Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8042,2,Mod(1,8042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8042, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8042 = 2 \cdot 4021 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8042.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: | \(64.2156933055\) |
Analytic rank: | \(0\) |
Dimension: | \(86\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 8042.1 |
$q$-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 | ||||||||
\(3\) | −2.78277 | −1.60663 | −0.803316 | − | 0.595553i | \(-0.796933\pi\) | ||||
−0.803316 | + | 0.595553i | \(0.796933\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −4.36753 | −1.95322 | −0.976609 | − | 0.215024i | \(-0.931017\pi\) | ||||
−0.976609 | + | 0.215024i | \(0.931017\pi\) | |||||||
\(6\) | 2.78277 | 1.13606 | ||||||||
\(7\) | −3.26500 | −1.23405 | −0.617026 | − | 0.786942i | \(-0.711663\pi\) | ||||
−0.617026 | + | 0.786942i | \(0.711663\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 4.74379 | 1.58126 | ||||||||
\(10\) | 4.36753 | 1.38113 | ||||||||
\(11\) | −3.11755 | −0.939976 | −0.469988 | − | 0.882673i | \(-0.655742\pi\) | ||||
−0.469988 | + | 0.882673i | \(0.655742\pi\) | |||||||
\(12\) | −2.78277 | −0.803316 | ||||||||
\(13\) | 2.74460 | 0.761215 | 0.380607 | − | 0.924737i | \(-0.375715\pi\) | ||||
0.380607 | + | 0.924737i | \(0.375715\pi\) | |||||||
\(14\) | 3.26500 | 0.872607 | ||||||||
\(15\) | 12.1538 | 3.13810 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.733217 | −0.177831 | −0.0889156 | − | 0.996039i | \(-0.528340\pi\) | ||||
−0.0889156 | + | 0.996039i | \(0.528340\pi\) | |||||||
\(18\) | −4.74379 | −1.11812 | ||||||||
\(19\) | 3.29698 | 0.756380 | 0.378190 | − | 0.925728i | \(-0.376547\pi\) | ||||
0.378190 | + | 0.925728i | \(0.376547\pi\) | |||||||
\(20\) | −4.36753 | −0.976609 | ||||||||
\(21\) | 9.08573 | 1.98267 | ||||||||
\(22\) | 3.11755 | 0.664664 | ||||||||
\(23\) | −3.92947 | −0.819352 | −0.409676 | − | 0.912231i | \(-0.634358\pi\) | ||||
−0.409676 | + | 0.912231i | \(0.634358\pi\) | |||||||
\(24\) | 2.78277 | 0.568030 | ||||||||
\(25\) | 14.0753 | 2.81506 | ||||||||
\(26\) | −2.74460 | −0.538260 | ||||||||
\(27\) | −4.85257 | −0.933878 | ||||||||
\(28\) | −3.26500 | −0.617026 | ||||||||
\(29\) | −0.134478 | −0.0249720 | −0.0124860 | − | 0.999922i | \(-0.503975\pi\) | ||||
−0.0124860 | + | 0.999922i | \(0.503975\pi\) | |||||||
\(30\) | −12.1538 | −2.21897 | ||||||||
\(31\) | −0.0430877 | −0.00773878 | −0.00386939 | − | 0.999993i | \(-0.501232\pi\) | ||||
−0.00386939 | + | 0.999993i | \(0.501232\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 8.67541 | 1.51020 | ||||||||
\(34\) | 0.733217 | 0.125746 | ||||||||
\(35\) | 14.2600 | 2.41037 | ||||||||
\(36\) | 4.74379 | 0.790632 | ||||||||
\(37\) | 5.10334 | 0.838983 | 0.419492 | − | 0.907759i | \(-0.362208\pi\) | ||||
0.419492 | + | 0.907759i | \(0.362208\pi\) | |||||||
\(38\) | −3.29698 | −0.534841 | ||||||||
\(39\) | −7.63758 | −1.22299 | ||||||||
\(40\) | 4.36753 | 0.690567 | ||||||||
\(41\) | −7.00654 | −1.09424 | −0.547119 | − | 0.837055i | \(-0.684275\pi\) | ||||
−0.547119 | + | 0.837055i | \(0.684275\pi\) | |||||||
\(42\) | −9.08573 | −1.40196 | ||||||||
\(43\) | 6.34974 | 0.968326 | 0.484163 | − | 0.874978i | \(-0.339124\pi\) | ||||
0.484163 | + | 0.874978i | \(0.339124\pi\) | |||||||
\(44\) | −3.11755 | −0.469988 | ||||||||
\(45\) | −20.7187 | −3.08855 | ||||||||
\(46\) | 3.92947 | 0.579369 | ||||||||
\(47\) | 3.45793 | 0.504392 | 0.252196 | − | 0.967676i | \(-0.418847\pi\) | ||||
0.252196 | + | 0.967676i | \(0.418847\pi\) | |||||||
\(48\) | −2.78277 | −0.401658 | ||||||||
\(49\) | 3.66020 | 0.522886 | ||||||||
\(50\) | −14.0753 | −1.99055 | ||||||||
\(51\) | 2.04037 | 0.285709 | ||||||||
\(52\) | 2.74460 | 0.380607 | ||||||||
\(53\) | −9.77167 | −1.34224 | −0.671121 | − | 0.741348i | \(-0.734187\pi\) | ||||
−0.671121 | + | 0.741348i | \(0.734187\pi\) | |||||||
\(54\) | 4.85257 | 0.660352 | ||||||||
\(55\) | 13.6160 | 1.83598 | ||||||||
\(56\) | 3.26500 | 0.436304 | ||||||||
\(57\) | −9.17474 | −1.21522 | ||||||||
\(58\) | 0.134478 | 0.0176579 | ||||||||
\(59\) | −0.605095 | −0.0787767 | −0.0393883 | − | 0.999224i | \(-0.512541\pi\) | ||||
−0.0393883 | + | 0.999224i | \(0.512541\pi\) | |||||||
\(60\) | 12.1538 | 1.56905 | ||||||||
\(61\) | −9.60040 | −1.22921 | −0.614603 | − | 0.788837i | \(-0.710684\pi\) | ||||
−0.614603 | + | 0.788837i | \(0.710684\pi\) | |||||||
\(62\) | 0.0430877 | 0.00547214 | ||||||||
\(63\) | −15.4885 | −1.95136 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −11.9871 | −1.48682 | ||||||||
\(66\) | −8.67541 | −1.06787 | ||||||||
\(67\) | 2.80505 | 0.342692 | 0.171346 | − | 0.985211i | \(-0.445188\pi\) | ||||
0.171346 | + | 0.985211i | \(0.445188\pi\) | |||||||
\(68\) | −0.733217 | −0.0889156 | ||||||||
\(69\) | 10.9348 | 1.31640 | ||||||||
\(70\) | −14.2600 | −1.70439 | ||||||||
\(71\) | −1.07101 | −0.127106 | −0.0635529 | − | 0.997978i | \(-0.520243\pi\) | ||||
−0.0635529 | + | 0.997978i | \(0.520243\pi\) | |||||||
\(72\) | −4.74379 | −0.559062 | ||||||||
\(73\) | 10.9618 | 1.28299 | 0.641493 | − | 0.767129i | \(-0.278315\pi\) | ||||
0.641493 | + | 0.767129i | \(0.278315\pi\) | |||||||
\(74\) | −5.10334 | −0.593251 | ||||||||
\(75\) | −39.1683 | −4.52276 | ||||||||
\(76\) | 3.29698 | 0.378190 | ||||||||
\(77\) | 10.1788 | 1.15998 | ||||||||
\(78\) | 7.63758 | 0.864786 | ||||||||
\(79\) | −4.01696 | −0.451943 | −0.225971 | − | 0.974134i | \(-0.572556\pi\) | ||||
−0.225971 | + | 0.974134i | \(0.572556\pi\) | |||||||
\(80\) | −4.36753 | −0.488304 | ||||||||
\(81\) | −0.727798 | −0.0808665 | ||||||||
\(82\) | 7.00654 | 0.773743 | ||||||||
\(83\) | 3.72621 | 0.409004 | 0.204502 | − | 0.978866i | \(-0.434442\pi\) | ||||
0.204502 | + | 0.978866i | \(0.434442\pi\) | |||||||
\(84\) | 9.08573 | 0.991334 | ||||||||
\(85\) | 3.20234 | 0.347343 | ||||||||
\(86\) | −6.34974 | −0.684710 | ||||||||
\(87\) | 0.374222 | 0.0401208 | ||||||||
\(88\) | 3.11755 | 0.332332 | ||||||||
\(89\) | −3.02088 | −0.320212 | −0.160106 | − | 0.987100i | \(-0.551184\pi\) | ||||
−0.160106 | + | 0.987100i | \(0.551184\pi\) | |||||||
\(90\) | 20.7187 | 2.18394 | ||||||||
\(91\) | −8.96111 | −0.939379 | ||||||||
\(92\) | −3.92947 | −0.409676 | ||||||||
\(93\) | 0.119903 | 0.0124334 | ||||||||
\(94\) | −3.45793 | −0.356659 | ||||||||
\(95\) | −14.3997 | −1.47737 | ||||||||
\(96\) | 2.78277 | 0.284015 | ||||||||
\(97\) | −15.4949 | −1.57327 | −0.786633 | − | 0.617421i | \(-0.788177\pi\) | ||||
−0.786633 | + | 0.617421i | \(0.788177\pi\) | |||||||
\(98\) | −3.66020 | −0.369736 | ||||||||
\(99\) | −14.7890 | −1.48635 | ||||||||
\(100\) | 14.0753 | 1.40753 | ||||||||
\(101\) | −15.2192 | −1.51436 | −0.757181 | − | 0.653205i | \(-0.773424\pi\) | ||||
−0.757181 | + | 0.653205i | \(0.773424\pi\) | |||||||
\(102\) | −2.04037 | −0.202027 | ||||||||
\(103\) | 4.49261 | 0.442670 | 0.221335 | − | 0.975198i | \(-0.428959\pi\) | ||||
0.221335 | + | 0.975198i | \(0.428959\pi\) | |||||||
\(104\) | −2.74460 | −0.269130 | ||||||||
\(105\) | −39.6822 | −3.87258 | ||||||||
\(106\) | 9.77167 | 0.949108 | ||||||||
