Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7938,2,Mod(1,7938)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7938, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7938.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7938 = 2 \cdot 3^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7938.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.3852491245\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{15})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 16x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 882) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.44572\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7938.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.44572 | −1.54097 | −0.770486 | − | 0.637457i | \(-0.779987\pi\) | ||||
−0.770486 | + | 0.637457i | \(0.779987\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.44572 | −1.08963 | ||||||||
\(11\) | 4.00000 | 1.20605 | 0.603023 | − | 0.797724i | \(-0.293963\pi\) | ||||
0.603023 | + | 0.797724i | \(0.293963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.24264 | −1.17670 | −0.588348 | − | 0.808608i | \(-0.700222\pi\) | ||||
−0.588348 | + | 0.808608i | \(0.700222\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.41421 | 0.342997 | 0.171499 | − | 0.985184i | \(-0.445139\pi\) | ||||
0.171499 | + | 0.985184i | \(0.445139\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.27415 | −1.43939 | −0.719694 | − | 0.694291i | \(-0.755718\pi\) | ||||
−0.719694 | + | 0.694291i | \(0.755718\pi\) | |||||||
\(20\) | −3.44572 | −0.770486 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.00000 | 0.852803 | ||||||||
\(23\) | −8.74597 | −1.82366 | −0.911830 | − | 0.410568i | \(-0.865331\pi\) | ||||
−0.911830 | + | 0.410568i | \(0.865331\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.87298 | 1.37460 | ||||||||
\(26\) | −4.24264 | −0.832050 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.12702 | 0.209282 | 0.104641 | − | 0.994510i | \(-0.466631\pi\) | ||||
0.104641 | + | 0.994510i | \(0.466631\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.47723 | 0.983739 | 0.491869 | − | 0.870669i | \(-0.336314\pi\) | ||||
0.491869 | + | 0.870669i | \(0.336314\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.41421 | 0.242536 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.74597 | 0.944631 | 0.472316 | − | 0.881430i | \(-0.343418\pi\) | ||||
0.472316 | + | 0.881430i | \(0.343418\pi\) | |||||||
\(38\) | −6.27415 | −1.01780 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.44572 | −0.544816 | ||||||||
\(41\) | 5.65685 | 0.883452 | 0.441726 | − | 0.897150i | \(-0.354366\pi\) | ||||
0.441726 | + | 0.897150i | \(0.354366\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.12702 | 0.171868 | 0.0859342 | − | 0.996301i | \(-0.472613\pi\) | ||||
0.0859342 | + | 0.996301i | \(0.472613\pi\) | |||||||
\(44\) | 4.00000 | 0.603023 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.74597 | −1.28952 | ||||||||
\(47\) | −4.06301 | −0.592651 | −0.296326 | − | 0.955087i | \(-0.595761\pi\) | ||||
−0.296326 | + | 0.955087i | \(0.595761\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 6.87298 | 0.971987 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.24264 | −0.588348 | ||||||||
\(53\) | 12.6190 | 1.73335 | 0.866673 | − | 0.498877i | \(-0.166254\pi\) | ||||
0.866673 | + | 0.498877i | \(0.166254\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −13.7829 | −1.85848 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.12702 | 0.147985 | ||||||||
\(59\) | −8.30565 | −1.08130 | −0.540652 | − | 0.841246i | \(-0.681822\pi\) | ||||
−0.540652 | + | 0.841246i | \(0.681822\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.27415 | 0.803322 | 0.401661 | − | 0.915788i | \(-0.368433\pi\) | ||||
0.401661 | + | 0.915788i | \(0.368433\pi\) | |||||||
\(62\) | 5.47723 | 0.695608 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 14.6190 | 1.81326 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.87298 | −0.839669 | −0.419834 | − | 0.907601i | \(-0.637912\pi\) | ||||
−0.419834 | + | 0.907601i | \(0.637912\pi\) | |||||||
\(68\) | 1.41421 | 0.171499 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.87298 | −1.17171 | −0.585854 | − | 0.810417i | \(-0.699241\pi\) | ||||
−0.585854 | + | 0.810417i | \(0.699241\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.42227 | 0.517587 | 0.258794 | − | 0.965933i | \(-0.416675\pi\) | ||||
0.258794 | + | 0.965933i | \(0.416675\pi\) | |||||||
\(74\) | 5.74597 | 0.667955 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.27415 | −0.719694 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.87298 | −0.210727 | −0.105364 | − | 0.994434i | \(-0.533601\pi\) | ||||
−0.105364 | + | 0.994434i | \(0.533601\pi\) | |||||||
\(80\) | −3.44572 | −0.385243 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.65685 | 0.624695 | ||||||||
\(83\) | −2.64880 | −0.290743 | −0.145372 | − | 0.989377i | \(-0.546438\pi\) | ||||
−0.145372 | + | 0.989377i | \(0.546438\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.87298 | −0.528549 | ||||||||
\(86\) | 1.12702 | 0.121529 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.00000 | 0.426401 | ||||||||
\(89\) | 7.07107 | 0.749532 | 0.374766 | − | 0.927119i | \(-0.377723\pi\) | ||||
0.374766 | + | 0.927119i | \(0.377723\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.74597 | −0.911830 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.06301 | −0.419068 | ||||||||
\(95\) | 21.6190 | 2.21806 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.0175 | 1.52479 | 0.762396 | − | 0.647111i | \(-0.224023\pi\) | ||||
0.762396 | + | 0.647111i | \(0.224023\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.87298 | 0.687298 | ||||||||
\(101\) | −13.3452 | −1.32790 | −0.663949 | − | 0.747778i | \(-0.731121\pi\) | ||||
−0.663949 | + | 0.747778i | \(0.731121\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.88338 | 0.382641 | 0.191321 | − | 0.981528i | \(-0.438723\pi\) | ||||
0.191321 | + | 0.981528i | \(0.438723\pi\) | |||||||
\(104\) | −4.24264 | −0.416025 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.6190 | 1.22566 | ||||||||
\(107\) | 0.254033 | 0.0245583 | 0.0122792 | − | 0.999925i | \(-0.496091\pi\) | ||||
0.0122792 | + | 0.999925i | \(0.496091\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.8730 | 1.61614 | 0.808069 | − | 0.589087i | \(-0.200513\pi\) | ||||
0.808069 | + | 0.589087i | \(0.200513\pi\) | |||||||
