Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.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: | \(32.0040411301\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 23x^{6} - 3x^{5} + 163x^{4} + 13x^{3} - 418x^{2} + 4x + 269 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.12535\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-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 | ||||||||
\(5\) | −2.12535 | −0.950486 | −0.475243 | − | 0.879855i | \(-0.657640\pi\) | ||||
−0.475243 | + | 0.879855i | \(0.657640\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.08900 | 0.789569 | 0.394785 | − | 0.918774i | \(-0.370819\pi\) | ||||
0.394785 | + | 0.918774i | \(0.370819\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.99111 | −1.20336 | −0.601682 | − | 0.798736i | \(-0.705503\pi\) | ||||
−0.601682 | + | 0.798736i | \(0.705503\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.23865 | 0.898240 | 0.449120 | − | 0.893471i | \(-0.351738\pi\) | ||||
0.449120 | + | 0.893471i | \(0.351738\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.12535 | 0.548764 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.33878 | −0.324702 | −0.162351 | − | 0.986733i | \(-0.551908\pi\) | ||||
−0.162351 | + | 0.986733i | \(0.551908\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.48827 | 0.570848 | 0.285424 | − | 0.958401i | \(-0.407866\pi\) | ||||
0.285424 | + | 0.958401i | \(0.407866\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.08900 | −0.455858 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.08900 | −0.227073 | −0.113537 | − | 0.993534i | \(-0.536218\pi\) | ||||
−0.113537 | + | 0.993534i | \(0.536218\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.482879 | −0.0965758 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.80941 | 1.07878 | 0.539390 | − | 0.842056i | \(-0.318655\pi\) | ||||
0.539390 | + | 0.842056i | \(0.318655\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.89064 | −1.77641 | −0.888205 | − | 0.459447i | \(-0.848048\pi\) | ||||
−0.888205 | + | 0.459447i | \(0.848048\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.99111 | 0.694763 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.43987 | −0.750475 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.35179 | 1.20863 | 0.604314 | − | 0.796746i | \(-0.293447\pi\) | ||||
0.604314 | + | 0.796746i | \(0.293447\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.23865 | −0.518599 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.3049 | −1.60935 | −0.804675 | − | 0.593716i | \(-0.797660\pi\) | ||||
−0.804675 | + | 0.593716i | \(0.797660\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.90969 | 0.901220 | 0.450610 | − | 0.892721i | \(-0.351207\pi\) | ||||
0.450610 | + | 0.892721i | \(0.351207\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.12535 | −0.316829 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.5733 | 1.68814 | 0.844070 | − | 0.536234i | \(-0.180153\pi\) | ||||
0.844070 | + | 0.536234i | \(0.180153\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.63606 | −0.376580 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.33878 | 0.187467 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.50865 | 0.756671 | 0.378336 | − | 0.925669i | \(-0.376497\pi\) | ||||
0.378336 | + | 0.925669i | \(0.376497\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.48251 | 1.14378 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.48827 | −0.329579 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.9870 | −1.82096 | −0.910478 | − | 0.413558i | \(-0.864286\pi\) | ||||
−0.910478 | + | 0.413558i | \(0.864286\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.75964 | −0.353336 | −0.176668 | − | 0.984270i | \(-0.556532\pi\) | ||||
−0.176668 | + | 0.984270i | \(0.556532\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.08900 | 0.263190 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.88327 | −0.853765 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.87335 | 1.08405 | 0.542026 | − | 0.840362i | \(-0.317657\pi\) | ||||
0.542026 | + | 0.840362i | \(0.317657\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.08900 | 0.131101 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.828726 | −0.0983516 | −0.0491758 | − | 0.998790i | \(-0.515659\pi\) | ||||
−0.0491758 | + | 0.998790i | \(0.515659\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.0949232 | −0.0111099 | −0.00555496 | − | 0.999985i | \(-0.501768\pi\) | ||||
−0.00555496 | + | 0.999985i | \(0.501768\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.482879 | 0.0557581 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.33744 | −0.950139 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.8260 | 1.78057 | 0.890285 | − | 0.455404i | \(-0.150505\pi\) | ||||
0.890285 | + | 0.455404i | \(0.150505\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.15253 | −0.894856 | −0.447428 | − | 0.894320i | \(-0.647660\pi\) | ||||
−0.447428 | + | 0.894320i | \(0.647660\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.84538 | 0.308624 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.80941 | −0.622834 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.10300 | −0.540917 | −0.270459 | − | 0.962732i | \(-0.587175\pi\) | ||||
−0.270459 | + | 0.962732i | \(0.587175\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.76556 | 0.709223 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.89064 | 1.02561 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.28845 | −0.542583 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.8568 | 1.61001 | 0.805005 | − | 0.593268i | \(-0.202163\pi\) | ||||
0.805005 | + | 0.593268i | \(0.202163\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.99111 | −0.401121 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.72977 | −0.868645 | −0.434322 | − | 0.900758i | \(-0.643012\pi\) | ||||
−0.434322 | + | 0.900758i | \(0.643012\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −19.1263 | −1.88457 | −0.942287 | − | 0.334807i | \(-0.891329\pi\) | ||||
−0.942287 | + | 0.334807i | \(0.891329\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.43987 | 0.433287 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.36186 | −0.325004 | −0.162502 | − | 0.986708i | \(-0.551956\pi\) | ||||
−0.162502 | + | 0.986708i | \(0.551956\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.7988 | −1.03434 | −0.517171 | − | 0.855882i | \(-0.673015\pi\) | ||||
