Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6762,2,Mod(1,6762)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6762, 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("6762.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6762.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: | \(53.9948418468\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.16448.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 7x^{2} + 8x + 14 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.18398\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6762.1 |
$q$-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 | ||||||||
\(5\) | −3.18398 | −1.42392 | −0.711959 | − | 0.702221i | \(-0.752192\pi\) | ||||
−0.711959 | + | 0.702221i | \(0.752192\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.18398 | −1.00686 | ||||||||
\(11\) | −1.67440 | −0.504850 | −0.252425 | − | 0.967616i | \(-0.581228\pi\) | ||||
−0.252425 | + | 0.967616i | \(0.581228\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 2.27259 | 0.630304 | 0.315152 | − | 0.949041i | \(-0.397945\pi\) | ||||
0.315152 | + | 0.949041i | \(0.397945\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.18398 | −0.822100 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.367959 | 0.0892431 | 0.0446215 | − | 0.999004i | \(-0.485792\pi\) | ||||
0.0446215 | + | 0.999004i | \(0.485792\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −3.41421 | −0.783274 | −0.391637 | − | 0.920120i | \(-0.628091\pi\) | ||||
−0.391637 | + | 0.920120i | \(0.628091\pi\) | |||||||
\(20\) | −3.18398 | −0.711959 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.67440 | −0.356983 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 5.13772 | 1.02754 | ||||||||
\(26\) | 2.27259 | 0.445692 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.44417 | 0.639565 | 0.319783 | − | 0.947491i | \(-0.396390\pi\) | ||||
0.319783 | + | 0.947491i | \(0.396390\pi\) | |||||||
\(30\) | −3.18398 | −0.581312 | ||||||||
\(31\) | −3.41421 | −0.613211 | −0.306605 | − | 0.951837i | \(-0.599193\pi\) | ||||
−0.306605 | + | 0.951837i | \(0.599193\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.67440 | −0.291476 | ||||||||
\(34\) | 0.367959 | 0.0631044 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −0.0953661 | −0.0156781 | −0.00783905 | − | 0.999969i | \(-0.502495\pi\) | ||||
−0.00783905 | + | 0.999969i | \(0.502495\pi\) | |||||||
\(38\) | −3.41421 | −0.553859 | ||||||||
\(39\) | 2.27259 | 0.363906 | ||||||||
\(40\) | −3.18398 | −0.503431 | ||||||||
\(41\) | −0.681153 | −0.106378 | −0.0531891 | − | 0.998584i | \(-0.516939\pi\) | ||||
−0.0531891 | + | 0.998584i | \(0.516939\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.94699 | −1.21190 | −0.605952 | − | 0.795501i | \(-0.707208\pi\) | ||||
−0.605952 | + | 0.795501i | \(0.707208\pi\) | |||||||
\(44\) | −1.67440 | −0.252425 | ||||||||
\(45\) | −3.18398 | −0.474640 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −1.64445 | −0.239867 | −0.119934 | − | 0.992782i | \(-0.538268\pi\) | ||||
−0.119934 | + | 0.992782i | \(0.538268\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 5.13772 | 0.726584 | ||||||||
\(51\) | 0.367959 | 0.0515245 | ||||||||
\(52\) | 2.27259 | 0.315152 | ||||||||
\(53\) | 9.69921 | 1.33229 | 0.666145 | − | 0.745823i | \(-0.267943\pi\) | ||||
0.666145 | + | 0.745823i | \(0.267943\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 5.33125 | 0.718866 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.41421 | −0.452224 | ||||||||
\(58\) | 3.44417 | 0.452241 | ||||||||
\(59\) | −3.15403 | −0.410619 | −0.205310 | − | 0.978697i | \(-0.565820\pi\) | ||||
−0.205310 | + | 0.978697i | \(0.565820\pi\) | |||||||
\(60\) | −3.18398 | −0.411050 | ||||||||
\(61\) | −13.9594 | −1.78732 | −0.893659 | − | 0.448747i | \(-0.851870\pi\) | ||||
−0.893659 | + | 0.448747i | \(0.851870\pi\) | |||||||
\(62\) | −3.41421 | −0.433606 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −7.23589 | −0.897501 | ||||||||
\(66\) | −1.67440 | −0.206104 | ||||||||
\(67\) | 5.19639 | 0.634840 | 0.317420 | − | 0.948285i | \(-0.397184\pi\) | ||||
0.317420 | + | 0.948285i | \(0.397184\pi\) | |||||||
\(68\) | 0.367959 | 0.0446215 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.67440 | 0.198715 | 0.0993573 | − | 0.995052i | \(-0.468321\pi\) | ||||
0.0993573 | + | 0.995052i | \(0.468321\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −11.1310 | −1.30278 | −0.651391 | − | 0.758742i | \(-0.725814\pi\) | ||||
−0.651391 | + | 0.758742i | \(0.725814\pi\) | |||||||
\(74\) | −0.0953661 | −0.0110861 | ||||||||
\(75\) | 5.13772 | 0.593253 | ||||||||
\(76\) | −3.41421 | −0.391637 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.27259 | 0.257320 | ||||||||
\(79\) | −4.32560 | −0.486668 | −0.243334 | − | 0.969943i | \(-0.578241\pi\) | ||||
−0.243334 | + | 0.969943i | \(0.578241\pi\) | |||||||
\(80\) | −3.18398 | −0.355980 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.681153 | −0.0752207 | ||||||||
\(83\) | 4.74547 | 0.520883 | 0.260441 | − | 0.965490i | \(-0.416132\pi\) | ||||
0.260441 | + | 0.965490i | \(0.416132\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.17157 | −0.127075 | ||||||||
\(86\) | −7.94699 | −0.856946 | ||||||||
\(87\) | 3.44417 | 0.369253 | ||||||||
\(88\) | −1.67440 | −0.178492 | ||||||||
\(89\) | −11.3912 | −1.20746 | −0.603730 | − | 0.797189i | \(-0.706320\pi\) | ||||
−0.603730 | + | 0.797189i | \(0.706320\pi\) | |||||||
\(90\) | −3.18398 | −0.335621 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | −3.41421 | −0.354037 | ||||||||
\(94\) | −1.64445 | −0.169612 | ||||||||
\(95\) | 10.8708 | 1.11532 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −8.29014 | −0.841736 | −0.420868 | − | 0.907122i | \(-0.638274\pi\) | ||||
−0.420868 | + | 0.907122i | \(0.638274\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.67440 | −0.168283 | ||||||||
\(100\) | 5.13772 | 0.513772 | ||||||||
\(101\) | −10.1597 | −1.01093 | −0.505463 | − | 0.862848i | \(-0.668678\pi\) | ||||
−0.505463 | + | 0.862848i | \(0.668678\pi\) | |||||||
\(102\) | 0.367959 | 0.0364333 | ||||||||
\(103\) | −8.27259 | −0.815123 | −0.407561 | − | 0.913178i | \(-0.633621\pi\) | ||||
−0.407561 | + | 0.913178i | \(0.633621\pi\) | |||||||
\(104\) | 2.27259 | 0.222846 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.69921 | 0.942071 | ||||||||
\(107\) | −0.283242 | −0.0273820 | −0.0136910 | − | 0.999906i | \(-0.504358\pi\) | ||||
−0.0136910 | + | 0.999906i | \(0.504358\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −15.1857 | −1.45453 | −0.727265 | − | 0.686357i | \(-0.759209\pi\) | ||||
−0.727265 | + | 0.686357i | \(0.759209\pi\) | |||||||
\(110\) | 5.33125 | 0.508315 | ||||||||
\(111\) | −0.0953661 | −0.00905175 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.57903 | 0.712975 | 0.356488 | − | 0.934300i | \(-0.383974\pi\) | ||||
0.356488 | + | 0.934300i | \(0.383974\pi\) | |||||||