\(110\) | −13.7829 | −1.31415 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.87298 | 0.364340 | 0.182170 | − | 0.983267i | \(-0.441688\pi\) | ||||
0.182170 | + | 0.983267i | \(0.441688\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 30.1361 | 2.81021 | ||||||||
\(116\) | 1.12702 | 0.104641 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.30565 | −0.764597 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 6.27415 | 0.568035 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.47723 | 0.491869 | ||||||||
\(125\) | −6.45378 | −0.577243 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.745967 | −0.0661938 | −0.0330969 | − | 0.999452i | \(-0.510537\pi\) | ||||
−0.0330969 | + | 0.999452i | \(0.510537\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 14.6190 | 1.28217 | ||||||||
\(131\) | 13.3452 | 1.16598 | 0.582988 | − | 0.812480i | \(-0.301883\pi\) | ||||
0.582988 | + | 0.812480i | \(0.301883\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −6.87298 | −0.593735 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.41421 | 0.121268 | ||||||||
\(137\) | −15.4919 | −1.32357 | −0.661783 | − | 0.749696i | \(-0.730200\pi\) | ||||
−0.661783 | + | 0.749696i | \(0.730200\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.8774 | 1.68598 | 0.842989 | − | 0.537930i | \(-0.180794\pi\) | ||||
0.842989 | + | 0.537930i | \(0.180794\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.87298 | −0.828522 | ||||||||
\(143\) | −16.9706 | −1.41915 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.88338 | −0.322497 | ||||||||
\(146\) | 4.42227 | 0.365990 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.74597 | 0.472316 | ||||||||
\(149\) | −15.7460 | −1.28996 | −0.644980 | − | 0.764200i | \(-0.723134\pi\) | ||||
−0.644980 | + | 0.764200i | \(0.723134\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.0000 | 0.895167 | 0.447584 | − | 0.894242i | \(-0.352285\pi\) | ||||
0.447584 | + | 0.894242i | \(0.352285\pi\) | |||||||
\(152\) | −6.27415 | −0.508900 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −18.8730 | −1.51591 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.9310 | 0.952198 | 0.476099 | − | 0.879392i | \(-0.342050\pi\) | ||||
0.476099 | + | 0.879392i | \(0.342050\pi\) | |||||||
\(158\) | −1.87298 | −0.149007 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.44572 | −0.272408 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.0000 | 0.783260 | 0.391630 | − | 0.920123i | \(-0.371911\pi\) | ||||
0.391630 | + | 0.920123i | \(0.371911\pi\) | |||||||
\(164\) | 5.65685 | 0.441726 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.64880 | −0.205587 | ||||||||
\(167\) | 9.54024 | 0.738246 | 0.369123 | − | 0.929381i | \(-0.379658\pi\) | ||||
0.369123 | + | 0.929381i | \(0.379658\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | −4.87298 | −0.373741 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.12702 | 0.0859342 | ||||||||
\(173\) | 12.7279 | 0.967686 | 0.483843 | − | 0.875155i | \(-0.339241\pi\) | ||||
0.483843 | + | 0.875155i | \(0.339241\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.00000 | 0.301511 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.07107 | 0.529999 | ||||||||
\(179\) | −6.87298 | −0.513711 | −0.256855 | − | 0.966450i | \(-0.582686\pi\) | ||||
−0.256855 | + | 0.966450i | \(0.582686\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.3452 | −0.991942 | −0.495971 | − | 0.868339i | \(-0.665188\pi\) | ||||
−0.495971 | + | 0.868339i | \(0.665188\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.74597 | −0.644761 | ||||||||
\(185\) | −19.7990 | −1.45565 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.65685 | 0.413670 | ||||||||
\(188\) | −4.06301 | −0.296326 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 21.6190 | 1.56840 | ||||||||
\(191\) | −6.12702 | −0.443335 | −0.221668 | − | 0.975122i | \(-0.571150\pi\) | ||||
−0.221668 | + | 0.975122i | \(0.571150\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.8730 | 1.71841 | 0.859207 | − | 0.511627i | \(-0.170957\pi\) | ||||
0.859207 | + | 0.511627i | \(0.170957\pi\) | |||||||
\(194\) | 15.0175 | 1.07819 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.6190 | 1.18405 | 0.592026 | − | 0.805919i | \(-0.298328\pi\) | ||||
0.592026 | + | 0.805919i | \(0.298328\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.1890 | 0.864058 | 0.432029 | − | 0.901860i | \(-0.357798\pi\) | ||||
0.432029 | + | 0.901860i | \(0.357798\pi\) | |||||||
\(200\) | 6.87298 | 0.485993 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −13.3452 | −0.938966 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −19.4919 | −1.36138 | ||||||||
\(206\) | 3.88338 | 0.270568 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.24264 | −0.294174 | ||||||||
\(209\) | −25.0966 | −1.73597 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.6190 | 1.41947 | 0.709734 | − | 0.704470i | \(-0.248815\pi\) | ||||
0.709734 | + | 0.704470i | \(0.248815\pi\) | |||||||
\(212\) | 12.6190 | 0.866673 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.254033 | 0.0173654 | ||||||||
\(215\) | −3.88338 | −0.264845 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 16.8730 | 1.14278 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −13.7829 | −0.929241 | ||||||||
\(221\) | −6.00000 | −0.403604 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.4478 | −1.50322 | −0.751608 | − | 0.659611i | \(-0.770721\pi\) | ||||
−0.751608 | + | 0.659611i | \(0.770721\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.87298 | 0.257627 | ||||||||
\(227\) | 10.3372 | 0.686101 | 0.343051 | − | 0.939317i | \(-0.388540\pi\) | ||||
0.343051 | + | 0.939317i | \(0.388540\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.3452 | 0.881877 | 0.440938 | − | 0.897537i | \(-0.354646\pi\) | ||||
0.440938 | + | 0.897537i | \(0.354646\pi\) | |||||||
\(230\) | 30.1361 | 1.98712 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.12702 | 0.0739923 | ||||||||
\(233\) | 7.25403 | 0.475228 | 0.237614 | − | 0.971360i | \(-0.423635\pi\) | ||||
0.237614 | + | 0.971360i | \(0.423635\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.0000 | 0.913259 | ||||||||
\(236\) | −8.30565 | −0.540652 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.0000 | −0.970269 | −0.485135 | − | 0.874439i | \(-0.661229\pi\) | ||||
−0.485135 | + | 0.874439i | \(0.661229\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.6824 | −1.52552 | −0.762758 | − | 0.646684i | \(-0.776155\pi\) | ||||
−0.762758 | + | 0.646684i | \(0.776155\pi\) | |||||||
