Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8023,2,Mod(1,8023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8023, 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("8023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8023 = 71 \cdot 113 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8023.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: | \(64.0639775417\) |
Analytic rank: | \(1\) |
Dimension: | \(158\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 8023.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.67852 | −1.89400 | −0.946998 | − | 0.321239i | \(-0.895901\pi\) | ||||
−0.946998 | + | 0.321239i | \(0.895901\pi\) | |||||||
\(3\) | 0.688962 | 0.397772 | 0.198886 | − | 0.980023i | \(-0.436268\pi\) | ||||
0.198886 | + | 0.980023i | \(0.436268\pi\) | |||||||
\(4\) | 5.17445 | 2.58722 | ||||||||
\(5\) | −3.33373 | −1.49089 | −0.745445 | − | 0.666567i | \(-0.767763\pi\) | ||||
−0.745445 | + | 0.666567i | \(0.767763\pi\) | |||||||
\(6\) | −1.84540 | −0.753380 | ||||||||
\(7\) | 3.78681 | 1.43128 | 0.715641 | − | 0.698469i | \(-0.246135\pi\) | ||||
0.715641 | + | 0.698469i | \(0.246135\pi\) | |||||||
\(8\) | −8.50280 | −3.00619 | ||||||||
\(9\) | −2.52533 | −0.841777 | ||||||||
\(10\) | 8.92945 | 2.82374 | ||||||||
\(11\) | 1.45005 | 0.437208 | 0.218604 | − | 0.975814i | \(-0.429850\pi\) | ||||
0.218604 | + | 0.975814i | \(0.429850\pi\) | |||||||
\(12\) | 3.56500 | 1.02913 | ||||||||
\(13\) | 3.73900 | 1.03701 | 0.518506 | − | 0.855074i | \(-0.326488\pi\) | ||||
0.518506 | + | 0.855074i | \(0.326488\pi\) | |||||||
\(14\) | −10.1430 | −2.71084 | ||||||||
\(15\) | −2.29681 | −0.593035 | ||||||||
\(16\) | 12.4260 | 3.10650 | ||||||||
\(17\) | −0.457265 | −0.110903 | −0.0554515 | − | 0.998461i | \(-0.517660\pi\) | ||||
−0.0554515 | + | 0.998461i | \(0.517660\pi\) | |||||||
\(18\) | 6.76414 | 1.59432 | ||||||||
\(19\) | −4.11903 | −0.944969 | −0.472485 | − | 0.881339i | \(-0.656643\pi\) | ||||
−0.472485 | + | 0.881339i | \(0.656643\pi\) | |||||||
\(20\) | −17.2502 | −3.85726 | ||||||||
\(21\) | 2.60897 | 0.569324 | ||||||||
\(22\) | −3.88399 | −0.828070 | ||||||||
\(23\) | −6.37891 | −1.33010 | −0.665048 | − | 0.746801i | \(-0.731589\pi\) | ||||
−0.665048 | + | 0.746801i | \(0.731589\pi\) | |||||||
\(24\) | −5.85811 | −1.19578 | ||||||||
\(25\) | 6.11376 | 1.22275 | ||||||||
\(26\) | −10.0150 | −1.96410 | ||||||||
\(27\) | −3.80674 | −0.732608 | ||||||||
\(28\) | 19.5947 | 3.70304 | ||||||||
\(29\) | −7.35059 | −1.36497 | −0.682485 | − | 0.730900i | \(-0.739101\pi\) | ||||
−0.682485 | + | 0.730900i | \(0.739101\pi\) | |||||||
\(30\) | 6.15205 | 1.12321 | ||||||||
\(31\) | 5.96142 | 1.07070 | 0.535351 | − | 0.844629i | \(-0.320179\pi\) | ||||
0.535351 | + | 0.844629i | \(0.320179\pi\) | |||||||
\(32\) | −16.2776 | −2.87750 | ||||||||
\(33\) | 0.999033 | 0.173909 | ||||||||
\(34\) | 1.22479 | 0.210050 | ||||||||
\(35\) | −12.6242 | −2.13388 | ||||||||
\(36\) | −13.0672 | −2.17786 | ||||||||
\(37\) | 11.4442 | 1.88141 | 0.940706 | − | 0.339222i | \(-0.110164\pi\) | ||||
0.940706 | + | 0.339222i | \(0.110164\pi\) | |||||||
\(38\) | 11.0329 | 1.78977 | ||||||||
\(39\) | 2.57603 | 0.412495 | ||||||||
\(40\) | 28.3461 | 4.48191 | ||||||||
\(41\) | 7.78118 | 1.21522 | 0.607608 | − | 0.794237i | \(-0.292129\pi\) | ||||
0.607608 | + | 0.794237i | \(0.292129\pi\) | |||||||
\(42\) | −6.98817 | −1.07830 | ||||||||
\(43\) | −9.44692 | −1.44064 | −0.720321 | − | 0.693641i | \(-0.756006\pi\) | ||||
−0.720321 | + | 0.693641i | \(0.756006\pi\) | |||||||
\(44\) | 7.50323 | 1.13115 | ||||||||
\(45\) | 8.41877 | 1.25500 | ||||||||
\(46\) | 17.0860 | 2.51920 | ||||||||
\(47\) | 11.7459 | 1.71331 | 0.856655 | − | 0.515889i | \(-0.172538\pi\) | ||||
0.856655 | + | 0.515889i | \(0.172538\pi\) | |||||||
\(48\) | 8.56104 | 1.23568 | ||||||||
\(49\) | 7.33996 | 1.04857 | ||||||||
\(50\) | −16.3758 | −2.31589 | ||||||||
\(51\) | −0.315038 | −0.0441141 | ||||||||
\(52\) | 19.3472 | 2.68298 | ||||||||
\(53\) | −2.37933 | −0.326826 | −0.163413 | − | 0.986558i | \(-0.552250\pi\) | ||||
−0.163413 | + | 0.986558i | \(0.552250\pi\) | |||||||
\(54\) | 10.1964 | 1.38756 | ||||||||
\(55\) | −4.83409 | −0.651829 | ||||||||
\(56\) | −32.1985 | −4.30271 | ||||||||
\(57\) | −2.83785 | −0.375883 | ||||||||
\(58\) | 19.6887 | 2.58525 | ||||||||
\(59\) | 8.26952 | 1.07660 | 0.538300 | − | 0.842753i | \(-0.319067\pi\) | ||||
0.538300 | + | 0.842753i | \(0.319067\pi\) | |||||||
\(60\) | −11.8847 | −1.53431 | ||||||||
\(61\) | −6.75010 | −0.864261 | −0.432131 | − | 0.901811i | \(-0.642238\pi\) | ||||
−0.432131 | + | 0.901811i | \(0.642238\pi\) | |||||||
\(62\) | −15.9678 | −2.02791 | ||||||||
\(63\) | −9.56296 | −1.20482 | ||||||||
\(64\) | 18.7479 | 2.34348 | ||||||||
\(65\) | −12.4648 | −1.54607 | ||||||||
\(66\) | −2.67592 | −0.329384 | ||||||||
\(67\) | −4.48494 | −0.547922 | −0.273961 | − | 0.961741i | \(-0.588334\pi\) | ||||
−0.273961 | + | 0.961741i | \(0.588334\pi\) | |||||||
\(68\) | −2.36609 | −0.286931 | ||||||||
\(69\) | −4.39483 | −0.529075 | ||||||||
\(70\) | 33.8142 | 4.04157 | ||||||||
\(71\) | −1.00000 | −0.118678 | ||||||||
\(72\) | 21.4724 | 2.53055 | ||||||||
\(73\) | −7.70485 | −0.901785 | −0.450892 | − | 0.892578i | \(-0.648894\pi\) | ||||
−0.450892 | + | 0.892578i | \(0.648894\pi\) | |||||||
\(74\) | −30.6534 | −3.56339 | ||||||||
\(75\) | 4.21215 | 0.486377 | ||||||||
\(76\) | −21.3137 | −2.44485 | ||||||||
\(77\) | 5.49109 | 0.625767 | ||||||||
\(78\) | −6.89993 | −0.781263 | ||||||||
\(79\) | −11.2483 | −1.26554 | −0.632768 | − | 0.774341i | \(-0.718082\pi\) | ||||
−0.632768 | + | 0.774341i | \(0.718082\pi\) | |||||||
\(80\) | −41.4249 | −4.63145 | ||||||||
\(81\) | 4.95329 | 0.550366 | ||||||||
\(82\) | −20.8420 | −2.30162 | ||||||||
\(83\) | −4.14568 | −0.455047 | −0.227524 | − | 0.973773i | \(-0.573063\pi\) | ||||
−0.227524 | + | 0.973773i | \(0.573063\pi\) | |||||||
\(84\) | 13.5000 | 1.47297 | ||||||||
\(85\) | 1.52440 | 0.165344 | ||||||||
\(86\) | 25.3037 | 2.72857 | ||||||||
\(87\) | −5.06428 | −0.542947 | ||||||||
\(88\) | −12.3295 | −1.31433 | ||||||||
\(89\) | 10.3144 | 1.09333 | 0.546663 | − | 0.837353i | \(-0.315898\pi\) | ||||
0.546663 | + | 0.837353i | \(0.315898\pi\) | |||||||
\(90\) | −22.5498 | −2.37696 | ||||||||
\(91\) | 14.1589 | 1.48426 | ||||||||
\(92\) | −33.0073 | −3.44125 | ||||||||
\(93\) | 4.10719 | 0.425896 | ||||||||
\(94\) | −31.4615 | −3.24500 | ||||||||
\(95\) | 13.7317 | 1.40885 | ||||||||
\(96\) | −11.2147 | −1.14459 | ||||||||
\(97\) | −9.49652 | −0.964226 | −0.482113 | − | 0.876109i | \(-0.660131\pi\) | ||||
−0.482113 | + | 0.876109i | \(0.660131\pi\) | |||||||
\(98\) | −19.6602 | −1.98598 | ||||||||
\(99\) | −3.66187 | −0.368032 | ||||||||
\(100\) | 31.6353 | 3.16353 | ||||||||
\(101\) | −15.4740 | −1.53972 | −0.769860 | − | 0.638213i | \(-0.779674\pi\) | ||||
−0.769860 | + | 0.638213i | \(0.779674\pi\) | |||||||
\(102\) | 0.843834 | 0.0835520 | ||||||||
\(103\) | 13.4795 | 1.32817 | 0.664085 | − | 0.747657i | \(-0.268821\pi\) | ||||
0.664085 | + | 0.747657i | \(0.268821\pi\) | |||||||
\(104\) | −31.7920 | −3.11746 | ||||||||
\(105\) | −8.69761 | −0.848800 | ||||||||
