Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6018,2,Mod(1,6018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6018.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: | \(48.0539719364\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - 34x^{8} + 30x^{7} + 341x^{6} - 276x^{5} - 1032x^{4} + 1176x^{3} + 416x^{2} - 896x + 272 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.580342\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6018.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.580342 | 0.259537 | 0.129768 | − | 0.991544i | \(-0.458577\pi\) | ||||
0.129768 | + | 0.991544i | \(0.458577\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 4.77865 | 1.80616 | 0.903080 | − | 0.429473i | \(-0.141301\pi\) | ||||
0.903080 | + | 0.429473i | \(0.141301\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.580342 | −0.183520 | ||||||||
\(11\) | 1.62859 | 0.491037 | 0.245518 | − | 0.969392i | \(-0.421042\pi\) | ||||
0.245518 | + | 0.969392i | \(0.421042\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 5.47999 | 1.51988 | 0.759938 | − | 0.649996i | \(-0.225229\pi\) | ||||
0.759938 | + | 0.649996i | \(0.225229\pi\) | |||||||
\(14\) | −4.77865 | −1.27715 | ||||||||
\(15\) | −0.580342 | −0.149844 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 1.16709 | 0.267750 | 0.133875 | − | 0.990998i | \(-0.457258\pi\) | ||||
0.133875 | + | 0.990998i | \(0.457258\pi\) | |||||||
\(20\) | 0.580342 | 0.129768 | ||||||||
\(21\) | −4.77865 | −1.04279 | ||||||||
\(22\) | −1.62859 | −0.347216 | ||||||||
\(23\) | −7.82087 | −1.63076 | −0.815382 | − | 0.578923i | \(-0.803473\pi\) | ||||
−0.815382 | + | 0.578923i | \(0.803473\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.66320 | −0.932641 | ||||||||
\(26\) | −5.47999 | −1.07471 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.77865 | 0.903080 | ||||||||
\(29\) | 1.14006 | 0.211704 | 0.105852 | − | 0.994382i | \(-0.466243\pi\) | ||||
0.105852 | + | 0.994382i | \(0.466243\pi\) | |||||||
\(30\) | 0.580342 | 0.105955 | ||||||||
\(31\) | 7.10961 | 1.27692 | 0.638461 | − | 0.769654i | \(-0.279571\pi\) | ||||
0.638461 | + | 0.769654i | \(0.279571\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.62859 | −0.283500 | ||||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | 2.77325 | 0.468765 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.66923 | 0.274419 | 0.137209 | − | 0.990542i | \(-0.456187\pi\) | ||||
0.137209 | + | 0.990542i | \(0.456187\pi\) | |||||||
\(38\) | −1.16709 | −0.189328 | ||||||||
\(39\) | −5.47999 | −0.877501 | ||||||||
\(40\) | −0.580342 | −0.0917601 | ||||||||
\(41\) | −0.211924 | −0.0330970 | −0.0165485 | − | 0.999863i | \(-0.505268\pi\) | ||||
−0.0165485 | + | 0.999863i | \(0.505268\pi\) | |||||||
\(42\) | 4.77865 | 0.737361 | ||||||||
\(43\) | 9.35293 | 1.42631 | 0.713154 | − | 0.701007i | \(-0.247266\pi\) | ||||
0.713154 | + | 0.701007i | \(0.247266\pi\) | |||||||
\(44\) | 1.62859 | 0.245518 | ||||||||
\(45\) | 0.580342 | 0.0865122 | ||||||||
\(46\) | 7.82087 | 1.15312 | ||||||||
\(47\) | 4.12655 | 0.601920 | 0.300960 | − | 0.953637i | \(-0.402693\pi\) | ||||
0.300960 | + | 0.953637i | \(0.402693\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 15.8355 | 2.26221 | ||||||||
\(50\) | 4.66320 | 0.659477 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 5.47999 | 0.759938 | ||||||||
\(53\) | 6.63557 | 0.911465 | 0.455733 | − | 0.890117i | \(-0.349377\pi\) | ||||
0.455733 | + | 0.890117i | \(0.349377\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0.945136 | 0.127442 | ||||||||
\(56\) | −4.77865 | −0.638574 | ||||||||
\(57\) | −1.16709 | −0.154585 | ||||||||
\(58\) | −1.14006 | −0.149698 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | −0.580342 | −0.0749218 | ||||||||
\(61\) | 1.75157 | 0.224266 | 0.112133 | − | 0.993693i | \(-0.464232\pi\) | ||||
0.112133 | + | 0.993693i | \(0.464232\pi\) | |||||||
\(62\) | −7.10961 | −0.902921 | ||||||||
\(63\) | 4.77865 | 0.602053 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.18027 | 0.394463 | ||||||||
\(66\) | 1.62859 | 0.200465 | ||||||||
\(67\) | 0.972991 | 0.118870 | 0.0594349 | − | 0.998232i | \(-0.481070\pi\) | ||||
0.0594349 | + | 0.998232i | \(0.481070\pi\) | |||||||
\(68\) | 1.00000 | 0.121268 | ||||||||
\(69\) | 7.82087 | 0.941522 | ||||||||
\(70\) | −2.77325 | −0.331467 | ||||||||
\(71\) | 0.225978 | 0.0268187 | 0.0134093 | − | 0.999910i | \(-0.495732\pi\) | ||||
0.0134093 | + | 0.999910i | \(0.495732\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 1.96236 | 0.229676 | 0.114838 | − | 0.993384i | \(-0.463365\pi\) | ||||
0.114838 | + | 0.993384i | \(0.463365\pi\) | |||||||
\(74\) | −1.66923 | −0.194044 | ||||||||
\(75\) | 4.66320 | 0.538460 | ||||||||
\(76\) | 1.16709 | 0.133875 | ||||||||
\(77\) | 7.78244 | 0.886891 | ||||||||
\(78\) | 5.47999 | 0.620487 | ||||||||
\(79\) | −8.26320 | −0.929682 | −0.464841 | − | 0.885394i | \(-0.653889\pi\) | ||||
−0.464841 | + | 0.885394i | \(0.653889\pi\) | |||||||
\(80\) | 0.580342 | 0.0648842 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.211924 | 0.0234031 | ||||||||
\(83\) | 8.22544 | 0.902859 | 0.451429 | − | 0.892307i | \(-0.350914\pi\) | ||||
0.451429 | + | 0.892307i | \(0.350914\pi\) | |||||||
\(84\) | −4.77865 | −0.521393 | ||||||||
\(85\) | 0.580342 | 0.0629469 | ||||||||
\(86\) | −9.35293 | −1.00855 | ||||||||
\(87\) | −1.14006 | −0.122228 | ||||||||
\(88\) | −1.62859 | −0.173608 | ||||||||
\(89\) | −1.59874 | −0.169466 | −0.0847330 | − | 0.996404i | \(-0.527004\pi\) | ||||
−0.0847330 | + | 0.996404i | \(0.527004\pi\) | |||||||
\(90\) | −0.580342 | −0.0611734 | ||||||||
\(91\) | 26.1869 | 2.74514 | ||||||||
\(92\) | −7.82087 | −0.815382 | ||||||||
\(93\) | −7.10961 | −0.737232 | ||||||||
\(94\) | −4.12655 | −0.425622 | ||||||||
\(95\) | 0.677313 | 0.0694909 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −7.65509 | −0.777257 | −0.388628 | − | 0.921395i | \(-0.627051\pi\) | ||||
−0.388628 | + | 0.921395i | \(0.627051\pi\) | |||||||
\(98\) | −15.8355 | −1.59962 | ||||||||
\(99\) | 1.62859 | 0.163679 | ||||||||
\(100\) | −4.66320 | −0.466320 | ||||||||
\(101\) | 2.30869 | 0.229723 | 0.114861 | − | 0.993382i | \(-0.463358\pi\) | ||||
0.114861 | + | 0.993382i | \(0.463358\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | −6.10597 | −0.601639 | −0.300819 | − | 0.953681i | \(-0.597260\pi\) | ||||
−0.300819 | + | 0.953681i | \(0.597260\pi\) | |||||||
\(104\) | −5.47999 | −0.537357 | ||||||||
\(105\) | −2.77325 | −0.270641 | ||||||||
\(106\) | −6.63557 | −0.644503 | ||||||||
\(107\) | −0.192091 | −0.0185701 | −0.00928506 | − | 0.999957i | \(-0.502956\pi\) | ||||
−0.00928506 | + | 0.999957i | \(0.502956\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −0.690652 | −0.0661525 | −0.0330762 | − | 0.999453i | \(-0.510530\pi\) | ||||
−0.0330762 | + | 0.999453i | \(0.510530\pi\) | |||||||
\(110\) | −0.945136 | −0.0901152 | ||||||||
\(111\) | −1.66923 | −0.158436 | ||||||||
\(112\) | 4.77865 | 0.451540 | ||||||||
\(113\) | −18.0322 | −1.69633 | −0.848164 | − | 0.529733i | \(-0.822292\pi\) | ||||
−0.848164 | + | 0.529733i | \(0.822292\pi\) | |||||||