−0.517171 | + | 0.855882i | \(0.673015\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.35179 | −0.697801 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.16836 | −0.392127 | −0.196063 | − | 0.980591i | \(-0.562816\pi\) | ||||
−0.196063 | + | 0.980591i | \(0.562816\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.31452 | 0.215830 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.23865 | 0.299413 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.79671 | −0.256374 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.92893 | 0.448085 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.3049 | 0.929159 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.6530 | 1.04228 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −21.8072 | −1.93507 | −0.967537 | − | 0.252730i | \(-0.918672\pi\) | ||||
−0.967537 | + | 0.252730i | \(0.918672\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.90969 | −0.520320 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.2842 | −1.68487 | −0.842433 | − | 0.538801i | \(-0.818877\pi\) | ||||
−0.842433 | + | 0.538801i | \(0.818877\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.19801 | 0.450724 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.12535 | 0.182921 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.5983 | 0.905471 | 0.452735 | − | 0.891645i | \(-0.350448\pi\) | ||||
0.452735 | + | 0.891645i | \(0.350448\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.68531 | 0.227765 | 0.113883 | − | 0.993494i | \(-0.463671\pi\) | ||||
0.113883 | + | 0.993494i | \(0.463671\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.5733 | −0.974648 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.9258 | −1.08091 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.3470 | −1.02537 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.63606 | 0.217419 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.98625 | 0.162720 | 0.0813598 | − | 0.996685i | \(-0.474074\pi\) | ||||
0.0813598 | + | 0.996685i | \(0.474074\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.0079 | −1.70960 | −0.854799 | − | 0.518959i | \(-0.826320\pi\) | ||||
−0.854799 | + | 0.518959i | \(0.826320\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.33878 | −0.108234 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 21.0211 | 1.68845 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.27178 | −0.261116 | −0.130558 | − | 0.991441i | \(-0.541677\pi\) | ||||
−0.130558 | + | 0.991441i | \(0.541677\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.50865 | −0.436864 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.27493 | −0.179290 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.72813 | −0.448662 | −0.224331 | − | 0.974513i | \(-0.572020\pi\) | ||||
−0.224331 | + | 0.974513i | \(0.572020\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.48251 | −0.660362 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.51114 | −0.193165 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.48827 | 0.190283 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.82828 | −0.443116 | −0.221558 | − | 0.975147i | \(-0.571114\pi\) | ||||
−0.221558 | + | 0.975147i | \(0.571114\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00874 | −0.0762533 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.9870 | 1.05133 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.47026 | −0.408867 | −0.204433 | − | 0.978880i | \(-0.565535\pi\) | ||||
−0.204433 | + | 0.978880i | \(0.565535\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.5026 | 1.89559 | 0.947797 | − | 0.318875i | \(-0.103305\pi\) | ||||
0.947797 | + | 0.318875i | \(0.103305\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.75964 | 0.203999 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −15.6251 | −1.14878 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.34321 | 0.390734 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.08900 | −0.151953 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −27.2999 | −1.97535 | −0.987675 | − | 0.156522i | \(-0.949972\pi\) | ||||
−0.987675 | + | 0.156522i | \(0.949972\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.3998 | −1.32445 | −0.662223 | − | 0.749306i | \(-0.730387\pi\) | ||||
−0.662223 | + | 0.749306i | \(0.730387\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.88327 | 0.492921 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.3315 | 1.23482 | 0.617408 | − | 0.786643i | \(-0.288183\pi\) | ||||
0.617408 | + | 0.786643i | \(0.288183\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.1446 | 1.00268 | 0.501341 | − | 0.865250i | \(-0.332840\pi\) | ||||
0.501341 | + | 0.865250i | \(0.332840\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.87335 | −0.625878 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.1359 | 0.851772 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 21.9015 | 1.52966 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.08900 | −0.0756910 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.93095 | −0.686938 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.22231 | −0.634890 | −0.317445 | − | 0.948277i | \(-0.602825\pi\) | ||||
−0.317445 | + | 0.948277i | \(0.602825\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.828726 | 0.0567834 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.5602 | −0.856597 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.6616 | −1.40260 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.0949232 | 0.00641432 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.33584 | −0.291660 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.7400 | −1.32189 | −0.660944 | − | 0.750435i | \(-0.729844\pi\) | ||||
−0.660944 | + | 0.750435i | \(0.729844\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.482879 | −0.0321919 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.79089 | −0.384355 | −0.192177 | − | 0.981360i | \(-0.561555\pi\) | ||||
−0.192177 | + | 0.981360i | \(0.561555\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.43319 | 0.0947079 | 0.0473540 | − | 0.998878i | \(-0.484921\pi\) | ||||
0.0473540 | + | 0.998878i | \(0.484921\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.33744 | 0.548563 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.0534 | −0.855157 | −0.427579 | − | 0.903978i | \(-0.640633\pi\) | ||||