\(106\) | 6.37306 | 0.619007 | ||||||||
\(107\) | 17.8700 | 1.72756 | 0.863779 | − | 0.503870i | \(-0.168091\pi\) | ||||
0.863779 | + | 0.503870i | \(0.168091\pi\) | |||||||
\(108\) | −19.6978 | −1.89542 | ||||||||
\(109\) | 5.37901 | 0.515216 | 0.257608 | − | 0.966250i | \(-0.417066\pi\) | ||||
0.257608 | + | 0.966250i | \(0.417066\pi\) | |||||||
\(110\) | 12.9482 | 1.23456 | ||||||||
\(111\) | 7.88461 | 0.748374 | ||||||||
\(112\) | 47.0549 | 4.44627 | ||||||||
\(113\) | −1.00000 | −0.0940721 | ||||||||
\(114\) | 7.60123 | 0.711921 | ||||||||
\(115\) | 21.2656 | 1.98303 | ||||||||
\(116\) | −38.0352 | −3.53148 | ||||||||
\(117\) | −9.44221 | −0.872932 | ||||||||
\(118\) | −22.1500 | −2.03908 | ||||||||
\(119\) | −1.73158 | −0.158733 | ||||||||
\(120\) | 19.5294 | 1.78278 | ||||||||
\(121\) | −8.89734 | −0.808849 | ||||||||
\(122\) | 18.0802 | 1.63691 | ||||||||
\(123\) | 5.36094 | 0.483380 | ||||||||
\(124\) | 30.8471 | 2.77015 | ||||||||
\(125\) | −3.71298 | −0.332099 | ||||||||
\(126\) | 25.6145 | 2.28192 | ||||||||
\(127\) | −9.21300 | −0.817522 | −0.408761 | − | 0.912642i | \(-0.634039\pi\) | ||||
−0.408761 | + | 0.912642i | \(0.634039\pi\) | |||||||
\(128\) | −17.6612 | −1.56105 | ||||||||
\(129\) | −6.50857 | −0.573048 | ||||||||
\(130\) | 33.3872 | 2.92825 | ||||||||
\(131\) | −17.4164 | −1.52168 | −0.760841 | − | 0.648938i | \(-0.775213\pi\) | ||||
−0.760841 | + | 0.648938i | \(0.775213\pi\) | |||||||
\(132\) | 5.16944 | 0.449942 | ||||||||
\(133\) | −15.5980 | −1.35252 | ||||||||
\(134\) | 12.0130 | 1.03776 | ||||||||
\(135\) | 12.6907 | 1.09224 | ||||||||
\(136\) | 3.88803 | 0.333396 | ||||||||
\(137\) | −8.09267 | −0.691404 | −0.345702 | − | 0.938344i | \(-0.612359\pi\) | ||||
−0.345702 | + | 0.938344i | \(0.612359\pi\) | |||||||
\(138\) | 11.7716 | 1.00207 | ||||||||
\(139\) | 11.1930 | 0.949381 | 0.474691 | − | 0.880153i | \(-0.342560\pi\) | ||||
0.474691 | + | 0.880153i | \(0.342560\pi\) | |||||||
\(140\) | −65.3233 | −5.52083 | ||||||||
\(141\) | 8.09246 | 0.681508 | ||||||||
\(142\) | 2.67852 | 0.224776 | ||||||||
\(143\) | 5.42175 | 0.453390 | ||||||||
\(144\) | −31.3798 | −2.61498 | ||||||||
\(145\) | 24.5049 | 2.03502 | ||||||||
\(146\) | 20.6376 | 1.70798 | ||||||||
\(147\) | 5.05696 | 0.417091 | ||||||||
\(148\) | 59.2173 | 4.86763 | ||||||||
\(149\) | −17.9349 | −1.46928 | −0.734640 | − | 0.678457i | \(-0.762649\pi\) | ||||
−0.734640 | + | 0.678457i | \(0.762649\pi\) | |||||||
\(150\) | −11.2823 | −0.921197 | ||||||||
\(151\) | −17.6506 | −1.43639 | −0.718194 | − | 0.695843i | \(-0.755031\pi\) | ||||
−0.718194 | + | 0.695843i | \(0.755031\pi\) | |||||||
\(152\) | 35.0233 | 2.84076 | ||||||||
\(153\) | 1.15474 | 0.0933556 | ||||||||
\(154\) | −14.7080 | −1.18520 | ||||||||
\(155\) | −19.8738 | −1.59630 | ||||||||
\(156\) | 13.3295 | 1.06722 | ||||||||
\(157\) | 11.7147 | 0.934933 | 0.467466 | − | 0.884011i | \(-0.345167\pi\) | ||||
0.467466 | + | 0.884011i | \(0.345167\pi\) | |||||||
\(158\) | 30.1289 | 2.39692 | ||||||||
\(159\) | −1.63927 | −0.130002 | ||||||||
\(160\) | 54.2652 | 4.29004 | ||||||||
\(161\) | −24.1558 | −1.90374 | ||||||||
\(162\) | −13.2675 | −1.04239 | ||||||||
\(163\) | 17.8070 | 1.39475 | 0.697377 | − | 0.716704i | \(-0.254350\pi\) | ||||
0.697377 | + | 0.716704i | \(0.254350\pi\) | |||||||
\(164\) | 40.2633 | 3.14404 | ||||||||
\(165\) | −3.33051 | −0.259280 | ||||||||
\(166\) | 11.1043 | 0.861858 | ||||||||
\(167\) | 3.69353 | 0.285814 | 0.142907 | − | 0.989736i | \(-0.454355\pi\) | ||||
0.142907 | + | 0.989736i | \(0.454355\pi\) | |||||||
\(168\) | −22.1836 | −1.71150 | ||||||||
\(169\) | 0.980105 | 0.0753927 | ||||||||
\(170\) | −4.08312 | −0.313161 | ||||||||
\(171\) | 10.4019 | 0.795454 | ||||||||
\(172\) | −48.8826 | −3.72726 | ||||||||
\(173\) | 15.8196 | 1.20274 | 0.601370 | − | 0.798971i | \(-0.294622\pi\) | ||||
0.601370 | + | 0.798971i | \(0.294622\pi\) | |||||||
\(174\) | 13.5647 | 1.02834 | ||||||||
\(175\) | 23.1517 | 1.75010 | ||||||||
\(176\) | 18.0184 | 1.35819 | ||||||||
\(177\) | 5.69739 | 0.428242 | ||||||||
\(178\) | −27.6273 | −2.07076 | ||||||||
\(179\) | −4.59611 | −0.343529 | −0.171765 | − | 0.985138i | \(-0.554947\pi\) | ||||
−0.171765 | + | 0.985138i | \(0.554947\pi\) | |||||||
\(180\) | 43.5625 | 3.24696 | ||||||||
\(181\) | 3.24026 | 0.240847 | 0.120423 | − | 0.992723i | \(-0.461575\pi\) | ||||
0.120423 | + | 0.992723i | \(0.461575\pi\) | |||||||
\(182\) | −37.9248 | −2.81117 | ||||||||
\(183\) | −4.65056 | −0.343779 | ||||||||
\(184\) | 54.2386 | 3.99852 | ||||||||
\(185\) | −38.1518 | −2.80498 | ||||||||
\(186\) | −11.0012 | −0.806646 | ||||||||
\(187\) | −0.663059 | −0.0484876 | ||||||||
\(188\) | 60.7783 | 4.43272 | ||||||||
\(189\) | −14.4154 | −1.04857 | ||||||||
\(190\) | −36.7806 | −2.66835 | ||||||||
\(191\) | 3.41034 | 0.246764 | 0.123382 | − | 0.992359i | \(-0.460626\pi\) | ||||
0.123382 | + | 0.992359i | \(0.460626\pi\) | |||||||
\(192\) | 12.9166 | 0.932174 | ||||||||
\(193\) | −21.8959 | −1.57610 | −0.788051 | − | 0.615610i | \(-0.788910\pi\) | ||||
−0.788051 | + | 0.615610i | \(0.788910\pi\) | |||||||
\(194\) | 25.4366 | 1.82624 | ||||||||
\(195\) | −8.58778 | −0.614984 | ||||||||
\(196\) | 37.9802 | 2.71287 | ||||||||
\(197\) | 7.48921 | 0.533584 | 0.266792 | − | 0.963754i | \(-0.414036\pi\) | ||||
0.266792 | + | 0.963754i | \(0.414036\pi\) | |||||||
\(198\) | 9.80837 | 0.697051 | ||||||||
\(199\) | −18.3820 | −1.30306 | −0.651531 | − | 0.758622i | \(-0.725873\pi\) | ||||
−0.651531 | + | 0.758622i | \(0.725873\pi\) | |||||||
\(200\) | −51.9841 | −3.67583 | ||||||||
\(201\) | −3.08995 | −0.217948 | ||||||||
\(202\) | 41.4473 | 2.91622 | ||||||||
\(203\) | −27.8353 | −1.95366 | ||||||||
\(204\) | −1.63015 | −0.114133 | ||||||||
\(205\) | −25.9404 | −1.81175 | ||||||||
\(206\) | −36.1049 | −2.51555 | ||||||||
\(207\) | 16.1089 | 1.11964 | ||||||||
\(208\) | 46.4608 | 3.22148 | ||||||||
\(209\) | −5.97281 | −0.413148 | ||||||||
\(210\) | 23.2967 | 1.60762 | ||||||||
\(211\) | 14.3897 | 0.990626 | 0.495313 | − | 0.868714i | \(-0.335053\pi\) | ||||
0.495313 | + | 0.868714i | \(0.335053\pi\) | |||||||
\(212\) | −12.3117 | −0.845571 | ||||||||
\(213\) | −0.688962 | −0.0472069 | ||||||||
\(214\) | −47.8651 | −3.27199 | ||||||||
\(215\) | 31.4935 | 2.14784 | ||||||||
\(216\) | 32.3680 | 2.20236 | ||||||||
\(217\) | 22.5748 | 1.53248 | ||||||||
\(218\) | −14.4078 | −0.975817 | ||||||||
\(219\) | −5.30835 | −0.358705 | ||||||||
\(220\) | −25.0137 | −1.68643 | ||||||||
\(221\) | −1.70971 | −0.115008 | ||||||||
\(222\) | −21.1191 | −1.41742 | ||||||||
\(223\) | −5.90794 | −0.395625 | −0.197812 | − | 0.980240i | \(-0.563384\pi\) | ||||
−0.197812 | + | 0.980240i | \(0.563384\pi\) | |||||||
\(224\) | −61.6403 | −4.11852 | ||||||||
\(225\) | −15.4393 | −1.02928 | ||||||||
\(226\) | 2.67852 | 0.178172 | ||||||||
\(227\) | 11.7556 | 0.780249 | 0.390124 | − | 0.920762i | \(-0.372432\pi\) | ||||
0.390124 | + | 0.920762i | \(0.372432\pi\) | |||||||
\(228\) | −14.6843 | −0.972493 | ||||||||
\(229\) | 3.52788 | 0.233129 | 0.116565 | − | 0.993183i | \(-0.462812\pi\) | ||||
0.116565 | + | 0.993183i | \(0.462812\pi\) | |||||||
