Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3483,2,Mod(1,3483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3483, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3483.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3483 = 3^{4} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3483.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: | \(27.8118950240\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 6 x^{19} - 13 x^{18} + 137 x^{17} - 24 x^{16} - 1247 x^{15} + 1257 x^{14} + 5756 x^{13} + \cdots - 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | no (minimal twist has level 387) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.82281\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3483.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.82281 | −1.28892 | −0.644460 | − | 0.764638i | \(-0.722918\pi\) | ||||
−0.644460 | + | 0.764638i | \(0.722918\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.32263 | 0.661315 | ||||||||
\(5\) | 0.432883 | 0.193591 | 0.0967957 | − | 0.995304i | \(-0.469141\pi\) | ||||
0.0967957 | + | 0.995304i | \(0.469141\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.691058 | −0.261195 | −0.130598 | − | 0.991435i | \(-0.541690\pi\) | ||||
−0.130598 | + | 0.991435i | \(0.541690\pi\) | |||||||
\(8\) | 1.23472 | 0.436538 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.789063 | −0.249524 | ||||||||
\(11\) | −2.53559 | −0.764509 | −0.382255 | − | 0.924057i | \(-0.624852\pi\) | ||||
−0.382255 | + | 0.924057i | \(0.624852\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.20272 | −1.99767 | −0.998837 | − | 0.0482173i | \(-0.984646\pi\) | ||||
−0.998837 | + | 0.0482173i | \(0.984646\pi\) | |||||||
\(14\) | 1.25967 | 0.336660 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.89591 | −1.22398 | ||||||||
\(17\) | −4.46895 | −1.08388 | −0.541940 | − | 0.840417i | \(-0.682310\pi\) | ||||
−0.541940 | + | 0.840417i | \(0.682310\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.05843 | 1.38990 | 0.694950 | − | 0.719058i | \(-0.255427\pi\) | ||||
0.694950 | + | 0.719058i | \(0.255427\pi\) | |||||||
\(20\) | 0.572545 | 0.128025 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.62190 | 0.985391 | ||||||||
\(23\) | 4.11156 | 0.857319 | 0.428660 | − | 0.903466i | \(-0.358986\pi\) | ||||
0.428660 | + | 0.903466i | \(0.358986\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.81261 | −0.962522 | ||||||||
\(26\) | 13.1292 | 2.57484 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.914014 | −0.172732 | ||||||||
\(29\) | −6.46148 | −1.19987 | −0.599933 | − | 0.800050i | \(-0.704806\pi\) | ||||
−0.599933 | + | 0.800050i | \(0.704806\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.53897 | −0.456012 | −0.228006 | − | 0.973660i | \(-0.573221\pi\) | ||||
−0.228006 | + | 0.973660i | \(0.573221\pi\) | |||||||
\(32\) | 6.45487 | 1.14107 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.14604 | 1.39704 | ||||||||
\(35\) | −0.299147 | −0.0505651 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.14340 | −1.50317 | −0.751583 | − | 0.659638i | \(-0.770709\pi\) | ||||
−0.751583 | + | 0.659638i | \(0.770709\pi\) | |||||||
\(38\) | −11.0434 | −1.79147 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.534488 | 0.0845099 | ||||||||
\(41\) | −0.910760 | −0.142237 | −0.0711184 | − | 0.997468i | \(-0.522657\pi\) | ||||
−0.0711184 | + | 0.997468i | \(0.522657\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | −3.35365 | −0.505582 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.49459 | −1.10502 | ||||||||
\(47\) | 9.59426 | 1.39947 | 0.699733 | − | 0.714404i | \(-0.253302\pi\) | ||||
0.699733 | + | 0.714404i | \(0.253302\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.52244 | −0.931777 | ||||||||
\(50\) | 8.77247 | 1.24061 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −9.52653 | −1.32109 | ||||||||
\(53\) | 8.85806 | 1.21675 | 0.608374 | − | 0.793650i | \(-0.291822\pi\) | ||||
0.608374 | + | 0.793650i | \(0.291822\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.09761 | −0.148002 | ||||||||
\(56\) | −0.853259 | −0.114022 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 11.7780 | 1.54653 | ||||||||
\(59\) | 13.0226 | 1.69540 | 0.847699 | − | 0.530478i | \(-0.177987\pi\) | ||||
0.847699 | + | 0.530478i | \(0.177987\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.793492 | 0.101596 | 0.0507981 | − | 0.998709i | \(-0.483824\pi\) | ||||
0.0507981 | + | 0.998709i | \(0.483824\pi\) | |||||||
\(62\) | 4.62805 | 0.587763 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.97418 | −0.246772 | ||||||||
\(65\) | −3.11794 | −0.386732 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.3997 | 1.39270 | 0.696349 | − | 0.717704i | \(-0.254807\pi\) | ||||
0.696349 | + | 0.717704i | \(0.254807\pi\) | |||||||
\(68\) | −5.91077 | −0.716786 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.545288 | 0.0651744 | ||||||||
\(71\) | 13.2707 | 1.57495 | 0.787473 | − | 0.616349i | \(-0.211389\pi\) | ||||
0.787473 | + | 0.616349i | \(0.211389\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.01445 | −0.469856 | −0.234928 | − | 0.972013i | \(-0.575485\pi\) | ||||
−0.234928 | + | 0.972013i | \(0.575485\pi\) | |||||||
\(74\) | 16.6667 | 1.93746 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.01307 | 0.919162 | ||||||||
\(77\) | 1.75224 | 0.199686 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.8858 | −1.33726 | −0.668628 | − | 0.743597i | \(-0.733118\pi\) | ||||
−0.668628 | + | 0.743597i | \(0.733118\pi\) | |||||||
\(80\) | −2.11936 | −0.236951 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.66014 | 0.183332 | ||||||||
\(83\) | 9.76179 | 1.07150 | 0.535748 | − | 0.844378i | \(-0.320030\pi\) | ||||
0.535748 | + | 0.844378i | \(0.320030\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.93454 | −0.209830 | ||||||||
\(86\) | 1.82281 | 0.196558 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.13073 | −0.333737 | ||||||||
\(89\) | −8.04947 | −0.853242 | −0.426621 | − | 0.904431i | \(-0.640296\pi\) | ||||
−0.426621 | + | 0.904431i | \(0.640296\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.97749 | 0.521783 | ||||||||
\(92\) | 5.43807 | 0.566958 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −17.4885 | −1.80380 | ||||||||
\(95\) | 2.62259 | 0.269073 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.9889 | 1.52189 | 0.760947 | − | 0.648815i | \(-0.224735\pi\) | ||||
0.760947 | + | 0.648815i | \(0.224735\pi\) | |||||||
\(98\) | 11.8892 | 1.20099 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −6.36531 | −0.636531 | ||||||||
\(101\) | 3.10620 | 0.309078 | 0.154539 | − | 0.987987i | \(-0.450611\pi\) | ||||
0.154539 | + | 0.987987i | \(0.450611\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.96258 | 0.686044 | 0.343022 | − | 0.939327i | \(-0.388550\pi\) | ||||