\(114\) | 1.16709 | 0.109308 | ||||||||
\(115\) | −4.53878 | −0.423243 | ||||||||
\(116\) | 1.14006 | 0.105852 | ||||||||
\(117\) | 5.47999 | 0.506625 | ||||||||
\(118\) | 1.00000 | 0.0920575 | ||||||||
\(119\) | 4.77865 | 0.438058 | ||||||||
\(120\) | 0.580342 | 0.0529777 | ||||||||
\(121\) | −8.34771 | −0.758883 | ||||||||
\(122\) | −1.75157 | −0.158580 | ||||||||
\(123\) | 0.211924 | 0.0191085 | ||||||||
\(124\) | 7.10961 | 0.638461 | ||||||||
\(125\) | −5.60796 | −0.501591 | ||||||||
\(126\) | −4.77865 | −0.425716 | ||||||||
\(127\) | −4.20613 | −0.373233 | −0.186617 | − | 0.982433i | \(-0.559752\pi\) | ||||
−0.186617 | + | 0.982433i | \(0.559752\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −9.35293 | −0.823479 | ||||||||
\(130\) | −3.18027 | −0.278928 | ||||||||
\(131\) | 4.74754 | 0.414794 | 0.207397 | − | 0.978257i | \(-0.433501\pi\) | ||||
0.207397 | + | 0.978257i | \(0.433501\pi\) | |||||||
\(132\) | −1.62859 | −0.141750 | ||||||||
\(133\) | 5.57713 | 0.483599 | ||||||||
\(134\) | −0.972991 | −0.0840536 | ||||||||
\(135\) | −0.580342 | −0.0499479 | ||||||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | −5.83732 | −0.498716 | −0.249358 | − | 0.968411i | \(-0.580220\pi\) | ||||
−0.249358 | + | 0.968411i | \(0.580220\pi\) | |||||||
\(138\) | −7.82087 | −0.665757 | ||||||||
\(139\) | 1.62853 | 0.138130 | 0.0690651 | − | 0.997612i | \(-0.477998\pi\) | ||||
0.0690651 | + | 0.997612i | \(0.477998\pi\) | |||||||
\(140\) | 2.77325 | 0.234382 | ||||||||
\(141\) | −4.12655 | −0.347519 | ||||||||
\(142\) | −0.225978 | −0.0189637 | ||||||||
\(143\) | 8.92463 | 0.746315 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0.661626 | 0.0549450 | ||||||||
\(146\) | −1.96236 | −0.162406 | ||||||||
\(147\) | −15.8355 | −1.30609 | ||||||||
\(148\) | 1.66923 | 0.137209 | ||||||||
\(149\) | 5.84752 | 0.479047 | 0.239524 | − | 0.970891i | \(-0.423009\pi\) | ||||
0.239524 | + | 0.970891i | \(0.423009\pi\) | |||||||
\(150\) | −4.66320 | −0.380749 | ||||||||
\(151\) | −0.333013 | −0.0271002 | −0.0135501 | − | 0.999908i | \(-0.504313\pi\) | ||||
−0.0135501 | + | 0.999908i | \(0.504313\pi\) | |||||||
\(152\) | −1.16709 | −0.0946638 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −7.78244 | −0.627126 | ||||||||
\(155\) | 4.12600 | 0.331408 | ||||||||
\(156\) | −5.47999 | −0.438750 | ||||||||
\(157\) | 13.5429 | 1.08084 | 0.540422 | − | 0.841394i | \(-0.318265\pi\) | ||||
0.540422 | + | 0.841394i | \(0.318265\pi\) | |||||||
\(158\) | 8.26320 | 0.657385 | ||||||||
\(159\) | −6.63557 | −0.526235 | ||||||||
\(160\) | −0.580342 | −0.0458800 | ||||||||
\(161\) | −37.3732 | −2.94542 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −6.84383 | −0.536050 | −0.268025 | − | 0.963412i | \(-0.586371\pi\) | ||||
−0.268025 | + | 0.963412i | \(0.586371\pi\) | |||||||
\(164\) | −0.211924 | −0.0165485 | ||||||||
\(165\) | −0.945136 | −0.0735787 | ||||||||
\(166\) | −8.22544 | −0.638418 | ||||||||
\(167\) | −5.73420 | −0.443726 | −0.221863 | − | 0.975078i | \(-0.571214\pi\) | ||||
−0.221863 | + | 0.975078i | \(0.571214\pi\) | |||||||
\(168\) | 4.77865 | 0.368681 | ||||||||
\(169\) | 17.0303 | 1.31002 | ||||||||
\(170\) | −0.580342 | −0.0445102 | ||||||||
\(171\) | 1.16709 | 0.0892499 | ||||||||
\(172\) | 9.35293 | 0.713154 | ||||||||
\(173\) | 9.65505 | 0.734060 | 0.367030 | − | 0.930209i | \(-0.380375\pi\) | ||||
0.367030 | + | 0.930209i | \(0.380375\pi\) | |||||||
\(174\) | 1.14006 | 0.0864279 | ||||||||
\(175\) | −22.2838 | −1.68450 | ||||||||
\(176\) | 1.62859 | 0.122759 | ||||||||
\(177\) | 1.00000 | 0.0751646 | ||||||||
\(178\) | 1.59874 | 0.119831 | ||||||||
\(179\) | 0.791546 | 0.0591629 | 0.0295815 | − | 0.999562i | \(-0.490583\pi\) | ||||
0.0295815 | + | 0.999562i | \(0.490583\pi\) | |||||||
\(180\) | 0.580342 | 0.0432561 | ||||||||
\(181\) | 1.53099 | 0.113797 | 0.0568987 | − | 0.998380i | \(-0.481879\pi\) | ||||
0.0568987 | + | 0.998380i | \(0.481879\pi\) | |||||||
\(182\) | −26.1869 | −1.94110 | ||||||||
\(183\) | −1.75157 | −0.129480 | ||||||||
\(184\) | 7.82087 | 0.576562 | ||||||||
\(185\) | 0.968721 | 0.0712218 | ||||||||
\(186\) | 7.10961 | 0.521302 | ||||||||
\(187\) | 1.62859 | 0.119094 | ||||||||
\(188\) | 4.12655 | 0.300960 | ||||||||
\(189\) | −4.77865 | −0.347595 | ||||||||
\(190\) | −0.677313 | −0.0491375 | ||||||||
\(191\) | −3.79389 | −0.274516 | −0.137258 | − | 0.990535i | \(-0.543829\pi\) | ||||
−0.137258 | + | 0.990535i | \(0.543829\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 8.98705 | 0.646902 | 0.323451 | − | 0.946245i | \(-0.395157\pi\) | ||||
0.323451 | + | 0.946245i | \(0.395157\pi\) | |||||||
\(194\) | 7.65509 | 0.549604 | ||||||||
\(195\) | −3.18027 | −0.227744 | ||||||||
\(196\) | 15.8355 | 1.13111 | ||||||||
\(197\) | −5.73976 | −0.408941 | −0.204471 | − | 0.978873i | \(-0.565547\pi\) | ||||
−0.204471 | + | 0.978873i | \(0.565547\pi\) | |||||||
\(198\) | −1.62859 | −0.115739 | ||||||||
\(199\) | 14.0439 | 0.995546 | 0.497773 | − | 0.867307i | \(-0.334151\pi\) | ||||
0.497773 | + | 0.867307i | \(0.334151\pi\) | |||||||
\(200\) | 4.66320 | 0.329738 | ||||||||
\(201\) | −0.972991 | −0.0686295 | ||||||||
\(202\) | −2.30869 | −0.162439 | ||||||||
\(203\) | 5.44796 | 0.382372 | ||||||||
\(204\) | −1.00000 | −0.0700140 | ||||||||
\(205\) | −0.122988 | −0.00858988 | ||||||||
\(206\) | 6.10597 | 0.425423 | ||||||||
\(207\) | −7.82087 | −0.543588 | ||||||||
\(208\) | 5.47999 | 0.379969 | ||||||||
\(209\) | 1.90071 | 0.131475 | ||||||||
\(210\) | 2.77325 | 0.191372 | ||||||||
\(211\) | −25.2857 | −1.74074 | −0.870369 | − | 0.492401i | \(-0.836119\pi\) | ||||
−0.870369 | + | 0.492401i | \(0.836119\pi\) | |||||||
\(212\) | 6.63557 | 0.455733 | ||||||||
\(213\) | −0.225978 | −0.0154838 | ||||||||
\(214\) | 0.192091 | 0.0131311 | ||||||||
\(215\) | 5.42789 | 0.370179 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 33.9743 | 2.30633 | ||||||||
\(218\) | 0.690652 | 0.0467768 | ||||||||
\(219\) | −1.96236 | −0.132604 | ||||||||
\(220\) | 0.945136 | 0.0637211 | ||||||||
\(221\) | 5.47999 | 0.368624 | ||||||||
\(222\) | 1.66923 | 0.112031 | ||||||||
\(223\) | −9.53502 | −0.638512 | −0.319256 | − | 0.947669i | \(-0.603433\pi\) | ||||
−0.319256 | + | 0.947669i | \(0.603433\pi\) | |||||||
\(224\) | −4.77865 | −0.319287 | ||||||||
\(225\) | −4.66320 | −0.310880 | ||||||||
\(226\) | 18.0322 | 1.19949 | ||||||||
\(227\) | 20.1882 | 1.33994 | 0.669969 | − | 0.742389i | \(-0.266307\pi\) | ||||
0.669969 | + | 0.742389i | \(0.266307\pi\) | |||||||
\(228\) | −1.16709 | −0.0772927 | ||||||||
\(229\) | −2.84520 | −0.188016 | −0.0940079 | − | 0.995571i | \(-0.529968\pi\) | ||||
−0.0940079 | + | 0.995571i | \(0.529968\pi\) | |||||||
\(230\) | 4.53878 | 0.299278 | ||||||||
\(231\) | −7.78244 | −0.512047 | ||||||||
\(232\) | −1.14006 | −0.0748488 | ||||||||
\(233\) | −7.66783 | −0.502336 | −0.251168 | − | 0.967943i | \(-0.580815\pi\) | ||||
−0.251168 | + | 0.967943i | \(0.580815\pi\) | |||||||
\(234\) | −5.47999 | −0.358238 | ||||||||
\(235\) | 2.39481 | 0.156220 | ||||||||
\(236\) | −1.00000 | −0.0650945 | ||||||||
\(237\) | 8.26320 | 0.536752 | ||||||||
