Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8021,2,Mod(1,8021)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8021, 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("8021.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8021 = 13 \cdot 617 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8021.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: | \(64.0480074613\) |
Analytic rank: | \(1\) |
Dimension: | \(134\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 8021.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.51883 | −1.78108 | −0.890542 | − | 0.454901i | \(-0.849675\pi\) | ||||
−0.890542 | + | 0.454901i | \(0.849675\pi\) | |||||||
\(3\) | −2.43350 | −1.40498 | −0.702492 | − | 0.711692i | \(-0.747929\pi\) | ||||
−0.702492 | + | 0.711692i | \(0.747929\pi\) | |||||||
\(4\) | 4.34452 | 2.17226 | ||||||||
\(5\) | −0.221192 | −0.0989199 | −0.0494599 | − | 0.998776i | \(-0.515750\pi\) | ||||
−0.0494599 | + | 0.998776i | \(0.515750\pi\) | |||||||
\(6\) | 6.12959 | 2.50239 | ||||||||
\(7\) | −1.84924 | −0.698948 | −0.349474 | − | 0.936946i | \(-0.613640\pi\) | ||||
−0.349474 | + | 0.936946i | \(0.613640\pi\) | |||||||
\(8\) | −5.90546 | −2.08790 | ||||||||
\(9\) | 2.92194 | 0.973980 | ||||||||
\(10\) | 0.557145 | 0.176185 | ||||||||
\(11\) | −0.570132 | −0.171901 | −0.0859507 | − | 0.996299i | \(-0.527393\pi\) | ||||
−0.0859507 | + | 0.996299i | \(0.527393\pi\) | |||||||
\(12\) | −10.5724 | −3.05199 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 4.65793 | 1.24488 | ||||||||
\(15\) | 0.538271 | 0.138981 | ||||||||
\(16\) | 6.18583 | 1.54646 | ||||||||
\(17\) | −2.72385 | −0.660631 | −0.330315 | − | 0.943871i | \(-0.607155\pi\) | ||||
−0.330315 | + | 0.943871i | \(0.607155\pi\) | |||||||
\(18\) | −7.35988 | −1.73474 | ||||||||
\(19\) | 0.725895 | 0.166532 | 0.0832659 | − | 0.996527i | \(-0.473465\pi\) | ||||
0.0832659 | + | 0.996527i | \(0.473465\pi\) | |||||||
\(20\) | −0.960972 | −0.214880 | ||||||||
\(21\) | 4.50014 | 0.982010 | ||||||||
\(22\) | 1.43607 | 0.306171 | ||||||||
\(23\) | 9.23887 | 1.92644 | 0.963218 | − | 0.268720i | \(-0.0866005\pi\) | ||||
0.963218 | + | 0.268720i | \(0.0866005\pi\) | |||||||
\(24\) | 14.3710 | 2.93346 | ||||||||
\(25\) | −4.95107 | −0.990215 | ||||||||
\(26\) | −2.51883 | −0.493984 | ||||||||
\(27\) | 0.189961 | 0.0365579 | ||||||||
\(28\) | −8.03407 | −1.51830 | ||||||||
\(29\) | −5.17059 | −0.960154 | −0.480077 | − | 0.877226i | \(-0.659391\pi\) | ||||
−0.480077 | + | 0.877226i | \(0.659391\pi\) | |||||||
\(30\) | −1.35581 | −0.247537 | ||||||||
\(31\) | −1.94484 | −0.349304 | −0.174652 | − | 0.984630i | \(-0.555880\pi\) | ||||
−0.174652 | + | 0.984630i | \(0.555880\pi\) | |||||||
\(32\) | −3.77015 | −0.666474 | ||||||||
\(33\) | 1.38742 | 0.241519 | ||||||||
\(34\) | 6.86093 | 1.17664 | ||||||||
\(35\) | 0.409037 | 0.0691398 | ||||||||
\(36\) | 12.6944 | 2.11574 | ||||||||
\(37\) | 3.04393 | 0.500419 | 0.250210 | − | 0.968192i | \(-0.419500\pi\) | ||||
0.250210 | + | 0.968192i | \(0.419500\pi\) | |||||||
\(38\) | −1.82841 | −0.296607 | ||||||||
\(39\) | −2.43350 | −0.389672 | ||||||||
\(40\) | 1.30624 | 0.206534 | ||||||||
\(41\) | −10.8334 | −1.69189 | −0.845946 | − | 0.533269i | \(-0.820963\pi\) | ||||
−0.845946 | + | 0.533269i | \(0.820963\pi\) | |||||||
\(42\) | −11.3351 | −1.74904 | ||||||||
\(43\) | 1.96107 | 0.299060 | 0.149530 | − | 0.988757i | \(-0.452224\pi\) | ||||
0.149530 | + | 0.988757i | \(0.452224\pi\) | |||||||
\(44\) | −2.47695 | −0.373415 | ||||||||
\(45\) | −0.646308 | −0.0963460 | ||||||||
\(46\) | −23.2712 | −3.43115 | ||||||||
\(47\) | −6.01145 | −0.876860 | −0.438430 | − | 0.898765i | \(-0.644465\pi\) | ||||
−0.438430 | + | 0.898765i | \(0.644465\pi\) | |||||||
\(48\) | −15.0532 | −2.17275 | ||||||||
\(49\) | −3.58031 | −0.511472 | ||||||||
\(50\) | 12.4709 | 1.76366 | ||||||||
\(51\) | 6.62850 | 0.928176 | ||||||||
\(52\) | 4.34452 | 0.602477 | ||||||||
\(53\) | 8.41021 | 1.15523 | 0.577615 | − | 0.816309i | \(-0.303983\pi\) | ||||
0.577615 | + | 0.816309i | \(0.303983\pi\) | |||||||
\(54\) | −0.478479 | −0.0651127 | ||||||||
\(55\) | 0.126109 | 0.0170045 | ||||||||
\(56\) | 10.9206 | 1.45933 | ||||||||
\(57\) | −1.76647 | −0.233975 | ||||||||
\(58\) | 13.0238 | 1.71011 | ||||||||
\(59\) | 12.7351 | 1.65797 | 0.828987 | − | 0.559268i | \(-0.188918\pi\) | ||||
0.828987 | + | 0.559268i | \(0.188918\pi\) | |||||||
\(60\) | 2.33853 | 0.301903 | ||||||||
\(61\) | 4.56498 | 0.584486 | 0.292243 | − | 0.956344i | \(-0.405598\pi\) | ||||
0.292243 | + | 0.956344i | \(0.405598\pi\) | |||||||
\(62\) | 4.89874 | 0.622141 | ||||||||
\(63\) | −5.40337 | −0.680761 | ||||||||
\(64\) | −2.87528 | −0.359410 | ||||||||
\(65\) | −0.221192 | −0.0274354 | ||||||||
\(66\) | −3.49468 | −0.430165 | ||||||||
\(67\) | −7.92183 | −0.967805 | −0.483903 | − | 0.875122i | \(-0.660781\pi\) | ||||
−0.483903 | + | 0.875122i | \(0.660781\pi\) | |||||||
\(68\) | −11.8338 | −1.43506 | ||||||||
\(69\) | −22.4828 | −2.70661 | ||||||||
\(70\) | −1.03030 | −0.123144 | ||||||||
\(71\) | −1.61023 | −0.191099 | −0.0955495 | − | 0.995425i | \(-0.530461\pi\) | ||||
−0.0955495 | + | 0.995425i | \(0.530461\pi\) | |||||||
\(72\) | −17.2554 | −2.03357 | ||||||||
\(73\) | 10.2770 | 1.20284 | 0.601418 | − | 0.798934i | \(-0.294603\pi\) | ||||
0.601418 | + | 0.798934i | \(0.294603\pi\) | |||||||
\(74\) | −7.66716 | −0.891289 | ||||||||
\(75\) | 12.0485 | 1.39124 | ||||||||
\(76\) | 3.15367 | 0.361751 | ||||||||
\(77\) | 1.05431 | 0.120150 | ||||||||
\(78\) | 6.12959 | 0.694039 | ||||||||
\(79\) | −9.24103 | −1.03970 | −0.519849 | − | 0.854258i | \(-0.674012\pi\) | ||||
−0.519849 | + | 0.854258i | \(0.674012\pi\) | |||||||
\(80\) | −1.36825 | −0.152975 | ||||||||
\(81\) | −9.22809 | −1.02534 | ||||||||
\(82\) | 27.2875 | 3.01340 | ||||||||
\(83\) | 16.4887 | 1.80987 | 0.904937 | − | 0.425545i | \(-0.139918\pi\) | ||||
0.904937 | + | 0.425545i | \(0.139918\pi\) | |||||||
\(84\) | 19.5509 | 2.13318 | ||||||||
\(85\) | 0.602493 | 0.0653495 | ||||||||
\(86\) | −4.93960 | −0.532651 | ||||||||
\(87\) | 12.5826 | 1.34900 | ||||||||
\(88\) | 3.36689 | 0.358912 | ||||||||
\(89\) | 12.2808 | 1.30176 | 0.650879 | − | 0.759182i | \(-0.274401\pi\) | ||||
0.650879 | + | 0.759182i | \(0.274401\pi\) | |||||||
\(90\) | 1.62794 | 0.171600 | ||||||||
\(91\) | −1.84924 | −0.193853 | ||||||||
\(92\) | 40.1385 | 4.18472 | ||||||||
\(93\) | 4.73279 | 0.490767 | ||||||||
\(94\) | 15.1418 | 1.56176 | ||||||||
\(95\) | −0.160562 | −0.0164733 | ||||||||
\(96\) | 9.17467 | 0.936386 | ||||||||
\(97\) | −8.85175 | −0.898759 | −0.449380 | − | 0.893341i | \(-0.648355\pi\) | ||||
−0.449380 | + | 0.893341i | \(0.648355\pi\) | |||||||
\(98\) | 9.01819 | 0.910975 | ||||||||
\(99\) | −1.66589 | −0.167429 | ||||||||
\(100\) | −21.5101 | −2.15101 | ||||||||
\(101\) | −7.08468 | −0.704952 | −0.352476 | − | 0.935821i | \(-0.614660\pi\) | ||||
−0.352476 | + | 0.935821i | \(0.614660\pi\) | |||||||
\(102\) | −16.6961 | −1.65316 | ||||||||
\(103\) | −4.57406 | −0.450696 | −0.225348 | − | 0.974278i | \(-0.572352\pi\) | ||||
−0.225348 | + | 0.974278i | \(0.572352\pi\) | |||||||
\(104\) | −5.90546 | −0.579078 | ||||||||
\(105\) | −0.995392 | −0.0971403 | ||||||||