\(114\) | −3.41421 | −0.319770 | ||||||||
\(115\) | 3.18398 | 0.296908 | ||||||||
\(116\) | 3.44417 | 0.319783 | ||||||||
\(117\) | 2.27259 | 0.210101 | ||||||||
\(118\) | −3.15403 | −0.290352 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.18398 | −0.290656 | ||||||||
\(121\) | −8.19639 | −0.745126 | ||||||||
\(122\) | −13.9594 | −1.26382 | ||||||||
\(123\) | −0.681153 | −0.0614175 | ||||||||
\(124\) | −3.41421 | −0.306605 | ||||||||
\(125\) | −0.438512 | −0.0392217 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.62139 | 0.498818 | 0.249409 | − | 0.968398i | \(-0.419764\pi\) | ||||
0.249409 | + | 0.968398i | \(0.419764\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −7.94699 | −0.699694 | ||||||||
\(130\) | −7.23589 | −0.634629 | ||||||||
\(131\) | 6.23309 | 0.544588 | 0.272294 | − | 0.962214i | \(-0.412218\pi\) | ||||
0.272294 | + | 0.962214i | \(0.412218\pi\) | |||||||
\(132\) | −1.67440 | −0.145738 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 5.19639 | 0.448899 | ||||||||
\(135\) | −3.18398 | −0.274033 | ||||||||
\(136\) | 0.367959 | 0.0315522 | ||||||||
\(137\) | 7.51913 | 0.642403 | 0.321201 | − | 0.947011i | \(-0.395913\pi\) | ||||
0.321201 | + | 0.947011i | \(0.395913\pi\) | |||||||
\(138\) | −1.00000 | −0.0851257 | ||||||||
\(139\) | −4.46736 | −0.378917 | −0.189458 | − | 0.981889i | \(-0.560673\pi\) | ||||
−0.189458 | + | 0.981889i | \(0.560673\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.64445 | −0.138487 | ||||||||
\(142\) | 1.67440 | 0.140512 | ||||||||
\(143\) | −3.80523 | −0.318209 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −10.9662 | −0.910689 | ||||||||
\(146\) | −11.1310 | −0.921206 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.0953661 | −0.00783905 | ||||||||
\(149\) | −16.8956 | −1.38414 | −0.692071 | − | 0.721830i | \(-0.743301\pi\) | ||||
−0.692071 | + | 0.721830i | \(0.743301\pi\) | |||||||
\(150\) | 5.13772 | 0.419493 | ||||||||
\(151\) | −5.81212 | −0.472984 | −0.236492 | − | 0.971633i | \(-0.575998\pi\) | ||||
−0.236492 | + | 0.971633i | \(0.575998\pi\) | |||||||
\(152\) | −3.41421 | −0.276929 | ||||||||
\(153\) | 0.367959 | 0.0297477 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.8708 | 0.873163 | ||||||||
\(156\) | 2.27259 | 0.181953 | ||||||||
\(157\) | −13.0136 | −1.03860 | −0.519301 | − | 0.854591i | \(-0.673808\pi\) | ||||
−0.519301 | + | 0.854591i | \(0.673808\pi\) | |||||||
\(158\) | −4.32560 | −0.344126 | ||||||||
\(159\) | 9.69921 | 0.769198 | ||||||||
\(160\) | −3.18398 | −0.251716 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 8.48528 | 0.664619 | 0.332309 | − | 0.943170i | \(-0.392172\pi\) | ||||
0.332309 | + | 0.943170i | \(0.392172\pi\) | |||||||
\(164\) | −0.681153 | −0.0531891 | ||||||||
\(165\) | 5.33125 | 0.415038 | ||||||||
\(166\) | 4.74547 | 0.368320 | ||||||||
\(167\) | 0.685564 | 0.0530505 | 0.0265253 | − | 0.999648i | \(-0.491556\pi\) | ||||
0.0265253 | + | 0.999648i | \(0.491556\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.83532 | −0.602717 | ||||||||
\(170\) | −1.17157 | −0.0898555 | ||||||||
\(171\) | −3.41421 | −0.261091 | ||||||||
\(172\) | −7.94699 | −0.605952 | ||||||||
\(173\) | 2.26974 | 0.172565 | 0.0862824 | − | 0.996271i | \(-0.472501\pi\) | ||||
0.0862824 | + | 0.996271i | \(0.472501\pi\) | |||||||
\(174\) | 3.44417 | 0.261102 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.67440 | −0.126213 | ||||||||
\(177\) | −3.15403 | −0.237071 | ||||||||
\(178\) | −11.3912 | −0.853803 | ||||||||
\(179\) | 5.32840 | 0.398263 | 0.199132 | − | 0.979973i | \(-0.436188\pi\) | ||||
0.199132 | + | 0.979973i | \(0.436188\pi\) | |||||||
\(180\) | −3.18398 | −0.237320 | ||||||||
\(181\) | −1.41017 | −0.104817 | −0.0524087 | − | 0.998626i | \(-0.516690\pi\) | ||||
−0.0524087 | + | 0.998626i | \(0.516690\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.9594 | −1.03191 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 0.303644 | 0.0223243 | ||||||||
\(186\) | −3.41421 | −0.250342 | ||||||||
\(187\) | −0.616110 | −0.0450544 | ||||||||
\(188\) | −1.64445 | −0.119934 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.8708 | 0.788650 | ||||||||
\(191\) | −10.3329 | −0.747660 | −0.373830 | − | 0.927497i | \(-0.621956\pi\) | ||||
−0.373830 | + | 0.927497i | \(0.621956\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 1.70986 | 0.123079 | 0.0615393 | − | 0.998105i | \(-0.480399\pi\) | ||||
0.0615393 | + | 0.998105i | \(0.480399\pi\) | |||||||
\(194\) | −8.29014 | −0.595197 | ||||||||
\(195\) | −7.23589 | −0.518173 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.81778 | −0.485747 | −0.242873 | − | 0.970058i | \(-0.578090\pi\) | ||||
−0.242873 | + | 0.970058i | \(0.578090\pi\) | |||||||
\(198\) | −1.67440 | −0.118994 | ||||||||
\(199\) | −13.4690 | −0.954791 | −0.477395 | − | 0.878689i | \(-0.658419\pi\) | ||||
−0.477395 | + | 0.878689i | \(0.658419\pi\) | |||||||
\(200\) | 5.13772 | 0.363292 | ||||||||
\(201\) | 5.19639 | 0.366525 | ||||||||
\(202\) | −10.1597 | −0.714833 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.367959 | 0.0257623 | ||||||||
\(205\) | 2.16878 | 0.151474 | ||||||||
\(206\) | −8.27259 | −0.576379 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 2.27259 | 0.157576 | ||||||||
\(209\) | 5.71676 | 0.395436 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.44292 | −0.443549 | −0.221775 | − | 0.975098i | \(-0.571185\pi\) | ||||
−0.221775 | + | 0.975098i | \(0.571185\pi\) | |||||||
\(212\) | 9.69921 | 0.666145 | ||||||||
\(213\) | 1.67440 | 0.114728 | ||||||||
\(214\) | −0.283242 | −0.0193620 | ||||||||
\(215\) | 25.3031 | 1.72565 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −15.1857 | −1.02851 | ||||||||
\(219\) | −11.1310 | −0.752161 | ||||||||
\(220\) | 5.33125 | 0.359433 | ||||||||
\(221\) | 0.836220 | 0.0562503 | ||||||||
\(222\) | −0.0953661 | −0.00640056 | ||||||||
\(223\) | 3.85962 | 0.258459 | 0.129230 | − | 0.991615i | \(-0.458750\pi\) | ||||
0.129230 | + | 0.991615i | \(0.458750\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.13772 | 0.342515 | ||||||||
\(226\) | 7.57903 | 0.504150 | ||||||||
\(227\) | −6.05476 | −0.401869 | −0.200934 | − | 0.979605i | \(-0.564398\pi\) | ||||
−0.200934 | + | 0.979605i | \(0.564398\pi\) | |||||||
\(228\) | −3.41421 | −0.226112 | ||||||||
\(229\) | −14.0943 | −0.931375 | −0.465688 | − | 0.884949i | \(-0.654193\pi\) | ||||
−0.465688 | + | 0.884949i | \(0.654193\pi\) | |||||||
\(230\) | 3.18398 | 0.209945 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.44417 | 0.226121 | ||||||||
\(233\) | −1.69921 | −0.111319 | −0.0556596 | − | 0.998450i | \(-0.517726\pi\) | ||||
−0.0556596 | + | 0.998450i | \(0.517726\pi\) | |||||||
\(234\) | 2.27259 | 0.148564 | ||||||||
\(235\) | 5.23589 | 0.341552 | ||||||||
\(236\) | −3.15403 | −0.205310 | ||||||||