0.343022 | + | 0.939327i | \(0.388550\pi\) | |||||||
\(104\) | −8.89330 | −0.872060 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −16.1466 | −1.56829 | ||||||||
\(107\) | −8.10561 | −0.783599 | −0.391800 | − | 0.920051i | \(-0.628147\pi\) | ||||
−0.391800 | + | 0.920051i | \(0.628147\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.0751888 | −0.00720178 | −0.00360089 | − | 0.999994i | \(-0.501146\pi\) | ||||
−0.00360089 | + | 0.999994i | \(0.501146\pi\) | |||||||
\(110\) | 2.00074 | 0.190763 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.38336 | 0.319697 | ||||||||
\(113\) | −7.68859 | −0.723282 | −0.361641 | − | 0.932317i | \(-0.617783\pi\) | ||||
−0.361641 | + | 0.932317i | \(0.617783\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.77983 | 0.165970 | ||||||||
\(116\) | −8.54615 | −0.793490 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −23.7377 | −2.18523 | ||||||||
\(119\) | 3.08830 | 0.283104 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.57078 | −0.415526 | ||||||||
\(122\) | −1.44638 | −0.130949 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.35811 | −0.301567 | ||||||||
\(125\) | −4.24772 | −0.379927 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.411999 | 0.0365590 | 0.0182795 | − | 0.999833i | \(-0.494181\pi\) | ||||
0.0182795 | + | 0.999833i | \(0.494181\pi\) | |||||||
\(128\) | −9.31120 | −0.823001 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.68340 | 0.498467 | ||||||||
\(131\) | −3.03110 | −0.264828 | −0.132414 | − | 0.991194i | \(-0.542273\pi\) | ||||
−0.132414 | + | 0.991194i | \(0.542273\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.18673 | −0.363035 | ||||||||
\(134\) | −20.7795 | −1.79508 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.51788 | −0.473155 | ||||||||
\(137\) | 10.6888 | 0.913209 | 0.456604 | − | 0.889670i | \(-0.349065\pi\) | ||||
0.456604 | + | 0.889670i | \(0.349065\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.7296 | −1.92790 | −0.963951 | − | 0.266080i | \(-0.914271\pi\) | ||||
−0.963951 | + | 0.266080i | \(0.914271\pi\) | |||||||
\(140\) | −0.395661 | −0.0334395 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −24.1900 | −2.02998 | ||||||||
\(143\) | 18.2631 | 1.52724 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.79707 | −0.232284 | ||||||||
\(146\) | 7.31757 | 0.605607 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −12.0933 | −0.994066 | ||||||||
\(149\) | −14.9854 | −1.22765 | −0.613824 | − | 0.789443i | \(-0.710369\pi\) | ||||
−0.613824 | + | 0.789443i | \(0.710369\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.03500 | 0.653879 | 0.326939 | − | 0.945045i | \(-0.393983\pi\) | ||||
0.326939 | + | 0.945045i | \(0.393983\pi\) | |||||||
\(152\) | 7.48044 | 0.606744 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.19400 | −0.257380 | ||||||||
\(155\) | −1.09908 | −0.0882799 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.89260 | 0.550089 | 0.275045 | − | 0.961431i | \(-0.411307\pi\) | ||||
0.275045 | + | 0.961431i | \(0.411307\pi\) | |||||||
\(158\) | 21.6655 | 1.72362 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.79421 | 0.220902 | ||||||||
\(161\) | −2.84132 | −0.223928 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.87193 | 0.538251 | 0.269125 | − | 0.963105i | \(-0.413265\pi\) | ||||
0.269125 | + | 0.963105i | \(0.413265\pi\) | |||||||
\(164\) | −1.20460 | −0.0940634 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −17.7939 | −1.38107 | ||||||||
\(167\) | −15.5912 | −1.20649 | −0.603243 | − | 0.797557i | \(-0.706125\pi\) | ||||
−0.603243 | + | 0.797557i | \(0.706125\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 38.8791 | 2.99070 | ||||||||
\(170\) | 3.52629 | 0.270454 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.32263 | −0.100850 | ||||||||
\(173\) | 3.07147 | 0.233519 | 0.116760 | − | 0.993160i | \(-0.462749\pi\) | ||||
0.116760 | + | 0.993160i | \(0.462749\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.32579 | 0.251406 | ||||||||
\(176\) | 12.4140 | 0.935742 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 14.6726 | 1.09976 | ||||||||
\(179\) | −6.81694 | −0.509522 | −0.254761 | − | 0.967004i | \(-0.581997\pi\) | ||||
−0.254761 | + | 0.967004i | \(0.581997\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.26156 | −0.465418 | −0.232709 | − | 0.972546i | \(-0.574759\pi\) | ||||
−0.232709 | + | 0.972546i | \(0.574759\pi\) | |||||||
\(182\) | −9.07301 | −0.672536 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.07661 | 0.374252 | ||||||||
\(185\) | −3.95803 | −0.291000 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.3314 | 0.828636 | ||||||||
\(188\) | 12.6897 | 0.925488 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.78049 | −0.346813 | ||||||||
\(191\) | 9.78970 | 0.708358 | 0.354179 | − | 0.935178i | \(-0.384760\pi\) | ||||
0.354179 | + | 0.935178i | \(0.384760\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.45556 | 0.464681 | 0.232341 | − | 0.972635i | \(-0.425362\pi\) | ||||
0.232341 | + | 0.972635i | \(0.425362\pi\) | |||||||
\(194\) | −27.3219 | −1.96160 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.62678 | −0.616198 | ||||||||
\(197\) | 9.52049 | 0.678307 | 0.339154 | − | 0.940731i | \(-0.389859\pi\) | ||||
0.339154 | + | 0.940731i | \(0.389859\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.8531 | 1.19469 | 0.597344 | − | 0.801985i | \(-0.296223\pi\) | ||||
0.597344 | + | 0.801985i | \(0.296223\pi\) | |||||||
\(200\) | −5.94221 | −0.420177 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.66200 | −0.398377 | ||||||||
\(203\) | 4.46526 | 0.313400 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.394253 | −0.0275358 | ||||||||
\(206\) | −12.6915 | −0.884256 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 35.2638 | 2.44511 | ||||||||
\(209\) | −15.3617 | −1.06259 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.31253 | 0.0903583 | 0.0451792 | − | 0.998979i | \(-0.485614\pi\) | ||||
0.0451792 | + | 0.998979i | \(0.485614\pi\) | |||||||
\(212\) | 11.7159 | 0.804654 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 14.7750 | 1.01000 | ||||||||
\(215\) | −0.432883 | −0.0295224 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.75457 | 0.119108 | ||||||||
\(218\) | 0.137055 | 0.00928252 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.45174 | −0.0978762 | ||||||||
\(221\) | 32.1886 | 2.16524 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.89997 | −0.127231 | −0.0636157 | − | 0.997974i | \(-0.520263\pi\) | ||||
−0.0636157 | + | 0.997974i | \(0.520263\pi\) | |||||||
\(224\) | −4.46069 | −0.298042 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.0148 | 0.932252 | ||||||||
\(227\) | 12.7393 | 0.845535 | 0.422767 | − | 0.906238i | \(-0.361059\pi\) | ||||
