\(393\) | −11.1962 | −0.564771 | ||||||||
\(394\) | 0.339746 | 0.0171162 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 5.19615 | 0.261116 | ||||||||
\(397\) | 34.1244 | 1.71265 | 0.856326 | − | 0.516435i | \(-0.172741\pi\) | ||||
0.856326 | + | 0.516435i | \(0.172741\pi\) | |||||||
\(398\) | −3.07180 | −0.153975 | ||||||||
\(399\) | −2.73205 | −0.136774 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.7128 | 0.934473 | 0.467237 | − | 0.884132i | \(-0.345250\pi\) | ||||
0.467237 | + | 0.884132i | \(0.345250\pi\) | |||||||
\(402\) | −5.19615 | −0.259161 | ||||||||
\(403\) | 28.0526 | 1.39740 | ||||||||
\(404\) | −11.6603 | −0.580119 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −25.1244 | −1.24690 | ||||||||
\(407\) | 46.3923 | 2.29958 | ||||||||
\(408\) | −2.73205 | −0.135257 | ||||||||
\(409\) | 17.3205 | 0.856444 | 0.428222 | − | 0.903674i | \(-0.359140\pi\) | ||||
0.428222 | + | 0.903674i | \(0.359140\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.3923 | −0.808573 | ||||||||
\(412\) | 14.8564 | 0.731923 | ||||||||
\(413\) | −6.00000 | −0.295241 | ||||||||
\(414\) | 8.46410 | 0.415988 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.73205 | 0.232008 | ||||||||
\(417\) | −3.80385 | −0.186275 | ||||||||
\(418\) | −5.19615 | −0.254152 | ||||||||
\(419\) | −5.85641 | −0.286104 | −0.143052 | − | 0.989715i | \(-0.545692\pi\) | ||||
−0.143052 | + | 0.989715i | \(0.545692\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.00000 | −0.0974740 | −0.0487370 | − | 0.998812i | \(-0.515520\pi\) | ||||
−0.0487370 | + | 0.998812i | \(0.515520\pi\) | |||||||
\(422\) | −7.19615 | −0.350303 | ||||||||
\(423\) | 3.46410 | 0.168430 | ||||||||
\(424\) | −4.66025 | −0.226322 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 10.1962 | 0.494005 | ||||||||
\(427\) | −22.5885 | −1.09313 | ||||||||
\(428\) | −4.19615 | −0.202829 | ||||||||
\(429\) | −24.5885 | −1.18714 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.60770 | −0.0774400 | −0.0387200 | − | 0.999250i | \(-0.512328\pi\) | ||||
−0.0387200 | + | 0.999250i | \(0.512328\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −5.80385 | −0.278915 | −0.139458 | − | 0.990228i | \(-0.544536\pi\) | ||||
−0.139458 | + | 0.990228i | \(0.544536\pi\) | |||||||
\(434\) | −16.1962 | −0.777440 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.3923 | −0.497701 | ||||||||
\(437\) | −8.46410 | −0.404893 | ||||||||
\(438\) | 14.4641 | 0.691122 | ||||||||
\(439\) | 3.39230 | 0.161906 | 0.0809529 | − | 0.996718i | \(-0.474204\pi\) | ||||
0.0809529 | + | 0.996718i | \(0.474204\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.464102 | 0.0221001 | ||||||||
\(442\) | 12.9282 | 0.614932 | ||||||||
\(443\) | 20.5167 | 0.974776 | 0.487388 | − | 0.873186i | \(-0.337950\pi\) | ||||
0.487388 | + | 0.873186i | \(0.337950\pi\) | |||||||
\(444\) | 8.92820 | 0.423714 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 17.9282 | 0.848925 | ||||||||
\(447\) | −21.8564 | −1.03377 | ||||||||
\(448\) | −2.73205 | −0.129077 | ||||||||
\(449\) | 0.464102 | 0.0219023 | 0.0109512 | − | 0.999940i | \(-0.496514\pi\) | ||||
0.0109512 | + | 0.999940i | \(0.496514\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 14.3205 | 0.673580 | ||||||||
\(453\) | 10.3923 | 0.488273 | ||||||||
\(454\) | 2.00000 | 0.0938647 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.00000 | −0.0468293 | ||||||||
\(457\) | 32.0000 | 1.49690 | 0.748448 | − | 0.663193i | \(-0.230799\pi\) | ||||
0.748448 | + | 0.663193i | \(0.230799\pi\) | |||||||
\(458\) | −5.19615 | −0.242800 | ||||||||
\(459\) | 2.73205 | 0.127521 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.85641 | −0.0864615 | −0.0432307 | − | 0.999065i | \(-0.513765\pi\) | ||||
−0.0432307 | + | 0.999065i | \(0.513765\pi\) | |||||||
\(462\) | 14.1962 | 0.660465 | ||||||||
\(463\) | −11.6077 | −0.539455 | −0.269728 | − | 0.962937i | \(-0.586934\pi\) | ||||
−0.269728 | + | 0.962937i | \(0.586934\pi\) | |||||||
\(464\) | −9.19615 | −0.426921 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17.6603 | −0.818095 | ||||||||