\(238\) | −4.77865 | −0.309754 | ||||||||
\(239\) | −2.50181 | −0.161829 | −0.0809143 | − | 0.996721i | \(-0.525784\pi\) | ||||
−0.0809143 | + | 0.996721i | \(0.525784\pi\) | |||||||
\(240\) | −0.580342 | −0.0374609 | ||||||||
\(241\) | 17.2582 | 1.11170 | 0.555849 | − | 0.831283i | \(-0.312393\pi\) | ||||
0.555849 | + | 0.831283i | \(0.312393\pi\) | |||||||
\(242\) | 8.34771 | 0.536611 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.75157 | 0.112133 | ||||||||
\(245\) | 9.18999 | 0.587127 | ||||||||
\(246\) | −0.211924 | −0.0135118 | ||||||||
\(247\) | 6.39566 | 0.406946 | ||||||||
\(248\) | −7.10961 | −0.451460 | ||||||||
\(249\) | −8.22544 | −0.521266 | ||||||||
\(250\) | 5.60796 | 0.354679 | ||||||||
\(251\) | −19.8854 | −1.25515 | −0.627576 | − | 0.778555i | \(-0.715953\pi\) | ||||
−0.627576 | + | 0.778555i | \(0.715953\pi\) | |||||||
\(252\) | 4.77865 | 0.301027 | ||||||||
\(253\) | −12.7370 | −0.800765 | ||||||||
\(254\) | 4.20613 | 0.263916 | ||||||||
\(255\) | −0.580342 | −0.0363424 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.13485 | 0.507438 | 0.253719 | − | 0.967278i | \(-0.418346\pi\) | ||||
0.253719 | + | 0.967278i | \(0.418346\pi\) | |||||||
\(258\) | 9.35293 | 0.582288 | ||||||||
\(259\) | 7.97664 | 0.495644 | ||||||||
\(260\) | 3.18027 | 0.197232 | ||||||||
\(261\) | 1.14006 | 0.0705681 | ||||||||
\(262\) | −4.74754 | −0.293304 | ||||||||
\(263\) | 10.5725 | 0.651928 | 0.325964 | − | 0.945382i | \(-0.394311\pi\) | ||||
0.325964 | + | 0.945382i | \(0.394311\pi\) | |||||||
\(264\) | 1.62859 | 0.100232 | ||||||||
\(265\) | 3.85090 | 0.236559 | ||||||||
\(266\) | −5.57713 | −0.341956 | ||||||||
\(267\) | 1.59874 | 0.0978412 | ||||||||
\(268\) | 0.972991 | 0.0594349 | ||||||||
\(269\) | −21.8410 | −1.33167 | −0.665834 | − | 0.746100i | \(-0.731924\pi\) | ||||
−0.665834 | + | 0.746100i | \(0.731924\pi\) | |||||||
\(270\) | 0.580342 | 0.0353185 | ||||||||
\(271\) | 25.2327 | 1.53278 | 0.766389 | − | 0.642376i | \(-0.222051\pi\) | ||||
0.766389 | + | 0.642376i | \(0.222051\pi\) | |||||||
\(272\) | 1.00000 | 0.0606339 | ||||||||
\(273\) | −26.1869 | −1.58491 | ||||||||
\(274\) | 5.83732 | 0.352645 | ||||||||
\(275\) | −7.59442 | −0.457961 | ||||||||
\(276\) | 7.82087 | 0.470761 | ||||||||
\(277\) | −14.1564 | −0.850574 | −0.425287 | − | 0.905058i | \(-0.639827\pi\) | ||||
−0.425287 | + | 0.905058i | \(0.639827\pi\) | |||||||
\(278\) | −1.62853 | −0.0976728 | ||||||||
\(279\) | 7.10961 | 0.425641 | ||||||||
\(280\) | −2.77325 | −0.165733 | ||||||||
\(281\) | −2.81297 | −0.167808 | −0.0839039 | − | 0.996474i | \(-0.526739\pi\) | ||||
−0.0839039 | + | 0.996474i | \(0.526739\pi\) | |||||||
\(282\) | 4.12655 | 0.245733 | ||||||||
\(283\) | −31.2649 | −1.85851 | −0.929253 | − | 0.369445i | \(-0.879548\pi\) | ||||
−0.929253 | + | 0.369445i | \(0.879548\pi\) | |||||||
\(284\) | 0.225978 | 0.0134093 | ||||||||
\(285\) | −0.677313 | −0.0401206 | ||||||||
\(286\) | −8.92463 | −0.527724 | ||||||||
\(287\) | −1.01271 | −0.0597784 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −0.661626 | −0.0388520 | ||||||||
\(291\) | 7.65509 | 0.448749 | ||||||||
\(292\) | 1.96236 | 0.114838 | ||||||||
\(293\) | 0.689982 | 0.0403092 | 0.0201546 | − | 0.999797i | \(-0.493584\pi\) | ||||
0.0201546 | + | 0.999797i | \(0.493584\pi\) | |||||||
\(294\) | 15.8355 | 0.923544 | ||||||||
\(295\) | −0.580342 | −0.0337888 | ||||||||
\(296\) | −1.66923 | −0.0970218 | ||||||||
\(297\) | −1.62859 | −0.0945001 | ||||||||
\(298\) | −5.84752 | −0.338738 | ||||||||
\(299\) | −42.8583 | −2.47856 | ||||||||
\(300\) | 4.66320 | 0.269230 | ||||||||
\(301\) | 44.6943 | 2.57614 | ||||||||
\(302\) | 0.333013 | 0.0191627 | ||||||||
\(303\) | −2.30869 | −0.132631 | ||||||||
\(304\) | 1.16709 | 0.0669374 | ||||||||
\(305\) | 1.01651 | 0.0582051 | ||||||||
\(306\) | −1.00000 | −0.0571662 | ||||||||
\(307\) | 5.97982 | 0.341287 | 0.170643 | − | 0.985333i | \(-0.445415\pi\) | ||||
0.170643 | + | 0.985333i | \(0.445415\pi\) | |||||||
\(308\) | 7.78244 | 0.443445 | ||||||||
\(309\) | 6.10597 | 0.347356 | ||||||||
\(310\) | −4.12600 | −0.234341 | ||||||||
\(311\) | 25.5624 | 1.44951 | 0.724756 | − | 0.689006i | \(-0.241953\pi\) | ||||
0.724756 | + | 0.689006i | \(0.241953\pi\) | |||||||
\(312\) | 5.47999 | 0.310243 | ||||||||
\(313\) | −21.2681 | −1.20214 | −0.601071 | − | 0.799195i | \(-0.705259\pi\) | ||||
−0.601071 | + | 0.799195i | \(0.705259\pi\) | |||||||
\(314\) | −13.5429 | −0.764271 | ||||||||
\(315\) | 2.77325 | 0.156255 | ||||||||
\(316\) | −8.26320 | −0.464841 | ||||||||
\(317\) | −27.9593 | −1.57035 | −0.785176 | − | 0.619273i | \(-0.787428\pi\) | ||||
−0.785176 | + | 0.619273i | \(0.787428\pi\) | |||||||
\(318\) | 6.63557 | 0.372104 | ||||||||
\(319\) | 1.85669 | 0.103955 | ||||||||
\(320\) | 0.580342 | 0.0324421 | ||||||||
\(321\) | 0.192091 | 0.0107215 | ||||||||
\(322\) | 37.3732 | 2.08273 | ||||||||
\(323\) | 1.16709 | 0.0649389 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −25.5543 | −1.41750 | ||||||||
\(326\) | 6.84383 | 0.379044 | ||||||||
\(327\) | 0.690652 | 0.0381931 | ||||||||
\(328\) | 0.211924 | 0.0117015 | ||||||||
\(329\) | 19.7194 | 1.08716 | ||||||||
\(330\) | 0.945136 | 0.0520280 | ||||||||
\(331\) | −17.4034 | −0.956578 | −0.478289 | − | 0.878203i | \(-0.658743\pi\) | ||||
−0.478289 | + | 0.878203i | \(0.658743\pi\) | |||||||
\(332\) | 8.22544 | 0.451429 | ||||||||
\(333\) | 1.66923 | 0.0914730 | ||||||||
\(334\) | 5.73420 | 0.313762 | ||||||||
\(335\) | 0.564667 | 0.0308511 | ||||||||
\(336\) | −4.77865 | −0.260697 | ||||||||
\(337\) | 19.7159 | 1.07399 | 0.536996 | − | 0.843585i | \(-0.319559\pi\) | ||||
0.536996 | + | 0.843585i | \(0.319559\pi\) | |||||||
\(338\) | −17.0303 | −0.926325 | ||||||||
\(339\) | 18.0322 | 0.979376 | ||||||||
\(340\) | 0.580342 | 0.0314735 | ||||||||
\(341\) | 11.5786 | 0.627016 | ||||||||
\(342\) | −1.16709 | −0.0631092 | ||||||||
\(343\) | 42.2216 | 2.27975 | ||||||||
\(344\) | −9.35293 | −0.504276 | ||||||||
\(345\) | 4.53878 | 0.244360 | ||||||||
\(346\) | −9.65505 | −0.519059 | ||||||||
\(347\) | −19.2525 | −1.03353 | −0.516765 | − | 0.856127i | \(-0.672864\pi\) | ||||
−0.516765 | + | 0.856127i | \(0.672864\pi\) | |||||||
\(348\) | −1.14006 | −0.0611138 | ||||||||
\(349\) | −24.6206 | −1.31791 | −0.658955 | − | 0.752182i | \(-0.729001\pi\) | ||||
−0.658955 | + | 0.752182i | \(0.729001\pi\) | |||||||
\(350\) | 22.2838 | 1.19112 | ||||||||
\(351\) | −5.47999 | −0.292500 | ||||||||
\(352\) | −1.62859 | −0.0868039 | ||||||||
\(353\) | 21.4591 | 1.14216 | 0.571078 | − | 0.820896i | \(-0.306526\pi\) | ||||
0.571078 | + | 0.820896i | \(0.306526\pi\) | |||||||
\(354\) | −1.00000 | −0.0531494 | ||||||||
\(355\) | 0.131145 | 0.00696044 | ||||||||
\(356\) | −1.59874 | −0.0847330 | ||||||||
\(357\) | −4.77865 | −0.252913 | ||||||||
\(358\) | −0.791546 | −0.0418345 | ||||||||
\(359\) | 33.9256 | 1.79053 | 0.895263 | − | 0.445538i | \(-0.146988\pi\) | ||||
0.895263 | + | 0.445538i | \(0.146988\pi\) | |||||||
\(360\) | −0.580342 | −0.0305867 | ||||||||
\(361\) | −17.6379 | −0.928310 | ||||||||
\(362\) | −1.53099 | −0.0804669 | ||||||||
\(363\) | 8.34771 | 0.438141 | ||||||||