−0.427579 | + | 0.903978i | \(0.640633\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.5973 | −1.60455 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.8260 | −1.02801 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.3163 | 1.05541 | 0.527706 | − | 0.849427i | \(-0.323052\pi\) | ||||
0.527706 | + | 0.849427i | \(0.323052\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.4205 | −1.57306 | −0.786531 | − | 0.617550i | \(-0.788125\pi\) | ||||
−0.786531 | + | 0.617550i | \(0.788125\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.60256 | 0.357934 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.05864 | 0.512759 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.15253 | 0.516645 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.91841 | −0.626045 | −0.313022 | − | 0.949746i | \(-0.601341\pi\) | ||||
−0.313022 | + | 0.949746i | \(0.601341\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.34633 | 0.273252 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.84538 | −0.178184 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.97086 | 0.372452 | 0.186226 | − | 0.982507i | \(-0.440374\pi\) | ||||
0.186226 | + | 0.982507i | \(0.440374\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.3579 | 0.954295 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.80941 | 0.359593 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.79794 | −0.234191 | −0.117096 | − | 0.993121i | \(-0.537358\pi\) | ||||
−0.117096 | + | 0.993121i | \(0.537358\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.7078 | −0.719205 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.10300 | 0.312299 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.1289 | 1.10534 | 0.552670 | − | 0.833400i | \(-0.313609\pi\) | ||||
0.552670 | + | 0.833400i | \(0.313609\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.8658 | −1.69273 | −0.846364 | − | 0.532605i | \(-0.821213\pi\) | ||||
−0.846364 | + | 0.532605i | \(0.821213\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.76556 | −0.409470 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.92722 | 0.116216 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.45511 | −0.447934 | −0.223967 | − | 0.974597i | \(-0.571901\pi\) | ||||
−0.223967 | + | 0.974597i | \(0.571901\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.89064 | −0.592137 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.09663 | 0.125075 | 0.0625373 | − | 0.998043i | \(-0.480081\pi\) | ||||
0.0625373 | + | 0.998043i | \(0.480081\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.62190 | 0.155856 | 0.0779279 | − | 0.996959i | \(-0.475170\pi\) | ||||
0.0779279 | + | 0.996959i | \(0.475170\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.28845 | 0.313261 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −21.5269 | −1.27069 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.2077 | −0.894569 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −15.8568 | −0.929539 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.86788 | −0.576488 | −0.288244 | − | 0.957557i | \(-0.593071\pi\) | ||||
−0.288244 | + | 0.957557i | \(0.593071\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 29.7274 | 1.73079 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.99111 | 0.231588 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.52690 | −0.203966 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.3454 | 0.711576 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.72977 | 0.501512 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.86521 | 0.335841 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.4538 | 1.28151 | 0.640753 | − | 0.767747i | \(-0.278622\pi\) | ||||
0.640753 | + | 0.767747i | \(0.278622\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 19.1263 | 1.08806 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.7217 | −1.11831 | −0.559157 | − | 0.829062i | \(-0.688875\pi\) | ||||
−0.559157 | + | 0.829062i | \(0.688875\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.4601 | 1.26952 | 0.634761 | − | 0.772709i | \(-0.281099\pi\) | ||||
0.634761 | + | 0.772709i | \(0.281099\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.43987 | −0.250158 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.6210 | −0.596534 | −0.298267 | − | 0.954482i | \(-0.596409\pi\) | ||||
−0.298267 | + | 0.954482i | \(0.596409\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −23.1860 | −1.29817 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.36186 | 0.187641 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.33124 | −0.185355 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.56388 | −0.0867483 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.7988 | 0.597177 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 24.1767 | 1.33290 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.2975 | −1.28055 | −0.640273 | − | 0.768147i | \(-0.721179\pi\) | ||||
−0.640273 | + | 0.768147i | \(0.721179\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.35179 | 0.402876 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −18.8590 | −1.03038 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.74585 | −0.421943 | −0.210972 | − | 0.977492i | \(-0.567663\pi\) | ||||
−0.210972 | + | 0.977492i | \(0.567663\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.16836 | 0.226394 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 39.4746 | 2.13767 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1298 | −1.08691 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.31452 | −0.124609 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −30.3702 | −1.63036 | −0.815178 | − | 0.579210i | \(-0.803361\pi\) | ||||
−0.815178 | + | 0.579210i | \(0.803361\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.3020 | −1.19380 | −0.596900 | − | 0.802316i | \(-0.703601\pi\) | ||||
−0.596900 | + | 0.802316i | \(0.703601\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.23865 | −0.172866 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.2540 | −0.598990 | −0.299495 | − | 0.954098i | \(-0.596818\pi\) | ||||
−0.299495 | + | 0.954098i | \(0.596818\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.76133 | 0.0934819 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.79671 | 0.148018 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −26.4040 | −1.39355 | −0.696775 | − | 0.717289i | \(-0.745383\pi\) | ||||