\(242\) | 5.00000 | 0.321412 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.27415 | 0.401661 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.6190 | 1.69372 | ||||||||
\(248\) | 5.47723 | 0.347804 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.45378 | −0.408173 | ||||||||
\(251\) | 9.46183 | 0.597225 | 0.298613 | − | 0.954374i | \(-0.403476\pi\) | ||||
0.298613 | + | 0.954374i | \(0.403476\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −34.9839 | −2.19942 | ||||||||
\(254\) | −0.745967 | −0.0468061 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.00806 | 0.187637 | 0.0938187 | − | 0.995589i | \(-0.470093\pi\) | ||||
0.0938187 | + | 0.995589i | \(0.470093\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 14.6190 | 0.906629 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13.3452 | 0.824470 | ||||||||
\(263\) | −17.6190 | −1.08643 | −0.543216 | − | 0.839593i | \(-0.682793\pi\) | ||||
−0.543216 | + | 0.839593i | \(0.682793\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −43.4814 | −2.67104 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.87298 | −0.419834 | ||||||||
\(269\) | −2.03151 | −0.123863 | −0.0619316 | − | 0.998080i | \(-0.519726\pi\) | ||||
−0.0619316 | + | 0.998080i | \(0.519726\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.07107 | 0.429537 | 0.214768 | − | 0.976665i | \(-0.431100\pi\) | ||||
0.214768 | + | 0.976665i | \(0.431100\pi\) | |||||||
\(272\) | 1.41421 | 0.0857493 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.4919 | −0.935902 | ||||||||
\(275\) | 27.4919 | 1.65783 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.3649 | 0.863104 | 0.431552 | − | 0.902088i | \(-0.357966\pi\) | ||||
0.431552 | + | 0.902088i | \(0.357966\pi\) | |||||||
\(278\) | 19.8774 | 1.19217 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.74597 | 0.521741 | 0.260870 | − | 0.965374i | \(-0.415991\pi\) | ||||
0.260870 | + | 0.965374i | \(0.415991\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.03956 | 0.299571 | 0.149785 | − | 0.988719i | \(-0.452142\pi\) | ||||
0.149785 | + | 0.988719i | \(0.452142\pi\) | |||||||
\(284\) | −9.87298 | −0.585854 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −16.9706 | −1.00349 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.0000 | −0.882353 | ||||||||
\(290\) | −3.88338 | −0.228040 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.42227 | 0.258794 | ||||||||
\(293\) | −0.796921 | −0.0465566 | −0.0232783 | − | 0.999729i | \(-0.507410\pi\) | ||||
−0.0232783 | + | 0.999729i | \(0.507410\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 28.6190 | 1.66626 | ||||||||
\(296\) | 5.74597 | 0.333978 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −15.7460 | −0.912139 | ||||||||
\(299\) | 37.1060 | 2.14590 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 11.0000 | 0.632979 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.27415 | −0.359847 | ||||||||
\(305\) | −21.6190 | −1.23790 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.2205 | 0.811609 | 0.405805 | − | 0.913960i | \(-0.366991\pi\) | ||||
0.405805 | + | 0.913960i | \(0.366991\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −18.8730 | −1.07191 | ||||||||
\(311\) | −1.41421 | −0.0801927 | −0.0400963 | − | 0.999196i | \(-0.512766\pi\) | ||||
−0.0400963 | + | 0.999196i | \(0.512766\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.7360 | 0.889450 | 0.444725 | − | 0.895667i | \(-0.353301\pi\) | ||||
0.444725 | + | 0.895667i | \(0.353301\pi\) | |||||||
\(314\) | 11.9310 | 0.673305 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.87298 | −0.105364 | ||||||||
\(317\) | 24.6190 | 1.38274 | 0.691369 | − | 0.722502i | \(-0.257008\pi\) | ||||
0.691369 | + | 0.722502i | \(0.257008\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.50807 | 0.252403 | ||||||||
\(320\) | −3.44572 | −0.192622 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.87298 | −0.493706 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −29.1596 | −1.61748 | ||||||||
\(326\) | 10.0000 | 0.553849 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.65685 | 0.312348 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.3649 | 1.11936 | 0.559679 | − | 0.828710i | \(-0.310925\pi\) | ||||
0.559679 | + | 0.828710i | \(0.310925\pi\) | |||||||
\(332\) | −2.64880 | −0.145372 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.54024 | 0.522019 | ||||||||
\(335\) | 23.6824 | 1.29391 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.7460 | 0.857737 | 0.428869 | − | 0.903367i | \(-0.358912\pi\) | ||||
0.428869 | + | 0.903367i | \(0.358912\pi\) | |||||||
\(338\) | 5.00000 | 0.271964 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.87298 | −0.264275 | ||||||||
\(341\) | 21.9089 | 1.18643 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.12702 | 0.0607647 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.7279 | 0.684257 | ||||||||
\(347\) | 7.74597 | 0.415825 | 0.207913 | − | 0.978147i | \(-0.433333\pi\) | ||||
0.207913 | + | 0.978147i | \(0.433333\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.4317 | −0.879567 | −0.439784 | − | 0.898104i | \(-0.644945\pi\) | ||||
−0.439784 | + | 0.898104i | \(0.644945\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.00000 | 0.213201 | ||||||||
\(353\) | 3.88338 | 0.206692 | 0.103346 | − | 0.994645i | \(-0.467045\pi\) | ||||
0.103346 | + | 0.994645i | \(0.467045\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 34.0195 | 1.80557 | ||||||||
\(356\) | 7.07107 | 0.374766 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.87298 | −0.363248 | ||||||||
\(359\) | 18.2379 | 0.962560 | 0.481280 | − | 0.876567i | \(-0.340172\pi\) | ||||
0.481280 | + | 0.876567i | \(0.340172\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.3649 | 1.07184 | ||||||||
\(362\) | −13.3452 | −0.701409 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.2379 | −0.797588 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.89144 | 0.359730 | 0.179865 | − | 0.983691i | \(-0.442434\pi\) | ||||
0.179865 | + | 0.983691i | \(0.442434\pi\) | |||||||
\(368\) | −8.74597 | −0.455915 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −19.7990 | −1.02930 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.12702 | −0.0583547 | −0.0291774 | − | 0.999574i | \(-0.509289\pi\) | ||||
−0.0291774 | + | 0.999574i | \(0.509289\pi\) | |||||||
\(374\) | 5.65685 | 0.292509 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.06301 | −0.209534 | ||||||||
