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: | \(0\) |
Dimension: | \(165\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.52899 | −1.78826 | −0.894132 | − | 0.447804i | \(-0.852206\pi\) | ||||
−0.894132 | + | 0.447804i | \(0.852206\pi\) | |||||||
\(3\) | 1.55552 | 0.898078 | 0.449039 | − | 0.893512i | \(-0.351766\pi\) | ||||
0.449039 | + | 0.893512i | \(0.351766\pi\) | |||||||
\(4\) | 4.39577 | 2.19788 | ||||||||
\(5\) | −1.46602 | −0.655624 | −0.327812 | − | 0.944743i | \(-0.606311\pi\) | ||||
−0.327812 | + | 0.944743i | \(0.606311\pi\) | |||||||
\(6\) | −3.93388 | −1.60600 | ||||||||
\(7\) | 0.126533 | 0.0478251 | 0.0239125 | − | 0.999714i | \(-0.492388\pi\) | ||||
0.0239125 | + | 0.999714i | \(0.492388\pi\) | |||||||
\(8\) | −6.05887 | −2.14213 | ||||||||
\(9\) | −0.580366 | −0.193455 | ||||||||
\(10\) | 3.70754 | 1.17243 | ||||||||
\(11\) | −4.01915 | −1.21182 | −0.605909 | − | 0.795534i | \(-0.707191\pi\) | ||||
−0.605909 | + | 0.795534i | \(0.707191\pi\) | |||||||
\(12\) | 6.83770 | 1.97387 | ||||||||
\(13\) | −5.72744 | −1.58851 | −0.794253 | − | 0.607587i | \(-0.792138\pi\) | ||||
−0.794253 | + | 0.607587i | \(0.792138\pi\) | |||||||
\(14\) | −0.320001 | −0.0855238 | ||||||||
\(15\) | −2.28042 | −0.588801 | ||||||||
\(16\) | 6.53125 | 1.63281 | ||||||||
\(17\) | −2.33060 | −0.565253 | −0.282626 | − | 0.959230i | \(-0.591206\pi\) | ||||
−0.282626 | + | 0.959230i | \(0.591206\pi\) | |||||||
\(18\) | 1.46774 | 0.345949 | ||||||||
\(19\) | −5.14352 | −1.18000 | −0.590002 | − | 0.807402i | \(-0.700873\pi\) | ||||
−0.590002 | + | 0.807402i | \(0.700873\pi\) | |||||||
\(20\) | −6.44428 | −1.44099 | ||||||||
\(21\) | 0.196825 | 0.0429507 | ||||||||
\(22\) | 10.1644 | 2.16705 | ||||||||
\(23\) | −2.19537 | −0.457767 | −0.228884 | − | 0.973454i | \(-0.573508\pi\) | ||||
−0.228884 | + | 0.973454i | \(0.573508\pi\) | |||||||
\(24\) | −9.42467 | −1.92380 | ||||||||
\(25\) | −2.85079 | −0.570158 | ||||||||
\(26\) | 14.4846 | 2.84067 | ||||||||
\(27\) | −5.56932 | −1.07182 | ||||||||
\(28\) | 0.556211 | 0.105114 | ||||||||
\(29\) | 5.20671 | 0.966862 | 0.483431 | − | 0.875382i | \(-0.339390\pi\) | ||||
0.483431 | + | 0.875382i | \(0.339390\pi\) | |||||||
\(30\) | 5.76715 | 1.05293 | ||||||||
\(31\) | 8.59587 | 1.54386 | 0.771932 | − | 0.635705i | \(-0.219291\pi\) | ||||
0.771932 | + | 0.635705i | \(0.219291\pi\) | |||||||
\(32\) | −4.39971 | −0.777766 | ||||||||
\(33\) | −6.25185 | −1.08831 | ||||||||
\(34\) | 5.89405 | 1.01082 | ||||||||
\(35\) | −0.185500 | −0.0313553 | ||||||||
\(36\) | −2.55115 | −0.425192 | ||||||||
\(37\) | −8.51681 | −1.40016 | −0.700078 | − | 0.714067i | \(-0.746851\pi\) | ||||
−0.700078 | + | 0.714067i | \(0.746851\pi\) | |||||||
\(38\) | 13.0079 | 2.11016 | ||||||||
\(39\) | −8.90914 | −1.42660 | ||||||||
\(40\) | 8.88242 | 1.40443 | ||||||||
\(41\) | 4.39062 | 0.685699 | 0.342850 | − | 0.939390i | \(-0.388608\pi\) | ||||
0.342850 | + | 0.939390i | \(0.388608\pi\) | |||||||
\(42\) | −0.497767 | −0.0768071 | ||||||||
\(43\) | −4.38155 | −0.668181 | −0.334090 | − | 0.942541i | \(-0.608429\pi\) | ||||
−0.334090 | + | 0.942541i | \(0.608429\pi\) | |||||||
\(44\) | −17.6672 | −2.66344 | ||||||||
\(45\) | 0.850827 | 0.126834 | ||||||||
\(46\) | 5.55207 | 0.818608 | ||||||||
\(47\) | 6.14196 | 0.895896 | 0.447948 | − | 0.894060i | \(-0.352155\pi\) | ||||
0.447948 | + | 0.894060i | \(0.352155\pi\) | |||||||
\(48\) | 10.1595 | 1.46639 | ||||||||
\(49\) | −6.98399 | −0.997713 | ||||||||
\(50\) | 7.20960 | 1.01959 | ||||||||
\(51\) | −3.62528 | −0.507641 | ||||||||
\(52\) | −25.1765 | −3.49135 | ||||||||
\(53\) | 8.38992 | 1.15244 | 0.576222 | − | 0.817293i | \(-0.304526\pi\) | ||||
0.576222 | + | 0.817293i | \(0.304526\pi\) | |||||||
\(54\) | 14.0847 | 1.91669 | ||||||||
\(55\) | 5.89215 | 0.794497 | ||||||||
\(56\) | −0.766649 | −0.102448 | ||||||||
\(57\) | −8.00083 | −1.05974 | ||||||||
\(58\) | −13.1677 | −1.72900 | ||||||||
\(59\) | −14.9961 | −1.95232 | −0.976162 | − | 0.217041i | \(-0.930359\pi\) | ||||
−0.976162 | + | 0.217041i | \(0.930359\pi\) | |||||||
\(60\) | −10.0242 | −1.29412 | ||||||||
\(61\) | −7.23445 | −0.926277 | −0.463138 | − | 0.886286i | \(-0.653277\pi\) | ||||
−0.463138 | + | 0.886286i | \(0.653277\pi\) | |||||||
\(62\) | −21.7388 | −2.76083 | ||||||||
\(63\) | −0.0734356 | −0.00925202 | ||||||||
\(64\) | −1.93570 | −0.241963 | ||||||||
\(65\) | 8.39654 | 1.04146 | ||||||||
\(66\) | 15.8108 | 1.94618 | ||||||||
\(67\) | −8.80712 | −1.07596 | −0.537981 | − | 0.842957i | \(-0.680813\pi\) | ||||
−0.537981 | + | 0.842957i | \(0.680813\pi\) | |||||||
\(68\) | −10.2448 | −1.24236 | ||||||||
\(69\) | −3.41494 | −0.411111 | ||||||||
\(70\) | 0.469127 | 0.0560715 | ||||||||
\(71\) | 1.00000 | 0.118678 | ||||||||
\(72\) | 3.51636 | 0.414407 | ||||||||
\(73\) | 11.1257 | 1.30217 | 0.651083 | − | 0.759006i | \(-0.274315\pi\) | ||||
0.651083 | + | 0.759006i | \(0.274315\pi\) | |||||||
\(74\) | 21.5389 | 2.50385 | ||||||||
\(75\) | −4.43445 | −0.512046 | ||||||||
\(76\) | −22.6097 | −2.59351 | ||||||||
\(77\) | −0.508556 | −0.0579553 | ||||||||
\(78\) | 22.5311 | 2.55114 | ||||||||
\(79\) | −4.90725 | −0.552109 | −0.276054 | − | 0.961142i | \(-0.589027\pi\) | ||||
−0.276054 | + | 0.961142i | \(0.589027\pi\) | |||||||
\(80\) | −9.57494 | −1.07051 | ||||||||
\(81\) | −6.92208 | −0.769120 | ||||||||
\(82\) | −11.1038 | −1.22621 | ||||||||
\(83\) | 1.13933 | 0.125057 | 0.0625287 | − | 0.998043i | \(-0.480083\pi\) | ||||
0.0625287 | + | 0.998043i | \(0.480083\pi\) | |||||||
\(84\) | 0.865196 | 0.0944006 | ||||||||
\(85\) | 3.41670 | 0.370593 | ||||||||
\(86\) | 11.0809 | 1.19488 | ||||||||
\(87\) | 8.09913 | 0.868318 | ||||||||
\(88\) | 24.3515 | 2.59588 | ||||||||
\(89\) | −15.1049 | −1.60112 | −0.800558 | − | 0.599255i | \(-0.795464\pi\) | ||||
−0.800558 | + | 0.599255i | \(0.795464\pi\) | |||||||
\(90\) | −2.15173 | −0.226812 | ||||||||
\(91\) | −0.724712 | −0.0759705 | ||||||||
\(92\) | −9.65036 | −1.00612 | ||||||||
\(93\) | 13.3710 | 1.38651 | ||||||||
\(94\) | −15.5329 | −1.60210 | ||||||||
\(95\) | 7.54049 | 0.773638 | ||||||||
\(96\) | −6.84382 | −0.698495 | ||||||||
\(97\) | −6.13881 | −0.623302 | −0.311651 | − | 0.950197i | \(-0.600882\pi\) | ||||
−0.311651 | + | 0.950197i | \(0.600882\pi\) | |||||||
\(98\) | 17.6624 | 1.78417 | ||||||||
\(99\) | 2.33258 | 0.234433 | ||||||||
\(100\) | −12.5314 | −1.25314 | ||||||||
\(101\) | 0.0789165 | 0.00785249 | 0.00392624 | − | 0.999992i | \(-0.498750\pi\) | ||||
0.00392624 | + | 0.999992i | \(0.498750\pi\) | |||||||
\(102\) | 9.16829 | 0.907796 | ||||||||
\(103\) | 7.10686 | 0.700260 | 0.350130 | − | 0.936701i | \(-0.386137\pi\) | ||||
0.350130 | + | 0.936701i | \(0.386137\pi\) | |||||||
\(104\) | 34.7018 | 3.40279 | ||||||||
\(105\) | −0.288549 | −0.0281595 | ||||||||
\(106\) | −21.2180 | −2.06087 | ||||||||
\(107\) | −10.0930 | −0.975730 | −0.487865 | − | 0.872919i | \(-0.662224\pi\) | ||||
−0.487865 | + | 0.872919i | \(0.662224\pi\) | |||||||
\(108\) | −24.4815 | −2.35573 | ||||||||
\(109\) | 4.69787 | 0.449974 | 0.224987 | − | 0.974362i | \(-0.427766\pi\) | ||||
0.224987 | + | 0.974362i | \(0.427766\pi\) | |||||||