\(237\) | −4.32560 | −0.280978 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.0982225 | −0.00635349 | −0.00317674 | − | 0.999995i | \(-0.501011\pi\) | ||||
−0.00317674 | + | 0.999995i | \(0.501011\pi\) | |||||||
\(240\) | −3.18398 | −0.205525 | ||||||||
\(241\) | 22.9775 | 1.48011 | 0.740054 | − | 0.672547i | \(-0.234800\pi\) | ||||
0.740054 | + | 0.672547i | \(0.234800\pi\) | |||||||
\(242\) | −8.19639 | −0.526884 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −13.9594 | −0.893659 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.681153 | −0.0434287 | ||||||||
\(247\) | −7.75912 | −0.493701 | ||||||||
\(248\) | −3.41421 | −0.216803 | ||||||||
\(249\) | 4.74547 | 0.300732 | ||||||||
\(250\) | −0.438512 | −0.0277339 | ||||||||
\(251\) | 0.128174 | 0.00809030 | 0.00404515 | − | 0.999992i | \(-0.498712\pi\) | ||||
0.00404515 | + | 0.999992i | \(0.498712\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.67440 | 0.105269 | ||||||||
\(254\) | 5.62139 | 0.352717 | ||||||||
\(255\) | −1.17157 | −0.0733667 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.4757 | 0.653458 | 0.326729 | − | 0.945118i | \(-0.394054\pi\) | ||||
0.326729 | + | 0.945118i | \(0.394054\pi\) | |||||||
\(258\) | −7.94699 | −0.494758 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −7.23589 | −0.448751 | ||||||||
\(261\) | 3.44417 | 0.213188 | ||||||||
\(262\) | 6.23309 | 0.385082 | ||||||||
\(263\) | 4.48814 | 0.276750 | 0.138375 | − | 0.990380i | \(-0.455812\pi\) | ||||
0.138375 | + | 0.990380i | \(0.455812\pi\) | |||||||
\(264\) | −1.67440 | −0.103052 | ||||||||
\(265\) | −30.8821 | −1.89707 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.3912 | −0.697128 | ||||||||
\(268\) | 5.19639 | 0.317420 | ||||||||
\(269\) | 30.0594 | 1.83275 | 0.916376 | − | 0.400318i | \(-0.131100\pi\) | ||||
0.916376 | + | 0.400318i | \(0.131100\pi\) | |||||||
\(270\) | −3.18398 | −0.193771 | ||||||||
\(271\) | 8.14442 | 0.494738 | 0.247369 | − | 0.968921i | \(-0.420434\pi\) | ||||
0.247369 | + | 0.968921i | \(0.420434\pi\) | |||||||
\(272\) | 0.367959 | 0.0223108 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.51913 | 0.454247 | ||||||||
\(275\) | −8.60260 | −0.518757 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | 23.3561 | 1.40333 | 0.701665 | − | 0.712507i | \(-0.252440\pi\) | ||||
0.701665 | + | 0.712507i | \(0.252440\pi\) | |||||||
\(278\) | −4.46736 | −0.267935 | ||||||||
\(279\) | −3.41421 | −0.204404 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.1434 | −0.664758 | −0.332379 | − | 0.943146i | \(-0.607851\pi\) | ||||
−0.332379 | + | 0.943146i | \(0.607851\pi\) | |||||||
\(282\) | −1.64445 | −0.0979254 | ||||||||
\(283\) | 29.9707 | 1.78157 | 0.890787 | − | 0.454422i | \(-0.150154\pi\) | ||||
0.890787 | + | 0.454422i | \(0.150154\pi\) | |||||||
\(284\) | 1.67440 | 0.0993573 | ||||||||
\(285\) | 10.8708 | 0.643930 | ||||||||
\(286\) | −3.80523 | −0.225008 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −16.8646 | −0.992036 | ||||||||
\(290\) | −10.9662 | −0.643955 | ||||||||
\(291\) | −8.29014 | −0.485976 | ||||||||
\(292\) | −11.1310 | −0.651391 | ||||||||
\(293\) | −2.47002 | −0.144300 | −0.0721500 | − | 0.997394i | \(-0.522986\pi\) | ||||
−0.0721500 | + | 0.997394i | \(0.522986\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.0424 | 0.584689 | ||||||||
\(296\) | −0.0953661 | −0.00554304 | ||||||||
\(297\) | −1.67440 | −0.0971585 | ||||||||
\(298\) | −16.8956 | −0.978736 | ||||||||
\(299\) | −2.27259 | −0.131427 | ||||||||
\(300\) | 5.13772 | 0.296627 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5.81212 | −0.334450 | ||||||||
\(303\) | −10.1597 | −0.583658 | ||||||||
\(304\) | −3.41421 | −0.195819 | ||||||||
\(305\) | 44.4464 | 2.54500 | ||||||||
\(306\) | 0.367959 | 0.0210348 | ||||||||
\(307\) | −34.4787 | −1.96780 | −0.983901 | − | 0.178715i | \(-0.942806\pi\) | ||||
−0.983901 | + | 0.178715i | \(0.942806\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.27259 | −0.470611 | ||||||||
\(310\) | 10.8708 | 0.617419 | ||||||||
\(311\) | 7.85962 | 0.445678 | 0.222839 | − | 0.974855i | \(-0.428468\pi\) | ||||
0.222839 | + | 0.974855i | \(0.428468\pi\) | |||||||
\(312\) | 2.27259 | 0.128660 | ||||||||
\(313\) | −13.0982 | −0.740352 | −0.370176 | − | 0.928962i | \(-0.620703\pi\) | ||||
−0.370176 | + | 0.928962i | \(0.620703\pi\) | |||||||
\(314\) | −13.0136 | −0.734403 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.32560 | −0.243334 | ||||||||
\(317\) | −17.3956 | −0.977032 | −0.488516 | − | 0.872555i | \(-0.662462\pi\) | ||||
−0.488516 | + | 0.872555i | \(0.662462\pi\) | |||||||
\(318\) | 9.69921 | 0.543905 | ||||||||
\(319\) | −5.76691 | −0.322885 | ||||||||
\(320\) | −3.18398 | −0.177990 | ||||||||
\(321\) | −0.283242 | −0.0158090 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.25629 | −0.0699018 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 11.6760 | 0.647665 | ||||||||
\(326\) | 8.48528 | 0.469956 | ||||||||
\(327\) | −15.1857 | −0.839773 | ||||||||
\(328\) | −0.681153 | −0.0376104 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 5.33125 | 0.293476 | ||||||||
\(331\) | −7.96491 | −0.437791 | −0.218896 | − | 0.975748i | \(-0.570245\pi\) | ||||
−0.218896 | + | 0.975748i | \(0.570245\pi\) | |||||||
\(332\) | 4.74547 | 0.260441 | ||||||||
\(333\) | −0.0953661 | −0.00522603 | ||||||||
\(334\) | 0.685564 | 0.0375124 | ||||||||
\(335\) | −16.5452 | −0.903960 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.71514 | 0.147903 | 0.0739517 | − | 0.997262i | \(-0.476439\pi\) | ||||
0.0739517 | + | 0.997262i | \(0.476439\pi\) | |||||||
\(338\) | −7.83532 | −0.426185 | ||||||||
\(339\) | 7.57903 | 0.411637 | ||||||||
\(340\) | −1.17157 | −0.0635375 | ||||||||
\(341\) | 5.71676 | 0.309580 | ||||||||
\(342\) | −3.41421 | −0.184620 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −7.94699 | −0.428473 | ||||||||
\(345\) | 3.18398 | 0.171420 | ||||||||
\(346\) | 2.26974 | 0.122022 | ||||||||
\(347\) | 0.459285 | 0.0246557 | 0.0123279 | − | 0.999924i | \(-0.496076\pi\) | ||||
0.0123279 | + | 0.999924i | \(0.496076\pi\) | |||||||
\(348\) | 3.44417 | 0.184627 | ||||||||
\(349\) | −3.49313 | −0.186983 | −0.0934916 | − | 0.995620i | \(-0.529803\pi\) | ||||
−0.0934916 | + | 0.995620i | \(0.529803\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.27259 | 0.121302 | ||||||||
\(352\) | −1.67440 | −0.0892458 | ||||||||
\(353\) | −33.8811 | −1.80331 | −0.901653 | − | 0.432460i | \(-0.857646\pi\) | ||||
−0.901653 | + | 0.432460i | \(0.857646\pi\) | |||||||
\(354\) | −3.15403 | −0.167635 | ||||||||
\(355\) | −5.33125 | −0.282954 | ||||||||
\(356\) | −11.3912 | −0.603730 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.32840 | 0.281615 | ||||||||
\(359\) | −5.85044 | −0.308775 | −0.154387 | − | 0.988010i | \(-0.549340\pi\) | ||||
−0.154387 | + | 0.988010i | \(0.549340\pi\) | |||||||
\(360\) | −3.18398 | −0.167810 | ||||||||
\(361\) | −7.34315 | −0.386481 | ||||||||
\(362\) | −1.41017 | −0.0741171 | ||||||||