0.422767 | + | 0.906238i | \(0.361059\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.7441 | 1.56905 | 0.784526 | − | 0.620096i | \(-0.212906\pi\) | ||||
0.784526 | + | 0.620096i | \(0.212906\pi\) | |||||||
\(230\) | −3.24428 | −0.213922 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.97809 | −0.523787 | ||||||||
\(233\) | 7.78814 | 0.510218 | 0.255109 | − | 0.966912i | \(-0.417889\pi\) | ||||
0.255109 | + | 0.966912i | \(0.417889\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.15319 | 0.270925 | ||||||||
\(236\) | 17.2241 | 1.12119 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.62939 | −0.364899 | ||||||||
\(239\) | 3.41301 | 0.220769 | 0.110385 | − | 0.993889i | \(-0.464792\pi\) | ||||
0.110385 | + | 0.993889i | \(0.464792\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.3354 | −0.794593 | −0.397296 | − | 0.917690i | \(-0.630051\pi\) | ||||
−0.397296 | + | 0.917690i | \(0.630051\pi\) | |||||||
\(242\) | 8.33166 | 0.535579 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.04950 | 0.0671871 | ||||||||
\(245\) | −2.82346 | −0.180384 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −43.6372 | −2.77657 | ||||||||
\(248\) | −3.13490 | −0.199066 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.74277 | 0.489696 | ||||||||
\(251\) | −7.32241 | −0.462186 | −0.231093 | − | 0.972932i | \(-0.574230\pi\) | ||||
−0.231093 | + | 0.972932i | \(0.574230\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.4252 | −0.655429 | ||||||||
\(254\) | −0.750996 | −0.0471217 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.9209 | 1.30756 | ||||||||
\(257\) | −4.99494 | −0.311576 | −0.155788 | − | 0.987791i | \(-0.549792\pi\) | ||||
−0.155788 | + | 0.987791i | \(0.549792\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.31862 | 0.392620 | ||||||||
\(260\) | −4.12388 | −0.255752 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.52511 | 0.341342 | ||||||||
\(263\) | 18.1100 | 1.11671 | 0.558355 | − | 0.829602i | \(-0.311433\pi\) | ||||
0.558355 | + | 0.829602i | \(0.311433\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.83451 | 0.235552 | ||||||||
\(266\) | 7.63160 | 0.467923 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 15.0776 | 0.921012 | ||||||||
\(269\) | −12.3502 | −0.753004 | −0.376502 | − | 0.926416i | \(-0.622873\pi\) | ||||
−0.376502 | + | 0.926416i | \(0.622873\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.1352 | −0.676418 | −0.338209 | − | 0.941071i | \(-0.609821\pi\) | ||||
−0.338209 | + | 0.941071i | \(0.609821\pi\) | |||||||
\(272\) | 21.8796 | 1.32664 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −19.4837 | −1.17705 | ||||||||
\(275\) | 12.2028 | 0.735857 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.8511 | 0.952399 | 0.476200 | − | 0.879337i | \(-0.342014\pi\) | ||||
0.476200 | + | 0.879337i | \(0.342014\pi\) | |||||||
\(278\) | 41.4318 | 2.48491 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.369362 | −0.0220736 | ||||||||
\(281\) | 8.89152 | 0.530424 | 0.265212 | − | 0.964190i | \(-0.414558\pi\) | ||||
0.265212 | + | 0.964190i | \(0.414558\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.86993 | −0.467819 | −0.233909 | − | 0.972258i | \(-0.575152\pi\) | ||||
−0.233909 | + | 0.972258i | \(0.575152\pi\) | |||||||
\(284\) | 17.5523 | 1.04154 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −33.2902 | −1.96849 | ||||||||
\(287\) | 0.629388 | 0.0371516 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.97154 | 0.174796 | ||||||||
\(290\) | 5.09852 | 0.299395 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.30963 | −0.310723 | ||||||||
\(293\) | 33.5108 | 1.95772 | 0.978859 | − | 0.204534i | \(-0.0655679\pi\) | ||||
0.978859 | + | 0.204534i | \(0.0655679\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.63727 | 0.328214 | ||||||||
\(296\) | −11.2895 | −0.656189 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 27.3154 | 1.58234 | ||||||||
\(299\) | −29.6144 | −1.71264 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.691058 | 0.0398319 | ||||||||
\(302\) | −14.6463 | −0.842798 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −29.6615 | −1.70121 | ||||||||
\(305\) | 0.343489 | 0.0196681 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.9225 | 0.737524 | 0.368762 | − | 0.929524i | \(-0.379782\pi\) | ||||
0.368762 | + | 0.929524i | \(0.379782\pi\) | |||||||
\(308\) | 2.31756 | 0.132055 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.00340 | 0.113786 | ||||||||
\(311\) | 13.5621 | 0.769036 | 0.384518 | − | 0.923117i | \(-0.374368\pi\) | ||||
0.384518 | + | 0.923117i | \(0.374368\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.3819 | −1.32162 | −0.660812 | − | 0.750552i | \(-0.729788\pi\) | ||||
−0.660812 | + | 0.750552i | \(0.729788\pi\) | |||||||
\(314\) | −12.5639 | −0.709021 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15.7205 | −0.884348 | ||||||||
\(317\) | −1.61143 | −0.0905067 | −0.0452533 | − | 0.998976i | \(-0.514410\pi\) | ||||
−0.0452533 | + | 0.998976i | \(0.514410\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.3837 | 0.917309 | ||||||||
\(320\) | −0.854590 | −0.0477730 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.17919 | 0.288625 | ||||||||
\(323\) | −27.0748 | −1.50648 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 34.6639 | 1.92281 | ||||||||
\(326\) | −12.5262 | −0.693762 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.12453 | −0.0620917 | ||||||||
\(329\) | −6.63019 | −0.365534 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 34.2553 | 1.88284 | 0.941422 | − | 0.337232i | \(-0.109491\pi\) | ||||
0.941422 | + | 0.337232i | \(0.109491\pi\) | |||||||
\(332\) | 12.9112 | 0.708597 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 28.4198 | 1.55506 | ||||||||
\(335\) | 4.93475 | 0.269614 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.3568 | 0.836539 | 0.418269 | − | 0.908323i | \(-0.362637\pi\) | ||||
0.418269 | + | 0.908323i | \(0.362637\pi\) | |||||||
\(338\) | −70.8692 | −3.85477 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.55867 | −0.138764 | ||||||||
\(341\) | 6.43778 | 0.348625 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.34478 | 0.504571 | ||||||||
\(344\) | −1.23472 | −0.0665714 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.59869 | −0.300988 | ||||||||
\(347\) | 1.93444 | 0.103846 | 0.0519232 | − | 0.998651i | \(-0.483465\pi\) | ||||
0.0519232 | + | 0.998651i | \(0.483465\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.58879 | 0.299161 | 0.149580 | − | 0.988750i | \(-0.452208\pi\) | ||||
0.149580 | + | 0.988750i | \(0.452208\pi\) | |||||||
\(350\) | −6.06228 | −0.324043 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −16.3669 | −0.872360 | ||||||||
\(353\) | 4.53839 | 0.241554 | 0.120777 | − | 0.992680i | \(-0.461461\pi\) | ||||