\(107\) | 15.0718 | 1.45704 | 0.728522 | − | 0.685022i | \(-0.240207\pi\) | ||||
0.728522 | + | 0.685022i | \(0.240207\pi\) | |||||||
\(108\) | −4.85257 | −0.466939 | ||||||||
\(109\) | −10.3524 | −0.991580 | −0.495790 | − | 0.868442i | \(-0.665121\pi\) | ||||
−0.495790 | + | 0.868442i | \(0.665121\pi\) | |||||||
\(110\) | −13.6160 | −1.29823 | ||||||||
\(111\) | −14.2014 | −1.34794 | ||||||||
\(112\) | −3.26500 | −0.308513 | ||||||||
\(113\) | −8.10425 | −0.762384 | −0.381192 | − | 0.924496i | \(-0.624486\pi\) | ||||
−0.381192 | + | 0.924496i | \(0.624486\pi\) | |||||||
\(114\) | 9.17474 | 0.859293 | ||||||||
\(115\) | 17.1621 | 1.60037 | ||||||||
\(116\) | −0.134478 | −0.0124860 | ||||||||
\(117\) | 13.0198 | 1.20368 | ||||||||
\(118\) | 0.605095 | 0.0557035 | ||||||||
\(119\) | 2.39395 | 0.219453 | ||||||||
\(120\) | −12.1538 | −1.10949 | ||||||||
\(121\) | −1.28089 | −0.116444 | ||||||||
\(122\) | 9.60040 | 0.869180 | ||||||||
\(123\) | 19.4976 | 1.75804 | ||||||||
\(124\) | −0.0430877 | −0.00386939 | ||||||||
\(125\) | −39.6366 | −3.54521 | ||||||||
\(126\) | 15.4885 | 1.37982 | ||||||||
\(127\) | 5.29846 | 0.470162 | 0.235081 | − | 0.971976i | \(-0.424464\pi\) | ||||
0.235081 | + | 0.971976i | \(0.424464\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −17.6699 | −1.55574 | ||||||||
\(130\) | 11.9871 | 1.05134 | ||||||||
\(131\) | −1.68600 | −0.147307 | −0.0736533 | − | 0.997284i | \(-0.523466\pi\) | ||||
−0.0736533 | + | 0.997284i | \(0.523466\pi\) | |||||||
\(132\) | 8.67541 | 0.755098 | ||||||||
\(133\) | −10.7646 | −0.933413 | ||||||||
\(134\) | −2.80505 | −0.242320 | ||||||||
\(135\) | 21.1938 | 1.82407 | ||||||||
\(136\) | 0.733217 | 0.0628728 | ||||||||
\(137\) | −4.54990 | −0.388724 | −0.194362 | − | 0.980930i | \(-0.562264\pi\) | ||||
−0.194362 | + | 0.980930i | \(0.562264\pi\) | |||||||
\(138\) | −10.9348 | −0.930833 | ||||||||
\(139\) | −3.78163 | −0.320753 | −0.160377 | − | 0.987056i | \(-0.551271\pi\) | ||||
−0.160377 | + | 0.987056i | \(0.551271\pi\) | |||||||
\(140\) | 14.2600 | 1.20519 | ||||||||
\(141\) | −9.62263 | −0.810371 | ||||||||
\(142\) | 1.07101 | 0.0898774 | ||||||||
\(143\) | −8.55642 | −0.715524 | ||||||||
\(144\) | 4.74379 | 0.395316 | ||||||||
\(145\) | 0.587338 | 0.0487757 | ||||||||
\(146\) | −10.9618 | −0.907208 | ||||||||
\(147\) | −10.1855 | −0.840085 | ||||||||
\(148\) | 5.10334 | 0.419492 | ||||||||
\(149\) | −3.03435 | −0.248583 | −0.124292 | − | 0.992246i | \(-0.539666\pi\) | ||||
−0.124292 | + | 0.992246i | \(0.539666\pi\) | |||||||
\(150\) | 39.1683 | 3.19808 | ||||||||
\(151\) | −11.0635 | −0.900338 | −0.450169 | − | 0.892943i | \(-0.648636\pi\) | ||||
−0.450169 | + | 0.892943i | \(0.648636\pi\) | |||||||
\(152\) | −3.29698 | −0.267421 | ||||||||
\(153\) | −3.47823 | −0.281198 | ||||||||
\(154\) | −10.1788 | −0.820230 | ||||||||
\(155\) | 0.188187 | 0.0151155 | ||||||||
\(156\) | −7.63758 | −0.611496 | ||||||||
\(157\) | −11.2183 | −0.895320 | −0.447660 | − | 0.894204i | \(-0.647743\pi\) | ||||
−0.447660 | + | 0.894204i | \(0.647743\pi\) | |||||||
\(158\) | 4.01696 | 0.319572 | ||||||||
\(159\) | 27.1923 | 2.15649 | ||||||||
\(160\) | 4.36753 | 0.345283 | ||||||||
\(161\) | 12.8297 | 1.01112 | ||||||||
\(162\) | 0.727798 | 0.0571812 | ||||||||
\(163\) | 17.9514 | 1.40606 | 0.703029 | − | 0.711161i | \(-0.251830\pi\) | ||||
0.703029 | + | 0.711161i | \(0.251830\pi\) | |||||||
\(164\) | −7.00654 | −0.547119 | ||||||||
\(165\) | −37.8901 | −2.94974 | ||||||||
\(166\) | −3.72621 | −0.289210 | ||||||||
\(167\) | 17.7999 | 1.37739 | 0.688697 | − | 0.725049i | \(-0.258183\pi\) | ||||
0.688697 | + | 0.725049i | \(0.258183\pi\) | |||||||
\(168\) | −9.08573 | −0.700979 | ||||||||
\(169\) | −5.46717 | −0.420552 | ||||||||
\(170\) | −3.20234 | −0.245609 | ||||||||
\(171\) | 15.6402 | 1.19604 | ||||||||
\(172\) | 6.34974 | 0.484163 | ||||||||
\(173\) | 3.92053 | 0.298072 | 0.149036 | − | 0.988832i | \(-0.452383\pi\) | ||||
0.149036 | + | 0.988832i | \(0.452383\pi\) | |||||||
\(174\) | −0.374222 | −0.0283697 | ||||||||
\(175\) | −45.9558 | −3.47393 | ||||||||
\(176\) | −3.11755 | −0.234994 | ||||||||
\(177\) | 1.68384 | 0.126565 | ||||||||
\(178\) | 3.02088 | 0.226424 | ||||||||
\(179\) | 2.73828 | 0.204668 | 0.102334 | − | 0.994750i | \(-0.467369\pi\) | ||||
0.102334 | + | 0.994750i | \(0.467369\pi\) | |||||||
\(180\) | −20.7187 | −1.54428 | ||||||||
\(181\) | 7.17351 | 0.533203 | 0.266601 | − | 0.963807i | \(-0.414099\pi\) | ||||
0.266601 | + | 0.963807i | \(0.414099\pi\) | |||||||
\(182\) | 8.96111 | 0.664242 | ||||||||
\(183\) | 26.7157 | 1.97488 | ||||||||
\(184\) | 3.92947 | 0.289685 | ||||||||
\(185\) | −22.2890 | −1.63872 | ||||||||
\(186\) | −0.119903 | −0.00879172 | ||||||||
\(187\) | 2.28584 | 0.167157 | ||||||||
\(188\) | 3.45793 | 0.252196 | ||||||||
\(189\) | 15.8436 | 1.15246 | ||||||||
\(190\) | 14.3997 | 1.04466 | ||||||||
\(191\) | −17.7616 | −1.28519 | −0.642593 | − | 0.766208i | \(-0.722141\pi\) | ||||
−0.642593 | + | 0.766208i | \(0.722141\pi\) | |||||||
\(192\) | −2.78277 | −0.200829 | ||||||||
\(193\) | −12.3999 | −0.892568 | −0.446284 | − | 0.894891i | \(-0.647253\pi\) | ||||
−0.446284 | + | 0.894891i | \(0.647253\pi\) | |||||||
\(194\) | 15.4949 | 1.11247 | ||||||||
\(195\) | 33.3573 | 2.38877 | ||||||||
\(196\) | 3.66020 | 0.261443 | ||||||||
\(197\) | −7.82326 | −0.557384 | −0.278692 | − | 0.960380i | \(-0.589901\pi\) | ||||
−0.278692 | + | 0.960380i | \(0.589901\pi\) | |||||||
\(198\) | 14.7890 | 1.05101 | ||||||||
\(199\) | −7.84733 | −0.556283 | −0.278141 | − | 0.960540i | \(-0.589718\pi\) | ||||
−0.278141 | + | 0.960540i | \(0.589718\pi\) | |||||||
\(200\) | −14.0753 | −0.995274 | ||||||||
\(201\) | −7.80581 | −0.550579 | ||||||||
\(202\) | 15.2192 | 1.07082 | ||||||||
\(203\) | 0.439071 | 0.0308168 | ||||||||
\(204\) | 2.04037 | 0.142855 | ||||||||
\(205\) | 30.6013 | 2.13729 | ||||||||
\(206\) | −4.49261 | −0.313015 | ||||||||
\(207\) | −18.6406 | −1.29561 | ||||||||
\(208\) | 2.74460 | 0.190304 | ||||||||
\(209\) | −10.2785 | −0.710979 | ||||||||
\(210\) | 39.6822 | 2.73833 | ||||||||
\(211\) | −17.0065 | −1.17078 | −0.585388 | − | 0.810753i | \(-0.699058\pi\) | ||||
−0.585388 | + | 0.810753i | \(0.699058\pi\) | |||||||
\(212\) | −9.77167 | −0.671121 | ||||||||
\(213\) | 2.98038 | 0.204212 | ||||||||
\(214\) | −15.0718 | −1.03029 | ||||||||
\(215\) | −27.7327 | −1.89135 | ||||||||
\(216\) | 4.85257 | 0.330176 | ||||||||
\(217\) | 0.140681 | 0.00955006 | ||||||||
\(218\) | 10.3524 | 0.701153 | ||||||||
\(219\) | −30.5042 | −2.06128 | ||||||||
\(220\) | 13.6160 | 0.917989 | ||||||||
\(221\) | −2.01239 | −0.135368 | ||||||||
\(222\) | 14.2014 | 0.953135 | ||||||||
\(223\) | −8.08309 | −0.541283 | −0.270642 | − | 0.962680i | \(-0.587236\pi\) | ||||
−0.270642 | + | 0.962680i | \(0.587236\pi\) | |||||||
\(224\) | 3.26500 | 0.218152 | ||||||||
\(225\) | 66.7703 | 4.45135 | ||||||||
\(226\) | 8.10425 | 0.539087 | ||||||||
\(227\) | −11.9799 | −0.795133 | −0.397566 | − | 0.917573i | \(-0.630145\pi\) | ||||
−0.397566 | + | 0.917573i | \(0.630145\pi\) | |||||||
\(228\) | −9.17474 | −0.607612 | ||||||||
\(229\) | 3.60531 | 0.238246 | 0.119123 | − | 0.992880i | \(-0.461992\pi\) | ||||
0.119123 | + | 0.992880i | \(0.461992\pi\) | |||||||