\(467\) | −16.6603 | −0.770945 | −0.385472 | − | 0.922719i | \(-0.625961\pi\) | ||||
−0.385472 | + | 0.922719i | \(0.625961\pi\) | |||||||
\(468\) | −4.73205 | −0.218739 | ||||||||
\(469\) | −14.1962 | −0.655517 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −21.8564 | −1.00709 | ||||||||
\(472\) | −2.19615 | −0.101086 | ||||||||
\(473\) | −45.3731 | −2.08626 | ||||||||
\(474\) | −5.92820 | −0.272291 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.46410 | −0.342117 | ||||||||
\(477\) | 4.66025 | 0.213378 | ||||||||
\(478\) | 7.07180 | 0.323456 | ||||||||
\(479\) | −16.6077 | −0.758825 | −0.379412 | − | 0.925228i | \(-0.623874\pi\) | ||||
−0.379412 | + | 0.925228i | \(0.623874\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −42.2487 | −1.92638 | ||||||||
\(482\) | −7.80385 | −0.355456 | ||||||||
\(483\) | 23.1244 | 1.05219 | ||||||||
\(484\) | 16.0000 | 0.727273 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 13.0718 | 0.592340 | 0.296170 | − | 0.955135i | \(-0.404291\pi\) | ||||
0.296170 | + | 0.955135i | \(0.404291\pi\) | |||||||
\(488\) | −8.26795 | −0.374272 | ||||||||
\(489\) | 10.0000 | 0.452216 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.9282 | −1.57629 | −0.788144 | − | 0.615491i | \(-0.788958\pi\) | ||||
−0.788144 | + | 0.615491i | \(0.788958\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −25.1244 | −1.13154 | ||||||||
\(494\) | 4.73205 | 0.212905 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.92820 | −0.266184 | ||||||||
\(497\) | 27.8564 | 1.24953 | ||||||||
\(498\) | 16.6603 | 0.746564 | ||||||||
\(499\) | 13.1244 | 0.587527 | 0.293763 | − | 0.955878i | \(-0.405092\pi\) | ||||
0.293763 | + | 0.955878i | \(0.405092\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.00000 | −0.0893534 | ||||||||
\(502\) | −3.46410 | −0.154610 | ||||||||
\(503\) | 12.7846 | 0.570038 | 0.285019 | − | 0.958522i | \(-0.408000\pi\) | ||||
0.285019 | + | 0.958522i | \(0.408000\pi\) | |||||||
\(504\) | 2.73205 | 0.121695 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 43.9808 | 1.95518 | ||||||||
\(507\) | 9.39230 | 0.417127 | ||||||||
\(508\) | 9.39230 | 0.416716 | ||||||||
\(509\) | 0.267949 | 0.0118766 | 0.00593832 | − | 0.999982i | \(-0.498110\pi\) | ||||
0.00593832 | + | 0.999982i | \(0.498110\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 39.5167 | 1.74811 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | −15.9282 | −0.702563 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −8.73205 | −0.384407 | ||||||||
\(517\) | 18.0000 | 0.791639 | ||||||||
\(518\) | 24.3923 | 1.07174 | ||||||||
\(519\) | −22.6603 | −0.994675 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.67949 | 0.161201 | 0.0806007 | − | 0.996746i | \(-0.474316\pi\) | ||||
0.0806007 | + | 0.996746i | \(0.474316\pi\) | |||||||
\(522\) | 9.19615 | 0.402505 | ||||||||
\(523\) | −17.8564 | −0.780806 | −0.390403 | − | 0.920644i | \(-0.627664\pi\) | ||||
−0.390403 | + | 0.920644i | \(0.627664\pi\) | |||||||
\(524\) | −11.1962 | −0.489106 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.4641 | 0.543461 | ||||||||
\(527\) | −16.1962 | −0.705515 | ||||||||
\(528\) | 5.19615 | 0.226134 | ||||||||
\(529\) | 48.6410 | 2.11483 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.19615 | 0.0953049 | ||||||||
\(532\) | −2.73205 | −0.118449 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −3.92820 | −0.169990 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −5.19615 | −0.224440 | ||||||||
\(537\) | −9.85641 | −0.425335 | ||||||||
\(538\) | −15.4641 | −0.666705 | ||||||||
\(539\) | 2.41154 | 0.103872 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.66025 | 0.372333 | 0.186167 | − | 0.982518i | \(-0.440394\pi\) | ||||
0.186167 | + | 0.982518i | \(0.440394\pi\) | |||||||
\(542\) | 25.1244 | 1.07918 | ||||||||
\(543\) | 19.2679 | 0.826867 | ||||||||
\(544\) | −2.73205 | −0.117136 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −12.9282 | −0.553276 | ||||||||