\(364\) | 26.1869 | 1.37257 | ||||||||
\(365\) | 1.13884 | 0.0596095 | ||||||||
\(366\) | 1.75157 | 0.0915560 | ||||||||
\(367\) | −2.51893 | −0.131487 | −0.0657434 | − | 0.997837i | \(-0.520942\pi\) | ||||
−0.0657434 | + | 0.997837i | \(0.520942\pi\) | |||||||
\(368\) | −7.82087 | −0.407691 | ||||||||
\(369\) | −0.211924 | −0.0110323 | ||||||||
\(370\) | −0.968721 | −0.0503614 | ||||||||
\(371\) | 31.7090 | 1.64625 | ||||||||
\(372\) | −7.10961 | −0.368616 | ||||||||
\(373\) | −17.7784 | −0.920528 | −0.460264 | − | 0.887782i | \(-0.652245\pi\) | ||||
−0.460264 | + | 0.887782i | \(0.652245\pi\) | |||||||
\(374\) | −1.62859 | −0.0842121 | ||||||||
\(375\) | 5.60796 | 0.289594 | ||||||||
\(376\) | −4.12655 | −0.212811 | ||||||||
\(377\) | 6.24753 | 0.321764 | ||||||||
\(378\) | 4.77865 | 0.245787 | ||||||||
\(379\) | 8.51794 | 0.437537 | 0.218769 | − | 0.975777i | \(-0.429796\pi\) | ||||
0.218769 | + | 0.975777i | \(0.429796\pi\) | |||||||
\(380\) | 0.677313 | 0.0347454 | ||||||||
\(381\) | 4.20613 | 0.215486 | ||||||||
\(382\) | 3.79389 | 0.194112 | ||||||||
\(383\) | 0.841850 | 0.0430165 | 0.0215083 | − | 0.999769i | \(-0.493153\pi\) | ||||
0.0215083 | + | 0.999769i | \(0.493153\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 4.51647 | 0.230181 | ||||||||
\(386\) | −8.98705 | −0.457429 | ||||||||
\(387\) | 9.35293 | 0.475436 | ||||||||
\(388\) | −7.65509 | −0.388628 | ||||||||
\(389\) | −0.461026 | −0.0233749 | −0.0116875 | − | 0.999932i | \(-0.503720\pi\) | ||||
−0.0116875 | + | 0.999932i | \(0.503720\pi\) | |||||||
\(390\) | 3.18027 | 0.161039 | ||||||||
\(391\) | −7.82087 | −0.395518 | ||||||||
\(392\) | −15.8355 | −0.799812 | ||||||||
\(393\) | −4.74754 | −0.239482 | ||||||||
\(394\) | 5.73976 | 0.289165 | ||||||||
\(395\) | −4.79548 | −0.241287 | ||||||||
\(396\) | 1.62859 | 0.0818395 | ||||||||
\(397\) | 7.85404 | 0.394183 | 0.197091 | − | 0.980385i | \(-0.436850\pi\) | ||||
0.197091 | + | 0.980385i | \(0.436850\pi\) | |||||||
\(398\) | −14.0439 | −0.703958 | ||||||||
\(399\) | −5.57713 | −0.279206 | ||||||||
\(400\) | −4.66320 | −0.233160 | ||||||||
\(401\) | 22.4214 | 1.11967 | 0.559835 | − | 0.828604i | \(-0.310864\pi\) | ||||
0.559835 | + | 0.828604i | \(0.310864\pi\) | |||||||
\(402\) | 0.972991 | 0.0485284 | ||||||||
\(403\) | 38.9606 | 1.94076 | ||||||||
\(404\) | 2.30869 | 0.114861 | ||||||||
\(405\) | 0.580342 | 0.0288374 | ||||||||
\(406\) | −5.44796 | −0.270378 | ||||||||
\(407\) | 2.71848 | 0.134750 | ||||||||
\(408\) | 1.00000 | 0.0495074 | ||||||||
\(409\) | 10.5913 | 0.523704 | 0.261852 | − | 0.965108i | \(-0.415667\pi\) | ||||
0.261852 | + | 0.965108i | \(0.415667\pi\) | |||||||
\(410\) | 0.122988 | 0.00607396 | ||||||||
\(411\) | 5.83732 | 0.287934 | ||||||||
\(412\) | −6.10597 | −0.300819 | ||||||||
\(413\) | −4.77865 | −0.235142 | ||||||||
\(414\) | 7.82087 | 0.384375 | ||||||||
\(415\) | 4.77356 | 0.234325 | ||||||||
\(416\) | −5.47999 | −0.268679 | ||||||||
\(417\) | −1.62853 | −0.0797495 | ||||||||
\(418\) | −1.90071 | −0.0929669 | ||||||||
\(419\) | 33.0129 | 1.61279 | 0.806394 | − | 0.591379i | \(-0.201416\pi\) | ||||
0.806394 | + | 0.591379i | \(0.201416\pi\) | |||||||
\(420\) | −2.77325 | −0.135321 | ||||||||
\(421\) | −12.7986 | −0.623764 | −0.311882 | − | 0.950121i | \(-0.600959\pi\) | ||||
−0.311882 | + | 0.950121i | \(0.600959\pi\) | |||||||
\(422\) | 25.2857 | 1.23089 | ||||||||
\(423\) | 4.12655 | 0.200640 | ||||||||
\(424\) | −6.63557 | −0.322252 | ||||||||
\(425\) | −4.66320 | −0.226199 | ||||||||
\(426\) | 0.225978 | 0.0109487 | ||||||||
\(427\) | 8.37014 | 0.405059 | ||||||||
\(428\) | −0.192091 | −0.00928506 | ||||||||
\(429\) | −8.92463 | −0.430885 | ||||||||
\(430\) | −5.42789 | −0.261756 | ||||||||
\(431\) | −6.11123 | −0.294368 | −0.147184 | − | 0.989109i | \(-0.547021\pi\) | ||||
−0.147184 | + | 0.989109i | \(0.547021\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 9.07872 | 0.436296 | 0.218148 | − | 0.975916i | \(-0.429999\pi\) | ||||
0.218148 | + | 0.975916i | \(0.429999\pi\) | |||||||
\(434\) | −33.9743 | −1.63082 | ||||||||
\(435\) | −0.661626 | −0.0317225 | ||||||||
\(436\) | −0.690652 | −0.0330762 | ||||||||
\(437\) | −9.12769 | −0.436637 | ||||||||
\(438\) | 1.96236 | 0.0937650 | ||||||||
\(439\) | 4.51957 | 0.215707 | 0.107854 | − | 0.994167i | \(-0.465602\pi\) | ||||
0.107854 | + | 0.994167i | \(0.465602\pi\) | |||||||
\(440\) | −0.945136 | −0.0450576 | ||||||||
\(441\) | 15.8355 | 0.754070 | ||||||||
\(442\) | −5.47999 | −0.260656 | ||||||||
\(443\) | 9.45160 | 0.449059 | 0.224529 | − | 0.974467i | \(-0.427915\pi\) | ||||
0.224529 | + | 0.974467i | \(0.427915\pi\) | |||||||
\(444\) | −1.66923 | −0.0792179 | ||||||||
\(445\) | −0.927815 | −0.0439826 | ||||||||
\(446\) | 9.53502 | 0.451496 | ||||||||
\(447\) | −5.84752 | −0.276578 | ||||||||
\(448\) | 4.77865 | 0.225770 | ||||||||
\(449\) | −7.59507 | −0.358434 | −0.179217 | − | 0.983810i | \(-0.557356\pi\) | ||||
−0.179217 | + | 0.983810i | \(0.557356\pi\) | |||||||
\(450\) | 4.66320 | 0.219826 | ||||||||
\(451\) | −0.345136 | −0.0162518 | ||||||||
\(452\) | −18.0322 | −0.848164 | ||||||||
\(453\) | 0.333013 | 0.0156463 | ||||||||
\(454\) | −20.1882 | −0.947480 | ||||||||
\(455\) | 15.1974 | 0.712464 | ||||||||
\(456\) | 1.16709 | 0.0546542 | ||||||||
\(457\) | −9.84114 | −0.460349 | −0.230175 | − | 0.973149i | \(-0.573930\pi\) | ||||
−0.230175 | + | 0.973149i | \(0.573930\pi\) | |||||||
\(458\) | 2.84520 | 0.132947 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −4.53878 | −0.211622 | ||||||||
\(461\) | −12.8726 | −0.599538 | −0.299769 | − | 0.954012i | \(-0.596910\pi\) | ||||
−0.299769 | + | 0.954012i | \(0.596910\pi\) | |||||||
\(462\) | 7.78244 | 0.362072 | ||||||||
\(463\) | −3.67175 | −0.170641 | −0.0853204 | − | 0.996354i | \(-0.527191\pi\) | ||||
−0.0853204 | + | 0.996354i | \(0.527191\pi\) | |||||||
\(464\) | 1.14006 | 0.0529261 | ||||||||
\(465\) | −4.12600 | −0.191339 | ||||||||
\(466\) | 7.66783 | 0.355205 | ||||||||
\(467\) | 9.76462 | 0.451853 | 0.225926 | − | 0.974144i | \(-0.427459\pi\) | ||||
0.225926 | + | 0.974144i | \(0.427459\pi\) | |||||||
\(468\) | 5.47999 | 0.253313 | ||||||||
\(469\) | 4.64958 | 0.214698 | ||||||||
\(470\) | −2.39481 | −0.110464 | ||||||||
\(471\) | −13.5429 | −0.624025 | ||||||||
\(472\) | 1.00000 | 0.0460287 | ||||||||
\(473\) | 15.2320 | 0.700370 | ||||||||
\(474\) | −8.26320 | −0.379541 | ||||||||
\(475\) | −5.44240 | −0.249714 | ||||||||
\(476\) | 4.77865 | 0.219029 | ||||||||
\(477\) | 6.63557 | 0.303822 | ||||||||
\(478\) | 2.50181 | 0.114430 | ||||||||
\(479\) | 5.99020 | 0.273699 | 0.136850 | − | 0.990592i | \(-0.456302\pi\) | ||||
0.136850 | + | 0.990592i | \(0.456302\pi\) | |||||||
\(480\) | 0.580342 | 0.0264889 | ||||||||
\(481\) | 9.14734 | 0.417083 | ||||||||
\(482\) | −17.2582 | −0.786089 | ||||||||
\(483\) | 37.3732 | 1.70054 | ||||||||
\(484\) | −8.34771 | −0.379441 | ||||||||
\(485\) | −4.44257 | −0.201727 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 19.1635 | 0.868383 | 0.434192 | − | 0.900821i | \(-0.357034\pi\) | ||||
0.434192 | + | 0.900821i | \(0.357034\pi\) | |||||||