\(363\) | −8.19639 | −0.430199 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 35.4408 | 1.85506 | ||||||||
\(366\) | −13.9594 | −0.729669 | ||||||||
\(367\) | 16.5072 | 0.861671 | 0.430835 | − | 0.902431i | \(-0.358219\pi\) | ||||
0.430835 | + | 0.902431i | \(0.358219\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | −0.681153 | −0.0354594 | ||||||||
\(370\) | 0.303644 | 0.0157857 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −3.41421 | −0.177019 | ||||||||
\(373\) | 5.31619 | 0.275262 | 0.137631 | − | 0.990484i | \(-0.456051\pi\) | ||||
0.137631 | + | 0.990484i | \(0.456051\pi\) | |||||||
\(374\) | −0.616110 | −0.0318583 | ||||||||
\(375\) | −0.438512 | −0.0226447 | ||||||||
\(376\) | −1.64445 | −0.0848059 | ||||||||
\(377\) | 7.82718 | 0.403121 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.0722 | −0.671472 | −0.335736 | − | 0.941956i | \(-0.608985\pi\) | ||||
−0.335736 | + | 0.941956i | \(0.608985\pi\) | |||||||
\(380\) | 10.8708 | 0.557660 | ||||||||
\(381\) | 5.62139 | 0.287993 | ||||||||
\(382\) | −10.3329 | −0.528676 | ||||||||
\(383\) | 1.81654 | 0.0928206 | 0.0464103 | − | 0.998922i | \(-0.485222\pi\) | ||||
0.0464103 | + | 0.998922i | \(0.485222\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.70986 | 0.0870297 | ||||||||
\(387\) | −7.94699 | −0.403968 | ||||||||
\(388\) | −8.29014 | −0.420868 | ||||||||
\(389\) | 24.5101 | 1.24271 | 0.621356 | − | 0.783529i | \(-0.286582\pi\) | ||||
0.621356 | + | 0.783529i | \(0.286582\pi\) | |||||||
\(390\) | −7.23589 | −0.366403 | ||||||||
\(391\) | −0.367959 | −0.0186085 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.23309 | 0.314418 | ||||||||
\(394\) | −6.81778 | −0.343475 | ||||||||
\(395\) | 13.7726 | 0.692976 | ||||||||
\(396\) | −1.67440 | −0.0841417 | ||||||||
\(397\) | −29.3385 | −1.47246 | −0.736229 | − | 0.676732i | \(-0.763395\pi\) | ||||
−0.736229 | + | 0.676732i | \(0.763395\pi\) | |||||||
\(398\) | −13.4690 | −0.675139 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.13772 | 0.256886 | ||||||||
\(401\) | −7.65114 | −0.382080 | −0.191040 | − | 0.981582i | \(-0.561186\pi\) | ||||
−0.191040 | + | 0.981582i | \(0.561186\pi\) | |||||||
\(402\) | 5.19639 | 0.259172 | ||||||||
\(403\) | −7.75912 | −0.386509 | ||||||||
\(404\) | −10.1597 | −0.505463 | ||||||||
\(405\) | −3.18398 | −0.158213 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.159681 | 0.00791509 | ||||||||
\(408\) | 0.367959 | 0.0182167 | ||||||||
\(409\) | 14.4798 | 0.715979 | 0.357989 | − | 0.933726i | \(-0.383462\pi\) | ||||
0.357989 | + | 0.933726i | \(0.383462\pi\) | |||||||
\(410\) | 2.16878 | 0.107108 | ||||||||
\(411\) | 7.51913 | 0.370891 | ||||||||
\(412\) | −8.27259 | −0.407561 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | −15.1095 | −0.741695 | ||||||||
\(416\) | 2.27259 | 0.111423 | ||||||||
\(417\) | −4.46736 | −0.218768 | ||||||||
\(418\) | 5.71676 | 0.279616 | ||||||||
\(419\) | −12.4838 | −0.609874 | −0.304937 | − | 0.952373i | \(-0.598635\pi\) | ||||
−0.304937 | + | 0.952373i | \(0.598635\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.0301 | −1.21989 | −0.609946 | − | 0.792443i | \(-0.708809\pi\) | ||||
−0.609946 | + | 0.792443i | \(0.708809\pi\) | |||||||
\(422\) | −6.44292 | −0.313637 | ||||||||
\(423\) | −1.64445 | −0.0799558 | ||||||||
\(424\) | 9.69921 | 0.471035 | ||||||||
\(425\) | 1.89047 | 0.0917013 | ||||||||
\(426\) | 1.67440 | 0.0811249 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.283242 | −0.0136910 | ||||||||
\(429\) | −3.80523 | −0.183718 | ||||||||
\(430\) | 25.3031 | 1.22022 | ||||||||
\(431\) | −35.8866 | −1.72859 | −0.864297 | − | 0.502981i | \(-0.832237\pi\) | ||||
−0.864297 | + | 0.502981i | \(0.832237\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −26.7538 | −1.28571 | −0.642854 | − | 0.765989i | \(-0.722250\pi\) | ||||
−0.642854 | + | 0.765989i | \(0.722250\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.9662 | −0.525787 | ||||||||
\(436\) | −15.1857 | −0.727265 | ||||||||
\(437\) | 3.41421 | 0.163324 | ||||||||
\(438\) | −11.1310 | −0.531858 | ||||||||
\(439\) | 20.5046 | 0.978630 | 0.489315 | − | 0.872107i | \(-0.337247\pi\) | ||||
0.489315 | + | 0.872107i | \(0.337247\pi\) | |||||||
\(440\) | 5.33125 | 0.254158 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.836220 | 0.0397749 | ||||||||
\(443\) | 16.0916 | 0.764536 | 0.382268 | − | 0.924052i | \(-0.375143\pi\) | ||||
0.382268 | + | 0.924052i | \(0.375143\pi\) | |||||||
\(444\) | −0.0953661 | −0.00452588 | ||||||||
\(445\) | 36.2692 | 1.71933 | ||||||||
\(446\) | 3.85962 | 0.182758 | ||||||||
\(447\) | −16.8956 | −0.799134 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 37.7122 | 1.77975 | 0.889874 | − | 0.456206i | \(-0.150792\pi\) | ||||
0.889874 | + | 0.456206i | \(0.150792\pi\) | |||||||
\(450\) | 5.13772 | 0.242195 | ||||||||
\(451\) | 1.14052 | 0.0537051 | ||||||||
\(452\) | 7.57903 | 0.356488 | ||||||||
\(453\) | −5.81212 | −0.273077 | ||||||||
\(454\) | −6.05476 | −0.284164 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.41421 | −0.159885 | ||||||||
\(457\) | 1.65934 | 0.0776206 | 0.0388103 | − | 0.999247i | \(-0.487643\pi\) | ||||
0.0388103 | + | 0.999247i | \(0.487643\pi\) | |||||||
\(458\) | −14.0943 | −0.658582 | ||||||||
\(459\) | 0.367959 | 0.0171748 | ||||||||
\(460\) | 3.18398 | 0.148454 | ||||||||
\(461\) | 15.0455 | 0.700740 | 0.350370 | − | 0.936611i | \(-0.386056\pi\) | ||||
0.350370 | + | 0.936611i | \(0.386056\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.98935 | 0.278349 | 0.139174 | − | 0.990268i | \(-0.455555\pi\) | ||||
0.139174 | + | 0.990268i | \(0.455555\pi\) | |||||||
\(464\) | 3.44417 | 0.159891 | ||||||||
\(465\) | 10.8708 | 0.504121 | ||||||||
\(466\) | −1.69921 | −0.0787145 | ||||||||
\(467\) | 4.07635 | 0.188631 | 0.0943155 | − | 0.995542i | \(-0.469934\pi\) | ||||
0.0943155 | + | 0.995542i | \(0.469934\pi\) | |||||||
\(468\) | 2.27259 | 0.105051 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 5.23589 | 0.241513 | ||||||||
\(471\) | −13.0136 | −0.599637 | ||||||||
\(472\) | −3.15403 | −0.145176 | ||||||||
\(473\) | 13.3064 | 0.611831 | ||||||||
\(474\) | −4.32560 | −0.198681 | ||||||||
\(475\) | −17.5413 | −0.804850 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.69921 | 0.444096 | ||||||||
\(478\) | −0.0982225 | −0.00449259 | ||||||||
\(479\) | −29.1999 | −1.33418 | −0.667089 | − | 0.744978i | \(-0.732460\pi\) | ||||
−0.667089 | + | 0.744978i | \(0.732460\pi\) | |||||||
\(480\) | −3.18398 | −0.145328 | ||||||||
\(481\) | −0.216728 | −0.00988196 | ||||||||
\(482\) | 22.9775 | 1.04659 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.19639 | −0.372563 | ||||||||
\(485\) | 26.3956 | 1.19856 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 28.3413 | 1.28427 | 0.642134 | − | 0.766593i | \(-0.278049\pi\) | ||||
0.642134 | + | 0.766593i | \(0.278049\pi\) | |||||||