\(230\) | −56.9602 | −3.75584 | ||||||||
\(231\) | 3.78315 | 0.248913 | ||||||||
\(232\) | 62.5006 | 4.10337 | ||||||||
\(233\) | −17.6528 | −1.15648 | −0.578238 | − | 0.815868i | \(-0.696259\pi\) | ||||
−0.578238 | + | 0.815868i | \(0.696259\pi\) | |||||||
\(234\) | 25.2911 | 1.65333 | ||||||||
\(235\) | −39.1576 | −2.55436 | ||||||||
\(236\) | 42.7902 | 2.78540 | ||||||||
\(237\) | −7.74968 | −0.503396 | ||||||||
\(238\) | 4.63805 | 0.300640 | ||||||||
\(239\) | −9.53899 | −0.617026 | −0.308513 | − | 0.951220i | \(-0.599831\pi\) | ||||
−0.308513 | + | 0.951220i | \(0.599831\pi\) | |||||||
\(240\) | −28.5402 | −1.84226 | ||||||||
\(241\) | 11.4891 | 0.740079 | 0.370040 | − | 0.929016i | \(-0.379344\pi\) | ||||
0.370040 | + | 0.929016i | \(0.379344\pi\) | |||||||
\(242\) | 23.8317 | 1.53196 | ||||||||
\(243\) | 14.8329 | 0.951529 | ||||||||
\(244\) | −34.9280 | −2.23604 | ||||||||
\(245\) | −24.4695 | −1.56330 | ||||||||
\(246\) | −14.3594 | −0.915519 | ||||||||
\(247\) | −15.4010 | −0.979944 | ||||||||
\(248\) | −50.6888 | −3.21874 | ||||||||
\(249\) | −2.85621 | −0.181005 | ||||||||
\(250\) | 9.94529 | 0.628995 | ||||||||
\(251\) | 21.4538 | 1.35415 | 0.677075 | − | 0.735914i | \(-0.263247\pi\) | ||||
0.677075 | + | 0.735914i | \(0.263247\pi\) | |||||||
\(252\) | −49.4830 | −3.11714 | ||||||||
\(253\) | −9.24977 | −0.581528 | ||||||||
\(254\) | 24.6772 | 1.54838 | ||||||||
\(255\) | 1.05025 | 0.0657693 | ||||||||
\(256\) | 9.81012 | 0.613133 | ||||||||
\(257\) | 20.2895 | 1.26563 | 0.632813 | − | 0.774304i | \(-0.281900\pi\) | ||||
0.632813 | + | 0.774304i | \(0.281900\pi\) | |||||||
\(258\) | 17.4333 | 1.08535 | ||||||||
\(259\) | 43.3370 | 2.69283 | ||||||||
\(260\) | −64.4985 | −4.00003 | ||||||||
\(261\) | 18.5627 | 1.14900 | ||||||||
\(262\) | 46.6502 | 2.88206 | ||||||||
\(263\) | −23.9610 | −1.47750 | −0.738748 | − | 0.673982i | \(-0.764583\pi\) | ||||
−0.738748 | + | 0.673982i | \(0.764583\pi\) | |||||||
\(264\) | −8.49458 | −0.522805 | ||||||||
\(265\) | 7.93204 | 0.487261 | ||||||||
\(266\) | 41.7794 | 2.56166 | ||||||||
\(267\) | 7.10624 | 0.434895 | ||||||||
\(268\) | −23.2071 | −1.41760 | ||||||||
\(269\) | 18.4345 | 1.12397 | 0.561986 | − | 0.827147i | \(-0.310037\pi\) | ||||
0.561986 | + | 0.827147i | \(0.310037\pi\) | |||||||
\(270\) | −33.9921 | −2.06870 | ||||||||
\(271\) | −4.33208 | −0.263155 | −0.131578 | − | 0.991306i | \(-0.542004\pi\) | ||||
−0.131578 | + | 0.991306i | \(0.542004\pi\) | |||||||
\(272\) | −5.68197 | −0.344520 | ||||||||
\(273\) | 9.75494 | 0.590396 | ||||||||
\(274\) | 21.6764 | 1.30952 | ||||||||
\(275\) | 8.86529 | 0.534597 | ||||||||
\(276\) | −22.7408 | −1.36884 | ||||||||
\(277\) | −31.2168 | −1.87564 | −0.937819 | − | 0.347126i | \(-0.887158\pi\) | ||||
−0.937819 | + | 0.347126i | \(0.887158\pi\) | |||||||
\(278\) | −29.9807 | −1.79812 | ||||||||
\(279\) | −15.0546 | −0.901293 | ||||||||
\(280\) | 107.341 | 6.41487 | ||||||||
\(281\) | 15.9306 | 0.950338 | 0.475169 | − | 0.879895i | \(-0.342387\pi\) | ||||
0.475169 | + | 0.879895i | \(0.342387\pi\) | |||||||
\(282\) | −21.6758 | −1.29077 | ||||||||
\(283\) | 7.44917 | 0.442807 | 0.221404 | − | 0.975182i | \(-0.428936\pi\) | ||||
0.221404 | + | 0.975182i | \(0.428936\pi\) | |||||||
\(284\) | −5.17445 | −0.307047 | ||||||||
\(285\) | 9.46064 | 0.560400 | ||||||||
\(286\) | −14.5222 | −0.858718 | ||||||||
\(287\) | 29.4659 | 1.73932 | ||||||||
\(288\) | 41.1064 | 2.42222 | ||||||||
\(289\) | −16.7909 | −0.987701 | ||||||||
\(290\) | −65.6367 | −3.85432 | ||||||||
\(291\) | −6.54275 | −0.383543 | ||||||||
\(292\) | −39.8683 | −2.33312 | ||||||||
\(293\) | −12.5486 | −0.733097 | −0.366548 | − | 0.930399i | \(-0.619461\pi\) | ||||
−0.366548 | + | 0.930399i | \(0.619461\pi\) | |||||||
\(294\) | −13.5451 | −0.789968 | ||||||||
\(295\) | −27.5684 | −1.60509 | ||||||||
\(296\) | −97.3077 | −5.65589 | ||||||||
\(297\) | −5.51999 | −0.320302 | ||||||||
\(298\) | 48.0388 | 2.78281 | ||||||||
\(299\) | −23.8507 | −1.37932 | ||||||||
\(300\) | 21.7955 | 1.25837 | ||||||||
\(301\) | −35.7737 | −2.06196 | ||||||||
\(302\) | 47.2775 | 2.72051 | ||||||||
\(303\) | −10.6610 | −0.612458 | ||||||||
\(304\) | −51.1830 | −2.93555 | ||||||||
\(305\) | 22.5030 | 1.28852 | ||||||||
\(306\) | −3.09300 | −0.176815 | ||||||||
\(307\) | −5.83419 | −0.332975 | −0.166487 | − | 0.986044i | \(-0.553243\pi\) | ||||
−0.166487 | + | 0.986044i | \(0.553243\pi\) | |||||||
\(308\) | 28.4133 | 1.61900 | ||||||||
\(309\) | 9.28684 | 0.528310 | ||||||||
\(310\) | 53.2322 | 3.02339 | ||||||||
\(311\) | 17.3662 | 0.984747 | 0.492373 | − | 0.870384i | \(-0.336129\pi\) | ||||
0.492373 | + | 0.870384i | \(0.336129\pi\) | |||||||
\(312\) | −21.9035 | −1.24004 | ||||||||
\(313\) | −32.5151 | −1.83786 | −0.918931 | − | 0.394419i | \(-0.870946\pi\) | ||||
−0.918931 | + | 0.394419i | \(0.870946\pi\) | |||||||
\(314\) | −31.3779 | −1.77076 | ||||||||
\(315\) | 31.8803 | 1.79625 | ||||||||
\(316\) | −58.2039 | −3.27423 | ||||||||
\(317\) | −10.7018 | −0.601075 | −0.300537 | − | 0.953770i | \(-0.597166\pi\) | ||||
−0.300537 | + | 0.953770i | \(0.597166\pi\) | |||||||
\(318\) | 4.39080 | 0.246224 | ||||||||
\(319\) | −10.6588 | −0.596776 | ||||||||
\(320\) | −62.5004 | −3.49388 | ||||||||
\(321\) | 12.3118 | 0.687175 | ||||||||
\(322\) | 64.7016 | 3.60568 | ||||||||
\(323\) | 1.88348 | 0.104800 | ||||||||
\(324\) | 25.6305 | 1.42392 | ||||||||
\(325\) | 22.8593 | 1.26801 | ||||||||
\(326\) | −47.6964 | −2.64166 | ||||||||
\(327\) | 3.70594 | 0.204939 | ||||||||
\(328\) | −66.1618 | −3.65318 | ||||||||
\(329\) | 44.4794 | 2.45223 | ||||||||
\(330\) | 8.92081 | 0.491075 | ||||||||
\(331\) | 11.2927 | 0.620700 | 0.310350 | − | 0.950622i | \(-0.399554\pi\) | ||||
0.310350 | + | 0.950622i | \(0.399554\pi\) | |||||||
\(332\) | −21.4516 | −1.17731 | ||||||||
\(333\) | −28.9004 | −1.58373 | ||||||||
\(334\) | −9.89317 | −0.541330 | ||||||||
\(335\) | 14.9516 | 0.816892 | ||||||||
\(336\) | 32.4191 | 1.76861 | ||||||||
\(337\) | 20.1870 | 1.09965 | 0.549827 | − | 0.835279i | \(-0.314694\pi\) | ||||
0.549827 | + | 0.835279i | \(0.314694\pi\) | |||||||
\(338\) | −2.62523 | −0.142794 | ||||||||
\(339\) | −0.688962 | −0.0374193 | ||||||||
\(340\) | 7.88791 | 0.427782 | ||||||||
\(341\) | 8.64439 | 0.468120 | ||||||||
\(342\) | −27.8617 | −1.50659 | ||||||||
\(343\) | 1.28738 | 0.0695118 | ||||||||
\(344\) | 80.3253 | 4.33085 | ||||||||
\(345\) | 14.6512 | 0.788793 | ||||||||
\(346\) | −42.3730 | −2.27798 | ||||||||
\(347\) | −24.3693 | −1.30821 | −0.654107 | − | 0.756402i | \(-0.726955\pi\) | ||||
−0.654107 | + | 0.756402i | \(0.726955\pi\) | |||||||
\(348\) | −26.2048 | −1.40473 | ||||||||
\(349\) | 2.48012 | 0.132758 | 0.0663788 | − | 0.997794i | \(-0.478855\pi\) | ||||
0.0663788 | + | 0.997794i | \(0.478855\pi\) | |||||||
\(350\) | −62.0121 | −3.31469 | ||||||||
\(351\) | −14.2334 | −0.759723 | ||||||||
\(352\) | −23.6034 | −1.25807 | ||||||||
\(353\) | −5.10893 | −0.271921 | −0.135961 | − | 0.990714i | \(-0.543412\pi\) | ||||
−0.135961 | + | 0.990714i | \(0.543412\pi\) | |||||||
\(354\) | −15.2605 | −0.811088 | ||||||||
\(355\) | 3.33373 | 0.176936 | ||||||||
