Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6047,2,Mod(1,6047)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6047, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6047.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6047 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6047.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: | \(48.2855381023\) |
Analytic rank: | \(1\) |
Dimension: | \(217\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 6047.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.62503 | −1.85618 | −0.928090 | − | 0.372357i | \(-0.878550\pi\) | ||||
−0.928090 | + | 0.372357i | \(0.878550\pi\) | |||||||
\(3\) | 1.59617 | 0.921551 | 0.460776 | − | 0.887517i | \(-0.347571\pi\) | ||||
0.460776 | + | 0.887517i | \(0.347571\pi\) | |||||||
\(4\) | 4.89080 | 2.44540 | ||||||||
\(5\) | 2.83370 | 1.26727 | 0.633635 | − | 0.773632i | \(-0.281562\pi\) | ||||
0.633635 | + | 0.773632i | \(0.281562\pi\) | |||||||
\(6\) | −4.19001 | −1.71056 | ||||||||
\(7\) | −4.08027 | −1.54220 | −0.771098 | − | 0.636717i | \(-0.780292\pi\) | ||||
−0.771098 | + | 0.636717i | \(0.780292\pi\) | |||||||
\(8\) | −7.58846 | −2.68293 | ||||||||
\(9\) | −0.452230 | −0.150743 | ||||||||
\(10\) | −7.43856 | −2.35228 | ||||||||
\(11\) | −4.35517 | −1.31313 | −0.656567 | − | 0.754268i | \(-0.727992\pi\) | ||||
−0.656567 | + | 0.754268i | \(0.727992\pi\) | |||||||
\(12\) | 7.80657 | 2.25356 | ||||||||
\(13\) | 1.46745 | 0.406998 | 0.203499 | − | 0.979075i | \(-0.434769\pi\) | ||||
0.203499 | + | 0.979075i | \(0.434769\pi\) | |||||||
\(14\) | 10.7108 | 2.86259 | ||||||||
\(15\) | 4.52308 | 1.16785 | ||||||||
\(16\) | 10.1384 | 2.53459 | ||||||||
\(17\) | 0.159171 | 0.0386046 | 0.0193023 | − | 0.999814i | \(-0.493856\pi\) | ||||
0.0193023 | + | 0.999814i | \(0.493856\pi\) | |||||||
\(18\) | 1.18712 | 0.279807 | ||||||||
\(19\) | 6.75436 | 1.54956 | 0.774778 | − | 0.632233i | \(-0.217862\pi\) | ||||
0.774778 | + | 0.632233i | \(0.217862\pi\) | |||||||
\(20\) | 13.8591 | 3.09898 | ||||||||
\(21\) | −6.51281 | −1.42121 | ||||||||
\(22\) | 11.4325 | 2.43741 | ||||||||
\(23\) | 2.68913 | 0.560721 | 0.280361 | − | 0.959895i | \(-0.409546\pi\) | ||||
0.280361 | + | 0.959895i | \(0.409546\pi\) | |||||||
\(24\) | −12.1125 | −2.47245 | ||||||||
\(25\) | 3.02987 | 0.605973 | ||||||||
\(26\) | −3.85211 | −0.755461 | ||||||||
\(27\) | −5.51036 | −1.06047 | ||||||||
\(28\) | −19.9558 | −3.77129 | ||||||||
\(29\) | 4.32781 | 0.803654 | 0.401827 | − | 0.915716i | \(-0.368375\pi\) | ||||
0.401827 | + | 0.915716i | \(0.368375\pi\) | |||||||
\(30\) | −11.8732 | −2.16775 | ||||||||
\(31\) | 3.01180 | 0.540934 | 0.270467 | − | 0.962729i | \(-0.412822\pi\) | ||||
0.270467 | + | 0.962729i | \(0.412822\pi\) | |||||||
\(32\) | −11.4366 | −2.02173 | ||||||||
\(33\) | −6.95161 | −1.21012 | ||||||||
\(34\) | −0.417829 | −0.0716570 | ||||||||
\(35\) | −11.5623 | −1.95438 | ||||||||
\(36\) | −2.21177 | −0.368628 | ||||||||
\(37\) | −6.79443 | −1.11700 | −0.558499 | − | 0.829505i | \(-0.688622\pi\) | ||||
−0.558499 | + | 0.829505i | \(0.688622\pi\) | |||||||
\(38\) | −17.7304 | −2.87625 | ||||||||
\(39\) | 2.34231 | 0.375069 | ||||||||
\(40\) | −21.5034 | −3.39999 | ||||||||
\(41\) | 10.9065 | 1.70332 | 0.851658 | − | 0.524098i | \(-0.175597\pi\) | ||||
0.851658 | + | 0.524098i | \(0.175597\pi\) | |||||||
\(42\) | 17.0964 | 2.63802 | ||||||||
\(43\) | −5.59742 | −0.853599 | −0.426799 | − | 0.904346i | \(-0.640359\pi\) | ||||
−0.426799 | + | 0.904346i | \(0.640359\pi\) | |||||||
\(44\) | −21.3003 | −3.21114 | ||||||||
\(45\) | −1.28149 | −0.191033 | ||||||||
\(46\) | −7.05905 | −1.04080 | ||||||||
\(47\) | −3.88077 | −0.566068 | −0.283034 | − | 0.959110i | \(-0.591341\pi\) | ||||
−0.283034 | + | 0.959110i | \(0.591341\pi\) | |||||||
\(48\) | 16.1826 | 2.33575 | ||||||||
\(49\) | 9.64856 | 1.37837 | ||||||||
\(50\) | −7.95350 | −1.12480 | ||||||||
\(51\) | 0.254064 | 0.0355761 | ||||||||
\(52\) | 7.17702 | 0.995273 | ||||||||
\(53\) | −10.8337 | −1.48812 | −0.744061 | − | 0.668111i | \(-0.767103\pi\) | ||||
−0.744061 | + | 0.668111i | \(0.767103\pi\) | |||||||
\(54\) | 14.4649 | 1.96842 | ||||||||
\(55\) | −12.3413 | −1.66410 | ||||||||
\(56\) | 30.9629 | 4.13760 | ||||||||
\(57\) | 10.7811 | 1.42800 | ||||||||
\(58\) | −11.3606 | −1.49173 | ||||||||
\(59\) | −2.01215 | −0.261960 | −0.130980 | − | 0.991385i | \(-0.541812\pi\) | ||||
−0.130980 | + | 0.991385i | \(0.541812\pi\) | |||||||
\(60\) | 22.1215 | 2.85587 | ||||||||
\(61\) | −11.7386 | −1.50298 | −0.751489 | − | 0.659745i | \(-0.770664\pi\) | ||||
−0.751489 | + | 0.659745i | \(0.770664\pi\) | |||||||
\(62\) | −7.90607 | −1.00407 | ||||||||
\(63\) | 1.84522 | 0.232476 | ||||||||
\(64\) | 9.74479 | 1.21810 | ||||||||
\(65\) | 4.15832 | 0.515776 | ||||||||
\(66\) | 18.2482 | 2.24620 | ||||||||
\(67\) | −9.50300 | −1.16098 | −0.580488 | − | 0.814269i | \(-0.697138\pi\) | ||||
−0.580488 | + | 0.814269i | \(0.697138\pi\) | |||||||
\(68\) | 0.778473 | 0.0944037 | ||||||||
\(69\) | 4.29231 | 0.516733 | ||||||||
\(70\) | 30.3513 | 3.62768 | ||||||||
\(71\) | −2.45794 | −0.291703 | −0.145852 | − | 0.989306i | \(-0.546592\pi\) | ||||
−0.145852 | + | 0.989306i | \(0.546592\pi\) | |||||||
\(72\) | 3.43173 | 0.404433 | ||||||||
\(73\) | −5.70698 | −0.667952 | −0.333976 | − | 0.942582i | \(-0.608390\pi\) | ||||
−0.333976 | + | 0.942582i | \(0.608390\pi\) | |||||||
\(74\) | 17.8356 | 2.07335 | ||||||||
\(75\) | 4.83619 | 0.558435 | ||||||||
\(76\) | 33.0342 | 3.78929 | ||||||||
\(77\) | 17.7703 | 2.02511 | ||||||||
\(78\) | −6.14864 | −0.696196 | ||||||||
\(79\) | 11.2325 | 1.26376 | 0.631879 | − | 0.775067i | \(-0.282284\pi\) | ||||
0.631879 | + | 0.775067i | \(0.282284\pi\) | |||||||
\(80\) | 28.7291 | 3.21201 | ||||||||
\(81\) | −7.43880 | −0.826533 | ||||||||
\(82\) | −28.6301 | −3.16166 | ||||||||
\(83\) | 11.6365 | 1.27727 | 0.638636 | − | 0.769509i | \(-0.279499\pi\) | ||||
0.638636 | + | 0.769509i | \(0.279499\pi\) | |||||||
\(84\) | −31.8529 | −3.47543 | ||||||||
\(85\) | 0.451042 | 0.0489224 | ||||||||
\(86\) | 14.6934 | 1.58443 | ||||||||
\(87\) | 6.90794 | 0.740608 | ||||||||
\(88\) | 33.0491 | 3.52304 | ||||||||
\(89\) | −4.27952 | −0.453629 | −0.226814 | − | 0.973938i | \(-0.572831\pi\) | ||||
−0.226814 | + | 0.973938i | \(0.572831\pi\) | |||||||
\(90\) | 3.36394 | 0.354591 | ||||||||
\(91\) | −5.98759 | −0.627670 | ||||||||
\(92\) | 13.1520 | 1.37119 | ||||||||
\(93\) | 4.80735 | 0.498499 | ||||||||
\(94\) | 10.1871 | 1.05072 | ||||||||
\(95\) | 19.1398 | 1.96371 | ||||||||
\(96\) | −18.2548 | −1.86312 | ||||||||
\(97\) | −3.38747 | −0.343946 | −0.171973 | − | 0.985102i | \(-0.555014\pi\) | ||||
−0.171973 | + | 0.985102i | \(0.555014\pi\) | |||||||
\(98\) | −25.3278 | −2.55850 | ||||||||
\(99\) | 1.96954 | 0.197946 | ||||||||
\(100\) | 14.8185 | 1.48185 | ||||||||
\(101\) | −8.26141 | −0.822041 | −0.411020 | − | 0.911626i | \(-0.634827\pi\) | ||||
−0.411020 | + | 0.911626i | \(0.634827\pi\) | |||||||
\(102\) | −0.666927 | −0.0660356 | ||||||||
\(103\) | 8.96269 | 0.883120 | 0.441560 | − | 0.897232i | \(-0.354425\pi\) | ||||
0.441560 | + | 0.897232i | \(0.354425\pi\) | |||||||