\(377\) | −4.78153 | −0.246261 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.3649 | 1.35427 | 0.677137 | − | 0.735857i | \(-0.263220\pi\) | ||||
0.677137 | + | 0.735857i | \(0.263220\pi\) | |||||||
\(380\) | 21.6190 | 1.10903 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.12702 | −0.313485 | ||||||||
\(383\) | −12.9076 | −0.659545 | −0.329773 | − | 0.944060i | \(-0.606972\pi\) | ||||
−0.329773 | + | 0.944060i | \(0.606972\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 23.8730 | 1.21510 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 15.0175 | 0.762396 | ||||||||
\(389\) | 13.1270 | 0.665566 | 0.332783 | − | 0.943003i | \(-0.392012\pi\) | ||||
0.332783 | + | 0.943003i | \(0.392012\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.3687 | −0.625510 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 16.6190 | 0.837251 | ||||||||
\(395\) | 6.45378 | 0.324725 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.07107 | 0.354887 | 0.177443 | − | 0.984131i | \(-0.443217\pi\) | ||||
0.177443 | + | 0.984131i | \(0.443217\pi\) | |||||||
\(398\) | 12.1890 | 0.610981 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.87298 | 0.343649 | ||||||||
\(401\) | −3.87298 | −0.193408 | −0.0967038 | − | 0.995313i | \(-0.530830\pi\) | ||||
−0.0967038 | + | 0.995313i | \(0.530830\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.2379 | −1.15756 | ||||||||
\(404\) | −13.3452 | −0.663949 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 22.9839 | 1.13927 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.1435 | 1.14437 | 0.572186 | − | 0.820124i | \(-0.306096\pi\) | ||||
0.572186 | + | 0.820124i | \(0.306096\pi\) | |||||||
\(410\) | −19.4919 | −0.962638 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.88338 | 0.191321 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.12702 | 0.448028 | ||||||||
\(416\) | −4.24264 | −0.208013 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −25.0966 | −1.22751 | ||||||||
\(419\) | −31.3707 | −1.53256 | −0.766280 | − | 0.642506i | \(-0.777895\pi\) | ||||
−0.766280 | + | 0.642506i | \(0.777895\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.8730 | −0.627391 | −0.313695 | − | 0.949524i | \(-0.601567\pi\) | ||||
−0.313695 | + | 0.949524i | \(0.601567\pi\) | |||||||
\(422\) | 20.6190 | 1.00371 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12.6190 | 0.612830 | ||||||||
\(425\) | 9.71987 | 0.471483 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.254033 | 0.0122792 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.88338 | −0.187273 | ||||||||
\(431\) | −21.4919 | −1.03523 | −0.517615 | − | 0.855614i | \(-0.673180\pi\) | ||||
−0.517615 | + | 0.855614i | \(0.673180\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.6985 | −1.42722 | −0.713609 | − | 0.700544i | \(-0.752941\pi\) | ||||
−0.713609 | + | 0.700544i | \(0.752941\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 16.8730 | 0.808069 | ||||||||
\(437\) | 54.8735 | 2.62495 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.9545 | −0.522827 | −0.261414 | − | 0.965227i | \(-0.584189\pi\) | ||||
−0.261414 | + | 0.965227i | \(0.584189\pi\) | |||||||
\(440\) | −13.7829 | −0.657073 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.00000 | −0.285391 | ||||||||
\(443\) | −14.3649 | −0.682498 | −0.341249 | − | 0.939973i | \(-0.610850\pi\) | ||||
−0.341249 | + | 0.939973i | \(0.610850\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.3649 | −1.15501 | ||||||||
\(446\) | −22.4478 | −1.06293 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.00000 | 0.424736 | 0.212368 | − | 0.977190i | \(-0.431882\pi\) | ||||
0.212368 | + | 0.977190i | \(0.431882\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.6274 | 1.06548 | ||||||||
\(452\) | 3.87298 | 0.182170 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10.3372 | 0.485147 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.1270 | 1.22217 | 0.611085 | − | 0.791565i | \(-0.290733\pi\) | ||||
0.611085 | + | 0.791565i | \(0.290733\pi\) | |||||||
\(458\) | 13.3452 | 0.623581 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 30.1361 | 1.40511 | ||||||||
\(461\) | 28.3627 | 1.32098 | 0.660491 | − | 0.750834i | \(-0.270348\pi\) | ||||
0.660491 | + | 0.750834i | \(0.270348\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.61895 | −0.0752390 | −0.0376195 | − | 0.999292i | \(-0.511977\pi\) | ||||
−0.0376195 | + | 0.999292i | \(0.511977\pi\) | |||||||
\(464\) | 1.12702 | 0.0523204 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.25403 | 0.336037 | ||||||||
\(467\) | 6.19574 | 0.286705 | 0.143352 | − | 0.989672i | \(-0.454212\pi\) | ||||
0.143352 | + | 0.989672i | \(0.454212\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 14.0000 | 0.645772 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8.30565 | −0.382299 | ||||||||
\(473\) | 4.50807 | 0.207281 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −43.1221 | −1.97858 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −15.0000 | −0.686084 | ||||||||
\(479\) | 3.88338 | 0.177436 | 0.0887182 | − | 0.996057i | \(-0.471723\pi\) | ||||
0.0887182 | + | 0.996057i | \(0.471723\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.3781 | −1.11154 | ||||||||
\(482\) | −23.6824 | −1.07870 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.00000 | 0.227273 | ||||||||
\(485\) | −51.7460 | −2.34966 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.491933 | −0.0222916 | −0.0111458 | − | 0.999938i | \(-0.503548\pi\) | ||||
−0.0111458 | + | 0.999938i | \(0.503548\pi\) | |||||||
\(488\) | 6.27415 | 0.284017 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.74597 | 0.0787944 | 0.0393972 | − | 0.999224i | \(-0.487456\pi\) | ||||
0.0393972 | + | 0.999224i | \(0.487456\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.59384 | 0.0717830 | ||||||||
\(494\) | 26.6190 | 1.19764 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.47723 | 0.245935 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.7460 | −1.33161 | −0.665806 | − | 0.746125i | \(-0.731912\pi\) | ||||
−0.665806 | + | 0.746125i | \(0.731912\pi\) | |||||||
\(500\) | −6.45378 | −0.288622 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.46183 | 0.422302 | ||||||||
\(503\) | −3.88338 | −0.173152 | −0.0865758 | − | 0.996245i | \(-0.527592\pi\) | ||||
−0.0865758 | + | 0.996245i | \(0.527592\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 45.9839 | 2.04626 | ||||||||
\(506\) | −34.9839 | −1.55522 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.745967 | −0.0330969 | ||||||||
