Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3192,2,Mod(1,3192)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3192, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("3192.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3192 = 2^{3} \cdot 3 \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3192.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: | \(25.4882483252\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.316.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 4x + 2 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.81361\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3192.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.62721 | −1.69667 | −0.848334 | − | 0.529461i | \(-0.822394\pi\) | ||||
−0.848334 | + | 0.529461i | \(0.822394\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.57834 | −0.715102 | −0.357551 | − | 0.933894i | \(-0.616388\pi\) | ||||
−0.357551 | + | 0.933894i | \(0.616388\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.20555 | 1.50507 | 0.752533 | − | 0.658554i | \(-0.228832\pi\) | ||||
0.752533 | + | 0.658554i | \(0.228832\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.83276 | 1.63324 | 0.816622 | − | 0.577173i | \(-0.195844\pi\) | ||||
0.816622 | + | 0.577173i | \(0.195844\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −1.00000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.42166 | −0.635387 | −0.317693 | − | 0.948193i | \(-0.602908\pi\) | ||||
−0.317693 | + | 0.948193i | \(0.602908\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.04888 | 0.906805 | 0.453402 | − | 0.891306i | \(-0.350210\pi\) | ||||
0.453402 | + | 0.891306i | \(0.350210\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.62721 | −0.979572 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.04888 | −1.15883 | −0.579414 | − | 0.815033i | \(-0.696719\pi\) | ||||
−0.579414 | + | 0.815033i | \(0.696719\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.57834 | −0.412864 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.25443 | −1.44530 | −0.722649 | − | 0.691215i | \(-0.757076\pi\) | ||||
−0.722649 | + | 0.691215i | \(0.757076\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.25443 | 1.10629 | 0.553145 | − | 0.833085i | \(-0.313428\pi\) | ||||
0.553145 | + | 0.833085i | \(0.313428\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.62721 | 0.529083 | 0.264542 | − | 0.964374i | \(-0.414779\pi\) | ||||
0.264542 | + | 0.964374i | \(0.414779\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.20555 | 0.868951 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.57834 | −1.17833 | −0.589163 | − | 0.808014i | \(-0.700542\pi\) | ||||
−0.589163 | + | 0.808014i | \(0.700542\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.41110 | −1.09503 | −0.547516 | − | 0.836795i | \(-0.684426\pi\) | ||||
−0.547516 | + | 0.836795i | \(0.684426\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.4111 | −1.84515 | −0.922576 | − | 0.385815i | \(-0.873920\pi\) | ||||
−0.922576 | + | 0.385815i | \(0.873920\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.8816 | −1.57374 | −0.786871 | − | 0.617117i | \(-0.788300\pi\) | ||||
−0.786871 | + | 0.617117i | \(0.788300\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.83276 | 0.942954 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.8328 | −1.64165 | −0.820823 | − | 0.571182i | \(-0.806485\pi\) | ||||
−0.820823 | + | 0.571182i | \(0.806485\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.25443 | 1.08315 | 0.541574 | − | 0.840653i | \(-0.317828\pi\) | ||||
0.541574 | + | 0.840653i | \(0.317828\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.00000 | −0.577350 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.62721 | 0.641280 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.67609 | −0.751119 | −0.375559 | − | 0.926798i | \(-0.622549\pi\) | ||||
−0.375559 | + | 0.926798i | \(0.622549\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.6761 | −1.39138 | −0.695691 | − | 0.718341i | \(-0.744902\pi\) | ||||
−0.695691 | + | 0.718341i | \(0.744902\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.42166 | −0.366841 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.15667 | −0.758606 | −0.379303 | − | 0.925273i | \(-0.623836\pi\) | ||||
−0.379303 | + | 0.925273i | \(0.623836\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.57834 | 0.270283 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.04888 | 0.523544 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.78389 | 0.485730 | 0.242865 | − | 0.970060i | \(-0.421913\pi\) | ||||
0.242865 | + | 0.970060i | \(0.421913\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.62721 | −0.565556 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.00000 | −0.796030 | −0.398015 | − | 0.917379i | \(-0.630301\pi\) | ||||
−0.398015 | + | 0.917379i | \(0.630301\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.45998 | 0.932119 | 0.466060 | − | 0.884753i | \(-0.345673\pi\) | ||||
0.466060 | + | 0.884753i | \(0.345673\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.9894 | −1.06239 | −0.531195 | − | 0.847250i | \(-0.678257\pi\) | ||||
−0.531195 | + | 0.847250i | \(0.678257\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.6167 | −1.59159 | −0.795793 | − | 0.605568i | \(-0.792946\pi\) | ||||
−0.795793 | + | 0.605568i | \(0.792946\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.04888 | −0.669050 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.6761 | −1.00432 | −0.502161 | − | 0.864774i | \(-0.667462\pi\) | ||||