\(230\) | −17.1621 | −1.13163 | ||||||||
\(231\) | −28.3252 | −1.86366 | ||||||||
\(232\) | 0.134478 | 0.00882893 | ||||||||
\(233\) | −15.7848 | −1.03409 | −0.517047 | − | 0.855957i | \(-0.672969\pi\) | ||||
−0.517047 | + | 0.855957i | \(0.672969\pi\) | |||||||
\(234\) | −13.0198 | −0.851132 | ||||||||
\(235\) | −15.1026 | −0.985186 | ||||||||
\(236\) | −0.605095 | −0.0393883 | ||||||||
\(237\) | 11.1783 | 0.726106 | ||||||||
\(238\) | −2.39395 | −0.155177 | ||||||||
\(239\) | 23.8660 | 1.54376 | 0.771881 | − | 0.635767i | \(-0.219316\pi\) | ||||
0.771881 | + | 0.635767i | \(0.219316\pi\) | |||||||
\(240\) | 12.1538 | 0.784525 | ||||||||
\(241\) | −10.1267 | −0.652321 | −0.326160 | − | 0.945314i | \(-0.605755\pi\) | ||||
−0.326160 | + | 0.945314i | \(0.605755\pi\) | |||||||
\(242\) | 1.28089 | 0.0823385 | ||||||||
\(243\) | 16.5830 | 1.06380 | ||||||||
\(244\) | −9.60040 | −0.614603 | ||||||||
\(245\) | −15.9860 | −1.02131 | ||||||||
\(246\) | −19.4976 | −1.24312 | ||||||||
\(247\) | 9.04890 | 0.575768 | ||||||||
\(248\) | 0.0430877 | 0.00273607 | ||||||||
\(249\) | −10.3692 | −0.657119 | ||||||||
\(250\) | 39.6366 | 2.50684 | ||||||||
\(251\) | 14.6540 | 0.924955 | 0.462478 | − | 0.886631i | \(-0.346961\pi\) | ||||
0.462478 | + | 0.886631i | \(0.346961\pi\) | |||||||
\(252\) | −15.4885 | −0.975682 | ||||||||
\(253\) | 12.2503 | 0.770172 | ||||||||
\(254\) | −5.29846 | −0.332455 | ||||||||
\(255\) | −8.91138 | −0.558052 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 17.8500 | 1.11345 | 0.556727 | − | 0.830696i | \(-0.312057\pi\) | ||||
0.556727 | + | 0.830696i | \(0.312057\pi\) | |||||||
\(258\) | 17.6699 | 1.10008 | ||||||||
\(259\) | −16.6624 | −1.03535 | ||||||||
\(260\) | −11.9871 | −0.743409 | ||||||||
\(261\) | −0.637938 | −0.0394873 | ||||||||
\(262\) | 1.68600 | 0.104161 | ||||||||
\(263\) | 12.8351 | 0.791448 | 0.395724 | − | 0.918369i | \(-0.370494\pi\) | ||||
0.395724 | + | 0.918369i | \(0.370494\pi\) | |||||||
\(264\) | −8.67541 | −0.533935 | ||||||||
\(265\) | 42.6780 | 2.62169 | ||||||||
\(266\) | 10.7646 | 0.660022 | ||||||||
\(267\) | 8.40640 | 0.514463 | ||||||||
\(268\) | 2.80505 | 0.171346 | ||||||||
\(269\) | 3.38381 | 0.206315 | 0.103157 | − | 0.994665i | \(-0.467105\pi\) | ||||
0.103157 | + | 0.994665i | \(0.467105\pi\) | |||||||
\(270\) | −21.1938 | −1.28981 | ||||||||
\(271\) | −28.7294 | −1.74519 | −0.872594 | − | 0.488447i | \(-0.837564\pi\) | ||||
−0.872594 | + | 0.488447i | \(0.837564\pi\) | |||||||
\(272\) | −0.733217 | −0.0444578 | ||||||||
\(273\) | 24.9367 | 1.50924 | ||||||||
\(274\) | 4.54990 | 0.274870 | ||||||||
\(275\) | −43.8804 | −2.64609 | ||||||||
\(276\) | 10.9348 | 0.658198 | ||||||||
\(277\) | 31.1705 | 1.87285 | 0.936426 | − | 0.350865i | \(-0.114112\pi\) | ||||
0.936426 | + | 0.350865i | \(0.114112\pi\) | |||||||
\(278\) | 3.78163 | 0.226807 | ||||||||
\(279\) | −0.204399 | −0.0122371 | ||||||||
\(280\) | −14.2600 | −0.852196 | ||||||||
\(281\) | 10.2220 | 0.609796 | 0.304898 | − | 0.952385i | \(-0.401378\pi\) | ||||
0.304898 | + | 0.952385i | \(0.401378\pi\) | |||||||
\(282\) | 9.62263 | 0.573019 | ||||||||
\(283\) | −15.6991 | −0.933214 | −0.466607 | − | 0.884465i | \(-0.654524\pi\) | ||||
−0.466607 | + | 0.884465i | \(0.654524\pi\) | |||||||
\(284\) | −1.07101 | −0.0635529 | ||||||||
\(285\) | 40.0709 | 2.37360 | ||||||||
\(286\) | 8.55642 | 0.505952 | ||||||||
\(287\) | 22.8763 | 1.35035 | ||||||||
\(288\) | −4.74379 | −0.279531 | ||||||||
\(289\) | −16.4624 | −0.968376 | ||||||||
\(290\) | −0.587338 | −0.0344897 | ||||||||
\(291\) | 43.1186 | 2.52766 | ||||||||
\(292\) | 10.9618 | 0.641493 | ||||||||
\(293\) | −12.3158 | −0.719495 | −0.359748 | − | 0.933050i | \(-0.617137\pi\) | ||||
−0.359748 | + | 0.933050i | \(0.617137\pi\) | |||||||
\(294\) | 10.1855 | 0.594030 | ||||||||
\(295\) | 2.64277 | 0.153868 | ||||||||
\(296\) | −5.10334 | −0.296625 | ||||||||
\(297\) | 15.1281 | 0.877824 | ||||||||
\(298\) | 3.03435 | 0.175775 | ||||||||
\(299\) | −10.7848 | −0.623703 | ||||||||
\(300\) | −39.1683 | −2.26138 | ||||||||
\(301\) | −20.7319 | −1.19497 | ||||||||
\(302\) | 11.0635 | 0.636635 | ||||||||
\(303\) | 42.3514 | 2.43302 | ||||||||
\(304\) | 3.29698 | 0.189095 | ||||||||
\(305\) | 41.9300 | 2.40091 | ||||||||
\(306\) | 3.47823 | 0.198837 | ||||||||
\(307\) | −1.13457 | −0.0647535 | −0.0323767 | − | 0.999476i | \(-0.510308\pi\) | ||||
−0.0323767 | + | 0.999476i | \(0.510308\pi\) | |||||||
\(308\) | 10.1788 | 0.579990 | ||||||||
\(309\) | −12.5019 | −0.711208 | ||||||||
\(310\) | −0.188187 | −0.0106883 | ||||||||
\(311\) | −17.2736 | −0.979494 | −0.489747 | − | 0.871865i | \(-0.662911\pi\) | ||||
−0.489747 | + | 0.871865i | \(0.662911\pi\) | |||||||
\(312\) | 7.63758 | 0.432393 | ||||||||
\(313\) | −11.3761 | −0.643015 | −0.321507 | − | 0.946907i | \(-0.604189\pi\) | ||||
−0.321507 | + | 0.946907i | \(0.604189\pi\) | |||||||
\(314\) | 11.2183 | 0.633087 | ||||||||
\(315\) | 67.6463 | 3.81144 | ||||||||
\(316\) | −4.01696 | −0.225971 | ||||||||
\(317\) | 1.16065 | 0.0651884 | 0.0325942 | − | 0.999469i | \(-0.489623\pi\) | ||||
0.0325942 | + | 0.999469i | \(0.489623\pi\) | |||||||
\(318\) | −27.1923 | −1.52487 | ||||||||
\(319\) | 0.419243 | 0.0234731 | ||||||||
\(320\) | −4.36753 | −0.244152 | ||||||||
\(321\) | −41.9413 | −2.34093 | ||||||||
\(322\) | −12.8297 | −0.714972 | ||||||||
\(323\) | −2.41740 | −0.134508 | ||||||||
\(324\) | −0.727798 | −0.0404332 | ||||||||
\(325\) | 38.6311 | 2.14287 | ||||||||
\(326\) | −17.9514 | −0.994234 | ||||||||
\(327\) | 28.8083 | 1.59310 | ||||||||
\(328\) | 7.00654 | 0.386872 | ||||||||
\(329\) | −11.2901 | −0.622446 | ||||||||
\(330\) | 37.8901 | 2.08578 | ||||||||
\(331\) | 18.7672 | 1.03154 | 0.515769 | − | 0.856728i | \(-0.327506\pi\) | ||||
0.515769 | + | 0.856728i | \(0.327506\pi\) | |||||||
\(332\) | 3.72621 | 0.204502 | ||||||||
\(333\) | 24.2092 | 1.32665 | ||||||||
\(334\) | −17.7999 | −0.973965 | ||||||||
\(335\) | −12.2511 | −0.669351 | ||||||||
\(336\) | 9.08573 | 0.495667 | ||||||||
\(337\) | −18.2617 | −0.994781 | −0.497390 | − | 0.867527i | \(-0.665708\pi\) | ||||
−0.497390 | + | 0.867527i | \(0.665708\pi\) | |||||||
\(338\) | 5.46717 | 0.297375 | ||||||||
\(339\) | 22.5522 | 1.22487 | ||||||||
\(340\) | 3.20234 | 0.173671 | ||||||||
\(341\) | 0.134328 | 0.00727427 | ||||||||
\(342\) | −15.6402 | −0.845726 | ||||||||
\(343\) | 10.9044 | 0.588784 | ||||||||
\(344\) | −6.34974 | −0.342355 | ||||||||
\(345\) | −47.7581 | −2.57121 | ||||||||
\(346\) | −3.92053 | −0.210769 | ||||||||
\(347\) | −0.263336 | −0.0141366 | −0.00706831 | − | 0.999975i | \(-0.502250\pi\) | ||||
−0.00706831 | + | 0.999975i | \(0.502250\pi\) | |||||||
\(348\) | 0.374222 | 0.0200604 | ||||||||
\(349\) | 1.19989 | 0.0642287 | 0.0321144 | − | 0.999484i | \(-0.489776\pi\) | ||||
0.0321144 | + | 0.999484i | \(0.489776\pi\) | |||||||
\(350\) | 45.9558 | 2.45644 | ||||||||
\(351\) | −13.3184 | −0.710882 | ||||||||
\(352\) | 3.11755 | 0.166166 | ||||||||
\(353\) | 5.56876 | 0.296395 | 0.148198 | − | 0.988958i | \(-0.452653\pi\) | ||||
0.148198 | + | 0.988958i | \(0.452653\pi\) | |||||||
\(354\) | −1.68384 | −0.0894951 | ||||||||