\(106\) | −21.1839 | −2.05756 | ||||||||
\(107\) | −16.3395 | −1.57959 | −0.789797 | − | 0.613368i | \(-0.789814\pi\) | ||||
−0.789797 | + | 0.613368i | \(0.789814\pi\) | |||||||
\(108\) | 0.825288 | 0.0794134 | ||||||||
\(109\) | 5.94027 | 0.568975 | 0.284487 | − | 0.958680i | \(-0.408177\pi\) | ||||
0.284487 | + | 0.958680i | \(0.408177\pi\) | |||||||
\(110\) | −0.317646 | −0.0302864 | ||||||||
\(111\) | −7.40742 | −0.703081 | ||||||||
\(112\) | −11.4391 | −1.08089 | ||||||||
\(113\) | 2.62243 | 0.246697 | 0.123349 | − | 0.992363i | \(-0.460637\pi\) | ||||
0.123349 | + | 0.992363i | \(0.460637\pi\) | |||||||
\(114\) | 4.44944 | 0.416728 | ||||||||
\(115\) | −2.04356 | −0.190563 | ||||||||
\(116\) | −22.4637 | −2.08570 | ||||||||
\(117\) | 2.92194 | 0.270133 | ||||||||
\(118\) | −32.0777 | −2.95299 | ||||||||
\(119\) | 5.03706 | 0.461746 | ||||||||
\(120\) | −3.17874 | −0.290178 | ||||||||
\(121\) | −10.6749 | −0.970450 | ||||||||
\(122\) | −11.4984 | −1.04102 | ||||||||
\(123\) | 26.3631 | 2.37708 | ||||||||
\(124\) | −8.44942 | −0.758780 | ||||||||
\(125\) | 2.20109 | 0.196872 | ||||||||
\(126\) | 13.6102 | 1.21249 | ||||||||
\(127\) | 4.62182 | 0.410120 | 0.205060 | − | 0.978749i | \(-0.434261\pi\) | ||||
0.205060 | + | 0.978749i | \(0.434261\pi\) | |||||||
\(128\) | 14.7826 | 1.30661 | ||||||||
\(129\) | −4.77226 | −0.420174 | ||||||||
\(130\) | 0.557145 | 0.0488648 | ||||||||
\(131\) | −11.0299 | −0.963691 | −0.481845 | − | 0.876256i | \(-0.660033\pi\) | ||||
−0.481845 | + | 0.876256i | \(0.660033\pi\) | |||||||
\(132\) | 6.02767 | 0.524642 | ||||||||
\(133\) | −1.34236 | −0.116397 | ||||||||
\(134\) | 19.9538 | 1.72374 | ||||||||
\(135\) | −0.0420177 | −0.00361631 | ||||||||
\(136\) | 16.0856 | 1.37933 | ||||||||
\(137\) | 2.40317 | 0.205316 | 0.102658 | − | 0.994717i | \(-0.467265\pi\) | ||||
0.102658 | + | 0.994717i | \(0.467265\pi\) | |||||||
\(138\) | 56.6305 | 4.82071 | ||||||||
\(139\) | −1.55707 | −0.132069 | −0.0660345 | − | 0.997817i | \(-0.521035\pi\) | ||||
−0.0660345 | + | 0.997817i | \(0.521035\pi\) | |||||||
\(140\) | 1.77707 | 0.150190 | ||||||||
\(141\) | 14.6289 | 1.23197 | ||||||||
\(142\) | 4.05590 | 0.340363 | ||||||||
\(143\) | −0.570132 | −0.0476769 | ||||||||
\(144\) | 18.0746 | 1.50622 | ||||||||
\(145\) | 1.14369 | 0.0949783 | ||||||||
\(146\) | −25.8862 | −2.14235 | ||||||||
\(147\) | 8.71269 | 0.718610 | ||||||||
\(148\) | 13.2244 | 1.08704 | ||||||||
\(149\) | 11.1268 | 0.911541 | 0.455770 | − | 0.890097i | \(-0.349364\pi\) | ||||
0.455770 | + | 0.890097i | \(0.349364\pi\) | |||||||
\(150\) | −30.3481 | −2.47791 | ||||||||
\(151\) | 8.31701 | 0.676829 | 0.338414 | − | 0.940997i | \(-0.390109\pi\) | ||||
0.338414 | + | 0.940997i | \(0.390109\pi\) | |||||||
\(152\) | −4.28675 | −0.347701 | ||||||||
\(153\) | −7.95893 | −0.643441 | ||||||||
\(154\) | −2.65564 | −0.213997 | ||||||||
\(155\) | 0.430183 | 0.0345532 | ||||||||
\(156\) | −10.5724 | −0.846470 | ||||||||
\(157\) | −10.5305 | −0.840423 | −0.420212 | − | 0.907426i | \(-0.638044\pi\) | ||||
−0.420212 | + | 0.907426i | \(0.638044\pi\) | |||||||
\(158\) | 23.2766 | 1.85179 | ||||||||
\(159\) | −20.4663 | −1.62308 | ||||||||
\(160\) | 0.833925 | 0.0659276 | ||||||||
\(161\) | −17.0849 | −1.34648 | ||||||||
\(162\) | 23.2440 | 1.82622 | ||||||||
\(163\) | −4.92927 | −0.386090 | −0.193045 | − | 0.981190i | \(-0.561836\pi\) | ||||
−0.193045 | + | 0.981190i | \(0.561836\pi\) | |||||||
\(164\) | −47.0659 | −3.67523 | ||||||||
\(165\) | −0.306886 | −0.0238910 | ||||||||
\(166\) | −41.5324 | −3.22354 | ||||||||
\(167\) | −15.5438 | −1.20281 | −0.601406 | − | 0.798944i | \(-0.705393\pi\) | ||||
−0.601406 | + | 0.798944i | \(0.705393\pi\) | |||||||
\(168\) | −26.5754 | −2.05033 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −1.51758 | −0.116393 | ||||||||
\(171\) | 2.12102 | 0.162199 | ||||||||
\(172\) | 8.51989 | 0.649636 | ||||||||
\(173\) | 15.5327 | 1.18093 | 0.590465 | − | 0.807063i | \(-0.298944\pi\) | ||||
0.590465 | + | 0.807063i | \(0.298944\pi\) | |||||||
\(174\) | −31.6936 | −2.40268 | ||||||||
\(175\) | 9.15573 | 0.692108 | ||||||||
\(176\) | −3.52674 | −0.265838 | ||||||||
\(177\) | −30.9910 | −2.32943 | ||||||||
\(178\) | −30.9332 | −2.31854 | ||||||||
\(179\) | 7.93161 | 0.592836 | 0.296418 | − | 0.955058i | \(-0.404208\pi\) | ||||
0.296418 | + | 0.955058i | \(0.404208\pi\) | |||||||
\(180\) | −2.80790 | −0.209289 | ||||||||
\(181\) | −7.42017 | −0.551537 | −0.275769 | − | 0.961224i | \(-0.588932\pi\) | ||||
−0.275769 | + | 0.961224i | \(0.588932\pi\) | |||||||
\(182\) | 4.65793 | 0.345269 | ||||||||
\(183\) | −11.1089 | −0.821194 | ||||||||
\(184\) | −54.5598 | −4.02220 | ||||||||
\(185\) | −0.673292 | −0.0495014 | ||||||||
\(186\) | −11.9211 | −0.874097 | ||||||||
\(187\) | 1.55296 | 0.113563 | ||||||||
\(188\) | −26.1169 | −1.90477 | ||||||||
\(189\) | −0.351283 | −0.0255521 | ||||||||
\(190\) | 0.404429 | 0.0293404 | ||||||||
\(191\) | 5.40208 | 0.390881 | 0.195440 | − | 0.980716i | \(-0.437386\pi\) | ||||
0.195440 | + | 0.980716i | \(0.437386\pi\) | |||||||
\(192\) | 6.99700 | 0.504965 | ||||||||
\(193\) | 19.0924 | 1.37430 | 0.687151 | − | 0.726515i | \(-0.258861\pi\) | ||||
0.687151 | + | 0.726515i | \(0.258861\pi\) | |||||||
\(194\) | 22.2961 | 1.60077 | ||||||||
\(195\) | 0.538271 | 0.0385464 | ||||||||
\(196\) | −15.5547 | −1.11105 | ||||||||
\(197\) | 4.96836 | 0.353981 | 0.176990 | − | 0.984213i | \(-0.443364\pi\) | ||||
0.176990 | + | 0.984213i | \(0.443364\pi\) | |||||||
\(198\) | 4.19611 | 0.298204 | ||||||||
\(199\) | −12.2242 | −0.866553 | −0.433276 | − | 0.901261i | \(-0.642643\pi\) | ||||
−0.433276 | + | 0.901261i | \(0.642643\pi\) | |||||||
\(200\) | 29.2384 | 2.06747 | ||||||||
\(201\) | 19.2778 | 1.35975 | ||||||||
\(202\) | 17.8451 | 1.25558 | ||||||||
\(203\) | 9.56166 | 0.671097 | ||||||||
\(204\) | 28.7977 | 2.01624 | ||||||||
\(205\) | 2.39626 | 0.167362 | ||||||||
\(206\) | 11.5213 | 0.802727 | ||||||||
\(207\) | 26.9954 | 1.87631 | ||||||||
\(208\) | 6.18583 | 0.428910 | ||||||||
\(209\) | −0.413857 | −0.0286271 | ||||||||
\(210\) | 2.50723 | 0.173015 | ||||||||
\(211\) | 18.0902 | 1.24538 | 0.622691 | − | 0.782468i | \(-0.286039\pi\) | ||||
0.622691 | + | 0.782468i | \(0.286039\pi\) | |||||||
\(212\) | 36.5383 | 2.50946 | ||||||||
\(213\) | 3.91850 | 0.268491 | ||||||||
\(214\) | 41.1564 | 2.81339 | ||||||||
\(215\) | −0.433771 | −0.0295830 | ||||||||
\(216\) | −1.12180 | −0.0763291 | ||||||||
\(217\) | 3.59649 | 0.244145 | ||||||||
\(218\) | −14.9626 | −1.01339 | ||||||||
\(219\) | −25.0092 | −1.68997 | ||||||||
\(220\) | 0.547881 | 0.0369381 | ||||||||
\(221\) | −2.72385 | −0.183226 | ||||||||
\(222\) | 18.6581 | 1.25225 | ||||||||
\(223\) | −9.93760 | −0.665471 | −0.332736 | − | 0.943020i | \(-0.607972\pi\) | ||||
−0.332736 | + | 0.943020i | \(0.607972\pi\) | |||||||
\(224\) | 6.97191 | 0.465831 | ||||||||
\(225\) | −14.4667 | −0.964449 | ||||||||
\(226\) | −6.60545 | −0.439388 | ||||||||
\(227\) | −1.44380 | −0.0958283 | −0.0479142 | − | 0.998851i | \(-0.515257\pi\) | ||||
−0.0479142 | + | 0.998851i | \(0.515257\pi\) | |||||||
\(228\) | −7.67446 | −0.508254 | ||||||||