\(488\) | −1.75157 | −0.0792898 | ||||||||
\(489\) | 6.84383 | 0.309489 | ||||||||
\(490\) | −9.18999 | −0.415161 | ||||||||
\(491\) | −35.5803 | −1.60572 | −0.802859 | − | 0.596169i | \(-0.796689\pi\) | ||||
−0.802859 | + | 0.596169i | \(0.796689\pi\) | |||||||
\(492\) | 0.211924 | 0.00955427 | ||||||||
\(493\) | 1.14006 | 0.0513458 | ||||||||
\(494\) | −6.39566 | −0.287754 | ||||||||
\(495\) | 0.945136 | 0.0424807 | ||||||||
\(496\) | 7.10961 | 0.319231 | ||||||||
\(497\) | 1.07987 | 0.0484388 | ||||||||
\(498\) | 8.22544 | 0.368591 | ||||||||
\(499\) | 37.3473 | 1.67190 | 0.835948 | − | 0.548809i | \(-0.184918\pi\) | ||||
0.835948 | + | 0.548809i | \(0.184918\pi\) | |||||||
\(500\) | −5.60796 | −0.250796 | ||||||||
\(501\) | 5.73420 | 0.256185 | ||||||||
\(502\) | 19.8854 | 0.887527 | ||||||||
\(503\) | −40.2022 | −1.79253 | −0.896264 | − | 0.443521i | \(-0.853729\pi\) | ||||
−0.896264 | + | 0.443521i | \(0.853729\pi\) | |||||||
\(504\) | −4.77865 | −0.212858 | ||||||||
\(505\) | 1.33983 | 0.0596215 | ||||||||
\(506\) | 12.7370 | 0.566227 | ||||||||
\(507\) | −17.0303 | −0.756341 | ||||||||
\(508\) | −4.20613 | −0.186617 | ||||||||
\(509\) | −30.0994 | −1.33413 | −0.667066 | − | 0.744998i | \(-0.732450\pi\) | ||||
−0.667066 | + | 0.744998i | \(0.732450\pi\) | |||||||
\(510\) | 0.580342 | 0.0256980 | ||||||||
\(511\) | 9.37741 | 0.414832 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.16709 | −0.0515285 | ||||||||
\(514\) | −8.13485 | −0.358813 | ||||||||
\(515\) | −3.54355 | −0.156147 | ||||||||
\(516\) | −9.35293 | −0.411740 | ||||||||
\(517\) | 6.72045 | 0.295565 | ||||||||
\(518\) | −7.97664 | −0.350473 | ||||||||
\(519\) | −9.65505 | −0.423810 | ||||||||
\(520\) | −3.18027 | −0.139464 | ||||||||
\(521\) | 38.2781 | 1.67700 | 0.838498 | − | 0.544905i | \(-0.183434\pi\) | ||||
0.838498 | + | 0.544905i | \(0.183434\pi\) | |||||||
\(522\) | −1.14006 | −0.0498992 | ||||||||
\(523\) | 39.3589 | 1.72105 | 0.860523 | − | 0.509412i | \(-0.170137\pi\) | ||||
0.860523 | + | 0.509412i | \(0.170137\pi\) | |||||||
\(524\) | 4.74754 | 0.207397 | ||||||||
\(525\) | 22.2838 | 0.972545 | ||||||||
\(526\) | −10.5725 | −0.460983 | ||||||||
\(527\) | 7.10961 | 0.309699 | ||||||||
\(528\) | −1.62859 | −0.0708751 | ||||||||
\(529\) | 38.1660 | 1.65939 | ||||||||
\(530\) | −3.85090 | −0.167272 | ||||||||
\(531\) | −1.00000 | −0.0433963 | ||||||||
\(532\) | 5.57713 | 0.241799 | ||||||||
\(533\) | −1.16134 | −0.0503033 | ||||||||
\(534\) | −1.59874 | −0.0691842 | ||||||||
\(535\) | −0.111478 | −0.00481963 | ||||||||
\(536\) | −0.972991 | −0.0420268 | ||||||||
\(537\) | −0.791546 | −0.0341577 | ||||||||
\(538\) | 21.8410 | 0.941631 | ||||||||
\(539\) | 25.7894 | 1.11083 | ||||||||
\(540\) | −0.580342 | −0.0249739 | ||||||||
\(541\) | 17.1469 | 0.737201 | 0.368601 | − | 0.929588i | \(-0.379837\pi\) | ||||
0.368601 | + | 0.929588i | \(0.379837\pi\) | |||||||
\(542\) | −25.2327 | −1.08384 | ||||||||
\(543\) | −1.53099 | −0.0657010 | ||||||||
\(544\) | −1.00000 | −0.0428746 | ||||||||
\(545\) | −0.400814 | −0.0171690 | ||||||||
\(546\) | 26.1869 | 1.12070 | ||||||||
\(547\) | −33.9397 | −1.45116 | −0.725578 | − | 0.688140i | \(-0.758428\pi\) | ||||
−0.725578 | + | 0.688140i | \(0.758428\pi\) | |||||||
\(548\) | −5.83732 | −0.249358 | ||||||||
\(549\) | 1.75157 | 0.0747552 | ||||||||
\(550\) | 7.59442 | 0.323827 | ||||||||
\(551\) | 1.33056 | 0.0566838 | ||||||||
\(552\) | −7.82087 | −0.332878 | ||||||||
\(553\) | −39.4869 | −1.67915 | ||||||||
\(554\) | 14.1564 | 0.601447 | ||||||||
\(555\) | −0.968721 | −0.0411199 | ||||||||
\(556\) | 1.62853 | 0.0690651 | ||||||||
\(557\) | 16.7397 | 0.709286 | 0.354643 | − | 0.935002i | \(-0.384602\pi\) | ||||
0.354643 | + | 0.935002i | \(0.384602\pi\) | |||||||
\(558\) | −7.10961 | −0.300974 | ||||||||
\(559\) | 51.2539 | 2.16781 | ||||||||
\(560\) | 2.77325 | 0.117191 | ||||||||
\(561\) | −1.62859 | −0.0687589 | ||||||||
\(562\) | 2.81297 | 0.118658 | ||||||||
\(563\) | 35.6193 | 1.50117 | 0.750586 | − | 0.660772i | \(-0.229771\pi\) | ||||
0.750586 | + | 0.660772i | \(0.229771\pi\) | |||||||
\(564\) | −4.12655 | −0.173759 | ||||||||
\(565\) | −10.4648 | −0.440260 | ||||||||
\(566\) | 31.2649 | 1.31416 | ||||||||
\(567\) | 4.77865 | 0.200684 | ||||||||
\(568\) | −0.225978 | −0.00948184 | ||||||||
\(569\) | −4.63130 | −0.194154 | −0.0970772 | − | 0.995277i | \(-0.530949\pi\) | ||||
−0.0970772 | + | 0.995277i | \(0.530949\pi\) | |||||||
\(570\) | 0.677313 | 0.0283695 | ||||||||
\(571\) | −7.01576 | −0.293600 | −0.146800 | − | 0.989166i | \(-0.546897\pi\) | ||||
−0.146800 | + | 0.989166i | \(0.546897\pi\) | |||||||
\(572\) | 8.92463 | 0.373157 | ||||||||
\(573\) | 3.79389 | 0.158492 | ||||||||
\(574\) | 1.01271 | 0.0422697 | ||||||||
\(575\) | 36.4703 | 1.52092 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 14.7211 | 0.612847 | 0.306423 | − | 0.951895i | \(-0.400868\pi\) | ||||
0.306423 | + | 0.951895i | \(0.400868\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | −8.98705 | −0.373489 | ||||||||
\(580\) | 0.661626 | 0.0274725 | ||||||||
\(581\) | 39.3065 | 1.63071 | ||||||||
\(582\) | −7.65509 | −0.317314 | ||||||||
\(583\) | 10.8066 | 0.447563 | ||||||||
\(584\) | −1.96236 | −0.0812029 | ||||||||
\(585\) | 3.18027 | 0.131488 | ||||||||
\(586\) | −0.689982 | −0.0285029 | ||||||||
\(587\) | −5.22657 | −0.215724 | −0.107862 | − | 0.994166i | \(-0.534400\pi\) | ||||
−0.107862 | + | 0.994166i | \(0.534400\pi\) | |||||||
\(588\) | −15.8355 | −0.653044 | ||||||||
\(589\) | 8.29758 | 0.341896 | ||||||||
\(590\) | 0.580342 | 0.0238923 | ||||||||
\(591\) | 5.73976 | 0.236102 | ||||||||
\(592\) | 1.66923 | 0.0686047 | ||||||||
\(593\) | −3.08693 | −0.126765 | −0.0633824 | − | 0.997989i | \(-0.520189\pi\) | ||||
−0.0633824 | + | 0.997989i | \(0.520189\pi\) | |||||||
\(594\) | 1.62859 | 0.0668217 | ||||||||
\(595\) | 2.77325 | 0.113692 | ||||||||
\(596\) | 5.84752 | 0.239524 | ||||||||
\(597\) | −14.0439 | −0.574779 | ||||||||
\(598\) | 42.8583 | 1.75261 | ||||||||
\(599\) | −18.1055 | −0.739771 | −0.369885 | − | 0.929077i | \(-0.620603\pi\) | ||||
−0.369885 | + | 0.929077i | \(0.620603\pi\) | |||||||
\(600\) | −4.66320 | −0.190374 | ||||||||
\(601\) | 24.7259 | 1.00859 | 0.504296 | − | 0.863531i | \(-0.331752\pi\) | ||||
0.504296 | + | 0.863531i | \(0.331752\pi\) | |||||||
\(602\) | −44.6943 | −1.82161 | ||||||||
\(603\) | 0.972991 | 0.0396233 | ||||||||
\(604\) | −0.333013 | −0.0135501 | ||||||||
\(605\) | −4.84452 | −0.196958 | ||||||||
\(606\) | 2.30869 | 0.0937839 | ||||||||
\(607\) | 47.5956 | 1.93184 | 0.965922 | − | 0.258833i | \(-0.0833379\pi\) | ||||
0.965922 | + | 0.258833i | \(0.0833379\pi\) | |||||||
\(608\) | −1.16709 | −0.0473319 | ||||||||
\(609\) | −5.44796 | −0.220762 | ||||||||
\(610\) | −1.01651 | −0.0411573 | ||||||||
\(611\) | 22.6135 | 0.914843 | ||||||||
\(612\) | 1.00000 | 0.0404226 | ||||||||
\(613\) | −6.03601 | −0.243792 | −0.121896 | − | 0.992543i | \(-0.538897\pi\) | ||||
−0.121896 | + | 0.992543i | \(0.538897\pi\) | |||||||
\(614\) | −5.97982 | −0.241326 | ||||||||
\(615\) | 0.122988 | 0.00495937 | ||||||||
\(616\) | −7.78244 | −0.313563 | ||||||||