−0.502161 | + | 0.864774i | \(0.667462\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.57834 | −0.238367 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.20555 | −0.568862 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.6655 | 1.87868 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.25443 | −0.834443 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.8328 | 1.04999 | 0.524994 | − | 0.851106i | \(-0.324068\pi\) | ||||
0.524994 | + | 0.851106i | \(0.324068\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.25443 | 0.638717 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.2439 | 1.59397 | 0.796987 | − | 0.603997i | \(-0.206426\pi\) | ||||
0.796987 | + | 0.603997i | \(0.206426\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.00000 | 0.0867110 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.66553 | 0.825782 | 0.412891 | − | 0.910781i | \(-0.364519\pi\) | ||||
0.412891 | + | 0.910781i | \(0.364519\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.25443 | 0.276037 | 0.138018 | − | 0.990430i | \(-0.455927\pi\) | ||||
0.138018 | + | 0.990430i | \(0.455927\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.62721 | 0.305466 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.5089 | 1.21329 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.4600 | −1.26653 | −0.633265 | − | 0.773935i | \(-0.718286\pi\) | ||||
−0.633265 | + | 0.773935i | \(0.718286\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.9894 | 1.05707 | 0.528533 | − | 0.848913i | \(-0.322742\pi\) | ||||
0.528533 | + | 0.848913i | \(0.322742\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.20555 | 0.501689 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.15667 | 0.571165 | 0.285582 | − | 0.958354i | \(-0.407813\pi\) | ||||
0.285582 | + | 0.958354i | \(0.407813\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.57834 | −0.680306 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.83276 | −0.617308 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.2544 | 1.19482 | 0.597409 | − | 0.801936i | \(-0.296197\pi\) | ||||
0.597409 | + | 0.801936i | \(0.296197\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.25443 | −0.561364 | −0.280682 | − | 0.959801i | \(-0.590561\pi\) | ||||
−0.280682 | + | 0.959801i | \(0.590561\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.35218 | −0.488629 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.66553 | 0.430742 | 0.215371 | − | 0.976532i | \(-0.430904\pi\) | ||||
0.215371 | + | 0.976532i | \(0.430904\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.00000 | 0.377964 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.41110 | −0.632217 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.6761 | 1.24643 | 0.623215 | − | 0.782051i | \(-0.285826\pi\) | ||||
0.623215 | + | 0.782051i | \(0.285826\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.57834 | −0.488964 | −0.244482 | − | 0.969654i | \(-0.578618\pi\) | ||||
−0.244482 | + | 0.969654i | \(0.578618\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.4111 | −1.06530 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −34.9200 | −2.55360 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.67609 | −0.483065 | −0.241532 | − | 0.970393i | \(-0.577650\pi\) | ||||
−0.241532 | + | 0.970393i | \(0.577650\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.0978 | 0.870815 | 0.435408 | − | 0.900233i | \(-0.356604\pi\) | ||||
0.435408 | + | 0.900233i | \(0.356604\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.7144 | 0.763370 | 0.381685 | − | 0.924293i | \(-0.375344\pi\) | ||||
0.381685 | + | 0.924293i | \(0.375344\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.6655 | −1.39405 | −0.697026 | − | 0.717046i | \(-0.745494\pi\) | ||||
−0.697026 | + | 0.717046i | \(0.745494\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.8816 | −0.908601 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.42166 | 0.240154 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.83276 | 0.544415 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.62721 | 0.389242 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.3728 | 0.714092 | 0.357046 | − | 0.934087i | \(-0.383784\pi\) | ||||
0.357046 | + | 0.934087i | \(0.383784\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.8328 | −0.947805 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.04888 | −0.342740 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.25443 | 0.625356 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.0000 | −1.07628 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.51890 | −0.570468 | −0.285234 | − | 0.958458i | \(-0.592071\pi\) | ||||
−0.285234 | + | 0.958458i | \(0.592071\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.00000 | −0.333333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.2544 | 1.27796 | 0.638981 | − | 0.769223i | \(-0.279356\pi\) | ||||
0.638981 | + | 0.769223i | \(0.279356\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.15667 | 0.208599 | 0.104299 | − | 0.994546i | \(-0.466740\pi\) | ||||
0.104299 | + | 0.994546i | \(0.466740\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.62721 | 0.370243 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.4111 | −0.944103 | −0.472051 | − | 0.881571i | \(-0.656486\pi\) | ||||
−0.472051 | + | 0.881571i | \(0.656486\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.67609 | −0.433659 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.57834 | 0.554886 | 0.277443 | − | 0.960742i | \(-0.410513\pi\) | ||||