\(509\) | 22.8070 | 1.01090 | 0.505452 | − | 0.862855i | \(-0.331326\pi\) | ||||
0.505452 | + | 0.862855i | \(0.331326\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.00806 | 0.132680 | ||||||||
\(515\) | −13.3810 | −0.589640 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.2520 | −0.714764 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 14.6190 | 0.641083 | ||||||||
\(521\) | 1.41421 | 0.0619578 | 0.0309789 | − | 0.999520i | \(-0.490138\pi\) | ||||
0.0309789 | + | 0.999520i | \(0.490138\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.2836 | 0.799484 | 0.399742 | − | 0.916628i | \(-0.369100\pi\) | ||||
0.399742 | + | 0.916628i | \(0.369100\pi\) | |||||||
\(524\) | 13.3452 | 0.582988 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.6190 | −0.768223 | ||||||||
\(527\) | 7.74597 | 0.337420 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 53.4919 | 2.32574 | ||||||||
\(530\) | −43.4814 | −1.88871 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −24.0000 | −1.03956 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.875328 | −0.0378437 | ||||||||
\(536\) | −6.87298 | −0.296868 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.03151 | −0.0875844 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −38.1109 | −1.63851 | −0.819257 | − | 0.573426i | \(-0.805614\pi\) | ||||
−0.819257 | + | 0.573426i | \(0.805614\pi\) | |||||||
\(542\) | 7.07107 | 0.303728 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.41421 | 0.0606339 | ||||||||
\(545\) | −58.1396 | −2.49043 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.9839 | −1.41029 | −0.705144 | − | 0.709064i | \(-0.749118\pi\) | ||||
−0.705144 | + | 0.709064i | \(0.749118\pi\) | |||||||
\(548\) | −15.4919 | −0.661783 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 27.4919 | 1.17226 | ||||||||
\(551\) | −7.07107 | −0.301238 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 14.3649 | 0.610307 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 19.8774 | 0.842989 | ||||||||
\(557\) | 26.6190 | 1.12788 | 0.563941 | − | 0.825815i | \(-0.309285\pi\) | ||||
0.563941 | + | 0.825815i | \(0.309285\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.78153 | −0.202237 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.74597 | 0.368926 | ||||||||
\(563\) | −21.6509 | −0.912475 | −0.456238 | − | 0.889858i | \(-0.650803\pi\) | ||||
−0.456238 | + | 0.889858i | \(0.650803\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.3452 | −0.561437 | ||||||||
\(566\) | 5.03956 | 0.211829 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.87298 | −0.414261 | ||||||||
\(569\) | −23.4919 | −0.984833 | −0.492417 | − | 0.870360i | \(-0.663886\pi\) | ||||
−0.492417 | + | 0.870360i | \(0.663886\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.4919 | 1.31790 | 0.658948 | − | 0.752188i | \(-0.271002\pi\) | ||||
0.658948 | + | 0.752188i | \(0.271002\pi\) | |||||||
\(572\) | −16.9706 | −0.709575 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −60.1109 | −2.50680 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.2213 | 1.00834 | 0.504172 | − | 0.863603i | \(-0.331798\pi\) | ||||
0.504172 | + | 0.863603i | \(0.331798\pi\) | |||||||
\(578\) | −15.0000 | −0.623918 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.88338 | −0.161249 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 50.4758 | 2.09049 | ||||||||
\(584\) | 4.42227 | 0.182995 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.796921 | −0.0329205 | ||||||||
\(587\) | 8.56369 | 0.353461 | 0.176731 | − | 0.984259i | \(-0.443448\pi\) | ||||
0.176731 | + | 0.984259i | \(0.443448\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −34.3649 | −1.41598 | ||||||||
\(590\) | 28.6190 | 1.17822 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.74597 | 0.236158 | ||||||||
\(593\) | 33.7615 | 1.38642 | 0.693209 | − | 0.720736i | \(-0.256196\pi\) | ||||
0.693209 | + | 0.720736i | \(0.256196\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −15.7460 | −0.644980 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 37.1060 | 1.51738 | ||||||||
\(599\) | −45.2379 | −1.84837 | −0.924185 | − | 0.381945i | \(-0.875255\pi\) | ||||
−0.924185 | + | 0.381945i | \(0.875255\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.78153 | −0.195043 | −0.0975213 | − | 0.995233i | \(-0.531091\pi\) | ||||
−0.0975213 | + | 0.995233i | \(0.531091\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 11.0000 | 0.447584 | ||||||||
\(605\) | −17.2286 | −0.700442 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.6904 | 1.08333 | 0.541666 | − | 0.840594i | \(-0.317794\pi\) | ||||
0.541666 | + | 0.840594i | \(0.317794\pi\) | |||||||
\(608\) | −6.27415 | −0.254450 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −21.6190 | −0.875326 | ||||||||
\(611\) | 17.2379 | 0.697371 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.6190 | 1.07513 | 0.537565 | − | 0.843223i | \(-0.319344\pi\) | ||||
0.537565 | + | 0.843223i | \(0.319344\pi\) | |||||||
\(614\) | 14.2205 | 0.573894 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.2540 | −0.493329 | −0.246664 | − | 0.969101i | \(-0.579335\pi\) | ||||
−0.246664 | + | 0.969101i | \(0.579335\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −37.9029 | −1.52345 | −0.761723 | − | 0.647902i | \(-0.775646\pi\) | ||||
−0.761723 | + | 0.647902i | \(0.775646\pi\) | |||||||
\(620\) | −18.8730 | −0.757957 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.41421 | −0.0567048 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.1270 | −0.485081 | ||||||||
\(626\) | 15.7360 | 0.628936 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11.9310 | 0.476099 | ||||||||
\(629\) | 8.12602 | 0.324006 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.38105 | −0.174407 | −0.0872034 | − | 0.996191i | \(-0.527793\pi\) | ||||
−0.0872034 | + | 0.996191i | \(0.527793\pi\) | |||||||
\(632\) | −1.87298 | −0.0745033 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 24.6190 | 0.977743 | ||||||||
\(635\) | 2.57039 | 0.102003 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.50807 | 0.178476 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.44572 | −0.136204 | ||||||||
\(641\) | 17.1109 | 0.675839 | 0.337920 | − | 0.941175i | \(-0.390277\pi\) | ||||
0.337920 | + | 0.941175i | \(0.390277\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.52413 | 0.138978 | 0.0694890 | − | 0.997583i | \(-0.477863\pi\) | ||||