0.120777 | + | 0.992680i | \(0.461461\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.74468 | 0.304896 | ||||||||
\(356\) | −10.6465 | −0.564262 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.4260 | 0.656733 | ||||||||
\(359\) | 11.5921 | 0.611809 | 0.305904 | − | 0.952062i | \(-0.401041\pi\) | ||||
0.305904 | + | 0.952062i | \(0.401041\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.7046 | 0.931821 | ||||||||
\(362\) | 11.4136 | 0.599887 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.58338 | 0.345063 | ||||||||
\(365\) | −1.73779 | −0.0909600 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.23499 | −0.377663 | −0.188832 | − | 0.982009i | \(-0.560470\pi\) | ||||
−0.188832 | + | 0.982009i | \(0.560470\pi\) | |||||||
\(368\) | −20.1298 | −1.04934 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7.21472 | 0.375076 | ||||||||
\(371\) | −6.12143 | −0.317809 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.7599 | 0.608906 | 0.304453 | − | 0.952527i | \(-0.401526\pi\) | ||||
0.304453 | + | 0.952527i | \(0.401526\pi\) | |||||||
\(374\) | −20.6550 | −1.06805 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.8462 | 0.610920 | ||||||||
\(377\) | 46.5402 | 2.39694 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.11108 | −0.262539 | −0.131269 | − | 0.991347i | \(-0.541905\pi\) | ||||
−0.131269 | + | 0.991347i | \(0.541905\pi\) | |||||||
\(380\) | 3.46872 | 0.177942 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −17.8447 | −0.913017 | ||||||||
\(383\) | −16.1519 | −0.825321 | −0.412661 | − | 0.910885i | \(-0.635400\pi\) | ||||
−0.412661 | + | 0.910885i | \(0.635400\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.758515 | 0.0386575 | ||||||||
\(386\) | −11.7672 | −0.598937 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 19.8248 | 1.00645 | ||||||||
\(389\) | −17.2323 | −0.873714 | −0.436857 | − | 0.899531i | \(-0.643908\pi\) | ||||
−0.436857 | + | 0.899531i | \(0.643908\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.3744 | −0.929232 | ||||||||
\(392\) | −8.05336 | −0.406756 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −17.3540 | −0.874284 | ||||||||
\(395\) | −5.14516 | −0.258881 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.6151 | −1.48634 | −0.743170 | − | 0.669103i | \(-0.766679\pi\) | ||||
−0.743170 | + | 0.669103i | \(0.766679\pi\) | |||||||
\(398\) | −30.7201 | −1.53986 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 23.5621 | 1.17811 | ||||||||
\(401\) | 14.3050 | 0.714358 | 0.357179 | − | 0.934036i | \(-0.383739\pi\) | ||||
0.357179 | + | 0.934036i | \(0.383739\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.2874 | 0.910962 | ||||||||
\(404\) | 4.10835 | 0.204398 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.13931 | −0.403947 | ||||||||
\(407\) | 23.1839 | 1.14918 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.8663 | 0.833983 | 0.416992 | − | 0.908910i | \(-0.363084\pi\) | ||||
0.416992 | + | 0.908910i | \(0.363084\pi\) | |||||||
\(410\) | 0.718647 | 0.0354915 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.20892 | 0.453691 | ||||||||
\(413\) | −8.99937 | −0.442830 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.22572 | 0.207432 | ||||||||
\(416\) | −46.4926 | −2.27949 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 28.0014 | 1.36960 | ||||||||
\(419\) | 1.44141 | 0.0704176 | 0.0352088 | − | 0.999380i | \(-0.488790\pi\) | ||||
0.0352088 | + | 0.999380i | \(0.488790\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.38698 | −0.0675972 | −0.0337986 | − | 0.999429i | \(-0.510760\pi\) | ||||
−0.0337986 | + | 0.999429i | \(0.510760\pi\) | |||||||
\(422\) | −2.39249 | −0.116465 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10.9372 | 0.531157 | ||||||||
\(425\) | 21.5073 | 1.04326 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.548348 | −0.0265364 | ||||||||
\(428\) | −10.7207 | −0.518206 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.789063 | 0.0380520 | ||||||||
\(431\) | 19.8758 | 0.957383 | 0.478692 | − | 0.877983i | \(-0.341111\pi\) | ||||
0.478692 | + | 0.877983i | \(0.341111\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.09155 | −0.148570 | −0.0742851 | − | 0.997237i | \(-0.523667\pi\) | ||||
−0.0742851 | + | 0.997237i | \(0.523667\pi\) | |||||||
\(434\) | −3.19825 | −0.153521 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.0994470 | −0.00476265 | ||||||||
\(437\) | 24.9096 | 1.19159 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.90197 | 0.424868 | 0.212434 | − | 0.977175i | \(-0.431861\pi\) | ||||
0.212434 | + | 0.977175i | \(0.431861\pi\) | |||||||
\(440\) | −1.35524 | −0.0646086 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −58.6736 | −2.79082 | ||||||||
\(443\) | 10.9765 | 0.521510 | 0.260755 | − | 0.965405i | \(-0.416029\pi\) | ||||
0.260755 | + | 0.965405i | \(0.416029\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.48448 | −0.165180 | ||||||||
\(446\) | 3.46328 | 0.163991 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.36427 | 0.0644558 | ||||||||
\(449\) | −18.7937 | −0.886931 | −0.443465 | − | 0.896292i | \(-0.646251\pi\) | ||||
−0.443465 | + | 0.896292i | \(0.646251\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.30931 | 0.108741 | ||||||||
\(452\) | −10.1692 | −0.478317 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −23.2212 | −1.08983 | ||||||||
\(455\) | 2.15467 | 0.101013 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.7161 | 0.922279 | 0.461140 | − | 0.887328i | \(-0.347441\pi\) | ||||
0.461140 | + | 0.887328i | \(0.347441\pi\) | |||||||
\(458\) | −43.2809 | −2.02238 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.35405 | 0.109758 | ||||||||
\(461\) | 40.1745 | 1.87111 | 0.935556 | − | 0.353177i | \(-0.114899\pi\) | ||||
0.935556 | + | 0.353177i | \(0.114899\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.2931 | 1.03605 | 0.518024 | − | 0.855366i | \(-0.326668\pi\) | ||||
0.518024 | + | 0.855366i | \(0.326668\pi\) | |||||||
\(464\) | 31.6348 | 1.46861 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.1963 | −0.657630 | ||||||||
\(467\) | −2.81433 | −0.130232 | −0.0651158 | − | 0.997878i | \(-0.520742\pi\) | ||||
−0.0651158 | + | 0.997878i | \(0.520742\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.87786 | −0.363766 | ||||||||
\(470\) | −7.57048 | −0.349200 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 16.0792 | 0.740105 | ||||||||
\(473\) | 2.53559 | 0.116587 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −29.1569 | −1.33781 | ||||||||
\(476\) | 4.08468 | 0.187221 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.22126 | −0.284554 | ||||||||
\(479\) | −15.6891 | −0.716855 | −0.358428 | − | 0.933558i | \(-0.616687\pi\) | ||||
−0.358428 | + | 0.933558i | \(0.616687\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 65.8573 | 3.00284 | ||||||||