−0.696775 | + | 0.717289i | \(0.745383\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.8085 | −0.674132 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.92893 | −0.258702 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.201745 | 0.0105598 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.04475 | 0.315533 | 0.157767 | − | 0.987476i | \(-0.449571\pi\) | ||||
0.157767 | + | 0.987476i | \(0.449571\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.3049 | −0.536450 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.5076 | 0.597444 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.2217 | 1.46127 | 0.730633 | − | 0.682771i | \(-0.239225\pi\) | ||||
0.730633 | + | 0.682771i | \(0.239225\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.6530 | −0.601761 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.8147 | 0.969004 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.6625 | 0.907262 | 0.453631 | − | 0.891190i | \(-0.350128\pi\) | ||||
0.453631 | + | 0.891190i | \(0.350128\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 21.8072 | 1.11722 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.85617 | −0.503627 | −0.251813 | − | 0.967776i | \(-0.581027\pi\) | ||||
−0.251813 | + | 0.967776i | \(0.581027\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17.7200 | 0.903094 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.90969 | 0.300407 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.8070 | 0.700044 | 0.350022 | − | 0.936741i | \(-0.386174\pi\) | ||||
0.350022 | + | 0.936741i | \(0.386174\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.45794 | 0.0737310 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 19.2842 | 0.972758 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −33.6359 | −1.69241 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.6133 | −0.984366 | −0.492183 | − | 0.870492i | \(-0.663801\pi\) | ||||
−0.492183 | + | 0.870492i | \(0.663801\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.19801 | −0.260226 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 36.4301 | 1.81923 | 0.909617 | − | 0.415448i | \(-0.136375\pi\) | ||||
0.909617 | + | 0.415448i | \(0.136375\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −32.0323 | −1.59564 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.12535 | −0.105610 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −29.3418 | −1.45442 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.4129 | 0.861010 | 0.430505 | − | 0.902588i | \(-0.358335\pi\) | ||||
0.430505 | + | 0.902588i | \(0.358335\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.5983 | −0.522774 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −29.2190 | −1.43777 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.3270 | 0.850548 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.68531 | −0.131500 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.8440 | −0.578620 | −0.289310 | − | 0.957236i | \(-0.593426\pi\) | ||||
−0.289310 | + | 0.957236i | \(0.593426\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.454844 | 0.0221677 | 0.0110839 | − | 0.999939i | \(-0.496472\pi\) | ||||
0.0110839 | + | 0.999939i | \(0.496472\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.5733 | 0.562713 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.646468 | 0.0313583 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.76491 | −0.278983 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 12.9258 | 0.624064 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.2521 | −1.26452 | −0.632260 | − | 0.774756i | \(-0.717873\pi\) | ||||
−0.632260 | + | 0.774756i | \(0.717873\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.98898 | −0.0955843 | −0.0477922 | − | 0.998857i | \(-0.515219\pi\) | ||||
−0.0477922 | + | 0.998857i | \(0.515219\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.3470 | 0.591995 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.70974 | −0.129624 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −29.9321 | −1.42858 | −0.714290 | − | 0.699850i | \(-0.753250\pi\) | ||||
−0.714290 | + | 0.699850i | \(0.753250\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.63606 | −0.125527 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.28558 | −0.108591 | −0.0542956 | − | 0.998525i | \(-0.517291\pi\) | ||||
−0.0542956 | + | 0.998525i | \(0.517291\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.8457 | 0.514134 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.98625 | −0.0939462 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.0752 | 0.569865 | 0.284933 | − | 0.958548i | \(-0.408029\pi\) | ||||
0.284933 | + | 0.958548i | \(0.408029\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 41.1278 | 1.93663 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 21.0079 | 0.987037 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.3792 | −0.674107 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.1051 | 1.50181 | 0.750906 | − | 0.660409i | \(-0.229617\pi\) | ||||
0.750906 | + | 0.660409i | \(0.229617\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.33878 | 0.0624888 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.07193 | −0.329372 | −0.164686 | − | 0.986346i | \(-0.552661\pi\) | ||||
−0.164686 | + | 0.986346i | \(0.552661\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.6733 | 0.542502 | 0.271251 | − | 0.962509i | \(-0.412563\pi\) | ||||
0.271251 | + | 0.962509i | \(0.412563\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −21.0211 | −0.974829 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.4693 | −0.530734 | −0.265367 | − | 0.964147i | \(-0.585493\pi\) | ||||
−0.265367 | + | 0.964147i | \(0.585493\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.5365 | 0.855934 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.27178 | 0.150756 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −23.5862 | −1.08450 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.20153 | −0.0551301 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.50865 | 0.252224 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.0875 | 1.00921 | 0.504603 | − | 0.863352i | \(-0.331639\pi\) | ||||
0.504603 | + | 0.863352i | \(0.331639\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23.8099 | 1.08564 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.27493 | 0.103513 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −33.7012 | −1.53029 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 38.3362 | 1.73718 | 0.868589 | − | 0.495533i | \(-0.165027\pi\) | ||||