\(110\) | −14.9012 | −1.42077 | ||||||||
\(111\) | −13.2480 | −1.25745 | ||||||||
\(112\) | 0.826421 | 0.0780894 | ||||||||
\(113\) | −1.00000 | −0.0940721 | ||||||||
\(114\) | 20.2340 | 1.89509 | ||||||||
\(115\) | 3.21846 | 0.300123 | ||||||||
\(116\) | 22.8875 | 2.12505 | ||||||||
\(117\) | 3.32401 | 0.307305 | ||||||||
\(118\) | 37.9249 | 3.49127 | ||||||||
\(119\) | −0.294898 | −0.0270333 | ||||||||
\(120\) | 13.8168 | 1.26129 | ||||||||
\(121\) | 5.15354 | 0.468504 | ||||||||
\(122\) | 18.2958 | 1.65643 | ||||||||
\(123\) | 6.82968 | 0.615812 | ||||||||
\(124\) | 37.7855 | 3.39323 | ||||||||
\(125\) | 11.5094 | 1.02943 | ||||||||
\(126\) | 0.185718 | 0.0165450 | ||||||||
\(127\) | −7.71496 | −0.684592 | −0.342296 | − | 0.939592i | \(-0.611205\pi\) | ||||
−0.342296 | + | 0.939592i | \(0.611205\pi\) | |||||||
\(128\) | 13.6948 | 1.21046 | ||||||||
\(129\) | −6.81558 | −0.600079 | ||||||||
\(130\) | −21.2347 | −1.86241 | ||||||||
\(131\) | −19.8278 | −1.73236 | −0.866180 | − | 0.499732i | \(-0.833432\pi\) | ||||
−0.866180 | + | 0.499732i | \(0.833432\pi\) | |||||||
\(132\) | −27.4817 | −2.39198 | ||||||||
\(133\) | −0.650826 | −0.0564338 | ||||||||
\(134\) | 22.2731 | 1.92410 | ||||||||
\(135\) | 8.16473 | 0.702708 | ||||||||
\(136\) | 14.1208 | 1.21085 | ||||||||
\(137\) | −7.06541 | −0.603638 | −0.301819 | − | 0.953365i | \(-0.597594\pi\) | ||||
−0.301819 | + | 0.953365i | \(0.597594\pi\) | |||||||
\(138\) | 8.63634 | 0.735174 | ||||||||
\(139\) | −21.3743 | −1.81294 | −0.906471 | − | 0.422269i | \(-0.861234\pi\) | ||||
−0.906471 | + | 0.422269i | \(0.861234\pi\) | |||||||
\(140\) | −0.815416 | −0.0689153 | ||||||||
\(141\) | 9.55392 | 0.804585 | ||||||||
\(142\) | −2.52899 | −0.212228 | ||||||||
\(143\) | 23.0194 | 1.92498 | ||||||||
\(144\) | −3.79051 | −0.315876 | ||||||||
\(145\) | −7.63314 | −0.633898 | ||||||||
\(146\) | −28.1368 | −2.32862 | ||||||||
\(147\) | −10.8637 | −0.896024 | ||||||||
\(148\) | −37.4379 | −3.07738 | ||||||||
\(149\) | 0.898542 | 0.0736114 | 0.0368057 | − | 0.999322i | \(-0.488282\pi\) | ||||
0.0368057 | + | 0.999322i | \(0.488282\pi\) | |||||||
\(150\) | 11.2147 | 0.915673 | ||||||||
\(151\) | −1.43144 | −0.116489 | −0.0582443 | − | 0.998302i | \(-0.518550\pi\) | ||||
−0.0582443 | + | 0.998302i | \(0.518550\pi\) | |||||||
\(152\) | 31.1639 | 2.52772 | ||||||||
\(153\) | 1.35260 | 0.109351 | ||||||||
\(154\) | 1.28613 | 0.103639 | ||||||||
\(155\) | −12.6017 | −1.01219 | ||||||||
\(156\) | −39.1625 | −3.13551 | ||||||||
\(157\) | 14.0110 | 1.11820 | 0.559100 | − | 0.829100i | \(-0.311147\pi\) | ||||
0.559100 | + | 0.829100i | \(0.311147\pi\) | |||||||
\(158\) | 12.4104 | 0.987315 | ||||||||
\(159\) | 13.0507 | 1.03499 | ||||||||
\(160\) | 6.45006 | 0.509922 | ||||||||
\(161\) | −0.277788 | −0.0218928 | ||||||||
\(162\) | 17.5058 | 1.37539 | ||||||||
\(163\) | −4.43070 | −0.347040 | −0.173520 | − | 0.984830i | \(-0.555514\pi\) | ||||
−0.173520 | + | 0.984830i | \(0.555514\pi\) | |||||||
\(164\) | 19.3001 | 1.50709 | ||||||||
\(165\) | 9.16533 | 0.713520 | ||||||||
\(166\) | −2.88134 | −0.223636 | ||||||||
\(167\) | 11.0476 | 0.854890 | 0.427445 | − | 0.904041i | \(-0.359414\pi\) | ||||
0.427445 | + | 0.904041i | \(0.359414\pi\) | |||||||
\(168\) | −1.19254 | −0.0920061 | ||||||||
\(169\) | 19.8036 | 1.52335 | ||||||||
\(170\) | −8.64079 | −0.662718 | ||||||||
\(171\) | 2.98512 | 0.228278 | ||||||||
\(172\) | −19.2603 | −1.46858 | ||||||||
\(173\) | −7.55934 | −0.574726 | −0.287363 | − | 0.957822i | \(-0.592779\pi\) | ||||
−0.287363 | + | 0.957822i | \(0.592779\pi\) | |||||||
\(174\) | −20.4826 | −1.55278 | ||||||||
\(175\) | −0.360720 | −0.0272678 | ||||||||
\(176\) | −26.2501 | −1.97867 | ||||||||
\(177\) | −23.3267 | −1.75334 | ||||||||
\(178\) | 38.2001 | 2.86322 | ||||||||
\(179\) | 25.9799 | 1.94183 | 0.970915 | − | 0.239423i | \(-0.0769583\pi\) | ||||
0.970915 | + | 0.239423i | \(0.0769583\pi\) | |||||||
\(180\) | 3.74004 | 0.278766 | ||||||||
\(181\) | −9.53223 | −0.708525 | −0.354263 | − | 0.935146i | \(-0.615268\pi\) | ||||
−0.354263 | + | 0.935146i | \(0.615268\pi\) | |||||||
\(182\) | 1.83279 | 0.135855 | ||||||||
\(183\) | −11.2533 | −0.831869 | ||||||||
\(184\) | 13.3015 | 0.980598 | ||||||||
\(185\) | 12.4858 | 0.917975 | ||||||||
\(186\) | −33.8151 | −2.47945 | ||||||||
\(187\) | 9.36701 | 0.684984 | ||||||||
\(188\) | 26.9986 | 1.96908 | ||||||||
\(189\) | −0.704705 | −0.0512597 | ||||||||
\(190\) | −19.0698 | −1.38347 | ||||||||
\(191\) | 13.0590 | 0.944916 | 0.472458 | − | 0.881353i | \(-0.343367\pi\) | ||||
0.472458 | + | 0.881353i | \(0.343367\pi\) | |||||||
\(192\) | −3.01102 | −0.217302 | ||||||||
\(193\) | −8.36874 | −0.602395 | −0.301197 | − | 0.953562i | \(-0.597386\pi\) | ||||
−0.301197 | + | 0.953562i | \(0.597386\pi\) | |||||||
\(194\) | 15.5250 | 1.11463 | ||||||||
\(195\) | 13.0610 | 0.935315 | ||||||||
\(196\) | −30.7000 | −2.19286 | ||||||||
\(197\) | 7.30532 | 0.520482 | 0.260241 | − | 0.965544i | \(-0.416198\pi\) | ||||
0.260241 | + | 0.965544i | \(0.416198\pi\) | |||||||
\(198\) | −5.89905 | −0.419227 | ||||||||
\(199\) | −20.9848 | −1.48757 | −0.743787 | − | 0.668417i | \(-0.766972\pi\) | ||||
−0.743787 | + | 0.668417i | \(0.766972\pi\) | |||||||
\(200\) | 17.2725 | 1.22135 | ||||||||
\(201\) | −13.6996 | −0.966298 | ||||||||
\(202\) | −0.199579 | −0.0140423 | ||||||||
\(203\) | 0.658822 | 0.0462403 | ||||||||
\(204\) | −15.9359 | −1.11574 | ||||||||
\(205\) | −6.43673 | −0.449561 | ||||||||
\(206\) | −17.9731 | −1.25225 | ||||||||
\(207\) | 1.27412 | 0.0885575 | ||||||||
\(208\) | −37.4074 | −2.59373 | ||||||||
\(209\) | 20.6725 | 1.42995 | ||||||||
\(210\) | 0.729736 | 0.0503566 | ||||||||
\(211\) | 25.0490 | 1.72444 | 0.862222 | − | 0.506530i | \(-0.169072\pi\) | ||||
0.862222 | + | 0.506530i | \(0.169072\pi\) | |||||||
\(212\) | 36.8802 | 2.53294 | ||||||||
\(213\) | 1.55552 | 0.106582 | ||||||||
\(214\) | 25.5251 | 1.74486 | ||||||||
\(215\) | 6.42344 | 0.438075 | ||||||||
\(216\) | 33.7438 | 2.29597 | ||||||||
\(217\) | 1.08766 | 0.0738354 | ||||||||
\(218\) | −11.8808 | −0.804672 | ||||||||
\(219\) | 17.3062 | 1.16945 | ||||||||
\(220\) | 25.9005 | 1.74621 | ||||||||
\(221\) | 13.3484 | 0.897908 | ||||||||
\(222\) | 33.5041 | 2.24865 | ||||||||
\(223\) | 0.793743 | 0.0531530 | 0.0265765 | − | 0.999647i | \(-0.491539\pi\) | ||||
0.0265765 | + | 0.999647i | \(0.491539\pi\) | |||||||
\(224\) | −0.556710 | −0.0371967 | ||||||||
\(225\) | 1.65450 | 0.110300 | ||||||||
\(226\) | 2.52899 | 0.168226 | ||||||||
\(227\) | −3.86706 | −0.256666 | −0.128333 | − | 0.991731i | \(-0.540963\pi\) | ||||
−0.128333 | + | 0.991731i | \(0.540963\pi\) | |||||||
\(228\) | −35.1698 | −2.32918 | ||||||||
\(229\) | −13.0632 | −0.863241 | −0.431620 | − | 0.902055i | \(-0.642058\pi\) | ||||
−0.431620 | + | 0.902055i | \(0.642058\pi\) | |||||||
\(230\) | −8.13944 | −0.536699 | ||||||||
\(231\) | −0.791068 | −0.0520484 | ||||||||
\(232\) | −31.5468 | −2.07115 | ||||||||
\(233\) | 10.7712 | 0.705643 | 0.352821 | − | 0.935691i | \(-0.385222\pi\) | ||||
0.352821 | + | 0.935691i | \(0.385222\pi\) | |||||||