\(482\) | 22.4851 | 1.02417 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.04545 | −0.274793 | ||||||||
\(485\) | 6.48845 | 0.294625 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.31905 | −0.376972 | −0.188486 | − | 0.982076i | \(-0.560358\pi\) | ||||
−0.188486 | + | 0.982076i | \(0.560358\pi\) | |||||||
\(488\) | 0.979736 | 0.0443506 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 5.14662 | 0.232501 | ||||||||
\(491\) | −21.4599 | −0.968474 | −0.484237 | − | 0.874937i | \(-0.660903\pi\) | ||||
−0.484237 | + | 0.874937i | \(0.660903\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 28.8761 | 1.30051 | ||||||||
\(494\) | 79.5422 | 3.57877 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.4305 | 0.558148 | ||||||||
\(497\) | −9.17085 | −0.411369 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.86371 | −0.396794 | −0.198397 | − | 0.980122i | \(-0.563574\pi\) | ||||
−0.198397 | + | 0.980122i | \(0.563574\pi\) | |||||||
\(500\) | −5.61816 | −0.251252 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.3473 | 0.595721 | ||||||||
\(503\) | 18.4384 | 0.822126 | 0.411063 | − | 0.911607i | \(-0.365158\pi\) | ||||
0.411063 | + | 0.911607i | \(0.365158\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.34462 | 0.0598349 | ||||||||
\(506\) | 19.0032 | 0.844795 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.544923 | 0.0241770 | ||||||||
\(509\) | 5.39526 | 0.239141 | 0.119570 | − | 0.992826i | \(-0.461848\pi\) | ||||
0.119570 | + | 0.992826i | \(0.461848\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.77422 | 0.122724 | ||||||||
\(512\) | −19.5124 | −0.862333 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.10483 | 0.401597 | ||||||||
\(515\) | 3.01399 | 0.132812 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −24.3271 | −1.06991 | ||||||||
\(518\) | −11.5176 | −0.506056 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.84976 | −0.168823 | ||||||||
\(521\) | −34.0231 | −1.49058 | −0.745290 | − | 0.666741i | \(-0.767689\pi\) | ||||
−0.745290 | + | 0.666741i | \(0.767689\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.5996 | 0.769576 | 0.384788 | − | 0.923005i | \(-0.374275\pi\) | ||||
0.384788 | + | 0.923005i | \(0.374275\pi\) | |||||||
\(524\) | −4.00902 | −0.175135 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −33.0110 | −1.43935 | ||||||||
\(527\) | 11.3465 | 0.494262 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.09508 | −0.265003 | ||||||||
\(530\) | −6.98957 | −0.303608 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.53749 | −0.240081 | ||||||||
\(533\) | 6.55994 | 0.284143 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.50879 | −0.151698 | ||||||||
\(536\) | 14.0754 | 0.607965 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 22.5120 | 0.970562 | ||||||||
\(539\) | 16.5382 | 0.712352 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.6744 | 0.845868 | 0.422934 | − | 0.906160i | \(-0.361000\pi\) | ||||
0.422934 | + | 0.906160i | \(0.361000\pi\) | |||||||
\(542\) | 20.2974 | 0.871848 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −28.8465 | −1.23678 | ||||||||
\(545\) | −0.0325480 | −0.00139420 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.3233 | −0.612421 | −0.306211 | − | 0.951964i | \(-0.599061\pi\) | ||||
−0.306211 | + | 0.951964i | \(0.599061\pi\) | |||||||
\(548\) | 14.1374 | 0.603919 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −22.2434 | −0.948461 | ||||||||
\(551\) | −39.1464 | −1.66769 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.21377 | 0.349285 | ||||||||
\(554\) | −28.8935 | −1.22757 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −30.0629 | −1.27495 | ||||||||
\(557\) | −1.21426 | −0.0514499 | −0.0257250 | − | 0.999669i | \(-0.508189\pi\) | ||||
−0.0257250 | + | 0.999669i | \(0.508189\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.20272 | 0.304642 | ||||||||
\(560\) | 1.46460 | 0.0618906 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16.2075 | −0.683674 | ||||||||
\(563\) | −31.6272 | −1.33293 | −0.666464 | − | 0.745537i | \(-0.732193\pi\) | ||||
−0.666464 | + | 0.745537i | \(0.732193\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.32826 | −0.140021 | ||||||||
\(566\) | 14.3454 | 0.602981 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 16.3856 | 0.687524 | ||||||||
\(569\) | 47.0142 | 1.97094 | 0.985468 | − | 0.169859i | \(-0.0543311\pi\) | ||||
0.985468 | + | 0.169859i | \(0.0543311\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.6050 | 1.32263 | 0.661314 | − | 0.750109i | \(-0.269999\pi\) | ||||
0.661314 | + | 0.750109i | \(0.269999\pi\) | |||||||
\(572\) | 24.1554 | 1.00999 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.14725 | −0.0478854 | ||||||||
\(575\) | −19.7873 | −0.825189 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −35.2559 | −1.46772 | −0.733860 | − | 0.679300i | \(-0.762283\pi\) | ||||
−0.733860 | + | 0.679300i | \(0.762283\pi\) | |||||||
\(578\) | −5.41655 | −0.225299 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.69949 | −0.153613 | ||||||||
\(581\) | −6.74596 | −0.279870 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.4604 | −0.930216 | ||||||||
\(584\) | −4.95670 | −0.205110 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −61.0837 | −2.52334 | ||||||||
\(587\) | 28.4801 | 1.17550 | 0.587749 | − | 0.809043i | \(-0.300014\pi\) | ||||
0.587749 | + | 0.809043i | \(0.300014\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.3821 | −0.633810 | ||||||||
\(590\) | −10.2757 | −0.423042 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 44.7653 | 1.83984 | ||||||||
\(593\) | 4.79696 | 0.196987 | 0.0984937 | − | 0.995138i | \(-0.468598\pi\) | ||||
0.0984937 | + | 0.995138i | \(0.468598\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.33688 | 0.0548065 | ||||||||
\(596\) | −19.8201 | −0.811862 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 53.9814 | 2.20746 | ||||||||
\(599\) | −5.06413 | −0.206915 | −0.103457 | − | 0.994634i | \(-0.532991\pi\) | ||||
−0.103457 | + | 0.994634i | \(0.532991\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.9289 | −1.46557 | −0.732785 | − | 0.680460i | \(-0.761780\pi\) | ||||
−0.732785 | + | 0.680460i | \(0.761780\pi\) | |||||||
\(602\) | −1.25967 | −0.0513401 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.6273 | 0.432420 | ||||||||
\(605\) | −1.97862 | −0.0804421 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.25566 | −0.213321 | −0.106660 | − | 0.994296i | \(-0.534016\pi\) | ||||
−0.106660 | + | 0.994296i | \(0.534016\pi\) | |||||||
\(608\) | 39.1064 | 1.58597 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.626115 | −0.0253507 | ||||||||
\(611\) | −69.1047 | −2.79568 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.9713 | −0.887412 | −0.443706 | − | 0.896172i | \(-0.646337\pi\) | ||||