\(355\) | 4.67768 | 0.248265 | ||||||||
\(356\) | −3.02088 | −0.160106 | ||||||||
\(357\) | −6.66180 | −0.352580 | ||||||||
\(358\) | −2.73828 | −0.144722 | ||||||||
\(359\) | 8.04904 | 0.424812 | 0.212406 | − | 0.977182i | \(-0.431870\pi\) | ||||
0.212406 | + | 0.977182i | \(0.431870\pi\) | |||||||
\(360\) | 20.7187 | 1.09197 | ||||||||
\(361\) | −8.12990 | −0.427890 | ||||||||
\(362\) | −7.17351 | −0.377031 | ||||||||
\(363\) | 3.56441 | 0.187083 | ||||||||
\(364\) | −8.96111 | −0.469690 | ||||||||
\(365\) | −47.8761 | −2.50595 | ||||||||
\(366\) | −26.7157 | −1.39645 | ||||||||
\(367\) | −22.6472 | −1.18218 | −0.591088 | − | 0.806607i | \(-0.701301\pi\) | ||||
−0.591088 | + | 0.806607i | \(0.701301\pi\) | |||||||
\(368\) | −3.92947 | −0.204838 | ||||||||
\(369\) | −33.2376 | −1.73028 | ||||||||
\(370\) | 22.2890 | 1.15875 | ||||||||
\(371\) | 31.9045 | 1.65640 | ||||||||
\(372\) | 0.119903 | 0.00621668 | ||||||||
\(373\) | −17.7569 | −0.919415 | −0.459708 | − | 0.888070i | \(-0.652046\pi\) | ||||
−0.459708 | + | 0.888070i | \(0.652046\pi\) | |||||||
\(374\) | −2.28584 | −0.118198 | ||||||||
\(375\) | 110.299 | 5.69584 | ||||||||
\(376\) | −3.45793 | −0.178329 | ||||||||
\(377\) | −0.369089 | −0.0190091 | ||||||||
\(378\) | −15.8436 | −0.814909 | ||||||||
\(379\) | 37.0912 | 1.90525 | 0.952623 | − | 0.304154i | \(-0.0983737\pi\) | ||||
0.952623 | + | 0.304154i | \(0.0983737\pi\) | |||||||
\(380\) | −14.3997 | −0.738687 | ||||||||
\(381\) | −14.7444 | −0.755377 | ||||||||
\(382\) | 17.7616 | 0.908763 | ||||||||
\(383\) | −6.53919 | −0.334137 | −0.167069 | − | 0.985945i | \(-0.553430\pi\) | ||||
−0.167069 | + | 0.985945i | \(0.553430\pi\) | |||||||
\(384\) | 2.78277 | 0.142008 | ||||||||
\(385\) | −44.4561 | −2.26569 | ||||||||
\(386\) | 12.3999 | 0.631141 | ||||||||
\(387\) | 30.1219 | 1.53118 | ||||||||
\(388\) | −15.4949 | −0.786633 | ||||||||
\(389\) | 2.35711 | 0.119510 | 0.0597552 | − | 0.998213i | \(-0.480968\pi\) | ||||
0.0597552 | + | 0.998213i | \(0.480968\pi\) | |||||||
\(390\) | −33.3573 | −1.68911 | ||||||||
\(391\) | 2.88116 | 0.145706 | ||||||||
\(392\) | −3.66020 | −0.184868 | ||||||||
\(393\) | 4.69175 | 0.236667 | ||||||||
\(394\) | 7.82326 | 0.394130 | ||||||||
\(395\) | 17.5442 | 0.882743 | ||||||||
\(396\) | −14.7890 | −0.743176 | ||||||||
\(397\) | −13.4473 | −0.674901 | −0.337450 | − | 0.941343i | \(-0.609564\pi\) | ||||
−0.337450 | + | 0.941343i | \(0.609564\pi\) | |||||||
\(398\) | 7.84733 | 0.393351 | ||||||||
\(399\) | 29.9555 | 1.49965 | ||||||||
\(400\) | 14.0753 | 0.703765 | ||||||||
\(401\) | 26.5582 | 1.32626 | 0.663128 | − | 0.748506i | \(-0.269229\pi\) | ||||
0.663128 | + | 0.748506i | \(0.269229\pi\) | |||||||
\(402\) | 7.80581 | 0.389318 | ||||||||
\(403\) | −0.118258 | −0.00589087 | ||||||||
\(404\) | −15.2192 | −0.757181 | ||||||||
\(405\) | 3.17868 | 0.157950 | ||||||||
\(406\) | −0.439071 | −0.0217907 | ||||||||
\(407\) | −15.9099 | −0.788625 | ||||||||
\(408\) | −2.04037 | −0.101013 | ||||||||
\(409\) | 20.6602 | 1.02158 | 0.510790 | − | 0.859706i | \(-0.329353\pi\) | ||||
0.510790 | + | 0.859706i | \(0.329353\pi\) | |||||||
\(410\) | −30.6013 | −1.51129 | ||||||||
\(411\) | 12.6613 | 0.624537 | ||||||||
\(412\) | 4.49261 | 0.221335 | ||||||||
\(413\) | 1.97563 | 0.0972146 | ||||||||
\(414\) | 18.6406 | 0.916136 | ||||||||
\(415\) | −16.2743 | −0.798875 | ||||||||
\(416\) | −2.74460 | −0.134565 | ||||||||
\(417\) | 10.5234 | 0.515333 | ||||||||
\(418\) | 10.2785 | 0.502738 | ||||||||
\(419\) | −26.8045 | −1.30949 | −0.654743 | − | 0.755851i | \(-0.727223\pi\) | ||||
−0.654743 | + | 0.755851i | \(0.727223\pi\) | |||||||
\(420\) | −39.6822 | −1.93629 | ||||||||
\(421\) | −6.85131 | −0.333912 | −0.166956 | − | 0.985964i | \(-0.553394\pi\) | ||||
−0.166956 | + | 0.985964i | \(0.553394\pi\) | |||||||
\(422\) | 17.0065 | 0.827864 | ||||||||
\(423\) | 16.4037 | 0.797577 | ||||||||
\(424\) | 9.77167 | 0.474554 | ||||||||
\(425\) | −10.3202 | −0.500605 | ||||||||
\(426\) | −2.98038 | −0.144400 | ||||||||
\(427\) | 31.3453 | 1.51690 | ||||||||
\(428\) | 15.0718 | 0.728522 | ||||||||
\(429\) | 23.8105 | 1.14958 | ||||||||
\(430\) | 27.7327 | 1.33739 | ||||||||
\(431\) | −5.53959 | −0.266832 | −0.133416 | − | 0.991060i | \(-0.542595\pi\) | ||||
−0.133416 | + | 0.991060i | \(0.542595\pi\) | |||||||
\(432\) | −4.85257 | −0.233470 | ||||||||
\(433\) | 5.11384 | 0.245755 | 0.122878 | − | 0.992422i | \(-0.460788\pi\) | ||||
0.122878 | + | 0.992422i | \(0.460788\pi\) | |||||||
\(434\) | −0.140681 | −0.00675291 | ||||||||
\(435\) | −1.63442 | −0.0783647 | ||||||||
\(436\) | −10.3524 | −0.495790 | ||||||||
\(437\) | −12.9554 | −0.619741 | ||||||||
\(438\) | 30.5042 | 1.45755 | ||||||||
\(439\) | 8.98166 | 0.428671 | 0.214336 | − | 0.976760i | \(-0.431241\pi\) | ||||
0.214336 | + | 0.976760i | \(0.431241\pi\) | |||||||
\(440\) | −13.6160 | −0.649116 | ||||||||
\(441\) | 17.3633 | 0.826822 | ||||||||
\(442\) | 2.01239 | 0.0957194 | ||||||||
\(443\) | 5.64420 | 0.268164 | 0.134082 | − | 0.990970i | \(-0.457191\pi\) | ||||
0.134082 | + | 0.990970i | \(0.457191\pi\) | |||||||
\(444\) | −14.2014 | −0.673969 | ||||||||
\(445\) | 13.1938 | 0.625445 | ||||||||
\(446\) | 8.08309 | 0.382745 | ||||||||
\(447\) | 8.44388 | 0.399382 | ||||||||
\(448\) | −3.26500 | −0.154257 | ||||||||
\(449\) | −23.5286 | −1.11038 | −0.555191 | − | 0.831723i | \(-0.687355\pi\) | ||||
−0.555191 | + | 0.831723i | \(0.687355\pi\) | |||||||
\(450\) | −66.7703 | −3.14758 | ||||||||
\(451\) | 21.8432 | 1.02856 | ||||||||
\(452\) | −8.10425 | −0.381192 | ||||||||
\(453\) | 30.7873 | 1.44651 | ||||||||
\(454\) | 11.9799 | 0.562244 | ||||||||
\(455\) | 39.1379 | 1.83481 | ||||||||
\(456\) | 9.17474 | 0.429646 | ||||||||
\(457\) | 38.0044 | 1.77777 | 0.888885 | − | 0.458131i | \(-0.151481\pi\) | ||||
0.888885 | + | 0.458131i | \(0.151481\pi\) | |||||||
\(458\) | −3.60531 | −0.168465 | ||||||||
\(459\) | 3.55799 | 0.166073 | ||||||||
\(460\) | 17.1621 | 0.800186 | ||||||||
\(461\) | −32.4326 | −1.51054 | −0.755268 | − | 0.655416i | \(-0.772493\pi\) | ||||
−0.755268 | + | 0.655416i | \(0.772493\pi\) | |||||||
\(462\) | 28.3252 | 1.31781 | ||||||||
\(463\) | −33.2441 | −1.54499 | −0.772493 | − | 0.635024i | \(-0.780990\pi\) | ||||
−0.772493 | + | 0.635024i | \(0.780990\pi\) | |||||||
\(464\) | −0.134478 | −0.00624300 | ||||||||
\(465\) | −0.523680 | −0.0242851 | ||||||||
\(466\) | 15.7848 | 0.731215 | ||||||||
\(467\) | 17.4265 | 0.806401 | 0.403200 | − | 0.915112i | \(-0.367898\pi\) | ||||
0.403200 | + | 0.915112i | \(0.367898\pi\) | |||||||
\(468\) | 13.0198 | 0.601841 | ||||||||
\(469\) | −9.15848 | −0.422900 | ||||||||
\(470\) | 15.1026 | 0.696632 | ||||||||
\(471\) | 31.2180 | 1.43845 | ||||||||
\(472\) | 0.605095 | 0.0278518 | ||||||||
\(473\) | −19.7956 | −0.910204 | ||||||||
\(474\) | −11.1783 | −0.513434 | ||||||||
\(475\) | 46.4060 | 2.12925 | ||||||||
\(476\) | 2.39395 | 0.109726 | ||||||||
\(477\) | −46.3548 | −2.12244 | ||||||||
\(478\) | −23.8660 | −1.09160 | ||||||||
\(479\) | −39.9799 | −1.82673 | −0.913363 | − | 0.407146i | \(-0.866524\pi\) | ||||
−0.913363 | + | 0.407146i | \(0.866524\pi\) | |||||||
\(480\) | −12.1538 | −0.554743 | ||||||||