\(104\) | −11.1357 | −1.09194 | ||||||||
\(105\) | −18.4554 | −1.80106 | ||||||||
\(106\) | 28.4388 | 2.76222 | ||||||||
\(107\) | 3.83017 | 0.370276 | 0.185138 | − | 0.982713i | \(-0.440727\pi\) | ||||
0.185138 | + | 0.982713i | \(0.440727\pi\) | |||||||
\(108\) | −26.9501 | −2.59327 | ||||||||
\(109\) | 6.24446 | 0.598111 | 0.299055 | − | 0.954236i | \(-0.403328\pi\) | ||||
0.299055 | + | 0.954236i | \(0.403328\pi\) | |||||||
\(110\) | 32.3962 | 3.08886 | ||||||||
\(111\) | −10.8451 | −1.02937 | ||||||||
\(112\) | −41.3672 | −3.90883 | ||||||||
\(113\) | 4.52680 | 0.425845 | 0.212923 | − | 0.977069i | \(-0.431702\pi\) | ||||
0.212923 | + | 0.977069i | \(0.431702\pi\) | |||||||
\(114\) | −28.3008 | −2.65062 | ||||||||
\(115\) | 7.62018 | 0.710585 | ||||||||
\(116\) | 21.1665 | 1.96526 | ||||||||
\(117\) | −0.663626 | −0.0613522 | ||||||||
\(118\) | 5.28196 | 0.486244 | ||||||||
\(119\) | −0.649459 | −0.0595358 | ||||||||
\(120\) | −34.3232 | −3.13327 | ||||||||
\(121\) | 7.96753 | 0.724321 | ||||||||
\(122\) | 30.8143 | 2.78980 | ||||||||
\(123\) | 17.4087 | 1.56969 | ||||||||
\(124\) | 14.7301 | 1.32280 | ||||||||
\(125\) | −5.58277 | −0.499338 | ||||||||
\(126\) | −4.84376 | −0.431517 | ||||||||
\(127\) | 5.55519 | 0.492943 | 0.246472 | − | 0.969150i | \(-0.420729\pi\) | ||||
0.246472 | + | 0.969150i | \(0.420729\pi\) | |||||||
\(128\) | −2.70717 | −0.239282 | ||||||||
\(129\) | −8.93446 | −0.786635 | ||||||||
\(130\) | −10.9157 | −0.957373 | ||||||||
\(131\) | −13.5798 | −1.18647 | −0.593236 | − | 0.805029i | \(-0.702150\pi\) | ||||
−0.593236 | + | 0.805029i | \(0.702150\pi\) | |||||||
\(132\) | −33.9990 | −2.95923 | ||||||||
\(133\) | −27.5596 | −2.38972 | ||||||||
\(134\) | 24.9457 | 2.15498 | ||||||||
\(135\) | −15.6147 | −1.34390 | ||||||||
\(136\) | −1.20786 | −0.103573 | ||||||||
\(137\) | −13.6882 | −1.16946 | −0.584731 | − | 0.811227i | \(-0.698800\pi\) | ||||
−0.584731 | + | 0.811227i | \(0.698800\pi\) | |||||||
\(138\) | −11.2675 | −0.959150 | ||||||||
\(139\) | 0.845489 | 0.0717134 | 0.0358567 | − | 0.999357i | \(-0.488584\pi\) | ||||
0.0358567 | + | 0.999357i | \(0.488584\pi\) | |||||||
\(140\) | −56.5487 | −4.77924 | ||||||||
\(141\) | −6.19438 | −0.521661 | ||||||||
\(142\) | 6.45217 | 0.541454 | ||||||||
\(143\) | −6.39101 | −0.534443 | ||||||||
\(144\) | −4.58487 | −0.382073 | ||||||||
\(145\) | 12.2637 | 1.01845 | ||||||||
\(146\) | 14.9810 | 1.23984 | ||||||||
\(147\) | 15.4008 | 1.27024 | ||||||||
\(148\) | −33.2302 | −2.73151 | ||||||||
\(149\) | −13.6187 | −1.11569 | −0.557845 | − | 0.829945i | \(-0.688372\pi\) | ||||
−0.557845 | + | 0.829945i | \(0.688372\pi\) | |||||||
\(150\) | −12.6952 | −1.03656 | ||||||||
\(151\) | −3.32677 | −0.270729 | −0.135364 | − | 0.990796i | \(-0.543221\pi\) | ||||
−0.135364 | + | 0.990796i | \(0.543221\pi\) | |||||||
\(152\) | −51.2552 | −4.15734 | ||||||||
\(153\) | −0.0719818 | −0.00581938 | ||||||||
\(154\) | −46.6475 | −3.75897 | ||||||||
\(155\) | 8.53453 | 0.685510 | ||||||||
\(156\) | 11.4558 | 0.917195 | ||||||||
\(157\) | −13.7185 | −1.09486 | −0.547429 | − | 0.836852i | \(-0.684393\pi\) | ||||
−0.547429 | + | 0.836852i | \(0.684393\pi\) | |||||||
\(158\) | −29.4858 | −2.34576 | ||||||||
\(159\) | −17.2925 | −1.37138 | ||||||||
\(160\) | −32.4080 | −2.56207 | ||||||||
\(161\) | −10.9723 | −0.864742 | ||||||||
\(162\) | 19.5271 | 1.53419 | ||||||||
\(163\) | −12.9331 | −1.01300 | −0.506500 | − | 0.862240i | \(-0.669061\pi\) | ||||
−0.506500 | + | 0.862240i | \(0.669061\pi\) | |||||||
\(164\) | 53.3418 | 4.16529 | ||||||||
\(165\) | −19.6988 | −1.53355 | ||||||||
\(166\) | −30.5462 | −2.37085 | ||||||||
\(167\) | 20.5685 | 1.59164 | 0.795819 | − | 0.605535i | \(-0.207041\pi\) | ||||
0.795819 | + | 0.605535i | \(0.207041\pi\) | |||||||
\(168\) | 49.4222 | 3.81301 | ||||||||
\(169\) | −10.8466 | −0.834353 | ||||||||
\(170\) | −1.18400 | −0.0908088 | ||||||||
\(171\) | −3.05452 | −0.233585 | ||||||||
\(172\) | −27.3759 | −2.08739 | ||||||||
\(173\) | −17.4901 | −1.32975 | −0.664875 | − | 0.746955i | \(-0.731515\pi\) | ||||
−0.664875 | + | 0.746955i | \(0.731515\pi\) | |||||||
\(174\) | −18.1336 | −1.37470 | ||||||||
\(175\) | −12.3627 | −0.934529 | ||||||||
\(176\) | −44.1543 | −3.32826 | ||||||||
\(177\) | −3.21174 | −0.241409 | ||||||||
\(178\) | 11.2339 | 0.842016 | ||||||||
\(179\) | 3.53375 | 0.264125 | 0.132062 | − | 0.991241i | \(-0.457840\pi\) | ||||
0.132062 | + | 0.991241i | \(0.457840\pi\) | |||||||
\(180\) | −6.26749 | −0.467151 | ||||||||
\(181\) | 16.8008 | 1.24879 | 0.624395 | − | 0.781109i | \(-0.285345\pi\) | ||||
0.624395 | + | 0.781109i | \(0.285345\pi\) | |||||||
\(182\) | 15.7176 | 1.16507 | ||||||||
\(183\) | −18.7369 | −1.38507 | ||||||||
\(184\) | −20.4063 | −1.50437 | ||||||||
\(185\) | −19.2534 | −1.41554 | ||||||||
\(186\) | −12.6195 | −0.925303 | ||||||||
\(187\) | −0.693216 | −0.0506930 | ||||||||
\(188\) | −18.9801 | −1.38426 | ||||||||
\(189\) | 22.4837 | 1.63545 | ||||||||
\(190\) | −50.2427 | −3.64499 | ||||||||
\(191\) | 16.7452 | 1.21164 | 0.605820 | − | 0.795602i | \(-0.292845\pi\) | ||||
0.605820 | + | 0.795602i | \(0.292845\pi\) | |||||||
\(192\) | 15.5544 | 1.12254 | ||||||||
\(193\) | −14.4285 | −1.03859 | −0.519294 | − | 0.854596i | \(-0.673805\pi\) | ||||
−0.519294 | + | 0.854596i | \(0.673805\pi\) | |||||||
\(194\) | 8.89223 | 0.638425 | ||||||||
\(195\) | 6.63740 | 0.475314 | ||||||||
\(196\) | 47.1892 | 3.37066 | ||||||||
\(197\) | 12.4474 | 0.886842 | 0.443421 | − | 0.896313i | \(-0.353765\pi\) | ||||
0.443421 | + | 0.896313i | \(0.353765\pi\) | |||||||
\(198\) | −5.17011 | −0.367424 | ||||||||
\(199\) | 12.8130 | 0.908287 | 0.454144 | − | 0.890928i | \(-0.349945\pi\) | ||||
0.454144 | + | 0.890928i | \(0.349945\pi\) | |||||||
\(200\) | −22.9920 | −1.62578 | ||||||||
\(201\) | −15.1684 | −1.06990 | ||||||||
\(202\) | 21.6865 | 1.52585 | ||||||||
\(203\) | −17.6586 | −1.23939 | ||||||||
\(204\) | 1.24258 | 0.0869979 | ||||||||
\(205\) | 30.9059 | 2.15856 | ||||||||
\(206\) | −23.5274 | −1.63923 | ||||||||
\(207\) | −1.21610 | −0.0845250 | ||||||||
\(208\) | 14.8775 | 1.03157 | ||||||||
\(209\) | −29.4164 | −2.03477 | ||||||||
\(210\) | 48.4460 | 3.34309 | ||||||||
\(211\) | −1.14362 | −0.0787300 | −0.0393650 | − | 0.999225i | \(-0.512534\pi\) | ||||
−0.0393650 | + | 0.999225i | \(0.512534\pi\) | |||||||
\(212\) | −52.9855 | −3.63906 | ||||||||
\(213\) | −3.92329 | −0.268820 | ||||||||
\(214\) | −10.0543 | −0.687299 | ||||||||
\(215\) | −15.8614 | −1.08174 | ||||||||
\(216\) | 41.8151 | 2.84516 | ||||||||
\(217\) | −12.2889 | −0.834226 | ||||||||
\(218\) | −16.3919 | −1.11020 | ||||||||
\(219\) | −9.10933 | −0.615552 | ||||||||
\(220\) | −60.3587 | −4.06938 | ||||||||
\(221\) | 0.233575 | 0.0157120 | ||||||||
\(222\) | 28.4687 | 1.91070 | ||||||||
\(223\) | −28.6960 | −1.92163 | −0.960815 | − | 0.277192i | \(-0.910596\pi\) | ||||
−0.960815 | + | 0.277192i | \(0.910596\pi\) | |||||||
\(224\) | 46.6644 | 3.11790 | ||||||||
\(225\) | −1.37020 | −0.0913465 | ||||||||
\(226\) | −11.8830 | −0.790445 | ||||||||
\(227\) | 24.5098 | 1.62677 | 0.813386 | − | 0.581725i | \(-0.197622\pi\) | ||||
0.813386 | + | 0.581725i | \(0.197622\pi\) | |||||||