0.277443 | + | 0.960742i | \(0.410513\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.21611 | 0.464831 | 0.232415 | − | 0.972617i | \(-0.425337\pi\) | ||||
0.232415 | + | 0.972617i | \(0.425337\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.57834 | 0.164056 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.6761 | −0.803314 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.2439 | 1.15154 | 0.575771 | − | 0.817611i | \(-0.304702\pi\) | ||||
0.575771 | + | 0.817611i | \(0.304702\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −44.0766 | −2.77107 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.25443 | 0.0782489 | 0.0391245 | − | 0.999234i | \(-0.487543\pi\) | ||||
0.0391245 | + | 0.999234i | \(0.487543\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.04888 | 0.437996 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.42166 | −0.211796 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.67609 | −0.165015 | −0.0825074 | − | 0.996590i | \(-0.526293\pi\) | ||||
−0.0825074 | + | 0.996590i | \(0.526293\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.15667 | −0.437981 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.4111 | −1.12254 | −0.561272 | − | 0.827631i | \(-0.689688\pi\) | ||||
−0.561272 | + | 0.827631i | \(0.689688\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | −0.485965 | −0.242983 | − | 0.970031i | \(-0.578126\pi\) | ||||
−0.242983 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.57834 | 0.156048 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 28.1361 | 1.69667 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.6655 | 1.54209 | 0.771046 | − | 0.636779i | \(-0.219734\pi\) | ||||
0.771046 | + | 0.636779i | \(0.219734\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.04888 | 0.302268 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28.9894 | −1.72936 | −0.864682 | − | 0.502319i | \(-0.832480\pi\) | ||||
−0.864682 | + | 0.502319i | \(0.832480\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.5678 | 1.28207 | 0.641036 | − | 0.767511i | \(-0.278505\pi\) | ||||
0.641036 | + | 0.767511i | \(0.278505\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.25443 | 0.546271 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.5089 | 1.26523 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.78389 | 0.280436 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.9411 | 0.872867 | 0.436434 | − | 0.899736i | \(-0.356241\pi\) | ||||
0.436434 | + | 0.899736i | \(0.356241\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.62721 | −0.326524 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −20.1955 | −1.16794 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.25443 | −0.418138 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.00000 | −0.459588 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.6655 | −1.12237 | −0.561185 | − | 0.827690i | \(-0.689655\pi\) | ||||
−0.561185 | + | 0.827690i | \(0.689655\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.45998 | 0.538159 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.1361 | −1.25522 | −0.627611 | − | 0.778527i | \(-0.715967\pi\) | ||||
−0.627611 | + | 0.778527i | \(0.715967\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.0977518 | −0.00552526 | −0.00276263 | − | 0.999996i | \(-0.500879\pi\) | ||||
−0.00276263 | + | 0.999996i | \(0.500879\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.7738 | −0.942113 | −0.471056 | − | 0.882103i | \(-0.656127\pi\) | ||||
−0.471056 | + | 0.882103i | \(0.656127\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.2544 | 1.07804 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.9894 | −0.613371 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.20555 | −0.345286 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.8917 | 0.715102 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.6167 | −0.918903 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.62721 | −0.199975 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.05944 | 0.223127 | 0.111563 | − | 0.993757i | \(-0.464414\pi\) | ||||
0.111563 | + | 0.993757i | \(0.464414\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.04888 | −0.386276 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.0978 | 0.876900 | 0.438450 | − | 0.898755i | \(-0.355528\pi\) | ||||
0.438450 | + | 0.898755i | \(0.355528\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.6761 | −0.579846 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −28.4111 | −1.53855 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 30.9794 | 1.66306 | 0.831530 | − | 0.555479i | \(-0.187465\pi\) | ||||
0.831530 | + | 0.555479i | \(0.187465\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.843326 | −0.0451422 | −0.0225711 | − | 0.999745i | \(-0.507185\pi\) | ||||
−0.0225711 | + | 0.999745i | \(0.507185\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.57834 | −0.137621 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.1078 | 0.644433 | 0.322217 | − | 0.946666i | \(-0.395572\pi\) | ||||
0.322217 | + | 0.946666i | \(0.395572\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.20555 | −0.328433 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25.9305 | −1.36856 | −0.684280 | − | 0.729219i | \(-0.739883\pi\) | ||||
−0.684280 | + | 0.729219i | \(0.739883\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 20.6655 | 1.08466 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −35.6655 | −1.86173 | −0.930863 | − | 0.365369i | \(-0.880943\pi\) | ||||