\(481\) | 14.0066 | 0.638647 | ||||||||
\(482\) | 10.1267 | 0.461260 | ||||||||
\(483\) | −35.7021 | −1.62450 | ||||||||
\(484\) | −1.28089 | −0.0582221 | ||||||||
\(485\) | 67.6743 | 3.07293 | ||||||||
\(486\) | −16.5830 | −0.752221 | ||||||||
\(487\) | −25.2224 | −1.14294 | −0.571468 | − | 0.820624i | \(-0.693626\pi\) | ||||
−0.571468 | + | 0.820624i | \(0.693626\pi\) | |||||||
\(488\) | 9.60040 | 0.434590 | ||||||||
\(489\) | −49.9544 | −2.25902 | ||||||||
\(490\) | 15.9860 | 0.722176 | ||||||||
\(491\) | 14.3680 | 0.648421 | 0.324211 | − | 0.945985i | \(-0.394901\pi\) | ||||
0.324211 | + | 0.945985i | \(0.394901\pi\) | |||||||
\(492\) | 19.4976 | 0.879019 | ||||||||
\(493\) | 0.0986017 | 0.00444080 | ||||||||
\(494\) | −9.04890 | −0.407129 | ||||||||
\(495\) | 64.5914 | 2.90317 | ||||||||
\(496\) | −0.0430877 | −0.00193469 | ||||||||
\(497\) | 3.49685 | 0.156855 | ||||||||
\(498\) | 10.3692 | 0.464654 | ||||||||
\(499\) | 24.4553 | 1.09477 | 0.547384 | − | 0.836882i | \(-0.315624\pi\) | ||||
0.547384 | + | 0.836882i | \(0.315624\pi\) | |||||||
\(500\) | −39.6366 | −1.77260 | ||||||||
\(501\) | −49.5329 | −2.21296 | ||||||||
\(502\) | −14.6540 | −0.654042 | ||||||||
\(503\) | −4.69182 | −0.209198 | −0.104599 | − | 0.994514i | \(-0.533356\pi\) | ||||
−0.104599 | + | 0.994514i | \(0.533356\pi\) | |||||||
\(504\) | 15.4885 | 0.689911 | ||||||||
\(505\) | 66.4701 | 2.95788 | ||||||||
\(506\) | −12.2503 | −0.544594 | ||||||||
\(507\) | 15.2139 | 0.675672 | ||||||||
\(508\) | 5.29846 | 0.235081 | ||||||||
\(509\) | 22.5963 | 1.00157 | 0.500783 | − | 0.865573i | \(-0.333046\pi\) | ||||
0.500783 | + | 0.865573i | \(0.333046\pi\) | |||||||
\(510\) | 8.91138 | 0.394602 | ||||||||
\(511\) | −35.7903 | −1.58327 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −15.9989 | −0.706367 | ||||||||
\(514\) | −17.8500 | −0.787331 | ||||||||
\(515\) | −19.6216 | −0.864631 | ||||||||
\(516\) | −17.6699 | −0.777872 | ||||||||
\(517\) | −10.7803 | −0.474116 | ||||||||
\(518\) | 16.6624 | 0.732103 | ||||||||
\(519\) | −10.9099 | −0.478892 | ||||||||
\(520\) | 11.9871 | 0.525670 | ||||||||
\(521\) | −4.89976 | −0.214663 | −0.107331 | − | 0.994223i | \(-0.534231\pi\) | ||||
−0.107331 | + | 0.994223i | \(0.534231\pi\) | |||||||
\(522\) | 0.637938 | 0.0279218 | ||||||||
\(523\) | −22.3032 | −0.975249 | −0.487624 | − | 0.873054i | \(-0.662136\pi\) | ||||
−0.487624 | + | 0.873054i | \(0.662136\pi\) | |||||||
\(524\) | −1.68600 | −0.0736533 | ||||||||
\(525\) | 127.884 | 5.58133 | ||||||||
\(526\) | −12.8351 | −0.559638 | ||||||||
\(527\) | 0.0315926 | 0.00137620 | ||||||||
\(528\) | 8.67541 | 0.377549 | ||||||||
\(529\) | −7.55924 | −0.328662 | ||||||||
\(530\) | −42.6780 | −1.85381 | ||||||||
\(531\) | −2.87045 | −0.124567 | ||||||||
\(532\) | −10.7646 | −0.466706 | ||||||||
\(533\) | −19.2302 | −0.832950 | ||||||||
\(534\) | −8.40640 | −0.363781 | ||||||||
\(535\) | −65.8265 | −2.84593 | ||||||||
\(536\) | −2.80505 | −0.121160 | ||||||||
\(537\) | −7.61999 | −0.328827 | ||||||||
\(538\) | −3.38381 | −0.145886 | ||||||||
\(539\) | −11.4109 | −0.491501 | ||||||||
\(540\) | 21.1938 | 0.912034 | ||||||||
\(541\) | 4.81851 | 0.207164 | 0.103582 | − | 0.994621i | \(-0.466970\pi\) | ||||
0.103582 | + | 0.994621i | \(0.466970\pi\) | |||||||
\(542\) | 28.7294 | 1.23403 | ||||||||
\(543\) | −19.9622 | −0.856661 | ||||||||
\(544\) | 0.733217 | 0.0314364 | ||||||||
\(545\) | 45.2144 | 1.93677 | ||||||||
\(546\) | −24.9367 | −1.06719 | ||||||||
\(547\) | −28.8973 | −1.23556 | −0.617780 | − | 0.786351i | \(-0.711968\pi\) | ||||
−0.617780 | + | 0.786351i | \(0.711968\pi\) | |||||||
\(548\) | −4.54990 | −0.194362 | ||||||||
\(549\) | −45.5423 | −1.94370 | ||||||||
\(550\) | 43.8804 | 1.87107 | ||||||||
\(551\) | −0.443373 | −0.0188883 | ||||||||
\(552\) | −10.9348 | −0.465416 | ||||||||
\(553\) | 13.1154 | 0.557721 | ||||||||
\(554\) | −31.1705 | −1.32431 | ||||||||
\(555\) | 62.0250 | 2.63281 | ||||||||
\(556\) | −3.78163 | −0.160377 | ||||||||
\(557\) | 16.9780 | 0.719380 | 0.359690 | − | 0.933072i | \(-0.382882\pi\) | ||||
0.359690 | + | 0.933072i | \(0.382882\pi\) | |||||||
\(558\) | 0.204399 | 0.00865291 | ||||||||
\(559\) | 17.4275 | 0.737105 | ||||||||
\(560\) | 14.2600 | 0.602593 | ||||||||
\(561\) | −6.36096 | −0.268560 | ||||||||
\(562\) | −10.2220 | −0.431191 | ||||||||
\(563\) | 5.42232 | 0.228524 | 0.114262 | − | 0.993451i | \(-0.463550\pi\) | ||||
0.114262 | + | 0.993451i | \(0.463550\pi\) | |||||||
\(564\) | −9.62263 | −0.405186 | ||||||||
\(565\) | 35.3955 | 1.48910 | ||||||||
\(566\) | 15.6991 | 0.659882 | ||||||||
\(567\) | 2.37626 | 0.0997935 | ||||||||
\(568\) | 1.07101 | 0.0449387 | ||||||||
\(569\) | −36.6814 | −1.53776 | −0.768881 | − | 0.639391i | \(-0.779186\pi\) | ||||
−0.768881 | + | 0.639391i | \(0.779186\pi\) | |||||||
\(570\) | −40.0709 | −1.67839 | ||||||||
\(571\) | 8.07612 | 0.337975 | 0.168988 | − | 0.985618i | \(-0.445950\pi\) | ||||
0.168988 | + | 0.985618i | \(0.445950\pi\) | |||||||
\(572\) | −8.55642 | −0.357762 | ||||||||
\(573\) | 49.4264 | 2.06482 | ||||||||
\(574\) | −22.8763 | −0.954840 | ||||||||
\(575\) | −55.3085 | −2.30652 | ||||||||
\(576\) | 4.74379 | 0.197658 | ||||||||
\(577\) | −13.2727 | −0.552551 | −0.276276 | − | 0.961078i | \(-0.589100\pi\) | ||||
−0.276276 | + | 0.961078i | \(0.589100\pi\) | |||||||
\(578\) | 16.4624 | 0.684745 | ||||||||
\(579\) | 34.5062 | 1.43403 | ||||||||
\(580\) | 0.587338 | 0.0243879 | ||||||||
\(581\) | −12.1661 | −0.504733 | ||||||||
\(582\) | −43.1186 | −1.78732 | ||||||||
\(583\) | 30.4637 | 1.26168 | ||||||||
\(584\) | −10.9618 | −0.453604 | ||||||||
\(585\) | −56.8644 | −2.35105 | ||||||||
\(586\) | 12.3158 | 0.508760 | ||||||||
\(587\) | 29.3679 | 1.21214 | 0.606071 | − | 0.795411i | \(-0.292745\pi\) | ||||
0.606071 | + | 0.795411i | \(0.292745\pi\) | |||||||
\(588\) | −10.1855 | −0.420043 | ||||||||
\(589\) | −0.142059 | −0.00585346 | ||||||||
\(590\) | −2.64277 | −0.108801 | ||||||||
\(591\) | 21.7703 | 0.895511 | ||||||||
\(592\) | 5.10334 | 0.209746 | ||||||||
\(593\) | −24.5766 | −1.00924 | −0.504619 | − | 0.863342i | \(-0.668367\pi\) | ||||
−0.504619 | + | 0.863342i | \(0.668367\pi\) | |||||||
\(594\) | −15.1281 | −0.620715 | ||||||||
\(595\) | −10.4556 | −0.428639 | ||||||||
\(596\) | −3.03435 | −0.124292 | ||||||||
\(597\) | 21.8373 | 0.893741 | ||||||||
\(598\) | 10.7848 | 0.441025 | ||||||||
\(599\) | 11.6195 | 0.474759 | 0.237380 | − | 0.971417i | \(-0.423711\pi\) | ||||
0.237380 | + | 0.971417i | \(0.423711\pi\) | |||||||
\(600\) | 39.1683 | 1.59904 | ||||||||
\(601\) | −37.8896 | −1.54555 | −0.772775 | − | 0.634680i | \(-0.781132\pi\) | ||||
−0.772775 | + | 0.634680i | \(0.781132\pi\) | |||||||
\(602\) | 20.7319 | 0.844969 | ||||||||
\(603\) | 13.3066 | 0.541886 | ||||||||
\(604\) | −11.0635 | −0.450169 | ||||||||
\(605\) | 5.59431 | 0.227441 | ||||||||
\(606\) | −42.3514 | −1.72041 | ||||||||
\(607\) | −19.7543 | −0.801801 | −0.400901 | − | 0.916122i | \(-0.631303\pi\) | ||||
−0.400901 | + | 0.916122i | \(0.631303\pi\) | |||||||
\(608\) | −3.29698 | −0.133710 | ||||||||
\(609\) | −1.22183 | −0.0495112 | ||||||||
\(610\) | −41.9300 | −1.69770 | ||||||||
\(611\) | 9.49064 | 0.383950 | ||||||||