\(547\) | −3.58846 | −0.153431 | −0.0767157 | − | 0.997053i | \(-0.524443\pi\) | ||||
−0.0767157 | + | 0.997053i | \(0.524443\pi\) | |||||||
\(548\) | −16.3923 | −0.700245 | ||||||||
\(549\) | 8.26795 | 0.352867 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.19615 | −0.391769 | ||||||||
\(552\) | 8.46410 | 0.360256 | ||||||||
\(553\) | −16.1962 | −0.688730 | ||||||||
\(554\) | −24.5167 | −1.04161 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.80385 | −0.161319 | ||||||||
\(557\) | 38.5885 | 1.63505 | 0.817523 | − | 0.575896i | \(-0.195347\pi\) | ||||
0.817523 | + | 0.575896i | \(0.195347\pi\) | |||||||
\(558\) | 5.92820 | 0.250961 | ||||||||
\(559\) | 41.3205 | 1.74767 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.1962 | 0.599362 | ||||||||
\(562\) | 11.0000 | 0.464007 | ||||||||
\(563\) | 32.1962 | 1.35691 | 0.678453 | − | 0.734644i | \(-0.262651\pi\) | ||||
0.678453 | + | 0.734644i | \(0.262651\pi\) | |||||||
\(564\) | 3.46410 | 0.145865 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.00000 | −0.168133 | ||||||||
\(567\) | −2.73205 | −0.114735 | ||||||||
\(568\) | 10.1962 | 0.427821 | ||||||||
\(569\) | 13.7128 | 0.574871 | 0.287436 | − | 0.957800i | \(-0.407197\pi\) | ||||
0.287436 | + | 0.957800i | \(0.407197\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.7321 | −0.449122 | −0.224561 | − | 0.974460i | \(-0.572095\pi\) | ||||
−0.224561 | + | 0.974460i | \(0.572095\pi\) | |||||||
\(572\) | −24.5885 | −1.02810 | ||||||||
\(573\) | −24.4641 | −1.02200 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 20.3205 | 0.845954 | 0.422977 | − | 0.906140i | \(-0.360985\pi\) | ||||
0.422977 | + | 0.906140i | \(0.360985\pi\) | |||||||
\(578\) | 9.53590 | 0.396641 | ||||||||
\(579\) | 10.1962 | 0.423738 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 45.5167 | 1.88835 | ||||||||
\(582\) | 17.1244 | 0.709827 | ||||||||
\(583\) | 24.2154 | 1.00290 | ||||||||
\(584\) | 14.4641 | 0.598529 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −26.6603 | −1.10132 | ||||||||
\(587\) | 18.2679 | 0.753999 | 0.376999 | − | 0.926213i | \(-0.376956\pi\) | ||||
0.376999 | + | 0.926213i | \(0.376956\pi\) | |||||||
\(588\) | 0.464102 | 0.0191392 | ||||||||
\(589\) | −5.92820 | −0.244267 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.339746 | −0.0139753 | ||||||||
\(592\) | 8.92820 | 0.366947 | ||||||||
\(593\) | 30.2487 | 1.24217 | 0.621083 | − | 0.783745i | \(-0.286693\pi\) | ||||
0.621083 | + | 0.783745i | \(0.286693\pi\) | |||||||
\(594\) | −5.19615 | −0.213201 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −21.8564 | −0.895273 | ||||||||
\(597\) | 3.07180 | 0.125720 | ||||||||
\(598\) | −40.0526 | −1.63787 | ||||||||
\(599\) | −16.9808 | −0.693815 | −0.346908 | − | 0.937899i | \(-0.612768\pi\) | ||||
−0.346908 | + | 0.937899i | \(0.612768\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.8038 | 1.05256 | 0.526280 | − | 0.850311i | \(-0.323586\pi\) | ||||
0.526280 | + | 0.850311i | \(0.323586\pi\) | |||||||
\(602\) | −23.8564 | −0.972315 | ||||||||
\(603\) | 5.19615 | 0.211604 | ||||||||
\(604\) | 10.3923 | 0.422857 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 11.6603 | 0.473665 | ||||||||
\(607\) | 35.1051 | 1.42487 | 0.712436 | − | 0.701737i | \(-0.247592\pi\) | ||||
0.712436 | + | 0.701737i | \(0.247592\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 25.1244 | 1.01809 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.3923 | −0.663162 | ||||||||
\(612\) | 2.73205 | 0.110437 | ||||||||
\(613\) | −7.07180 | −0.285627 | −0.142814 | − | 0.989750i | \(-0.545615\pi\) | ||||
−0.142814 | + | 0.989750i | \(0.545615\pi\) | |||||||
\(614\) | 4.66025 | 0.188073 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 14.1962 | 0.571979 | ||||||||
\(617\) | −1.32051 | −0.0531617 | −0.0265808 | − | 0.999647i | \(-0.508462\pi\) | ||||
−0.0265808 | + | 0.999647i | \(0.508462\pi\) | |||||||
\(618\) | −14.8564 | −0.597612 | ||||||||
\(619\) | 26.9808 | 1.08445 | 0.542224 | − | 0.840234i | \(-0.317582\pi\) | ||||