\(234\) | −8.40638 | −0.549542 | ||||||||
\(235\) | −9.00423 | −0.587371 | ||||||||
\(236\) | −65.9194 | −4.29098 | ||||||||
\(237\) | −7.63331 | −0.495837 | ||||||||
\(238\) | 0.745793 | 0.0483426 | ||||||||
\(239\) | 24.3711 | 1.57644 | 0.788218 | − | 0.615397i | \(-0.211004\pi\) | ||||
0.788218 | + | 0.615397i | \(0.211004\pi\) | |||||||
\(240\) | −14.8940 | −0.961403 | ||||||||
\(241\) | 0.551876 | 0.0355494 | 0.0177747 | − | 0.999842i | \(-0.494342\pi\) | ||||
0.0177747 | + | 0.999842i | \(0.494342\pi\) | |||||||
\(242\) | −13.0332 | −0.837808 | ||||||||
\(243\) | 5.94055 | 0.381086 | ||||||||
\(244\) | −31.8010 | −2.03585 | ||||||||
\(245\) | 10.2387 | 0.654124 | ||||||||
\(246\) | −17.2722 | −1.10123 | ||||||||
\(247\) | 29.4592 | 1.87444 | ||||||||
\(248\) | −52.0812 | −3.30716 | ||||||||
\(249\) | 1.77224 | 0.112311 | ||||||||
\(250\) | −29.1071 | −1.84090 | ||||||||
\(251\) | 20.9235 | 1.32068 | 0.660341 | − | 0.750966i | \(-0.270412\pi\) | ||||
0.660341 | + | 0.750966i | \(0.270412\pi\) | |||||||
\(252\) | −0.322806 | −0.0203349 | ||||||||
\(253\) | 8.82353 | 0.554731 | ||||||||
\(254\) | 19.5110 | 1.22423 | ||||||||
\(255\) | 5.31474 | 0.332822 | ||||||||
\(256\) | −30.7625 | −1.92266 | ||||||||
\(257\) | 16.9880 | 1.05968 | 0.529841 | − | 0.848097i | \(-0.322251\pi\) | ||||
0.529841 | + | 0.848097i | \(0.322251\pi\) | |||||||
\(258\) | 17.2365 | 1.07310 | ||||||||
\(259\) | −1.07766 | −0.0669626 | ||||||||
\(260\) | 36.9093 | 2.28901 | ||||||||
\(261\) | −3.02180 | −0.187045 | ||||||||
\(262\) | 50.1442 | 3.09792 | ||||||||
\(263\) | −27.7246 | −1.70957 | −0.854785 | − | 0.518982i | \(-0.826311\pi\) | ||||
−0.854785 | + | 0.518982i | \(0.826311\pi\) | |||||||
\(264\) | 37.8791 | 2.33130 | ||||||||
\(265\) | −12.2998 | −0.755570 | ||||||||
\(266\) | 1.64593 | 0.100918 | ||||||||
\(267\) | −23.4959 | −1.43793 | ||||||||
\(268\) | −38.7141 | −2.36484 | ||||||||
\(269\) | −19.1130 | −1.16534 | −0.582670 | − | 0.812709i | \(-0.697992\pi\) | ||||
−0.582670 | + | 0.812709i | \(0.697992\pi\) | |||||||
\(270\) | −20.6485 | −1.25663 | ||||||||
\(271\) | 3.93835 | 0.239238 | 0.119619 | − | 0.992820i | \(-0.461833\pi\) | ||||
0.119619 | + | 0.992820i | \(0.461833\pi\) | |||||||
\(272\) | −15.2217 | −0.922952 | ||||||||
\(273\) | −1.12730 | −0.0682274 | ||||||||
\(274\) | 17.8683 | 1.07946 | ||||||||
\(275\) | 11.4577 | 0.690927 | ||||||||
\(276\) | −15.0113 | −0.903574 | ||||||||
\(277\) | 6.43083 | 0.386391 | 0.193195 | − | 0.981160i | \(-0.438115\pi\) | ||||
0.193195 | + | 0.981160i | \(0.438115\pi\) | |||||||
\(278\) | 54.0552 | 3.24202 | ||||||||
\(279\) | −4.98875 | −0.298669 | ||||||||
\(280\) | 1.12392 | 0.0671671 | ||||||||
\(281\) | 28.7027 | 1.71226 | 0.856129 | − | 0.516762i | \(-0.172863\pi\) | ||||
0.856129 | + | 0.516762i | \(0.172863\pi\) | |||||||
\(282\) | −24.1617 | −1.43881 | ||||||||
\(283\) | 0.593602 | 0.0352860 | 0.0176430 | − | 0.999844i | \(-0.494384\pi\) | ||||
0.0176430 | + | 0.999844i | \(0.494384\pi\) | |||||||
\(284\) | 4.39577 | 0.260841 | ||||||||
\(285\) | 11.7294 | 0.694788 | ||||||||
\(286\) | −58.2158 | −3.44237 | ||||||||
\(287\) | 0.555559 | 0.0327936 | ||||||||
\(288\) | 2.55344 | 0.150463 | ||||||||
\(289\) | −11.5683 | −0.680489 | ||||||||
\(290\) | 19.3041 | 1.13358 | ||||||||
\(291\) | −9.54903 | −0.559774 | ||||||||
\(292\) | 48.9061 | 2.86201 | ||||||||
\(293\) | 20.9179 | 1.22204 | 0.611020 | − | 0.791616i | \(-0.290760\pi\) | ||||
0.611020 | + | 0.791616i | \(0.290760\pi\) | |||||||
\(294\) | 27.4742 | 1.60233 | ||||||||
\(295\) | 21.9846 | 1.27999 | ||||||||
\(296\) | 51.6022 | 2.99932 | ||||||||
\(297\) | 22.3839 | 1.29885 | ||||||||
\(298\) | −2.27240 | −0.131637 | ||||||||
\(299\) | 12.5739 | 0.727166 | ||||||||
\(300\) | −19.4928 | −1.12542 | ||||||||
\(301\) | −0.554412 | −0.0319558 | ||||||||
\(302\) | 3.62008 | 0.208312 | ||||||||
\(303\) | 0.122756 | 0.00705215 | ||||||||
\(304\) | −33.5936 | −1.92672 | ||||||||
\(305\) | 10.6058 | 0.607289 | ||||||||
\(306\) | −3.42070 | −0.195549 | ||||||||
\(307\) | 19.8380 | 1.13221 | 0.566107 | − | 0.824332i | \(-0.308449\pi\) | ||||
0.566107 | + | 0.824332i | \(0.308449\pi\) | |||||||
\(308\) | −2.23549 | −0.127379 | ||||||||
\(309\) | 11.0548 | 0.628888 | ||||||||
\(310\) | 31.8695 | 1.81007 | ||||||||
\(311\) | 35.0957 | 1.99010 | 0.995048 | − | 0.0993923i | \(-0.0316899\pi\) | ||||
0.995048 | + | 0.0993923i | \(0.0316899\pi\) | |||||||
\(312\) | 53.9793 | 3.05597 | ||||||||
\(313\) | −6.78306 | −0.383401 | −0.191701 | − | 0.981453i | \(-0.561400\pi\) | ||||
−0.191701 | + | 0.981453i | \(0.561400\pi\) | |||||||
\(314\) | −35.4336 | −1.99964 | ||||||||
\(315\) | 0.107658 | 0.00606584 | ||||||||
\(316\) | −21.5711 | −1.21347 | ||||||||
\(317\) | −11.7428 | −0.659544 | −0.329772 | − | 0.944061i | \(-0.606972\pi\) | ||||
−0.329772 | + | 0.944061i | \(0.606972\pi\) | |||||||
\(318\) | −33.0050 | −1.85083 | ||||||||
\(319\) | −20.9265 | −1.17166 | ||||||||
\(320\) | 2.83778 | 0.158637 | ||||||||
\(321\) | −15.6999 | −0.876282 | ||||||||
\(322\) | 0.702522 | 0.0391500 | ||||||||
\(323\) | 11.9875 | 0.667000 | ||||||||
\(324\) | −30.4279 | −1.69044 | ||||||||
\(325\) | 16.3277 | 0.905699 | ||||||||
\(326\) | 11.2052 | 0.620598 | ||||||||
\(327\) | 7.30761 | 0.404112 | ||||||||
\(328\) | −26.6022 | −1.46886 | ||||||||
\(329\) | 0.777162 | 0.0428463 | ||||||||
\(330\) | −23.1790 | −1.27596 | ||||||||
\(331\) | −25.7407 | −1.41483 | −0.707417 | − | 0.706796i | \(-0.750140\pi\) | ||||
−0.707417 | + | 0.706796i | \(0.750140\pi\) | |||||||
\(332\) | 5.00822 | 0.274862 | ||||||||
\(333\) | 4.94287 | 0.270867 | ||||||||
\(334\) | −27.9393 | −1.52877 | ||||||||
\(335\) | 12.9114 | 0.705426 | ||||||||
\(336\) | 1.28551 | 0.0701304 | ||||||||
\(337\) | 12.9394 | 0.704857 | 0.352428 | − | 0.935839i | \(-0.385356\pi\) | ||||
0.352428 | + | 0.935839i | \(0.385356\pi\) | |||||||
\(338\) | −50.0830 | −2.72416 | ||||||||
\(339\) | −1.55552 | −0.0844841 | ||||||||
\(340\) | 15.0190 | 0.814521 | ||||||||
\(341\) | −34.5481 | −1.87088 | ||||||||
\(342\) | −7.54933 | −0.408221 | ||||||||
\(343\) | −1.76944 | −0.0955408 | ||||||||
\(344\) | 26.5473 | 1.43133 | ||||||||
\(345\) | 5.00637 | 0.269534 | ||||||||
\(346\) | 19.1175 | 1.02776 | ||||||||
\(347\) | −2.10574 | −0.113042 | −0.0565209 | − | 0.998401i | \(-0.518001\pi\) | ||||
−0.0565209 | + | 0.998401i | \(0.518001\pi\) | |||||||
\(348\) | 35.6019 | 1.90846 | ||||||||
\(349\) | 16.0672 | 0.860056 | 0.430028 | − | 0.902815i | \(-0.358504\pi\) | ||||
0.430028 | + | 0.902815i | \(0.358504\pi\) | |||||||
\(350\) | 0.912255 | 0.0487621 | ||||||||
\(351\) | 31.8980 | 1.70259 | ||||||||
\(352\) | 17.6831 | 0.942511 | ||||||||
\(353\) | 31.3616 | 1.66921 | 0.834604 | − | 0.550850i | \(-0.185696\pi\) | ||||
0.834604 | + | 0.550850i | \(0.185696\pi\) | |||||||
\(354\) | 58.9928 | 3.13543 | ||||||||
\(355\) | −1.46602 | −0.0778082 | ||||||||
\(356\) | −66.3977 | −3.51907 | ||||||||
\(357\) | −0.458719 | −0.0242780 | ||||||||
\(358\) | −65.7029 | −3.47250 | ||||||||
\(359\) | −9.84325 | −0.519507 | −0.259753 | − | 0.965675i | \(-0.583641\pi\) | ||||