\(356\) | 53.3714 | 2.82868 | ||||||||
\(357\) | −1.19299 | −0.0631397 | ||||||||
\(358\) | 12.3107 | 0.650643 | ||||||||
\(359\) | −9.80284 | −0.517374 | −0.258687 | − | 0.965961i | \(-0.583290\pi\) | ||||
−0.258687 | + | 0.965961i | \(0.583290\pi\) | |||||||
\(360\) | −71.5832 | −3.77276 | ||||||||
\(361\) | −2.03363 | −0.107033 | ||||||||
\(362\) | −8.67910 | −0.456163 | ||||||||
\(363\) | −6.12993 | −0.321738 | ||||||||
\(364\) | 73.2644 | 3.84010 | ||||||||
\(365\) | 25.6859 | 1.34446 | ||||||||
\(366\) | 12.4566 | 0.651117 | ||||||||
\(367\) | 20.5968 | 1.07515 | 0.537573 | − | 0.843217i | \(-0.319341\pi\) | ||||
0.537573 | + | 0.843217i | \(0.319341\pi\) | |||||||
\(368\) | −79.2644 | −4.13194 | ||||||||
\(369\) | −19.6501 | −1.02294 | ||||||||
\(370\) | 102.190 | 5.31262 | ||||||||
\(371\) | −9.01007 | −0.467779 | ||||||||
\(372\) | 21.2525 | 1.10189 | ||||||||
\(373\) | 15.8345 | 0.819880 | 0.409940 | − | 0.912112i | \(-0.365550\pi\) | ||||
0.409940 | + | 0.912112i | \(0.365550\pi\) | |||||||
\(374\) | 1.77601 | 0.0918354 | ||||||||
\(375\) | −2.55811 | −0.132100 | ||||||||
\(376\) | −99.8728 | −5.15055 | ||||||||
\(377\) | −27.4838 | −1.41549 | ||||||||
\(378\) | 38.6120 | 1.98599 | ||||||||
\(379\) | −9.23204 | −0.474218 | −0.237109 | − | 0.971483i | \(-0.576200\pi\) | ||||
−0.237109 | + | 0.971483i | \(0.576200\pi\) | |||||||
\(380\) | 71.0541 | 3.64500 | ||||||||
\(381\) | −6.34741 | −0.325188 | ||||||||
\(382\) | −9.13465 | −0.467369 | ||||||||
\(383\) | −21.1520 | −1.08082 | −0.540409 | − | 0.841403i | \(-0.681730\pi\) | ||||
−0.540409 | + | 0.841403i | \(0.681730\pi\) | |||||||
\(384\) | −12.1679 | −0.620941 | ||||||||
\(385\) | −18.3058 | −0.932950 | ||||||||
\(386\) | 58.6485 | 2.98513 | ||||||||
\(387\) | 23.8566 | 1.21270 | ||||||||
\(388\) | −49.1392 | −2.49467 | ||||||||
\(389\) | −3.13204 | −0.158801 | −0.0794003 | − | 0.996843i | \(-0.525301\pi\) | ||||
−0.0794003 | + | 0.996843i | \(0.525301\pi\) | |||||||
\(390\) | 23.0025 | 1.16478 | ||||||||
\(391\) | 2.91685 | 0.147511 | ||||||||
\(392\) | −62.4103 | −3.15219 | ||||||||
\(393\) | −11.9993 | −0.605283 | ||||||||
\(394\) | −20.0600 | −1.01061 | ||||||||
\(395\) | 37.4989 | 1.88678 | ||||||||
\(396\) | −18.9481 | −0.952180 | ||||||||
\(397\) | 18.4583 | 0.926394 | 0.463197 | − | 0.886255i | \(-0.346702\pi\) | ||||
0.463197 | + | 0.886255i | \(0.346702\pi\) | |||||||
\(398\) | 49.2364 | 2.46800 | ||||||||
\(399\) | −10.7464 | −0.537994 | ||||||||
\(400\) | 75.9696 | 3.79848 | ||||||||
\(401\) | 36.3460 | 1.81503 | 0.907516 | − | 0.420018i | \(-0.137976\pi\) | ||||
0.907516 | + | 0.420018i | \(0.137976\pi\) | |||||||
\(402\) | 8.27649 | 0.412794 | ||||||||
\(403\) | 22.2897 | 1.11033 | ||||||||
\(404\) | −80.0693 | −3.98360 | ||||||||
\(405\) | −16.5129 | −0.820535 | ||||||||
\(406\) | 74.5573 | 3.70022 | ||||||||
\(407\) | 16.5947 | 0.822568 | ||||||||
\(408\) | 2.67871 | 0.132616 | ||||||||
\(409\) | −19.6794 | −0.973083 | −0.486542 | − | 0.873657i | \(-0.661742\pi\) | ||||
−0.486542 | + | 0.873657i | \(0.661742\pi\) | |||||||
\(410\) | 69.4817 | 3.43146 | ||||||||
\(411\) | −5.57555 | −0.275021 | ||||||||
\(412\) | 69.7487 | 3.43627 | ||||||||
\(413\) | 31.3151 | 1.54092 | ||||||||
\(414\) | −43.1478 | −2.12060 | ||||||||
\(415\) | 13.8206 | 0.678425 | ||||||||
\(416\) | −60.8620 | −2.98401 | ||||||||
\(417\) | 7.71158 | 0.377638 | ||||||||
\(418\) | 15.9983 | 0.782501 | ||||||||
\(419\) | −6.27320 | −0.306466 | −0.153233 | − | 0.988190i | \(-0.548968\pi\) | ||||
−0.153233 | + | 0.988190i | \(0.548968\pi\) | |||||||
\(420\) | −45.0053 | −2.19603 | ||||||||
\(421\) | −16.1872 | −0.788915 | −0.394458 | − | 0.918914i | \(-0.629068\pi\) | ||||
−0.394458 | + | 0.918914i | \(0.629068\pi\) | |||||||
\(422\) | −38.5430 | −1.87624 | ||||||||
\(423\) | −29.6622 | −1.44223 | ||||||||
\(424\) | 20.2309 | 0.982502 | ||||||||
\(425\) | −2.79561 | −0.135607 | ||||||||
\(426\) | 1.84540 | 0.0894097 | ||||||||
\(427\) | −25.5614 | −1.23700 | ||||||||
\(428\) | 92.4674 | 4.46958 | ||||||||
\(429\) | 3.73538 | 0.180346 | ||||||||
\(430\) | −84.3558 | −4.06800 | ||||||||
\(431\) | 7.19713 | 0.346674 | 0.173337 | − | 0.984863i | \(-0.444545\pi\) | ||||
0.173337 | + | 0.984863i | \(0.444545\pi\) | |||||||
\(432\) | −47.3026 | −2.27585 | ||||||||
\(433\) | 25.2844 | 1.21509 | 0.607544 | − | 0.794286i | \(-0.292155\pi\) | ||||
0.607544 | + | 0.794286i | \(0.292155\pi\) | |||||||
\(434\) | −60.4669 | −2.90251 | ||||||||
\(435\) | 16.8829 | 0.809475 | ||||||||
\(436\) | 27.8334 | 1.33298 | ||||||||
\(437\) | 26.2749 | 1.25690 | ||||||||
\(438\) | 14.2185 | 0.679386 | ||||||||
\(439\) | 30.5362 | 1.45741 | 0.728706 | − | 0.684827i | \(-0.240122\pi\) | ||||
0.728706 | + | 0.684827i | \(0.240122\pi\) | |||||||
\(440\) | 41.1033 | 1.95952 | ||||||||
\(441\) | −18.5358 | −0.882659 | ||||||||
\(442\) | 4.57949 | 0.217824 | ||||||||
\(443\) | 31.3445 | 1.48922 | 0.744611 | − | 0.667499i | \(-0.232635\pi\) | ||||
0.744611 | + | 0.667499i | \(0.232635\pi\) | |||||||
\(444\) | 40.7985 | 1.93621 | ||||||||
\(445\) | −34.3855 | −1.63003 | ||||||||
\(446\) | 15.8245 | 0.749312 | ||||||||
\(447\) | −12.3564 | −0.584439 | ||||||||
\(448\) | 70.9947 | 3.35419 | ||||||||
\(449\) | −1.33785 | −0.0631372 | −0.0315686 | − | 0.999502i | \(-0.510050\pi\) | ||||
−0.0315686 | + | 0.999502i | \(0.510050\pi\) | |||||||
\(450\) | 41.3543 | 1.94946 | ||||||||
\(451\) | 11.2831 | 0.531302 | ||||||||
\(452\) | −5.17445 | −0.243385 | ||||||||
\(453\) | −12.1606 | −0.571356 | ||||||||
\(454\) | −31.4876 | −1.47779 | ||||||||
\(455\) | −47.2019 | −2.21286 | ||||||||
\(456\) | 24.1297 | 1.12998 | ||||||||
\(457\) | −14.3544 | −0.671469 | −0.335735 | − | 0.941957i | \(-0.608985\pi\) | ||||
−0.335735 | + | 0.941957i | \(0.608985\pi\) | |||||||
\(458\) | −9.44949 | −0.441546 | ||||||||
\(459\) | 1.74069 | 0.0812484 | ||||||||
\(460\) | 110.038 | 5.13053 | ||||||||
\(461\) | −5.97884 | −0.278462 | −0.139231 | − | 0.990260i | \(-0.544463\pi\) | ||||
−0.139231 | + | 0.990260i | \(0.544463\pi\) | |||||||
\(462\) | −10.1332 | −0.471441 | ||||||||
\(463\) | −13.6196 | −0.632959 | −0.316479 | − | 0.948599i | \(-0.602501\pi\) | ||||
−0.316479 | + | 0.948599i | \(0.602501\pi\) | |||||||
\(464\) | −91.3384 | −4.24028 | ||||||||
\(465\) | −13.6923 | −0.634964 | ||||||||
\(466\) | 47.2834 | 2.19036 | ||||||||
\(467\) | −14.1078 | −0.652832 | −0.326416 | − | 0.945226i | \(-0.605841\pi\) | ||||
−0.326416 | + | 0.945226i | \(0.605841\pi\) | |||||||
\(468\) | −48.8582 | −2.25847 | ||||||||
\(469\) | −16.9836 | −0.784231 | ||||||||
\(470\) | 104.884 | 4.83794 | ||||||||
\(471\) | 8.07097 | 0.371891 | ||||||||
\(472\) | −70.3141 | −3.23647 | ||||||||
\(473\) | −13.6986 | −0.629860 | ||||||||
\(474\) | 20.7576 | 0.953430 | ||||||||
\(475\) | −25.1827 | −1.15546 | ||||||||
\(476\) | −8.95995 | −0.410678 | ||||||||
\(477\) | 6.00859 | 0.275114 | ||||||||
\(478\) | 25.5503 | 1.16864 | ||||||||
\(479\) | −14.8749 | −0.679653 | −0.339826 | − | 0.940488i | \(-0.610368\pi\) | ||||
−0.339826 | + | 0.940488i | \(0.610368\pi\) | |||||||
\(480\) | 37.3867 | 1.70646 | ||||||||
\(481\) | 42.7898 | 1.95105 | ||||||||