−0.443706 | + | 0.896172i | \(0.646337\pi\) | |||||||
\(614\) | −23.5552 | −0.950610 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.16352 | 0.0871706 | ||||||||
\(617\) | 31.7381 | 1.27773 | 0.638864 | − | 0.769320i | \(-0.279405\pi\) | ||||
0.638864 | + | 0.769320i | \(0.279405\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −36.4514 | −1.46511 | −0.732554 | − | 0.680709i | \(-0.761672\pi\) | ||||
−0.732554 | + | 0.680709i | \(0.761672\pi\) | |||||||
\(620\) | −1.45367 | −0.0583808 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −24.7211 | −0.991226 | ||||||||
\(623\) | 5.56264 | 0.222863 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.2243 | 0.888972 | ||||||||
\(626\) | 42.6207 | 1.70347 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.11636 | 0.363782 | ||||||||
\(629\) | 40.8614 | 1.62925 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.25533 | −0.249021 | −0.124510 | − | 0.992218i | \(-0.539736\pi\) | ||||
−0.124510 | + | 0.992218i | \(0.539736\pi\) | |||||||
\(632\) | −14.6756 | −0.583763 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.93732 | 0.116656 | ||||||||
\(635\) | 0.178348 | 0.00707751 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 46.9793 | 1.86139 | ||||||||
\(638\) | −29.8643 | −1.18234 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4.03066 | −0.159326 | ||||||||
\(641\) | −39.3213 | −1.55310 | −0.776550 | − | 0.630056i | \(-0.783032\pi\) | ||||
−0.776550 | + | 0.630056i | \(0.783032\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.00103 | 0.354966 | 0.177483 | − | 0.984124i | \(-0.443205\pi\) | ||||
0.177483 | + | 0.984124i | \(0.443205\pi\) | |||||||
\(644\) | −3.75802 | −0.148087 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 49.3523 | 1.94174 | ||||||||
\(647\) | −49.7161 | −1.95454 | −0.977271 | − | 0.211996i | \(-0.932004\pi\) | ||||
−0.977271 | + | 0.211996i | \(0.932004\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −33.0200 | −1.29615 | ||||||||
\(650\) | −63.1856 | −2.47834 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.08902 | 0.355953 | ||||||||
\(653\) | 27.8105 | 1.08831 | 0.544155 | − | 0.838985i | \(-0.316850\pi\) | ||||
0.544155 | + | 0.838985i | \(0.316850\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.31211 | −0.0512684 | ||||||||
\(656\) | 4.45900 | 0.174095 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 12.0856 | 0.471144 | ||||||||
\(659\) | −8.76051 | −0.341261 | −0.170631 | − | 0.985335i | \(-0.554580\pi\) | ||||
−0.170631 | + | 0.985335i | \(0.554580\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.63090 | −0.180121 | −0.0900606 | − | 0.995936i | \(-0.528706\pi\) | ||||
−0.0900606 | + | 0.995936i | \(0.528706\pi\) | |||||||
\(662\) | −62.4409 | −2.42683 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.0530 | 0.467748 | ||||||||
\(665\) | −1.81236 | −0.0702805 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −26.5668 | −1.02867 | ||||||||
\(668\) | −20.6214 | −0.797868 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8.99510 | −0.347511 | ||||||||
\(671\) | −2.01197 | −0.0776712 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.5345 | 0.406076 | 0.203038 | − | 0.979171i | \(-0.434918\pi\) | ||||
0.203038 | + | 0.979171i | \(0.434918\pi\) | |||||||
\(674\) | −27.9925 | −1.07823 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 51.4227 | 1.97780 | ||||||||
\(677\) | 2.02418 | 0.0777957 | 0.0388978 | − | 0.999243i | \(-0.487615\pi\) | ||||
0.0388978 | + | 0.999243i | \(0.487615\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.3582 | −0.397511 | ||||||||
\(680\) | −2.38860 | −0.0915986 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −11.7348 | −0.449350 | ||||||||
\(683\) | 30.3719 | 1.16215 | 0.581075 | − | 0.813850i | \(-0.302632\pi\) | ||||
0.581075 | + | 0.813850i | \(0.302632\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.62702 | 0.176789 | ||||||||
\(686\) | −17.0338 | −0.650352 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.89591 | 0.186655 | ||||||||
\(689\) | −63.8021 | −2.43067 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.3536 | −0.698205 | −0.349102 | − | 0.937085i | \(-0.613513\pi\) | ||||
−0.349102 | + | 0.937085i | \(0.613513\pi\) | |||||||
\(692\) | 4.06241 | 0.154430 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.52612 | −0.133850 | ||||||||
\(695\) | −9.83928 | −0.373225 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.07014 | 0.154168 | ||||||||
\(698\) | −10.1873 | −0.385595 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.39879 | 0.166259 | ||||||||
\(701\) | 4.98491 | 0.188277 | 0.0941387 | − | 0.995559i | \(-0.469990\pi\) | ||||
0.0941387 | + | 0.995559i | \(0.469990\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −55.3947 | −2.08925 | ||||||||
\(704\) | 5.00571 | 0.188660 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.27261 | −0.311344 | ||||||||
\(707\) | −2.14656 | −0.0807298 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.8837 | 1.04719 | 0.523597 | − | 0.851966i | \(-0.324590\pi\) | ||||
0.523597 | + | 0.851966i | \(0.324590\pi\) | |||||||
\(710\) | −10.4715 | −0.392987 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.93880 | −0.372472 | ||||||||
\(713\) | −10.4391 | −0.390948 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.90581 | 0.295660 | ||||||||
\(716\) | −9.01629 | −0.336954 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −21.1302 | −0.788573 | ||||||||
\(719\) | 10.7704 | 0.401668 | 0.200834 | − | 0.979625i | \(-0.435635\pi\) | ||||
0.200834 | + | 0.979625i | \(0.435635\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.81155 | −0.179191 | ||||||||
\(722\) | −32.2721 | −1.20104 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.28173 | −0.307788 | ||||||||
\(725\) | 31.0966 | 1.15490 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.46886 | 0.0915651 | 0.0457826 | − | 0.998951i | \(-0.485422\pi\) | ||||
0.0457826 | + | 0.998951i | \(0.485422\pi\) | |||||||
\(728\) | 6.14578 | 0.227778 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.16766 | 0.117240 | ||||||||
\(731\) | 4.46895 | 0.165290 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.4103 | −0.458383 | −0.229192 | − | 0.973381i | \(-0.573608\pi\) | ||||
−0.229192 | + | 0.973381i | \(0.573608\pi\) | |||||||
\(734\) | 13.1880 | 0.486778 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 26.5396 | 0.978263 | ||||||||
\(737\) | −28.9050 | −1.06473 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38.5237 | 1.41712 | 0.708559 | − | 0.705651i | \(-0.249346\pi\) | ||||
0.708559 | + | 0.705651i | \(0.249346\pi\) | |||||||
\(740\) | −5.23501 | −0.192443 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.1582 | 0.409630 | ||||||||
\(743\) | −36.8075 | −1.35034 | −0.675168 | − | 0.737664i | \(-0.735929\pi\) | ||||