−0.259753 | + | 0.965675i | \(0.583641\pi\) | |||||||
\(360\) | −5.15505 | −0.271695 | ||||||||
\(361\) | 7.45576 | 0.392408 | ||||||||
\(362\) | 24.1069 | 1.26703 | ||||||||
\(363\) | 8.01642 | 0.420753 | ||||||||
\(364\) | −3.18567 | −0.166974 | ||||||||
\(365\) | −16.3105 | −0.853731 | ||||||||
\(366\) | 28.4595 | 1.48760 | ||||||||
\(367\) | 10.5454 | 0.550466 | 0.275233 | − | 0.961378i | \(-0.411245\pi\) | ||||
0.275233 | + | 0.961378i | \(0.411245\pi\) | |||||||
\(368\) | −14.3385 | −0.747448 | ||||||||
\(369\) | −2.54816 | −0.132652 | ||||||||
\(370\) | −31.5764 | −1.64158 | ||||||||
\(371\) | 1.06160 | 0.0551158 | ||||||||
\(372\) | 58.7759 | 3.04739 | ||||||||
\(373\) | 5.72131 | 0.296238 | 0.148119 | − | 0.988970i | \(-0.452678\pi\) | ||||
0.148119 | + | 0.988970i | \(0.452678\pi\) | |||||||
\(374\) | −23.6890 | −1.22493 | ||||||||
\(375\) | 17.9031 | 0.924511 | ||||||||
\(376\) | −37.2133 | −1.91913 | ||||||||
\(377\) | −29.8211 | −1.53587 | ||||||||
\(378\) | 1.78219 | 0.0916659 | ||||||||
\(379\) | −13.7764 | −0.707647 | −0.353823 | − | 0.935312i | \(-0.615119\pi\) | ||||
−0.353823 | + | 0.935312i | \(0.615119\pi\) | |||||||
\(380\) | 33.1463 | 1.70037 | ||||||||
\(381\) | −12.0008 | −0.614817 | ||||||||
\(382\) | −33.0260 | −1.68976 | ||||||||
\(383\) | 30.7625 | 1.57189 | 0.785944 | − | 0.618297i | \(-0.212177\pi\) | ||||
0.785944 | + | 0.618297i | \(0.212177\pi\) | |||||||
\(384\) | 21.3025 | 1.08709 | ||||||||
\(385\) | 0.745553 | 0.0379969 | ||||||||
\(386\) | 21.1644 | 1.07724 | ||||||||
\(387\) | 2.54290 | 0.129263 | ||||||||
\(388\) | −26.9848 | −1.36995 | ||||||||
\(389\) | −0.515274 | −0.0261254 | −0.0130627 | − | 0.999915i | \(-0.504158\pi\) | ||||
−0.0130627 | + | 0.999915i | \(0.504158\pi\) | |||||||
\(390\) | −33.0310 | −1.67259 | ||||||||
\(391\) | 5.11653 | 0.258754 | ||||||||
\(392\) | 42.3151 | 2.13723 | ||||||||
\(393\) | −30.8424 | −1.55580 | ||||||||
\(394\) | −18.4750 | −0.930760 | ||||||||
\(395\) | 7.19412 | 0.361975 | ||||||||
\(396\) | 10.2535 | 0.515256 | ||||||||
\(397\) | −7.32240 | −0.367501 | −0.183750 | − | 0.982973i | \(-0.558824\pi\) | ||||
−0.183750 | + | 0.982973i | \(0.558824\pi\) | |||||||
\(398\) | 53.0703 | 2.66017 | ||||||||
\(399\) | −1.01237 | −0.0506820 | ||||||||
\(400\) | −18.6192 | −0.930961 | ||||||||
\(401\) | −38.4911 | −1.92215 | −0.961076 | − | 0.276284i | \(-0.910897\pi\) | ||||
−0.961076 | + | 0.276284i | \(0.910897\pi\) | |||||||
\(402\) | 34.6462 | 1.72799 | ||||||||
\(403\) | −49.2323 | −2.45244 | ||||||||
\(404\) | 0.346899 | 0.0172589 | ||||||||
\(405\) | 10.1479 | 0.504253 | ||||||||
\(406\) | −1.66615 | −0.0826898 | ||||||||
\(407\) | 34.2303 | 1.69673 | ||||||||
\(408\) | 21.9651 | 1.08744 | ||||||||
\(409\) | 18.5224 | 0.915874 | 0.457937 | − | 0.888985i | \(-0.348589\pi\) | ||||
0.457937 | + | 0.888985i | \(0.348589\pi\) | |||||||
\(410\) | 16.2784 | 0.803933 | ||||||||
\(411\) | −10.9904 | −0.542115 | ||||||||
\(412\) | 31.2401 | 1.53909 | ||||||||
\(413\) | −1.89750 | −0.0933701 | ||||||||
\(414\) | −3.22223 | −0.158364 | ||||||||
\(415\) | −1.67028 | −0.0819906 | ||||||||
\(416\) | 25.1991 | 1.23549 | ||||||||
\(417\) | −33.2480 | −1.62816 | ||||||||
\(418\) | −52.2806 | −2.55713 | ||||||||
\(419\) | −19.4289 | −0.949163 | −0.474582 | − | 0.880211i | \(-0.657401\pi\) | ||||
−0.474582 | + | 0.880211i | \(0.657401\pi\) | |||||||
\(420\) | −1.26839 | −0.0618913 | ||||||||
\(421\) | 25.6738 | 1.25127 | 0.625633 | − | 0.780118i | \(-0.284841\pi\) | ||||
0.625633 | + | 0.780118i | \(0.284841\pi\) | |||||||
\(422\) | −63.3486 | −3.08376 | ||||||||
\(423\) | −3.56458 | −0.173316 | ||||||||
\(424\) | −50.8334 | −2.46869 | ||||||||
\(425\) | 6.64404 | 0.322283 | ||||||||
\(426\) | −3.93388 | −0.190597 | ||||||||
\(427\) | −0.915399 | −0.0442993 | ||||||||
\(428\) | −44.3666 | −2.14454 | ||||||||
\(429\) | 35.8071 | 1.72878 | ||||||||
\(430\) | −16.2448 | −0.783393 | ||||||||
\(431\) | −37.9485 | −1.82791 | −0.913957 | − | 0.405812i | \(-0.866989\pi\) | ||||
−0.913957 | + | 0.405812i | \(0.866989\pi\) | |||||||
\(432\) | −36.3746 | −1.75008 | ||||||||
\(433\) | −0.953598 | −0.0458270 | −0.0229135 | − | 0.999737i | \(-0.507294\pi\) | ||||
−0.0229135 | + | 0.999737i | \(0.507294\pi\) | |||||||
\(434\) | −2.75069 | −0.132037 | ||||||||
\(435\) | −11.8735 | −0.569290 | ||||||||
\(436\) | 20.6507 | 0.988991 | ||||||||
\(437\) | 11.2919 | 0.540167 | ||||||||
\(438\) | −43.7673 | −2.09128 | ||||||||
\(439\) | −15.7958 | −0.753891 | −0.376946 | − | 0.926235i | \(-0.623026\pi\) | ||||
−0.376946 | + | 0.926235i | \(0.623026\pi\) | |||||||
\(440\) | −35.6997 | −1.70192 | ||||||||
\(441\) | 4.05327 | 0.193013 | ||||||||
\(442\) | −33.7578 | −1.60570 | ||||||||
\(443\) | −21.0372 | −0.999506 | −0.499753 | − | 0.866168i | \(-0.666576\pi\) | ||||
−0.499753 | + | 0.866168i | \(0.666576\pi\) | |||||||
\(444\) | −58.2354 | −2.76373 | ||||||||
\(445\) | 22.1441 | 1.04973 | ||||||||
\(446\) | −2.00737 | −0.0950515 | ||||||||
\(447\) | 1.39770 | 0.0661088 | ||||||||
\(448\) | −0.244931 | −0.0115719 | ||||||||
\(449\) | −1.23116 | −0.0581020 | −0.0290510 | − | 0.999578i | \(-0.509249\pi\) | ||||
−0.0290510 | + | 0.999578i | \(0.509249\pi\) | |||||||
\(450\) | −4.18421 | −0.197245 | ||||||||
\(451\) | −17.6465 | −0.830943 | ||||||||
\(452\) | −4.39577 | −0.206760 | ||||||||
\(453\) | −2.22662 | −0.104616 | ||||||||
\(454\) | 9.77974 | 0.458986 | ||||||||
\(455\) | 1.06244 | 0.0498080 | ||||||||
\(456\) | 48.4760 | 2.27009 | ||||||||
\(457\) | −33.7008 | −1.57646 | −0.788229 | − | 0.615383i | \(-0.789002\pi\) | ||||
−0.788229 | + | 0.615383i | \(0.789002\pi\) | |||||||
\(458\) | 33.0367 | 1.54370 | ||||||||
\(459\) | 12.9798 | 0.605847 | ||||||||
\(460\) | 14.1476 | 0.659636 | ||||||||
\(461\) | 35.6808 | 1.66182 | 0.830911 | − | 0.556405i | \(-0.187820\pi\) | ||||
0.830911 | + | 0.556405i | \(0.187820\pi\) | |||||||
\(462\) | 2.00060 | 0.0930763 | ||||||||
\(463\) | 23.4896 | 1.09166 | 0.545828 | − | 0.837897i | \(-0.316215\pi\) | ||||
0.545828 | + | 0.837897i | \(0.316215\pi\) | |||||||
\(464\) | 34.0063 | 1.57870 | ||||||||
\(465\) | −19.6022 | −0.909029 | ||||||||
\(466\) | −27.2401 | −1.26187 | ||||||||
\(467\) | 10.7281 | 0.496439 | 0.248220 | − | 0.968704i | \(-0.420155\pi\) | ||||
0.248220 | + | 0.968704i | \(0.420155\pi\) | |||||||
\(468\) | 14.6116 | 0.675421 | ||||||||
\(469\) | −1.11439 | −0.0514579 | ||||||||
\(470\) | 22.7716 | 1.05037 | ||||||||
\(471\) | 21.7944 | 1.00423 | ||||||||
\(472\) | 90.8593 | 4.18214 | ||||||||
\(473\) | 17.6101 | 0.809713 | ||||||||
\(474\) | 19.3045 | 0.886687 | ||||||||
\(475\) | 14.6631 | 0.672788 | ||||||||
\(476\) | −1.29630 | −0.0594160 | ||||||||
\(477\) | −4.86922 | −0.222946 | ||||||||
\(478\) | −61.6342 | −2.81908 | ||||||||
\(479\) | 21.4770 | 0.981307 | 0.490654 | − | 0.871355i | \(-0.336758\pi\) | ||||
0.490654 | + | 0.871355i | \(0.336758\pi\) | |||||||
\(480\) | 10.0332 | 0.457950 | ||||||||
\(481\) | 48.7796 | 2.22416 | ||||||||
\(482\) | −1.39569 | −0.0635717 | ||||||||
\(483\) | −0.432104 | −0.0196614 | ||||||||
\(484\) | 22.6538 | 1.02972 | ||||||||
\(485\) | 8.99961 | 0.408651 | ||||||||