\(482\) | −30.7738 | −1.40171 | ||||||||
\(483\) | −16.6424 | −0.757255 | ||||||||
\(484\) | −46.0388 | −2.09267 | ||||||||
\(485\) | 31.6589 | 1.43755 | ||||||||
\(486\) | −39.7301 | −1.80219 | ||||||||
\(487\) | −32.2608 | −1.46188 | −0.730938 | − | 0.682443i | \(-0.760917\pi\) | ||||
−0.730938 | + | 0.682443i | \(0.760917\pi\) | |||||||
\(488\) | 57.3947 | 2.59814 | ||||||||
\(489\) | 12.2684 | 0.554795 | ||||||||
\(490\) | 65.5418 | 2.96088 | ||||||||
\(491\) | 7.19456 | 0.324686 | 0.162343 | − | 0.986734i | \(-0.448095\pi\) | ||||
0.162343 | + | 0.986734i | \(0.448095\pi\) | |||||||
\(492\) | 27.7399 | 1.25061 | ||||||||
\(493\) | 3.36116 | 0.151379 | ||||||||
\(494\) | 41.2519 | 1.85601 | ||||||||
\(495\) | 12.2077 | 0.548695 | ||||||||
\(496\) | 74.0766 | 3.32614 | ||||||||
\(497\) | −3.78681 | −0.169862 | ||||||||
\(498\) | 7.65042 | 0.342823 | ||||||||
\(499\) | −34.5718 | −1.54765 | −0.773823 | − | 0.633402i | \(-0.781658\pi\) | ||||
−0.773823 | + | 0.633402i | \(0.781658\pi\) | |||||||
\(500\) | −19.2126 | −0.859215 | ||||||||
\(501\) | 2.54470 | 0.113689 | ||||||||
\(502\) | −57.4642 | −2.56475 | ||||||||
\(503\) | −34.8596 | −1.55431 | −0.777156 | − | 0.629308i | \(-0.783338\pi\) | ||||
−0.777156 | + | 0.629308i | \(0.783338\pi\) | |||||||
\(504\) | 81.3120 | 3.62192 | ||||||||
\(505\) | 51.5861 | 2.29555 | ||||||||
\(506\) | 24.7757 | 1.10141 | ||||||||
\(507\) | 0.675255 | 0.0299891 | ||||||||
\(508\) | −47.6722 | −2.11511 | ||||||||
\(509\) | −8.94075 | −0.396292 | −0.198146 | − | 0.980173i | \(-0.563492\pi\) | ||||
−0.198146 | + | 0.980173i | \(0.563492\pi\) | |||||||
\(510\) | −2.81312 | −0.124567 | ||||||||
\(511\) | −29.1768 | −1.29071 | ||||||||
\(512\) | 9.04589 | 0.399775 | ||||||||
\(513\) | 15.6801 | 0.692292 | ||||||||
\(514\) | −54.3459 | −2.39709 | ||||||||
\(515\) | −44.9369 | −1.98016 | ||||||||
\(516\) | −33.6783 | −1.48260 | ||||||||
\(517\) | 17.0321 | 0.749073 | ||||||||
\(518\) | −116.079 | −5.10021 | ||||||||
\(519\) | 10.8991 | 0.478417 | ||||||||
\(520\) | 105.986 | 4.64779 | ||||||||
\(521\) | −31.6200 | −1.38530 | −0.692648 | − | 0.721276i | \(-0.743556\pi\) | ||||
−0.692648 | + | 0.721276i | \(0.743556\pi\) | |||||||
\(522\) | −49.7204 | −2.17620 | ||||||||
\(523\) | −1.19072 | −0.0520667 | −0.0260333 | − | 0.999661i | \(-0.508288\pi\) | ||||
−0.0260333 | + | 0.999661i | \(0.508288\pi\) | |||||||
\(524\) | −90.1205 | −3.93693 | ||||||||
\(525\) | 15.9506 | 0.696143 | ||||||||
\(526\) | 64.1798 | 2.79837 | ||||||||
\(527\) | −2.72595 | −0.118744 | ||||||||
\(528\) | 12.4140 | 0.540249 | ||||||||
\(529\) | 17.6905 | 0.769153 | ||||||||
\(530\) | −21.2461 | −0.922871 | ||||||||
\(531\) | −20.8833 | −0.906257 | ||||||||
\(532\) | −80.7109 | −3.49926 | ||||||||
\(533\) | 29.0938 | 1.26019 | ||||||||
\(534\) | −19.0342 | −0.823690 | ||||||||
\(535\) | −59.5738 | −2.57560 | ||||||||
\(536\) | 38.1345 | 1.64716 | ||||||||
\(537\) | −3.16654 | −0.136646 | ||||||||
\(538\) | −49.3771 | −2.12880 | ||||||||
\(539\) | 10.6433 | 0.458441 | ||||||||
\(540\) | 65.6671 | 2.82586 | ||||||||
\(541\) | −16.8249 | −0.723359 | −0.361680 | − | 0.932302i | \(-0.617797\pi\) | ||||
−0.361680 | + | 0.932302i | \(0.617797\pi\) | |||||||
\(542\) | 11.6036 | 0.498415 | ||||||||
\(543\) | 2.23242 | 0.0958023 | ||||||||
\(544\) | 7.44318 | 0.319124 | ||||||||
\(545\) | −17.9322 | −0.768130 | ||||||||
\(546\) | −26.1288 | −1.11821 | ||||||||
\(547\) | −37.0439 | −1.58388 | −0.791941 | − | 0.610598i | \(-0.790929\pi\) | ||||
−0.791941 | + | 0.610598i | \(0.790929\pi\) | |||||||
\(548\) | −41.8751 | −1.78882 | ||||||||
\(549\) | 17.0462 | 0.727515 | ||||||||
\(550\) | −23.7458 | −1.01252 | ||||||||
\(551\) | 30.2773 | 1.28985 | ||||||||
\(552\) | 37.3684 | 1.59050 | ||||||||
\(553\) | −42.5954 | −1.81134 | ||||||||
\(554\) | 83.6147 | 3.55245 | ||||||||
\(555\) | −26.2852 | −1.11574 | ||||||||
\(556\) | 57.9178 | 2.45626 | ||||||||
\(557\) | 37.2863 | 1.57987 | 0.789935 | − | 0.613190i | \(-0.210114\pi\) | ||||
0.789935 | + | 0.613190i | \(0.210114\pi\) | |||||||
\(558\) | 40.3239 | 1.70705 | ||||||||
\(559\) | −35.3220 | −1.49396 | ||||||||
\(560\) | −156.869 | −6.62891 | ||||||||
\(561\) | −0.456822 | −0.0192871 | ||||||||
\(562\) | −42.6703 | −1.79994 | ||||||||
\(563\) | 41.0502 | 1.73006 | 0.865031 | − | 0.501719i | \(-0.167299\pi\) | ||||
0.865031 | + | 0.501719i | \(0.167299\pi\) | |||||||
\(564\) | 41.8740 | 1.76321 | ||||||||
\(565\) | 3.33373 | 0.140251 | ||||||||
\(566\) | −19.9527 | −0.838676 | ||||||||
\(567\) | 18.7572 | 0.787728 | ||||||||
\(568\) | 8.50280 | 0.356770 | ||||||||
\(569\) | −27.6922 | −1.16092 | −0.580459 | − | 0.814289i | \(-0.697127\pi\) | ||||
−0.580459 | + | 0.814289i | \(0.697127\pi\) | |||||||
\(570\) | −25.3405 | −1.06140 | ||||||||
\(571\) | −29.6663 | −1.24149 | −0.620747 | − | 0.784011i | \(-0.713171\pi\) | ||||
−0.620747 | + | 0.784011i | \(0.713171\pi\) | |||||||
\(572\) | 28.0546 | 1.17302 | ||||||||
\(573\) | 2.34960 | 0.0981558 | ||||||||
\(574\) | −78.9248 | −3.29426 | ||||||||
\(575\) | −38.9992 | −1.62638 | ||||||||
\(576\) | −47.3446 | −1.97269 | ||||||||
\(577\) | 27.8718 | 1.16032 | 0.580159 | − | 0.814503i | \(-0.302990\pi\) | ||||
0.580159 | + | 0.814503i | \(0.302990\pi\) | |||||||
\(578\) | 44.9747 | 1.87070 | ||||||||
\(579\) | −15.0855 | −0.626930 | ||||||||
\(580\) | 126.799 | 5.26505 | ||||||||
\(581\) | −15.6989 | −0.651300 | ||||||||
\(582\) | 17.5248 | 0.726428 | ||||||||
\(583\) | −3.45015 | −0.142891 | ||||||||
\(584\) | 65.5129 | 2.71094 | ||||||||
\(585\) | 31.4778 | 1.30145 | ||||||||
\(586\) | 33.6116 | 1.38848 | ||||||||
\(587\) | −6.95666 | −0.287132 | −0.143566 | − | 0.989641i | \(-0.545857\pi\) | ||||
−0.143566 | + | 0.989641i | \(0.545857\pi\) | |||||||
\(588\) | 26.1669 | 1.07911 | ||||||||
\(589\) | −24.5553 | −1.01178 | ||||||||
\(590\) | 73.8423 | 3.04004 | ||||||||
\(591\) | 5.15978 | 0.212245 | ||||||||
\(592\) | 142.205 | 5.84461 | ||||||||
\(593\) | −18.3748 | −0.754561 | −0.377280 | − | 0.926099i | \(-0.623141\pi\) | ||||
−0.377280 | + | 0.926099i | \(0.623141\pi\) | |||||||
\(594\) | 14.7854 | 0.606651 | ||||||||
\(595\) | 5.77261 | 0.236654 | ||||||||
\(596\) | −92.8029 | −3.80136 | ||||||||
\(597\) | −12.6645 | −0.518323 | ||||||||
\(598\) | 63.8846 | 2.61243 | ||||||||
\(599\) | 34.7708 | 1.42070 | 0.710348 | − | 0.703851i | \(-0.248538\pi\) | ||||
0.710348 | + | 0.703851i | \(0.248538\pi\) | |||||||
\(600\) | −35.8151 | −1.46214 | ||||||||
\(601\) | 12.8285 | 0.523286 | 0.261643 | − | 0.965165i | \(-0.415736\pi\) | ||||
0.261643 | + | 0.965165i | \(0.415736\pi\) | |||||||
\(602\) | 95.8205 | 3.90535 | ||||||||
\(603\) | 11.3260 | 0.461228 | ||||||||
\(604\) | −91.3322 | −3.71626 | ||||||||
\(605\) | 29.6613 | 1.20591 | ||||||||
\(606\) | 28.5556 | 1.15999 | ||||||||
\(607\) | −46.6434 | −1.89320 | −0.946598 | − | 0.322417i | \(-0.895505\pi\) | ||||
−0.946598 | + | 0.322417i | \(0.895505\pi\) | |||||||
\(608\) | 67.0480 | 2.71915 | ||||||||
\(609\) | −19.1775 | −0.777111 | ||||||||
\(610\) | −60.2746 | −2.44045 | ||||||||
\(611\) | 43.9178 | 1.77672 | ||||||||
\(612\) | 5.97516 | 0.241532 | ||||||||