0.542224 | + | 0.840234i | \(0.317582\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.46410 | −0.339653 | ||||||||
\(622\) | 15.4641 | 0.620054 | ||||||||
\(623\) | −10.7321 | −0.429971 | ||||||||
\(624\) | −4.73205 | −0.189434 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −4.85641 | −0.194101 | ||||||||
\(627\) | 5.19615 | 0.207514 | ||||||||
\(628\) | −21.8564 | −0.872166 | ||||||||
\(629\) | 24.3923 | 0.972585 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.92820 | −0.116570 | −0.0582850 | − | 0.998300i | \(-0.518563\pi\) | ||||
−0.0582850 | + | 0.998300i | \(0.518563\pi\) | |||||||
\(632\) | −5.92820 | −0.235811 | ||||||||
\(633\) | 7.19615 | 0.286021 | ||||||||
\(634\) | 23.0526 | 0.915534 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.66025 | 0.184791 | ||||||||
\(637\) | −2.19615 | −0.0870147 | ||||||||
\(638\) | 47.7846 | 1.89181 | ||||||||
\(639\) | −10.1962 | −0.403354 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.3923 | −0.489467 | −0.244733 | − | 0.969590i | \(-0.578700\pi\) | ||||
−0.244733 | + | 0.969590i | \(0.578700\pi\) | |||||||
\(642\) | 4.19615 | 0.165609 | ||||||||
\(643\) | −32.9282 | −1.29856 | −0.649281 | − | 0.760549i | \(-0.724930\pi\) | ||||
−0.649281 | + | 0.760549i | \(0.724930\pi\) | |||||||
\(644\) | 23.1244 | 0.911227 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.73205 | −0.107491 | ||||||||
\(647\) | 13.9282 | 0.547574 | 0.273787 | − | 0.961790i | \(-0.411724\pi\) | ||||
0.273787 | + | 0.961790i | \(0.411724\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 11.4115 | 0.447942 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.1962 | 0.634777 | ||||||||
\(652\) | 10.0000 | 0.391630 | ||||||||
\(653\) | −25.1769 | −0.985249 | −0.492624 | − | 0.870242i | \(-0.663962\pi\) | ||||
−0.492624 | + | 0.870242i | \(0.663962\pi\) | |||||||
\(654\) | 10.3923 | 0.406371 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.4641 | −0.564298 | ||||||||
\(658\) | 9.46410 | 0.368949 | ||||||||
\(659\) | −7.26795 | −0.283119 | −0.141560 | − | 0.989930i | \(-0.545212\pi\) | ||||
−0.141560 | + | 0.989930i | \(0.545212\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.9282 | 1.04739 | 0.523693 | − | 0.851907i | \(-0.324554\pi\) | ||||
0.523693 | + | 0.851907i | \(0.324554\pi\) | |||||||
\(662\) | −19.1962 | −0.746080 | ||||||||
\(663\) | −12.9282 | −0.502090 | ||||||||
\(664\) | 16.6603 | 0.646543 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.92820 | −0.345961 | ||||||||
\(667\) | 77.8372 | 3.01387 | ||||||||
\(668\) | −2.00000 | −0.0773823 | ||||||||
\(669\) | −17.9282 | −0.693144 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 42.9615 | 1.65851 | ||||||||
\(672\) | 2.73205 | 0.105391 | ||||||||
\(673\) | 29.2679 | 1.12820 | 0.564098 | − | 0.825708i | \(-0.309224\pi\) | ||||
0.564098 | + | 0.825708i | \(0.309224\pi\) | |||||||
\(674\) | 15.3205 | 0.590124 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.39230 | 0.361242 | ||||||||
\(677\) | 23.8756 | 0.917616 | 0.458808 | − | 0.888536i | \(-0.348277\pi\) | ||||
0.458808 | + | 0.888536i | \(0.348277\pi\) | |||||||
\(678\) | −14.3205 | −0.549976 | ||||||||
\(679\) | 46.7846 | 1.79543 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.00000 | −0.0766402 | ||||||||
\(682\) | 30.8038 | 1.17954 | ||||||||
\(683\) | 20.8756 | 0.798784 | 0.399392 | − | 0.916780i | \(-0.369221\pi\) | ||||
0.399392 | + | 0.916780i | \(0.369221\pi\) | |||||||
\(684\) | 1.00000 | 0.0382360 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −17.8564 | −0.681761 | ||||||||
\(687\) | 5.19615 | 0.198246 | ||||||||
\(688\) | −8.73205 | −0.332906 | ||||||||
\(689\) | −22.0526 | −0.840136 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.1244 | 0.727525 | 0.363762 | − | 0.931492i | \(-0.381492\pi\) | ||||
0.363762 | + | 0.931492i | \(0.381492\pi\) | |||||||
\(692\) | −22.6603 | −0.861414 | ||||||||
\(693\) | −14.1962 | −0.539267 | ||||||||
\(694\) | 1.07180 | 0.0406848 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 9.19615 | 0.348579 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 13.5885 | 0.514331 | ||||||||