\(229\) | 3.36100 | 0.222101 | 0.111051 | − | 0.993815i | \(-0.464578\pi\) | ||||
0.111051 | + | 0.993815i | \(0.464578\pi\) | |||||||
\(230\) | 5.14739 | 0.339409 | ||||||||
\(231\) | −2.56567 | −0.168809 | ||||||||
\(232\) | 30.5347 | 2.00470 | ||||||||
\(233\) | 13.8966 | 0.910400 | 0.455200 | − | 0.890389i | \(-0.349568\pi\) | ||||
0.455200 | + | 0.890389i | \(0.349568\pi\) | |||||||
\(234\) | −7.35988 | −0.481130 | ||||||||
\(235\) | 1.32968 | 0.0867389 | ||||||||
\(236\) | 55.3281 | 3.60155 | ||||||||
\(237\) | 22.4881 | 1.46076 | ||||||||
\(238\) | −12.6875 | −0.822409 | ||||||||
\(239\) | −8.83495 | −0.571485 | −0.285743 | − | 0.958306i | \(-0.592240\pi\) | ||||
−0.285743 | + | 0.958306i | \(0.592240\pi\) | |||||||
\(240\) | 3.32965 | 0.214928 | ||||||||
\(241\) | 10.5701 | 0.680883 | 0.340441 | − | 0.940266i | \(-0.389424\pi\) | ||||
0.340441 | + | 0.940266i | \(0.389424\pi\) | |||||||
\(242\) | 26.8884 | 1.72845 | ||||||||
\(243\) | 21.8867 | 1.40403 | ||||||||
\(244\) | 19.8327 | 1.26966 | ||||||||
\(245\) | 0.791934 | 0.0505948 | ||||||||
\(246\) | −66.4043 | −4.23378 | ||||||||
\(247\) | 0.725895 | 0.0461876 | ||||||||
\(248\) | 11.4852 | 0.729311 | ||||||||
\(249\) | −40.1254 | −2.54284 | ||||||||
\(250\) | −5.54419 | −0.350645 | ||||||||
\(251\) | 10.9621 | 0.691923 | 0.345961 | − | 0.938249i | \(-0.387553\pi\) | ||||
0.345961 | + | 0.938249i | \(0.387553\pi\) | |||||||
\(252\) | −23.4751 | −1.47879 | ||||||||
\(253\) | −5.26738 | −0.331157 | ||||||||
\(254\) | −11.6416 | −0.730459 | ||||||||
\(255\) | −1.46617 | −0.0918151 | ||||||||
\(256\) | −31.4845 | −1.96778 | ||||||||
\(257\) | 22.1898 | 1.38416 | 0.692080 | − | 0.721821i | \(-0.256695\pi\) | ||||
0.692080 | + | 0.721821i | \(0.256695\pi\) | |||||||
\(258\) | 12.0205 | 0.748366 | ||||||||
\(259\) | −5.62896 | −0.349767 | ||||||||
\(260\) | −0.960972 | −0.0595969 | ||||||||
\(261\) | −15.1081 | −0.935170 | ||||||||
\(262\) | 27.7826 | 1.71641 | ||||||||
\(263\) | −4.69101 | −0.289260 | −0.144630 | − | 0.989486i | \(-0.546199\pi\) | ||||
−0.144630 | + | 0.989486i | \(0.546199\pi\) | |||||||
\(264\) | −8.19335 | −0.504266 | ||||||||
\(265\) | −1.86027 | −0.114275 | ||||||||
\(266\) | 3.38117 | 0.207313 | ||||||||
\(267\) | −29.8853 | −1.82895 | ||||||||
\(268\) | −34.4165 | −2.10233 | ||||||||
\(269\) | 27.3934 | 1.67021 | 0.835104 | − | 0.550092i | \(-0.185407\pi\) | ||||
0.835104 | + | 0.550092i | \(0.185407\pi\) | |||||||
\(270\) | 0.105836 | 0.00644095 | ||||||||
\(271\) | −6.28478 | −0.381773 | −0.190887 | − | 0.981612i | \(-0.561136\pi\) | ||||
−0.190887 | + | 0.981612i | \(0.561136\pi\) | |||||||
\(272\) | −16.8493 | −1.02164 | ||||||||
\(273\) | 4.50014 | 0.272361 | ||||||||
\(274\) | −6.05317 | −0.365686 | ||||||||
\(275\) | 2.82277 | 0.170219 | ||||||||
\(276\) | −97.6771 | −5.87947 | ||||||||
\(277\) | 16.3770 | 0.983996 | 0.491998 | − | 0.870596i | \(-0.336267\pi\) | ||||
0.491998 | + | 0.870596i | \(0.336267\pi\) | |||||||
\(278\) | 3.92200 | 0.235226 | ||||||||
\(279\) | −5.68272 | −0.340215 | ||||||||
\(280\) | −2.41555 | −0.144357 | ||||||||
\(281\) | −8.13368 | −0.485215 | −0.242607 | − | 0.970125i | \(-0.578003\pi\) | ||||
−0.242607 | + | 0.970125i | \(0.578003\pi\) | |||||||
\(282\) | −36.8477 | −2.19425 | ||||||||
\(283\) | 15.6804 | 0.932104 | 0.466052 | − | 0.884757i | \(-0.345676\pi\) | ||||
0.466052 | + | 0.884757i | \(0.345676\pi\) | |||||||
\(284\) | −6.99567 | −0.415117 | ||||||||
\(285\) | 0.390728 | 0.0231447 | ||||||||
\(286\) | 1.43607 | 0.0849165 | ||||||||
\(287\) | 20.0336 | 1.18254 | ||||||||
\(288\) | −11.0161 | −0.649133 | ||||||||
\(289\) | −9.58063 | −0.563567 | ||||||||
\(290\) | −2.88077 | −0.169164 | ||||||||
\(291\) | 21.5408 | 1.26274 | ||||||||
\(292\) | 44.6488 | 2.61287 | ||||||||
\(293\) | 18.8635 | 1.10202 | 0.551008 | − | 0.834500i | \(-0.314243\pi\) | ||||
0.551008 | + | 0.834500i | \(0.314243\pi\) | |||||||
\(294\) | −21.9458 | −1.27991 | ||||||||
\(295\) | −2.81691 | −0.164007 | ||||||||
\(296\) | −17.9758 | −1.04482 | ||||||||
\(297\) | −0.108303 | −0.00628436 | ||||||||
\(298\) | −28.0265 | −1.62353 | ||||||||
\(299\) | 9.23887 | 0.534297 | ||||||||
\(300\) | 52.3448 | 3.02213 | ||||||||
\(301\) | −3.62648 | −0.209027 | ||||||||
\(302\) | −20.9492 | −1.20549 | ||||||||
\(303\) | 17.2406 | 0.990447 | ||||||||
\(304\) | 4.49026 | 0.257534 | ||||||||
\(305\) | −1.00974 | −0.0578173 | ||||||||
\(306\) | 20.0472 | 1.14602 | ||||||||
\(307\) | −22.7774 | −1.29997 | −0.649987 | − | 0.759945i | \(-0.725226\pi\) | ||||
−0.649987 | + | 0.759945i | \(0.725226\pi\) | |||||||
\(308\) | 4.58048 | 0.260997 | ||||||||
\(309\) | 11.1310 | 0.633220 | ||||||||
\(310\) | −1.08356 | −0.0615421 | ||||||||
\(311\) | −9.62933 | −0.546029 | −0.273014 | − | 0.962010i | \(-0.588021\pi\) | ||||
−0.273014 | + | 0.962010i | \(0.588021\pi\) | |||||||
\(312\) | 14.3710 | 0.813595 | ||||||||
\(313\) | −30.0545 | −1.69878 | −0.849391 | − | 0.527765i | \(-0.823030\pi\) | ||||
−0.849391 | + | 0.527765i | \(0.823030\pi\) | |||||||
\(314\) | 26.5245 | 1.49686 | ||||||||
\(315\) | 1.19518 | 0.0673408 | ||||||||
\(316\) | −40.1479 | −2.25849 | ||||||||
\(317\) | −9.99419 | −0.561330 | −0.280665 | − | 0.959806i | \(-0.590555\pi\) | ||||
−0.280665 | + | 0.959806i | \(0.590555\pi\) | |||||||
\(318\) | 51.5511 | 2.89084 | ||||||||
\(319\) | 2.94792 | 0.165052 | ||||||||
\(320\) | 0.635988 | 0.0355528 | ||||||||
\(321\) | 39.7621 | 2.21931 | ||||||||
\(322\) | 43.0340 | 2.39819 | ||||||||
\(323\) | −1.97723 | −0.110016 | ||||||||
\(324\) | −40.0916 | −2.22731 | ||||||||
\(325\) | −4.95107 | −0.274636 | ||||||||
\(326\) | 12.4160 | 0.687660 | ||||||||
\(327\) | −14.4557 | −0.799400 | ||||||||
\(328\) | 63.9762 | 3.53249 | ||||||||
\(329\) | 11.1166 | 0.612879 | ||||||||
\(330\) | 0.772994 | 0.0425519 | ||||||||
\(331\) | −1.61217 | −0.0886128 | −0.0443064 | − | 0.999018i | \(-0.514108\pi\) | ||||
−0.0443064 | + | 0.999018i | \(0.514108\pi\) | |||||||
\(332\) | 71.6357 | 3.93152 | ||||||||
\(333\) | 8.89418 | 0.487398 | ||||||||
\(334\) | 39.1521 | 2.14231 | ||||||||
\(335\) | 1.75224 | 0.0957352 | ||||||||
\(336\) | 27.8371 | 1.51864 | ||||||||
\(337\) | 26.2381 | 1.42928 | 0.714640 | − | 0.699493i | \(-0.246591\pi\) | ||||
0.714640 | + | 0.699493i | \(0.246591\pi\) | |||||||
\(338\) | −2.51883 | −0.137006 | ||||||||
\(339\) | −6.38168 | −0.346605 | ||||||||
\(340\) | 2.61754 | 0.141956 | ||||||||
\(341\) | 1.10882 | 0.0600459 | ||||||||
\(342\) | −5.34250 | −0.288889 | ||||||||
\(343\) | 19.5655 | 1.05644 | ||||||||
\(344\) | −11.5810 | −0.624406 | ||||||||
\(345\) | 4.97301 | 0.267738 | ||||||||
\(346\) | −39.1243 | −2.10334 | ||||||||
\(347\) | −9.84301 | −0.528401 | −0.264200 | − | 0.964468i | \(-0.585108\pi\) | ||||
−0.264200 | + | 0.964468i | \(0.585108\pi\) | |||||||
\(348\) | 54.6656 | 2.93038 | ||||||||
\(349\) | 32.5097 | 1.74020 | 0.870102 | − | 0.492872i | \(-0.164053\pi\) | ||||
0.870102 | + | 0.492872i | \(0.164053\pi\) | |||||||
\(350\) | −23.0618 | −1.23270 | ||||||||
\(351\) | 0.189961 | 0.0101393 | ||||||||
\(352\) | 2.14948 | 0.114568 | ||||||||
\(353\) | 35.8101 | 1.90598 | 0.952991 | − | 0.303000i | \(-0.0979882\pi\) | ||||
0.952991 | + | 0.303000i | \(0.0979882\pi\) | |||||||