\(228\) | 52.7284 | 3.49202 | ||||||||
\(229\) | −27.2245 | −1.79904 | −0.899522 | − | 0.436875i | \(-0.856085\pi\) | ||||
−0.899522 | + | 0.436875i | \(0.856085\pi\) | |||||||
\(230\) | −20.0032 | −1.31897 | ||||||||
\(231\) | 28.3644 | 1.86624 | ||||||||
\(232\) | −32.8414 | −2.15614 | ||||||||
\(233\) | −18.4644 | −1.20964 | −0.604821 | − | 0.796362i | \(-0.706755\pi\) | ||||
−0.604821 | + | 0.796362i | \(0.706755\pi\) | |||||||
\(234\) | 1.74204 | 0.113881 | ||||||||
\(235\) | −10.9969 | −0.717361 | ||||||||
\(236\) | −9.84103 | −0.640597 | ||||||||
\(237\) | 17.9291 | 1.16462 | ||||||||
\(238\) | 1.70485 | 0.110509 | ||||||||
\(239\) | −16.0912 | −1.04085 | −0.520427 | − | 0.853906i | \(-0.674227\pi\) | ||||
−0.520427 | + | 0.853906i | \(0.674227\pi\) | |||||||
\(240\) | 45.8566 | 2.96003 | ||||||||
\(241\) | 26.4312 | 1.70258 | 0.851290 | − | 0.524695i | \(-0.175821\pi\) | ||||
0.851290 | + | 0.524695i | \(0.175821\pi\) | |||||||
\(242\) | −20.9150 | −1.34447 | ||||||||
\(243\) | 4.65746 | 0.298776 | ||||||||
\(244\) | −57.4114 | −3.67539 | ||||||||
\(245\) | 27.3412 | 1.74676 | ||||||||
\(246\) | −45.6985 | −2.91363 | ||||||||
\(247\) | 9.91169 | 0.630666 | ||||||||
\(248\) | −22.8549 | −1.45129 | ||||||||
\(249\) | 18.5739 | 1.17707 | ||||||||
\(250\) | 14.6550 | 0.926861 | ||||||||
\(251\) | −8.36179 | −0.527791 | −0.263896 | − | 0.964551i | \(-0.585007\pi\) | ||||
−0.263896 | + | 0.964551i | \(0.585007\pi\) | |||||||
\(252\) | 9.02460 | 0.568497 | ||||||||
\(253\) | −11.7116 | −0.736302 | ||||||||
\(254\) | −14.5826 | −0.914991 | ||||||||
\(255\) | 0.719942 | 0.0450845 | ||||||||
\(256\) | −12.3832 | −0.773947 | ||||||||
\(257\) | 11.1136 | 0.693245 | 0.346622 | − | 0.938005i | \(-0.387328\pi\) | ||||
0.346622 | + | 0.938005i | \(0.387328\pi\) | |||||||
\(258\) | 23.4533 | 1.46014 | ||||||||
\(259\) | 27.7231 | 1.72263 | ||||||||
\(260\) | 20.3375 | 1.26128 | ||||||||
\(261\) | −1.95717 | −0.121146 | ||||||||
\(262\) | 35.6474 | 2.20230 | ||||||||
\(263\) | 12.8396 | 0.791722 | 0.395861 | − | 0.918310i | \(-0.370446\pi\) | ||||
0.395861 | + | 0.918310i | \(0.370446\pi\) | |||||||
\(264\) | 52.7520 | 3.24666 | ||||||||
\(265\) | −30.6995 | −1.88585 | ||||||||
\(266\) | 72.3448 | 4.43574 | ||||||||
\(267\) | −6.83086 | −0.418042 | ||||||||
\(268\) | −46.4773 | −2.83905 | ||||||||
\(269\) | 9.21004 | 0.561546 | 0.280773 | − | 0.959774i | \(-0.409409\pi\) | ||||
0.280773 | + | 0.959774i | \(0.409409\pi\) | |||||||
\(270\) | 40.9892 | 2.49452 | ||||||||
\(271\) | 2.06421 | 0.125392 | 0.0626959 | − | 0.998033i | \(-0.480030\pi\) | ||||
0.0626959 | + | 0.998033i | \(0.480030\pi\) | |||||||
\(272\) | 1.61373 | 0.0978467 | ||||||||
\(273\) | −9.55723 | −0.578430 | ||||||||
\(274\) | 35.9320 | 2.17073 | ||||||||
\(275\) | −13.1956 | −0.795724 | ||||||||
\(276\) | 20.9928 | 1.26362 | ||||||||
\(277\) | −14.1120 | −0.847910 | −0.423955 | − | 0.905683i | \(-0.639359\pi\) | ||||
−0.423955 | + | 0.905683i | \(0.639359\pi\) | |||||||
\(278\) | −2.21944 | −0.133113 | ||||||||
\(279\) | −1.36202 | −0.0815423 | ||||||||
\(280\) | 87.7397 | 5.24345 | ||||||||
\(281\) | −7.56810 | −0.451475 | −0.225737 | − | 0.974188i | \(-0.572479\pi\) | ||||
−0.225737 | + | 0.974188i | \(0.572479\pi\) | |||||||
\(282\) | 16.2605 | 0.968296 | ||||||||
\(283\) | 25.3302 | 1.50573 | 0.752863 | − | 0.658178i | \(-0.228672\pi\) | ||||
0.752863 | + | 0.658178i | \(0.228672\pi\) | |||||||
\(284\) | −12.0213 | −0.713332 | ||||||||
\(285\) | 30.5505 | 1.80966 | ||||||||
\(286\) | 16.7766 | 0.992022 | ||||||||
\(287\) | −44.5016 | −2.62685 | ||||||||
\(288\) | 5.17198 | 0.304762 | ||||||||
\(289\) | −16.9747 | −0.998510 | ||||||||
\(290\) | −32.1927 | −1.89042 | ||||||||
\(291\) | −5.40699 | −0.316963 | ||||||||
\(292\) | −27.9117 | −1.63341 | ||||||||
\(293\) | −4.60976 | −0.269305 | −0.134653 | − | 0.990893i | \(-0.542992\pi\) | ||||
−0.134653 | + | 0.990893i | \(0.542992\pi\) | |||||||
\(294\) | −40.4276 | −2.35778 | ||||||||
\(295\) | −5.70183 | −0.331974 | ||||||||
\(296\) | 51.5593 | 2.99682 | ||||||||
\(297\) | 23.9986 | 1.39254 | ||||||||
\(298\) | 35.7496 | 2.07092 | ||||||||
\(299\) | 3.94616 | 0.228212 | ||||||||
\(300\) | 23.6529 | 1.36560 | ||||||||
\(301\) | 22.8390 | 1.31642 | ||||||||
\(302\) | 8.73289 | 0.502521 | ||||||||
\(303\) | −13.1866 | −0.757552 | ||||||||
\(304\) | 68.4781 | 3.92749 | ||||||||
\(305\) | −33.2638 | −1.90468 | ||||||||
\(306\) | 0.188955 | 0.0108018 | ||||||||
\(307\) | 4.39386 | 0.250771 | 0.125385 | − | 0.992108i | \(-0.459983\pi\) | ||||
0.125385 | + | 0.992108i | \(0.459983\pi\) | |||||||
\(308\) | 86.9109 | 4.95221 | ||||||||
\(309\) | 14.3060 | 0.813841 | ||||||||
\(310\) | −22.4034 | −1.27243 | ||||||||
\(311\) | 1.98084 | 0.112323 | 0.0561614 | − | 0.998422i | \(-0.482114\pi\) | ||||
0.0561614 | + | 0.998422i | \(0.482114\pi\) | |||||||
\(312\) | −17.7745 | −1.00628 | ||||||||
\(313\) | −2.68152 | −0.151569 | −0.0757843 | − | 0.997124i | \(-0.524146\pi\) | ||||
−0.0757843 | + | 0.997124i | \(0.524146\pi\) | |||||||
\(314\) | 36.0116 | 2.03225 | ||||||||
\(315\) | 5.22880 | 0.294610 | ||||||||
\(316\) | 54.9361 | 3.09040 | ||||||||
\(317\) | 9.72262 | 0.546077 | 0.273038 | − | 0.962003i | \(-0.411971\pi\) | ||||
0.273038 | + | 0.962003i | \(0.411971\pi\) | |||||||
\(318\) | 45.3933 | 2.54553 | ||||||||
\(319\) | −18.8484 | −1.05531 | ||||||||
\(320\) | 27.6138 | 1.54366 | ||||||||
\(321\) | 6.11361 | 0.341229 | ||||||||
\(322\) | 28.8028 | 1.60512 | ||||||||
\(323\) | 1.07510 | 0.0598200 | ||||||||
\(324\) | −36.3817 | −2.02121 | ||||||||
\(325\) | 4.44618 | 0.246630 | ||||||||
\(326\) | 33.9499 | 1.88031 | ||||||||
\(327\) | 9.96724 | 0.551190 | ||||||||
\(328\) | −82.7639 | −4.56987 | ||||||||
\(329\) | 15.8346 | 0.872988 | ||||||||
\(330\) | 51.7100 | 2.84654 | ||||||||
\(331\) | −13.1429 | −0.722399 | −0.361199 | − | 0.932489i | \(-0.617633\pi\) | ||||
−0.361199 | + | 0.932489i | \(0.617633\pi\) | |||||||
\(332\) | 56.9119 | 3.12344 | ||||||||
\(333\) | 3.07265 | 0.168380 | ||||||||
\(334\) | −53.9930 | −2.95436 | ||||||||
\(335\) | −26.9287 | −1.47127 | ||||||||
\(336\) | −66.0292 | −3.60219 | ||||||||
\(337\) | −30.6858 | −1.67156 | −0.835781 | − | 0.549063i | \(-0.814985\pi\) | ||||
−0.835781 | + | 0.549063i | \(0.814985\pi\) | |||||||
\(338\) | 28.4727 | 1.54871 | ||||||||
\(339\) | 7.22556 | 0.392438 | ||||||||
\(340\) | 2.20596 | 0.119635 | ||||||||
\(341\) | −13.1169 | −0.710319 | ||||||||
\(342\) | 8.01823 | 0.433576 | ||||||||
\(343\) | −10.8068 | −0.583515 | ||||||||
\(344\) | 42.4758 | 2.29014 | ||||||||
\(345\) | 12.1631 | 0.654841 | ||||||||
\(346\) | 45.9122 | 2.46825 | ||||||||
\(347\) | −5.98399 | −0.321237 | −0.160619 | − | 0.987017i | \(-0.551349\pi\) | ||||
−0.160619 | + | 0.987017i | \(0.551349\pi\) | |||||||
\(348\) | 33.7854 | 1.81109 | ||||||||
\(349\) | −22.2652 | −1.19183 | −0.595914 | − | 0.803048i | \(-0.703210\pi\) | ||||
−0.595914 | + | 0.803048i | \(0.703210\pi\) | |||||||
\(350\) | 32.4524 | 1.73465 | ||||||||
\(351\) | −8.08618 | −0.431609 | ||||||||
\(352\) | 49.8084 | 2.65480 | ||||||||
\(353\) | 1.40596 | 0.0748315 | 0.0374157 | − | 0.999300i | \(-0.488087\pi\) | ||||