−0.930863 | + | 0.365369i | \(0.880943\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.25443 | −0.481766 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.57834 | 0.445365 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.7144 | 0.968995 | 0.484498 | − | 0.874793i | \(-0.339002\pi\) | ||||
0.484498 | + | 0.874793i | \(0.339002\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.82220 | 0.454366 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.8816 | 1.89448 | 0.947241 | − | 0.320521i | \(-0.103858\pi\) | ||||
0.947241 | + | 0.320521i | \(0.103858\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.8328 | 0.606211 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.6655 | 1.41364 | 0.706821 | − | 0.707392i | \(-0.250129\pi\) | ||||
0.706821 | + | 0.707392i | \(0.250129\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.25443 | 0.368763 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.5189 | 0.533329 | 0.266665 | − | 0.963789i | \(-0.414078\pi\) | ||||
0.266665 | + | 0.963789i | \(0.414078\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 48.6066 | 2.45814 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.2439 | 0.920281 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.0766 | 1.30875 | 0.654374 | − | 0.756171i | \(-0.272932\pi\) | ||||
0.654374 | + | 0.756171i | \(0.272932\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.00000 | 0.0500626 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −31.4983 | −1.57295 | −0.786475 | − | 0.617622i | \(-0.788096\pi\) | ||||
−0.786475 | + | 0.617622i | \(0.788096\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.0177 | −0.648458 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 39.6655 | 1.96615 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.3139 | 0.658328 | 0.329164 | − | 0.944273i | \(-0.393233\pi\) | ||||
0.329164 | + | 0.944273i | \(0.393233\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.66553 | 0.476765 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.41110 | 0.413883 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.25443 | 0.159370 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.3416 | −0.993753 | −0.496876 | − | 0.867821i | \(-0.665520\pi\) | ||||
−0.496876 | + | 0.867821i | \(0.665520\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.87108 | 0.383613 | 0.191806 | − | 0.981433i | \(-0.438565\pi\) | ||||
0.191806 | + | 0.981433i | \(0.438565\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.62721 | 0.176361 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −31.0278 | −1.50507 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.4111 | 0.697402 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 14.5089 | 0.700494 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.48059 | 0.215822 | 0.107911 | − | 0.994161i | \(-0.465584\pi\) | ||||
0.107911 | + | 0.994161i | \(0.465584\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.157190 | 0.00755409 | 0.00377705 | − | 0.999993i | \(-0.498798\pi\) | ||||
0.00377705 | + | 0.999993i | \(0.498798\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.83276 | −0.374692 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.4600 | −1.21514 | −0.607569 | − | 0.794267i | \(-0.707855\pi\) | ||||
−0.607569 | + | 0.794267i | \(0.707855\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −27.6061 | −1.31160 | −0.655802 | − | 0.754933i | \(-0.727670\pi\) | ||||
−0.655802 | + | 0.754933i | \(0.727670\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.4600 | −0.731232 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −39.8328 | −1.87982 | −0.939912 | − | 0.341416i | \(-0.889093\pi\) | ||||
−0.939912 | + | 0.341416i | \(0.889093\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 52.0766 | 2.45219 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.9894 | 0.610297 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.3311 | −1.18494 | −0.592468 | − | 0.805594i | \(-0.701846\pi\) | ||||
−0.592468 | + | 0.805594i | \(0.701846\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.20555 | 0.289650 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.41110 | 0.205445 | 0.102723 | − | 0.994710i | \(-0.467245\pi\) | ||||
0.102723 | + | 0.994710i | \(0.467245\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.49115 | 0.0692995 | 0.0346498 | − | 0.999400i | \(-0.488968\pi\) | ||||
0.0346498 | + | 0.999400i | \(0.488968\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.67609 | 0.216384 | 0.108192 | − | 0.994130i | \(-0.465494\pi\) | ||||
0.108192 | + | 0.994130i | \(0.465494\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.8816 | 0.594819 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.15667 | 0.329762 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −40.8222 | −1.87701 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.00000 | 0.229416 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.57834 | −0.392775 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.3139 | 0.608326 | 0.304163 | − | 0.952620i | \(-0.401623\pi\) | ||||
0.304163 | + | 0.952620i | \(0.401623\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.1744 | 0.828680 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.83276 | −0.356403 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.08719 | 0.139894 | 0.0699469 | − | 0.997551i | \(-0.477717\pi\) | ||||
0.0699469 | + | 0.997551i | \(0.477717\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 15.2544 | 0.689829 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.88164 | 0.220305 | 0.110153 | − | 0.993915i | \(-0.464866\pi\) | ||||