\(354\) | 78.0612 | 4.14891 | ||||||||
\(355\) | 0.356169 | 0.0189035 | ||||||||
\(356\) | 53.3540 | 2.82776 | ||||||||
\(357\) | −12.2577 | −0.648746 | ||||||||
\(358\) | −19.9784 | −1.05589 | ||||||||
\(359\) | 12.8975 | 0.680706 | 0.340353 | − | 0.940298i | \(-0.389453\pi\) | ||||
0.340353 | + | 0.940298i | \(0.389453\pi\) | |||||||
\(360\) | 3.81675 | 0.201160 | ||||||||
\(361\) | −18.4731 | −0.972267 | ||||||||
\(362\) | 18.6902 | 0.982334 | ||||||||
\(363\) | 25.9775 | 1.36347 | ||||||||
\(364\) | −8.03407 | −0.421100 | ||||||||
\(365\) | −2.27319 | −0.118984 | ||||||||
\(366\) | 27.9815 | 1.46262 | ||||||||
\(367\) | 28.5603 | 1.49084 | 0.745419 | − | 0.666596i | \(-0.232249\pi\) | ||||
0.745419 | + | 0.666596i | \(0.232249\pi\) | |||||||
\(368\) | 57.1500 | 2.97915 | ||||||||
\(369\) | −31.6545 | −1.64787 | ||||||||
\(370\) | 1.69591 | 0.0881662 | ||||||||
\(371\) | −15.5525 | −0.807446 | ||||||||
\(372\) | 20.5617 | 1.06607 | ||||||||
\(373\) | 0.246560 | 0.0127664 | 0.00638318 | − | 0.999980i | \(-0.497968\pi\) | ||||
0.00638318 | + | 0.999980i | \(0.497968\pi\) | |||||||
\(374\) | −3.91164 | −0.202266 | ||||||||
\(375\) | −5.35637 | −0.276602 | ||||||||
\(376\) | 35.5004 | 1.83079 | ||||||||
\(377\) | −5.17059 | −0.266299 | ||||||||
\(378\) | 0.884823 | 0.0455104 | ||||||||
\(379\) | −10.8613 | −0.557905 | −0.278953 | − | 0.960305i | \(-0.589987\pi\) | ||||
−0.278953 | + | 0.960305i | \(0.589987\pi\) | |||||||
\(380\) | −0.697565 | −0.0357843 | ||||||||
\(381\) | −11.2472 | −0.576212 | ||||||||
\(382\) | −13.6069 | −0.696192 | ||||||||
\(383\) | 22.8063 | 1.16535 | 0.582674 | − | 0.812706i | \(-0.302006\pi\) | ||||
0.582674 | + | 0.812706i | \(0.302006\pi\) | |||||||
\(384\) | −35.9736 | −1.83577 | ||||||||
\(385\) | −0.233205 | −0.0118852 | ||||||||
\(386\) | −48.0906 | −2.44775 | ||||||||
\(387\) | 5.73012 | 0.291278 | ||||||||
\(388\) | −38.4566 | −1.95234 | ||||||||
\(389\) | −17.0529 | −0.864618 | −0.432309 | − | 0.901726i | \(-0.642301\pi\) | ||||
−0.432309 | + | 0.901726i | \(0.642301\pi\) | |||||||
\(390\) | −1.35581 | −0.0686543 | ||||||||
\(391\) | −25.1653 | −1.27266 | ||||||||
\(392\) | 21.1434 | 1.06790 | ||||||||
\(393\) | 26.8414 | 1.35397 | ||||||||
\(394\) | −12.5145 | −0.630470 | ||||||||
\(395\) | 2.04404 | 0.102847 | ||||||||
\(396\) | −7.23751 | −0.363698 | ||||||||
\(397\) | 26.8577 | 1.34795 | 0.673975 | − | 0.738754i | \(-0.264585\pi\) | ||||
0.673975 | + | 0.738754i | \(0.264585\pi\) | |||||||
\(398\) | 30.7908 | 1.54340 | ||||||||
\(399\) | 3.26663 | 0.163536 | ||||||||
\(400\) | −30.6265 | −1.53132 | ||||||||
\(401\) | 23.9948 | 1.19824 | 0.599122 | − | 0.800658i | \(-0.295516\pi\) | ||||
0.599122 | + | 0.800658i | \(0.295516\pi\) | |||||||
\(402\) | −48.5575 | −2.42183 | ||||||||
\(403\) | −1.94484 | −0.0968796 | ||||||||
\(404\) | −30.7796 | −1.53134 | ||||||||
\(405\) | 2.04118 | 0.101427 | ||||||||
\(406\) | −24.0842 | −1.19528 | ||||||||
\(407\) | −1.73544 | −0.0860228 | ||||||||
\(408\) | −39.1444 | −1.93793 | ||||||||
\(409\) | 3.97701 | 0.196650 | 0.0983251 | − | 0.995154i | \(-0.468651\pi\) | ||||
0.0983251 | + | 0.995154i | \(0.468651\pi\) | |||||||
\(410\) | −6.03577 | −0.298085 | ||||||||
\(411\) | −5.84811 | −0.288466 | ||||||||
\(412\) | −19.8721 | −0.979028 | ||||||||
\(413\) | −23.5504 | −1.15884 | ||||||||
\(414\) | −67.9969 | −3.34187 | ||||||||
\(415\) | −3.64717 | −0.179033 | ||||||||
\(416\) | −3.77015 | −0.184847 | ||||||||
\(417\) | 3.78914 | 0.185555 | ||||||||
\(418\) | 1.04244 | 0.0509872 | ||||||||
\(419\) | −7.30573 | −0.356908 | −0.178454 | − | 0.983948i | \(-0.557110\pi\) | ||||
−0.178454 | + | 0.983948i | \(0.557110\pi\) | |||||||
\(420\) | −4.32450 | −0.211014 | ||||||||
\(421\) | −17.6314 | −0.859301 | −0.429650 | − | 0.902995i | \(-0.641363\pi\) | ||||
−0.429650 | + | 0.902995i | \(0.641363\pi\) | |||||||
\(422\) | −45.5663 | −2.21813 | ||||||||
\(423\) | −17.5651 | −0.854044 | ||||||||
\(424\) | −49.6661 | −2.41200 | ||||||||
\(425\) | 13.4860 | 0.654167 | ||||||||
\(426\) | −9.87004 | −0.478205 | ||||||||
\(427\) | −8.44176 | −0.408525 | ||||||||
\(428\) | −70.9871 | −3.43129 | ||||||||
\(429\) | 1.38742 | 0.0669852 | ||||||||
\(430\) | 1.09260 | 0.0526897 | ||||||||
\(431\) | −10.8027 | −0.520348 | −0.260174 | − | 0.965562i | \(-0.583780\pi\) | ||||
−0.260174 | + | 0.965562i | \(0.583780\pi\) | |||||||
\(432\) | 1.17506 | 0.0565353 | ||||||||
\(433\) | 0.408217 | 0.0196177 | 0.00980883 | − | 0.999952i | \(-0.496878\pi\) | ||||
0.00980883 | + | 0.999952i | \(0.496878\pi\) | |||||||
\(434\) | −9.05895 | −0.434844 | ||||||||
\(435\) | −2.78317 | −0.133443 | ||||||||
\(436\) | 25.8076 | 1.23596 | ||||||||
\(437\) | 6.70645 | 0.320813 | ||||||||
\(438\) | 62.9940 | 3.00997 | ||||||||
\(439\) | −19.1821 | −0.915510 | −0.457755 | − | 0.889078i | \(-0.651346\pi\) | ||||
−0.457755 | + | 0.889078i | \(0.651346\pi\) | |||||||
\(440\) | −0.744729 | −0.0355036 | ||||||||
\(441\) | −10.4614 | −0.498164 | ||||||||
\(442\) | 6.86093 | 0.326341 | ||||||||
\(443\) | 15.8699 | 0.754001 | 0.377001 | − | 0.926213i | \(-0.376955\pi\) | ||||
0.377001 | + | 0.926213i | \(0.376955\pi\) | |||||||
\(444\) | −32.1817 | −1.52728 | ||||||||
\(445\) | −2.71640 | −0.128770 | ||||||||
\(446\) | 25.0312 | 1.18526 | ||||||||
\(447\) | −27.0770 | −1.28070 | ||||||||
\(448\) | 5.31709 | 0.251209 | ||||||||
\(449\) | −26.3949 | −1.24565 | −0.622825 | − | 0.782361i | \(-0.714015\pi\) | ||||
−0.622825 | + | 0.782361i | \(0.714015\pi\) | |||||||
\(450\) | 36.4393 | 1.71777 | ||||||||
\(451\) | 6.17647 | 0.290839 | ||||||||
\(452\) | 11.3932 | 0.535890 | ||||||||
\(453\) | −20.2395 | −0.950934 | ||||||||
\(454\) | 3.63669 | 0.170678 | ||||||||
\(455\) | 0.409037 | 0.0191759 | ||||||||
\(456\) | 10.4318 | 0.488514 | ||||||||
\(457\) | 4.92449 | 0.230358 | 0.115179 | − | 0.993345i | \(-0.463256\pi\) | ||||
0.115179 | + | 0.993345i | \(0.463256\pi\) | |||||||
\(458\) | −8.46580 | −0.395581 | ||||||||
\(459\) | −0.517424 | −0.0241513 | ||||||||
\(460\) | −8.87829 | −0.413952 | ||||||||
\(461\) | 34.8301 | 1.62220 | 0.811101 | − | 0.584907i | \(-0.198869\pi\) | ||||
0.811101 | + | 0.584907i | \(0.198869\pi\) | |||||||
\(462\) | 6.46250 | 0.300663 | ||||||||
\(463\) | −0.487675 | −0.0226642 | −0.0113321 | − | 0.999936i | \(-0.503607\pi\) | ||||
−0.0113321 | + | 0.999936i | \(0.503607\pi\) | |||||||
\(464\) | −31.9844 | −1.48484 | ||||||||
\(465\) | −1.04685 | −0.0485466 | ||||||||
\(466\) | −35.0033 | −1.62150 | ||||||||
\(467\) | −37.9178 | −1.75463 | −0.877313 | − | 0.479918i | \(-0.840666\pi\) | ||||
−0.877313 | + | 0.479918i | \(0.840666\pi\) | |||||||
\(468\) | 12.6944 | 0.586800 | ||||||||
\(469\) | 14.6494 | 0.676445 | ||||||||
\(470\) | −3.34925 | −0.154489 | ||||||||
\(471\) | 25.6259 | 1.18078 | ||||||||
\(472\) | −75.2069 | −3.46168 | ||||||||
\(473\) | −1.11807 | −0.0514088 | ||||||||
\(474\) | −56.6438 | −2.60173 | ||||||||
\(475\) | −3.59396 | −0.164902 | ||||||||
\(476\) | 21.8836 | 1.00303 | ||||||||
\(477\) | 24.5741 | 1.12517 | ||||||||
\(478\) | 22.2538 | 1.01786 | ||||||||
\(479\) | −11.6961 | −0.534406 | −0.267203 | − | 0.963640i | \(-0.586099\pi\) | ||||
−0.267203 | + | 0.963640i | \(0.586099\pi\) | |||||||