0.0374157 | + | 0.999300i | \(0.488087\pi\) | |||||||
\(354\) | 8.43093 | 0.448099 | ||||||||
\(355\) | −6.96506 | −0.369667 | ||||||||
\(356\) | −20.9303 | −1.10930 | ||||||||
\(357\) | −1.03665 | −0.0548653 | ||||||||
\(358\) | −9.27621 | −0.490263 | ||||||||
\(359\) | −17.7435 | −0.936464 | −0.468232 | − | 0.883606i | \(-0.655109\pi\) | ||||
−0.468232 | + | 0.883606i | \(0.655109\pi\) | |||||||
\(360\) | 9.72450 | 0.512526 | ||||||||
\(361\) | 26.6213 | 1.40112 | ||||||||
\(362\) | −44.1026 | −2.31798 | ||||||||
\(363\) | 12.7176 | 0.667499 | ||||||||
\(364\) | −29.2841 | −1.53491 | ||||||||
\(365\) | −16.1719 | −0.846475 | ||||||||
\(366\) | 49.1850 | 2.57094 | ||||||||
\(367\) | −12.9260 | −0.674731 | −0.337366 | − | 0.941374i | \(-0.609536\pi\) | ||||
−0.337366 | + | 0.941374i | \(0.609536\pi\) | |||||||
\(368\) | 27.2633 | 1.42120 | ||||||||
\(369\) | −4.93227 | −0.256764 | ||||||||
\(370\) | 50.5408 | 2.62749 | ||||||||
\(371\) | 44.2044 | 2.29498 | ||||||||
\(372\) | 23.5118 | 1.21903 | ||||||||
\(373\) | −15.3574 | −0.795177 | −0.397588 | − | 0.917564i | \(-0.630153\pi\) | ||||
−0.397588 | + | 0.917564i | \(0.630153\pi\) | |||||||
\(374\) | 1.81972 | 0.0940953 | ||||||||
\(375\) | −8.91107 | −0.460166 | ||||||||
\(376\) | 29.4491 | 1.51872 | ||||||||
\(377\) | 6.35085 | 0.327086 | ||||||||
\(378\) | −59.0205 | −3.03569 | ||||||||
\(379\) | −32.6068 | −1.67490 | −0.837449 | − | 0.546516i | \(-0.815954\pi\) | ||||
−0.837449 | + | 0.546516i | \(0.815954\pi\) | |||||||
\(380\) | 93.6092 | 4.80205 | ||||||||
\(381\) | 8.86705 | 0.454273 | ||||||||
\(382\) | −43.9567 | −2.24902 | ||||||||
\(383\) | −20.0159 | −1.02277 | −0.511384 | − | 0.859353i | \(-0.670867\pi\) | ||||
−0.511384 | + | 0.859353i | \(0.670867\pi\) | |||||||
\(384\) | −4.32112 | −0.220511 | ||||||||
\(385\) | 50.3556 | 2.56636 | ||||||||
\(386\) | 37.8754 | 1.92781 | ||||||||
\(387\) | 2.53132 | 0.128674 | ||||||||
\(388\) | −16.5675 | −0.841085 | ||||||||
\(389\) | 27.0756 | 1.37279 | 0.686393 | − | 0.727230i | \(-0.259193\pi\) | ||||
0.686393 | + | 0.727230i | \(0.259193\pi\) | |||||||
\(390\) | −17.4234 | −0.882268 | ||||||||
\(391\) | 0.428030 | 0.0216464 | ||||||||
\(392\) | −73.2177 | −3.69805 | ||||||||
\(393\) | −21.6757 | −1.09339 | ||||||||
\(394\) | −32.6749 | −1.64614 | ||||||||
\(395\) | 31.8296 | 1.60152 | ||||||||
\(396\) | 9.63264 | 0.484058 | ||||||||
\(397\) | 17.6271 | 0.884679 | 0.442340 | − | 0.896848i | \(-0.354149\pi\) | ||||
0.442340 | + | 0.896848i | \(0.354149\pi\) | |||||||
\(398\) | −33.6345 | −1.68594 | ||||||||
\(399\) | −43.9899 | −2.20225 | ||||||||
\(400\) | 30.7179 | 1.53589 | ||||||||
\(401\) | −34.3268 | −1.71420 | −0.857098 | − | 0.515153i | \(-0.827735\pi\) | ||||
−0.857098 | + | 0.515153i | \(0.827735\pi\) | |||||||
\(402\) | 39.8177 | 1.98592 | ||||||||
\(403\) | 4.41966 | 0.220159 | ||||||||
\(404\) | −40.4049 | −2.01022 | ||||||||
\(405\) | −21.0793 | −1.04744 | ||||||||
\(406\) | 46.3545 | 2.30053 | ||||||||
\(407\) | 29.5909 | 1.46677 | ||||||||
\(408\) | −1.92796 | −0.0954480 | ||||||||
\(409\) | −31.5756 | −1.56131 | −0.780656 | − | 0.624961i | \(-0.785115\pi\) | ||||
−0.780656 | + | 0.624961i | \(0.785115\pi\) | |||||||
\(410\) | −81.1290 | −4.00668 | ||||||||
\(411\) | −21.8487 | −1.07772 | ||||||||
\(412\) | 43.8348 | 2.15958 | ||||||||
\(413\) | 8.21011 | 0.403993 | ||||||||
\(414\) | 3.19231 | 0.156894 | ||||||||
\(415\) | 32.9744 | 1.61865 | ||||||||
\(416\) | −16.7827 | −0.822838 | ||||||||
\(417\) | 1.34955 | 0.0660876 | ||||||||
\(418\) | 77.2190 | 3.77691 | ||||||||
\(419\) | 29.4354 | 1.43801 | 0.719006 | − | 0.695003i | \(-0.244597\pi\) | ||||
0.719006 | + | 0.695003i | \(0.244597\pi\) | |||||||
\(420\) | −90.2616 | −4.40431 | ||||||||
\(421\) | −24.2341 | −1.18110 | −0.590549 | − | 0.807002i | \(-0.701089\pi\) | ||||
−0.590549 | + | 0.807002i | \(0.701089\pi\) | |||||||
\(422\) | 3.00204 | 0.146137 | ||||||||
\(423\) | 1.75500 | 0.0853310 | ||||||||
\(424\) | 82.2111 | 3.99252 | ||||||||
\(425\) | 0.482266 | 0.0233933 | ||||||||
\(426\) | 10.2988 | 0.498977 | ||||||||
\(427\) | 47.8968 | 2.31789 | ||||||||
\(428\) | 18.7326 | 0.905474 | ||||||||
\(429\) | −10.2012 | −0.492516 | ||||||||
\(430\) | 41.6368 | 2.00790 | ||||||||
\(431\) | −17.2810 | −0.832396 | −0.416198 | − | 0.909274i | \(-0.636638\pi\) | ||||
−0.416198 | + | 0.909274i | \(0.636638\pi\) | |||||||
\(432\) | −55.8660 | −2.68785 | ||||||||
\(433\) | −10.1189 | −0.486281 | −0.243140 | − | 0.969991i | \(-0.578178\pi\) | ||||
−0.243140 | + | 0.969991i | \(0.578178\pi\) | |||||||
\(434\) | 32.2588 | 1.54847 | ||||||||
\(435\) | 19.5750 | 0.938551 | ||||||||
\(436\) | 30.5404 | 1.46262 | ||||||||
\(437\) | 18.1633 | 0.868869 | ||||||||
\(438\) | 23.9123 | 1.14257 | ||||||||
\(439\) | −31.6553 | −1.51082 | −0.755411 | − | 0.655251i | \(-0.772563\pi\) | ||||
−0.755411 | + | 0.655251i | \(0.772563\pi\) | |||||||
\(440\) | 93.6512 | 4.46464 | ||||||||
\(441\) | −4.36337 | −0.207780 | ||||||||
\(442\) | −0.613143 | −0.0291643 | ||||||||
\(443\) | −30.0671 | −1.42853 | −0.714265 | − | 0.699876i | \(-0.753239\pi\) | ||||
−0.714265 | + | 0.699876i | \(0.753239\pi\) | |||||||
\(444\) | −53.0412 | −2.51722 | ||||||||
\(445\) | −12.1269 | −0.574870 | ||||||||
\(446\) | 75.3281 | 3.56689 | ||||||||
\(447\) | −21.7379 | −1.02817 | ||||||||
\(448\) | −39.7613 | −1.87855 | ||||||||
\(449\) | 4.89363 | 0.230945 | 0.115472 | − | 0.993311i | \(-0.463162\pi\) | ||||
0.115472 | + | 0.993311i | \(0.463162\pi\) | |||||||
\(450\) | 3.59681 | 0.169555 | ||||||||
\(451\) | −47.4999 | −2.23668 | ||||||||
\(452\) | 22.1397 | 1.04136 | ||||||||
\(453\) | −5.31010 | −0.249490 | ||||||||
\(454\) | −64.3390 | −3.01958 | ||||||||
\(455\) | −16.9670 | −0.795428 | ||||||||
\(456\) | −81.8121 | −3.83120 | ||||||||
\(457\) | −34.7775 | −1.62682 | −0.813412 | − | 0.581688i | \(-0.802393\pi\) | ||||
−0.813412 | + | 0.581688i | \(0.802393\pi\) | |||||||
\(458\) | 71.4652 | 3.33935 | ||||||||
\(459\) | −0.877088 | −0.0409390 | ||||||||
\(460\) | 37.2688 | 1.73767 | ||||||||
\(461\) | 25.0822 | 1.16819 | 0.584097 | − | 0.811684i | \(-0.301449\pi\) | ||||
0.584097 | + | 0.811684i | \(0.301449\pi\) | |||||||
\(462\) | −74.4576 | −3.46408 | ||||||||
\(463\) | −20.6225 | −0.958407 | −0.479203 | − | 0.877704i | \(-0.659074\pi\) | ||||
−0.479203 | + | 0.877704i | \(0.659074\pi\) | |||||||
\(464\) | 43.8769 | 2.03693 | ||||||||
\(465\) | 13.6226 | 0.631732 | ||||||||
\(466\) | 48.4696 | 2.24531 | ||||||||
\(467\) | −7.12670 | −0.329784 | −0.164892 | − | 0.986312i | \(-0.552728\pi\) | ||||
−0.164892 | + | 0.986312i | \(0.552728\pi\) | |||||||
\(468\) | −3.24566 | −0.150031 | ||||||||
\(469\) | 38.7748 | 1.79045 | ||||||||
\(470\) | 28.8673 | 1.33155 | ||||||||
\(471\) | −21.8971 | −1.00897 | ||||||||
\(472\) | 15.2691 | 0.702818 | ||||||||
\(473\) | 24.3777 | 1.12089 | ||||||||
\(474\) | −47.0644 | −2.16174 | ||||||||
\(475\) | 20.4648 | 0.938989 | ||||||||
\(476\) | −3.17638 | −0.145589 | ||||||||
\(477\) | 4.89932 | 0.224325 | ||||||||
\(478\) | 42.2400 | 1.93201 | ||||||||
\(479\) | −6.29914 | −0.287815 | −0.143907 | − | 0.989591i | \(-0.545967\pi\) | ||||
−0.143907 | + | 0.989591i | \(0.545967\pi\) | |||||||