−0.675168 | + | 0.737664i | \(0.735929\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.48691 | −0.237662 | ||||||||
\(746\) | −21.4361 | −0.784831 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 14.9873 | 0.547990 | ||||||||
\(749\) | 5.60145 | 0.204672 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.1985 | 0.518111 | 0.259055 | − | 0.965862i | \(-0.416589\pi\) | ||||
0.259055 | + | 0.965862i | \(0.416589\pi\) | |||||||
\(752\) | −46.9726 | −1.71292 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −84.8339 | −3.08947 | ||||||||
\(755\) | 3.47822 | 0.126585 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.5676 | 0.384085 | 0.192042 | − | 0.981387i | \(-0.438489\pi\) | ||||
0.192042 | + | 0.981387i | \(0.438489\pi\) | |||||||
\(758\) | 9.31652 | 0.338391 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.23816 | 0.117460 | ||||||||
\(761\) | −27.4842 | −0.996302 | −0.498151 | − | 0.867090i | \(-0.665988\pi\) | ||||
−0.498151 | + | 0.867090i | \(0.665988\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.0519598 | 0.00188107 | ||||||||
\(764\) | 12.9482 | 0.468448 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 29.4417 | 1.06377 | ||||||||
\(767\) | −93.7981 | −3.38685 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.0083 | −0.396969 | −0.198485 | − | 0.980104i | \(-0.563602\pi\) | ||||
−0.198485 | + | 0.980104i | \(0.563602\pi\) | |||||||
\(770\) | −1.38263 | −0.0498264 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8.53831 | 0.307301 | ||||||||
\(773\) | 40.1139 | 1.44280 | 0.721398 | − | 0.692521i | \(-0.243500\pi\) | ||||
0.721398 | + | 0.692521i | \(0.243500\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.2191 | 0.438921 | ||||||||
\(776\) | 18.5070 | 0.664364 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 31.4112 | 1.12615 | ||||||||
\(779\) | −5.51778 | −0.197695 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −33.6492 | −1.20406 | ||||||||
\(782\) | 33.4929 | 1.19771 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 31.9333 | 1.14047 | ||||||||
\(785\) | 2.98369 | 0.106492 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.6905 | −0.559306 | −0.279653 | − | 0.960101i | \(-0.590219\pi\) | ||||
−0.279653 | + | 0.960101i | \(0.590219\pi\) | |||||||
\(788\) | 12.5921 | 0.448575 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 9.37865 | 0.333677 | ||||||||
\(791\) | 5.31326 | 0.188918 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.71529 | −0.202956 | ||||||||
\(794\) | 53.9827 | 1.91577 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 22.2905 | 0.790065 | ||||||||
\(797\) | 42.7721 | 1.51507 | 0.757533 | − | 0.652797i | \(-0.226404\pi\) | ||||
0.757533 | + | 0.652797i | \(0.226404\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −42.8763 | −1.51685 | ||||||||
\(800\) | −31.0648 | −1.09831 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −26.0753 | −0.920751 | ||||||||
\(803\) | 10.1790 | 0.359209 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.22996 | −0.0433505 | ||||||||
\(806\) | −33.3345 | −1.17416 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.83527 | 0.134924 | ||||||||
\(809\) | −45.5750 | −1.60233 | −0.801166 | − | 0.598442i | \(-0.795787\pi\) | ||||
−0.801166 | + | 0.598442i | \(0.795787\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.9527 | 0.700634 | 0.350317 | − | 0.936631i | \(-0.386074\pi\) | ||||
0.350317 | + | 0.936631i | \(0.386074\pi\) | |||||||
\(812\) | 5.90588 | 0.207256 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −42.2598 | −1.48121 | ||||||||
\(815\) | 2.97474 | 0.104201 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.05843 | −0.211958 | ||||||||
\(818\) | −30.7440 | −1.07494 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.521451 | −0.0182098 | ||||||||
\(821\) | −47.1393 | −1.64517 | −0.822587 | − | 0.568640i | \(-0.807470\pi\) | ||||
−0.822587 | + | 0.568640i | \(0.807470\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.2522 | 0.775663 | 0.387831 | − | 0.921730i | \(-0.373224\pi\) | ||||
0.387831 | + | 0.921730i | \(0.373224\pi\) | |||||||
\(824\) | 8.59681 | 0.299484 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16.4041 | 0.570772 | ||||||||
\(827\) | 46.9285 | 1.63186 | 0.815931 | − | 0.578149i | \(-0.196225\pi\) | ||||
0.815931 | + | 0.578149i | \(0.196225\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 48.4646 | 1.68324 | 0.841622 | − | 0.540067i | \(-0.181601\pi\) | ||||
0.841622 | + | 0.540067i | \(0.181601\pi\) | |||||||
\(830\) | −7.70267 | −0.267364 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 14.2195 | 0.492971 | ||||||||
\(833\) | 29.1485 | 1.00993 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.74919 | −0.233565 | ||||||||
\(836\) | −20.3179 | −0.702708 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.62742 | −0.0907627 | ||||||||
\(839\) | −9.26196 | −0.319758 | −0.159879 | − | 0.987137i | \(-0.551110\pi\) | ||||
−0.159879 | + | 0.987137i | \(0.551110\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.7507 | 0.439681 | ||||||||
\(842\) | 2.52820 | 0.0871275 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.73599 | 0.0597553 | ||||||||
\(845\) | 16.8301 | 0.578974 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.15867 | 0.108533 | ||||||||
\(848\) | −43.3683 | −1.48927 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −39.2038 | −1.34468 | ||||||||
\(851\) | −37.5936 | −1.28869 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.7761 | −1.05375 | −0.526877 | − | 0.849941i | \(-0.676637\pi\) | ||||
−0.526877 | + | 0.849941i | \(0.676637\pi\) | |||||||
\(854\) | 0.999534 | 0.0342034 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.0081 | −0.342071 | ||||||||
\(857\) | 20.4236 | 0.697656 | 0.348828 | − | 0.937187i | \(-0.386580\pi\) | ||||
0.348828 | + | 0.937187i | \(0.386580\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.6527 | −1.21645 | −0.608226 | − | 0.793764i | \(-0.708119\pi\) | ||||
−0.608226 | + | 0.793764i | \(0.708119\pi\) | |||||||
\(860\) | −0.572545 | −0.0195236 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −36.2298 | −1.23399 | ||||||||
\(863\) | −9.21342 | −0.313628 | −0.156814 | − | 0.987628i | \(-0.550122\pi\) | ||||
−0.156814 | + | 0.987628i | \(0.550122\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.32959 | 0.0452073 | ||||||||
\(866\) | 5.63530 | 0.191495 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.32065 | 0.0787680 | ||||||||
\(869\) | 30.1375 | 1.02235 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −82.1089 | −2.78216 | ||||||||
\(872\) | −0.0928368 | −0.00314385 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −45.4054 | −1.53586 | ||||||||
\(875\) | 2.93542 | 0.0992352 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −57.8367 | −1.95301 | −0.976504 | − | 0.215501i | \(-0.930861\pi\) | ||||