0.868589 | + | 0.495533i | \(0.165027\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.72813 | 0.259035 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.8672 | 1.30276 | 0.651379 | − | 0.758753i | \(-0.274191\pi\) | ||||
0.651379 | + | 0.758753i | \(0.274191\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.77752 | −0.350282 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.48251 | 0.381260 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.73121 | −0.0776554 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.1802 | 0.634794 | 0.317397 | − | 0.948293i | \(-0.397191\pi\) | ||||
0.317397 | + | 0.948293i | \(0.397191\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 34.5400 | 1.54006 | 0.770032 | − | 0.638006i | \(-0.220240\pi\) | ||||
0.770032 | + | 0.638006i | \(0.220240\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.5538 | 0.825635 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.51114 | 0.111524 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 29.1481 | 1.29197 | 0.645984 | − | 0.763351i | \(-0.276447\pi\) | ||||
0.645984 | + | 0.763351i | \(0.276447\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.198295 | −0.00877205 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.48827 | −0.109860 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 40.6502 | 1.79126 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −46.1903 | −2.03145 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.82828 | 0.255833 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.9483 | 0.523463 | 0.261731 | − | 0.965141i | \(-0.415707\pi\) | ||||
0.261731 | + | 0.965141i | \(0.415707\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 41.6693 | 1.82207 | 0.911036 | − | 0.412327i | \(-0.135284\pi\) | ||||
0.911036 | + | 0.412327i | \(0.135284\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.00874 | 0.0440249 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.2414 | 0.576803 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.8141 | −0.948438 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.9870 | −0.606985 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −33.3739 | −1.44558 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.14514 | 0.308912 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.47026 | 0.236059 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.5208 | 0.453163 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.9098 | −0.727007 | −0.363504 | − | 0.931593i | \(-0.618420\pi\) | ||||
−0.363504 | + | 0.931593i | \(0.618420\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −25.5026 | −1.09442 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 22.9513 | 0.983127 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.2529 | 1.03698 | 0.518489 | − | 0.855085i | \(-0.326495\pi\) | ||||
0.518489 | + | 0.855085i | \(0.326495\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.75964 | −0.117779 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.4554 | 0.615820 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 33.0607 | 1.40588 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 15.6251 | 0.663251 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −28.4990 | −1.20754 | −0.603771 | − | 0.797158i | \(-0.706336\pi\) | ||||
−0.603771 | + | 0.797158i | \(0.706336\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.1394 | 0.809512 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.34321 | −0.225590 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16.8070 | −0.708332 | −0.354166 | − | 0.935183i | \(-0.615235\pi\) | ||||
−0.354166 | + | 0.935183i | \(0.615235\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.85924 | 0.372711 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.08900 | 0.0877299 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.50924 | −0.0632708 | −0.0316354 | − | 0.999499i | \(-0.510072\pi\) | ||||
−0.0316354 | + | 0.999499i | \(0.510072\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.7918 | 0.828262 | 0.414131 | − | 0.910217i | \(-0.364086\pi\) | ||||
0.414131 | + | 0.910217i | \(0.364086\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 27.2999 | 1.14047 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.525857 | 0.0219298 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.2655 | −1.17671 | −0.588354 | − | 0.808604i | \(-0.700224\pi\) | ||||
−0.588354 | + | 0.808604i | \(0.700224\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 18.3998 | 0.764670 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.0307 | −0.706551 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −21.9856 | −0.910551 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.88327 | −0.284588 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 38.5338 | 1.59046 | 0.795230 | − | 0.606307i | \(-0.207350\pi\) | ||||
0.795230 | + | 0.606307i | \(0.207350\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.6106 | −1.01406 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.3315 | −0.712922 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.07271 | 0.0440510 | 0.0220255 | − | 0.999757i | \(-0.492989\pi\) | ||||
0.0220255 | + | 0.999757i | \(0.492989\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.94400 | 0.243680 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −14.1446 | −0.578899 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.42396 | 0.385053 | 0.192526 | − | 0.981292i | \(-0.438332\pi\) | ||||
0.192526 | + | 0.981292i | \(0.438332\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.8272 | 0.482443 | 0.241221 | − | 0.970470i | \(-0.422452\pi\) | ||||
0.241221 | + | 0.970470i | \(0.422452\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.87335 | 0.361351 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.4757 | −0.425899 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.80749 | −0.235719 | −0.117859 | − | 0.993030i | \(-0.537603\pi\) | ||||
−0.117859 | + | 0.993030i | \(0.537603\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.1359 | −0.491771 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 37.4819 | 1.51635 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.0851 | 0.568890 | 0.284445 | − | 0.958692i | \(-0.408191\pi\) | ||||
0.284445 | + | 0.958692i | \(0.408191\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −21.9015 | −0.883152 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.8152 | −0.515922 | −0.257961 | − | 0.966155i | \(-0.583051\pi\) | ||||