\(480\) | −51.7287 | −2.36108 | ||||||||
\(481\) | −9.97050 | −0.454616 | ||||||||
\(482\) | −69.3827 | −3.16029 | ||||||||
\(483\) | −17.5138 | −0.796904 | ||||||||
\(484\) | 38.9676 | 1.77126 | ||||||||
\(485\) | −9.59908 | −0.435872 | ||||||||
\(486\) | −12.2260 | −0.554583 | ||||||||
\(487\) | −19.0471 | −0.863108 | −0.431554 | − | 0.902087i | \(-0.642035\pi\) | ||||
−0.431554 | + | 0.902087i | \(0.642035\pi\) | |||||||
\(488\) | 89.0782 | 4.03238 | ||||||||
\(489\) | −20.6435 | −0.933531 | ||||||||
\(490\) | −71.7715 | −3.24230 | ||||||||
\(491\) | −32.8632 | −1.48310 | −0.741548 | − | 0.670900i | \(-0.765908\pi\) | ||||
−0.741548 | + | 0.670900i | \(0.765908\pi\) | |||||||
\(492\) | 85.1427 | 3.83853 | ||||||||
\(493\) | 0.688861 | 0.0310247 | ||||||||
\(494\) | −26.0185 | −1.17063 | ||||||||
\(495\) | 5.58109 | 0.250851 | ||||||||
\(496\) | 30.5347 | 1.37105 | ||||||||
\(497\) | 10.0290 | 0.449864 | ||||||||
\(498\) | −48.7571 | −2.18486 | ||||||||
\(499\) | 22.2917 | 0.997911 | 0.498956 | − | 0.866627i | \(-0.333717\pi\) | ||||
0.498956 | + | 0.866627i | \(0.333717\pi\) | |||||||
\(500\) | −27.3042 | −1.22108 | ||||||||
\(501\) | 32.8309 | 1.46678 | ||||||||
\(502\) | 21.9500 | 0.979675 | ||||||||
\(503\) | 20.1406 | 0.898024 | 0.449012 | − | 0.893526i | \(-0.351776\pi\) | ||||
0.449012 | + | 0.893526i | \(0.351776\pi\) | |||||||
\(504\) | −14.0024 | −0.623715 | ||||||||
\(505\) | −23.4104 | −1.04175 | ||||||||
\(506\) | 30.7434 | 1.36671 | ||||||||
\(507\) | −17.3130 | −0.768899 | ||||||||
\(508\) | 27.1693 | 1.20544 | ||||||||
\(509\) | −38.4784 | −1.70553 | −0.852763 | − | 0.522298i | \(-0.825075\pi\) | ||||
−0.852763 | + | 0.522298i | \(0.825075\pi\) | |||||||
\(510\) | −1.88987 | −0.0836850 | ||||||||
\(511\) | 23.2860 | 1.03011 | ||||||||
\(512\) | 37.9206 | 1.67587 | ||||||||
\(513\) | −37.2189 | −1.64326 | ||||||||
\(514\) | −29.1735 | −1.28679 | ||||||||
\(515\) | 25.3976 | 1.11915 | ||||||||
\(516\) | −43.6967 | −1.92364 | ||||||||
\(517\) | 16.9014 | 0.743323 | ||||||||
\(518\) | −72.7740 | −3.19751 | ||||||||
\(519\) | −27.9173 | −1.22543 | ||||||||
\(520\) | −31.5552 | −1.38379 | ||||||||
\(521\) | 29.3759 | 1.28698 | 0.643491 | − | 0.765454i | \(-0.277485\pi\) | ||||
0.643491 | + | 0.765454i | \(0.277485\pi\) | |||||||
\(522\) | 5.13763 | 0.224868 | ||||||||
\(523\) | −2.88943 | −0.126346 | −0.0631730 | − | 0.998003i | \(-0.520122\pi\) | ||||
−0.0631730 | + | 0.998003i | \(0.520122\pi\) | |||||||
\(524\) | −66.4161 | −2.90140 | ||||||||
\(525\) | −19.7329 | −0.861216 | ||||||||
\(526\) | −33.7043 | −1.46958 | ||||||||
\(527\) | 0.479390 | 0.0208825 | ||||||||
\(528\) | −70.4779 | −3.06716 | ||||||||
\(529\) | −15.7686 | −0.685592 | ||||||||
\(530\) | 80.5871 | 3.50048 | ||||||||
\(531\) | 0.909955 | 0.0394887 | ||||||||
\(532\) | −134.788 | −5.84382 | ||||||||
\(533\) | 16.0048 | 0.693246 | ||||||||
\(534\) | 17.9312 | 0.775961 | ||||||||
\(535\) | 10.8536 | 0.469240 | ||||||||
\(536\) | 72.1131 | 3.11481 | ||||||||
\(537\) | 5.64048 | 0.243405 | ||||||||
\(538\) | −24.1767 | −1.04233 | ||||||||
\(539\) | −42.0212 | −1.80998 | ||||||||
\(540\) | −76.3685 | −3.28638 | ||||||||
\(541\) | 6.22221 | 0.267514 | 0.133757 | − | 0.991014i | \(-0.457296\pi\) | ||||
0.133757 | + | 0.991014i | \(0.457296\pi\) | |||||||
\(542\) | −5.41862 | −0.232750 | ||||||||
\(543\) | 26.8169 | 1.15082 | ||||||||
\(544\) | −1.82037 | −0.0780479 | ||||||||
\(545\) | 17.6949 | 0.757968 | ||||||||
\(546\) | 25.0881 | 1.07367 | ||||||||
\(547\) | 35.3320 | 1.51069 | 0.755344 | − | 0.655329i | \(-0.227470\pi\) | ||||
0.755344 | + | 0.655329i | \(0.227470\pi\) | |||||||
\(548\) | −66.9463 | −2.85980 | ||||||||
\(549\) | 5.30857 | 0.226564 | ||||||||
\(550\) | 34.6389 | 1.47701 | ||||||||
\(551\) | 29.2316 | 1.24531 | ||||||||
\(552\) | −32.5720 | −1.38636 | ||||||||
\(553\) | −45.8317 | −1.94896 | ||||||||
\(554\) | 37.0446 | 1.57387 | ||||||||
\(555\) | −30.7318 | −1.30449 | ||||||||
\(556\) | 4.13512 | 0.175368 | ||||||||
\(557\) | −45.8297 | −1.94187 | −0.970934 | − | 0.239346i | \(-0.923067\pi\) | ||||
−0.970934 | + | 0.239346i | \(0.923067\pi\) | |||||||
\(558\) | 3.57536 | 0.151357 | ||||||||
\(559\) | −8.21395 | −0.347413 | ||||||||
\(560\) | −117.222 | −4.95354 | ||||||||
\(561\) | −1.10649 | −0.0467162 | ||||||||
\(562\) | 19.8665 | 0.838018 | ||||||||
\(563\) | −15.3774 | −0.648079 | −0.324039 | − | 0.946044i | \(-0.605041\pi\) | ||||
−0.324039 | + | 0.946044i | \(0.605041\pi\) | |||||||
\(564\) | −30.2955 | −1.27567 | ||||||||
\(565\) | 12.8276 | 0.539661 | ||||||||
\(566\) | −66.4927 | −2.79490 | ||||||||
\(567\) | 30.3523 | 1.27468 | ||||||||
\(568\) | 18.6519 | 0.782618 | ||||||||
\(569\) | 38.4097 | 1.61022 | 0.805110 | − | 0.593125i | \(-0.202106\pi\) | ||||
0.805110 | + | 0.593125i | \(0.202106\pi\) | |||||||
\(570\) | −80.1961 | −3.35905 | ||||||||
\(571\) | −23.2921 | −0.974743 | −0.487371 | − | 0.873195i | \(-0.662044\pi\) | ||||
−0.487371 | + | 0.873195i | \(0.662044\pi\) | |||||||
\(572\) | −31.2572 | −1.30693 | ||||||||
\(573\) | 26.7283 | 1.11659 | ||||||||
\(574\) | 116.818 | 4.87590 | ||||||||
\(575\) | 8.14769 | 0.339782 | ||||||||
\(576\) | −4.40689 | −0.183620 | ||||||||
\(577\) | −9.37557 | −0.390310 | −0.195155 | − | 0.980772i | \(-0.562521\pi\) | ||||
−0.195155 | + | 0.980772i | \(0.562521\pi\) | |||||||
\(578\) | 44.5591 | 1.85341 | ||||||||
\(579\) | −23.0304 | −0.957112 | ||||||||
\(580\) | 59.9795 | 2.49051 | ||||||||
\(581\) | −47.4800 | −1.96980 | ||||||||
\(582\) | 14.1935 | 0.588341 | ||||||||
\(583\) | 47.1826 | 1.95410 | ||||||||
\(584\) | 43.3072 | 1.79206 | ||||||||
\(585\) | −1.88052 | −0.0777498 | ||||||||
\(586\) | 12.1008 | 0.499879 | ||||||||
\(587\) | 27.9399 | 1.15320 | 0.576602 | − | 0.817025i | \(-0.304378\pi\) | ||||
0.576602 | + | 0.817025i | \(0.304378\pi\) | |||||||
\(588\) | 75.3222 | 3.10624 | ||||||||
\(589\) | 20.3427 | 0.838208 | ||||||||
\(590\) | 14.9675 | 0.616203 | ||||||||
\(591\) | 19.8683 | 0.817271 | ||||||||
\(592\) | −68.8844 | −2.83113 | ||||||||
\(593\) | −5.27502 | −0.216619 | −0.108310 | − | 0.994117i | \(-0.534544\pi\) | ||||
−0.108310 | + | 0.994117i | \(0.534544\pi\) | |||||||
\(594\) | −62.9970 | −2.58480 | ||||||||
\(595\) | −1.84037 | −0.0754479 | ||||||||
\(596\) | −66.6065 | −2.72831 | ||||||||
\(597\) | 20.4517 | 0.837033 | ||||||||
\(598\) | −10.3588 | −0.423603 | ||||||||
\(599\) | 30.8260 | 1.25952 | 0.629759 | − | 0.776791i | \(-0.283154\pi\) | ||||
0.629759 | + | 0.776791i | \(0.283154\pi\) | |||||||
\(600\) | −36.6993 | −1.49824 | ||||||||
\(601\) | 4.66282 | 0.190200 | 0.0951001 | − | 0.995468i | \(-0.469683\pi\) | ||||
0.0951001 | + | 0.995468i | \(0.469683\pi\) | |||||||
\(602\) | −59.9531 | −2.44350 | ||||||||
\(603\) | 4.29754 | 0.175009 | ||||||||
\(604\) | −16.2706 | −0.662041 | ||||||||
\(605\) | 22.5776 | 0.917910 | ||||||||
\(606\) | 34.6154 | 1.40615 | ||||||||
\(607\) | 10.8487 | 0.440333 | 0.220167 | − | 0.975462i | \(-0.429340\pi\) | ||||
0.220167 | + | 0.975462i | \(0.429340\pi\) | |||||||
\(608\) | −77.2470 | −3.13278 | ||||||||
\(609\) | −28.1862 | −1.14216 | ||||||||
\(610\) | 87.3186 | 3.53543 | ||||||||