\(612\) | −3.47823 | −0.140599 | ||||||||
\(613\) | −1.06042 | −0.0428302 | −0.0214151 | − | 0.999771i | \(-0.506817\pi\) | ||||
−0.0214151 | + | 0.999771i | \(0.506817\pi\) | |||||||
\(614\) | 1.13457 | 0.0457876 | ||||||||
\(615\) | −85.1562 | −3.43383 | ||||||||
\(616\) | −10.1788 | −0.410115 | ||||||||
\(617\) | 34.5568 | 1.39120 | 0.695602 | − | 0.718428i | \(-0.255138\pi\) | ||||
0.695602 | + | 0.718428i | \(0.255138\pi\) | |||||||
\(618\) | 12.5019 | 0.502900 | ||||||||
\(619\) | −20.9560 | −0.842293 | −0.421147 | − | 0.906993i | \(-0.638372\pi\) | ||||
−0.421147 | + | 0.906993i | \(0.638372\pi\) | |||||||
\(620\) | 0.188187 | 0.00755776 | ||||||||
\(621\) | 19.0681 | 0.765175 | ||||||||
\(622\) | 17.2736 | 0.692607 | ||||||||
\(623\) | 9.86316 | 0.395159 | ||||||||
\(624\) | −7.63758 | −0.305748 | ||||||||
\(625\) | 102.737 | 4.10950 | ||||||||
\(626\) | 11.3761 | 0.454680 | ||||||||
\(627\) | 28.6027 | 1.14228 | ||||||||
\(628\) | −11.2183 | −0.447660 | ||||||||
\(629\) | −3.74185 | −0.149197 | ||||||||
\(630\) | −67.6463 | −2.69509 | ||||||||
\(631\) | −44.2350 | −1.76097 | −0.880483 | − | 0.474078i | \(-0.842781\pi\) | ||||
−0.880483 | + | 0.474078i | \(0.842781\pi\) | |||||||
\(632\) | 4.01696 | 0.159786 | ||||||||
\(633\) | 47.3252 | 1.88101 | ||||||||
\(634\) | −1.16065 | −0.0460951 | ||||||||
\(635\) | −23.1412 | −0.918329 | ||||||||
\(636\) | 27.1923 | 1.07824 | ||||||||
\(637\) | 10.0458 | 0.398029 | ||||||||
\(638\) | −0.419243 | −0.0165980 | ||||||||
\(639\) | −5.08067 | −0.200988 | ||||||||
\(640\) | 4.36753 | 0.172642 | ||||||||
\(641\) | 33.6782 | 1.33021 | 0.665105 | − | 0.746749i | \(-0.268387\pi\) | ||||
0.665105 | + | 0.746749i | \(0.268387\pi\) | |||||||
\(642\) | 41.9413 | 1.65529 | ||||||||
\(643\) | −46.0220 | −1.81493 | −0.907464 | − | 0.420129i | \(-0.861985\pi\) | ||||
−0.907464 | + | 0.420129i | \(0.861985\pi\) | |||||||
\(644\) | 12.8297 | 0.505562 | ||||||||
\(645\) | 77.1736 | 3.03871 | ||||||||
\(646\) | 2.41740 | 0.0951114 | ||||||||
\(647\) | −1.36238 | −0.0535607 | −0.0267803 | − | 0.999641i | \(-0.508525\pi\) | ||||
−0.0267803 | + | 0.999641i | \(0.508525\pi\) | |||||||
\(648\) | 0.727798 | 0.0285906 | ||||||||
\(649\) | 1.88641 | 0.0740482 | ||||||||
\(650\) | −38.6311 | −1.51523 | ||||||||
\(651\) | −0.391483 | −0.0153434 | ||||||||
\(652\) | 17.9514 | 0.703029 | ||||||||
\(653\) | −5.64681 | −0.220977 | −0.110488 | − | 0.993877i | \(-0.535242\pi\) | ||||
−0.110488 | + | 0.993877i | \(0.535242\pi\) | |||||||
\(654\) | −28.8083 | −1.12649 | ||||||||
\(655\) | 7.36365 | 0.287722 | ||||||||
\(656\) | −7.00654 | −0.273560 | ||||||||
\(657\) | 52.0007 | 2.02874 | ||||||||
\(658\) | 11.2901 | 0.440136 | ||||||||
\(659\) | 10.4139 | 0.405668 | 0.202834 | − | 0.979213i | \(-0.434985\pi\) | ||||
0.202834 | + | 0.979213i | \(0.434985\pi\) | |||||||
\(660\) | −37.8901 | −1.47487 | ||||||||
\(661\) | −50.4412 | −1.96193 | −0.980967 | − | 0.194176i | \(-0.937797\pi\) | ||||
−0.980967 | + | 0.194176i | \(0.937797\pi\) | |||||||
\(662\) | −18.7672 | −0.729407 | ||||||||
\(663\) | 5.60000 | 0.217486 | ||||||||
\(664\) | −3.72621 | −0.144605 | ||||||||
\(665\) | 47.0149 | 1.82316 | ||||||||
\(666\) | −24.2092 | −0.938087 | ||||||||
\(667\) | 0.528429 | 0.0204609 | ||||||||
\(668\) | 17.7999 | 0.688697 | ||||||||
\(669\) | 22.4933 | 0.869643 | ||||||||
\(670\) | 12.2511 | 0.473303 | ||||||||
\(671\) | 29.9297 | 1.15542 | ||||||||
\(672\) | −9.08573 | −0.350490 | ||||||||
\(673\) | 28.6209 | 1.10326 | 0.551628 | − | 0.834090i | \(-0.314007\pi\) | ||||
0.551628 | + | 0.834090i | \(0.314007\pi\) | |||||||
\(674\) | 18.2617 | 0.703416 | ||||||||
\(675\) | −68.3014 | −2.62892 | ||||||||
\(676\) | −5.46717 | −0.210276 | ||||||||
\(677\) | 28.3191 | 1.08839 | 0.544195 | − | 0.838959i | \(-0.316835\pi\) | ||||
0.544195 | + | 0.838959i | \(0.316835\pi\) | |||||||
\(678\) | −22.5522 | −0.866114 | ||||||||
\(679\) | 50.5907 | 1.94149 | ||||||||
\(680\) | −3.20234 | −0.122804 | ||||||||
\(681\) | 33.3372 | 1.27749 | ||||||||
\(682\) | −0.134328 | −0.00514369 | ||||||||
\(683\) | 15.8235 | 0.605469 | 0.302734 | − | 0.953075i | \(-0.402100\pi\) | ||||
0.302734 | + | 0.953075i | \(0.402100\pi\) | |||||||
\(684\) | 15.6402 | 0.598018 | ||||||||
\(685\) | 19.8718 | 0.759263 | ||||||||
\(686\) | −10.9044 | −0.416333 | ||||||||
\(687\) | −10.0327 | −0.382773 | ||||||||
\(688\) | 6.34974 | 0.242082 | ||||||||
\(689\) | −26.8193 | −1.02173 | ||||||||
\(690\) | 47.7581 | 1.81812 | ||||||||
\(691\) | −4.54799 | −0.173014 | −0.0865069 | − | 0.996251i | \(-0.527570\pi\) | ||||
−0.0865069 | + | 0.996251i | \(0.527570\pi\) | |||||||
\(692\) | 3.92053 | 0.149036 | ||||||||
\(693\) | 48.2861 | 1.83424 | ||||||||
\(694\) | 0.263336 | 0.00999610 | ||||||||
\(695\) | 16.5164 | 0.626501 | ||||||||
\(696\) | −0.374222 | −0.0141848 | ||||||||
\(697\) | 5.13731 | 0.194590 | ||||||||
\(698\) | −1.19989 | −0.0454166 | ||||||||
\(699\) | 43.9253 | 1.66141 | ||||||||
\(700\) | −45.9558 | −1.73697 | ||||||||
\(701\) | 28.3323 | 1.07010 | 0.535048 | − | 0.844822i | \(-0.320294\pi\) | ||||
0.535048 | + | 0.844822i | \(0.320294\pi\) | |||||||
\(702\) | 13.3184 | 0.502670 | ||||||||
\(703\) | 16.8256 | 0.634590 | ||||||||
\(704\) | −3.11755 | −0.117497 | ||||||||
\(705\) | 42.0271 | 1.58283 | ||||||||
\(706\) | −5.56876 | −0.209583 | ||||||||
\(707\) | 49.6905 | 1.86880 | ||||||||
\(708\) | 1.68384 | 0.0632826 | ||||||||
\(709\) | 36.9052 | 1.38601 | 0.693003 | − | 0.720935i | \(-0.256287\pi\) | ||||
0.693003 | + | 0.720935i | \(0.256287\pi\) | |||||||
\(710\) | −4.67768 | −0.175550 | ||||||||
\(711\) | −19.0556 | −0.714642 | ||||||||
\(712\) | 3.02088 | 0.113212 | ||||||||
\(713\) | 0.169312 | 0.00634078 | ||||||||
\(714\) | 6.66180 | 0.249312 | ||||||||
\(715\) | 37.3704 | 1.39757 | ||||||||
\(716\) | 2.73828 | 0.102334 | ||||||||
\(717\) | −66.4135 | −2.48026 | ||||||||
\(718\) | −8.04904 | −0.300387 | ||||||||
\(719\) | −8.35437 | −0.311566 | −0.155783 | − | 0.987791i | \(-0.549790\pi\) | ||||
−0.155783 | + | 0.987791i | \(0.549790\pi\) | |||||||
\(720\) | −20.7187 | −0.772139 | ||||||||
\(721\) | −14.6684 | −0.546278 | ||||||||
\(722\) | 8.12990 | 0.302564 | ||||||||
\(723\) | 28.1804 | 1.04804 | ||||||||
\(724\) | 7.17351 | 0.266601 | ||||||||
\(725\) | −1.89282 | −0.0702977 | ||||||||
\(726\) | −3.56441 | −0.132288 | ||||||||
\(727\) | 11.5600 | 0.428738 | 0.214369 | − | 0.976753i | \(-0.431230\pi\) | ||||
0.214369 | + | 0.976753i | \(0.431230\pi\) | |||||||
\(728\) | 8.96111 | 0.332121 | ||||||||
\(729\) | −43.9633 | −1.62827 | ||||||||
\(730\) | 47.8761 | 1.77197 | ||||||||
\(731\) | −4.65574 | −0.172199 | ||||||||
\(732\) | 26.7157 | 0.987440 | ||||||||
\(733\) | 3.06519 | 0.113216 | 0.0566078 | − | 0.998396i | \(-0.481972\pi\) | ||||
0.0566078 | + | 0.998396i | \(0.481972\pi\) | |||||||
\(734\) | 22.6472 | 0.835925 | ||||||||
\(735\) | 44.4854 | 1.64087 | ||||||||
\(736\) | 3.92947 | 0.144842 | ||||||||
\(737\) | −8.74489 | −0.322122 | ||||||||
\(738\) | 33.2376 | 1.22349 | ||||||||
\(739\) | 25.0419 | 0.921180 | 0.460590 | − | 0.887613i | \(-0.347638\pi\) | ||||
0.460590 | + | 0.887613i | \(0.347638\pi\) | |||||||
\(740\) | −22.2890 | −0.819359 | ||||||||