\(613\) | −2.38315 | −0.0962547 | −0.0481274 | − | 0.998841i | \(-0.515325\pi\) | ||||
−0.0481274 | + | 0.998841i | \(0.515325\pi\) | |||||||
\(614\) | 15.6270 | 0.630653 | ||||||||
\(615\) | −17.8719 | −0.720666 | ||||||||
\(616\) | −46.6896 | −1.88118 | ||||||||
\(617\) | −12.9686 | −0.522096 | −0.261048 | − | 0.965326i | \(-0.584068\pi\) | ||||
−0.261048 | + | 0.965326i | \(0.584068\pi\) | |||||||
\(618\) | −24.8749 | −1.00062 | ||||||||
\(619\) | −5.51505 | −0.221669 | −0.110834 | − | 0.993839i | \(-0.535352\pi\) | ||||
−0.110834 | + | 0.993839i | \(0.535352\pi\) | |||||||
\(620\) | −102.836 | −4.12998 | ||||||||
\(621\) | 24.2829 | 0.974439 | ||||||||
\(622\) | −46.5156 | −1.86511 | ||||||||
\(623\) | 39.0588 | 1.56486 | ||||||||
\(624\) | 32.0097 | 1.28141 | ||||||||
\(625\) | −18.1907 | −0.727629 | ||||||||
\(626\) | 87.0922 | 3.48090 | ||||||||
\(627\) | −4.11504 | −0.164339 | ||||||||
\(628\) | 60.6170 | 2.41888 | ||||||||
\(629\) | −5.23302 | −0.208654 | ||||||||
\(630\) | −85.3920 | −3.40210 | ||||||||
\(631\) | −5.46855 | −0.217699 | −0.108850 | − | 0.994058i | \(-0.534717\pi\) | ||||
−0.108850 | + | 0.994058i | \(0.534717\pi\) | |||||||
\(632\) | 95.6424 | 3.80445 | ||||||||
\(633\) | 9.91394 | 0.394044 | ||||||||
\(634\) | 28.6650 | 1.13843 | ||||||||
\(635\) | 30.7137 | 1.21884 | ||||||||
\(636\) | −8.48229 | −0.336345 | ||||||||
\(637\) | 27.4441 | 1.08738 | ||||||||
\(638\) | 28.5496 | 1.13029 | ||||||||
\(639\) | 2.52533 | 0.0999006 | ||||||||
\(640\) | 58.8778 | 2.32735 | ||||||||
\(641\) | −3.08693 | −0.121927 | −0.0609633 | − | 0.998140i | \(-0.519417\pi\) | ||||
−0.0609633 | + | 0.998140i | \(0.519417\pi\) | |||||||
\(642\) | −32.9772 | −1.30151 | ||||||||
\(643\) | −29.0813 | −1.14685 | −0.573427 | − | 0.819257i | \(-0.694386\pi\) | ||||
−0.573427 | + | 0.819257i | \(0.694386\pi\) | |||||||
\(644\) | −124.993 | −4.92540 | ||||||||
\(645\) | 21.6978 | 0.854351 | ||||||||
\(646\) | −5.04494 | −0.198491 | ||||||||
\(647\) | 6.81408 | 0.267889 | 0.133944 | − | 0.990989i | \(-0.457236\pi\) | ||||
0.133944 | + | 0.990989i | \(0.457236\pi\) | |||||||
\(648\) | −42.1169 | −1.65451 | ||||||||
\(649\) | 11.9913 | 0.470698 | ||||||||
\(650\) | −61.2291 | −2.40160 | ||||||||
\(651\) | 15.5532 | 0.609577 | ||||||||
\(652\) | 92.1415 | 3.60854 | ||||||||
\(653\) | −27.2333 | −1.06572 | −0.532860 | − | 0.846203i | \(-0.678883\pi\) | ||||
−0.532860 | + | 0.846203i | \(0.678883\pi\) | |||||||
\(654\) | −9.92641 | −0.388153 | ||||||||
\(655\) | 58.0618 | 2.26866 | ||||||||
\(656\) | 96.6889 | 3.77507 | ||||||||
\(657\) | 19.4573 | 0.759102 | ||||||||
\(658\) | −119.139 | −4.64451 | ||||||||
\(659\) | −28.3944 | −1.10609 | −0.553045 | − | 0.833151i | \(-0.686534\pi\) | ||||
−0.553045 | + | 0.833151i | \(0.686534\pi\) | |||||||
\(660\) | −17.2335 | −0.670814 | ||||||||
\(661\) | 0.134294 | 0.00522343 | 0.00261172 | − | 0.999997i | \(-0.499169\pi\) | ||||
0.00261172 | + | 0.999997i | \(0.499169\pi\) | |||||||
\(662\) | −30.2475 | −1.17560 | ||||||||
\(663\) | −1.17793 | −0.0457469 | ||||||||
\(664\) | 35.2499 | 1.36796 | ||||||||
\(665\) | 51.9995 | 2.01645 | ||||||||
\(666\) | 77.4101 | 2.99958 | ||||||||
\(667\) | 46.8888 | 1.81554 | ||||||||
\(668\) | 19.1120 | 0.739464 | ||||||||
\(669\) | −4.07035 | −0.157369 | ||||||||
\(670\) | −40.0480 | −1.54719 | ||||||||
\(671\) | −9.78801 | −0.377862 | ||||||||
\(672\) | −42.4679 | −1.63823 | ||||||||
\(673\) | 26.6102 | 1.02575 | 0.512874 | − | 0.858464i | \(-0.328581\pi\) | ||||
0.512874 | + | 0.858464i | \(0.328581\pi\) | |||||||
\(674\) | −54.0711 | −2.08274 | ||||||||
\(675\) | −23.2735 | −0.895799 | ||||||||
\(676\) | 5.07150 | 0.195058 | ||||||||
\(677\) | 10.4269 | 0.400737 | 0.200368 | − | 0.979721i | \(-0.435786\pi\) | ||||
0.200368 | + | 0.979721i | \(0.435786\pi\) | |||||||
\(678\) | 1.84540 | 0.0708720 | ||||||||
\(679\) | −35.9616 | −1.38008 | ||||||||
\(680\) | −12.9616 | −0.497056 | ||||||||
\(681\) | 8.09919 | 0.310362 | ||||||||
\(682\) | −23.1541 | −0.886617 | ||||||||
\(683\) | −31.9126 | −1.22110 | −0.610551 | − | 0.791977i | \(-0.709052\pi\) | ||||
−0.610551 | + | 0.791977i | \(0.709052\pi\) | |||||||
\(684\) | 53.8241 | 2.05802 | ||||||||
\(685\) | 26.9788 | 1.03081 | ||||||||
\(686\) | −3.44826 | −0.131655 | ||||||||
\(687\) | 2.43058 | 0.0927323 | ||||||||
\(688\) | −117.387 | −4.47535 | ||||||||
\(689\) | −8.89630 | −0.338922 | ||||||||
\(690\) | −39.2434 | −1.49397 | ||||||||
\(691\) | 37.3120 | 1.41942 | 0.709708 | − | 0.704496i | \(-0.248827\pi\) | ||||
0.709708 | + | 0.704496i | \(0.248827\pi\) | |||||||
\(692\) | 81.8575 | 3.11175 | ||||||||
\(693\) | −13.8668 | −0.526757 | ||||||||
\(694\) | 65.2736 | 2.47775 | ||||||||
\(695\) | −37.3146 | −1.41542 | ||||||||
\(696\) | 43.0605 | 1.63221 | ||||||||
\(697\) | −3.55806 | −0.134771 | ||||||||
\(698\) | −6.64303 | −0.251442 | ||||||||
\(699\) | −12.1621 | −0.460014 | ||||||||
\(700\) | 119.797 | 4.52791 | ||||||||
\(701\) | −21.1421 | −0.798524 | −0.399262 | − | 0.916837i | \(-0.630734\pi\) | ||||
−0.399262 | + | 0.916837i | \(0.630734\pi\) | |||||||
\(702\) | 38.1244 | 1.43891 | ||||||||
\(703\) | −47.1389 | −1.77788 | ||||||||
\(704\) | 27.1854 | 1.02459 | ||||||||
\(705\) | −26.9781 | −1.01605 | ||||||||
\(706\) | 13.6844 | 0.515017 | ||||||||
\(707\) | −58.5971 | −2.20377 | ||||||||
\(708\) | 29.4808 | 1.10796 | ||||||||
\(709\) | 18.2110 | 0.683929 | 0.341965 | − | 0.939713i | \(-0.388908\pi\) | ||||
0.341965 | + | 0.939713i | \(0.388908\pi\) | |||||||
\(710\) | −8.92945 | −0.335116 | ||||||||
\(711\) | 28.4058 | 1.06530 | ||||||||
\(712\) | −87.7015 | −3.28675 | ||||||||
\(713\) | −38.0274 | −1.42414 | ||||||||
\(714\) | 3.19544 | 0.119586 | ||||||||
\(715\) | −18.0747 | −0.675954 | ||||||||
\(716\) | −23.7823 | −0.888787 | ||||||||
\(717\) | −6.57200 | −0.245436 | ||||||||
\(718\) | 26.2571 | 0.979905 | ||||||||
\(719\) | 12.7240 | 0.474526 | 0.237263 | − | 0.971445i | \(-0.423750\pi\) | ||||
0.237263 | + | 0.971445i | \(0.423750\pi\) | |||||||
\(720\) | 104.612 | 3.89865 | ||||||||
\(721\) | 51.0442 | 1.90099 | ||||||||
\(722\) | 5.44710 | 0.202720 | ||||||||
\(723\) | 7.91557 | 0.294383 | ||||||||
\(724\) | 16.7666 | 0.623125 | ||||||||
\(725\) | −44.9397 | −1.66902 | ||||||||
\(726\) | 16.4191 | 0.609371 | ||||||||
\(727\) | −25.9533 | −0.962554 | −0.481277 | − | 0.876568i | \(-0.659827\pi\) | ||||
−0.481277 | + | 0.876568i | \(0.659827\pi\) | |||||||
\(728\) | −120.390 | −4.46196 | ||||||||
\(729\) | −4.64059 | −0.171874 | ||||||||
\(730\) | −68.8001 | −2.54641 | ||||||||
\(731\) | 4.31974 | 0.159771 | ||||||||
\(732\) | −24.0641 | −0.889434 | ||||||||
\(733\) | 29.1624 | 1.07714 | 0.538569 | − | 0.842581i | \(-0.318965\pi\) | ||||
0.538569 | + | 0.842581i | \(0.318965\pi\) | |||||||
\(734\) | −55.1689 | −2.03632 | ||||||||
\(735\) | −16.8585 | −0.621836 | ||||||||
\(736\) | 103.834 | 3.82736 | ||||||||
\(737\) | −6.50340 | −0.239556 | ||||||||
\(738\) | 52.6330 | 1.93745 | ||||||||
\(739\) | −33.0764 | −1.21674 | −0.608368 | − | 0.793655i | \(-0.708176\pi\) | ||||
−0.608368 | + | 0.793655i | \(0.708176\pi\) | |||||||
\(740\) | −197.415 | −7.25711 | ||||||||