\(611\) | −5.69484 | −0.230389 | ||||||||
\(612\) | −0.352049 | −0.0142307 | ||||||||
\(613\) | −29.7304 | −1.20080 | −0.600401 | − | 0.799699i | \(-0.704992\pi\) | ||||
−0.600401 | + | 0.799699i | \(0.704992\pi\) | |||||||
\(614\) | −11.5340 | −0.465475 | ||||||||
\(615\) | 49.3312 | 1.98922 | ||||||||
\(616\) | −134.849 | −5.43322 | ||||||||
\(617\) | 35.3186 | 1.42187 | 0.710937 | − | 0.703256i | \(-0.248271\pi\) | ||||
0.710937 | + | 0.703256i | \(0.248271\pi\) | |||||||
\(618\) | −37.5538 | −1.51063 | ||||||||
\(619\) | −40.6951 | −1.63568 | −0.817838 | − | 0.575449i | \(-0.804827\pi\) | ||||
−0.817838 | + | 0.575449i | \(0.804827\pi\) | |||||||
\(620\) | 41.7407 | 1.67635 | ||||||||
\(621\) | −14.8180 | −0.594628 | ||||||||
\(622\) | −5.19976 | −0.208491 | ||||||||
\(623\) | 17.4616 | 0.699584 | ||||||||
\(624\) | 23.7471 | 0.950647 | ||||||||
\(625\) | −30.9692 | −1.23877 | ||||||||
\(626\) | 7.03909 | 0.281339 | ||||||||
\(627\) | −46.9537 | −1.87515 | ||||||||
\(628\) | −67.0946 | −2.67737 | ||||||||
\(629\) | −1.08147 | −0.0431212 | ||||||||
\(630\) | −13.7258 | −0.546848 | ||||||||
\(631\) | −11.9926 | −0.477416 | −0.238708 | − | 0.971091i | \(-0.576724\pi\) | ||||
−0.238708 | + | 0.971091i | \(0.576724\pi\) | |||||||
\(632\) | −85.2376 | −3.39057 | ||||||||
\(633\) | −1.82541 | −0.0725537 | ||||||||
\(634\) | −25.5222 | −1.01362 | ||||||||
\(635\) | 15.7418 | 0.624692 | ||||||||
\(636\) | −84.5740 | −3.35358 | ||||||||
\(637\) | 14.1588 | 0.560992 | ||||||||
\(638\) | 49.4776 | 1.95884 | ||||||||
\(639\) | 1.11155 | 0.0439724 | ||||||||
\(640\) | −7.67132 | −0.303235 | ||||||||
\(641\) | −27.7186 | −1.09482 | −0.547410 | − | 0.836865i | \(-0.684386\pi\) | ||||
−0.547410 | + | 0.836865i | \(0.684386\pi\) | |||||||
\(642\) | −16.0484 | −0.633381 | ||||||||
\(643\) | −31.8431 | −1.25577 | −0.627886 | − | 0.778306i | \(-0.716079\pi\) | ||||
−0.627886 | + | 0.778306i | \(0.716079\pi\) | |||||||
\(644\) | −53.6636 | −2.11464 | ||||||||
\(645\) | −25.3176 | −0.996879 | ||||||||
\(646\) | −2.82216 | −0.111037 | ||||||||
\(647\) | 18.3307 | 0.720655 | 0.360327 | − | 0.932826i | \(-0.382665\pi\) | ||||
0.360327 | + | 0.932826i | \(0.382665\pi\) | |||||||
\(648\) | 56.4490 | 2.21753 | ||||||||
\(649\) | 8.76326 | 0.343988 | ||||||||
\(650\) | −11.6714 | −0.457789 | ||||||||
\(651\) | −19.6153 | −0.768782 | ||||||||
\(652\) | −63.2534 | −2.47719 | ||||||||
\(653\) | −8.48165 | −0.331912 | −0.165956 | − | 0.986133i | \(-0.553071\pi\) | ||||
−0.165956 | + | 0.986133i | \(0.553071\pi\) | |||||||
\(654\) | −26.1643 | −1.02311 | ||||||||
\(655\) | −38.4811 | −1.50358 | ||||||||
\(656\) | 110.574 | 4.31721 | ||||||||
\(657\) | 2.58087 | 0.100689 | ||||||||
\(658\) | −41.5663 | −1.62042 | ||||||||
\(659\) | 32.4044 | 1.26230 | 0.631149 | − | 0.775662i | \(-0.282584\pi\) | ||||
0.631149 | + | 0.775662i | \(0.282584\pi\) | |||||||
\(660\) | −96.3429 | −3.75014 | ||||||||
\(661\) | 29.9556 | 1.16514 | 0.582569 | − | 0.812781i | \(-0.302048\pi\) | ||||
0.582569 | + | 0.812781i | \(0.302048\pi\) | |||||||
\(662\) | 34.5005 | 1.34090 | ||||||||
\(663\) | 0.372827 | 0.0144794 | ||||||||
\(664\) | −88.3031 | −3.42683 | ||||||||
\(665\) | −78.0956 | −3.02842 | ||||||||
\(666\) | −8.06580 | −0.312544 | ||||||||
\(667\) | 11.6380 | 0.450626 | ||||||||
\(668\) | 100.596 | 3.89219 | ||||||||
\(669\) | −45.8039 | −1.77088 | ||||||||
\(670\) | 70.6887 | 2.73094 | ||||||||
\(671\) | 51.1238 | 1.97361 | ||||||||
\(672\) | 74.4845 | 2.87330 | ||||||||
\(673\) | 45.7702 | 1.76431 | 0.882155 | − | 0.470959i | \(-0.156092\pi\) | ||||
0.882155 | + | 0.470959i | \(0.156092\pi\) | |||||||
\(674\) | 80.5513 | 3.10272 | ||||||||
\(675\) | −16.6956 | −0.642616 | ||||||||
\(676\) | −53.0485 | −2.04033 | ||||||||
\(677\) | 16.0580 | 0.617158 | 0.308579 | − | 0.951199i | \(-0.400147\pi\) | ||||
0.308579 | + | 0.951199i | \(0.400147\pi\) | |||||||
\(678\) | −18.9673 | −0.728436 | ||||||||
\(679\) | 13.8218 | 0.530431 | ||||||||
\(680\) | −3.42272 | −0.131255 | ||||||||
\(681\) | 39.1219 | 1.49915 | ||||||||
\(682\) | 34.4323 | 1.31848 | ||||||||
\(683\) | 13.4133 | 0.513245 | 0.256623 | − | 0.966512i | \(-0.417390\pi\) | ||||
0.256623 | + | 0.966512i | \(0.417390\pi\) | |||||||
\(684\) | −14.9391 | −0.571210 | ||||||||
\(685\) | −38.7883 | −1.48202 | ||||||||
\(686\) | 28.3683 | 1.08311 | ||||||||
\(687\) | −43.4550 | −1.65791 | ||||||||
\(688\) | −56.7487 | −2.16352 | ||||||||
\(689\) | −15.8979 | −0.605663 | ||||||||
\(690\) | −31.9286 | −1.21550 | ||||||||
\(691\) | 13.1438 | 0.500015 | 0.250007 | − | 0.968244i | \(-0.419567\pi\) | ||||
0.250007 | + | 0.968244i | \(0.419567\pi\) | |||||||
\(692\) | −85.5408 | −3.25177 | ||||||||
\(693\) | −8.03625 | −0.305272 | ||||||||
\(694\) | 15.7082 | 0.596274 | ||||||||
\(695\) | 2.39586 | 0.0908803 | ||||||||
\(696\) | −52.4206 | −1.98700 | ||||||||
\(697\) | 1.73600 | 0.0657558 | ||||||||
\(698\) | 58.4469 | 2.21225 | ||||||||
\(699\) | −29.4724 | −1.11475 | ||||||||
\(700\) | −60.4633 | −2.28530 | ||||||||
\(701\) | −11.3745 | −0.429609 | −0.214805 | − | 0.976657i | \(-0.568911\pi\) | ||||
−0.214805 | + | 0.976657i | \(0.568911\pi\) | |||||||
\(702\) | 21.2265 | 0.801143 | ||||||||
\(703\) | −45.8920 | −1.73085 | ||||||||
\(704\) | −42.4402 | −1.59953 | ||||||||
\(705\) | −17.5530 | −0.661085 | ||||||||
\(706\) | −3.69068 | −0.138901 | ||||||||
\(707\) | 33.7087 | 1.26775 | ||||||||
\(708\) | −15.7080 | −0.590343 | ||||||||
\(709\) | 19.3343 | 0.726116 | 0.363058 | − | 0.931767i | \(-0.381733\pi\) | ||||
0.363058 | + | 0.931767i | \(0.381733\pi\) | |||||||
\(710\) | 18.2835 | 0.686168 | ||||||||
\(711\) | −5.07969 | −0.190503 | ||||||||
\(712\) | 32.4750 | 1.21705 | ||||||||
\(713\) | 8.09909 | 0.303313 | ||||||||
\(714\) | 2.72124 | 0.101840 | ||||||||
\(715\) | −18.1102 | −0.677283 | ||||||||
\(716\) | 17.2829 | 0.645891 | ||||||||
\(717\) | −25.6844 | −0.959200 | ||||||||
\(718\) | 46.5772 | 1.73824 | ||||||||
\(719\) | −9.36113 | −0.349111 | −0.174556 | − | 0.984647i | \(-0.555849\pi\) | ||||
−0.174556 | + | 0.984647i | \(0.555849\pi\) | |||||||
\(720\) | −12.9922 | −0.484189 | ||||||||
\(721\) | −36.5702 | −1.36194 | ||||||||
\(722\) | −69.8819 | −2.60074 | ||||||||
\(723\) | 42.1887 | 1.56901 | ||||||||
\(724\) | 82.1692 | 3.05380 | ||||||||
\(725\) | 13.1127 | 0.486993 | ||||||||
\(726\) | −33.3840 | −1.23900 | ||||||||
\(727\) | −16.7137 | −0.619876 | −0.309938 | − | 0.950757i | \(-0.600308\pi\) | ||||
−0.309938 | + | 0.950757i | \(0.600308\pi\) | |||||||
\(728\) | 45.4366 | 1.68399 | ||||||||
\(729\) | 29.7505 | 1.10187 | ||||||||
\(730\) | 42.4518 | 1.57121 | ||||||||
\(731\) | −0.890946 | −0.0329528 | ||||||||
\(732\) | −91.6385 | −3.38706 | ||||||||
\(733\) | −18.0210 | −0.665621 | −0.332810 | − | 0.942994i | \(-0.607997\pi\) | ||||
−0.332810 | + | 0.942994i | \(0.607997\pi\) | |||||||
\(734\) | 33.9312 | 1.25242 | ||||||||
\(735\) | 43.6412 | 1.60973 | ||||||||
\(736\) | −30.7545 | −1.13363 | ||||||||
\(737\) | 41.3872 | 1.52452 | ||||||||
\(738\) | 12.9474 | 0.476599 | ||||||||
\(739\) | −22.0901 | −0.812596 | −0.406298 | − | 0.913741i | \(-0.633181\pi\) | ||||
−0.406298 | + | 0.913741i | \(0.633181\pi\) | |||||||