\(480\) | −2.02936 | −0.0926272 | ||||||||
\(481\) | 3.04393 | 0.138791 | ||||||||
\(482\) | −26.6244 | −1.21271 | ||||||||
\(483\) | 41.5762 | 1.89178 | ||||||||
\(484\) | −46.3776 | −2.10807 | ||||||||
\(485\) | 1.95793 | 0.0889051 | ||||||||
\(486\) | −55.1290 | −2.50070 | ||||||||
\(487\) | −14.6131 | −0.662182 | −0.331091 | − | 0.943599i | \(-0.607417\pi\) | ||||
−0.331091 | + | 0.943599i | \(0.607417\pi\) | |||||||
\(488\) | −26.9583 | −1.22035 | ||||||||
\(489\) | 11.9954 | 0.542451 | ||||||||
\(490\) | −1.99475 | −0.0901136 | ||||||||
\(491\) | −4.38216 | −0.197764 | −0.0988821 | − | 0.995099i | \(-0.531527\pi\) | ||||
−0.0988821 | + | 0.995099i | \(0.531527\pi\) | |||||||
\(492\) | 114.535 | 5.16364 | ||||||||
\(493\) | 14.0839 | 0.634307 | ||||||||
\(494\) | −1.82841 | −0.0822640 | ||||||||
\(495\) | 0.368481 | 0.0165620 | ||||||||
\(496\) | −12.0305 | −0.540184 | ||||||||
\(497\) | 2.97770 | 0.133568 | ||||||||
\(498\) | 101.069 | 4.52902 | ||||||||
\(499\) | 8.36464 | 0.374453 | 0.187226 | − | 0.982317i | \(-0.440050\pi\) | ||||
0.187226 | + | 0.982317i | \(0.440050\pi\) | |||||||
\(500\) | 9.56270 | 0.427657 | ||||||||
\(501\) | 37.8258 | 1.68993 | ||||||||
\(502\) | −27.6117 | −1.23237 | ||||||||
\(503\) | 30.5505 | 1.36218 | 0.681089 | − | 0.732201i | \(-0.261507\pi\) | ||||
0.681089 | + | 0.732201i | \(0.261507\pi\) | |||||||
\(504\) | 31.9094 | 1.42136 | ||||||||
\(505\) | 1.56707 | 0.0697338 | ||||||||
\(506\) | 13.2676 | 0.589819 | ||||||||
\(507\) | −2.43350 | −0.108076 | ||||||||
\(508\) | 20.0796 | 0.890888 | ||||||||
\(509\) | 0.301504 | 0.0133639 | 0.00668196 | − | 0.999978i | \(-0.497873\pi\) | ||||
0.00668196 | + | 0.999978i | \(0.497873\pi\) | |||||||
\(510\) | 3.69304 | 0.163530 | ||||||||
\(511\) | −19.0047 | −0.840720 | ||||||||
\(512\) | 49.7388 | 2.19817 | ||||||||
\(513\) | 0.137891 | 0.00608806 | ||||||||
\(514\) | −55.8923 | −2.46530 | ||||||||
\(515\) | 1.01174 | 0.0445828 | ||||||||
\(516\) | −20.7332 | −0.912728 | ||||||||
\(517\) | 3.42732 | 0.150734 | ||||||||
\(518\) | 14.1784 | 0.622964 | ||||||||
\(519\) | −37.7989 | −1.65919 | ||||||||
\(520\) | 1.30624 | 0.0572823 | ||||||||
\(521\) | −23.4929 | −1.02924 | −0.514621 | − | 0.857418i | \(-0.672067\pi\) | ||||
−0.514621 | + | 0.857418i | \(0.672067\pi\) | |||||||
\(522\) | 38.0549 | 1.66562 | ||||||||
\(523\) | 19.8954 | 0.869965 | 0.434983 | − | 0.900439i | \(-0.356754\pi\) | ||||
0.434983 | + | 0.900439i | \(0.356754\pi\) | |||||||
\(524\) | −47.9198 | −2.09339 | ||||||||
\(525\) | −22.2805 | −0.972401 | ||||||||
\(526\) | 11.8159 | 0.515197 | ||||||||
\(527\) | 5.29747 | 0.230761 | ||||||||
\(528\) | 8.58234 | 0.373498 | ||||||||
\(529\) | 62.3567 | 2.71116 | ||||||||
\(530\) | 4.68570 | 0.203534 | ||||||||
\(531\) | 37.2113 | 1.61483 | ||||||||
\(532\) | −5.83189 | −0.252845 | ||||||||
\(533\) | −10.8334 | −0.469246 | ||||||||
\(534\) | 75.2760 | 3.25751 | ||||||||
\(535\) | 3.61415 | 0.156253 | ||||||||
\(536\) | 46.7820 | 2.02068 | ||||||||
\(537\) | −19.3016 | −0.832925 | ||||||||
\(538\) | −68.9995 | −2.97478 | ||||||||
\(539\) | 2.04125 | 0.0879228 | ||||||||
\(540\) | −0.182547 | −0.00785556 | ||||||||
\(541\) | −7.50470 | −0.322652 | −0.161326 | − | 0.986901i | \(-0.551577\pi\) | ||||
−0.161326 | + | 0.986901i | \(0.551577\pi\) | |||||||
\(542\) | 15.8303 | 0.679970 | ||||||||
\(543\) | 18.0570 | 0.774901 | ||||||||
\(544\) | 10.2693 | 0.440294 | ||||||||
\(545\) | −1.31394 | −0.0562829 | ||||||||
\(546\) | −11.3351 | −0.485097 | ||||||||
\(547\) | 19.3190 | 0.826020 | 0.413010 | − | 0.910727i | \(-0.364478\pi\) | ||||
0.413010 | + | 0.910727i | \(0.364478\pi\) | |||||||
\(548\) | 10.4406 | 0.446001 | ||||||||
\(549\) | 13.3386 | 0.569278 | ||||||||
\(550\) | −7.11008 | −0.303175 | ||||||||
\(551\) | −3.75331 | −0.159896 | ||||||||
\(552\) | 132.771 | 5.65112 | ||||||||
\(553\) | 17.0889 | 0.726694 | ||||||||
\(554\) | −41.2508 | −1.75258 | ||||||||
\(555\) | 1.63846 | 0.0695487 | ||||||||
\(556\) | −6.76473 | −0.286889 | ||||||||
\(557\) | 22.6330 | 0.958992 | 0.479496 | − | 0.877544i | \(-0.340819\pi\) | ||||
0.479496 | + | 0.877544i | \(0.340819\pi\) | |||||||
\(558\) | 14.3138 | 0.605952 | ||||||||
\(559\) | 1.96107 | 0.0829443 | ||||||||
\(560\) | 2.53023 | 0.106922 | ||||||||
\(561\) | −3.77912 | −0.159555 | ||||||||
\(562\) | 20.4874 | 0.864208 | ||||||||
\(563\) | −10.2983 | −0.434020 | −0.217010 | − | 0.976169i | \(-0.569630\pi\) | ||||
−0.217010 | + | 0.976169i | \(0.569630\pi\) | |||||||
\(564\) | 63.5555 | 2.67617 | ||||||||
\(565\) | −0.580059 | −0.0244033 | ||||||||
\(566\) | −39.4964 | −1.66016 | ||||||||
\(567\) | 17.0650 | 0.716661 | ||||||||
\(568\) | 9.50914 | 0.398995 | ||||||||
\(569\) | −5.28019 | −0.221357 | −0.110678 | − | 0.993856i | \(-0.535302\pi\) | ||||
−0.110678 | + | 0.993856i | \(0.535302\pi\) | |||||||
\(570\) | −0.984179 | −0.0412227 | ||||||||
\(571\) | −19.4225 | −0.812808 | −0.406404 | − | 0.913694i | \(-0.633217\pi\) | ||||
−0.406404 | + | 0.913694i | \(0.633217\pi\) | |||||||
\(572\) | −2.47695 | −0.103567 | ||||||||
\(573\) | −13.1460 | −0.549181 | ||||||||
\(574\) | −50.4612 | −2.10621 | ||||||||
\(575\) | −45.7423 | −1.90759 | ||||||||
\(576\) | −8.40139 | −0.350058 | ||||||||
\(577\) | −32.0820 | −1.33559 | −0.667796 | − | 0.744344i | \(-0.732762\pi\) | ||||
−0.667796 | + | 0.744344i | \(0.732762\pi\) | |||||||
\(578\) | 24.1320 | 1.00376 | ||||||||
\(579\) | −46.4614 | −1.93087 | ||||||||
\(580\) | 4.96879 | 0.206318 | ||||||||
\(581\) | −30.4917 | −1.26501 | ||||||||
\(582\) | −54.2576 | −2.24905 | ||||||||
\(583\) | −4.79493 | −0.198586 | ||||||||
\(584\) | −60.6907 | −2.51140 | ||||||||
\(585\) | −0.646308 | −0.0267216 | ||||||||
\(586\) | −47.5139 | −1.96278 | ||||||||
\(587\) | 10.4229 | 0.430198 | 0.215099 | − | 0.976592i | \(-0.430993\pi\) | ||||
0.215099 | + | 0.976592i | \(0.430993\pi\) | |||||||
\(588\) | 37.8525 | 1.56101 | ||||||||
\(589\) | −1.41175 | −0.0581703 | ||||||||
\(590\) | 7.09532 | 0.292110 | ||||||||
\(591\) | −12.0905 | −0.497338 | ||||||||
\(592\) | 18.8292 | 0.773877 | ||||||||
\(593\) | 36.0999 | 1.48244 | 0.741222 | − | 0.671260i | \(-0.234247\pi\) | ||||
0.741222 | + | 0.671260i | \(0.234247\pi\) | |||||||
\(594\) | 0.272796 | 0.0111930 | ||||||||
\(595\) | −1.11416 | −0.0456759 | ||||||||
\(596\) | 48.3405 | 1.98010 | ||||||||
\(597\) | 29.7477 | 1.21749 | ||||||||
\(598\) | −23.2712 | −0.951629 | ||||||||
\(599\) | 37.9352 | 1.54999 | 0.774996 | − | 0.631966i | \(-0.217752\pi\) | ||||
0.774996 | + | 0.631966i | \(0.217752\pi\) | |||||||
\(600\) | −71.1517 | −2.90476 | ||||||||
\(601\) | −24.4848 | −0.998755 | −0.499377 | − | 0.866385i | \(-0.666438\pi\) | ||||
−0.499377 | + | 0.866385i | \(0.666438\pi\) | |||||||
\(602\) | 9.13451 | 0.372295 | ||||||||
\(603\) | −23.1471 | −0.942623 | ||||||||
\(604\) | 36.1334 | 1.47025 | ||||||||
\(605\) | 2.36121 | 0.0959968 | ||||||||
\(606\) | −43.4262 | −1.76407 | ||||||||
\(607\) | −33.6918 | −1.36751 | −0.683753 | − | 0.729713i | \(-0.739654\pi\) | ||||
−0.683753 | + | 0.729713i | \(0.739654\pi\) | |||||||
\(608\) | −2.73673 | −0.110989 | ||||||||
\(609\) | −23.2683 | −0.942881 | ||||||||
\(610\) | 2.54336 | 0.102977 | ||||||||