−0.257961 | + | 0.966155i | \(0.583051\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −45.2871 | −1.82024 | −0.910122 | − | 0.414341i | \(-0.864012\pi\) | ||||
−0.910122 | + | 0.414341i | \(0.864012\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.08900 | 0.0437002 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.6602 | −0.427091 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.3524 | −0.894097 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.93095 | 0.396604 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.84243 | −0.392443 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.43728 | −0.0970264 | −0.0485132 | − | 0.998823i | \(-0.515448\pi\) | ||||
−0.0485132 | + | 0.998823i | \(0.515448\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.22231 | 0.366554 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 46.3479 | 1.83926 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.53728 | −0.338260 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.828726 | −0.0327839 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 37.4275 | 1.47830 | 0.739149 | − | 0.673542i | \(-0.235228\pi\) | ||||
0.739149 | + | 0.673542i | \(0.235228\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −32.1270 | −1.26697 | −0.633483 | − | 0.773757i | \(-0.718375\pi\) | ||||
−0.633483 | + | 0.773757i | \(0.718375\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.5602 | 0.494557 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −43.5139 | −1.71071 | −0.855353 | − | 0.518045i | \(-0.826660\pi\) | ||||
−0.855353 | + | 0.518045i | \(0.826660\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 55.8237 | 2.19127 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.6616 | 0.809791 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 30.4074 | 1.18993 | 0.594966 | − | 0.803751i | \(-0.297166\pi\) | ||||
0.594966 | + | 0.803751i | \(0.297166\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 40.9856 | 1.60144 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.0949232 | −0.00370331 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.7890 | −0.459235 | −0.229617 | − | 0.973281i | \(-0.573747\pi\) | ||||
−0.229617 | + | 0.973281i | \(0.573747\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.6952 | 1.50507 | 0.752534 | − | 0.658553i | \(-0.228831\pi\) | ||||
0.752534 | + | 0.658553i | \(0.228831\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.33584 | 0.168390 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.0476 | −0.428407 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.32647 | −0.244962 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19.7400 | 0.763192 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.0140 | 0.425192 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −48.5648 | −1.87203 | −0.936017 | − | 0.351955i | \(-0.885517\pi\) | ||||
−0.936017 | + | 0.351955i | \(0.885517\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.482879 | 0.0185860 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 42.0847 | 1.61745 | 0.808724 | − | 0.588189i | \(-0.200159\pi\) | ||||
0.808724 | + | 0.588189i | \(0.200159\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 33.1248 | 1.27121 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.79089 | 0.221907 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −32.7145 | −1.25179 | −0.625893 | − | 0.779909i | \(-0.715265\pi\) | ||||
−0.625893 | + | 0.779909i | \(0.715265\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.5250 | −0.860637 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.43319 | −0.0546797 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 17.8406 | 0.679672 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.5864 | 0.897268 | 0.448634 | − | 0.893715i | \(-0.351911\pi\) | ||||
0.448634 | + | 0.893715i | \(0.351911\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.33744 | −0.316713 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.70723 | −0.216488 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.7959 | 0.522558 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.0534 | 0.493725 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −43.8121 | −1.65476 | −0.827381 | − | 0.561641i | \(-0.810170\pi\) | ||||
−0.827381 | + | 0.561641i | \(0.810170\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.2932 | 0.689943 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 24.5973 | 0.926389 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.2365 | −0.685855 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.2772 | 1.28731 | 0.643653 | − | 0.765317i | \(-0.277418\pi\) | ||||
0.643653 | + | 0.765317i | \(0.277418\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.8260 | 0.593523 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.7709 | 0.403375 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 27.4719 | 1.02739 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16.3163 | −0.609342 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −41.3946 | −1.54376 | −0.771879 | − | 0.635770i | \(-0.780683\pi\) | ||||
−0.771879 | + | 0.635770i | \(0.780683\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −39.9550 | −1.48800 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 24.4205 | 0.908208 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.80524 | −0.104184 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.263467 | 0.00977146 | 0.00488573 | − | 0.999988i | \(-0.498445\pi\) | ||||
0.00488573 | + | 0.999988i | \(0.498445\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.91177 | −0.292628 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −43.2404 | −1.59712 | −0.798561 | − | 0.601914i | \(-0.794405\pi\) | ||||
−0.798561 | + | 0.601914i | \(0.794405\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.60256 | −0.206654 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −35.4145 | −1.30451 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.46955 | −0.0540582 | −0.0270291 | − | 0.999635i | \(-0.508605\pi\) | ||||
−0.0270291 | + | 0.999635i | \(0.508605\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.05864 | −0.296041 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 42.5588 | 1.56133 | 0.780666 | − | 0.624949i | \(-0.214880\pi\) | ||||