\(741\) | −25.1810 | −0.925046 | ||||||||
\(742\) | −31.9045 | −1.17125 | ||||||||
\(743\) | 14.6721 | 0.538269 | 0.269134 | − | 0.963103i | \(-0.413262\pi\) | ||||
0.269134 | + | 0.963103i | \(0.413262\pi\) | |||||||
\(744\) | −0.119903 | −0.00439586 | ||||||||
\(745\) | 13.2526 | 0.485537 | ||||||||
\(746\) | 17.7569 | 0.650125 | ||||||||
\(747\) | 17.6764 | 0.646744 | ||||||||
\(748\) | 2.28584 | 0.0835785 | ||||||||
\(749\) | −49.2093 | −1.79807 | ||||||||
\(750\) | −110.299 | −4.02757 | ||||||||
\(751\) | 24.2778 | 0.885911 | 0.442955 | − | 0.896544i | \(-0.353930\pi\) | ||||
0.442955 | + | 0.896544i | \(0.353930\pi\) | |||||||
\(752\) | 3.45793 | 0.126098 | ||||||||
\(753\) | −40.7788 | −1.48606 | ||||||||
\(754\) | 0.369089 | 0.0134414 | ||||||||
\(755\) | 48.3203 | 1.75856 | ||||||||
\(756\) | 15.8436 | 0.576228 | ||||||||
\(757\) | −12.3709 | −0.449627 | −0.224813 | − | 0.974402i | \(-0.572177\pi\) | ||||
−0.224813 | + | 0.974402i | \(0.572177\pi\) | |||||||
\(758\) | −37.0912 | −1.34721 | ||||||||
\(759\) | −34.0898 | −1.23738 | ||||||||
\(760\) | 14.3997 | 0.522331 | ||||||||
\(761\) | −31.8090 | −1.15307 | −0.576537 | − | 0.817071i | \(-0.695596\pi\) | ||||
−0.576537 | + | 0.817071i | \(0.695596\pi\) | |||||||
\(762\) | 14.7444 | 0.534132 | ||||||||
\(763\) | 33.8006 | 1.22366 | ||||||||
\(764\) | −17.7616 | −0.642593 | ||||||||
\(765\) | 15.1913 | 0.549241 | ||||||||
\(766\) | 6.53919 | 0.236271 | ||||||||
\(767\) | −1.66074 | −0.0599660 | ||||||||
\(768\) | −2.78277 | −0.100414 | ||||||||
\(769\) | 32.4092 | 1.16871 | 0.584353 | − | 0.811500i | \(-0.301348\pi\) | ||||
0.584353 | + | 0.811500i | \(0.301348\pi\) | |||||||
\(770\) | 44.4561 | 1.60209 | ||||||||
\(771\) | −49.6725 | −1.78891 | ||||||||
\(772\) | −12.3999 | −0.446284 | ||||||||
\(773\) | 26.2329 | 0.943533 | 0.471767 | − | 0.881723i | \(-0.343616\pi\) | ||||
0.471767 | + | 0.881723i | \(0.343616\pi\) | |||||||
\(774\) | −30.1219 | −1.08271 | ||||||||
\(775\) | −0.606472 | −0.0217851 | ||||||||
\(776\) | 15.4949 | 0.556233 | ||||||||
\(777\) | 46.3675 | 1.66343 | ||||||||
\(778\) | −2.35711 | −0.0845066 | ||||||||
\(779\) | −23.1005 | −0.827660 | ||||||||
\(780\) | 33.3573 | 1.19438 | ||||||||
\(781\) | 3.33894 | 0.119477 | ||||||||
\(782\) | −2.88116 | −0.103030 | ||||||||
\(783\) | 0.652566 | 0.0233208 | ||||||||
\(784\) | 3.66020 | 0.130722 | ||||||||
\(785\) | 48.9964 | 1.74875 | ||||||||
\(786\) | −4.69175 | −0.167349 | ||||||||
\(787\) | 29.7366 | 1.06000 | 0.529998 | − | 0.847999i | \(-0.322193\pi\) | ||||
0.529998 | + | 0.847999i | \(0.322193\pi\) | |||||||
\(788\) | −7.82326 | −0.278692 | ||||||||
\(789\) | −35.7172 | −1.27157 | ||||||||
\(790\) | −17.5442 | −0.624194 | ||||||||
\(791\) | 26.4604 | 0.940822 | ||||||||
\(792\) | 14.7890 | 0.525505 | ||||||||
\(793\) | −26.3493 | −0.935690 | ||||||||
\(794\) | 13.4473 | 0.477227 | ||||||||
\(795\) | −118.763 | −4.21209 | ||||||||
\(796\) | −7.84733 | −0.278141 | ||||||||
\(797\) | −33.4836 | −1.18605 | −0.593025 | − | 0.805184i | \(-0.702066\pi\) | ||||
−0.593025 | + | 0.805184i | \(0.702066\pi\) | |||||||
\(798\) | −29.9555 | −1.06041 | ||||||||
\(799\) | −2.53541 | −0.0896965 | ||||||||
\(800\) | −14.0753 | −0.497637 | ||||||||
\(801\) | −14.3304 | −0.506341 | ||||||||
\(802\) | −26.5582 | −0.937804 | ||||||||
\(803\) | −34.1740 | −1.20598 | ||||||||
\(804\) | −7.80581 | −0.275290 | ||||||||
\(805\) | −56.0342 | −1.97494 | ||||||||
\(806\) | 0.118258 | 0.00416548 | ||||||||
\(807\) | −9.41636 | −0.331472 | ||||||||
\(808\) | 15.2192 | 0.535408 | ||||||||
\(809\) | −21.9896 | −0.773114 | −0.386557 | − | 0.922265i | \(-0.626336\pi\) | ||||
−0.386557 | + | 0.922265i | \(0.626336\pi\) | |||||||
\(810\) | −3.17868 | −0.111687 | ||||||||
\(811\) | 45.8776 | 1.61098 | 0.805490 | − | 0.592610i | \(-0.201902\pi\) | ||||
0.805490 | + | 0.592610i | \(0.201902\pi\) | |||||||
\(812\) | 0.439071 | 0.0154084 | ||||||||
\(813\) | 79.9473 | 2.80387 | ||||||||
\(814\) | 15.9099 | 0.557642 | ||||||||
\(815\) | −78.4030 | −2.74634 | ||||||||
\(816\) | 2.04037 | 0.0714273 | ||||||||
\(817\) | 20.9350 | 0.732423 | ||||||||
\(818\) | −20.6602 | −0.722366 | ||||||||
\(819\) | −42.5097 | −1.48541 | ||||||||
\(820\) | 30.6013 | 1.06864 | ||||||||
\(821\) | −45.1300 | −1.57505 | −0.787523 | − | 0.616285i | \(-0.788637\pi\) | ||||
−0.787523 | + | 0.616285i | \(0.788637\pi\) | |||||||
\(822\) | −12.6613 | −0.441614 | ||||||||
\(823\) | −29.7704 | −1.03773 | −0.518866 | − | 0.854856i | \(-0.673646\pi\) | ||||
−0.518866 | + | 0.854856i | \(0.673646\pi\) | |||||||
\(824\) | −4.49261 | −0.156508 | ||||||||
\(825\) | 122.109 | 4.25129 | ||||||||
\(826\) | −1.97563 | −0.0687411 | ||||||||
\(827\) | −26.0286 | −0.905103 | −0.452551 | − | 0.891738i | \(-0.649486\pi\) | ||||
−0.452551 | + | 0.891738i | \(0.649486\pi\) | |||||||
\(828\) | −18.6406 | −0.647806 | ||||||||
\(829\) | 39.7301 | 1.37988 | 0.689942 | − | 0.723865i | \(-0.257636\pi\) | ||||
0.689942 | + | 0.723865i | \(0.257636\pi\) | |||||||
\(830\) | 16.2743 | 0.564890 | ||||||||
\(831\) | −86.7402 | −3.00898 | ||||||||
\(832\) | 2.74460 | 0.0951519 | ||||||||
\(833\) | −2.68372 | −0.0929855 | ||||||||
\(834\) | −10.5234 | −0.364395 | ||||||||
\(835\) | −77.7414 | −2.69035 | ||||||||
\(836\) | −10.2785 | −0.355490 | ||||||||
\(837\) | 0.209086 | 0.00722708 | ||||||||
\(838\) | 26.8045 | 0.925947 | ||||||||
\(839\) | −11.1615 | −0.385339 | −0.192669 | − | 0.981264i | \(-0.561715\pi\) | ||||
−0.192669 | + | 0.981264i | \(0.561715\pi\) | |||||||
\(840\) | 39.6822 | 1.36916 | ||||||||
\(841\) | −28.9819 | −0.999376 | ||||||||
\(842\) | 6.85131 | 0.236112 | ||||||||
\(843\) | −28.4456 | −0.979718 | ||||||||
\(844\) | −17.0065 | −0.585388 | ||||||||
\(845\) | 23.8780 | 0.821429 | ||||||||
\(846\) | −16.4037 | −0.563972 | ||||||||
\(847\) | 4.18209 | 0.143698 | ||||||||
\(848\) | −9.77167 | −0.335560 | ||||||||
\(849\) | 43.6869 | 1.49933 | ||||||||
\(850\) | 10.3202 | 0.353981 | ||||||||
\(851\) | −20.0534 | −0.687423 | ||||||||
\(852\) | 2.98038 | 0.102106 | ||||||||
\(853\) | −18.9199 | −0.647804 | −0.323902 | − | 0.946091i | \(-0.604995\pi\) | ||||
−0.323902 | + | 0.946091i | \(0.604995\pi\) | |||||||
\(854\) | −31.3453 | −1.07261 | ||||||||
\(855\) | −68.3090 | −2.33612 | ||||||||
\(856\) | −15.0718 | −0.515143 | ||||||||
\(857\) | −48.6070 | −1.66038 | −0.830191 | − | 0.557479i | \(-0.811769\pi\) | ||||
−0.830191 | + | 0.557479i | \(0.811769\pi\) | |||||||
\(858\) | −23.8105 | −0.812878 | ||||||||
\(859\) | 9.09030 | 0.310157 | 0.155079 | − | 0.987902i | \(-0.450437\pi\) | ||||
0.155079 | + | 0.987902i | \(0.450437\pi\) | |||||||
\(860\) | −27.7327 | −0.945676 | ||||||||
\(861\) | −63.6595 | −2.16951 | ||||||||
\(862\) | 5.53959 | 0.188679 | ||||||||
\(863\) | 34.9258 | 1.18889 | 0.594444 | − | 0.804137i | \(-0.297372\pi\) | ||||
0.594444 | + | 0.804137i | \(0.297372\pi\) | |||||||
\(864\) | 4.85257 | 0.165088 | ||||||||
\(865\) | −17.1230 | −0.582200 | ||||||||
\(866\) | −5.11384 | −0.173775 | ||||||||
\(867\) | 45.8110 | 1.55582 | ||||||||
\(868\) | 0.140681 | 0.00477503 | ||||||||
\(869\) | 12.5231 | 0.424816 | ||||||||
\(870\) | 1.63442 | 0.0554122 | ||||||||