0.110153 | + | 0.993915i | \(0.464866\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21.2333 | −0.956300 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.8328 | 0.620484 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.94108 | −0.221193 | −0.110597 | − | 0.993865i | \(-0.535276\pi\) | ||||
−0.110597 | + | 0.993865i | \(0.535276\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.25443 | −0.324104 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.1361 | −0.986998 | −0.493499 | − | 0.869746i | \(-0.664282\pi\) | ||||
−0.493499 | + | 0.869746i | \(0.664282\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.35218 | −0.282110 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −38.6066 | −1.71121 | −0.855604 | − | 0.517631i | \(-0.826814\pi\) | ||||
−0.855604 | + | 0.517631i | \(0.826814\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.25443 | −0.409392 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.00000 | −0.0441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.4111 | −0.897679 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.66553 | 0.248689 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.0177 | 1.18367 | 0.591834 | − | 0.806060i | \(-0.298404\pi\) | ||||
0.591834 | + | 0.806060i | \(0.298404\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −37.9789 | −1.66070 | −0.830350 | − | 0.557242i | \(-0.811860\pi\) | ||||
−0.830350 | + | 0.557242i | \(0.811860\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.00000 | 0.218218 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 31.3311 | 1.36480 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 38.3522 | 1.66749 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.41110 | −0.365011 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23.8610 | 1.03354 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16.6761 | 0.719626 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.62721 | −0.242381 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.66553 | −0.0716066 | −0.0358033 | − | 0.999359i | \(-0.511399\pi\) | ||||
−0.0358033 | + | 0.999359i | \(0.511399\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.57834 | −0.282303 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 46.1149 | 1.97173 | 0.985866 | − | 0.167534i | \(-0.0535805\pi\) | ||||
0.985866 | + | 0.167534i | \(0.0535805\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14.4111 | −0.615051 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.42166 | 0.145768 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.67609 | 0.283896 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −43.6555 | −1.84974 | −0.924871 | − | 0.380281i | \(-0.875827\pi\) | ||||
−0.924871 | + | 0.380281i | \(0.875827\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.7044 | −0.791110 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −34.9200 | −1.47432 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.5678 | 0.908973 | 0.454487 | − | 0.890754i | \(-0.349823\pi\) | ||||
0.454487 | + | 0.890754i | \(0.349823\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.01056 | −0.126209 | −0.0631047 | − | 0.998007i | \(-0.520100\pi\) | ||||
−0.0631047 | + | 0.998007i | \(0.520100\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.68665 | 0.405374 | 0.202687 | − | 0.979244i | \(-0.435033\pi\) | ||||
0.202687 | + | 0.979244i | \(0.435033\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.67609 | −0.278898 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −39.1638 | −1.63324 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.50885 | −0.187706 | −0.0938530 | − | 0.995586i | \(-0.529918\pi\) | ||||
−0.0938530 | + | 0.995586i | \(0.529918\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.0978 | 0.502765 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.6761 | 0.525893 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 48.2721 | 1.99923 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −40.5572 | −1.67398 | −0.836988 | − | 0.547222i | \(-0.815685\pi\) | ||||
−0.836988 | + | 0.547222i | \(0.815685\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.04888 | −0.208035 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.7144 | 0.440732 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.7144 | 0.686378 | 0.343189 | − | 0.939266i | \(-0.388493\pi\) | ||||
0.343189 | + | 0.939266i | \(0.388493\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −19.6655 | −0.804856 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.5194 | 1.12441 | 0.562206 | − | 0.826997i | \(-0.309953\pi\) | ||||
0.562206 | + | 0.826997i | \(0.309953\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.8227 | −0.808585 | −0.404293 | − | 0.914630i | \(-0.632482\pi\) | ||||
−0.404293 | + | 0.914630i | \(0.632482\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.8816 | −0.524581 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.7944 | −1.04696 | −0.523482 | − | 0.852037i | \(-0.675367\pi\) | ||||
−0.523482 | + | 0.852037i | \(0.675367\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.42166 | 0.138653 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.35218 | −0.378349 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.2544 | 0.858458 | 0.429229 | − | 0.903196i | \(-0.358785\pi\) | ||||
0.429229 | + | 0.903196i | \(0.358785\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.94108 | 0.118403 | 0.0592017 | − | 0.998246i | \(-0.481144\pi\) | ||||
0.0592017 | + | 0.998246i | \(0.481144\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.76328 | −0.392419 | −0.196210 | − | 0.980562i | \(-0.562863\pi\) | ||||