\(611\) | −6.01145 | −0.243197 | ||||||||
\(612\) | −34.5777 | −1.39772 | ||||||||
\(613\) | 0.00186567 | 7.53535e−5 0 | 3.76768e−5 | − | 1.00000i | \(-0.499988\pi\) | ||||
3.76768e−5 | 1.00000i | \(0.499988\pi\) | ||||||||
\(614\) | 57.3724 | 2.31536 | ||||||||
\(615\) | −5.83130 | −0.235141 | ||||||||
\(616\) | −6.22620 | −0.250861 | ||||||||
\(617\) | 1.00000 | 0.0402585 | ||||||||
\(618\) | −28.0371 | −1.12782 | ||||||||
\(619\) | −39.5169 | −1.58832 | −0.794158 | − | 0.607711i | \(-0.792088\pi\) | ||||
−0.794158 | + | 0.607711i | \(0.792088\pi\) | |||||||
\(620\) | 1.86894 | 0.0750585 | ||||||||
\(621\) | 1.75502 | 0.0704265 | ||||||||
\(622\) | 24.2547 | 0.972524 | ||||||||
\(623\) | −22.7101 | −0.909861 | ||||||||
\(624\) | −15.0532 | −0.602612 | ||||||||
\(625\) | 24.2685 | 0.970740 | ||||||||
\(626\) | 75.7023 | 3.02567 | ||||||||
\(627\) | 1.00712 | 0.0402206 | ||||||||
\(628\) | −45.7499 | −1.82562 | ||||||||
\(629\) | −8.29122 | −0.330592 | ||||||||
\(630\) | −3.01046 | −0.119940 | ||||||||
\(631\) | 5.96338 | 0.237398 | 0.118699 | − | 0.992930i | \(-0.462128\pi\) | ||||
0.118699 | + | 0.992930i | \(0.462128\pi\) | |||||||
\(632\) | 54.5726 | 2.17078 | ||||||||
\(633\) | −44.0226 | −1.74974 | ||||||||
\(634\) | 25.1737 | 0.999775 | ||||||||
\(635\) | −1.02231 | −0.0405691 | ||||||||
\(636\) | −88.9161 | −3.52575 | ||||||||
\(637\) | −3.58031 | −0.141857 | ||||||||
\(638\) | −7.42532 | −0.293971 | ||||||||
\(639\) | −4.70499 | −0.186126 | ||||||||
\(640\) | −3.26980 | −0.129250 | ||||||||
\(641\) | −3.04033 | −0.120086 | −0.0600428 | − | 0.998196i | \(-0.519124\pi\) | ||||
−0.0600428 | + | 0.998196i | \(0.519124\pi\) | |||||||
\(642\) | −100.154 | −3.95277 | ||||||||
\(643\) | −34.8329 | −1.37368 | −0.686838 | − | 0.726811i | \(-0.741002\pi\) | ||||
−0.686838 | + | 0.726811i | \(0.741002\pi\) | |||||||
\(644\) | −74.2257 | −2.92490 | ||||||||
\(645\) | 1.05558 | 0.0415636 | ||||||||
\(646\) | 4.98032 | 0.195948 | ||||||||
\(647\) | −2.21360 | −0.0870256 | −0.0435128 | − | 0.999053i | \(-0.513855\pi\) | ||||
−0.0435128 | + | 0.999053i | \(0.513855\pi\) | |||||||
\(648\) | 54.4961 | 2.14081 | ||||||||
\(649\) | −7.26072 | −0.285008 | ||||||||
\(650\) | 12.4709 | 0.489150 | ||||||||
\(651\) | −8.75206 | −0.343020 | ||||||||
\(652\) | −21.4153 | −0.838689 | ||||||||
\(653\) | −28.7597 | −1.12545 | −0.562726 | − | 0.826643i | \(-0.690247\pi\) | ||||
−0.562726 | + | 0.826643i | \(0.690247\pi\) | |||||||
\(654\) | 36.4114 | 1.42380 | ||||||||
\(655\) | 2.43973 | 0.0953282 | ||||||||
\(656\) | −67.0135 | −2.61644 | ||||||||
\(657\) | 30.0289 | 1.17154 | ||||||||
\(658\) | −28.0009 | −1.09159 | ||||||||
\(659\) | 21.6371 | 0.842864 | 0.421432 | − | 0.906860i | \(-0.361528\pi\) | ||||
0.421432 | + | 0.906860i | \(0.361528\pi\) | |||||||
\(660\) | −1.33327 | −0.0518975 | ||||||||
\(661\) | 13.0069 | 0.505909 | 0.252955 | − | 0.967478i | \(-0.418598\pi\) | ||||
0.252955 | + | 0.967478i | \(0.418598\pi\) | |||||||
\(662\) | 4.06078 | 0.157827 | ||||||||
\(663\) | 6.62850 | 0.257430 | ||||||||
\(664\) | −97.3736 | −3.77883 | ||||||||
\(665\) | 0.296918 | 0.0115140 | ||||||||
\(666\) | −22.4030 | −0.868097 | ||||||||
\(667\) | −47.7704 | −1.84968 | ||||||||
\(668\) | −67.5302 | −2.61282 | ||||||||
\(669\) | 24.1832 | 0.934976 | ||||||||
\(670\) | −4.41360 | −0.170512 | ||||||||
\(671\) | −2.60264 | −0.100474 | ||||||||
\(672\) | −16.9662 | −0.654485 | ||||||||
\(673\) | −17.9639 | −0.692456 | −0.346228 | − | 0.938150i | \(-0.612538\pi\) | ||||
−0.346228 | + | 0.938150i | \(0.612538\pi\) | |||||||
\(674\) | −66.0893 | −2.54567 | ||||||||
\(675\) | −0.940509 | −0.0362002 | ||||||||
\(676\) | 4.34452 | 0.167097 | ||||||||
\(677\) | −0.826149 | −0.0317515 | −0.0158757 | − | 0.999874i | \(-0.505054\pi\) | ||||
−0.0158757 | + | 0.999874i | \(0.505054\pi\) | |||||||
\(678\) | 16.0744 | 0.617334 | ||||||||
\(679\) | 16.3690 | 0.628185 | ||||||||
\(680\) | −3.55800 | −0.136443 | ||||||||
\(681\) | 3.51349 | 0.134637 | ||||||||
\(682\) | −2.79293 | −0.106947 | ||||||||
\(683\) | 21.0033 | 0.803670 | 0.401835 | − | 0.915712i | \(-0.368373\pi\) | ||||
0.401835 | + | 0.915712i | \(0.368373\pi\) | |||||||
\(684\) | 9.21483 | 0.352338 | ||||||||
\(685\) | −0.531560 | −0.0203099 | ||||||||
\(686\) | −49.2823 | −1.88161 | ||||||||
\(687\) | −8.17900 | −0.312048 | ||||||||
\(688\) | 12.1308 | 0.462483 | ||||||||
\(689\) | 8.41021 | 0.320403 | ||||||||
\(690\) | −12.5262 | −0.476864 | ||||||||
\(691\) | −23.2297 | −0.883699 | −0.441850 | − | 0.897089i | \(-0.645678\pi\) | ||||
−0.441850 | + | 0.897089i | \(0.645678\pi\) | |||||||
\(692\) | 67.4822 | 2.56529 | ||||||||
\(693\) | 3.08064 | 0.117024 | ||||||||
\(694\) | 24.7929 | 0.941126 | ||||||||
\(695\) | 0.344411 | 0.0130643 | ||||||||
\(696\) | −74.3063 | −2.81657 | ||||||||
\(697\) | 29.5086 | 1.11772 | ||||||||
\(698\) | −81.8865 | −3.09945 | ||||||||
\(699\) | −33.8175 | −1.27910 | ||||||||
\(700\) | 39.7773 | 1.50344 | ||||||||
\(701\) | −21.3033 | −0.804613 | −0.402307 | − | 0.915505i | \(-0.631791\pi\) | ||||
−0.402307 | + | 0.915505i | \(0.631791\pi\) | |||||||
\(702\) | −0.478479 | −0.0180590 | ||||||||
\(703\) | 2.20958 | 0.0833357 | ||||||||
\(704\) | 1.63929 | 0.0617831 | ||||||||
\(705\) | −3.23579 | −0.121867 | ||||||||
\(706\) | −90.1998 | −3.39471 | ||||||||
\(707\) | 13.1013 | 0.492725 | ||||||||
\(708\) | −134.641 | −5.06012 | ||||||||
\(709\) | −35.1976 | −1.32188 | −0.660938 | − | 0.750441i | \(-0.729841\pi\) | ||||
−0.660938 | + | 0.750441i | \(0.729841\pi\) | |||||||
\(710\) | −0.897130 | −0.0336687 | ||||||||
\(711\) | −27.0017 | −1.01264 | ||||||||
\(712\) | −72.5235 | −2.71793 | ||||||||
\(713\) | −17.9682 | −0.672913 | ||||||||
\(714\) | 30.8751 | 1.15547 | ||||||||
\(715\) | 0.126109 | 0.00471619 | ||||||||
\(716\) | 34.4590 | 1.28779 | ||||||||
\(717\) | 21.4999 | 0.802928 | ||||||||
\(718\) | −32.4867 | −1.21239 | ||||||||
\(719\) | −8.73898 | −0.325909 | −0.162954 | − | 0.986634i | \(-0.552102\pi\) | ||||
−0.162954 | + | 0.986634i | \(0.552102\pi\) | |||||||
\(720\) | −3.99795 | −0.148995 | ||||||||
\(721\) | 8.45854 | 0.315013 | ||||||||
\(722\) | 46.5306 | 1.73169 | ||||||||
\(723\) | −25.7225 | −0.956629 | ||||||||
\(724\) | −32.2371 | −1.19808 | ||||||||
\(725\) | 25.6000 | 0.950759 | ||||||||
\(726\) | −65.4331 | −2.42845 | ||||||||
\(727\) | 8.74126 | 0.324195 | 0.162098 | − | 0.986775i | \(-0.448174\pi\) | ||||
0.162098 | + | 0.986775i | \(0.448174\pi\) | |||||||
\(728\) | 10.9206 | 0.404745 | ||||||||
\(729\) | −25.5771 | −0.947300 | ||||||||
\(730\) | 5.72580 | 0.211921 | ||||||||
\(731\) | −5.34165 | −0.197568 | ||||||||
\(732\) | −48.2629 | −1.78385 | ||||||||
\(733\) | −24.1822 | −0.893189 | −0.446594 | − | 0.894736i | \(-0.647363\pi\) | ||||
−0.446594 | + | 0.894736i | \(0.647363\pi\) | |||||||
\(734\) | −71.9388 | −2.65531 | ||||||||
\(735\) | −1.92717 | −0.0710849 | ||||||||
\(736\) | −34.8319 | −1.28392 | ||||||||
\(737\) | 4.51649 | 0.166367 | ||||||||
\(738\) | 79.7325 | 2.93499 | ||||||||
\(739\) | −52.8767 | −1.94510 | −0.972550 | − | 0.232695i | \(-0.925246\pi\) | ||||
−0.972550 | + | 0.232695i | \(0.925246\pi\) | |||||||
\(740\) | −2.92513 | −0.107530 | ||||||||