\(740\) | −94.1646 | −3.46156 | ||||||||
\(741\) | 15.8208 | 0.581191 | ||||||||
\(742\) | −116.038 | −4.25989 | ||||||||
\(743\) | 16.7001 | 0.612669 | 0.306334 | − | 0.951924i | \(-0.400897\pi\) | ||||
0.306334 | + | 0.951924i | \(0.400897\pi\) | |||||||
\(744\) | −36.4804 | −1.33744 | ||||||||
\(745\) | −38.5914 | −1.41388 | ||||||||
\(746\) | 40.3137 | 1.47599 | ||||||||
\(747\) | −5.26238 | −0.192540 | ||||||||
\(748\) | −3.39038 | −0.123965 | ||||||||
\(749\) | −15.6281 | −0.571038 | ||||||||
\(750\) | 23.3919 | 0.854150 | ||||||||
\(751\) | 35.9062 | 1.31024 | 0.655118 | − | 0.755526i | \(-0.272619\pi\) | ||||
0.655118 | + | 0.755526i | \(0.272619\pi\) | |||||||
\(752\) | −39.3446 | −1.43475 | ||||||||
\(753\) | −13.3469 | −0.486387 | ||||||||
\(754\) | −16.6712 | −0.607129 | ||||||||
\(755\) | −9.42708 | −0.343086 | ||||||||
\(756\) | 109.963 | 3.99933 | ||||||||
\(757\) | 0.282655 | 0.0102733 | 0.00513663 | − | 0.999987i | \(-0.498365\pi\) | ||||
0.00513663 | + | 0.999987i | \(0.498365\pi\) | |||||||
\(758\) | 85.5939 | 3.10891 | ||||||||
\(759\) | −18.6938 | −0.678540 | ||||||||
\(760\) | −145.242 | −5.26848 | ||||||||
\(761\) | −25.6854 | −0.931096 | −0.465548 | − | 0.885023i | \(-0.654143\pi\) | ||||
−0.465548 | + | 0.885023i | \(0.654143\pi\) | |||||||
\(762\) | −23.2763 | −0.843211 | ||||||||
\(763\) | −25.4791 | −0.922404 | ||||||||
\(764\) | 81.8975 | 2.96295 | ||||||||
\(765\) | −0.203975 | −0.00737473 | ||||||||
\(766\) | 52.5425 | 1.89844 | ||||||||
\(767\) | −2.95273 | −0.106617 | ||||||||
\(768\) | −19.7657 | −0.713232 | ||||||||
\(769\) | 3.89942 | 0.140617 | 0.0703083 | − | 0.997525i | \(-0.477602\pi\) | ||||
0.0703083 | + | 0.997525i | \(0.477602\pi\) | |||||||
\(770\) | −132.185 | −4.76362 | ||||||||
\(771\) | 17.7392 | 0.638861 | ||||||||
\(772\) | −70.5671 | −2.53977 | ||||||||
\(773\) | −22.5597 | −0.811416 | −0.405708 | − | 0.914003i | \(-0.632975\pi\) | ||||
−0.405708 | + | 0.914003i | \(0.632975\pi\) | |||||||
\(774\) | −6.64481 | −0.238843 | ||||||||
\(775\) | 9.12534 | 0.327792 | ||||||||
\(776\) | 25.7057 | 0.922780 | ||||||||
\(777\) | 44.2509 | 1.58749 | ||||||||
\(778\) | −71.0743 | −2.54814 | ||||||||
\(779\) | 73.6667 | 2.63938 | ||||||||
\(780\) | 32.4622 | 1.16233 | ||||||||
\(781\) | 10.7047 | 0.383046 | ||||||||
\(782\) | −1.12359 | −0.0401796 | ||||||||
\(783\) | −23.8478 | −0.852250 | ||||||||
\(784\) | 97.8206 | 3.49359 | ||||||||
\(785\) | −38.8742 | −1.38748 | ||||||||
\(786\) | 56.8995 | 2.02954 | ||||||||
\(787\) | 6.16961 | 0.219923 | 0.109961 | − | 0.993936i | \(-0.464927\pi\) | ||||
0.109961 | + | 0.993936i | \(0.464927\pi\) | |||||||
\(788\) | 60.8779 | 2.16869 | ||||||||
\(789\) | 20.4942 | 0.729613 | ||||||||
\(790\) | −83.5539 | −2.97271 | ||||||||
\(791\) | −18.4705 | −0.656737 | ||||||||
\(792\) | −14.9458 | −0.531075 | ||||||||
\(793\) | −17.2259 | −0.611709 | ||||||||
\(794\) | −46.2718 | −1.64212 | ||||||||
\(795\) | −49.0017 | −1.73791 | ||||||||
\(796\) | 62.6657 | 2.22113 | ||||||||
\(797\) | −48.1768 | −1.70651 | −0.853254 | − | 0.521495i | \(-0.825375\pi\) | ||||
−0.853254 | + | 0.521495i | \(0.825375\pi\) | |||||||
\(798\) | 115.475 | 4.08777 | ||||||||
\(799\) | −0.617705 | −0.0218528 | ||||||||
\(800\) | −34.6514 | −1.22511 | ||||||||
\(801\) | 1.93533 | 0.0683815 | ||||||||
\(802\) | 90.1089 | 3.18186 | ||||||||
\(803\) | 24.8549 | 0.877110 | ||||||||
\(804\) | −74.1858 | −2.61633 | ||||||||
\(805\) | −31.0924 | −1.09586 | ||||||||
\(806\) | −11.6018 | −0.408655 | ||||||||
\(807\) | 14.7008 | 0.517494 | ||||||||
\(808\) | 62.6913 | 2.20547 | ||||||||
\(809\) | −13.9473 | −0.490360 | −0.245180 | − | 0.969478i | \(-0.578847\pi\) | ||||
−0.245180 | + | 0.969478i | \(0.578847\pi\) | |||||||
\(810\) | 55.3340 | 1.94424 | ||||||||
\(811\) | 8.73705 | 0.306799 | 0.153400 | − | 0.988164i | \(-0.450978\pi\) | ||||
0.153400 | + | 0.988164i | \(0.450978\pi\) | |||||||
\(812\) | −86.3648 | −3.03081 | ||||||||
\(813\) | 3.29484 | 0.115555 | ||||||||
\(814\) | −77.6772 | −2.72258 | ||||||||
\(815\) | −36.6486 | −1.28374 | ||||||||
\(816\) | 2.57579 | 0.0901708 | ||||||||
\(817\) | −37.8070 | −1.32270 | ||||||||
\(818\) | 82.8870 | 2.89807 | ||||||||
\(819\) | 2.70777 | 0.0946171 | ||||||||
\(820\) | 151.155 | 5.27855 | ||||||||
\(821\) | 49.0432 | 1.71162 | 0.855810 | − | 0.517291i | \(-0.173059\pi\) | ||||
0.855810 | + | 0.517291i | \(0.173059\pi\) | |||||||
\(822\) | 57.3537 | 2.00044 | ||||||||
\(823\) | −34.1875 | −1.19170 | −0.595851 | − | 0.803095i | \(-0.703185\pi\) | ||||
−0.595851 | + | 0.803095i | \(0.703185\pi\) | |||||||
\(824\) | −68.0130 | −2.36935 | ||||||||
\(825\) | −21.0625 | −0.733301 | ||||||||
\(826\) | −21.5518 | −0.749884 | ||||||||
\(827\) | 23.7110 | 0.824512 | 0.412256 | − | 0.911068i | \(-0.364741\pi\) | ||||
0.412256 | + | 0.911068i | \(0.364741\pi\) | |||||||
\(828\) | −5.94772 | −0.206698 | ||||||||
\(829\) | 18.4764 | 0.641711 | 0.320856 | − | 0.947128i | \(-0.396030\pi\) | ||||
0.320856 | + | 0.947128i | \(0.396030\pi\) | |||||||
\(830\) | −86.5589 | −3.00450 | ||||||||
\(831\) | −22.5253 | −0.781393 | ||||||||
\(832\) | 14.3000 | 0.495763 | ||||||||
\(833\) | 1.53577 | 0.0532113 | ||||||||
\(834\) | −3.54261 | −0.122670 | ||||||||
\(835\) | 58.2850 | 2.01703 | ||||||||
\(836\) | −143.870 | −4.97584 | ||||||||
\(837\) | −16.5961 | −0.573644 | ||||||||
\(838\) | −77.2689 | −2.66921 | ||||||||
\(839\) | 16.9350 | 0.584662 | 0.292331 | − | 0.956317i | \(-0.405569\pi\) | ||||
0.292331 | + | 0.956317i | \(0.405569\pi\) | |||||||
\(840\) | 140.048 | 4.83211 | ||||||||
\(841\) | −10.2701 | −0.354140 | ||||||||
\(842\) | 63.6153 | 2.19233 | ||||||||
\(843\) | −12.0800 | −0.416057 | ||||||||
\(844\) | −5.59322 | −0.192526 | ||||||||
\(845\) | −30.7360 | −1.05735 | ||||||||
\(846\) | −4.60694 | −0.158390 | ||||||||
\(847\) | −32.5096 | −1.11704 | ||||||||
\(848\) | −109.836 | −3.77178 | ||||||||
\(849\) | 40.4314 | 1.38760 | ||||||||
\(850\) | −1.26597 | −0.0434222 | ||||||||
\(851\) | −18.2711 | −0.626324 | ||||||||
\(852\) | −19.1881 | −0.657372 | ||||||||
\(853\) | −28.5643 | −0.978022 | −0.489011 | − | 0.872278i | \(-0.662642\pi\) | ||||
−0.489011 | + | 0.872278i | \(0.662642\pi\) | |||||||
\(854\) | −125.731 | −4.30241 | ||||||||
\(855\) | −8.65561 | −0.296016 | ||||||||
\(856\) | −29.0651 | −0.993424 | ||||||||
\(857\) | −5.17766 | −0.176865 | −0.0884327 | − | 0.996082i | \(-0.528186\pi\) | ||||
−0.0884327 | + | 0.996082i | \(0.528186\pi\) | |||||||
\(858\) | 26.7784 | 0.914199 | ||||||||
\(859\) | 35.1695 | 1.19997 | 0.599984 | − | 0.800012i | \(-0.295174\pi\) | ||||
0.599984 | + | 0.800012i | \(0.295174\pi\) | |||||||
\(860\) | −77.5751 | −2.64529 | ||||||||
\(861\) | −71.0323 | −2.42077 | ||||||||
\(862\) | 45.3632 | 1.54508 | ||||||||
\(863\) | −40.5264 | −1.37953 | −0.689767 | − | 0.724031i | \(-0.742287\pi\) | ||||
−0.689767 | + | 0.724031i | \(0.742287\pi\) | |||||||
\(864\) | 63.0198 | 2.14398 | ||||||||
\(865\) | −49.5618 | −1.68515 | ||||||||
\(866\) | 26.5623 | 0.902625 | ||||||||
\(867\) | −27.0945 | −0.920178 | ||||||||
\(868\) | −60.1027 | −2.04002 | ||||||||
\(869\) | −48.9196 | −1.65948 | ||||||||