\(741\) | −10.6107 | −0.389795 | ||||||||
\(742\) | 24.1336 | 0.885973 | ||||||||
\(743\) | −16.7457 | −0.614340 | −0.307170 | − | 0.951655i | \(-0.599382\pi\) | ||||
−0.307170 | + | 0.951655i | \(0.599382\pi\) | |||||||
\(744\) | −34.9227 | −1.28033 | ||||||||
\(745\) | 59.7900 | 2.19054 | ||||||||
\(746\) | −42.4130 | −1.55285 | ||||||||
\(747\) | 10.4692 | 0.383048 | ||||||||
\(748\) | −3.43096 | −0.125448 | ||||||||
\(749\) | 67.6704 | 2.47262 | ||||||||
\(750\) | 6.85193 | 0.250197 | ||||||||
\(751\) | 31.7810 | 1.15971 | 0.579853 | − | 0.814721i | \(-0.303110\pi\) | ||||
0.579853 | + | 0.814721i | \(0.303110\pi\) | |||||||
\(752\) | 145.954 | 5.32240 | ||||||||
\(753\) | 14.7808 | 0.538643 | ||||||||
\(754\) | 73.6159 | 2.68093 | ||||||||
\(755\) | 58.8425 | 2.14150 | ||||||||
\(756\) | −74.5919 | −2.71288 | ||||||||
\(757\) | −27.1125 | −0.985422 | −0.492711 | − | 0.870193i | \(-0.663994\pi\) | ||||
−0.492711 | + | 0.870193i | \(0.663994\pi\) | |||||||
\(758\) | 24.7282 | 0.898167 | ||||||||
\(759\) | −6.37274 | −0.231316 | ||||||||
\(760\) | −116.758 | −4.23526 | ||||||||
\(761\) | 8.76202 | 0.317623 | 0.158812 | − | 0.987309i | \(-0.449234\pi\) | ||||
0.158812 | + | 0.987309i | \(0.449234\pi\) | |||||||
\(762\) | 17.0016 | 0.615904 | ||||||||
\(763\) | 20.3693 | 0.737419 | ||||||||
\(764\) | 17.6466 | 0.638432 | ||||||||
\(765\) | −3.84961 | −0.139183 | ||||||||
\(766\) | 56.6560 | 2.04707 | ||||||||
\(767\) | 30.9197 | 1.11645 | ||||||||
\(768\) | 6.75880 | 0.243887 | ||||||||
\(769\) | 50.1723 | 1.80926 | 0.904630 | − | 0.426199i | \(-0.140148\pi\) | ||||
0.904630 | + | 0.426199i | \(0.140148\pi\) | |||||||
\(770\) | 49.0324 | 1.76700 | ||||||||
\(771\) | 13.9787 | 0.503432 | ||||||||
\(772\) | −113.299 | −4.07773 | ||||||||
\(773\) | −42.9464 | −1.54467 | −0.772337 | − | 0.635213i | \(-0.780912\pi\) | ||||
−0.772337 | + | 0.635213i | \(0.780912\pi\) | |||||||
\(774\) | −63.9003 | −2.29685 | ||||||||
\(775\) | 36.4467 | 1.30920 | ||||||||
\(776\) | 80.7471 | 2.89865 | ||||||||
\(777\) | 29.8576 | 1.07113 | ||||||||
\(778\) | 8.38921 | 0.300768 | ||||||||
\(779\) | −32.0509 | −1.14834 | ||||||||
\(780\) | −44.4370 | −1.59110 | ||||||||
\(781\) | −1.45005 | −0.0518870 | ||||||||
\(782\) | −7.81283 | −0.279386 | ||||||||
\(783\) | 27.9818 | 0.999988 | ||||||||
\(784\) | 91.2064 | 3.25737 | ||||||||
\(785\) | −39.0536 | −1.39388 | ||||||||
\(786\) | 32.1402 | 1.14640 | ||||||||
\(787\) | 22.8026 | 0.812826 | 0.406413 | − | 0.913689i | \(-0.366779\pi\) | ||||
0.406413 | + | 0.913689i | \(0.366779\pi\) | |||||||
\(788\) | 38.7525 | 1.38050 | ||||||||
\(789\) | −16.5082 | −0.587707 | ||||||||
\(790\) | −100.441 | −3.57355 | ||||||||
\(791\) | −3.78681 | −0.134644 | ||||||||
\(792\) | 31.1361 | 1.10637 | ||||||||
\(793\) | −25.2386 | −0.896249 | ||||||||
\(794\) | −49.4408 | −1.75459 | ||||||||
\(795\) | 5.46487 | 0.193819 | ||||||||
\(796\) | −95.1165 | −3.37131 | ||||||||
\(797\) | −47.0794 | −1.66764 | −0.833818 | − | 0.552039i | \(-0.813850\pi\) | ||||
−0.833818 | + | 0.552039i | \(0.813850\pi\) | |||||||
\(798\) | 28.7845 | 1.01896 | ||||||||
\(799\) | −5.37097 | −0.190011 | ||||||||
\(800\) | −99.5175 | −3.51848 | ||||||||
\(801\) | −26.0473 | −0.920337 | ||||||||
\(802\) | −97.3533 | −3.43766 | ||||||||
\(803\) | −11.1725 | −0.394267 | ||||||||
\(804\) | −15.9888 | −0.563881 | ||||||||
\(805\) | 80.5288 | 2.83827 | ||||||||
\(806\) | −59.7034 | −2.10296 | ||||||||
\(807\) | 12.7007 | 0.447085 | ||||||||
\(808\) | 131.572 | 4.62870 | ||||||||
\(809\) | 2.36449 | 0.0831309 | 0.0415655 | − | 0.999136i | \(-0.486765\pi\) | ||||
0.0415655 | + | 0.999136i | \(0.486765\pi\) | |||||||
\(810\) | 44.2302 | 1.55409 | ||||||||
\(811\) | 0.354600 | 0.0124517 | 0.00622585 | − | 0.999981i | \(-0.498018\pi\) | ||||
0.00622585 | + | 0.999981i | \(0.498018\pi\) | |||||||
\(812\) | −144.032 | −5.05454 | ||||||||
\(813\) | −2.98464 | −0.104676 | ||||||||
\(814\) | −44.4491 | −1.55794 | ||||||||
\(815\) | −59.3638 | −2.07942 | ||||||||
\(816\) | −3.91466 | −0.137041 | ||||||||
\(817\) | 38.9121 | 1.36136 | ||||||||
\(818\) | 52.7116 | 1.84302 | ||||||||
\(819\) | −35.7559 | −1.24941 | ||||||||
\(820\) | −134.227 | −4.68741 | ||||||||
\(821\) | 47.9186 | 1.67237 | 0.836186 | − | 0.548447i | \(-0.184781\pi\) | ||||
0.836186 | + | 0.548447i | \(0.184781\pi\) | |||||||
\(822\) | 14.9342 | 0.520890 | ||||||||
\(823\) | −39.1141 | −1.36343 | −0.681716 | − | 0.731617i | \(-0.738766\pi\) | ||||
−0.681716 | + | 0.731617i | \(0.738766\pi\) | |||||||
\(824\) | −114.613 | −3.99274 | ||||||||
\(825\) | 6.10785 | 0.212648 | ||||||||
\(826\) | −83.8781 | −2.91849 | ||||||||
\(827\) | −26.7323 | −0.929574 | −0.464787 | − | 0.885422i | \(-0.653869\pi\) | ||||
−0.464787 | + | 0.885422i | \(0.653869\pi\) | |||||||
\(828\) | 83.3545 | 2.89677 | ||||||||
\(829\) | −36.6354 | −1.27240 | −0.636200 | − | 0.771524i | \(-0.719495\pi\) | ||||
−0.636200 | + | 0.771524i | \(0.719495\pi\) | |||||||
\(830\) | −37.0186 | −1.28493 | ||||||||
\(831\) | −21.5072 | −0.746077 | ||||||||
\(832\) | 70.0983 | 2.43022 | ||||||||
\(833\) | −3.35630 | −0.116289 | ||||||||
\(834\) | −20.6556 | −0.715244 | ||||||||
\(835\) | −12.3132 | −0.426117 | ||||||||
\(836\) | −30.9060 | −1.06891 | ||||||||
\(837\) | −22.6936 | −0.784406 | ||||||||
\(838\) | 16.8029 | 0.580445 | ||||||||
\(839\) | 9.12535 | 0.315042 | 0.157521 | − | 0.987516i | \(-0.449650\pi\) | ||||
0.157521 | + | 0.987516i | \(0.449650\pi\) | |||||||
\(840\) | 73.9541 | 2.55166 | ||||||||
\(841\) | 25.0311 | 0.863143 | ||||||||
\(842\) | 43.3576 | 1.49420 | ||||||||
\(843\) | 10.9756 | 0.378018 | ||||||||
\(844\) | 74.4586 | 2.56297 | ||||||||
\(845\) | −3.26741 | −0.112402 | ||||||||
\(846\) | 79.4507 | 2.73157 | ||||||||
\(847\) | −33.6926 | −1.15769 | ||||||||
\(848\) | −29.5655 | −1.01528 | ||||||||
\(849\) | 5.13220 | 0.176137 | ||||||||
\(850\) | 7.48808 | 0.256839 | ||||||||
\(851\) | −73.0015 | −2.50246 | ||||||||
\(852\) | −3.56500 | −0.122135 | ||||||||
\(853\) | 33.9057 | 1.16091 | 0.580455 | − | 0.814292i | \(-0.302875\pi\) | ||||
0.580455 | + | 0.814292i | \(0.302875\pi\) | |||||||
\(854\) | 68.4665 | 2.34288 | ||||||||
\(855\) | −34.6772 | −1.18593 | ||||||||
\(856\) | −151.945 | −5.19338 | ||||||||
\(857\) | 22.6440 | 0.773505 | 0.386752 | − | 0.922184i | \(-0.373597\pi\) | ||||
0.386752 | + | 0.922184i | \(0.373597\pi\) | |||||||
\(858\) | −10.0053 | −0.341575 | ||||||||
\(859\) | 46.2344 | 1.57750 | 0.788748 | − | 0.614717i | \(-0.210730\pi\) | ||||
0.788748 | + | 0.614717i | \(0.210730\pi\) | |||||||
\(860\) | 162.961 | 5.55694 | ||||||||
\(861\) | 20.3009 | 0.691852 | ||||||||
\(862\) | −19.2776 | −0.656599 | ||||||||
\(863\) | 9.03043 | 0.307399 | 0.153700 | − | 0.988118i | \(-0.450881\pi\) | ||||
0.153700 | + | 0.988118i | \(0.450881\pi\) | |||||||
\(864\) | 61.9648 | 2.10808 | ||||||||
\(865\) | −52.7382 | −1.79315 | ||||||||
\(866\) | −67.7245 | −2.30137 | ||||||||
\(867\) | −11.5683 | −0.392880 | ||||||||
\(868\) | 116.812 | 3.96486 | ||||||||
\(869\) | −16.3107 | −0.553303 | ||||||||
\(870\) | −45.2212 | −1.53314 | ||||||||
\(871\) | −16.7692 | −0.568202 | ||||||||