0.0694890 | + | 0.997583i | \(0.477863\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.87298 | −0.349103 | ||||||||
\(647\) | −5.47723 | −0.215332 | −0.107666 | − | 0.994187i | \(-0.534338\pi\) | ||||
−0.107666 | + | 0.994187i | \(0.534338\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −33.2226 | −1.30410 | ||||||||
\(650\) | −29.1596 | −1.14373 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.0000 | 0.391630 | ||||||||
\(653\) | −14.5081 | −0.567745 | −0.283872 | − | 0.958862i | \(-0.591619\pi\) | ||||
−0.283872 | + | 0.958862i | \(0.591619\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −45.9839 | −1.79674 | ||||||||
\(656\) | 5.65685 | 0.220863 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.1270 | 1.13463 | 0.567314 | − | 0.823502i | \(-0.307983\pi\) | ||||
0.567314 | + | 0.823502i | \(0.307983\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −46.2086 | −1.79730 | −0.898652 | − | 0.438661i | \(-0.855453\pi\) | ||||
−0.898652 | + | 0.438661i | \(0.855453\pi\) | |||||||
\(662\) | 20.3649 | 0.791505 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.64880 | −0.102793 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.85685 | −0.381659 | ||||||||
\(668\) | 9.54024 | 0.369123 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 23.6824 | 0.914930 | ||||||||
\(671\) | 25.0966 | 0.968843 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.2379 | 0.548831 | 0.274415 | − | 0.961611i | \(-0.411516\pi\) | ||||
0.274415 | + | 0.961611i | \(0.411516\pi\) | |||||||
\(674\) | 15.7460 | 0.606512 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.00000 | 0.192308 | ||||||||
\(677\) | 12.7279 | 0.489174 | 0.244587 | − | 0.969627i | \(-0.421348\pi\) | ||||
0.244587 | + | 0.969627i | \(0.421348\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −4.87298 | −0.186870 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 21.9089 | 0.838935 | ||||||||
\(683\) | 7.74597 | 0.296391 | 0.148196 | − | 0.988958i | \(-0.452653\pi\) | ||||
0.148196 | + | 0.988958i | \(0.452653\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 53.3809 | 2.03958 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.12702 | 0.0429671 | ||||||||
\(689\) | −53.5377 | −2.03962 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.0490 | 0.648573 | 0.324287 | − | 0.945959i | \(-0.394876\pi\) | ||||
0.324287 | + | 0.945959i | \(0.394876\pi\) | |||||||
\(692\) | 12.7279 | 0.483843 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.74597 | 0.294033 | ||||||||
\(695\) | −68.4919 | −2.59805 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.00000 | 0.303022 | ||||||||
\(698\) | −16.4317 | −0.621948 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.2540 | −0.613906 | −0.306953 | − | 0.951725i | \(-0.599310\pi\) | ||||
−0.306953 | + | 0.951725i | \(0.599310\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −36.0510 | −1.35969 | ||||||||
\(704\) | 4.00000 | 0.150756 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.88338 | 0.146153 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −52.7298 | −1.98031 | −0.990155 | − | 0.139974i | \(-0.955298\pi\) | ||||
−0.990155 | + | 0.139974i | \(0.955298\pi\) | |||||||
\(710\) | 34.0195 | 1.27673 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.07107 | 0.264999 | ||||||||
\(713\) | −47.9036 | −1.79401 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 58.4758 | 2.18687 | ||||||||
\(716\) | −6.87298 | −0.256855 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 18.2379 | 0.680632 | ||||||||
\(719\) | −23.5027 | −0.876504 | −0.438252 | − | 0.898852i | \(-0.644402\pi\) | ||||
−0.438252 | + | 0.898852i | \(0.644402\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 20.3649 | 0.757904 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −13.3452 | −0.495971 | ||||||||
\(725\) | 7.74597 | 0.287678 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.36731 | 0.124887 | 0.0624434 | − | 0.998049i | \(-0.480111\pi\) | ||||
0.0624434 | + | 0.998049i | \(0.480111\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −15.2379 | −0.563980 | ||||||||
\(731\) | 1.59384 | 0.0589504 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −37.0276 | −1.36765 | −0.683823 | − | 0.729648i | \(-0.739684\pi\) | ||||
−0.683823 | + | 0.729648i | \(0.739684\pi\) | |||||||
\(734\) | 6.89144 | 0.254368 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.74597 | −0.322381 | ||||||||
\(737\) | −27.4919 | −1.01268 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.0000 | −1.10357 | −0.551784 | − | 0.833987i | \(-0.686053\pi\) | ||||
−0.551784 | + | 0.833987i | \(0.686053\pi\) | |||||||
\(740\) | −19.7990 | −0.727825 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.2540 | −0.449557 | −0.224778 | − | 0.974410i | \(-0.572166\pi\) | ||||
−0.224778 | + | 0.974410i | \(0.572166\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 54.2562 | 1.98779 | ||||||||
\(746\) | −1.12702 | −0.0412630 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.65685 | 0.206835 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.0000 | −0.474377 | −0.237188 | − | 0.971464i | \(-0.576226\pi\) | ||||
−0.237188 | + | 0.971464i | \(0.576226\pi\) | |||||||
\(752\) | −4.06301 | −0.148163 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.78153 | −0.174133 | ||||||||
\(755\) | −37.9029 | −1.37943 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.2379 | 1.13536 | 0.567680 | − | 0.823249i | \(-0.307841\pi\) | ||||
0.567680 | + | 0.823249i | \(0.307841\pi\) | |||||||
\(758\) | 26.3649 | 0.957617 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 21.6190 | 0.784202 | ||||||||
\(761\) | −30.5738 | −1.10830 | −0.554150 | − | 0.832417i | \(-0.686957\pi\) | ||||
−0.554150 | + | 0.832417i | \(0.686957\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −6.12702 | −0.221668 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12.9076 | −0.466369 | ||||||||
\(767\) | 35.2379 | 1.27237 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.23458 | −0.0445203 | −0.0222601 | − | 0.999752i | \(-0.507086\pi\) | ||||
−0.0222601 | + | 0.999752i | \(0.507086\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 23.8730 | 0.859207 | ||||||||
\(773\) | −2.03151 | −0.0730682 | −0.0365341 | − | 0.999332i | \(-0.511632\pi\) | ||||
−0.0365341 | + | 0.999332i | \(0.511632\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 37.6449 | 1.35224 | ||||||||
\(776\) | 15.0175 | 0.539096 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.1270 | 0.470626 | ||||||||