\(741\) | −1.76647 | −0.0648929 | ||||||||
\(742\) | 39.1742 | 1.43813 | ||||||||
\(743\) | 42.1241 | 1.54538 | 0.772691 | − | 0.634782i | \(-0.218910\pi\) | ||||
0.772691 | + | 0.634782i | \(0.218910\pi\) | |||||||
\(744\) | −27.9493 | −1.02467 | ||||||||
\(745\) | −2.46115 | −0.0901695 | ||||||||
\(746\) | −0.621042 | −0.0227380 | ||||||||
\(747\) | 48.1791 | 1.76278 | ||||||||
\(748\) | 6.74685 | 0.246689 | ||||||||
\(749\) | 30.2156 | 1.10405 | ||||||||
\(750\) | 13.4918 | 0.492651 | ||||||||
\(751\) | −18.7486 | −0.684145 | −0.342073 | − | 0.939673i | \(-0.611129\pi\) | ||||
−0.342073 | + | 0.939673i | \(0.611129\pi\) | |||||||
\(752\) | −37.1858 | −1.35603 | ||||||||
\(753\) | −26.6764 | −0.972140 | ||||||||
\(754\) | 13.0238 | 0.474300 | ||||||||
\(755\) | −1.83965 | −0.0669518 | ||||||||
\(756\) | −1.52616 | −0.0555058 | ||||||||
\(757\) | −30.3567 | −1.10333 | −0.551667 | − | 0.834065i | \(-0.686008\pi\) | ||||
−0.551667 | + | 0.834065i | \(0.686008\pi\) | |||||||
\(758\) | 27.3577 | 0.993676 | ||||||||
\(759\) | 12.8182 | 0.465271 | ||||||||
\(760\) | 0.948192 | 0.0343946 | ||||||||
\(761\) | 50.4071 | 1.82726 | 0.913629 | − | 0.406550i | \(-0.133268\pi\) | ||||
0.913629 | + | 0.406550i | \(0.133268\pi\) | |||||||
\(762\) | 28.3299 | 1.02628 | ||||||||
\(763\) | −10.9850 | −0.397683 | ||||||||
\(764\) | 23.4695 | 0.849095 | ||||||||
\(765\) | 1.76045 | 0.0636491 | ||||||||
\(766\) | −57.4453 | −2.07558 | ||||||||
\(767\) | 12.7351 | 0.459839 | ||||||||
\(768\) | 76.6176 | 2.76470 | ||||||||
\(769\) | 36.5832 | 1.31922 | 0.659611 | − | 0.751607i | \(-0.270721\pi\) | ||||
0.659611 | + | 0.751607i | \(0.270721\pi\) | |||||||
\(770\) | 0.587405 | 0.0211686 | ||||||||
\(771\) | −53.9989 | −1.94472 | ||||||||
\(772\) | 82.9474 | 2.98534 | ||||||||
\(773\) | −27.5777 | −0.991902 | −0.495951 | − | 0.868350i | \(-0.665181\pi\) | ||||
−0.495951 | + | 0.868350i | \(0.665181\pi\) | |||||||
\(774\) | −14.4332 | −0.518791 | ||||||||
\(775\) | 9.62907 | 0.345886 | ||||||||
\(776\) | 52.2737 | 1.87652 | ||||||||
\(777\) | 13.6981 | 0.491417 | ||||||||
\(778\) | 42.9535 | 1.53996 | ||||||||
\(779\) | −7.86391 | −0.281754 | ||||||||
\(780\) | 2.33853 | 0.0837327 | ||||||||
\(781\) | 0.918043 | 0.0328502 | ||||||||
\(782\) | 63.3872 | 2.26672 | ||||||||
\(783\) | −0.982207 | −0.0351012 | ||||||||
\(784\) | −22.1472 | −0.790970 | ||||||||
\(785\) | 2.32925 | 0.0831346 | ||||||||
\(786\) | −67.6090 | −2.41153 | ||||||||
\(787\) | 13.9134 | 0.495961 | 0.247980 | − | 0.968765i | \(-0.420233\pi\) | ||||
0.247980 | + | 0.968765i | \(0.420233\pi\) | |||||||
\(788\) | 21.5851 | 0.768939 | ||||||||
\(789\) | 11.4156 | 0.406406 | ||||||||
\(790\) | −5.14859 | −0.183179 | ||||||||
\(791\) | −4.84950 | −0.172428 | ||||||||
\(792\) | 9.83786 | 0.349573 | ||||||||
\(793\) | 4.56498 | 0.162107 | ||||||||
\(794\) | −67.6501 | −2.40081 | ||||||||
\(795\) | 4.52697 | 0.160555 | ||||||||
\(796\) | −53.1084 | −1.88238 | ||||||||
\(797\) | −24.5998 | −0.871369 | −0.435685 | − | 0.900099i | \(-0.643494\pi\) | ||||
−0.435685 | + | 0.900099i | \(0.643494\pi\) | |||||||
\(798\) | −8.22809 | −0.291271 | ||||||||
\(799\) | 16.3743 | 0.579281 | ||||||||
\(800\) | 18.6663 | 0.659953 | ||||||||
\(801\) | 35.8836 | 1.26789 | ||||||||
\(802\) | −60.4390 | −2.13417 | ||||||||
\(803\) | −5.85927 | −0.206769 | ||||||||
\(804\) | 83.7528 | 2.95373 | ||||||||
\(805\) | 3.77904 | 0.133193 | ||||||||
\(806\) | 4.89874 | 0.172551 | ||||||||
\(807\) | −66.6620 | −2.34661 | ||||||||
\(808\) | 41.8383 | 1.47187 | ||||||||
\(809\) | −8.80674 | −0.309629 | −0.154814 | − | 0.987944i | \(-0.549478\pi\) | ||||
−0.154814 | + | 0.987944i | \(0.549478\pi\) | |||||||
\(810\) | −5.14138 | −0.180650 | ||||||||
\(811\) | −48.2903 | −1.69570 | −0.847851 | − | 0.530235i | \(-0.822104\pi\) | ||||
−0.847851 | + | 0.530235i | \(0.822104\pi\) | |||||||
\(812\) | 41.5409 | 1.45780 | ||||||||
\(813\) | 15.2940 | 0.536385 | ||||||||
\(814\) | 4.37129 | 0.153214 | ||||||||
\(815\) | 1.09031 | 0.0381920 | ||||||||
\(816\) | 41.0028 | 1.43538 | ||||||||
\(817\) | 1.42353 | 0.0498030 | ||||||||
\(818\) | −10.0174 | −0.350251 | ||||||||
\(819\) | −5.40337 | −0.188809 | ||||||||
\(820\) | 10.4106 | 0.363553 | ||||||||
\(821\) | −8.02008 | −0.279903 | −0.139951 | − | 0.990158i | \(-0.544695\pi\) | ||||
−0.139951 | + | 0.990158i | \(0.544695\pi\) | |||||||
\(822\) | 14.7304 | 0.513782 | ||||||||
\(823\) | −46.9705 | −1.63729 | −0.818644 | − | 0.574302i | \(-0.805274\pi\) | ||||
−0.818644 | + | 0.574302i | \(0.805274\pi\) | |||||||
\(824\) | 27.0119 | 0.941005 | ||||||||
\(825\) | −6.86922 | −0.239155 | ||||||||
\(826\) | 59.3194 | 2.06399 | ||||||||
\(827\) | −45.7058 | −1.58935 | −0.794674 | − | 0.607037i | \(-0.792358\pi\) | ||||
−0.794674 | + | 0.607037i | \(0.792358\pi\) | |||||||
\(828\) | 117.282 | 4.07584 | ||||||||
\(829\) | −34.2326 | −1.18895 | −0.594474 | − | 0.804115i | \(-0.702640\pi\) | ||||
−0.594474 | + | 0.804115i | \(0.702640\pi\) | |||||||
\(830\) | 9.18662 | 0.318872 | ||||||||
\(831\) | −39.8534 | −1.38250 | ||||||||
\(832\) | −2.87528 | −0.0996824 | ||||||||
\(833\) | 9.75222 | 0.337894 | ||||||||
\(834\) | −9.54421 | −0.330489 | ||||||||
\(835\) | 3.43815 | 0.118982 | ||||||||
\(836\) | −1.79801 | −0.0621854 | ||||||||
\(837\) | −0.369444 | −0.0127698 | ||||||||
\(838\) | 18.4019 | 0.635684 | ||||||||
\(839\) | 12.2617 | 0.423322 | 0.211661 | − | 0.977343i | \(-0.432113\pi\) | ||||
0.211661 | + | 0.977343i | \(0.432113\pi\) | |||||||
\(840\) | 5.87825 | 0.202819 | ||||||||
\(841\) | −2.26504 | −0.0781047 | ||||||||
\(842\) | 44.4105 | 1.53049 | ||||||||
\(843\) | 19.7933 | 0.681719 | ||||||||
\(844\) | 78.5934 | 2.70530 | ||||||||
\(845\) | −0.221192 | −0.00760922 | ||||||||
\(846\) | 44.2436 | 1.52112 | ||||||||
\(847\) | 19.7406 | 0.678294 | ||||||||
\(848\) | 52.0241 | 1.78651 | ||||||||
\(849\) | −38.1584 | −1.30959 | ||||||||
\(850\) | −33.9690 | −1.16513 | ||||||||
\(851\) | 28.1225 | 0.964026 | ||||||||
\(852\) | 17.0240 | 0.583232 | ||||||||
\(853\) | 33.6911 | 1.15356 | 0.576781 | − | 0.816899i | \(-0.304309\pi\) | ||||
0.576781 | + | 0.816899i | \(0.304309\pi\) | |||||||
\(854\) | 21.2634 | 0.727618 | ||||||||
\(855\) | −0.469152 | −0.0160447 | ||||||||
\(856\) | 96.4920 | 3.29803 | ||||||||
\(857\) | 0.603596 | 0.0206184 | 0.0103092 | − | 0.999947i | \(-0.496718\pi\) | ||||
0.0103092 | + | 0.999947i | \(0.496718\pi\) | |||||||
\(858\) | −3.49468 | −0.119306 | ||||||||
\(859\) | 1.05988 | 0.0361626 | 0.0180813 | − | 0.999837i | \(-0.494244\pi\) | ||||
0.0180813 | + | 0.999837i | \(0.494244\pi\) | |||||||
\(860\) | −1.88453 | −0.0642619 | ||||||||
\(861\) | −48.7517 | −1.66145 | ||||||||
\(862\) | 27.2102 | 0.926783 | ||||||||
\(863\) | −26.6849 | −0.908363 | −0.454181 | − | 0.890909i | \(-0.650068\pi\) | ||||
−0.454181 | + | 0.890909i | \(0.650068\pi\) | |||||||
\(864\) | −0.716179 | −0.0243649 | ||||||||
\(865\) | −3.43570 | −0.116817 | ||||||||
\(866\) | −1.02823 | −0.0349407 | ||||||||
\(867\) | 23.3145 | 0.791802 | ||||||||
\(868\) | 15.6250 | 0.530348 | ||||||||
\(869\) | 5.26861 | 0.178725 | ||||||||
\(870\) | 7.01035 | 0.237673 | ||||||||
\(871\) | −7.92183 | −0.268421 | ||||||||