\(486\) | −15.0236 | −0.681483 | ||||||||
\(487\) | 38.0452 | 1.72399 | 0.861997 | − | 0.506913i | \(-0.169214\pi\) | ||||
0.861997 | + | 0.506913i | \(0.169214\pi\) | |||||||
\(488\) | 43.8326 | 1.98421 | ||||||||
\(489\) | −6.89204 | −0.311669 | ||||||||
\(490\) | −25.8934 | −1.16975 | ||||||||
\(491\) | 6.73665 | 0.304021 | 0.152010 | − | 0.988379i | \(-0.451425\pi\) | ||||
0.152010 | + | 0.988379i | \(0.451425\pi\) | |||||||
\(492\) | 30.0217 | 1.35348 | ||||||||
\(493\) | −12.1347 | −0.546521 | ||||||||
\(494\) | −74.5019 | −3.35200 | ||||||||
\(495\) | −3.41960 | −0.153700 | ||||||||
\(496\) | 56.1418 | 2.52084 | ||||||||
\(497\) | 0.126533 | 0.00567579 | ||||||||
\(498\) | −4.48198 | −0.200842 | ||||||||
\(499\) | 9.47595 | 0.424202 | 0.212101 | − | 0.977248i | \(-0.431969\pi\) | ||||
0.212101 | + | 0.977248i | \(0.431969\pi\) | |||||||
\(500\) | 50.5927 | 2.26257 | ||||||||
\(501\) | 17.1847 | 0.767758 | ||||||||
\(502\) | −52.9153 | −2.36173 | ||||||||
\(503\) | −6.68842 | −0.298222 | −0.149111 | − | 0.988820i | \(-0.547641\pi\) | ||||
−0.149111 | + | 0.988820i | \(0.547641\pi\) | |||||||
\(504\) | 0.444937 | 0.0198190 | ||||||||
\(505\) | −0.115693 | −0.00514828 | ||||||||
\(506\) | −22.3146 | −0.992004 | ||||||||
\(507\) | 30.8048 | 1.36809 | ||||||||
\(508\) | −33.9132 | −1.50465 | ||||||||
\(509\) | −27.2002 | −1.20563 | −0.602815 | − | 0.797881i | \(-0.705954\pi\) | ||||
−0.602815 | + | 0.797881i | \(0.705954\pi\) | |||||||
\(510\) | −13.4409 | −0.595173 | ||||||||
\(511\) | 1.40777 | 0.0622763 | ||||||||
\(512\) | 50.4084 | 2.22776 | ||||||||
\(513\) | 28.6459 | 1.26475 | ||||||||
\(514\) | −42.9624 | −1.89499 | ||||||||
\(515\) | −10.4188 | −0.459107 | ||||||||
\(516\) | −29.9597 | −1.31890 | ||||||||
\(517\) | −24.6854 | −1.08566 | ||||||||
\(518\) | 2.72539 | 0.119747 | ||||||||
\(519\) | −11.7587 | −0.516149 | ||||||||
\(520\) | −50.8735 | −2.23095 | ||||||||
\(521\) | 7.36141 | 0.322509 | 0.161255 | − | 0.986913i | \(-0.448446\pi\) | ||||
0.161255 | + | 0.986913i | \(0.448446\pi\) | |||||||
\(522\) | 7.64208 | 0.334485 | ||||||||
\(523\) | −30.0860 | −1.31557 | −0.657784 | − | 0.753206i | \(-0.728506\pi\) | ||||
−0.657784 | + | 0.753206i | \(0.728506\pi\) | |||||||
\(524\) | −87.1583 | −3.80753 | ||||||||
\(525\) | −0.561106 | −0.0244887 | ||||||||
\(526\) | 70.1151 | 3.05716 | ||||||||
\(527\) | −20.0335 | −0.872673 | ||||||||
\(528\) | −40.8324 | −1.77700 | ||||||||
\(529\) | −18.1803 | −0.790449 | ||||||||
\(530\) | 31.1060 | 1.35116 | ||||||||
\(531\) | 8.70322 | 0.377687 | ||||||||
\(532\) | −2.86088 | −0.124035 | ||||||||
\(533\) | −25.1470 | −1.08924 | ||||||||
\(534\) | 59.4209 | 2.57139 | ||||||||
\(535\) | 14.7966 | 0.639712 | ||||||||
\(536\) | 53.3612 | 2.30485 | ||||||||
\(537\) | 40.4122 | 1.74392 | ||||||||
\(538\) | 48.3365 | 2.08393 | ||||||||
\(539\) | 28.0697 | 1.20905 | ||||||||
\(540\) | 35.8903 | 1.54447 | ||||||||
\(541\) | −14.4789 | −0.622498 | −0.311249 | − | 0.950328i | \(-0.600747\pi\) | ||||
−0.311249 | + | 0.950328i | \(0.600747\pi\) | |||||||
\(542\) | −9.96003 | −0.427820 | ||||||||
\(543\) | −14.8276 | −0.636311 | ||||||||
\(544\) | 10.2539 | 0.439634 | ||||||||
\(545\) | −6.88716 | −0.295014 | ||||||||
\(546\) | 2.85093 | 0.122009 | ||||||||
\(547\) | 23.8536 | 1.01991 | 0.509954 | − | 0.860202i | \(-0.329663\pi\) | ||||
0.509954 | + | 0.860202i | \(0.329663\pi\) | |||||||
\(548\) | −31.0579 | −1.32673 | ||||||||
\(549\) | 4.19863 | 0.179193 | ||||||||
\(550\) | −28.9765 | −1.23556 | ||||||||
\(551\) | −26.7808 | −1.14090 | ||||||||
\(552\) | 20.6907 | 0.880654 | ||||||||
\(553\) | −0.620930 | −0.0264046 | ||||||||
\(554\) | −16.2635 | −0.690969 | ||||||||
\(555\) | 19.4219 | 0.824413 | ||||||||
\(556\) | −93.9563 | −3.98464 | ||||||||
\(557\) | 13.7010 | 0.580528 | 0.290264 | − | 0.956947i | \(-0.406257\pi\) | ||||
0.290264 | + | 0.956947i | \(0.406257\pi\) | |||||||
\(558\) | 12.6165 | 0.534098 | ||||||||
\(559\) | 25.0951 | 1.06141 | ||||||||
\(560\) | −1.21155 | −0.0511973 | ||||||||
\(561\) | 14.5705 | 0.615169 | ||||||||
\(562\) | −72.5887 | −3.06197 | ||||||||
\(563\) | −39.4919 | −1.66439 | −0.832193 | − | 0.554487i | \(-0.812915\pi\) | ||||
−0.832193 | + | 0.554487i | \(0.812915\pi\) | |||||||
\(564\) | 41.9968 | 1.76839 | ||||||||
\(565\) | 1.46602 | 0.0616759 | ||||||||
\(566\) | −1.50121 | −0.0631006 | ||||||||
\(567\) | −0.875873 | −0.0367832 | ||||||||
\(568\) | −6.05887 | −0.254224 | ||||||||
\(569\) | −16.0762 | −0.673950 | −0.336975 | − | 0.941514i | \(-0.609404\pi\) | ||||
−0.336975 | + | 0.941514i | \(0.609404\pi\) | |||||||
\(570\) | −29.6634 | −1.24246 | ||||||||
\(571\) | −26.2582 | −1.09887 | −0.549437 | − | 0.835535i | \(-0.685158\pi\) | ||||
−0.549437 | + | 0.835535i | \(0.685158\pi\) | |||||||
\(572\) | 101.188 | 4.23089 | ||||||||
\(573\) | 20.3135 | 0.848609 | ||||||||
\(574\) | −1.40500 | −0.0586437 | ||||||||
\(575\) | 6.25855 | 0.260999 | ||||||||
\(576\) | 1.12342 | 0.0468090 | ||||||||
\(577\) | 32.8109 | 1.36594 | 0.682968 | − | 0.730449i | \(-0.260689\pi\) | ||||
0.682968 | + | 0.730449i | \(0.260689\pi\) | |||||||
\(578\) | 29.2561 | 1.21689 | ||||||||
\(579\) | −13.0177 | −0.540998 | ||||||||
\(580\) | −33.5535 | −1.39323 | ||||||||
\(581\) | 0.144163 | 0.00598088 | ||||||||
\(582\) | 24.1494 | 1.00102 | ||||||||
\(583\) | −33.7203 | −1.39655 | ||||||||
\(584\) | −67.4093 | −2.78942 | ||||||||
\(585\) | −4.87306 | −0.201476 | ||||||||
\(586\) | −52.9012 | −2.18533 | ||||||||
\(587\) | −26.6680 | −1.10071 | −0.550354 | − | 0.834932i | \(-0.685507\pi\) | ||||
−0.550354 | + | 0.834932i | \(0.685507\pi\) | |||||||
\(588\) | −47.7544 | −1.96936 | ||||||||
\(589\) | −44.2130 | −1.82176 | ||||||||
\(590\) | −55.5986 | −2.28896 | ||||||||
\(591\) | 11.3636 | 0.467434 | ||||||||
\(592\) | −55.6254 | −2.28619 | ||||||||
\(593\) | −21.1873 | −0.870060 | −0.435030 | − | 0.900416i | \(-0.643262\pi\) | ||||
−0.435030 | + | 0.900416i | \(0.643262\pi\) | |||||||
\(594\) | −56.6086 | −2.32268 | ||||||||
\(595\) | 0.432326 | 0.0177236 | ||||||||
\(596\) | 3.94978 | 0.161789 | ||||||||
\(597\) | −32.6422 | −1.33596 | ||||||||
\(598\) | −31.7992 | −1.30036 | ||||||||
\(599\) | 22.5444 | 0.921141 | 0.460571 | − | 0.887623i | \(-0.347645\pi\) | ||||
0.460571 | + | 0.887623i | \(0.347645\pi\) | |||||||
\(600\) | 26.8677 | 1.09687 | ||||||||
\(601\) | 0.870084 | 0.0354915 | 0.0177457 | − | 0.999843i | \(-0.494351\pi\) | ||||
0.0177457 | + | 0.999843i | \(0.494351\pi\) | |||||||
\(602\) | 1.40210 | 0.0571454 | ||||||||
\(603\) | 5.11135 | 0.208150 | ||||||||
\(604\) | −6.29226 | −0.256028 | ||||||||
\(605\) | −7.55519 | −0.307162 | ||||||||
\(606\) | −0.310448 | −0.0126111 | ||||||||
\(607\) | −11.2962 | −0.458500 | −0.229250 | − | 0.973368i | \(-0.573627\pi\) | ||||
−0.229250 | + | 0.973368i | \(0.573627\pi\) | |||||||
\(608\) | 22.6300 | 0.917766 | ||||||||
\(609\) | 1.02481 | 0.0415274 | ||||||||
\(610\) | −26.8220 | −1.08599 | ||||||||
\(611\) | −35.1777 | −1.42314 | ||||||||
\(612\) | 5.94571 | 0.240341 | ||||||||
\(613\) | 43.7112 | 1.76548 | 0.882739 | − | 0.469864i | \(-0.155697\pi\) | ||||