\(779\) | −35.4919 | −1.27163 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −39.4919 | −1.41313 | ||||||||
\(782\) | −12.3687 | −0.442303 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −41.1109 | −1.46731 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.3687 | 0.440895 | 0.220448 | − | 0.975399i | \(-0.429248\pi\) | ||||
0.220448 | + | 0.975399i | \(0.429248\pi\) | |||||||
\(788\) | 16.6190 | 0.592026 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.45378 | 0.229615 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −26.6190 | −0.945267 | ||||||||
\(794\) | 7.07107 | 0.250943 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.1890 | 0.432029 | ||||||||
\(797\) | −20.5959 | −0.729545 | −0.364772 | − | 0.931097i | \(-0.618853\pi\) | ||||
−0.364772 | + | 0.931097i | \(0.618853\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.74597 | −0.203278 | ||||||||
\(800\) | 6.87298 | 0.242997 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.87298 | −0.136760 | ||||||||
\(803\) | 17.6891 | 0.624234 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −23.2379 | −0.818520 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −13.3452 | −0.469483 | ||||||||
\(809\) | 46.7298 | 1.64293 | 0.821467 | − | 0.570256i | \(-0.193156\pi\) | ||||
0.821467 | + | 0.570256i | \(0.193156\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.00806 | −0.105627 | −0.0528136 | − | 0.998604i | \(-0.516819\pi\) | ||||
−0.0528136 | + | 0.998604i | \(0.516819\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 22.9839 | 0.805584 | ||||||||
\(815\) | −34.4572 | −1.20698 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.07107 | −0.247385 | ||||||||
\(818\) | 23.1435 | 0.809193 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −19.4919 | −0.680688 | ||||||||
\(821\) | −9.49193 | −0.331271 | −0.165635 | − | 0.986187i | \(-0.552967\pi\) | ||||
−0.165635 | + | 0.986187i | \(0.552967\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.25403 | −0.218002 | −0.109001 | − | 0.994042i | \(-0.534765\pi\) | ||||
−0.109001 | + | 0.994042i | \(0.534765\pi\) | |||||||
\(824\) | 3.88338 | 0.135284 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.8730 | 1.69948 | 0.849740 | − | 0.527202i | \(-0.176759\pi\) | ||||
0.849740 | + | 0.527202i | \(0.176759\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.6180 | −0.368779 | −0.184389 | − | 0.982853i | \(-0.559031\pi\) | ||||
−0.184389 | + | 0.982853i | \(0.559031\pi\) | |||||||
\(830\) | 9.12702 | 0.316803 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.24264 | −0.147087 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −32.8730 | −1.13762 | ||||||||
\(836\) | −25.0966 | −0.867984 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −31.3707 | −1.08368 | ||||||||
\(839\) | 25.7923 | 0.890449 | 0.445224 | − | 0.895419i | \(-0.353124\pi\) | ||||
0.445224 | + | 0.895419i | \(0.353124\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.7298 | −0.956201 | ||||||||
\(842\) | −12.8730 | −0.443632 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 20.6190 | 0.709734 | ||||||||
\(845\) | −17.2286 | −0.592682 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 12.6190 | 0.433337 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 9.71987 | 0.333389 | ||||||||
\(851\) | −50.2540 | −1.72269 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.1267 | −0.620648 | −0.310324 | − | 0.950631i | \(-0.600438\pi\) | ||||
−0.310324 | + | 0.950631i | \(0.600438\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.254033 | 0.00868268 | ||||||||
\(857\) | 25.8151 | 0.881827 | 0.440914 | − | 0.897550i | \(-0.354655\pi\) | ||||
0.440914 | + | 0.897550i | \(0.354655\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.5738 | 1.04317 | 0.521583 | − | 0.853201i | \(-0.325342\pi\) | ||||
0.521583 | + | 0.853201i | \(0.325342\pi\) | |||||||
\(860\) | −3.88338 | −0.132422 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −21.4919 | −0.732018 | ||||||||
\(863\) | −43.8730 | −1.49345 | −0.746727 | − | 0.665131i | \(-0.768376\pi\) | ||||
−0.746727 | + | 0.665131i | \(0.768376\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −43.8569 | −1.49118 | ||||||||
\(866\) | −29.6985 | −1.00920 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.49193 | −0.254146 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29.1596 | 0.988035 | ||||||||
\(872\) | 16.8730 | 0.571391 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 54.8735 | 1.85612 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.1270 | 1.05108 | 0.525542 | − | 0.850767i | \(-0.323862\pi\) | ||||
0.525542 | + | 0.850767i | \(0.323862\pi\) | |||||||
\(878\) | −10.9545 | −0.369695 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −13.7829 | −0.464621 | ||||||||
\(881\) | 26.6904 | 0.899223 | 0.449612 | − | 0.893224i | \(-0.351562\pi\) | ||||
0.449612 | + | 0.893224i | \(0.351562\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.4919 | 1.19440 | 0.597199 | − | 0.802093i | \(-0.296280\pi\) | ||||
0.597199 | + | 0.802093i | \(0.296280\pi\) | |||||||
\(884\) | −6.00000 | −0.201802 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14.3649 | −0.482599 | ||||||||
\(887\) | 7.76677 | 0.260783 | 0.130391 | − | 0.991463i | \(-0.458377\pi\) | ||||
0.130391 | + | 0.991463i | \(0.458377\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −24.3649 | −0.816714 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −22.4478 | −0.751608 | ||||||||
\(893\) | 25.4919 | 0.853055 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23.6824 | 0.791614 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.00000 | 0.300334 | ||||||||
\(899\) | 6.17292 | 0.205879 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.8459 | 0.594533 | ||||||||
\(902\) | 22.6274 | 0.753411 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.87298 | 0.128814 | ||||||||
\(905\) | 45.9839 | 1.52856 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.6190 | 0.618232 | 0.309116 | − | 0.951024i | \(-0.399967\pi\) | ||||
0.309116 | + | 0.951024i | \(0.399967\pi\) | |||||||
\(908\) | 10.3372 | 0.343051 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.7460 | −1.28371 | −0.641856 | − | 0.766826i | \(-0.721835\pi\) | ||||
−0.641856 | + | 0.766826i | \(0.721835\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.5952 | −0.350650 | ||||||||
\(914\) | 26.1270 | 0.864205 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.3452 | 0.440938 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.635083 | −0.0209495 | −0.0104747 | − | 0.999945i | \(-0.503334\pi\) | ||||