\(871\) | 7.69874 | 0.260862 | ||||||||
\(872\) | 10.3524 | 0.350577 | ||||||||
\(873\) | −73.5045 | −2.48775 | ||||||||
\(874\) | 12.9554 | 0.438223 | ||||||||
\(875\) | 129.413 | 4.37497 | ||||||||
\(876\) | −30.5042 | −1.03064 | ||||||||
\(877\) | 33.2890 | 1.12409 | 0.562046 | − | 0.827106i | \(-0.310015\pi\) | ||||
0.562046 | + | 0.827106i | \(0.310015\pi\) | |||||||
\(878\) | −8.98166 | −0.303116 | ||||||||
\(879\) | 34.2719 | 1.15596 | ||||||||
\(880\) | 13.6160 | 0.458995 | ||||||||
\(881\) | 40.1397 | 1.35234 | 0.676170 | − | 0.736745i | \(-0.263638\pi\) | ||||
0.676170 | + | 0.736745i | \(0.263638\pi\) | |||||||
\(882\) | −17.3633 | −0.584651 | ||||||||
\(883\) | −11.4338 | −0.384779 | −0.192390 | − | 0.981319i | \(-0.561624\pi\) | ||||
−0.192390 | + | 0.981319i | \(0.561624\pi\) | |||||||
\(884\) | −2.01239 | −0.0676839 | ||||||||
\(885\) | −7.35421 | −0.247209 | ||||||||
\(886\) | −5.64420 | −0.189621 | ||||||||
\(887\) | −45.1721 | −1.51673 | −0.758365 | − | 0.651830i | \(-0.774001\pi\) | ||||
−0.758365 | + | 0.651830i | \(0.774001\pi\) | |||||||
\(888\) | 14.2014 | 0.476568 | ||||||||
\(889\) | −17.2995 | −0.580205 | ||||||||
\(890\) | −13.1938 | −0.442256 | ||||||||
\(891\) | 2.26895 | 0.0760126 | ||||||||
\(892\) | −8.08309 | −0.270642 | ||||||||
\(893\) | 11.4008 | 0.381512 | ||||||||
\(894\) | −8.44388 | −0.282406 | ||||||||
\(895\) | −11.9595 | −0.399762 | ||||||||
\(896\) | 3.26500 | 0.109076 | ||||||||
\(897\) | 30.0117 | 1.00206 | ||||||||
\(898\) | 23.5286 | 0.785158 | ||||||||
\(899\) | 0.00579436 | 0.000193253 0 | ||||||||
\(900\) | 66.7703 | 2.22568 | ||||||||
\(901\) | 7.16475 | 0.238692 | ||||||||
\(902\) | −21.8432 | −0.727300 | ||||||||
\(903\) | 57.6920 | 1.91987 | ||||||||
\(904\) | 8.10425 | 0.269543 | ||||||||
\(905\) | −31.3305 | −1.04146 | ||||||||
\(906\) | −30.7873 | −1.02284 | ||||||||
\(907\) | −20.0238 | −0.664879 | −0.332439 | − | 0.943125i | \(-0.607872\pi\) | ||||
−0.332439 | + | 0.943125i | \(0.607872\pi\) | |||||||
\(908\) | −11.9799 | −0.397566 | ||||||||
\(909\) | −72.1965 | −2.39461 | ||||||||
\(910\) | −39.1379 | −1.29741 | ||||||||
\(911\) | −3.09739 | −0.102621 | −0.0513106 | − | 0.998683i | \(-0.516340\pi\) | ||||
−0.0513106 | + | 0.998683i | \(0.516340\pi\) | |||||||
\(912\) | −9.17474 | −0.303806 | ||||||||
\(913\) | −11.6166 | −0.384455 | ||||||||
\(914\) | −38.0044 | −1.25707 | ||||||||
\(915\) | −116.681 | −3.85737 | ||||||||
\(916\) | 3.60531 | 0.119123 | ||||||||
\(917\) | 5.50479 | 0.181784 | ||||||||
\(918\) | −3.55799 | −0.117431 | ||||||||
\(919\) | 21.8272 | 0.720012 | 0.360006 | − | 0.932950i | \(-0.382775\pi\) | ||||
0.360006 | + | 0.932950i | \(0.382775\pi\) | |||||||
\(920\) | −17.1621 | −0.565817 | ||||||||
\(921\) | 3.15725 | 0.104035 | ||||||||
\(922\) | 32.4326 | 1.06811 | ||||||||
\(923\) | −2.93950 | −0.0967549 | ||||||||
\(924\) | −28.3252 | −0.931831 | ||||||||
\(925\) | 71.8310 | 2.36179 | ||||||||
\(926\) | 33.2441 | 1.09247 | ||||||||
\(927\) | 21.3120 | 0.699979 | ||||||||
\(928\) | 0.134478 | 0.00441447 | ||||||||
\(929\) | 27.9214 | 0.916072 | 0.458036 | − | 0.888934i | \(-0.348553\pi\) | ||||
0.458036 | + | 0.888934i | \(0.348553\pi\) | |||||||
\(930\) | 0.523680 | 0.0171721 | ||||||||
\(931\) | 12.0676 | 0.395501 | ||||||||
\(932\) | −15.7848 | −0.517047 | ||||||||
\(933\) | 48.0683 | 1.57369 | ||||||||
\(934\) | −17.4265 | −0.570211 | ||||||||
\(935\) | −9.98346 | −0.326494 | ||||||||
\(936\) | −13.0198 | −0.425566 | ||||||||
\(937\) | 11.4017 | 0.372477 | 0.186238 | − | 0.982505i | \(-0.440370\pi\) | ||||
0.186238 | + | 0.982505i | \(0.440370\pi\) | |||||||
\(938\) | 9.15848 | 0.299035 | ||||||||
\(939\) | 31.6570 | 1.03309 | ||||||||
\(940\) | −15.1026 | −0.492593 | ||||||||
\(941\) | 21.0014 | 0.684625 | 0.342312 | − | 0.939586i | \(-0.388790\pi\) | ||||
0.342312 | + | 0.939586i | \(0.388790\pi\) | |||||||
\(942\) | −31.2180 | −1.01714 | ||||||||
\(943\) | 27.5320 | 0.896566 | ||||||||
\(944\) | −0.605095 | −0.0196942 | ||||||||
\(945\) | −69.1975 | −2.25100 | ||||||||
\(946\) | 19.7956 | 0.643611 | ||||||||
\(947\) | −3.80613 | −0.123683 | −0.0618413 | − | 0.998086i | \(-0.519697\pi\) | ||||
−0.0618413 | + | 0.998086i | \(0.519697\pi\) | |||||||
\(948\) | 11.1783 | 0.363053 | ||||||||
\(949\) | 30.0858 | 0.976628 | ||||||||
\(950\) | −46.4060 | −1.50561 | ||||||||
\(951\) | −3.22981 | −0.104734 | ||||||||
\(952\) | −2.39395 | −0.0775884 | ||||||||
\(953\) | 1.64783 | 0.0533784 | 0.0266892 | − | 0.999644i | \(-0.491504\pi\) | ||||
0.0266892 | + | 0.999644i | \(0.491504\pi\) | |||||||
\(954\) | 46.3548 | 1.50079 | ||||||||
\(955\) | 77.5743 | 2.51025 | ||||||||
\(956\) | 23.8660 | 0.771881 | ||||||||
\(957\) | −1.16666 | −0.0377126 | ||||||||
\(958\) | 39.9799 | 1.29169 | ||||||||
\(959\) | 14.8554 | 0.479706 | ||||||||
\(960\) | 12.1538 | 0.392263 | ||||||||
\(961\) | −30.9981 | −0.999940 | ||||||||
\(962\) | −14.0066 | −0.451591 | ||||||||
\(963\) | 71.4975 | 2.30397 | ||||||||
\(964\) | −10.1267 | −0.326160 | ||||||||
\(965\) | 54.1571 | 1.74338 | ||||||||
\(966\) | 35.7021 | 1.14870 | ||||||||
\(967\) | 47.0385 | 1.51266 | 0.756328 | − | 0.654192i | \(-0.226991\pi\) | ||||
0.756328 | + | 0.654192i | \(0.226991\pi\) | |||||||
\(968\) | 1.28089 | 0.0411693 | ||||||||
\(969\) | 6.72707 | 0.216105 | ||||||||
\(970\) | −67.6743 | −2.17289 | ||||||||
\(971\) | 8.15072 | 0.261569 | 0.130785 | − | 0.991411i | \(-0.458250\pi\) | ||||
0.130785 | + | 0.991411i | \(0.458250\pi\) | |||||||
\(972\) | 16.5830 | 0.531900 | ||||||||
\(973\) | 12.3470 | 0.395827 | ||||||||
\(974\) | 25.2224 | 0.808178 | ||||||||
\(975\) | −107.501 | −3.44279 | ||||||||
\(976\) | −9.60040 | −0.307301 | ||||||||
\(977\) | −30.0991 | −0.962957 | −0.481478 | − | 0.876458i | \(-0.659900\pi\) | ||||
−0.481478 | + | 0.876458i | \(0.659900\pi\) | |||||||
\(978\) | 49.9544 | 1.59737 | ||||||||
\(979\) | 9.41774 | 0.300992 | ||||||||
\(980\) | −15.9860 | −0.510655 | ||||||||
\(981\) | −49.1097 | −1.56795 | ||||||||
\(982\) | −14.3680 | −0.458503 | ||||||||
\(983\) | −28.1701 | −0.898487 | −0.449243 | − | 0.893409i | \(-0.648306\pi\) | ||||
−0.449243 | + | 0.893409i | \(0.648306\pi\) | |||||||
\(984\) | −19.4976 | −0.621560 | ||||||||
\(985\) | 34.1683 | 1.08869 | ||||||||
\(986\) | −0.0986017 | −0.00314012 | ||||||||
\(987\) | 31.4178 | 1.00004 | ||||||||
\(988\) | 9.04890 | 0.287884 | ||||||||
\(989\) | −24.9511 | −0.793400 | ||||||||
\(990\) | −64.5914 | −2.05285 | ||||||||
\(991\) | 45.2685 | 1.43800 | 0.719001 | − | 0.695009i | \(-0.244600\pi\) | ||||
0.719001 | + | 0.695009i | \(0.244600\pi\) | |||||||
\(992\) | 0.0430877 | 0.00136804 | ||||||||
\(993\) | −52.2247 | −1.65730 | ||||||||
\(994\) | −3.49685 | −0.110913 | ||||||||
\(995\) | 34.2734 | 1.08654 | ||||||||
\(996\) | −10.3692 | −0.328560 | ||||||||
\(997\) | −12.6222 | −0.399750 | −0.199875 | − | 0.979821i | \(-0.564054\pi\) | ||||
−0.199875 | + | 0.979821i | \(0.564054\pi\) | |||||||
\(998\) | −24.4553 | −0.774118 | ||||||||
\(999\) | −24.7643 | −0.783508 |
(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 | 8042.2.a.c.1.5 | ✓ | 86 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8042.2.a.c.1.5 | ✓ | 86 | 1.1 | even | 1 | trivial |