\(872\) | −45.7367 | −1.54884 | ||||||||
\(873\) | 23.9819 | 0.811663 | ||||||||
\(874\) | −70.3777 | −2.38056 | ||||||||
\(875\) | −14.0604 | −0.475328 | ||||||||
\(876\) | −27.4678 | −0.928050 | ||||||||
\(877\) | 1.89433 | 0.0639671 | 0.0319836 | − | 0.999488i | \(-0.489818\pi\) | ||||
0.0319836 | + | 0.999488i | \(0.489818\pi\) | |||||||
\(878\) | −81.7916 | −2.76033 | ||||||||
\(879\) | −8.64551 | −0.291606 | ||||||||
\(880\) | −60.0684 | −2.02491 | ||||||||
\(881\) | −42.2893 | −1.42476 | −0.712381 | − | 0.701793i | \(-0.752383\pi\) | ||||
−0.712381 | + | 0.701793i | \(0.752383\pi\) | |||||||
\(882\) | 49.6485 | 1.67175 | ||||||||
\(883\) | −12.4612 | −0.419354 | −0.209677 | − | 0.977771i | \(-0.567241\pi\) | ||||
−0.209677 | + | 0.977771i | \(0.567241\pi\) | |||||||
\(884\) | −8.84681 | −0.297550 | ||||||||
\(885\) | −18.9936 | −0.638461 | ||||||||
\(886\) | −83.9567 | −2.82058 | ||||||||
\(887\) | −20.4076 | −0.685219 | −0.342609 | − | 0.939478i | \(-0.611311\pi\) | ||||
−0.342609 | + | 0.939478i | \(0.611311\pi\) | |||||||
\(888\) | −67.0413 | −2.24976 | ||||||||
\(889\) | −34.8879 | −1.17010 | ||||||||
\(890\) | 92.1021 | 3.08727 | ||||||||
\(891\) | 7.18254 | 0.240624 | ||||||||
\(892\) | −30.5703 | −1.02357 | ||||||||
\(893\) | −48.3815 | −1.61903 | ||||||||
\(894\) | 33.0969 | 1.10693 | ||||||||
\(895\) | 15.3222 | 0.512164 | ||||||||
\(896\) | −66.8798 | −2.23430 | ||||||||
\(897\) | −16.4323 | −0.548657 | ||||||||
\(898\) | 3.58346 | 0.119582 | ||||||||
\(899\) | −43.8200 | −1.46148 | ||||||||
\(900\) | −79.8897 | −2.66299 | ||||||||
\(901\) | 1.08798 | 0.0362459 | ||||||||
\(902\) | −30.2221 | −1.00628 | ||||||||
\(903\) | −24.6468 | −0.820193 | ||||||||
\(904\) | 8.50280 | 0.282799 | ||||||||
\(905\) | −10.8022 | −0.359076 | ||||||||
\(906\) | 32.5724 | 1.08215 | ||||||||
\(907\) | 13.8214 | 0.458931 | 0.229465 | − | 0.973317i | \(-0.426302\pi\) | ||||
0.229465 | + | 0.973317i | \(0.426302\pi\) | |||||||
\(908\) | 60.8289 | 2.01868 | ||||||||
\(909\) | 39.0769 | 1.29610 | ||||||||
\(910\) | 126.431 | 4.19115 | ||||||||
\(911\) | −42.3017 | −1.40152 | −0.700759 | − | 0.713398i | \(-0.747155\pi\) | ||||
−0.700759 | + | 0.713398i | \(0.747155\pi\) | |||||||
\(912\) | −35.2632 | −1.16768 | ||||||||
\(913\) | −6.01146 | −0.198950 | ||||||||
\(914\) | 38.4484 | 1.27176 | ||||||||
\(915\) | 15.5037 | 0.512537 | ||||||||
\(916\) | 18.2548 | 0.603157 | ||||||||
\(917\) | −65.9529 | −2.17796 | ||||||||
\(918\) | −4.66246 | −0.153884 | ||||||||
\(919\) | −47.5567 | −1.56875 | −0.784376 | − | 0.620286i | \(-0.787016\pi\) | ||||
−0.784376 | + | 0.620286i | \(0.787016\pi\) | |||||||
\(920\) | −180.817 | −5.96136 | ||||||||
\(921\) | −4.01954 | −0.132448 | ||||||||
\(922\) | 16.0144 | 0.527406 | ||||||||
\(923\) | −3.73900 | −0.123071 | ||||||||
\(924\) | 19.5757 | 0.643994 | ||||||||
\(925\) | 69.9670 | 2.30050 | ||||||||
\(926\) | 36.4804 | 1.19882 | ||||||||
\(927\) | −34.0401 | −1.11802 | ||||||||
\(928\) | 119.650 | 3.92771 | ||||||||
\(929\) | −40.6423 | −1.33343 | −0.666716 | − | 0.745312i | \(-0.732301\pi\) | ||||
−0.666716 | + | 0.745312i | \(0.732301\pi\) | |||||||
\(930\) | 36.6750 | 1.20262 | ||||||||
\(931\) | −30.2335 | −0.990863 | ||||||||
\(932\) | −91.3436 | −2.99206 | ||||||||
\(933\) | 11.9647 | 0.391705 | ||||||||
\(934\) | 37.7880 | 1.23646 | ||||||||
\(935\) | 2.21046 | 0.0722897 | ||||||||
\(936\) | 80.2852 | 2.62420 | ||||||||
\(937\) | −36.6631 | −1.19773 | −0.598866 | − | 0.800849i | \(-0.704382\pi\) | ||||
−0.598866 | + | 0.800849i | \(0.704382\pi\) | |||||||
\(938\) | 45.4909 | 1.48533 | ||||||||
\(939\) | −22.4017 | −0.731051 | ||||||||
\(940\) | −202.619 | −6.60869 | ||||||||
\(941\) | −40.8944 | −1.33312 | −0.666560 | − | 0.745452i | \(-0.732234\pi\) | ||||
−0.666560 | + | 0.745452i | \(0.732234\pi\) | |||||||
\(942\) | −21.6182 | −0.704359 | ||||||||
\(943\) | −49.6355 | −1.61635 | ||||||||
\(944\) | 102.757 | 3.34446 | ||||||||
\(945\) | 48.0572 | 1.56330 | ||||||||
\(946\) | 36.6918 | 1.19295 | ||||||||
\(947\) | 6.80385 | 0.221095 | 0.110548 | − | 0.993871i | \(-0.464740\pi\) | ||||
0.110548 | + | 0.993871i | \(0.464740\pi\) | |||||||
\(948\) | −40.1003 | −1.30240 | ||||||||
\(949\) | −28.8084 | −0.935161 | ||||||||
\(950\) | 67.4524 | 2.18844 | ||||||||
\(951\) | −7.37316 | −0.239091 | ||||||||
\(952\) | 14.7232 | 0.477183 | ||||||||
\(953\) | −5.91109 | −0.191479 | −0.0957395 | − | 0.995406i | \(-0.530522\pi\) | ||||
−0.0957395 | + | 0.995406i | \(0.530522\pi\) | |||||||
\(954\) | −16.0941 | −0.521066 | ||||||||
\(955\) | −11.3692 | −0.367897 | ||||||||
\(956\) | −49.3590 | −1.59638 | ||||||||
\(957\) | −7.34348 | −0.237381 | ||||||||
\(958\) | 39.8427 | 1.28726 | ||||||||
\(959\) | −30.6454 | −0.989593 | ||||||||
\(960\) | −43.0604 | −1.38977 | ||||||||
\(961\) | 4.53855 | 0.146405 | ||||||||
\(962\) | −114.613 | −3.69528 | ||||||||
\(963\) | −45.1277 | −1.45422 | ||||||||
\(964\) | 59.4498 | 1.91475 | ||||||||
\(965\) | 72.9951 | 2.34979 | ||||||||
\(966\) | 44.5769 | 1.43424 | ||||||||
\(967\) | −55.9694 | −1.79986 | −0.899928 | − | 0.436038i | \(-0.856381\pi\) | ||||
−0.899928 | + | 0.436038i | \(0.856381\pi\) | |||||||
\(968\) | 75.6523 | 2.43156 | ||||||||
\(969\) | 1.29765 | 0.0416865 | ||||||||
\(970\) | −84.7987 | −2.72272 | ||||||||
\(971\) | −30.9489 | −0.993197 | −0.496599 | − | 0.867980i | \(-0.665418\pi\) | ||||
−0.496599 | + | 0.867980i | \(0.665418\pi\) | |||||||
\(972\) | 76.7518 | 2.46182 | ||||||||
\(973\) | 42.3860 | 1.35883 | ||||||||
\(974\) | 86.4111 | 2.76879 | ||||||||
\(975\) | 15.7492 | 0.504379 | ||||||||
\(976\) | −83.8767 | −2.68483 | ||||||||
\(977\) | −41.9756 | −1.34292 | −0.671460 | − | 0.741041i | \(-0.734332\pi\) | ||||
−0.671460 | + | 0.741041i | \(0.734332\pi\) | |||||||
\(978\) | −32.8610 | −1.05078 | ||||||||
\(979\) | 14.9565 | 0.478011 | ||||||||
\(980\) | −126.616 | −4.04460 | ||||||||
\(981\) | −13.5838 | −0.433697 | ||||||||
\(982\) | −19.2707 | −0.614954 | ||||||||
\(983\) | −24.4535 | −0.779944 | −0.389972 | − | 0.920827i | \(-0.627515\pi\) | ||||
−0.389972 | + | 0.920827i | \(0.627515\pi\) | |||||||
\(984\) | −45.5830 | −1.45313 | ||||||||
\(985\) | −24.9670 | −0.795515 | ||||||||
\(986\) | −9.00293 | −0.286712 | ||||||||
\(987\) | 30.6446 | 0.975429 | ||||||||
\(988\) | −79.6918 | −2.53533 | ||||||||
\(989\) | 60.2611 | 1.91619 | ||||||||
\(990\) | −32.6985 | −1.03923 | ||||||||
\(991\) | −13.3971 | −0.425574 | −0.212787 | − | 0.977099i | \(-0.568254\pi\) | ||||
−0.212787 | + | 0.977099i | \(0.568254\pi\) | |||||||
\(992\) | −97.0378 | −3.08095 | ||||||||
\(993\) | 7.78021 | 0.246898 | ||||||||
\(994\) | 10.1430 | 0.321718 | ||||||||
\(995\) | 61.2805 | 1.94272 | ||||||||
\(996\) | −14.7793 | −0.468301 | ||||||||
\(997\) | −31.6661 | −1.00287 | −0.501437 | − | 0.865194i | \(-0.667195\pi\) | ||||
−0.501437 | + | 0.865194i | \(0.667195\pi\) | |||||||
\(998\) | 92.6011 | 2.93124 | ||||||||
\(999\) | −43.5651 | −1.37834 |
(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 | 8023.2.a.c.1.9 | ✓ | 158 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8023.2.a.c.1.9 | ✓ | 158 | 1.1 | even | 1 | trivial |