\(617\) | 17.3761 | 0.699536 | 0.349768 | − | 0.936836i | \(-0.386260\pi\) | ||||
0.349768 | + | 0.936836i | \(0.386260\pi\) | |||||||
\(618\) | −6.10597 | −0.245618 | ||||||||
\(619\) | −41.2754 | −1.65900 | −0.829500 | − | 0.558507i | \(-0.811374\pi\) | ||||
−0.829500 | + | 0.558507i | \(0.811374\pi\) | |||||||
\(620\) | 4.12600 | 0.165704 | ||||||||
\(621\) | 7.82087 | 0.313841 | ||||||||
\(622\) | −25.5624 | −1.02496 | ||||||||
\(623\) | −7.63981 | −0.306082 | ||||||||
\(624\) | −5.47999 | −0.219375 | ||||||||
\(625\) | 20.0615 | 0.802459 | ||||||||
\(626\) | 21.2681 | 0.850043 | ||||||||
\(627\) | −1.90071 | −0.0759071 | ||||||||
\(628\) | 13.5429 | 0.540422 | ||||||||
\(629\) | 1.66923 | 0.0665564 | ||||||||
\(630\) | −2.77325 | −0.110489 | ||||||||
\(631\) | −6.56631 | −0.261401 | −0.130700 | − | 0.991422i | \(-0.541723\pi\) | ||||
−0.130700 | + | 0.991422i | \(0.541723\pi\) | |||||||
\(632\) | 8.26320 | 0.328692 | ||||||||
\(633\) | 25.2857 | 1.00502 | ||||||||
\(634\) | 27.9593 | 1.11041 | ||||||||
\(635\) | −2.44099 | −0.0968678 | ||||||||
\(636\) | −6.63557 | −0.263117 | ||||||||
\(637\) | 86.7782 | 3.43828 | ||||||||
\(638\) | −1.85669 | −0.0735070 | ||||||||
\(639\) | 0.225978 | 0.00893957 | ||||||||
\(640\) | −0.580342 | −0.0229400 | ||||||||
\(641\) | −13.1408 | −0.519029 | −0.259515 | − | 0.965739i | \(-0.583563\pi\) | ||||
−0.259515 | + | 0.965739i | \(0.583563\pi\) | |||||||
\(642\) | −0.192091 | −0.00758122 | ||||||||
\(643\) | 27.1713 | 1.07153 | 0.535766 | − | 0.844366i | \(-0.320023\pi\) | ||||
0.535766 | + | 0.844366i | \(0.320023\pi\) | |||||||
\(644\) | −37.3732 | −1.47271 | ||||||||
\(645\) | −5.42789 | −0.213723 | ||||||||
\(646\) | −1.16709 | −0.0459187 | ||||||||
\(647\) | 2.94678 | 0.115850 | 0.0579250 | − | 0.998321i | \(-0.481552\pi\) | ||||
0.0579250 | + | 0.998321i | \(0.481552\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −1.62859 | −0.0639276 | ||||||||
\(650\) | 25.5543 | 1.00232 | ||||||||
\(651\) | −33.9743 | −1.33156 | ||||||||
\(652\) | −6.84383 | −0.268025 | ||||||||
\(653\) | 0.487703 | 0.0190853 | 0.00954264 | − | 0.999954i | \(-0.496962\pi\) | ||||
0.00954264 | + | 0.999954i | \(0.496962\pi\) | |||||||
\(654\) | −0.690652 | −0.0270066 | ||||||||
\(655\) | 2.75519 | 0.107654 | ||||||||
\(656\) | −0.211924 | −0.00827424 | ||||||||
\(657\) | 1.96236 | 0.0765588 | ||||||||
\(658\) | −19.7194 | −0.768740 | ||||||||
\(659\) | 8.26188 | 0.321837 | 0.160919 | − | 0.986968i | \(-0.448554\pi\) | ||||
0.160919 | + | 0.986968i | \(0.448554\pi\) | |||||||
\(660\) | −0.945136 | −0.0367894 | ||||||||
\(661\) | 12.3243 | 0.479359 | 0.239679 | − | 0.970852i | \(-0.422958\pi\) | ||||
0.239679 | + | 0.970852i | \(0.422958\pi\) | |||||||
\(662\) | 17.4034 | 0.676402 | ||||||||
\(663\) | −5.47999 | −0.212825 | ||||||||
\(664\) | −8.22544 | −0.319209 | ||||||||
\(665\) | 3.23664 | 0.125512 | ||||||||
\(666\) | −1.66923 | −0.0646812 | ||||||||
\(667\) | −8.91628 | −0.345240 | ||||||||
\(668\) | −5.73420 | −0.221863 | ||||||||
\(669\) | 9.53502 | 0.368645 | ||||||||
\(670\) | −0.564667 | −0.0218150 | ||||||||
\(671\) | 2.85258 | 0.110123 | ||||||||
\(672\) | 4.77865 | 0.184340 | ||||||||
\(673\) | −12.2900 | −0.473745 | −0.236873 | − | 0.971541i | \(-0.576122\pi\) | ||||
−0.236873 | + | 0.971541i | \(0.576122\pi\) | |||||||
\(674\) | −19.7159 | −0.759427 | ||||||||
\(675\) | 4.66320 | 0.179487 | ||||||||
\(676\) | 17.0303 | 0.655011 | ||||||||
\(677\) | 36.1627 | 1.38985 | 0.694923 | − | 0.719085i | \(-0.255439\pi\) | ||||
0.694923 | + | 0.719085i | \(0.255439\pi\) | |||||||
\(678\) | −18.0322 | −0.692523 | ||||||||
\(679\) | −36.5810 | −1.40385 | ||||||||
\(680\) | −0.580342 | −0.0222551 | ||||||||
\(681\) | −20.1882 | −0.773614 | ||||||||
\(682\) | −11.5786 | −0.443367 | ||||||||
\(683\) | 17.0937 | 0.654073 | 0.327037 | − | 0.945012i | \(-0.393950\pi\) | ||||
0.327037 | + | 0.945012i | \(0.393950\pi\) | |||||||
\(684\) | 1.16709 | 0.0446250 | ||||||||
\(685\) | −3.38764 | −0.129435 | ||||||||
\(686\) | −42.2216 | −1.61203 | ||||||||
\(687\) | 2.84520 | 0.108551 | ||||||||
\(688\) | 9.35293 | 0.356577 | ||||||||
\(689\) | 36.3628 | 1.38531 | ||||||||
\(690\) | −4.53878 | −0.172788 | ||||||||
\(691\) | −30.2593 | −1.15112 | −0.575558 | − | 0.817761i | \(-0.695215\pi\) | ||||
−0.575558 | + | 0.817761i | \(0.695215\pi\) | |||||||
\(692\) | 9.65505 | 0.367030 | ||||||||
\(693\) | 7.78244 | 0.295630 | ||||||||
\(694\) | 19.2525 | 0.730816 | ||||||||
\(695\) | 0.945105 | 0.0358499 | ||||||||
\(696\) | 1.14006 | 0.0432139 | ||||||||
\(697\) | −0.211924 | −0.00802719 | ||||||||
\(698\) | 24.6206 | 0.931904 | ||||||||
\(699\) | 7.66783 | 0.290024 | ||||||||
\(700\) | −22.2838 | −0.842249 | ||||||||
\(701\) | −28.6279 | −1.08126 | −0.540631 | − | 0.841260i | \(-0.681814\pi\) | ||||
−0.540631 | + | 0.841260i | \(0.681814\pi\) | |||||||
\(702\) | 5.47999 | 0.206829 | ||||||||
\(703\) | 1.94814 | 0.0734756 | ||||||||
\(704\) | 1.62859 | 0.0613796 | ||||||||
\(705\) | −2.39481 | −0.0901938 | ||||||||
\(706\) | −21.4591 | −0.807626 | ||||||||
\(707\) | 11.0324 | 0.414916 | ||||||||
\(708\) | 1.00000 | 0.0375823 | ||||||||
\(709\) | −1.67588 | −0.0629389 | −0.0314695 | − | 0.999505i | \(-0.510019\pi\) | ||||
−0.0314695 | + | 0.999505i | \(0.510019\pi\) | |||||||
\(710\) | −0.131145 | −0.00492177 | ||||||||
\(711\) | −8.26320 | −0.309894 | ||||||||
\(712\) | 1.59874 | 0.0599153 | ||||||||
\(713\) | −55.6033 | −2.08236 | ||||||||
\(714\) | 4.77865 | 0.178836 | ||||||||
\(715\) | 5.17933 | 0.193696 | ||||||||
\(716\) | 0.791546 | 0.0295815 | ||||||||
\(717\) | 2.50181 | 0.0934318 | ||||||||
\(718\) | −33.9256 | −1.26609 | ||||||||
\(719\) | −28.3153 | −1.05598 | −0.527991 | − | 0.849250i | \(-0.677054\pi\) | ||||
−0.527991 | + | 0.849250i | \(0.677054\pi\) | |||||||
\(720\) | 0.580342 | 0.0216281 | ||||||||
\(721\) | −29.1783 | −1.08666 | ||||||||
\(722\) | 17.6379 | 0.656414 | ||||||||
\(723\) | −17.2582 | −0.641839 | ||||||||
\(724\) | 1.53099 | 0.0568987 | ||||||||
\(725\) | −5.31634 | −0.197444 | ||||||||
\(726\) | −8.34771 | −0.309813 | ||||||||
\(727\) | 17.4072 | 0.645597 | 0.322798 | − | 0.946468i | \(-0.395376\pi\) | ||||
0.322798 | + | 0.946468i | \(0.395376\pi\) | |||||||
\(728\) | −26.1869 | −0.970552 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.13884 | −0.0421503 | ||||||||
\(731\) | 9.35293 | 0.345930 | ||||||||
\(732\) | −1.75157 | −0.0647399 | ||||||||
\(733\) | −39.9094 | −1.47409 | −0.737044 | − | 0.675845i | \(-0.763779\pi\) | ||||
−0.737044 | + | 0.675845i | \(0.763779\pi\) | |||||||
\(734\) | 2.51893 | 0.0929752 | ||||||||
\(735\) | −9.18999 | −0.338978 | ||||||||
\(736\) | 7.82087 | 0.288281 | ||||||||
\(737\) | 1.58460 | 0.0583695 | ||||||||
\(738\) | 0.211924 | 0.00780103 | ||||||||
\(739\) | 17.7834 | 0.654174 | 0.327087 | − | 0.944994i | \(-0.393933\pi\) | ||||
0.327087 | + | 0.944994i | \(0.393933\pi\) | |||||||
\(740\) | 0.968721 | 0.0356109 | ||||||||
\(741\) | −6.39566 | −0.234951 | ||||||||
\(742\) | −31.7090 | −1.16408 | ||||||||
\(743\) | 9.66656 | 0.354632 | 0.177316 | − | 0.984154i | \(-0.443259\pi\) | ||||