\(699\) | 17.6603 | 0.667972 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 43.3205 | 1.63619 | 0.818097 | − | 0.575081i | \(-0.195029\pi\) | ||||
0.818097 | + | 0.575081i | \(0.195029\pi\) | |||||||
\(702\) | 4.73205 | 0.178600 | ||||||||
\(703\) | 8.92820 | 0.336734 | ||||||||
\(704\) | 5.19615 | 0.195837 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.41154 | −0.128395 | ||||||||
\(707\) | 31.8564 | 1.19808 | ||||||||
\(708\) | 2.19615 | 0.0825365 | ||||||||
\(709\) | −29.4449 | −1.10583 | −0.552913 | − | 0.833239i | \(-0.686484\pi\) | ||||
−0.552913 | + | 0.833239i | \(0.686484\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.92820 | 0.222325 | ||||||||
\(712\) | −3.92820 | −0.147216 | ||||||||
\(713\) | 50.1769 | 1.87914 | ||||||||
\(714\) | 7.46410 | 0.279337 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9.85641 | −0.368351 | ||||||||
\(717\) | −7.07180 | −0.264101 | ||||||||
\(718\) | −19.8564 | −0.741035 | ||||||||
\(719\) | −40.5692 | −1.51298 | −0.756488 | − | 0.654007i | \(-0.773087\pi\) | ||||
−0.756488 | + | 0.654007i | \(0.773087\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −40.5885 | −1.51159 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 7.80385 | 0.290228 | ||||||||
\(724\) | 19.2679 | 0.716088 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −16.0000 | −0.593816 | ||||||||
\(727\) | 3.46410 | 0.128476 | 0.0642382 | − | 0.997935i | \(-0.479538\pi\) | ||||
0.0642382 | + | 0.997935i | \(0.479538\pi\) | |||||||
\(728\) | −12.9282 | −0.479151 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −23.8564 | −0.882361 | ||||||||
\(732\) | 8.26795 | 0.305592 | ||||||||
\(733\) | 11.7321 | 0.433333 | 0.216667 | − | 0.976246i | \(-0.430482\pi\) | ||||
0.216667 | + | 0.976246i | \(0.430482\pi\) | |||||||
\(734\) | 29.5167 | 1.08948 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.46410 | 0.311991 | ||||||||
\(737\) | 27.0000 | 0.994558 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.2487 | −0.818432 | −0.409216 | − | 0.912438i | \(-0.634198\pi\) | ||||
−0.409216 | + | 0.912438i | \(0.634198\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.73205 | −0.173836 | ||||||||
\(742\) | 12.7321 | 0.467408 | ||||||||
\(743\) | 16.7846 | 0.615768 | 0.307884 | − | 0.951424i | \(-0.400379\pi\) | ||||
0.307884 | + | 0.951424i | \(0.400379\pi\) | |||||||
\(744\) | 5.92820 | 0.217338 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 27.6603 | 1.01271 | ||||||||
\(747\) | −16.6603 | −0.609567 | ||||||||
\(748\) | 14.1962 | 0.519063 | ||||||||
\(749\) | 11.4641 | 0.418889 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.4641 | 1.14814 | 0.574071 | − | 0.818806i | \(-0.305363\pi\) | ||||
0.574071 | + | 0.818806i | \(0.305363\pi\) | |||||||
\(752\) | 3.46410 | 0.126323 | ||||||||
\(753\) | 3.46410 | 0.126239 | ||||||||
\(754\) | −43.5167 | −1.58478 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.73205 | −0.0993637 | ||||||||
\(757\) | −11.9808 | −0.435448 | −0.217724 | − | 0.976010i | \(-0.569863\pi\) | ||||
−0.217724 | + | 0.976010i | \(0.569863\pi\) | |||||||
\(758\) | 29.1769 | 1.05975 | ||||||||
\(759\) | −43.9808 | −1.59640 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.5167 | −0.779978 | −0.389989 | − | 0.920819i | \(-0.627521\pi\) | ||||
−0.389989 | + | 0.920819i | \(0.627521\pi\) | |||||||
\(762\) | −9.39230 | −0.340247 | ||||||||
\(763\) | 28.3923 | 1.02787 | ||||||||
\(764\) | −24.4641 | −0.885080 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.05256 | 0.146425 | ||||||||
\(767\) | −10.3923 | −0.375244 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 51.9282 | 1.87258 | 0.936289 | − | 0.351229i | \(-0.114236\pi\) | ||||
0.936289 | + | 0.351229i | \(0.114236\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.9282 | 0.573640 | ||||||||
\(772\) | 10.1962 | 0.366968 | ||||||||
\(773\) | 42.3923 | 1.52475 | 0.762373 | − | 0.647138i | \(-0.224034\pi\) | ||||
0.762373 | + | 0.647138i | \(0.224034\pi\) | |||||||
\(774\) | 8.73205 | 0.313867 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 17.1244 | 0.614729 | ||||||||