0.882739 | + | 0.469864i | \(0.155697\pi\) | |||||||
\(614\) | −50.1700 | −2.02470 | ||||||||
\(615\) | −10.0124 | −0.403741 | ||||||||
\(616\) | 3.08127 | 0.124148 | ||||||||
\(617\) | −41.3104 | −1.66310 | −0.831548 | − | 0.555454i | \(-0.812545\pi\) | ||||
−0.831548 | + | 0.555454i | \(0.812545\pi\) | |||||||
\(618\) | −27.9575 | −1.12462 | ||||||||
\(619\) | −30.6617 | −1.23240 | −0.616198 | − | 0.787591i | \(-0.711328\pi\) | ||||
−0.616198 | + | 0.787591i | \(0.711328\pi\) | |||||||
\(620\) | −55.3942 | −2.22468 | ||||||||
\(621\) | 12.2267 | 0.490642 | ||||||||
\(622\) | −88.7566 | −3.55882 | ||||||||
\(623\) | −1.91127 | −0.0765736 | ||||||||
\(624\) | −58.1878 | −2.32938 | ||||||||
\(625\) | −2.61907 | −0.104763 | ||||||||
\(626\) | 17.1543 | 0.685622 | ||||||||
\(627\) | 32.1565 | 1.28421 | ||||||||
\(628\) | 61.5892 | 2.45768 | ||||||||
\(629\) | 19.8493 | 0.791442 | ||||||||
\(630\) | −0.272266 | −0.0108473 | ||||||||
\(631\) | 3.94393 | 0.157005 | 0.0785026 | − | 0.996914i | \(-0.474986\pi\) | ||||
0.0785026 | + | 0.996914i | \(0.474986\pi\) | |||||||
\(632\) | 29.7324 | 1.18269 | ||||||||
\(633\) | 38.9642 | 1.54869 | ||||||||
\(634\) | 29.6975 | 1.17944 | ||||||||
\(635\) | 11.3103 | 0.448835 | ||||||||
\(636\) | 57.3677 | 2.27478 | ||||||||
\(637\) | 40.0004 | 1.58487 | ||||||||
\(638\) | 52.9229 | 2.09524 | ||||||||
\(639\) | −0.580366 | −0.0229589 | ||||||||
\(640\) | −20.0768 | −0.793606 | ||||||||
\(641\) | −33.6306 | −1.32833 | −0.664164 | − | 0.747587i | \(-0.731213\pi\) | ||||
−0.664164 | + | 0.747587i | \(0.731213\pi\) | |||||||
\(642\) | 39.7048 | 1.56702 | ||||||||
\(643\) | 1.95780 | 0.0772079 | 0.0386040 | − | 0.999255i | \(-0.487709\pi\) | ||||
0.0386040 | + | 0.999255i | \(0.487709\pi\) | |||||||
\(644\) | −1.22109 | −0.0481178 | ||||||||
\(645\) | 9.99177 | 0.393426 | ||||||||
\(646\) | −30.3161 | −1.19277 | ||||||||
\(647\) | −31.5865 | −1.24179 | −0.620896 | − | 0.783893i | \(-0.713231\pi\) | ||||
−0.620896 | + | 0.783893i | \(0.713231\pi\) | |||||||
\(648\) | 41.9400 | 1.64756 | ||||||||
\(649\) | 60.2715 | 2.36586 | ||||||||
\(650\) | −41.2926 | −1.61963 | ||||||||
\(651\) | 1.69188 | 0.0663100 | ||||||||
\(652\) | −19.4764 | −0.762753 | ||||||||
\(653\) | −40.4811 | −1.58415 | −0.792074 | − | 0.610425i | \(-0.790999\pi\) | ||||
−0.792074 | + | 0.610425i | \(0.790999\pi\) | |||||||
\(654\) | −18.4809 | −0.722659 | ||||||||
\(655\) | 29.0679 | 1.13578 | ||||||||
\(656\) | 28.6762 | 1.11962 | ||||||||
\(657\) | −6.45699 | −0.251911 | ||||||||
\(658\) | −1.96543 | −0.0766205 | ||||||||
\(659\) | 37.1392 | 1.44674 | 0.723369 | − | 0.690462i | \(-0.242593\pi\) | ||||
0.723369 | + | 0.690462i | \(0.242593\pi\) | |||||||
\(660\) | 40.2887 | 1.56824 | ||||||||
\(661\) | −20.1610 | −0.784172 | −0.392086 | − | 0.919929i | \(-0.628246\pi\) | ||||
−0.392086 | + | 0.919929i | \(0.628246\pi\) | |||||||
\(662\) | 65.0978 | 2.53010 | ||||||||
\(663\) | 20.7636 | 0.806392 | ||||||||
\(664\) | −6.90304 | −0.267890 | ||||||||
\(665\) | 0.954123 | 0.0369993 | ||||||||
\(666\) | −12.5004 | −0.484382 | ||||||||
\(667\) | −11.4307 | −0.442598 | ||||||||
\(668\) | 48.5627 | 1.87895 | ||||||||
\(669\) | 1.23468 | 0.0477356 | ||||||||
\(670\) | −32.6528 | −1.26149 | ||||||||
\(671\) | 29.0763 | 1.12248 | ||||||||
\(672\) | −0.865971 | −0.0334056 | ||||||||
\(673\) | −31.1525 | −1.20084 | −0.600420 | − | 0.799685i | \(-0.705000\pi\) | ||||
−0.600420 | + | 0.799685i | \(0.705000\pi\) | |||||||
\(674\) | −32.7237 | −1.26047 | ||||||||
\(675\) | 15.8770 | 0.611104 | ||||||||
\(676\) | 87.0521 | 3.34816 | ||||||||
\(677\) | 9.87390 | 0.379485 | 0.189742 | − | 0.981834i | \(-0.439235\pi\) | ||||
0.189742 | + | 0.981834i | \(0.439235\pi\) | |||||||
\(678\) | 3.93388 | 0.151080 | ||||||||
\(679\) | −0.776764 | −0.0298095 | ||||||||
\(680\) | −20.7013 | −0.793860 | ||||||||
\(681\) | −6.01528 | −0.230506 | ||||||||
\(682\) | 87.3716 | 3.34563 | ||||||||
\(683\) | −33.2088 | −1.27070 | −0.635350 | − | 0.772224i | \(-0.719144\pi\) | ||||
−0.635350 | + | 0.772224i | \(0.719144\pi\) | |||||||
\(684\) | 13.1219 | 0.501729 | ||||||||
\(685\) | 10.3580 | 0.395760 | ||||||||
\(686\) | 4.47489 | 0.170852 | ||||||||
\(687\) | −20.3200 | −0.775258 | ||||||||
\(688\) | −28.6170 | −1.09101 | ||||||||
\(689\) | −48.0528 | −1.83067 | ||||||||
\(690\) | −12.6610 | −0.481998 | ||||||||
\(691\) | −0.384714 | −0.0146352 | −0.00731761 | − | 0.999973i | \(-0.502329\pi\) | ||||
−0.00731761 | + | 0.999973i | \(0.502329\pi\) | |||||||
\(692\) | −33.2291 | −1.26318 | ||||||||
\(693\) | 0.295148 | 0.0112118 | ||||||||
\(694\) | 5.32538 | 0.202148 | ||||||||
\(695\) | 31.3351 | 1.18861 | ||||||||
\(696\) | −49.0716 | −1.86005 | ||||||||
\(697\) | −10.2328 | −0.387594 | ||||||||
\(698\) | −40.6337 | −1.53801 | ||||||||
\(699\) | 16.7547 | 0.633723 | ||||||||
\(700\) | −1.58564 | −0.0599316 | ||||||||
\(701\) | 25.6388 | 0.968363 | 0.484181 | − | 0.874968i | \(-0.339117\pi\) | ||||
0.484181 | + | 0.874968i | \(0.339117\pi\) | |||||||
\(702\) | −80.6695 | −3.04467 | ||||||||
\(703\) | 43.8064 | 1.65219 | ||||||||
\(704\) | 7.77988 | 0.293215 | ||||||||
\(705\) | −14.0062 | −0.527505 | ||||||||
\(706\) | −79.3130 | −2.98498 | ||||||||
\(707\) | 0.00998557 | 0.000375546 0 | ||||||||
\(708\) | −102.539 | −3.85364 | ||||||||
\(709\) | 10.0531 | 0.377552 | 0.188776 | − | 0.982020i | \(-0.439548\pi\) | ||||
0.188776 | + | 0.982020i | \(0.439548\pi\) | |||||||
\(710\) | 3.70754 | 0.139142 | ||||||||
\(711\) | 2.84800 | 0.106808 | ||||||||
\(712\) | 91.5186 | 3.42981 | ||||||||
\(713\) | −18.8711 | −0.706730 | ||||||||
\(714\) | 1.16009 | 0.0434154 | ||||||||
\(715\) | −33.7469 | −1.26206 | ||||||||
\(716\) | 114.202 | 4.26792 | ||||||||
\(717\) | 37.9097 | 1.41576 | ||||||||
\(718\) | 24.8934 | 0.929015 | ||||||||
\(719\) | −21.9236 | −0.817611 | −0.408806 | − | 0.912621i | \(-0.634055\pi\) | ||||
−0.408806 | + | 0.912621i | \(0.634055\pi\) | |||||||
\(720\) | 5.55697 | 0.207096 | ||||||||
\(721\) | 0.899254 | 0.0334900 | ||||||||
\(722\) | −18.8555 | −0.701729 | ||||||||
\(723\) | 0.858452 | 0.0319262 | ||||||||
\(724\) | −41.9015 | −1.55726 | ||||||||
\(725\) | −14.8432 | −0.551264 | ||||||||
\(726\) | −20.2734 | −0.752417 | ||||||||
\(727\) | −19.4429 | −0.721097 | −0.360548 | − | 0.932740i | \(-0.617410\pi\) | ||||
−0.360548 | + | 0.932740i | \(0.617410\pi\) | |||||||
\(728\) | 4.39094 | 0.162739 | ||||||||
\(729\) | 30.0069 | 1.11137 | ||||||||
\(730\) | 41.2491 | 1.52670 | ||||||||
\(731\) | 10.2116 | 0.377691 | ||||||||
\(732\) | −49.4670 | −1.82835 | ||||||||
\(733\) | 23.0709 | 0.852144 | 0.426072 | − | 0.904689i | \(-0.359897\pi\) | ||||
0.426072 | + | 0.904689i | \(0.359897\pi\) | |||||||
\(734\) | −26.6692 | −0.984378 | ||||||||
\(735\) | 15.9264 | 0.587455 | ||||||||
\(736\) | 9.65900 | 0.356036 | ||||||||
\(737\) | 35.3971 | 1.30387 | ||||||||
\(738\) | 6.44427 | 0.237217 | ||||||||
\(739\) | −14.3648 | −0.528419 | −0.264209 | − | 0.964465i | \(-0.585111\pi\) | ||||
−0.264209 | + | 0.964465i | \(0.585111\pi\) | |||||||
\(740\) | 54.8847 | 2.01760 | ||||||||
\(741\) | 45.8243 | 1.68340 | ||||||||