0.177316 | + | 0.984154i | \(0.443259\pi\) | |||||||
\(744\) | 7.10961 | 0.260651 | ||||||||
\(745\) | 3.39356 | 0.124330 | ||||||||
\(746\) | 17.7784 | 0.650912 | ||||||||
\(747\) | 8.22544 | 0.300953 | ||||||||
\(748\) | 1.62859 | 0.0595470 | ||||||||
\(749\) | −0.917935 | −0.0335406 | ||||||||
\(750\) | −5.60796 | −0.204774 | ||||||||
\(751\) | −11.3917 | −0.415689 | −0.207844 | − | 0.978162i | \(-0.566645\pi\) | ||||
−0.207844 | + | 0.978162i | \(0.566645\pi\) | |||||||
\(752\) | 4.12655 | 0.150480 | ||||||||
\(753\) | 19.8854 | 0.724663 | ||||||||
\(754\) | −6.24753 | −0.227522 | ||||||||
\(755\) | −0.193261 | −0.00703349 | ||||||||
\(756\) | −4.77865 | −0.173798 | ||||||||
\(757\) | 38.4001 | 1.39568 | 0.697839 | − | 0.716255i | \(-0.254145\pi\) | ||||
0.697839 | + | 0.716255i | \(0.254145\pi\) | |||||||
\(758\) | −8.51794 | −0.309386 | ||||||||
\(759\) | 12.7370 | 0.462322 | ||||||||
\(760\) | −0.677313 | −0.0245687 | ||||||||
\(761\) | −47.6314 | −1.72664 | −0.863318 | − | 0.504659i | \(-0.831618\pi\) | ||||
−0.863318 | + | 0.504659i | \(0.831618\pi\) | |||||||
\(762\) | −4.20613 | −0.152372 | ||||||||
\(763\) | −3.30038 | −0.119482 | ||||||||
\(764\) | −3.79389 | −0.137258 | ||||||||
\(765\) | 0.580342 | 0.0209823 | ||||||||
\(766\) | −0.841850 | −0.0304173 | ||||||||
\(767\) | −5.47999 | −0.197871 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −38.9500 | −1.40457 | −0.702287 | − | 0.711894i | \(-0.747838\pi\) | ||||
−0.702287 | + | 0.711894i | \(0.747838\pi\) | |||||||
\(770\) | −4.51647 | −0.162762 | ||||||||
\(771\) | −8.13485 | −0.292969 | ||||||||
\(772\) | 8.98705 | 0.323451 | ||||||||
\(773\) | −46.0313 | −1.65563 | −0.827815 | − | 0.561001i | \(-0.810416\pi\) | ||||
−0.827815 | + | 0.561001i | \(0.810416\pi\) | |||||||
\(774\) | −9.35293 | −0.336184 | ||||||||
\(775\) | −33.1535 | −1.19091 | ||||||||
\(776\) | 7.65509 | 0.274802 | ||||||||
\(777\) | −7.97664 | −0.286160 | ||||||||
\(778\) | 0.461026 | 0.0165286 | ||||||||
\(779\) | −0.247335 | −0.00886170 | ||||||||
\(780\) | −3.18027 | −0.113872 | ||||||||
\(781\) | 0.368025 | 0.0131690 | ||||||||
\(782\) | 7.82087 | 0.279674 | ||||||||
\(783\) | −1.14006 | −0.0407425 | ||||||||
\(784\) | 15.8355 | 0.565553 | ||||||||
\(785\) | 7.85952 | 0.280518 | ||||||||
\(786\) | 4.74754 | 0.169339 | ||||||||
\(787\) | 19.5827 | 0.698049 | 0.349025 | − | 0.937114i | \(-0.386513\pi\) | ||||
0.349025 | + | 0.937114i | \(0.386513\pi\) | |||||||
\(788\) | −5.73976 | −0.204471 | ||||||||
\(789\) | −10.5725 | −0.376391 | ||||||||
\(790\) | 4.79548 | 0.170615 | ||||||||
\(791\) | −86.1696 | −3.06384 | ||||||||
\(792\) | −1.62859 | −0.0578693 | ||||||||
\(793\) | 9.59858 | 0.340856 | ||||||||
\(794\) | −7.85404 | −0.278729 | ||||||||
\(795\) | −3.85090 | −0.136577 | ||||||||
\(796\) | 14.0439 | 0.497773 | ||||||||
\(797\) | −4.14326 | −0.146762 | −0.0733809 | − | 0.997304i | \(-0.523379\pi\) | ||||
−0.0733809 | + | 0.997304i | \(0.523379\pi\) | |||||||
\(798\) | 5.57713 | 0.197428 | ||||||||
\(799\) | 4.12655 | 0.145987 | ||||||||
\(800\) | 4.66320 | 0.164869 | ||||||||
\(801\) | −1.59874 | −0.0564887 | ||||||||
\(802\) | −22.4214 | −0.791727 | ||||||||
\(803\) | 3.19587 | 0.112780 | ||||||||
\(804\) | −0.972991 | −0.0343148 | ||||||||
\(805\) | −21.6892 | −0.764444 | ||||||||
\(806\) | −38.9606 | −1.37233 | ||||||||
\(807\) | 21.8410 | 0.768838 | ||||||||
\(808\) | −2.30869 | −0.0812193 | ||||||||
\(809\) | −16.6699 | −0.586084 | −0.293042 | − | 0.956100i | \(-0.594668\pi\) | ||||
−0.293042 | + | 0.956100i | \(0.594668\pi\) | |||||||
\(810\) | −0.580342 | −0.0203911 | ||||||||
\(811\) | 10.8325 | 0.380379 | 0.190190 | − | 0.981747i | \(-0.439090\pi\) | ||||
0.190190 | + | 0.981747i | \(0.439090\pi\) | |||||||
\(812\) | 5.44796 | 0.191186 | ||||||||
\(813\) | −25.2327 | −0.884950 | ||||||||
\(814\) | −2.71848 | −0.0952825 | ||||||||
\(815\) | −3.97176 | −0.139125 | ||||||||
\(816\) | −1.00000 | −0.0350070 | ||||||||
\(817\) | 10.9157 | 0.381894 | ||||||||
\(818\) | −10.5913 | −0.370314 | ||||||||
\(819\) | 26.1869 | 0.915046 | ||||||||
\(820\) | −0.122988 | −0.00429494 | ||||||||
\(821\) | −53.1173 | −1.85381 | −0.926903 | − | 0.375302i | \(-0.877539\pi\) | ||||
−0.926903 | + | 0.375302i | \(0.877539\pi\) | |||||||
\(822\) | −5.83732 | −0.203600 | ||||||||
\(823\) | −54.7971 | −1.91011 | −0.955053 | − | 0.296434i | \(-0.904202\pi\) | ||||
−0.955053 | + | 0.296434i | \(0.904202\pi\) | |||||||
\(824\) | 6.10597 | 0.212711 | ||||||||
\(825\) | 7.59442 | 0.264404 | ||||||||
\(826\) | 4.77865 | 0.166270 | ||||||||
\(827\) | −6.84173 | −0.237910 | −0.118955 | − | 0.992900i | \(-0.537954\pi\) | ||||
−0.118955 | + | 0.992900i | \(0.537954\pi\) | |||||||
\(828\) | −7.82087 | −0.271794 | ||||||||
\(829\) | 20.4322 | 0.709638 | 0.354819 | − | 0.934935i | \(-0.384542\pi\) | ||||
0.354819 | + | 0.934935i | \(0.384542\pi\) | |||||||
\(830\) | −4.77356 | −0.165693 | ||||||||
\(831\) | 14.1564 | 0.491079 | ||||||||
\(832\) | 5.47999 | 0.189984 | ||||||||
\(833\) | 15.8355 | 0.548667 | ||||||||
\(834\) | 1.62853 | 0.0563914 | ||||||||
\(835\) | −3.32780 | −0.115163 | ||||||||
\(836\) | 1.90071 | 0.0657375 | ||||||||
\(837\) | −7.10961 | −0.245744 | ||||||||
\(838\) | −33.0129 | −1.14041 | ||||||||
\(839\) | −5.68351 | −0.196216 | −0.0981082 | − | 0.995176i | \(-0.531279\pi\) | ||||
−0.0981082 | + | 0.995176i | \(0.531279\pi\) | |||||||
\(840\) | 2.77325 | 0.0956862 | ||||||||
\(841\) | −27.7003 | −0.955181 | ||||||||
\(842\) | 12.7986 | 0.441068 | ||||||||
\(843\) | 2.81297 | 0.0968839 | ||||||||
\(844\) | −25.2857 | −0.870369 | ||||||||
\(845\) | 9.88338 | 0.339999 | ||||||||
\(846\) | −4.12655 | −0.141874 | ||||||||
\(847\) | −39.8908 | −1.37066 | ||||||||
\(848\) | 6.63557 | 0.227866 | ||||||||
\(849\) | 31.2649 | 1.07301 | ||||||||
\(850\) | 4.66320 | 0.159947 | ||||||||
\(851\) | −13.0548 | −0.447513 | ||||||||
\(852\) | −0.225978 | −0.00774189 | ||||||||
\(853\) | −24.8870 | −0.852116 | −0.426058 | − | 0.904696i | \(-0.640098\pi\) | ||||
−0.426058 | + | 0.904696i | \(0.640098\pi\) | |||||||
\(854\) | −8.37014 | −0.286420 | ||||||||
\(855\) | 0.677313 | 0.0231636 | ||||||||
\(856\) | 0.192091 | 0.00656553 | ||||||||
\(857\) | 29.4230 | 1.00507 | 0.502536 | − | 0.864556i | \(-0.332400\pi\) | ||||
0.502536 | + | 0.864556i | \(0.332400\pi\) | |||||||
\(858\) | 8.92463 | 0.304682 | ||||||||
\(859\) | 2.31173 | 0.0788751 | 0.0394375 | − | 0.999222i | \(-0.487443\pi\) | ||||
0.0394375 | + | 0.999222i | \(0.487443\pi\) | |||||||
\(860\) | 5.42789 | 0.185090 | ||||||||
\(861\) | 1.01271 | 0.0345131 | ||||||||
\(862\) | 6.11123 | 0.208149 | ||||||||
\(863\) | 16.3119 | 0.555265 | 0.277632 | − | 0.960687i | \(-0.410450\pi\) | ||||
0.277632 | + | 0.960687i | \(0.410450\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 5.60323 | 0.190516 | ||||||||
\(866\) | −9.07872 | −0.308508 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 33.9743 | 1.15316 | ||||||||
\(869\) | −13.4573 | −0.456508 | ||||||||
\(870\) | 0.661626 | 0.0224312 | ||||||||
\(871\) | 5.33198 | 0.180667 | ||||||||
\(872\) | 0.690652 | 0.0233884 | ||||||||