\(777\) | −24.3923 | −0.875069 | ||||||||
\(778\) | −12.9282 | −0.463499 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −52.9808 | −1.89580 | ||||||||
\(782\) | 23.1244 | 0.826925 | ||||||||
\(783\) | −9.19615 | −0.328644 | ||||||||
\(784\) | 0.464102 | 0.0165751 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 11.1962 | 0.399354 | ||||||||
\(787\) | −41.9808 | −1.49645 | −0.748226 | − | 0.663444i | \(-0.769094\pi\) | ||||
−0.748226 | + | 0.663444i | \(0.769094\pi\) | |||||||
\(788\) | −0.339746 | −0.0121029 | ||||||||
\(789\) | −12.4641 | −0.443734 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −39.1244 | −1.39110 | ||||||||
\(792\) | −5.19615 | −0.184637 | ||||||||
\(793\) | −39.1244 | −1.38935 | ||||||||
\(794\) | −34.1244 | −1.21103 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.07180 | 0.108877 | ||||||||
\(797\) | −29.5692 | −1.04740 | −0.523698 | − | 0.851904i | \(-0.675448\pi\) | ||||
−0.523698 | + | 0.851904i | \(0.675448\pi\) | |||||||
\(798\) | 2.73205 | 0.0967136 | ||||||||
\(799\) | 9.46410 | 0.334816 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.92820 | 0.138796 | ||||||||
\(802\) | −18.7128 | −0.660772 | ||||||||
\(803\) | −75.1577 | −2.65226 | ||||||||
\(804\) | 5.19615 | 0.183254 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −28.0526 | −0.988109 | ||||||||
\(807\) | 15.4641 | 0.544362 | ||||||||
\(808\) | 11.6603 | 0.410206 | ||||||||
\(809\) | −19.1244 | −0.672377 | −0.336188 | − | 0.941795i | \(-0.609138\pi\) | ||||
−0.336188 | + | 0.941795i | \(0.609138\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.5167 | −0.650208 | −0.325104 | − | 0.945678i | \(-0.605399\pi\) | ||||
−0.325104 | + | 0.945678i | \(0.605399\pi\) | |||||||
\(812\) | 25.1244 | 0.881692 | ||||||||
\(813\) | −25.1244 | −0.881150 | ||||||||
\(814\) | −46.3923 | −1.62605 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.73205 | 0.0956409 | ||||||||
\(817\) | −8.73205 | −0.305496 | ||||||||
\(818\) | −17.3205 | −0.605597 | ||||||||
\(819\) | 12.9282 | 0.451748 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.1962 | 1.26325 | 0.631627 | − | 0.775272i | \(-0.282387\pi\) | ||||
0.631627 | + | 0.775272i | \(0.282387\pi\) | |||||||
\(822\) | 16.3923 | 0.571747 | ||||||||
\(823\) | 25.7128 | 0.896292 | 0.448146 | − | 0.893960i | \(-0.352084\pi\) | ||||
0.448146 | + | 0.893960i | \(0.352084\pi\) | |||||||
\(824\) | −14.8564 | −0.517547 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.00000 | 0.208767 | ||||||||
\(827\) | −12.7321 | −0.442737 | −0.221368 | − | 0.975190i | \(-0.571052\pi\) | ||||
−0.221368 | + | 0.975190i | \(0.571052\pi\) | |||||||
\(828\) | −8.46410 | −0.294148 | ||||||||
\(829\) | −6.73205 | −0.233814 | −0.116907 | − | 0.993143i | \(-0.537298\pi\) | ||||
−0.116907 | + | 0.993143i | \(0.537298\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.5167 | 0.850474 | ||||||||
\(832\) | −4.73205 | −0.164054 | ||||||||
\(833\) | 1.26795 | 0.0439318 | ||||||||
\(834\) | 3.80385 | 0.131716 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 5.19615 | 0.179713 | ||||||||
\(837\) | −5.92820 | −0.204909 | ||||||||
\(838\) | 5.85641 | 0.202306 | ||||||||
\(839\) | −35.9090 | −1.23972 | −0.619858 | − | 0.784714i | \(-0.712810\pi\) | ||||
−0.619858 | + | 0.784714i | \(0.712810\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 55.5692 | 1.91618 | ||||||||
\(842\) | 2.00000 | 0.0689246 | ||||||||
\(843\) | −11.0000 | −0.378860 | ||||||||
\(844\) | 7.19615 | 0.247702 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.46410 | −0.119098 | ||||||||
\(847\) | −43.7128 | −1.50199 | ||||||||
\(848\) | 4.66025 | 0.160034 | ||||||||
\(849\) | 4.00000 | 0.137280 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −75.5692 | −2.59048 | ||||||||
\(852\) | −10.1962 | −0.349314 | ||||||||
\(853\) | 11.1769 | 0.382690 | 0.191345 | − | 0.981523i | \(-0.438715\pi\) | ||||
0.191345 | + | 0.981523i | \(0.438715\pi\) | |||||||
\(854\) | 22.5885 | 0.772961 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.19615 | 0.143422 | ||||||||