\(742\) | −2.68478 | −0.0985615 | ||||||||
\(743\) | 5.22735 | 0.191773 | 0.0958865 | − | 0.995392i | \(-0.469431\pi\) | ||||
0.0958865 | + | 0.995392i | \(0.469431\pi\) | |||||||
\(744\) | −81.0133 | −2.97009 | ||||||||
\(745\) | −1.31728 | −0.0482614 | ||||||||
\(746\) | −14.4691 | −0.529751 | ||||||||
\(747\) | −0.661227 | −0.0241930 | ||||||||
\(748\) | 41.1752 | 1.50552 | ||||||||
\(749\) | −1.27710 | −0.0466644 | ||||||||
\(750\) | −45.2766 | −1.65327 | ||||||||
\(751\) | 27.8328 | 1.01563 | 0.507816 | − | 0.861465i | \(-0.330453\pi\) | ||||
0.507816 | + | 0.861465i | \(0.330453\pi\) | |||||||
\(752\) | 40.1147 | 1.46283 | ||||||||
\(753\) | 32.5469 | 1.18608 | ||||||||
\(754\) | 75.4172 | 2.74653 | ||||||||
\(755\) | 2.09851 | 0.0763726 | ||||||||
\(756\) | −3.09772 | −0.112663 | ||||||||
\(757\) | −45.9267 | −1.66923 | −0.834617 | − | 0.550831i | \(-0.814311\pi\) | ||||
−0.834617 | + | 0.550831i | \(0.814311\pi\) | |||||||
\(758\) | 34.8403 | 1.26546 | ||||||||
\(759\) | 13.7252 | 0.498192 | ||||||||
\(760\) | −45.6868 | −1.65724 | ||||||||
\(761\) | 6.73146 | 0.244015 | 0.122008 | − | 0.992529i | \(-0.461067\pi\) | ||||
0.122008 | + | 0.992529i | \(0.461067\pi\) | |||||||
\(762\) | 30.3497 | 1.09945 | ||||||||
\(763\) | 0.594437 | 0.0215201 | ||||||||
\(764\) | 57.4044 | 2.07682 | ||||||||
\(765\) | −1.98294 | −0.0716932 | ||||||||
\(766\) | −77.7978 | −2.81095 | ||||||||
\(767\) | 85.8893 | 3.10128 | ||||||||
\(768\) | −47.8516 | −1.72670 | ||||||||
\(769\) | 1.11139 | 0.0400779 | 0.0200389 | − | 0.999799i | \(-0.493621\pi\) | ||||
0.0200389 | + | 0.999799i | \(0.493621\pi\) | |||||||
\(770\) | −1.88549 | −0.0679484 | ||||||||
\(771\) | 26.4251 | 0.951678 | ||||||||
\(772\) | −36.7870 | −1.32399 | ||||||||
\(773\) | −9.34034 | −0.335949 | −0.167974 | − | 0.985791i | \(-0.553723\pi\) | ||||
−0.167974 | + | 0.985791i | \(0.553723\pi\) | |||||||
\(774\) | −6.43097 | −0.231156 | ||||||||
\(775\) | −24.5050 | −0.880246 | ||||||||
\(776\) | 37.1942 | 1.33520 | ||||||||
\(777\) | −1.67632 | −0.0601376 | ||||||||
\(778\) | 1.30312 | 0.0467192 | ||||||||
\(779\) | −22.5832 | −0.809128 | ||||||||
\(780\) | 57.4130 | 2.05571 | ||||||||
\(781\) | −4.01915 | −0.143816 | ||||||||
\(782\) | −12.9396 | −0.462721 | ||||||||
\(783\) | −28.9978 | −1.03630 | ||||||||
\(784\) | −45.6142 | −1.62908 | ||||||||
\(785\) | −20.5404 | −0.733119 | ||||||||
\(786\) | 78.0001 | 2.78217 | ||||||||
\(787\) | −22.3063 | −0.795134 | −0.397567 | − | 0.917573i | \(-0.630145\pi\) | ||||
−0.397567 | + | 0.917573i | \(0.630145\pi\) | |||||||
\(788\) | 32.1125 | 1.14396 | ||||||||
\(789\) | −43.1261 | −1.53533 | ||||||||
\(790\) | −18.1938 | −0.647307 | ||||||||
\(791\) | −0.126533 | −0.00449901 | ||||||||
\(792\) | −14.1328 | −0.502186 | ||||||||
\(793\) | 41.4349 | 1.47140 | ||||||||
\(794\) | 18.5182 | 0.657188 | ||||||||
\(795\) | −19.1325 | −0.678561 | ||||||||
\(796\) | −92.2444 | −3.26951 | ||||||||
\(797\) | 4.91016 | 0.173927 | 0.0869634 | − | 0.996212i | \(-0.472284\pi\) | ||||
0.0869634 | + | 0.996212i | \(0.472284\pi\) | |||||||
\(798\) | 2.56027 | 0.0906327 | ||||||||
\(799\) | −14.3144 | −0.506408 | ||||||||
\(800\) | 12.5426 | 0.443449 | ||||||||
\(801\) | 8.76637 | 0.309744 | ||||||||
\(802\) | 97.3434 | 3.43731 | ||||||||
\(803\) | −44.7159 | −1.57799 | ||||||||
\(804\) | −60.2204 | −2.12381 | ||||||||
\(805\) | 0.407242 | 0.0143534 | ||||||||
\(806\) | 124.508 | 4.38560 | ||||||||
\(807\) | −29.7306 | −1.04657 | ||||||||
\(808\) | −0.478145 | −0.0168211 | ||||||||
\(809\) | 23.7397 | 0.834644 | 0.417322 | − | 0.908759i | \(-0.362969\pi\) | ||||
0.417322 | + | 0.908759i | \(0.362969\pi\) | |||||||
\(810\) | −25.6639 | −0.901737 | ||||||||
\(811\) | 49.6713 | 1.74420 | 0.872098 | − | 0.489331i | \(-0.162759\pi\) | ||||
0.872098 | + | 0.489331i | \(0.162759\pi\) | |||||||
\(812\) | 2.89603 | 0.101631 | ||||||||
\(813\) | 6.12617 | 0.214854 | ||||||||
\(814\) | −86.5680 | −3.03421 | ||||||||
\(815\) | 6.49550 | 0.227527 | ||||||||
\(816\) | −23.6776 | −0.828883 | ||||||||
\(817\) | 22.5366 | 0.788455 | ||||||||
\(818\) | −46.8429 | −1.63782 | ||||||||
\(819\) | 0.420598 | 0.0146969 | ||||||||
\(820\) | −28.2944 | −0.988083 | ||||||||
\(821\) | −52.7231 | −1.84005 | −0.920025 | − | 0.391861i | \(-0.871832\pi\) | ||||
−0.920025 | + | 0.391861i | \(0.871832\pi\) | |||||||
\(822\) | 27.7945 | 0.969444 | ||||||||
\(823\) | 13.7554 | 0.479484 | 0.239742 | − | 0.970837i | \(-0.422937\pi\) | ||||
0.239742 | + | 0.970837i | \(0.422937\pi\) | |||||||
\(824\) | −43.0595 | −1.50005 | ||||||||
\(825\) | 17.8227 | 0.620507 | ||||||||
\(826\) | 4.79876 | 0.166970 | ||||||||
\(827\) | 37.9574 | 1.31991 | 0.659954 | − | 0.751306i | \(-0.270576\pi\) | ||||
0.659954 | + | 0.751306i | \(0.270576\pi\) | |||||||
\(828\) | 5.60074 | 0.194639 | ||||||||
\(829\) | 7.87068 | 0.273360 | 0.136680 | − | 0.990615i | \(-0.456357\pi\) | ||||
0.136680 | + | 0.990615i | \(0.456357\pi\) | |||||||
\(830\) | 4.22410 | 0.146621 | ||||||||
\(831\) | 10.0033 | 0.347009 | ||||||||
\(832\) | 11.0866 | 0.384360 | ||||||||
\(833\) | 16.2769 | 0.563960 | ||||||||
\(834\) | 84.0838 | 2.91158 | ||||||||
\(835\) | −16.1960 | −0.560486 | ||||||||
\(836\) | 90.8718 | 3.14287 | ||||||||
\(837\) | −47.8732 | −1.65474 | ||||||||
\(838\) | 49.1354 | 1.69735 | ||||||||
\(839\) | 11.2368 | 0.387936 | 0.193968 | − | 0.981008i | \(-0.437864\pi\) | ||||
0.193968 | + | 0.981008i | \(0.437864\pi\) | |||||||
\(840\) | 1.74828 | 0.0603214 | ||||||||
\(841\) | −1.89016 | −0.0651779 | ||||||||
\(842\) | −64.9288 | −2.23759 | ||||||||
\(843\) | 44.6475 | 1.53774 | ||||||||
\(844\) | 110.110 | 3.79013 | ||||||||
\(845\) | −29.0325 | −0.998747 | ||||||||
\(846\) | 9.01478 | 0.309934 | ||||||||
\(847\) | 0.652094 | 0.0224062 | ||||||||
\(848\) | 54.7967 | 1.88173 | ||||||||
\(849\) | 0.923358 | 0.0316896 | ||||||||
\(850\) | −16.8027 | −0.576327 | ||||||||
\(851\) | 18.6976 | 0.640945 | ||||||||
\(852\) | 6.83770 | 0.234256 | ||||||||
\(853\) | 4.26322 | 0.145970 | 0.0729850 | − | 0.997333i | \(-0.476747\pi\) | ||||
0.0729850 | + | 0.997333i | \(0.476747\pi\) | |||||||
\(854\) | 2.31503 | 0.0792188 | ||||||||
\(855\) | −4.37624 | −0.149664 | ||||||||
\(856\) | 61.1523 | 2.09014 | ||||||||
\(857\) | 18.9123 | 0.646032 | 0.323016 | − | 0.946394i | \(-0.395303\pi\) | ||||
0.323016 | + | 0.946394i | \(0.395303\pi\) | |||||||
\(858\) | −90.5557 | −3.09152 | ||||||||
\(859\) | −46.6730 | −1.59246 | −0.796230 | − | 0.604993i | \(-0.793176\pi\) | ||||
−0.796230 | + | 0.604993i | \(0.793176\pi\) | |||||||
\(860\) | 28.2360 | 0.962838 | ||||||||
\(861\) | 0.864182 | 0.0294513 | ||||||||
\(862\) | 95.9711 | 3.26879 | ||||||||
\(863\) | −35.5891 | −1.21147 | −0.605733 | − | 0.795668i | \(-0.707120\pi\) | ||||
−0.605733 | + | 0.795668i | \(0.707120\pi\) | |||||||
\(864\) | 24.5034 | 0.833622 | ||||||||
\(865\) | 11.0821 | 0.376804 | ||||||||
\(866\) | 2.41164 | 0.0819507 | ||||||||
\(867\) | −17.9947 | −0.611133 | ||||||||
\(868\) | 4.78112 | 0.162282 | ||||||||
\(869\) | 19.7230 | 0.669055 | ||||||||
\(870\) | 30.0279 | 1.01804 | ||||||||
\(871\) | 50.4423 | 1.70917 | ||||||||