\(870\) | −51.3851 | −1.74212 | ||||||||
\(871\) | −13.9452 | −0.472515 | ||||||||
\(872\) | −47.3858 | −1.60469 | ||||||||
\(873\) | 1.53192 | 0.0518475 | ||||||||
\(874\) | −47.6793 | −1.61278 | ||||||||
\(875\) | 22.7792 | 0.770077 | ||||||||
\(876\) | −44.5520 | −1.50527 | ||||||||
\(877\) | −4.37086 | −0.147594 | −0.0737968 | − | 0.997273i | \(-0.523512\pi\) | ||||
−0.0737968 | + | 0.997273i | \(0.523512\pi\) | |||||||
\(878\) | 83.0961 | 2.80436 | ||||||||
\(879\) | −7.35798 | −0.248179 | ||||||||
\(880\) | −125.120 | −4.21780 | ||||||||
\(881\) | 45.5309 | 1.53398 | 0.766988 | − | 0.641662i | \(-0.221755\pi\) | ||||
0.766988 | + | 0.641662i | \(0.221755\pi\) | |||||||
\(882\) | 11.4540 | 0.385676 | ||||||||
\(883\) | 2.53469 | 0.0852991 | 0.0426496 | − | 0.999090i | \(-0.486420\pi\) | ||||
0.0426496 | + | 0.999090i | \(0.486420\pi\) | |||||||
\(884\) | 1.14237 | 0.0384221 | ||||||||
\(885\) | −9.10112 | −0.305931 | ||||||||
\(886\) | 78.9271 | 2.65161 | ||||||||
\(887\) | −10.7805 | −0.361972 | −0.180986 | − | 0.983486i | \(-0.557929\pi\) | ||||
−0.180986 | + | 0.983486i | \(0.557929\pi\) | |||||||
\(888\) | 82.2975 | 2.76172 | ||||||||
\(889\) | −22.6666 | −0.760215 | ||||||||
\(890\) | 31.8335 | 1.06706 | ||||||||
\(891\) | 32.3972 | 1.08535 | ||||||||
\(892\) | −140.347 | −4.69916 | ||||||||
\(893\) | −26.2121 | −0.877154 | ||||||||
\(894\) | 57.0626 | 1.90846 | ||||||||
\(895\) | 10.0136 | 0.334717 | ||||||||
\(896\) | 11.0460 | 0.369020 | ||||||||
\(897\) | 6.29876 | 0.210309 | ||||||||
\(898\) | −12.8459 | −0.428675 | ||||||||
\(899\) | 13.0345 | 0.434724 | ||||||||
\(900\) | −6.70136 | −0.223379 | ||||||||
\(901\) | −1.72441 | −0.0574483 | ||||||||
\(902\) | 124.689 | 4.15168 | ||||||||
\(903\) | 36.4550 | 1.21314 | ||||||||
\(904\) | −34.3514 | −1.14251 | ||||||||
\(905\) | 47.6083 | 1.58255 | ||||||||
\(906\) | 13.9392 | 0.463099 | ||||||||
\(907\) | 16.1217 | 0.535312 | 0.267656 | − | 0.963515i | \(-0.413751\pi\) | ||||
0.267656 | + | 0.963515i | \(0.413751\pi\) | |||||||
\(908\) | 119.873 | 3.97811 | ||||||||
\(909\) | 3.73606 | 0.123917 | ||||||||
\(910\) | 44.5391 | 1.47646 | ||||||||
\(911\) | 25.7819 | 0.854192 | 0.427096 | − | 0.904206i | \(-0.359537\pi\) | ||||
0.427096 | + | 0.904206i | \(0.359537\pi\) | |||||||
\(912\) | 109.303 | 3.61938 | ||||||||
\(913\) | −50.6790 | −1.67723 | ||||||||
\(914\) | 91.2922 | 3.01968 | ||||||||
\(915\) | −53.0948 | −1.75526 | ||||||||
\(916\) | −133.150 | −4.39939 | ||||||||
\(917\) | 55.4092 | 1.82977 | ||||||||
\(918\) | 2.30239 | 0.0759901 | ||||||||
\(919\) | −13.8780 | −0.457793 | −0.228897 | − | 0.973451i | \(-0.573512\pi\) | ||||
−0.228897 | + | 0.973451i | \(0.573512\pi\) | |||||||
\(920\) | −57.8254 | −1.90645 | ||||||||
\(921\) | 7.01336 | 0.231098 | ||||||||
\(922\) | −65.8416 | −2.16838 | ||||||||
\(923\) | −3.60690 | −0.118723 | ||||||||
\(924\) | 138.725 | 4.56371 | ||||||||
\(925\) | −20.5862 | −0.676871 | ||||||||
\(926\) | 54.1347 | 1.77898 | ||||||||
\(927\) | −4.05320 | −0.133125 | ||||||||
\(928\) | −49.4955 | −1.62477 | ||||||||
\(929\) | −52.9687 | −1.73785 | −0.868923 | − | 0.494947i | \(-0.835187\pi\) | ||||
−0.868923 | + | 0.494947i | \(0.835187\pi\) | |||||||
\(930\) | −35.7598 | −1.17261 | ||||||||
\(931\) | 65.1699 | 2.13586 | ||||||||
\(932\) | −90.3057 | −2.95806 | ||||||||
\(933\) | 3.16176 | 0.103511 | ||||||||
\(934\) | 18.7078 | 0.612139 | ||||||||
\(935\) | −1.96437 | −0.0642417 | ||||||||
\(936\) | 5.03590 | 0.164603 | ||||||||
\(937\) | −26.2562 | −0.857753 | −0.428877 | − | 0.903363i | \(-0.641090\pi\) | ||||
−0.428877 | + | 0.903363i | \(0.641090\pi\) | |||||||
\(938\) | −101.785 | −3.32340 | ||||||||
\(939\) | −4.28018 | −0.139678 | ||||||||
\(940\) | −53.7839 | −1.75424 | ||||||||
\(941\) | 49.8404 | 1.62475 | 0.812375 | − | 0.583136i | \(-0.198174\pi\) | ||||
0.812375 | + | 0.583136i | \(0.198174\pi\) | |||||||
\(942\) | 57.4807 | 1.87282 | ||||||||
\(943\) | 29.3291 | 0.955086 | ||||||||
\(944\) | −20.3999 | −0.663960 | ||||||||
\(945\) | 63.7122 | 2.07256 | ||||||||
\(946\) | −63.9924 | −2.08057 | ||||||||
\(947\) | 52.4900 | 1.70570 | 0.852849 | − | 0.522158i | \(-0.174873\pi\) | ||||
0.852849 | + | 0.522158i | \(0.174873\pi\) | |||||||
\(948\) | 87.6875 | 2.84796 | ||||||||
\(949\) | −8.37472 | −0.271855 | ||||||||
\(950\) | −53.7208 | −1.74293 | ||||||||
\(951\) | 15.5190 | 0.503238 | ||||||||
\(952\) | 4.92839 | 0.159730 | ||||||||
\(953\) | 4.48607 | 0.145318 | 0.0726591 | − | 0.997357i | \(-0.476852\pi\) | ||||
0.0726591 | + | 0.997357i | \(0.476852\pi\) | |||||||
\(954\) | −12.8609 | −0.416387 | ||||||||
\(955\) | 47.4509 | 1.53548 | ||||||||
\(956\) | −78.6990 | −2.54531 | ||||||||
\(957\) | −30.0853 | −0.972518 | ||||||||
\(958\) | 16.5354 | 0.534236 | ||||||||
\(959\) | 55.8515 | 1.80354 | ||||||||
\(960\) | 44.0765 | 1.42256 | ||||||||
\(961\) | −21.9291 | −0.707390 | ||||||||
\(962\) | 26.1729 | 0.843848 | ||||||||
\(963\) | −1.73212 | −0.0558167 | ||||||||
\(964\) | 129.270 | 4.16349 | ||||||||
\(965\) | −40.8861 | −1.31617 | ||||||||
\(966\) | 45.9742 | 1.47920 | ||||||||
\(967\) | −46.6336 | −1.49964 | −0.749818 | − | 0.661644i | \(-0.769859\pi\) | ||||
−0.749818 | + | 0.661644i | \(0.769859\pi\) | |||||||
\(968\) | −60.4613 | −1.94330 | ||||||||
\(969\) | 1.71604 | 0.0551271 | ||||||||
\(970\) | 25.1979 | 0.809057 | ||||||||
\(971\) | 55.6584 | 1.78616 | 0.893082 | − | 0.449894i | \(-0.148538\pi\) | ||||
0.893082 | + | 0.449894i | \(0.148538\pi\) | |||||||
\(972\) | 22.7787 | 0.730629 | ||||||||
\(973\) | −3.44982 | −0.110596 | ||||||||
\(974\) | 49.9994 | 1.60208 | ||||||||
\(975\) | 7.09688 | 0.227282 | ||||||||
\(976\) | −119.011 | −3.80943 | ||||||||
\(977\) | 1.60392 | 0.0513139 | 0.0256569 | − | 0.999671i | \(-0.491832\pi\) | ||||
0.0256569 | + | 0.999671i | \(0.491832\pi\) | |||||||
\(978\) | 54.1899 | 1.73280 | ||||||||
\(979\) | 18.6381 | 0.595675 | ||||||||
\(980\) | 133.720 | 4.27154 | ||||||||
\(981\) | −2.82393 | −0.0901612 | ||||||||
\(982\) | 86.2670 | 2.75289 | ||||||||
\(983\) | 10.6627 | 0.340087 | 0.170044 | − | 0.985437i | \(-0.445609\pi\) | ||||
0.170044 | + | 0.985437i | \(0.445609\pi\) | |||||||
\(984\) | −132.106 | −4.21137 | ||||||||
\(985\) | 35.2723 | 1.12387 | ||||||||
\(986\) | −1.80828 | −0.0575875 | ||||||||
\(987\) | 25.2747 | 0.804503 | ||||||||
\(988\) | 48.4761 | 1.54223 | ||||||||
\(989\) | −15.0522 | −0.478631 | ||||||||
\(990\) | −14.6506 | −0.465625 | ||||||||
\(991\) | 12.4872 | 0.396669 | 0.198335 | − | 0.980134i | \(-0.436447\pi\) | ||||
0.198335 | + | 0.980134i | \(0.436447\pi\) | |||||||
\(992\) | −34.4447 | −1.09362 | ||||||||
\(993\) | −20.9783 | −0.665728 | ||||||||
\(994\) | −26.3266 | −0.835027 | ||||||||
\(995\) | 36.3081 | 1.15105 | ||||||||
\(996\) | 90.8412 | 2.87841 | ||||||||
\(997\) | 35.5503 | 1.12589 | 0.562945 | − | 0.826494i | \(-0.309668\pi\) | ||||
0.562945 | + | 0.826494i | \(0.309668\pi\) | |||||||
\(998\) | −58.5163 | −1.85230 | ||||||||
\(999\) | 37.4398 | 1.18454 |
(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 | 6047.2.a.a.1.10 | ✓ | 217 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6047.2.a.a.1.10 | ✓ | 217 | 1.1 | even | 1 | trivial |