\(488\) | −13.9594 | −0.631912 | ||||||||
\(489\) | 8.48528 | 0.383718 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.3680 | 1.55100 | 0.775502 | − | 0.631345i | \(-0.217497\pi\) | ||||
0.775502 | + | 0.631345i | \(0.217497\pi\) | |||||||
\(492\) | −0.681153 | −0.0307087 | ||||||||
\(493\) | 1.26731 | 0.0570768 | ||||||||
\(494\) | −7.75912 | −0.349099 | ||||||||
\(495\) | 5.33125 | 0.239622 | ||||||||
\(496\) | −3.41421 | −0.153303 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 4.74547 | 0.212649 | ||||||||
\(499\) | 14.8071 | 0.662858 | 0.331429 | − | 0.943480i | \(-0.392469\pi\) | ||||
0.331429 | + | 0.943480i | \(0.392469\pi\) | |||||||
\(500\) | −0.438512 | −0.0196108 | ||||||||
\(501\) | 0.685564 | 0.0306287 | ||||||||
\(502\) | 0.128174 | 0.00572070 | ||||||||
\(503\) | 14.4319 | 0.643487 | 0.321743 | − | 0.946827i | \(-0.395731\pi\) | ||||
0.321743 | + | 0.946827i | \(0.395731\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 32.3482 | 1.43948 | ||||||||
\(506\) | 1.67440 | 0.0744361 | ||||||||
\(507\) | −7.83532 | −0.347979 | ||||||||
\(508\) | 5.62139 | 0.249409 | ||||||||
\(509\) | −4.19229 | −0.185820 | −0.0929099 | − | 0.995675i | \(-0.529617\pi\) | ||||
−0.0929099 | + | 0.995675i | \(0.529617\pi\) | |||||||
\(510\) | −1.17157 | −0.0518781 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −3.41421 | −0.150741 | ||||||||
\(514\) | 10.4757 | 0.462065 | ||||||||
\(515\) | 26.3398 | 1.16067 | ||||||||
\(516\) | −7.94699 | −0.349847 | ||||||||
\(517\) | 2.75346 | 0.121097 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.26974 | 0.0996304 | ||||||||
\(520\) | −7.23589 | −0.317315 | ||||||||
\(521\) | −12.1116 | −0.530619 | −0.265310 | − | 0.964163i | \(-0.585474\pi\) | ||||
−0.265310 | + | 0.964163i | \(0.585474\pi\) | |||||||
\(522\) | 3.44417 | 0.150747 | ||||||||
\(523\) | 37.0187 | 1.61872 | 0.809358 | − | 0.587316i | \(-0.199815\pi\) | ||||
0.809358 | + | 0.587316i | \(0.199815\pi\) | |||||||
\(524\) | 6.23309 | 0.272294 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.48814 | 0.195692 | ||||||||
\(527\) | −1.25629 | −0.0547248 | ||||||||
\(528\) | −1.67440 | −0.0728689 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −30.8821 | −1.34143 | ||||||||
\(531\) | −3.15403 | −0.136873 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.54798 | −0.0670506 | ||||||||
\(534\) | −11.3912 | −0.492944 | ||||||||
\(535\) | 0.901837 | 0.0389898 | ||||||||
\(536\) | 5.19639 | 0.224450 | ||||||||
\(537\) | 5.32840 | 0.229937 | ||||||||
\(538\) | 30.0594 | 1.29595 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.18398 | −0.137017 | ||||||||
\(541\) | 38.0634 | 1.63647 | 0.818237 | − | 0.574881i | \(-0.194952\pi\) | ||||
0.818237 | + | 0.574881i | \(0.194952\pi\) | |||||||
\(542\) | 8.14442 | 0.349833 | ||||||||
\(543\) | −1.41017 | −0.0605164 | ||||||||
\(544\) | 0.367959 | 0.0157761 | ||||||||
\(545\) | 48.3511 | 2.07113 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.9999 | −0.555837 | −0.277919 | − | 0.960605i | \(-0.589645\pi\) | ||||
−0.277919 | + | 0.960605i | \(0.589645\pi\) | |||||||
\(548\) | 7.51913 | 0.321201 | ||||||||
\(549\) | −13.9594 | −0.595773 | ||||||||
\(550\) | −8.60260 | −0.366816 | ||||||||
\(551\) | −11.7591 | −0.500955 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 23.3561 | 0.992304 | ||||||||
\(555\) | 0.303644 | 0.0128890 | ||||||||
\(556\) | −4.46736 | −0.189458 | ||||||||
\(557\) | −1.65685 | −0.0702032 | −0.0351016 | − | 0.999384i | \(-0.511175\pi\) | ||||
−0.0351016 | + | 0.999384i | \(0.511175\pi\) | |||||||
\(558\) | −3.41421 | −0.144535 | ||||||||
\(559\) | −18.0603 | −0.763868 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.616110 | −0.0260122 | ||||||||
\(562\) | −11.1434 | −0.470055 | ||||||||
\(563\) | −5.67901 | −0.239342 | −0.119671 | − | 0.992814i | \(-0.538184\pi\) | ||||
−0.119671 | + | 0.992814i | \(0.538184\pi\) | |||||||
\(564\) | −1.64445 | −0.0692437 | ||||||||
\(565\) | −24.1315 | −1.01522 | ||||||||
\(566\) | 29.9707 | 1.25976 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.67440 | 0.0702562 | ||||||||
\(569\) | 0.205421 | 0.00861171 | 0.00430585 | − | 0.999991i | \(-0.498629\pi\) | ||||
0.00430585 | + | 0.999991i | \(0.498629\pi\) | |||||||
\(570\) | 10.8708 | 0.455327 | ||||||||
\(571\) | 23.3137 | 0.975648 | 0.487824 | − | 0.872942i | \(-0.337791\pi\) | ||||
0.487824 | + | 0.872942i | \(0.337791\pi\) | |||||||
\(572\) | −3.80523 | −0.159105 | ||||||||
\(573\) | −10.3329 | −0.431662 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.13772 | −0.214258 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −25.8574 | −1.07646 | −0.538229 | − | 0.842798i | \(-0.680907\pi\) | ||||
−0.538229 | + | 0.842798i | \(0.680907\pi\) | |||||||
\(578\) | −16.8646 | −0.701475 | ||||||||
\(579\) | 1.70986 | 0.0710594 | ||||||||
\(580\) | −10.9662 | −0.455345 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −8.29014 | −0.343637 | ||||||||
\(583\) | −16.2404 | −0.672607 | ||||||||
\(584\) | −11.1310 | −0.460603 | ||||||||
\(585\) | −7.23589 | −0.299167 | ||||||||
\(586\) | −2.47002 | −0.102036 | ||||||||
\(587\) | 14.4078 | 0.594675 | 0.297337 | − | 0.954772i | \(-0.403901\pi\) | ||||
0.297337 | + | 0.954772i | \(0.403901\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.6569 | 0.480312 | ||||||||
\(590\) | 10.0424 | 0.413437 | ||||||||
\(591\) | −6.81778 | −0.280446 | ||||||||
\(592\) | −0.0953661 | −0.00391952 | ||||||||
\(593\) | 27.0987 | 1.11281 | 0.556406 | − | 0.830911i | \(-0.312180\pi\) | ||||
0.556406 | + | 0.830911i | \(0.312180\pi\) | |||||||
\(594\) | −1.67440 | −0.0687014 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −16.8956 | −0.692071 | ||||||||
\(597\) | −13.4690 | −0.551249 | ||||||||
\(598\) | −2.27259 | −0.0929332 | ||||||||
\(599\) | −0.895598 | −0.0365932 | −0.0182966 | − | 0.999833i | \(-0.505824\pi\) | ||||
−0.0182966 | + | 0.999833i | \(0.505824\pi\) | |||||||
\(600\) | 5.13772 | 0.209747 | ||||||||
\(601\) | 7.77813 | 0.317277 | 0.158638 | − | 0.987337i | \(-0.449290\pi\) | ||||
0.158638 | + | 0.987337i | \(0.449290\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.19639 | 0.211613 | ||||||||
\(604\) | −5.81212 | −0.236492 | ||||||||
\(605\) | 26.0971 | 1.06100 | ||||||||
\(606\) | −10.1597 | −0.412709 | ||||||||
\(607\) | 9.07731 | 0.368436 | 0.184218 | − | 0.982885i | \(-0.441025\pi\) | ||||
0.184218 | + | 0.982885i | \(0.441025\pi\) | |||||||
\(608\) | −3.41421 | −0.138465 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 44.4464 | 1.79958 | ||||||||
\(611\) | −3.73716 | −0.151189 | ||||||||
\(612\) | 0.367959 | 0.0148738 | ||||||||
\(613\) | 29.6632 | 1.19809 | 0.599043 | − | 0.800717i | \(-0.295548\pi\) | ||||
0.599043 | + | 0.800717i | \(0.295548\pi\) | |||||||
\(614\) | −34.4787 | −1.39145 | ||||||||
\(615\) | 2.16878 | 0.0874535 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.6274 | 1.31353 | 0.656765 | − | 0.754095i | \(-0.271924\pi\) | ||||