−0.0104747 | + | 0.999945i | \(0.503334\pi\) | |||||||
\(920\) | 30.1361 | 0.993559 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 28.3627 | 0.934075 | ||||||||
\(923\) | 41.8875 | 1.37874 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 39.4919 | 1.29849 | ||||||||
\(926\) | −1.61895 | −0.0532020 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.12702 | 0.0369961 | ||||||||
\(929\) | −54.4358 | −1.78598 | −0.892991 | − | 0.450075i | \(-0.851397\pi\) | ||||
−0.892991 | + | 0.450075i | \(0.851397\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 7.25403 | 0.237614 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.19574 | 0.202731 | ||||||||
\(935\) | −19.4919 | −0.637454 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −45.2320 | −1.47767 | −0.738833 | − | 0.673889i | \(-0.764623\pi\) | ||||
−0.738833 | + | 0.673889i | \(0.764623\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 14.0000 | 0.456630 | ||||||||
\(941\) | 25.7139 | 0.838249 | 0.419124 | − | 0.907929i | \(-0.362337\pi\) | ||||
0.419124 | + | 0.907929i | \(0.362337\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −49.4747 | −1.61112 | ||||||||
\(944\) | −8.30565 | −0.270326 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.50807 | 0.146570 | ||||||||
\(947\) | −57.6028 | −1.87184 | −0.935920 | − | 0.352213i | \(-0.885429\pi\) | ||||
−0.935920 | + | 0.352213i | \(0.885429\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.7621 | −0.609044 | ||||||||
\(950\) | −43.1221 | −1.39907 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −59.4919 | −1.92713 | −0.963566 | − | 0.267469i | \(-0.913813\pi\) | ||||
−0.963566 | + | 0.267469i | \(0.913813\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.1120 | 0.683168 | ||||||||
\(956\) | −15.0000 | −0.485135 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.88338 | 0.125466 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.00000 | −0.0322581 | ||||||||
\(962\) | −24.3781 | −0.785981 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −23.6824 | −0.762758 | ||||||||
\(965\) | −82.2596 | −2.64803 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 60.4919 | 1.94529 | 0.972645 | − | 0.232298i | \(-0.0746244\pi\) | ||||
0.972645 | + | 0.232298i | \(0.0746244\pi\) | |||||||
\(968\) | 5.00000 | 0.160706 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −51.7460 | −1.66146 | ||||||||
\(971\) | 1.49262 | 0.0479005 | 0.0239502 | − | 0.999713i | \(-0.492376\pi\) | ||||
0.0239502 | + | 0.999713i | \(0.492376\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −0.491933 | −0.0157626 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.27415 | 0.200831 | ||||||||
\(977\) | 45.4919 | 1.45542 | 0.727708 | − | 0.685887i | \(-0.240586\pi\) | ||||
0.727708 | + | 0.685887i | \(0.240586\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28.2843 | 0.903969 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.74597 | 0.0557160 | ||||||||
\(983\) | −9.89949 | −0.315745 | −0.157872 | − | 0.987460i | \(-0.550463\pi\) | ||||
−0.157872 | + | 0.987460i | \(0.550463\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −57.2642 | −1.82459 | ||||||||
\(986\) | 1.59384 | 0.0507583 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 26.6190 | 0.846862 | ||||||||
\(989\) | −9.85685 | −0.313430 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.7460 | −0.373123 | −0.186561 | − | 0.982443i | \(-0.559734\pi\) | ||||
−0.186561 | + | 0.982443i | \(0.559734\pi\) | |||||||
\(992\) | 5.47723 | 0.173902 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −42.0000 | −1.33149 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −27.1281 | −0.859155 | −0.429578 | − | 0.903030i | \(-0.641338\pi\) | ||||
−0.429578 | + | 0.903030i | \(0.641338\pi\) | |||||||
\(998\) | −29.7460 | −0.941592 | ||||||||
\(999\) | 0 | 0 |
(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 | 7938.2.a.cu.1.1 | 4 | ||
3.2 | odd | 2 | 7938.2.a.cd.1.4 | 4 | |||
7.6 | odd | 2 | inner | 7938.2.a.cu.1.4 | 4 | ||
9.2 | odd | 6 | 2646.2.f.s.1765.1 | 8 | |||
9.4 | even | 3 | 882.2.f.p.295.3 | yes | 8 | ||
9.5 | odd | 6 | 2646.2.f.s.883.1 | 8 | |||
9.7 | even | 3 | 882.2.f.p.589.4 | yes | 8 | ||
21.20 | even | 2 | 7938.2.a.cd.1.1 | 4 | |||
63.2 | odd | 6 | 2646.2.h.s.361.4 | 8 | |||
63.4 | even | 3 | 882.2.h.r.79.1 | 8 | |||
63.5 | even | 6 | 2646.2.e.r.2125.4 | 8 | |||
63.11 | odd | 6 | 2646.2.e.r.1549.1 | 8 | |||
63.13 | odd | 6 | 882.2.f.p.295.2 | ✓ | 8 | ||
63.16 | even | 3 | 882.2.h.r.67.1 | 8 | |||
63.20 | even | 6 | 2646.2.f.s.1765.4 | 8 | |||
63.23 | odd | 6 | 2646.2.e.r.2125.1 | 8 | |||
63.25 | even | 3 | 882.2.e.t.373.3 | 8 | |||
63.31 | odd | 6 | 882.2.h.r.79.4 | 8 | |||
63.32 | odd | 6 | 2646.2.h.s.667.4 | 8 | |||
63.34 | odd | 6 | 882.2.f.p.589.1 | yes | 8 | ||
63.38 | even | 6 | 2646.2.e.r.1549.4 | 8 | |||
63.40 | odd | 6 | 882.2.e.t.655.2 | 8 | |||
63.41 | even | 6 | 2646.2.f.s.883.4 | 8 | |||
63.47 | even | 6 | 2646.2.h.s.361.1 | 8 | |||
63.52 | odd | 6 | 882.2.e.t.373.2 | 8 | |||
63.58 | even | 3 | 882.2.e.t.655.3 | 8 | |||
63.59 | even | 6 | 2646.2.h.s.667.1 | 8 | |||
63.61 | odd | 6 | 882.2.h.r.67.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
882.2.e.t.373.2 | 8 | 63.52 | odd | 6 | |||
882.2.e.t.373.3 | 8 | 63.25 | even | 3 | |||
882.2.e.t.655.2 | 8 | 63.40 | odd | 6 | |||
882.2.e.t.655.3 | 8 | 63.58 | even | 3 | |||
882.2.f.p.295.2 | ✓ | 8 | 63.13 | odd | 6 | ||
882.2.f.p.295.3 | yes | 8 | 9.4 | even | 3 | ||
882.2.f.p.589.1 | yes | 8 | 63.34 | odd | 6 | ||
882.2.f.p.589.4 | yes | 8 | 9.7 | even | 3 | ||
882.2.h.r.67.1 | 8 | 63.16 | even | 3 | |||
882.2.h.r.67.4 | 8 | 63.61 | odd | 6 | |||
882.2.h.r.79.1 | 8 | 63.4 | even | 3 | |||
882.2.h.r.79.4 | 8 | 63.31 | odd | 6 | |||
2646.2.e.r.1549.1 | 8 | 63.11 | odd | 6 | |||
2646.2.e.r.1549.4 | 8 | 63.38 | even | 6 | |||
2646.2.e.r.2125.1 | 8 | 63.23 | odd | 6 | |||
2646.2.e.r.2125.4 | 8 | 63.5 | even | 6 | |||
2646.2.f.s.883.1 | 8 | 9.5 | odd | 6 | |||
2646.2.f.s.883.4 | 8 | 63.41 | even | 6 | |||
2646.2.f.s.1765.1 | 8 | 9.2 | odd | 6 | |||
2646.2.f.s.1765.4 | 8 | 63.20 | even | 6 | |||
2646.2.h.s.361.1 | 8 | 63.47 | even | 6 | |||
2646.2.h.s.361.4 | 8 | 63.2 | odd | 6 | |||
2646.2.h.s.667.1 | 8 | 63.59 | even | 6 | |||
2646.2.h.s.667.4 | 8 | 63.32 | odd | 6 | |||
7938.2.a.cd.1.1 | 4 | 21.20 | even | 2 | |||
7938.2.a.cd.1.4 | 4 | 3.2 | odd | 2 | |||
7938.2.a.cu.1.1 | 4 | 1.1 | even | 1 | trivial | ||
7938.2.a.cu.1.4 | 4 | 7.6 | odd | 2 | inner |