−0.196210 | + | 0.980562i | \(0.562863\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.83276 | 0.314318 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.15667 | 0.286726 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.62721 | 0.224729 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −43.7422 | −1.74411 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.1567 | 1.00147 | 0.500736 | − | 0.865600i | \(-0.333063\pi\) | ||||
0.500736 | + | 0.865600i | \(0.333063\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.3728 | 0.412281 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.57834 | −0.102157 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.8328 | −0.547216 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.65838 | 0.0655023 | 0.0327511 | − | 0.999464i | \(-0.489573\pi\) | ||||
0.0327511 | + | 0.999464i | \(0.489573\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.4877 | 1.28119 | 0.640595 | − | 0.767879i | \(-0.278688\pi\) | ||||
0.640595 | + | 0.767879i | \(0.278688\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15.4116 | −0.605893 | −0.302947 | − | 0.953008i | \(-0.597970\pi\) | ||||
−0.302947 | + | 0.953008i | \(0.597970\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 47.3311 | 1.85791 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.04888 | −0.197881 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 43.6555 | 1.70837 | 0.854185 | − | 0.519968i | \(-0.174056\pi\) | ||||
0.854185 | + | 0.519968i | \(0.174056\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.25443 | 0.361050 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.83276 | −0.227212 | −0.113606 | − | 0.993526i | \(-0.536240\pi\) | ||||
−0.113606 | + | 0.993526i | \(0.536240\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.3416 | −1.10236 | −0.551181 | − | 0.834386i | \(-0.685822\pi\) | ||||
−0.551181 | + | 0.834386i | \(0.685822\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −16.0000 | −0.621389 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −26.8011 | −1.03774 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.51890 | −0.329360 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 81.0943 | 3.13061 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.4700 | 0.519231 | 0.259616 | − | 0.965712i | \(-0.416404\pi\) | ||||
0.259616 | + | 0.965712i | \(0.416404\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.00000 | −0.192450 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.1567 | −0.582518 | −0.291259 | − | 0.956644i | \(-0.594074\pi\) | ||||
−0.291259 | + | 0.956644i | \(0.594074\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.78389 | −0.183589 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.2544 | 0.737831 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.9305 | 0.762620 | 0.381310 | − | 0.924447i | \(-0.375473\pi\) | ||||
0.381310 | + | 0.924447i | \(0.375473\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.15667 | 0.120435 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.1178 | 0.842623 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.5089 | −1.31278 | −0.656389 | − | 0.754422i | \(-0.727917\pi\) | ||||
−0.656389 | + | 0.754422i | \(0.727917\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.62721 | 0.213760 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −57.4288 | −2.17527 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.4111 | −0.545078 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −43.4600 | −1.64146 | −0.820730 | − | 0.571316i | \(-0.806433\pi\) | ||||
−0.820730 | + | 0.571316i | \(0.806433\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.04888 | 0.265853 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.00000 | 0.300871 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.2333 | 1.17299 | 0.586496 | − | 0.809952i | \(-0.300507\pi\) | ||||
0.586496 | + | 0.809952i | \(0.300507\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.67609 | −0.250373 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 39.5466 | 1.48103 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.57834 | 0.320364 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31.9194 | −1.19039 | −0.595197 | − | 0.803580i | \(-0.702926\pi\) | ||||
−0.595197 | + | 0.803580i | \(0.702926\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.45998 | −0.352308 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.21611 | 0.268370 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.1083 | 0.635387 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.72445 | 0.249396 | 0.124698 | − | 0.992195i | \(-0.460204\pi\) | ||||
0.124698 | + | 0.992195i | \(0.460204\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 45.0177 | 1.66504 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −45.3311 | −1.67434 | −0.837170 | − | 0.546942i | \(-0.815792\pi\) | ||||
−0.837170 | + | 0.546942i | \(0.815792\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 72.4877 | 2.67012 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.5089 | 0.975144 | 0.487572 | − | 0.873083i | \(-0.337883\pi\) | ||||
0.487572 | + | 0.873083i | \(0.337883\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.57834 | 0.0947176 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.36274 | −0.0866805 | −0.0433403 | − | 0.999060i | \(-0.513800\pi\) | ||||
−0.0433403 | + | 0.999060i | \(0.513800\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.6761 | −0.463794 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.9894 | 0.401545 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.4605 | −0.673633 | −0.336816 | − | 0.941570i | \(-0.609350\pi\) | ||||