0.656765 | + | 0.754095i | \(0.271924\pi\) | |||||||
\(618\) | −8.27259 | −0.332772 | ||||||||
\(619\) | 41.7967 | 1.67995 | 0.839976 | − | 0.542624i | \(-0.182569\pi\) | ||||
0.839976 | + | 0.542624i | \(0.182569\pi\) | |||||||
\(620\) | 10.8708 | 0.436581 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 7.85962 | 0.315142 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2.27259 | 0.0909765 | ||||||||
\(625\) | −24.2924 | −0.971696 | ||||||||
\(626\) | −13.0982 | −0.523508 | ||||||||
\(627\) | 5.71676 | 0.228305 | ||||||||
\(628\) | −13.0136 | −0.519301 | ||||||||
\(629\) | −0.0350908 | −0.00139916 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −49.8551 | −1.98470 | −0.992351 | − | 0.123449i | \(-0.960604\pi\) | ||||
−0.992351 | + | 0.123449i | \(0.960604\pi\) | |||||||
\(632\) | −4.32560 | −0.172063 | ||||||||
\(633\) | −6.44292 | −0.256083 | ||||||||
\(634\) | −17.3956 | −0.690866 | ||||||||
\(635\) | −17.8984 | −0.710276 | ||||||||
\(636\) | 9.69921 | 0.384599 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.76691 | −0.228314 | ||||||||
\(639\) | 1.67440 | 0.0662382 | ||||||||
\(640\) | −3.18398 | −0.125858 | ||||||||
\(641\) | 19.0644 | 0.752998 | 0.376499 | − | 0.926417i | \(-0.377128\pi\) | ||||
0.376499 | + | 0.926417i | \(0.377128\pi\) | |||||||
\(642\) | −0.283242 | −0.0111787 | ||||||||
\(643\) | 17.7862 | 0.701420 | 0.350710 | − | 0.936484i | \(-0.385940\pi\) | ||||
0.350710 | + | 0.936484i | \(0.385940\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 25.3031 | 0.996307 | ||||||||
\(646\) | −1.25629 | −0.0494281 | ||||||||
\(647\) | 5.02092 | 0.197393 | 0.0986963 | − | 0.995118i | \(-0.468533\pi\) | ||||
0.0986963 | + | 0.995118i | \(0.468533\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 5.28110 | 0.207301 | ||||||||
\(650\) | 11.6760 | 0.457969 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.48528 | 0.332309 | ||||||||
\(653\) | −34.1205 | −1.33524 | −0.667618 | − | 0.744504i | \(-0.732686\pi\) | ||||
−0.667618 | + | 0.744504i | \(0.732686\pi\) | |||||||
\(654\) | −15.1857 | −0.593809 | ||||||||
\(655\) | −19.8460 | −0.775449 | ||||||||
\(656\) | −0.681153 | −0.0265945 | ||||||||
\(657\) | −11.1310 | −0.434261 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.22738 | 0.0867663 | 0.0433832 | − | 0.999059i | \(-0.486186\pi\) | ||||
0.0433832 | + | 0.999059i | \(0.486186\pi\) | |||||||
\(660\) | 5.33125 | 0.207519 | ||||||||
\(661\) | −18.0730 | −0.702957 | −0.351478 | − | 0.936196i | \(-0.614321\pi\) | ||||
−0.351478 | + | 0.936196i | \(0.614321\pi\) | |||||||
\(662\) | −7.96491 | −0.309565 | ||||||||
\(663\) | 0.836220 | 0.0324761 | ||||||||
\(664\) | 4.74547 | 0.184160 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.0953661 | −0.00369536 | ||||||||
\(667\) | −3.44417 | −0.133359 | ||||||||
\(668\) | 0.685564 | 0.0265253 | ||||||||
\(669\) | 3.85962 | 0.149222 | ||||||||
\(670\) | −16.5452 | −0.639196 | ||||||||
\(671\) | 23.3736 | 0.902328 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.32523 | −0.166725 | −0.0833627 | − | 0.996519i | \(-0.526566\pi\) | ||||
−0.0833627 | + | 0.996519i | \(0.526566\pi\) | |||||||
\(674\) | 2.71514 | 0.104583 | ||||||||
\(675\) | 5.13772 | 0.197751 | ||||||||
\(676\) | −7.83532 | −0.301359 | ||||||||
\(677\) | −18.9553 | −0.728511 | −0.364256 | − | 0.931299i | \(-0.618677\pi\) | ||||
−0.364256 | + | 0.931299i | \(0.618677\pi\) | |||||||
\(678\) | 7.57903 | 0.291071 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.17157 | −0.0449278 | ||||||||
\(681\) | −6.05476 | −0.232019 | ||||||||
\(682\) | 5.71676 | 0.218906 | ||||||||
\(683\) | −45.9659 | −1.75884 | −0.879419 | − | 0.476049i | \(-0.842069\pi\) | ||||
−0.879419 | + | 0.476049i | \(0.842069\pi\) | |||||||
\(684\) | −3.41421 | −0.130546 | ||||||||
\(685\) | −23.9408 | −0.914729 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.0943 | −0.537730 | ||||||||
\(688\) | −7.94699 | −0.302976 | ||||||||
\(689\) | 22.0424 | 0.839747 | ||||||||
\(690\) | 3.18398 | 0.121212 | ||||||||
\(691\) | 33.3093 | 1.26715 | 0.633573 | − | 0.773683i | \(-0.281588\pi\) | ||||
0.633573 | + | 0.773683i | \(0.281588\pi\) | |||||||
\(692\) | 2.26974 | 0.0862824 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.459285 | 0.0174342 | ||||||||
\(695\) | 14.2240 | 0.539547 | ||||||||
\(696\) | 3.44417 | 0.130551 | ||||||||
\(697\) | −0.250636 | −0.00949352 | ||||||||
\(698\) | −3.49313 | −0.132217 | ||||||||
\(699\) | −1.69921 | −0.0642701 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.9763 | −1.16996 | −0.584979 | − | 0.811049i | \(-0.698897\pi\) | ||||
−0.584979 | + | 0.811049i | \(0.698897\pi\) | |||||||
\(702\) | 2.27259 | 0.0857735 | ||||||||
\(703\) | 0.325600 | 0.0122802 | ||||||||
\(704\) | −1.67440 | −0.0631063 | ||||||||
\(705\) | 5.23589 | 0.197195 | ||||||||
\(706\) | −33.8811 | −1.27513 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −3.15403 | −0.118536 | ||||||||
\(709\) | 18.8908 | 0.709459 | 0.354730 | − | 0.934969i | \(-0.384573\pi\) | ||||
0.354730 | + | 0.934969i | \(0.384573\pi\) | |||||||
\(710\) | −5.33125 | −0.200078 | ||||||||
\(711\) | −4.32560 | −0.162223 | ||||||||
\(712\) | −11.3912 | −0.426902 | ||||||||
\(713\) | 3.41421 | 0.127863 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.1158 | 0.453104 | ||||||||
\(716\) | 5.32840 | 0.199132 | ||||||||
\(717\) | −0.0982225 | −0.00366819 | ||||||||
\(718\) | −5.85044 | −0.218337 | ||||||||
\(719\) | −19.2609 | −0.718310 | −0.359155 | − | 0.933278i | \(-0.616935\pi\) | ||||
−0.359155 | + | 0.933278i | \(0.616935\pi\) | |||||||
\(720\) | −3.18398 | −0.118660 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −7.34315 | −0.273284 | ||||||||
\(723\) | 22.9775 | 0.854541 | ||||||||
\(724\) | −1.41017 | −0.0524087 | ||||||||
\(725\) | 17.6952 | 0.657182 | ||||||||
\(726\) | −8.19639 | −0.304196 | ||||||||
\(727\) | 19.7281 | 0.731673 | 0.365837 | − | 0.930679i | \(-0.380783\pi\) | ||||
0.365837 | + | 0.930679i | \(0.380783\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 35.4408 | 1.31172 | ||||||||
\(731\) | −2.92416 | −0.108154 | ||||||||
\(732\) | −13.9594 | −0.515954 | ||||||||
\(733\) | 11.8070 | 0.436101 | 0.218050 | − | 0.975937i | \(-0.430030\pi\) | ||||
0.218050 | + | 0.975937i | \(0.430030\pi\) | |||||||
\(734\) | 16.5072 | 0.609293 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −8.70083 | −0.320499 | ||||||||
\(738\) | −0.681153 | −0.0250736 | ||||||||
\(739\) | −19.4273 | −0.714644 | −0.357322 | − | 0.933981i | \(-0.616310\pi\) | ||||
−0.357322 | + | 0.933981i | \(0.616310\pi\) | |||||||
\(740\) | 0.303644 | 0.0111622 | ||||||||
\(741\) | −7.75912 | −0.285038 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 51.9765 | 1.90683 | 0.953416 | − | 0.301657i | \(-0.0975398\pi\) | ||||
0.953416 | + | 0.301657i | \(0.0975398\pi\) | |||||||
\(744\) | −3.41421 | −0.125171 | ||||||||