\(873\) | −7.65509 | −0.259086 | ||||||||
\(874\) | 9.12769 | 0.308749 | ||||||||
\(875\) | −26.7985 | −0.905954 | ||||||||
\(876\) | −1.96236 | −0.0663019 | ||||||||
\(877\) | 30.0760 | 1.01560 | 0.507798 | − | 0.861476i | \(-0.330460\pi\) | ||||
0.507798 | + | 0.861476i | \(0.330460\pi\) | |||||||
\(878\) | −4.51957 | −0.152528 | ||||||||
\(879\) | −0.689982 | −0.0232725 | ||||||||
\(880\) | 0.945136 | 0.0318605 | ||||||||
\(881\) | 54.3583 | 1.83138 | 0.915690 | − | 0.401886i | \(-0.131645\pi\) | ||||
0.915690 | + | 0.401886i | \(0.131645\pi\) | |||||||
\(882\) | −15.8355 | −0.533208 | ||||||||
\(883\) | 24.5535 | 0.826292 | 0.413146 | − | 0.910665i | \(-0.364430\pi\) | ||||
0.413146 | + | 0.910665i | \(0.364430\pi\) | |||||||
\(884\) | 5.47999 | 0.184312 | ||||||||
\(885\) | 0.580342 | 0.0195080 | ||||||||
\(886\) | −9.45160 | −0.317533 | ||||||||
\(887\) | −8.10195 | −0.272037 | −0.136018 | − | 0.990706i | \(-0.543431\pi\) | ||||
−0.136018 | + | 0.990706i | \(0.543431\pi\) | |||||||
\(888\) | 1.66923 | 0.0560155 | ||||||||
\(889\) | −20.0996 | −0.674119 | ||||||||
\(890\) | 0.927815 | 0.0311004 | ||||||||
\(891\) | 1.62859 | 0.0545597 | ||||||||
\(892\) | −9.53502 | −0.319256 | ||||||||
\(893\) | 4.81608 | 0.161164 | ||||||||
\(894\) | 5.84752 | 0.195570 | ||||||||
\(895\) | 0.459367 | 0.0153550 | ||||||||
\(896\) | −4.77865 | −0.159643 | ||||||||
\(897\) | 42.8583 | 1.43100 | ||||||||
\(898\) | 7.59507 | 0.253451 | ||||||||
\(899\) | 8.10539 | 0.270330 | ||||||||
\(900\) | −4.66320 | −0.155440 | ||||||||
\(901\) | 6.63557 | 0.221063 | ||||||||
\(902\) | 0.345136 | 0.0114918 | ||||||||
\(903\) | −44.6943 | −1.48733 | ||||||||
\(904\) | 18.0322 | 0.599743 | ||||||||
\(905\) | 0.888496 | 0.0295346 | ||||||||
\(906\) | −0.333013 | −0.0110636 | ||||||||
\(907\) | 11.0364 | 0.366458 | 0.183229 | − | 0.983070i | \(-0.441345\pi\) | ||||
0.183229 | + | 0.983070i | \(0.441345\pi\) | |||||||
\(908\) | 20.1882 | 0.669969 | ||||||||
\(909\) | 2.30869 | 0.0765743 | ||||||||
\(910\) | −15.1974 | −0.503788 | ||||||||
\(911\) | −1.78247 | −0.0590559 | −0.0295280 | − | 0.999564i | \(-0.509400\pi\) | ||||
−0.0295280 | + | 0.999564i | \(0.509400\pi\) | |||||||
\(912\) | −1.16709 | −0.0386463 | ||||||||
\(913\) | 13.3958 | 0.443337 | ||||||||
\(914\) | 9.84114 | 0.325516 | ||||||||
\(915\) | −1.01651 | −0.0336048 | ||||||||
\(916\) | −2.84520 | −0.0940079 | ||||||||
\(917\) | 22.6868 | 0.749184 | ||||||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | 6.91066 | 0.227962 | 0.113981 | − | 0.993483i | \(-0.463640\pi\) | ||||
0.113981 | + | 0.993483i | \(0.463640\pi\) | |||||||
\(920\) | 4.53878 | 0.149639 | ||||||||
\(921\) | −5.97982 | −0.197042 | ||||||||
\(922\) | 12.8726 | 0.423937 | ||||||||
\(923\) | 1.23836 | 0.0407611 | ||||||||
\(924\) | −7.78244 | −0.256023 | ||||||||
\(925\) | −7.78394 | −0.255934 | ||||||||
\(926\) | 3.67175 | 0.120661 | ||||||||
\(927\) | −6.10597 | −0.200546 | ||||||||
\(928\) | −1.14006 | −0.0374244 | ||||||||
\(929\) | 21.1989 | 0.695513 | 0.347756 | − | 0.937585i | \(-0.386944\pi\) | ||||
0.347756 | + | 0.937585i | \(0.386944\pi\) | |||||||
\(930\) | 4.12600 | 0.135297 | ||||||||
\(931\) | 18.4815 | 0.605706 | ||||||||
\(932\) | −7.66783 | −0.251168 | ||||||||
\(933\) | −25.5624 | −0.836876 | ||||||||
\(934\) | −9.76462 | −0.319508 | ||||||||
\(935\) | 0.945136 | 0.0309093 | ||||||||
\(936\) | −5.47999 | −0.179119 | ||||||||
\(937\) | 47.8982 | 1.56477 | 0.782383 | − | 0.622798i | \(-0.214004\pi\) | ||||
0.782383 | + | 0.622798i | \(0.214004\pi\) | |||||||
\(938\) | −4.64958 | −0.151814 | ||||||||
\(939\) | 21.2681 | 0.694057 | ||||||||
\(940\) | 2.39481 | 0.0781102 | ||||||||
\(941\) | −50.5950 | −1.64935 | −0.824675 | − | 0.565607i | \(-0.808642\pi\) | ||||
−0.824675 | + | 0.565607i | \(0.808642\pi\) | |||||||
\(942\) | 13.5429 | 0.441252 | ||||||||
\(943\) | 1.65743 | 0.0539733 | ||||||||
\(944\) | −1.00000 | −0.0325472 | ||||||||
\(945\) | −2.77325 | −0.0902138 | ||||||||
\(946\) | −15.2320 | −0.495236 | ||||||||
\(947\) | 14.8078 | 0.481190 | 0.240595 | − | 0.970626i | \(-0.422657\pi\) | ||||
0.240595 | + | 0.970626i | \(0.422657\pi\) | |||||||
\(948\) | 8.26320 | 0.268376 | ||||||||
\(949\) | 10.7537 | 0.349080 | ||||||||
\(950\) | 5.44240 | 0.176575 | ||||||||
\(951\) | 27.9593 | 0.906643 | ||||||||
\(952\) | −4.77865 | −0.154877 | ||||||||
\(953\) | −48.4740 | −1.57023 | −0.785113 | − | 0.619352i | \(-0.787395\pi\) | ||||
−0.785113 | + | 0.619352i | \(0.787395\pi\) | |||||||
\(954\) | −6.63557 | −0.214834 | ||||||||
\(955\) | −2.20175 | −0.0712470 | ||||||||
\(956\) | −2.50181 | −0.0809143 | ||||||||
\(957\) | −1.85669 | −0.0600182 | ||||||||
\(958\) | −5.99020 | −0.193535 | ||||||||
\(959\) | −27.8945 | −0.900760 | ||||||||
\(960\) | −0.580342 | −0.0187304 | ||||||||
\(961\) | 19.5465 | 0.630532 | ||||||||
\(962\) | −9.14734 | −0.294922 | ||||||||
\(963\) | −0.192091 | −0.00619004 | ||||||||
\(964\) | 17.2582 | 0.555849 | ||||||||
\(965\) | 5.21556 | 0.167895 | ||||||||
\(966\) | −37.3732 | −1.20246 | ||||||||
\(967\) | 53.9593 | 1.73522 | 0.867608 | − | 0.497250i | \(-0.165657\pi\) | ||||
0.867608 | + | 0.497250i | \(0.165657\pi\) | |||||||
\(968\) | 8.34771 | 0.268306 | ||||||||
\(969\) | −1.16709 | −0.0374925 | ||||||||
\(970\) | 4.44257 | 0.142642 | ||||||||
\(971\) | 38.0035 | 1.21959 | 0.609795 | − | 0.792560i | \(-0.291252\pi\) | ||||
0.609795 | + | 0.792560i | \(0.291252\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 7.78218 | 0.249485 | ||||||||
\(974\) | −19.1635 | −0.614040 | ||||||||
\(975\) | 25.5543 | 0.818393 | ||||||||
\(976\) | 1.75157 | 0.0560664 | ||||||||
\(977\) | −17.6360 | −0.564224 | −0.282112 | − | 0.959381i | \(-0.591035\pi\) | ||||
−0.282112 | + | 0.959381i | \(0.591035\pi\) | |||||||
\(978\) | −6.84383 | −0.218841 | ||||||||
\(979\) | −2.60368 | −0.0832140 | ||||||||
\(980\) | 9.18999 | 0.293563 | ||||||||
\(981\) | −0.690652 | −0.0220508 | ||||||||
\(982\) | 35.5803 | 1.13541 | ||||||||
\(983\) | 60.0008 | 1.91373 | 0.956864 | − | 0.290535i | \(-0.0938331\pi\) | ||||
0.956864 | + | 0.290535i | \(0.0938331\pi\) | |||||||
\(984\) | −0.211924 | −0.00675589 | ||||||||
\(985\) | −3.33102 | −0.106135 | ||||||||
\(986\) | −1.14006 | −0.0363070 | ||||||||
\(987\) | −19.7194 | −0.627674 | ||||||||
\(988\) | 6.39566 | 0.203473 | ||||||||
\(989\) | −73.1480 | −2.32597 | ||||||||
\(990\) | −0.945136 | −0.0300384 | ||||||||
\(991\) | −1.80378 | −0.0572991 | −0.0286496 | − | 0.999590i | \(-0.509121\pi\) | ||||
−0.0286496 | + | 0.999590i | \(0.509121\pi\) | |||||||
\(992\) | −7.10961 | −0.225730 | ||||||||
\(993\) | 17.4034 | 0.552280 | ||||||||
\(994\) | −1.07987 | −0.0342514 | ||||||||
\(995\) | 8.15027 | 0.258381 | ||||||||
\(996\) | −8.22544 | −0.260633 | ||||||||
\(997\) | −24.8694 | −0.787623 | −0.393812 | − | 0.919191i | \(-0.628844\pi\) | ||||
−0.393812 | + | 0.919191i | \(0.628844\pi\) | |||||||
\(998\) | −37.3473 | −1.18221 | ||||||||
\(999\) | −1.66923 | −0.0528120 |
(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 | 6018.2.a.x.1.5 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.x.1.5 | ✓ | 10 | 1.1 | even | 1 | trivial |