−0.336816 | + | 0.941570i | \(0.609350\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18.2439 | 0.664843 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.6066 | −1.25780 | −0.628899 | − | 0.777487i | \(-0.716494\pi\) | ||||
−0.628899 | + | 0.777487i | \(0.716494\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −44.0766 | −1.59988 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.4011 | −0.522038 | −0.261019 | − | 0.965334i | \(-0.584058\pi\) | ||||
−0.261019 | + | 0.965334i | \(0.584058\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.6167 | 0.601563 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 21.6867 | 0.783060 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.7244 | 1.46856 | 0.734281 | − | 0.678846i | \(-0.237520\pi\) | ||||
0.734281 | + | 0.678846i | \(0.237520\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.25443 | 0.0451770 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.94108 | 0.249653 | 0.124827 | − | 0.992179i | \(-0.460163\pi\) | ||||
0.124827 | + | 0.992179i | \(0.460163\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −25.2444 | −0.906805 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.04888 | 0.252877 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.25443 | 0.331574 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 77.8399 | 2.78533 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.42166 | −0.122280 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.9411 | 0.746469 | 0.373234 | − | 0.927737i | \(-0.378249\pi\) | ||||
0.373234 | + | 0.927737i | \(0.378249\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.67609 | −0.0952713 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.6761 | 0.379598 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 37.1567 | 1.31947 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.33447 | −0.0826913 | −0.0413457 | − | 0.999145i | \(-0.513164\pi\) | ||||
−0.0413457 | + | 0.999145i | \(0.513164\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.5089 | 0.796306 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.15667 | −0.252869 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −52.0766 | −1.83774 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.4111 | −0.648101 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.4111 | 0.787932 | 0.393966 | − | 0.919125i | \(-0.371103\pi\) | ||||
0.393966 | + | 0.919125i | \(0.371103\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.8433 | 0.380761 | 0.190380 | − | 0.981710i | \(-0.439028\pi\) | ||||
0.190380 | + | 0.981710i | \(0.439028\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.00000 | −0.280572 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.25443 | −0.253800 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.57834 | 0.0900944 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 52.2822 | 1.82466 | 0.912330 | − | 0.409455i | \(-0.134281\pi\) | ||||
0.912330 | + | 0.409455i | \(0.134281\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.82220 | −0.307523 | −0.153761 | − | 0.988108i | \(-0.549139\pi\) | ||||
−0.153761 | + | 0.988108i | \(0.549139\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 28.1361 | 0.979572 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.4595 | 0.363711 | 0.181856 | − | 0.983325i | \(-0.441790\pi\) | ||||
0.181856 | + | 0.983325i | \(0.441790\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.3028 | 0.600951 | 0.300475 | − | 0.953790i | \(-0.402855\pi\) | ||||
0.300475 | + | 0.953790i | \(0.402855\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25.6655 | 0.890327 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.20555 | 0.215010 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.04888 | 0.174515 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.6066 | 1.40190 | 0.700948 | − | 0.713213i | \(-0.252761\pi\) | ||||
0.700948 | + | 0.713213i | \(0.252761\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.2922 | −0.596284 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −28.9894 | −0.998449 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.6655 | −0.710076 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 21.5678 | 0.740204 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −55.2122 | −1.89265 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.724449 | −0.0248046 | −0.0124023 | − | 0.999923i | \(-0.503948\pi\) | ||||
−0.0124023 | + | 0.999923i | \(0.503948\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 37.0388 | 1.26522 | 0.632611 | − | 0.774470i | \(-0.281983\pi\) | ||||
0.632611 | + | 0.774470i | \(0.281983\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.7422 | 1.35598 | 0.677992 | − | 0.735069i | \(-0.262850\pi\) | ||||
0.677992 | + | 0.735069i | \(0.262850\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.25443 | 0.315390 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25.1638 | −0.856586 | −0.428293 | − | 0.903640i | \(-0.640885\pi\) | ||||
−0.428293 | + | 0.903640i | \(0.640885\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 21.5089 | 0.730479 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 37.5678 | 1.27440 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.2132 | 1.12539 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.78389 | 0.161910 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.1844 | −1.15433 | −0.577163 | − | 0.816629i | \(-0.695840\pi\) | ||||
−0.577163 | + | 0.816629i | \(0.695840\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.9411 | 0.503950 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.69670 | −0.259308 | −0.129654 | − | 0.991559i | \(-0.541387\pi\) | ||||