\(872\) | −28.4638 | −0.963904 | ||||||||
\(873\) | 3.56276 | 0.120581 | ||||||||
\(874\) | −28.5572 | −0.965960 | ||||||||
\(875\) | 1.45632 | 0.0492327 | ||||||||
\(876\) | 76.0743 | 2.57031 | ||||||||
\(877\) | 7.85452 | 0.265228 | 0.132614 | − | 0.991168i | \(-0.457663\pi\) | ||||
0.132614 | + | 0.991168i | \(0.457663\pi\) | |||||||
\(878\) | 39.9473 | 1.34816 | ||||||||
\(879\) | 32.5382 | 1.09749 | ||||||||
\(880\) | 38.4831 | 1.29726 | ||||||||
\(881\) | −26.9723 | −0.908718 | −0.454359 | − | 0.890819i | \(-0.650132\pi\) | ||||
−0.454359 | + | 0.890819i | \(0.650132\pi\) | |||||||
\(882\) | −10.2507 | −0.345158 | ||||||||
\(883\) | 25.7185 | 0.865497 | 0.432749 | − | 0.901515i | \(-0.357544\pi\) | ||||
0.432749 | + | 0.901515i | \(0.357544\pi\) | |||||||
\(884\) | 58.6763 | 1.97350 | ||||||||
\(885\) | 34.1974 | 1.14953 | ||||||||
\(886\) | 53.2027 | 1.78738 | ||||||||
\(887\) | −23.8388 | −0.800429 | −0.400215 | − | 0.916421i | \(-0.631064\pi\) | ||||
−0.400215 | + | 0.916421i | \(0.631064\pi\) | |||||||
\(888\) | 80.2682 | 2.69362 | ||||||||
\(889\) | −0.976199 | −0.0327407 | ||||||||
\(890\) | −56.0021 | −1.87719 | ||||||||
\(891\) | 27.8208 | 0.932033 | ||||||||
\(892\) | 3.48911 | 0.116824 | ||||||||
\(893\) | −31.5913 | −1.05716 | ||||||||
\(894\) | −3.53476 | −0.118220 | ||||||||
\(895\) | −38.0871 | −1.27311 | ||||||||
\(896\) | 1.73285 | 0.0578903 | ||||||||
\(897\) | 19.5589 | 0.653052 | ||||||||
\(898\) | 3.11358 | 0.103902 | ||||||||
\(899\) | 44.7562 | 1.49270 | ||||||||
\(900\) | 7.27280 | 0.242427 | ||||||||
\(901\) | −19.5535 | −0.651422 | ||||||||
\(902\) | 44.6279 | 1.48594 | ||||||||
\(903\) | −0.862398 | −0.0286988 | ||||||||
\(904\) | 6.05887 | 0.201515 | ||||||||
\(905\) | 13.9744 | 0.464526 | ||||||||
\(906\) | 5.63110 | 0.187081 | ||||||||
\(907\) | 7.80841 | 0.259274 | 0.129637 | − | 0.991562i | \(-0.458619\pi\) | ||||
0.129637 | + | 0.991562i | \(0.458619\pi\) | |||||||
\(908\) | −16.9987 | −0.564122 | ||||||||
\(909\) | −0.0458004 | −0.00151910 | ||||||||
\(910\) | −2.68690 | −0.0890699 | ||||||||
\(911\) | 53.8829 | 1.78522 | 0.892610 | − | 0.450830i | \(-0.148872\pi\) | ||||
0.892610 | + | 0.450830i | \(0.148872\pi\) | |||||||
\(912\) | −52.2554 | −1.73035 | ||||||||
\(913\) | −4.57912 | −0.151547 | ||||||||
\(914\) | 85.2289 | 2.81912 | ||||||||
\(915\) | 16.4976 | 0.545393 | ||||||||
\(916\) | −57.4228 | −1.89730 | ||||||||
\(917\) | −2.50887 | −0.0828503 | ||||||||
\(918\) | −32.8258 | −1.08341 | ||||||||
\(919\) | 43.5175 | 1.43551 | 0.717755 | − | 0.696295i | \(-0.245170\pi\) | ||||
0.717755 | + | 0.696295i | \(0.245170\pi\) | |||||||
\(920\) | −19.5002 | −0.642903 | ||||||||
\(921\) | 30.8583 | 1.01682 | ||||||||
\(922\) | −90.2363 | −2.97177 | ||||||||
\(923\) | −5.72744 | −0.188521 | ||||||||
\(924\) | −3.47735 | −0.114396 | ||||||||
\(925\) | 24.2796 | 0.798309 | ||||||||
\(926\) | −59.4050 | −1.95217 | ||||||||
\(927\) | −4.12458 | −0.135469 | ||||||||
\(928\) | −22.9080 | −0.751992 | ||||||||
\(929\) | 27.1004 | 0.889135 | 0.444568 | − | 0.895745i | \(-0.353357\pi\) | ||||
0.444568 | + | 0.895745i | \(0.353357\pi\) | |||||||
\(930\) | 49.5736 | 1.62558 | ||||||||
\(931\) | 35.9223 | 1.17730 | ||||||||
\(932\) | 47.3476 | 1.55092 | ||||||||
\(933\) | 54.5920 | 1.78726 | ||||||||
\(934\) | −27.1313 | −0.887764 | ||||||||
\(935\) | −13.7322 | −0.449092 | ||||||||
\(936\) | −20.1397 | −0.658288 | ||||||||
\(937\) | 42.3293 | 1.38284 | 0.691419 | − | 0.722454i | \(-0.256986\pi\) | ||||
0.691419 | + | 0.722454i | \(0.256986\pi\) | |||||||
\(938\) | 2.81829 | 0.0920203 | ||||||||
\(939\) | −10.5512 | −0.344324 | ||||||||
\(940\) | −39.5805 | −1.29097 | ||||||||
\(941\) | −24.2063 | −0.789101 | −0.394551 | − | 0.918874i | \(-0.629100\pi\) | ||||
−0.394551 | + | 0.918874i | \(0.629100\pi\) | |||||||
\(942\) | −55.1176 | −1.79583 | ||||||||
\(943\) | −9.63905 | −0.313891 | ||||||||
\(944\) | −97.9432 | −3.18778 | ||||||||
\(945\) | 1.03311 | 0.0336071 | ||||||||
\(946\) | −44.5357 | −1.44798 | ||||||||
\(947\) | 45.6920 | 1.48479 | 0.742394 | − | 0.669963i | \(-0.233690\pi\) | ||||
0.742394 | + | 0.669963i | \(0.233690\pi\) | |||||||
\(948\) | −33.5543 | −1.08979 | ||||||||
\(949\) | −63.7219 | −2.06850 | ||||||||
\(950\) | −37.0827 | −1.20312 | ||||||||
\(951\) | −18.2662 | −0.592322 | ||||||||
\(952\) | 1.78675 | 0.0579089 | ||||||||
\(953\) | 19.4220 | 0.629139 | 0.314570 | − | 0.949234i | \(-0.398140\pi\) | ||||
0.314570 | + | 0.949234i | \(0.398140\pi\) | |||||||
\(954\) | 12.3142 | 0.398687 | ||||||||
\(955\) | −19.1447 | −0.619510 | ||||||||
\(956\) | 107.130 | 3.46482 | ||||||||
\(957\) | −32.5516 | −1.05224 | ||||||||
\(958\) | −54.3149 | −1.75484 | ||||||||
\(959\) | −0.894009 | −0.0288691 | ||||||||
\(960\) | 4.41422 | 0.142468 | ||||||||
\(961\) | 42.8890 | 1.38351 | ||||||||
\(962\) | −123.363 | −3.97738 | ||||||||
\(963\) | 5.85765 | 0.188760 | ||||||||
\(964\) | 2.42592 | 0.0781336 | ||||||||
\(965\) | 12.2687 | 0.394944 | ||||||||
\(966\) | 1.09278 | 0.0351598 | ||||||||
\(967\) | 4.88290 | 0.157023 | 0.0785117 | − | 0.996913i | \(-0.474983\pi\) | ||||
0.0785117 | + | 0.996913i | \(0.474983\pi\) | |||||||
\(968\) | −31.2246 | −1.00360 | ||||||||
\(969\) | 18.6467 | 0.599019 | ||||||||
\(970\) | −22.7599 | −0.730776 | ||||||||
\(971\) | −25.5279 | −0.819229 | −0.409614 | − | 0.912259i | \(-0.634337\pi\) | ||||
−0.409614 | + | 0.912259i | \(0.634337\pi\) | |||||||
\(972\) | 26.1133 | 0.837584 | ||||||||
\(973\) | −2.70456 | −0.0867041 | ||||||||
\(974\) | −96.2159 | −3.08296 | ||||||||
\(975\) | 25.3981 | 0.813389 | ||||||||
\(976\) | −47.2500 | −1.51244 | ||||||||
\(977\) | 42.9087 | 1.37277 | 0.686386 | − | 0.727238i | \(-0.259196\pi\) | ||||
0.686386 | + | 0.727238i | \(0.259196\pi\) | |||||||
\(978\) | 17.4299 | 0.557346 | ||||||||
\(979\) | 60.7088 | 1.94026 | ||||||||
\(980\) | 45.0068 | 1.43769 | ||||||||
\(981\) | −2.72648 | −0.0870499 | ||||||||
\(982\) | −17.0369 | −0.543669 | ||||||||
\(983\) | 46.7178 | 1.49007 | 0.745034 | − | 0.667027i | \(-0.232433\pi\) | ||||
0.745034 | + | 0.667027i | \(0.232433\pi\) | |||||||
\(984\) | −41.3801 | −1.31915 | ||||||||
\(985\) | −10.7097 | −0.341241 | ||||||||
\(986\) | 30.6886 | 0.977324 | ||||||||
\(987\) | 1.20889 | 0.0384794 | ||||||||
\(988\) | 129.496 | 4.11981 | ||||||||
\(989\) | 9.61915 | 0.305871 | ||||||||
\(990\) | 8.64812 | 0.274855 | ||||||||
\(991\) | −0.594536 | −0.0188861 | −0.00944303 | − | 0.999955i | \(-0.503006\pi\) | ||||
−0.00944303 | + | 0.999955i | \(0.503006\pi\) | |||||||
\(992\) | −37.8193 | −1.20076 | ||||||||
\(993\) | −40.0400 | −1.27063 | ||||||||
\(994\) | −0.320001 | −0.0101498 | ||||||||
\(995\) | 30.7641 | 0.975288 | ||||||||
\(996\) | 7.79038 | 0.246848 | ||||||||
\(997\) | −2.29730 | −0.0727562 | −0.0363781 | − | 0.999338i | \(-0.511582\pi\) | ||||
−0.0363781 | + | 0.999338i | \(0.511582\pi\) | |||||||
\(998\) | −23.9646 | −0.758585 | ||||||||
\(999\) | 47.4329 | 1.50071 |
(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.d.1.8 | ✓ | 165 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8023.2.a.d.1.8 | ✓ | 165 | 1.1 | even | 1 | trivial |