\(745\) | 53.7952 | 1.97090 | ||||||||
\(746\) | 5.31619 | 0.194640 | ||||||||
\(747\) | 4.74547 | 0.173628 | ||||||||
\(748\) | −0.616110 | −0.0225272 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.438512 | −0.0160122 | ||||||||
\(751\) | −5.61698 | −0.204967 | −0.102483 | − | 0.994735i | \(-0.532679\pi\) | ||||
−0.102483 | + | 0.994735i | \(0.532679\pi\) | |||||||
\(752\) | −1.64445 | −0.0599668 | ||||||||
\(753\) | 0.128174 | 0.00467093 | ||||||||
\(754\) | 7.82718 | 0.285049 | ||||||||
\(755\) | 18.5057 | 0.673491 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.2810 | −0.955201 | −0.477600 | − | 0.878577i | \(-0.658493\pi\) | ||||
−0.477600 | + | 0.878577i | \(0.658493\pi\) | |||||||
\(758\) | −13.0722 | −0.474802 | ||||||||
\(759\) | 1.67440 | 0.0607769 | ||||||||
\(760\) | 10.8708 | 0.394325 | ||||||||
\(761\) | 5.14280 | 0.186427 | 0.0932133 | − | 0.995646i | \(-0.470286\pi\) | ||||
0.0932133 | + | 0.995646i | \(0.470286\pi\) | |||||||
\(762\) | 5.62139 | 0.203642 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −10.3329 | −0.373830 | ||||||||
\(765\) | −1.17157 | −0.0423583 | ||||||||
\(766\) | 1.81654 | 0.0656341 | ||||||||
\(767\) | −7.16782 | −0.258815 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 29.0158 | 1.04634 | 0.523168 | − | 0.852230i | \(-0.324750\pi\) | ||||
0.523168 | + | 0.852230i | \(0.324750\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.4757 | 0.377274 | ||||||||
\(772\) | 1.70986 | 0.0615393 | ||||||||
\(773\) | −7.93092 | −0.285255 | −0.142628 | − | 0.989776i | \(-0.545555\pi\) | ||||
−0.142628 | + | 0.989776i | \(0.545555\pi\) | |||||||
\(774\) | −7.94699 | −0.285649 | ||||||||
\(775\) | −17.5413 | −0.630102 | ||||||||
\(776\) | −8.29014 | −0.297599 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 24.5101 | 0.878729 | ||||||||
\(779\) | 2.32560 | 0.0833233 | ||||||||
\(780\) | −7.23589 | −0.259086 | ||||||||
\(781\) | −2.80361 | −0.100321 | ||||||||
\(782\) | −0.367959 | −0.0131582 | ||||||||
\(783\) | 3.44417 | 0.123084 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 41.4352 | 1.47889 | ||||||||
\(786\) | 6.23309 | 0.222327 | ||||||||
\(787\) | 38.7584 | 1.38159 | 0.690795 | − | 0.723051i | \(-0.257261\pi\) | ||||
0.690795 | + | 0.723051i | \(0.257261\pi\) | |||||||
\(788\) | −6.81778 | −0.242873 | ||||||||
\(789\) | 4.48814 | 0.159782 | ||||||||
\(790\) | 13.7726 | 0.490008 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.67440 | −0.0594972 | ||||||||
\(793\) | −31.7240 | −1.12655 | ||||||||
\(794\) | −29.3385 | −1.04119 | ||||||||
\(795\) | −30.8821 | −1.09527 | ||||||||
\(796\) | −13.4690 | −0.477395 | ||||||||
\(797\) | 45.8149 | 1.62285 | 0.811424 | − | 0.584458i | \(-0.198693\pi\) | ||||
0.811424 | + | 0.584458i | \(0.198693\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.605089 | −0.0214065 | ||||||||
\(800\) | 5.13772 | 0.181646 | ||||||||
\(801\) | −11.3912 | −0.402487 | ||||||||
\(802\) | −7.65114 | −0.270171 | ||||||||
\(803\) | 18.6377 | 0.657710 | ||||||||
\(804\) | 5.19639 | 0.183262 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.75912 | −0.273303 | ||||||||
\(807\) | 30.0594 | 1.05814 | ||||||||
\(808\) | −10.1597 | −0.357416 | ||||||||
\(809\) | 42.9477 | 1.50996 | 0.754981 | − | 0.655747i | \(-0.227646\pi\) | ||||
0.754981 | + | 0.655747i | \(0.227646\pi\) | |||||||
\(810\) | −3.18398 | −0.111874 | ||||||||
\(811\) | 53.0023 | 1.86116 | 0.930581 | − | 0.366087i | \(-0.119303\pi\) | ||||
0.930581 | + | 0.366087i | \(0.119303\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.14442 | 0.285637 | ||||||||
\(814\) | 0.159681 | 0.00559682 | ||||||||
\(815\) | −27.0170 | −0.946363 | ||||||||
\(816\) | 0.367959 | 0.0128811 | ||||||||
\(817\) | 27.1327 | 0.949254 | ||||||||
\(818\) | 14.4798 | 0.506273 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.16878 | 0.0757369 | ||||||||
\(821\) | −21.1741 | −0.738980 | −0.369490 | − | 0.929235i | \(-0.620468\pi\) | ||||
−0.369490 | + | 0.929235i | \(0.620468\pi\) | |||||||
\(822\) | 7.51913 | 0.262260 | ||||||||
\(823\) | −7.06490 | −0.246267 | −0.123133 | − | 0.992390i | \(-0.539294\pi\) | ||||
−0.123133 | + | 0.992390i | \(0.539294\pi\) | |||||||
\(824\) | −8.27259 | −0.288189 | ||||||||
\(825\) | −8.60260 | −0.299504 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.5994 | −0.472899 | −0.236449 | − | 0.971644i | \(-0.575984\pi\) | ||||
−0.236449 | + | 0.971644i | \(0.575984\pi\) | |||||||
\(828\) | −1.00000 | −0.0347524 | ||||||||
\(829\) | 15.9075 | 0.552490 | 0.276245 | − | 0.961087i | \(-0.410910\pi\) | ||||
0.276245 | + | 0.961087i | \(0.410910\pi\) | |||||||
\(830\) | −15.1095 | −0.524457 | ||||||||
\(831\) | 23.3561 | 0.810213 | ||||||||
\(832\) | 2.27259 | 0.0787880 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −4.46736 | −0.154692 | ||||||||
\(835\) | −2.18282 | −0.0755396 | ||||||||
\(836\) | 5.71676 | 0.197718 | ||||||||
\(837\) | −3.41421 | −0.118012 | ||||||||
\(838\) | −12.4838 | −0.431246 | ||||||||
\(839\) | 29.2794 | 1.01084 | 0.505419 | − | 0.862874i | \(-0.331338\pi\) | ||||
0.505419 | + | 0.862874i | \(0.331338\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.1377 | −0.590956 | ||||||||
\(842\) | −25.0301 | −0.862594 | ||||||||
\(843\) | −11.1434 | −0.383798 | ||||||||
\(844\) | −6.44292 | −0.221775 | ||||||||
\(845\) | 24.9475 | 0.858220 | ||||||||
\(846\) | −1.64445 | −0.0565373 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 9.69921 | 0.333072 | ||||||||
\(849\) | 29.9707 | 1.02859 | ||||||||
\(850\) | 1.89047 | 0.0648426 | ||||||||
\(851\) | 0.0953661 | 0.00326911 | ||||||||
\(852\) | 1.67440 | 0.0573640 | ||||||||
\(853\) | −6.23750 | −0.213568 | −0.106784 | − | 0.994282i | \(-0.534055\pi\) | ||||
−0.106784 | + | 0.994282i | \(0.534055\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.8708 | 0.371773 | ||||||||
\(856\) | −0.283242 | −0.00968101 | ||||||||
\(857\) | 3.57976 | 0.122282 | 0.0611412 | − | 0.998129i | \(-0.480526\pi\) | ||||
0.0611412 | + | 0.998129i | \(0.480526\pi\) | |||||||
\(858\) | −3.80523 | −0.129908 | ||||||||
\(859\) | 31.3206 | 1.06865 | 0.534323 | − | 0.845281i | \(-0.320567\pi\) | ||||
0.534323 | + | 0.845281i | \(0.320567\pi\) | |||||||
\(860\) | 25.3031 | 0.862827 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −35.8866 | −1.22230 | ||||||||
\(863\) | 25.4232 | 0.865417 | 0.432709 | − | 0.901534i | \(-0.357558\pi\) | ||||
0.432709 | + | 0.901534i | \(0.357558\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −7.22679 | −0.245718 | ||||||||
\(866\) | −26.7538 | −0.909132 | ||||||||
\(867\) | −16.8646 | −0.572752 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.24278 | 0.245695 | ||||||||
\(870\) | −10.9662 | −0.371787 | ||||||||
\(871\) | 11.8093 | 0.400142 | ||||||||
\(872\) | −15.1857 | −0.514254 | ||||||||
\(873\) | −8.29014 | −0.280579 | ||||||||
\(874\) | 3.41421 | 0.115487 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −11.1310 | −0.376081 | ||||||||