−0.129654 | + | 0.991559i | \(0.541387\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.56777 | −0.0527598 | −0.0263799 | − | 0.999652i | \(-0.508398\pi\) | ||||
−0.0263799 | + | 0.999652i | \(0.508398\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.2544 | 0.512193 | 0.256097 | − | 0.966651i | \(-0.417563\pi\) | ||||
0.256097 | + | 0.966651i | \(0.417563\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.8328 | −0.396858 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.62721 | −0.188519 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.62721 | −0.121380 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −20.1955 | −0.674308 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.2756 | −0.576172 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −53.2333 | −1.77346 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.25443 | −0.241412 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42.8605 | 1.42316 | 0.711580 | − | 0.702605i | \(-0.247980\pi\) | ||||
0.711580 | + | 0.702605i | \(0.247980\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.00000 | −0.265343 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.0283 | 0.862355 | 0.431177 | − | 0.902267i | \(-0.358098\pi\) | ||||
0.431177 | + | 0.902267i | \(0.358098\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 71.3311 | 2.36071 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −18.2439 | −0.602465 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 37.0177 | 1.22110 | 0.610551 | − | 0.791977i | \(-0.290948\pi\) | ||||
0.610551 | + | 0.791977i | \(0.290948\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19.6655 | −0.648001 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 35.6655 | 1.17395 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 35.2444 | 1.15883 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.45998 | 0.310706 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.57885 | 0.0518005 | 0.0259002 | − | 0.999665i | \(-0.491755\pi\) | ||||
0.0259002 | + | 0.999665i | \(0.491755\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.00000 | −0.0327737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22.1361 | −0.724702 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.6655 | −0.707782 | −0.353891 | − | 0.935287i | \(-0.615142\pi\) | ||||
−0.353891 | + | 0.935287i | \(0.615142\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.0977518 | −0.00319001 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.9022 | −0.909587 | −0.454794 | − | 0.890597i | \(-0.650287\pi\) | ||||
−0.454794 | + | 0.890597i | \(0.650287\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −72.4877 | −2.36053 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.54717 | 0.277746 | 0.138873 | − | 0.990310i | \(-0.455652\pi\) | ||||
0.138873 | + | 0.990310i | \(0.455652\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23.8610 | −0.774562 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.7738 | −0.543929 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −44.0283 | −1.42622 | −0.713108 | − | 0.701054i | \(-0.752713\pi\) | ||||
−0.713108 | + | 0.701054i | \(0.752713\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 19.2544 | 0.622407 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.66553 | −0.312116 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.50885 | −0.177705 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.9894 | −0.354130 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40.4877 | −1.30200 | −0.650999 | − | 0.759079i | \(-0.725650\pi\) | ||||
−0.650999 | + | 0.759079i | \(0.725650\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.20555 | −0.199351 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.27555 | −0.169301 | −0.0846503 | − | 0.996411i | \(-0.526977\pi\) | ||||
−0.0846503 | + | 0.996411i | \(0.526977\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.25443 | −0.104332 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12.8917 | 0.412864 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.4595 | 0.398613 | 0.199307 | − | 0.979937i | \(-0.436131\pi\) | ||||
0.199307 | + | 0.979937i | \(0.436131\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 40.2721 | 1.28710 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.6167 | −0.530529 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.8222 | −0.536545 | −0.268272 | − | 0.963343i | \(-0.586453\pi\) | ||||
−0.268272 | + | 0.963343i | \(0.586453\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.62721 | −0.115455 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 56.8222 | 1.80684 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.08719 | −0.0980678 | −0.0490339 | − | 0.998797i | \(-0.515614\pi\) | ||||
−0.0490339 | + | 0.998797i | \(0.515614\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.05944 | 0.128822 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 49.8610 | 1.57911 | 0.789557 | − | 0.613677i | \(-0.210310\pi\) | ||||
0.789557 | + | 0.613677i | \(0.210310\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.04888 | −0.223017 |
(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 | 3192.2.a.v.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 9576.2.a.cc.1.3 | 3 | |||
4.3 | odd | 2 | 6384.2.a.bv.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3192.2.a.v.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
6384.2.a.bv.1.3 | 3 | 4.3 | odd | 2 | |||
9576.2.a.cc.1.3 | 3 | 3.2 | odd | 2 |