\(857\) | −13.8564 | −0.473326 | −0.236663 | − | 0.971592i | \(-0.576054\pi\) | ||||
−0.236663 | + | 0.971592i | \(0.576054\pi\) | |||||||
\(858\) | 24.5885 | 0.839436 | ||||||||
\(859\) | −30.7846 | −1.05036 | −0.525179 | − | 0.850992i | \(-0.676002\pi\) | ||||
−0.525179 | + | 0.850992i | \(0.676002\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.60770 | 0.0547583 | ||||||||
\(863\) | 23.6077 | 0.803615 | 0.401808 | − | 0.915724i | \(-0.368382\pi\) | ||||
0.401808 | + | 0.915724i | \(0.368382\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 5.80385 | 0.197223 | ||||||||
\(867\) | −9.53590 | −0.323856 | ||||||||
\(868\) | 16.1962 | 0.549733 | ||||||||
\(869\) | 30.8038 | 1.04495 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.5885 | −0.833148 | ||||||||
\(872\) | 10.3923 | 0.351928 | ||||||||
\(873\) | −17.1244 | −0.579572 | ||||||||
\(874\) | 8.46410 | 0.286303 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −14.4641 | −0.488697 | ||||||||
\(877\) | −51.4641 | −1.73782 | −0.868910 | − | 0.494971i | \(-0.835179\pi\) | ||||
−0.868910 | + | 0.494971i | \(0.835179\pi\) | |||||||
\(878\) | −3.39230 | −0.114485 | ||||||||
\(879\) | 26.6603 | 0.899228 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.6077 | 0.660600 | 0.330300 | − | 0.943876i | \(-0.392850\pi\) | ||||
0.330300 | + | 0.943876i | \(0.392850\pi\) | |||||||
\(882\) | −0.464102 | −0.0156271 | ||||||||
\(883\) | −43.9090 | −1.47765 | −0.738827 | − | 0.673895i | \(-0.764620\pi\) | ||||
−0.738827 | + | 0.673895i | \(0.764620\pi\) | |||||||
\(884\) | −12.9282 | −0.434823 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −20.5167 | −0.689271 | ||||||||
\(887\) | 1.46410 | 0.0491597 | 0.0245799 | − | 0.999698i | \(-0.492175\pi\) | ||||
0.0245799 | + | 0.999698i | \(0.492175\pi\) | |||||||
\(888\) | −8.92820 | −0.299611 | ||||||||
\(889\) | −25.6603 | −0.860617 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.19615 | 0.174078 | ||||||||
\(892\) | −17.9282 | −0.600281 | ||||||||
\(893\) | 3.46410 | 0.115922 | ||||||||
\(894\) | 21.8564 | 0.730988 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.73205 | 0.0912714 | ||||||||
\(897\) | 40.0526 | 1.33732 | ||||||||
\(898\) | −0.464102 | −0.0154873 | ||||||||
\(899\) | 54.5167 | 1.81823 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.7321 | 0.424166 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 23.8564 | 0.793891 | ||||||||
\(904\) | −14.3205 | −0.476293 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −10.3923 | −0.345261 | ||||||||
\(907\) | −6.67949 | −0.221789 | −0.110894 | − | 0.993832i | \(-0.535372\pi\) | ||||
−0.110894 | + | 0.993832i | \(0.535372\pi\) | |||||||
\(908\) | −2.00000 | −0.0663723 | ||||||||
\(909\) | −11.6603 | −0.386746 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.6077 | −0.583369 | −0.291684 | − | 0.956515i | \(-0.594216\pi\) | ||||
−0.291684 | + | 0.956515i | \(0.594216\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | −86.5692 | −2.86502 | ||||||||
\(914\) | −32.0000 | −1.05847 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.19615 | 0.171686 | ||||||||
\(917\) | 30.5885 | 1.01012 | ||||||||
\(918\) | −2.73205 | −0.0901711 | ||||||||
\(919\) | 36.8372 | 1.21515 | 0.607573 | − | 0.794264i | \(-0.292143\pi\) | ||||
0.607573 | + | 0.794264i | \(0.292143\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.66025 | −0.153561 | ||||||||
\(922\) | 1.85641 | 0.0611375 | ||||||||
\(923\) | 48.2487 | 1.58813 | ||||||||
\(924\) | −14.1962 | −0.467019 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 11.6077 | 0.381453 | ||||||||
\(927\) | 14.8564 | 0.487948 | ||||||||
\(928\) | 9.19615 | 0.301878 | ||||||||
\(929\) | 34.9282 | 1.14596 | 0.572979 | − | 0.819570i | \(-0.305788\pi\) | ||||
0.572979 | + | 0.819570i | \(0.305788\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.464102 | 0.0152103 | ||||||||
\(932\) | 17.6603 | 0.578481 | ||||||||
\(933\) | −15.4641 | −0.506272 | ||||||||