\(877\) | 25.4583 | 0.859667 | 0.429833 | − | 0.902908i | \(-0.358572\pi\) | ||||
0.429833 | + | 0.902908i | \(0.358572\pi\) | |||||||
\(878\) | 20.5046 | 0.691996 | ||||||||
\(879\) | −2.47002 | −0.0833117 | ||||||||
\(880\) | 5.33125 | 0.179717 | ||||||||
\(881\) | −41.3523 | −1.39319 | −0.696597 | − | 0.717462i | \(-0.745304\pi\) | ||||
−0.696597 | + | 0.717462i | \(0.745304\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.9342 | −0.973713 | −0.486857 | − | 0.873482i | \(-0.661857\pi\) | ||||
−0.486857 | + | 0.873482i | \(0.661857\pi\) | |||||||
\(884\) | 0.836220 | 0.0281251 | ||||||||
\(885\) | 10.0424 | 0.337570 | ||||||||
\(886\) | 16.0916 | 0.540608 | ||||||||
\(887\) | −27.6880 | −0.929672 | −0.464836 | − | 0.885397i | \(-0.653887\pi\) | ||||
−0.464836 | + | 0.885397i | \(0.653887\pi\) | |||||||
\(888\) | −0.0953661 | −0.00320028 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 36.2692 | 1.21575 | ||||||||
\(891\) | −1.67440 | −0.0560945 | ||||||||
\(892\) | 3.85962 | 0.129230 | ||||||||
\(893\) | 5.61450 | 0.187882 | ||||||||
\(894\) | −16.8956 | −0.565073 | ||||||||
\(895\) | −16.9655 | −0.567094 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.27259 | −0.0758797 | ||||||||
\(898\) | 37.7122 | 1.25847 | ||||||||
\(899\) | −11.7591 | −0.392188 | ||||||||
\(900\) | 5.13772 | 0.171257 | ||||||||
\(901\) | 3.56891 | 0.118898 | ||||||||
\(902\) | 1.14052 | 0.0379752 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.57903 | 0.252075 | ||||||||
\(905\) | 4.48996 | 0.149251 | ||||||||
\(906\) | −5.81212 | −0.193095 | ||||||||
\(907\) | 31.9831 | 1.06198 | 0.530991 | − | 0.847378i | \(-0.321820\pi\) | ||||
0.530991 | + | 0.847378i | \(0.321820\pi\) | |||||||
\(908\) | −6.05476 | −0.200934 | ||||||||
\(909\) | −10.1597 | −0.336975 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.7589 | −1.28414 | −0.642070 | − | 0.766646i | \(-0.721924\pi\) | ||||
−0.642070 | + | 0.766646i | \(0.721924\pi\) | |||||||
\(912\) | −3.41421 | −0.113056 | ||||||||
\(913\) | −7.94581 | −0.262968 | ||||||||
\(914\) | 1.65934 | 0.0548861 | ||||||||
\(915\) | 44.4464 | 1.46935 | ||||||||
\(916\) | −14.0943 | −0.465688 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.367959 | 0.0121444 | ||||||||
\(919\) | −52.0882 | −1.71823 | −0.859116 | − | 0.511781i | \(-0.828986\pi\) | ||||
−0.859116 | + | 0.511781i | \(0.828986\pi\) | |||||||
\(920\) | 3.18398 | 0.104973 | ||||||||
\(921\) | −34.4787 | −1.13611 | ||||||||
\(922\) | 15.0455 | 0.495498 | ||||||||
\(923\) | 3.80523 | 0.125251 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.489965 | −0.0161099 | ||||||||
\(926\) | 5.98935 | 0.196822 | ||||||||
\(927\) | −8.27259 | −0.271708 | ||||||||
\(928\) | 3.44417 | 0.113060 | ||||||||
\(929\) | −33.3337 | −1.09364 | −0.546821 | − | 0.837249i | \(-0.684162\pi\) | ||||
−0.546821 | + | 0.837249i | \(0.684162\pi\) | |||||||
\(930\) | 10.8708 | 0.356467 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.69921 | −0.0556596 | ||||||||
\(933\) | 7.85962 | 0.257312 | ||||||||
\(934\) | 4.07635 | 0.133382 | ||||||||
\(935\) | 1.96168 | 0.0641538 | ||||||||
\(936\) | 2.27259 | 0.0742820 | ||||||||
\(937\) | −5.66127 | −0.184945 | −0.0924727 | − | 0.995715i | \(-0.529477\pi\) | ||||
−0.0924727 | + | 0.995715i | \(0.529477\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −13.0982 | −0.427442 | ||||||||
\(940\) | 5.23589 | 0.170776 | ||||||||
\(941\) | −24.5250 | −0.799492 | −0.399746 | − | 0.916626i | \(-0.630902\pi\) | ||||
−0.399746 | + | 0.916626i | \(0.630902\pi\) | |||||||
\(942\) | −13.0136 | −0.424008 | ||||||||
\(943\) | 0.681153 | 0.0221814 | ||||||||
\(944\) | −3.15403 | −0.102655 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13.3064 | 0.432630 | ||||||||
\(947\) | 21.9392 | 0.712928 | 0.356464 | − | 0.934309i | \(-0.383982\pi\) | ||||
0.356464 | + | 0.934309i | \(0.383982\pi\) | |||||||
\(948\) | −4.32560 | −0.140489 | ||||||||
\(949\) | −25.2962 | −0.821148 | ||||||||
\(950\) | −17.5413 | −0.569115 | ||||||||
\(951\) | −17.3956 | −0.564090 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.6897 | 0.896959 | 0.448479 | − | 0.893793i | \(-0.351966\pi\) | ||||
0.448479 | + | 0.893793i | \(0.351966\pi\) | |||||||
\(954\) | 9.69921 | 0.314024 | ||||||||
\(955\) | 32.8996 | 1.06461 | ||||||||
\(956\) | −0.0982225 | −0.00317674 | ||||||||
\(957\) | −5.76691 | −0.186418 | ||||||||
\(958\) | −29.1999 | −0.943406 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.18398 | −0.102762 | ||||||||
\(961\) | −19.3431 | −0.623972 | ||||||||
\(962\) | −0.216728 | −0.00698760 | ||||||||
\(963\) | −0.283242 | −0.00912735 | ||||||||
\(964\) | 22.9775 | 0.740054 | ||||||||
\(965\) | −5.44417 | −0.175254 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.84510 | −0.123650 | −0.0618251 | − | 0.998087i | \(-0.519692\pi\) | ||||
−0.0618251 | + | 0.998087i | \(0.519692\pi\) | |||||||
\(968\) | −8.19639 | −0.263442 | ||||||||
\(969\) | −1.25629 | −0.0403578 | ||||||||
\(970\) | 26.3956 | 0.847513 | ||||||||
\(971\) | −23.3583 | −0.749605 | −0.374803 | − | 0.927105i | \(-0.622289\pi\) | ||||
−0.374803 | + | 0.927105i | \(0.622289\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 28.3413 | 0.908114 | ||||||||
\(975\) | 11.6760 | 0.373930 | ||||||||
\(976\) | −13.9594 | −0.446829 | ||||||||
\(977\) | 15.8034 | 0.505596 | 0.252798 | − | 0.967519i | \(-0.418649\pi\) | ||||
0.252798 | + | 0.967519i | \(0.418649\pi\) | |||||||
\(978\) | 8.48528 | 0.271329 | ||||||||
\(979\) | 19.0734 | 0.609587 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.1857 | −0.484843 | ||||||||
\(982\) | 34.3680 | 1.09673 | ||||||||
\(983\) | −17.6528 | −0.563037 | −0.281519 | − | 0.959556i | \(-0.590838\pi\) | ||||
−0.281519 | + | 0.959556i | \(0.590838\pi\) | |||||||
\(984\) | −0.681153 | −0.0217144 | ||||||||
\(985\) | 21.7077 | 0.691664 | ||||||||
\(986\) | 1.26731 | 0.0403594 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.75912 | −0.246850 | ||||||||
\(989\) | 7.94699 | 0.252700 | ||||||||
\(990\) | 5.33125 | 0.169438 | ||||||||
\(991\) | −15.0224 | −0.477202 | −0.238601 | − | 0.971118i | \(-0.576689\pi\) | ||||
−0.238601 | + | 0.971118i | \(0.576689\pi\) | |||||||
\(992\) | −3.41421 | −0.108401 | ||||||||
\(993\) | −7.96491 | −0.252759 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 42.8849 | 1.35954 | ||||||||
\(996\) | 4.74547 | 0.150366 | ||||||||
\(997\) | 33.9954 | 1.07665 | 0.538323 | − | 0.842739i | \(-0.319058\pi\) | ||||
0.538323 | + | 0.842739i | \(0.319058\pi\) | |||||||
\(998\) | 14.8071 | 0.468711 | ||||||||
\(999\) | −0.0953661 | −0.00301725 |
(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 | 6762.2.a.co.1.2 | yes | 4 | |
7.6 | odd | 2 | 6762.2.a.cn.1.3 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6762.2.a.cn.1.3 | ✓ | 4 | 7.6 | odd | 2 | ||
6762.2.a.co.1.2 | yes | 4 | 1.1 | even | 1 | trivial |