\(872\) | −35.0800 | −1.18796 | ||||||||
\(873\) | −25.8643 | −0.875373 | ||||||||
\(874\) | −16.8924 | −0.571395 | ||||||||
\(875\) | −4.07035 | −0.137603 | ||||||||
\(876\) | −108.653 | −3.67105 | ||||||||
\(877\) | −50.2110 | −1.69550 | −0.847752 | − | 0.530393i | \(-0.822044\pi\) | ||||
−0.847752 | + | 0.530393i | \(0.822044\pi\) | |||||||
\(878\) | 48.3164 | 1.63060 | ||||||||
\(879\) | −45.9043 | −1.54831 | ||||||||
\(880\) | 0.780086 | 0.0262967 | ||||||||
\(881\) | −41.5979 | −1.40147 | −0.700735 | − | 0.713422i | \(-0.747144\pi\) | ||||
−0.700735 | + | 0.713422i | \(0.747144\pi\) | |||||||
\(882\) | 26.3506 | 0.887272 | ||||||||
\(883\) | −38.4833 | −1.29507 | −0.647533 | − | 0.762037i | \(-0.724199\pi\) | ||||
−0.647533 | + | 0.762037i | \(0.724199\pi\) | |||||||
\(884\) | −11.8338 | −0.398015 | ||||||||
\(885\) | 6.85495 | 0.230427 | ||||||||
\(886\) | −39.9736 | −1.34294 | ||||||||
\(887\) | −9.38989 | −0.315282 | −0.157641 | − | 0.987497i | \(-0.550389\pi\) | ||||
−0.157641 | + | 0.987497i | \(0.550389\pi\) | |||||||
\(888\) | 43.7442 | 1.46796 | ||||||||
\(889\) | −8.54686 | −0.286653 | ||||||||
\(890\) | 6.84216 | 0.229350 | ||||||||
\(891\) | 5.26123 | 0.176258 | ||||||||
\(892\) | −43.1741 | −1.44558 | ||||||||
\(893\) | −4.36369 | −0.146025 | ||||||||
\(894\) | 68.2026 | 2.28103 | ||||||||
\(895\) | −1.75440 | −0.0586433 | ||||||||
\(896\) | −27.3367 | −0.913254 | ||||||||
\(897\) | −22.4828 | −0.750679 | ||||||||
\(898\) | 66.4843 | 2.21861 | ||||||||
\(899\) | 10.0560 | 0.335386 | ||||||||
\(900\) | −62.8511 | −2.09504 | ||||||||
\(901\) | −22.9082 | −0.763181 | ||||||||
\(902\) | −15.5575 | −0.518008 | ||||||||
\(903\) | 8.82506 | 0.293680 | ||||||||
\(904\) | −15.4866 | −0.515078 | ||||||||
\(905\) | 1.64128 | 0.0545580 | ||||||||
\(906\) | 50.9799 | 1.69369 | ||||||||
\(907\) | 37.4461 | 1.24338 | 0.621688 | − | 0.783265i | \(-0.286447\pi\) | ||||
0.621688 | + | 0.783265i | \(0.286447\pi\) | |||||||
\(908\) | −6.27262 | −0.208164 | ||||||||
\(909\) | −20.7010 | −0.686610 | ||||||||
\(910\) | −1.03030 | −0.0341540 | ||||||||
\(911\) | −12.3835 | −0.410283 | −0.205142 | − | 0.978732i | \(-0.565765\pi\) | ||||
−0.205142 | + | 0.978732i | \(0.565765\pi\) | |||||||
\(912\) | −10.9271 | −0.361832 | ||||||||
\(913\) | −9.40077 | −0.311120 | ||||||||
\(914\) | −12.4040 | −0.410287 | ||||||||
\(915\) | 2.45720 | 0.0812324 | ||||||||
\(916\) | 14.6019 | 0.482461 | ||||||||
\(917\) | 20.3970 | 0.673569 | ||||||||
\(918\) | 1.30331 | 0.0430155 | ||||||||
\(919\) | −48.5944 | −1.60298 | −0.801491 | − | 0.598007i | \(-0.795960\pi\) | ||||
−0.801491 | + | 0.598007i | \(0.795960\pi\) | |||||||
\(920\) | 12.0682 | 0.397875 | ||||||||
\(921\) | 55.4288 | 1.82644 | ||||||||
\(922\) | −87.7313 | −2.88928 | ||||||||
\(923\) | −1.61023 | −0.0530013 | ||||||||
\(924\) | −11.1466 | −0.366697 | ||||||||
\(925\) | −15.0707 | −0.495523 | ||||||||
\(926\) | 1.22837 | 0.0403668 | ||||||||
\(927\) | −13.3651 | −0.438968 | ||||||||
\(928\) | 19.4939 | 0.639918 | ||||||||
\(929\) | −23.5622 | −0.773051 | −0.386526 | − | 0.922279i | \(-0.626325\pi\) | ||||
−0.386526 | + | 0.922279i | \(0.626325\pi\) | |||||||
\(930\) | 2.63685 | 0.0864656 | ||||||||
\(931\) | −2.59893 | −0.0851764 | ||||||||
\(932\) | 60.3743 | 1.97763 | ||||||||
\(933\) | 23.4330 | 0.767162 | ||||||||
\(934\) | 95.5086 | 3.12514 | ||||||||
\(935\) | −0.343501 | −0.0112337 | ||||||||
\(936\) | −17.2554 | −0.564010 | ||||||||
\(937\) | 29.6586 | 0.968904 | 0.484452 | − | 0.874818i | \(-0.339019\pi\) | ||||
0.484452 | + | 0.874818i | \(0.339019\pi\) | |||||||
\(938\) | −36.8993 | −1.20481 | ||||||||
\(939\) | 73.1378 | 2.38676 | ||||||||
\(940\) | 5.77684 | 0.188420 | ||||||||
\(941\) | 0.179871 | 0.00586362 | 0.00293181 | − | 0.999996i | \(-0.499067\pi\) | ||||
0.00293181 | + | 0.999996i | \(0.499067\pi\) | |||||||
\(942\) | −64.5475 | −2.10307 | ||||||||
\(943\) | −100.088 | −3.25932 | ||||||||
\(944\) | 78.7774 | 2.56399 | ||||||||
\(945\) | 0.0777008 | 0.00252761 | ||||||||
\(946\) | 2.81623 | 0.0915634 | ||||||||
\(947\) | −55.6536 | −1.80850 | −0.904250 | − | 0.427003i | \(-0.859569\pi\) | ||||
−0.904250 | + | 0.427003i | \(0.859569\pi\) | |||||||
\(948\) | 97.7000 | 3.17315 | ||||||||
\(949\) | 10.2770 | 0.333607 | ||||||||
\(950\) | 9.05259 | 0.293705 | ||||||||
\(951\) | 24.3209 | 0.788659 | ||||||||
\(952\) | −29.7462 | −0.964078 | ||||||||
\(953\) | −44.7982 | −1.45116 | −0.725578 | − | 0.688140i | \(-0.758427\pi\) | ||||
−0.725578 | + | 0.688140i | \(0.758427\pi\) | |||||||
\(954\) | −61.8981 | −2.00402 | ||||||||
\(955\) | −1.19490 | −0.0386659 | ||||||||
\(956\) | −38.3836 | −1.24142 | ||||||||
\(957\) | −7.17377 | −0.231895 | ||||||||
\(958\) | 29.4604 | 0.951823 | ||||||||
\(959\) | −4.44403 | −0.143505 | ||||||||
\(960\) | −1.54768 | −0.0499511 | ||||||||
\(961\) | −27.2176 | −0.877986 | ||||||||
\(962\) | −7.66716 | −0.247199 | ||||||||
\(963\) | −47.7429 | −1.53849 | ||||||||
\(964\) | 45.9222 | 1.47905 | ||||||||
\(965\) | −4.22308 | −0.135946 | ||||||||
\(966\) | −104.723 | −3.36942 | ||||||||
\(967\) | −21.1099 | −0.678850 | −0.339425 | − | 0.940633i | \(-0.610232\pi\) | ||||
−0.339425 | + | 0.940633i | \(0.610232\pi\) | |||||||
\(968\) | 63.0405 | 2.02620 | ||||||||
\(969\) | 4.81160 | 0.154571 | ||||||||
\(970\) | −4.93171 | −0.158348 | ||||||||
\(971\) | −24.4654 | −0.785134 | −0.392567 | − | 0.919724i | \(-0.628413\pi\) | ||||
−0.392567 | + | 0.919724i | \(0.628413\pi\) | |||||||
\(972\) | 95.0873 | 3.04993 | ||||||||
\(973\) | 2.87940 | 0.0923094 | ||||||||
\(974\) | 36.8079 | 1.17940 | ||||||||
\(975\) | 12.0485 | 0.385859 | ||||||||
\(976\) | 28.2382 | 0.903883 | ||||||||
\(977\) | 5.96340 | 0.190786 | 0.0953930 | − | 0.995440i | \(-0.469589\pi\) | ||||
0.0953930 | + | 0.995440i | \(0.469589\pi\) | |||||||
\(978\) | −30.2144 | −0.966151 | ||||||||
\(979\) | −7.00166 | −0.223774 | ||||||||
\(980\) | 3.44057 | 0.109905 | ||||||||
\(981\) | 17.3571 | 0.554170 | ||||||||
\(982\) | 11.0379 | 0.352235 | ||||||||
\(983\) | −51.6942 | −1.64879 | −0.824395 | − | 0.566016i | \(-0.808484\pi\) | ||||
−0.824395 | + | 0.566016i | \(0.808484\pi\) | |||||||
\(984\) | −155.686 | −4.96310 | ||||||||
\(985\) | −1.09896 | −0.0350158 | ||||||||
\(986\) | −35.4750 | −1.12975 | ||||||||
\(987\) | −27.0523 | −0.861086 | ||||||||
\(988\) | 3.15367 | 0.100332 | ||||||||
\(989\) | 18.1180 | 0.576120 | ||||||||
\(990\) | −0.928143 | −0.0294983 | ||||||||
\(991\) | 51.1752 | 1.62563 | 0.812816 | − | 0.582520i | \(-0.197933\pi\) | ||||
0.812816 | + | 0.582520i | \(0.197933\pi\) | |||||||
\(992\) | 7.33235 | 0.232802 | ||||||||
\(993\) | 3.92322 | 0.124500 | ||||||||
\(994\) | −7.50033 | −0.237896 | ||||||||
\(995\) | 2.70390 | 0.0857193 | ||||||||
\(996\) | −174.326 | −5.52372 | ||||||||
\(997\) | 17.4998 | 0.554223 | 0.277112 | − | 0.960838i | \(-0.410623\pi\) | ||||
0.277112 | + | 0.960838i | \(0.410623\pi\) | |||||||
\(998\) | −21.0691 | −0.666932 | ||||||||
\(999\) | 0.578227 | 0.0182943 |
(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 | 8021.2.a.a.1.7 | ✓ | 134 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8021.2.a.a.1.7 | ✓ | 134 | 1.1 | even | 1 | trivial |