0.780666 | + | 0.624949i | \(0.214880\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.22147 | −0.154663 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.15253 | −0.298285 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.02295 | −0.256613 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.2612 | 0.410925 | 0.205463 | − | 0.978665i | \(-0.434130\pi\) | ||||
0.205463 | + | 0.978665i | \(0.434130\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.91841 | 0.361447 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 44.6492 | 1.62495 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.1221 | −1.31288 | −0.656440 | − | 0.754378i | \(-0.727939\pi\) | ||||
−0.656440 | + | 0.754378i | \(0.727939\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.34633 | −0.157762 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.3050 | 0.953556 | 0.476778 | − | 0.879024i | \(-0.341805\pi\) | ||||
0.476778 | + | 0.879024i | \(0.341805\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.5588 | −0.816684 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.84538 | 0.102875 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −45.2991 | −1.63566 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.5596 | −1.24625 | −0.623126 | − | 0.782121i | \(-0.714138\pi\) | ||||
−0.623126 | + | 0.782121i | \(0.714138\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.97086 | −0.215035 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 48.4403 | 1.74228 | 0.871139 | − | 0.491037i | \(-0.163382\pi\) | ||||
0.871139 | + | 0.491037i | \(0.163382\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.77598 | 0.171558 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −15.3579 | −0.550963 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −25.6413 | −0.918694 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.30753 | 0.118353 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.80941 | −0.207611 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.95368 | 0.248187 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −51.6378 | −1.84069 | −0.920345 | − | 0.391108i | \(-0.872092\pi\) | ||||
−0.920345 | + | 0.391108i | \(0.872092\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.79794 | 0.135210 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.70773 | −0.309611 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.93752 | −0.317381 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 11.7078 | 0.415233 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −32.9526 | −1.16724 | −0.583620 | − | 0.812027i | \(-0.698364\pi\) | ||||
−0.583620 | + | 0.812027i | \(0.698364\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.4941 | −0.548141 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.10300 | −0.180306 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.378849 | 0.0133693 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.83504 | 0.170413 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.1289 | −0.638168 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.0323 | 0.633981 | 0.316991 | − | 0.948429i | \(-0.397328\pi\) | ||||
0.316991 | + | 0.948429i | \(0.397328\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.2580 | 0.886928 | 0.443464 | − | 0.896292i | \(-0.353749\pi\) | ||||
0.443464 | + | 0.896292i | \(0.353749\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27.8658 | 0.977297 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.1743 | 0.426447 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.7049 | 0.514460 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.76556 | 0.236408 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.5226 | −0.367241 | −0.183621 | − | 0.982997i | \(-0.558782\pi\) | ||||
−0.183621 | + | 0.982997i | \(0.558782\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.6407 | 0.963493 | 0.481746 | − | 0.876311i | \(-0.340003\pi\) | ||||
0.481746 | + | 0.876311i | \(0.340003\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.92722 | −0.0670973 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.0893 | 0.559478 | 0.279739 | − | 0.960076i | \(-0.409752\pi\) | ||||
0.279739 | + | 0.960076i | \(0.409752\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −52.4489 | −1.82163 | −0.910813 | − | 0.412818i | \(-0.864544\pi\) | ||||
−0.910813 | + | 0.412818i | \(0.864544\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.45511 | 0.258615 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.52910 | 0.122276 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.12535 | −0.0735508 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.89064 | 0.341870 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −50.3239 | −1.73737 | −0.868687 | − | 0.495361i | \(-0.835036\pi\) | ||||
−0.868687 | + | 0.495361i | \(0.835036\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.74925 | 0.163767 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.09663 | −0.0722119 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.33705 | 0.183600 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.2966 | 0.353794 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.62190 | −0.0899833 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.00613 | −0.274447 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 46.8272 | 1.60333 | 0.801666 | − | 0.597773i | \(-0.203947\pi\) | ||||
0.801666 | + | 0.597773i | \(0.203947\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.28845 | −0.180861 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.7908 | −0.778518 | −0.389259 | − | 0.921128i | \(-0.627269\pi\) | ||||
−0.389259 | + | 0.921128i | \(0.627269\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.9399 | 1.73805 | 0.869024 | − | 0.494771i | \(-0.164748\pi\) | ||||
0.869024 | + | 0.494771i | \(0.164748\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 21.5269 | 0.733635 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21.1311 | −0.719312 | −0.359656 | − | 0.933085i | \(-0.617106\pi\) | ||||
−0.359656 | + | 0.933085i | \(0.617106\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.3871 | 0.421175 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15.2077 | 0.516480 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −63.1634 | −2.14267 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.7377 | 0.973739 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.8568 | 0.536670 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 24.3433 | 0.822953 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.6881 | 0.934961 | 0.467480 | − | 0.884003i | \(-0.345162\pi\) | ||||