\(934\) | 16.6603 | 0.545140 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.73205 | 0.154672 | ||||||||
\(937\) | −5.21539 | −0.170379 | −0.0851897 | − | 0.996365i | \(-0.527150\pi\) | ||||
−0.0851897 | + | 0.996365i | \(0.527150\pi\) | |||||||
\(938\) | 14.1962 | 0.463521 | ||||||||
\(939\) | 4.85641 | 0.158483 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.73205 | −0.252058 | −0.126029 | − | 0.992027i | \(-0.540223\pi\) | ||||
−0.126029 | + | 0.992027i | \(0.540223\pi\) | |||||||
\(942\) | 21.8564 | 0.712120 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 2.19615 | 0.0714787 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 45.3731 | 1.47521 | ||||||||
\(947\) | 29.8564 | 0.970203 | 0.485101 | − | 0.874458i | \(-0.338783\pi\) | ||||
0.485101 | + | 0.874458i | \(0.338783\pi\) | |||||||
\(948\) | 5.92820 | 0.192539 | ||||||||
\(949\) | 68.4449 | 2.22181 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.0526 | −0.747530 | ||||||||
\(952\) | 7.46410 | 0.241913 | ||||||||
\(953\) | 7.39230 | 0.239460 | 0.119730 | − | 0.992806i | \(-0.461797\pi\) | ||||
0.119730 | + | 0.992806i | \(0.461797\pi\) | |||||||
\(954\) | −4.66025 | −0.150881 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −7.07180 | −0.228718 | ||||||||
\(957\) | −47.7846 | −1.54466 | ||||||||
\(958\) | 16.6077 | 0.536570 | ||||||||
\(959\) | 44.7846 | 1.44617 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.14359 | 0.133664 | ||||||||
\(962\) | 42.2487 | 1.36215 | ||||||||
\(963\) | −4.19615 | −0.135219 | ||||||||
\(964\) | 7.80385 | 0.251345 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −23.1244 | −0.744014 | ||||||||
\(967\) | 49.0333 | 1.57681 | 0.788403 | − | 0.615160i | \(-0.210908\pi\) | ||||
0.788403 | + | 0.615160i | \(0.210908\pi\) | |||||||
\(968\) | −16.0000 | −0.514259 | ||||||||
\(969\) | 2.73205 | 0.0877661 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.8038 | −1.08482 | −0.542409 | − | 0.840115i | \(-0.682488\pi\) | ||||
−0.542409 | + | 0.840115i | \(0.682488\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 10.3923 | 0.333162 | ||||||||
\(974\) | −13.0718 | −0.418847 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.26795 | 0.264651 | ||||||||
\(977\) | 2.53590 | 0.0811306 | 0.0405653 | − | 0.999177i | \(-0.487084\pi\) | ||||
0.0405653 | + | 0.999177i | \(0.487084\pi\) | |||||||
\(978\) | −10.0000 | −0.319765 | ||||||||
\(979\) | 20.4115 | 0.652356 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.3923 | −0.331801 | ||||||||
\(982\) | 34.9282 | 1.11460 | ||||||||
\(983\) | 11.6603 | 0.371904 | 0.185952 | − | 0.982559i | \(-0.440463\pi\) | ||||
0.185952 | + | 0.982559i | \(0.440463\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 25.1244 | 0.800122 | ||||||||
\(987\) | −9.46410 | −0.301246 | ||||||||
\(988\) | −4.73205 | −0.150547 | ||||||||
\(989\) | 73.9090 | 2.35017 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.7846 | 0.437883 | 0.218941 | − | 0.975738i | \(-0.429740\pi\) | ||||
0.218941 | + | 0.975738i | \(0.429740\pi\) | |||||||
\(992\) | 5.92820 | 0.188221 | ||||||||
\(993\) | 19.1962 | 0.609171 | ||||||||
\(994\) | −27.8564 | −0.883552 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −16.6603 | −0.527900 | ||||||||
\(997\) | −23.3397 | −0.739177 | −0.369589 | − | 0.929196i | \(-0.620501\pi\) | ||||
−0.369589 | + | 0.929196i | \(0.620501\pi\) | |||||||
\(998\) | −13.1244 | −0.415444 | ||||||||
\(999\) | 8.92820 | 0.282476 |
(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 | 2850.2.a.be.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 8550.2.a.bz.1.1 | 2 | |||
5.2 | odd | 4 | 2850.2.d.u.799.1 | 4 | |||
5.3 | odd | 4 | 2850.2.d.u.799.4 | 4 | |||
5.4 | even | 2 | 2850.2.a.bh.1.2 | yes | 2 | ||
15.14 | odd | 2 | 8550.2.a.bt.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2850.2.a.be.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
2850.2.a.bh.1.2 | yes | 2 | 5.4 | even | 2 | ||
2850.2.d.u.799.1 | 4 | 5.2 | odd | 4 | |||
2850.2.d.u.799.4 | 4 | 5.3 | odd | 4 | |||
8550.2.a.bt.1.2 | 2 | 15.14 | odd | 2 | |||
8550.2.a.bz.1.1 | 2 | 3.2 | odd | 2 |