−0.976504 | + | 0.215501i | \(0.930861\pi\) | |||||||
\(878\) | −16.2266 | −0.547621 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.37382 | 0.181152 | ||||||||
\(881\) | 28.9309 | 0.974706 | 0.487353 | − | 0.873205i | \(-0.337962\pi\) | ||||
0.487353 | + | 0.873205i | \(0.337962\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.7957 | 1.47384 | 0.736922 | − | 0.675978i | \(-0.236278\pi\) | ||||
0.736922 | + | 0.675978i | \(0.236278\pi\) | |||||||
\(884\) | 42.5736 | 1.43191 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −20.0081 | −0.672185 | ||||||||
\(887\) | 30.1524 | 1.01242 | 0.506210 | − | 0.862410i | \(-0.331046\pi\) | ||||
0.506210 | + | 0.862410i | \(0.331046\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.284715 | −0.00954904 | ||||||||
\(890\) | 6.35154 | 0.212904 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.51296 | −0.0841401 | ||||||||
\(893\) | 58.1262 | 1.94512 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.95094 | −0.0986390 | ||||||||
\(896\) | 6.43457 | 0.214964 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 34.2574 | 1.14318 | ||||||||
\(899\) | 16.4055 | 0.547153 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −39.5863 | −1.31881 | ||||||||
\(902\) | −4.20944 | −0.140159 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.49322 | −0.315740 | ||||||||
\(905\) | −2.71053 | −0.0901009 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41.6983 | −1.38457 | −0.692284 | − | 0.721625i | \(-0.743396\pi\) | ||||
−0.692284 | + | 0.721625i | \(0.743396\pi\) | |||||||
\(908\) | 16.8493 | 0.559165 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.92756 | −0.130197 | ||||||||
\(911\) | −8.80971 | −0.291879 | −0.145939 | − | 0.989294i | \(-0.546620\pi\) | ||||
−0.145939 | + | 0.989294i | \(0.546620\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.7519 | −0.819169 | ||||||||
\(914\) | −35.9386 | −1.18874 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 31.4046 | 1.03764 | ||||||||
\(917\) | 2.09466 | 0.0691718 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.9520 | −0.361273 | −0.180636 | − | 0.983550i | \(-0.557816\pi\) | ||||
−0.180636 | + | 0.983550i | \(0.557816\pi\) | |||||||
\(920\) | 2.19758 | 0.0724520 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −73.2304 | −2.41171 | ||||||||
\(923\) | −95.5853 | −3.14623 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 44.0036 | 1.44683 | ||||||||
\(926\) | −40.6360 | −1.33538 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −41.7080 | −1.36913 | ||||||||
\(929\) | −28.2079 | −0.925470 | −0.462735 | − | 0.886497i | \(-0.653132\pi\) | ||||
−0.462735 | + | 0.886497i | \(0.653132\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −39.5158 | −1.29508 | ||||||||
\(932\) | 10.3008 | 0.337415 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.12998 | 0.167858 | ||||||||
\(935\) | 4.90519 | 0.160417 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32.3092 | −1.05550 | −0.527748 | − | 0.849401i | \(-0.676963\pi\) | ||||
−0.527748 | + | 0.849401i | \(0.676963\pi\) | |||||||
\(938\) | 14.3598 | 0.468865 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5.49314 | 0.179167 | ||||||||
\(941\) | −23.1402 | −0.754349 | −0.377175 | − | 0.926142i | \(-0.623104\pi\) | ||||
−0.377175 | + | 0.926142i | \(0.623104\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.74464 | −0.121942 | ||||||||
\(944\) | −63.7575 | −2.07513 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.62190 | −0.150271 | ||||||||
\(947\) | −26.2737 | −0.853780 | −0.426890 | − | 0.904303i | \(-0.640391\pi\) | ||||
−0.426890 | + | 0.904303i | \(0.640391\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28.9149 | 0.938619 | ||||||||
\(950\) | 53.1474 | 1.72433 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.81318 | 0.123586 | ||||||||
\(953\) | 8.01441 | 0.259612 | 0.129806 | − | 0.991539i | \(-0.458565\pi\) | ||||
0.129806 | + | 0.991539i | \(0.458565\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.23780 | 0.137132 | ||||||||
\(956\) | 4.51415 | 0.145998 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 28.5983 | 0.923969 | ||||||||
\(959\) | −7.38660 | −0.238526 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.5537 | −0.792053 | ||||||||
\(962\) | −120.045 | −3.87042 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −16.3152 | −0.525476 | ||||||||
\(965\) | 2.79450 | 0.0899582 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.4688 | 0.786865 | 0.393432 | − | 0.919354i | \(-0.371288\pi\) | ||||
0.393432 | + | 0.919354i | \(0.371288\pi\) | |||||||
\(968\) | −5.64361 | −0.181393 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11.8272 | −0.379749 | ||||||||
\(971\) | 20.7426 | 0.665662 | 0.332831 | − | 0.942987i | \(-0.391996\pi\) | ||||
0.332831 | + | 0.942987i | \(0.391996\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.7075 | 0.503559 | ||||||||
\(974\) | 15.1640 | 0.485887 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.88486 | −0.124351 | ||||||||
\(977\) | 4.62330 | 0.147912 | 0.0739562 | − | 0.997261i | \(-0.476438\pi\) | ||||
0.0739562 | + | 0.997261i | \(0.476438\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.4101 | 0.652311 | ||||||||
\(980\) | −3.73439 | −0.119291 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 39.1174 | 1.24829 | ||||||||
\(983\) | 43.9207 | 1.40085 | 0.700427 | − | 0.713725i | \(-0.252993\pi\) | ||||
0.700427 | + | 0.713725i | \(0.252993\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.12126 | 0.131314 | ||||||||
\(986\) | −52.6355 | −1.67626 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −57.7158 | −1.83619 | ||||||||
\(989\) | −4.11156 | −0.130740 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.0775 | 0.955442 | 0.477721 | − | 0.878511i | \(-0.341463\pi\) | ||||
0.477721 | + | 0.878511i | \(0.341463\pi\) | |||||||
\(992\) | −16.3887 | −0.520342 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 16.7167 | 0.530221 | ||||||||
\(995\) | 7.29545 | 0.231281 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.4260 | −0.805250 | −0.402625 | − | 0.915365i | \(-0.631902\pi\) | ||||
−0.402625 | + | 0.915365i | \(0.631902\pi\) | |||||||
\(998\) | 16.1568 | 0.511436 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3483.2.a.u.1.4 | 20 | ||
3.2 | odd | 2 | 3483.2.a.t.1.17 | 20 | |||
9.2 | odd | 6 | 387.2.f.d.130.4 | ✓ | 40 | ||
9.4 | even | 3 | 1161.2.f.d.775.17 | 40 | |||
9.5 | odd | 6 | 387.2.f.d.259.4 | yes | 40 | ||
9.7 | even | 3 | 1161.2.f.d.388.17 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
387.2.f.d.130.4 | ✓ | 40 | 9.2 | odd | 6 | ||
387.2.f.d.259.4 | yes | 40 | 9.5 | odd | 6 | ||
1161.2.f.d.388.17 | 40 | 9.7 | even | 3 | |||
1161.2.f.d.775.17 | 40 | 9.4 | even | 3 | |||
3483.2.a.t.1.17 | 20 | 3.2 | odd | 2 | |||
3483.2.a.u.1.4 | 20 | 1.1 | even | 1 | trivial |