0.467480 | + | 0.884003i | \(0.345162\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.86788 | 0.332835 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.856756 | −0.0288649 | −0.0144324 | − | 0.999896i | \(-0.504594\pi\) | ||||
−0.0144324 | + | 0.999896i | \(0.504594\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.6775 | −0.729507 | −0.364753 | − | 0.931104i | \(-0.618847\pi\) | ||||
−0.364753 | + | 0.931104i | \(0.618847\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −29.7274 | −0.999274 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.19244 | −0.207922 | −0.103961 | − | 0.994581i | \(-0.533152\pi\) | ||||
−0.103961 | + | 0.994581i | \(0.533152\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −45.5553 | −1.52788 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.99111 | −0.133707 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 28.7975 | 0.963671 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.6262 | 0.388622 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.52690 | 0.117760 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −57.4588 | −1.91636 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.37486 | −0.245692 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.3454 | −0.410828 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −54.2020 | −1.80174 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 47.2992 | 1.57054 | 0.785272 | − | 0.619152i | \(-0.212523\pi\) | ||||
0.785272 | + | 0.619152i | \(0.212523\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.72977 | −0.289548 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.3033 | 0.970862 | 0.485431 | − | 0.874275i | \(-0.338663\pi\) | ||||
0.485431 | + | 0.874275i | \(0.338663\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32.5376 | 1.07684 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.86521 | −0.193898 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −40.2847 | −1.33032 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.40652 | −0.0463967 | −0.0231984 | − | 0.999731i | \(-0.507385\pi\) | ||||
−0.0231984 | + | 0.999731i | \(0.507385\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.4538 | −0.739878 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.68395 | −0.0883434 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.55003 | −0.116724 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −19.1263 | −0.628191 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.9126 | 0.522075 | 0.261038 | − | 0.965329i | \(-0.415935\pi\) | ||||
0.261038 | + | 0.965329i | \(0.415935\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.55923 | −0.214970 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 19.7217 | 0.645659 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11.3562 | −0.371387 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.0686 | 0.949630 | 0.474815 | − | 0.880086i | \(-0.342515\pi\) | ||||
0.474815 | + | 0.880086i | \(0.342515\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.4601 | −0.732959 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.0504 | 0.360231 | 0.180116 | − | 0.983645i | \(-0.442353\pi\) | ||||
0.180116 | + | 0.983645i | \(0.442353\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.2220 | 0.365440 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.43987 | 0.144429 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.8317 | 1.35935 | 0.679674 | − | 0.733514i | \(-0.262121\pi\) | ||||
0.679674 | + | 0.733514i | \(0.262121\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.307423 | −0.00997938 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.6210 | 0.344409 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.30392 | −0.0422380 | −0.0211190 | − | 0.999777i | \(-0.506723\pi\) | ||||
−0.0211190 | + | 0.999777i | \(0.506723\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 58.0218 | 1.87754 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 23.1860 | 0.749496 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22.1398 | 0.714932 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 66.8247 | 2.15564 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.36186 | −0.108335 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 39.1061 | 1.25887 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.5523 | 1.30408 | 0.652038 | − | 0.758186i | \(-0.273914\pi\) | ||||
0.652038 | + | 0.758186i | \(0.273914\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.33124 | 0.107015 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36.8286 | −1.18189 | −0.590944 | − | 0.806713i | \(-0.701244\pi\) | ||||
−0.590944 | + | 0.806713i | \(0.701244\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.60963 | 0.179836 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.56388 | 0.0500842 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −26.3225 | −0.842133 | −0.421066 | − | 0.907030i | \(-0.638344\pi\) | ||||
−0.421066 | + | 0.907030i | \(0.638344\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.3666 | 0.650920 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.7988 | −0.344780 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 39.3825 | 1.25611 | 0.628054 | − | 0.778170i | \(-0.283852\pi\) | ||||
0.628054 | + | 0.778170i | \(0.283852\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −36.8355 | −1.17368 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −24.1767 | −0.769552 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.43568 | −0.204643 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −59.0907 | −1.87708 | −0.938539 | − | 0.345173i | \(-0.887820\pi\) | ||||
−0.938539 | + | 0.345173i | \(0.887820\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 23.2975 | 0.739324 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −30.0622 | −0.953036 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.7840 | 0.404873 | 0.202436 | − | 0.979295i | \(-0.435114\pi\) | ||||
0.202436 | + | 0.979295i | \(0.435114\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.35179 | −0.232600 |
(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 | 4008.2.a.h.1.3 | ✓ | 8 | |
4.3 | odd | 2 | 8016.2.a.y.1.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.h.1.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
8016.2.a.y.1.3 | 8 | 4.3 | odd | 2 |