Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6013,2,Mod(1,6013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6013, 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("6013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6013 = 7 \cdot 859 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6013.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: | \(48.0140467354\) |
Analytic rank: | \(0\) |
Dimension: | \(110\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 6013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.64365 | −1.86934 | −0.934672 | − | 0.355512i | \(-0.884307\pi\) | ||||
−0.934672 | + | 0.355512i | \(0.884307\pi\) | |||||||
\(3\) | 1.43905 | 0.830835 | 0.415418 | − | 0.909631i | \(-0.363635\pi\) | ||||
0.415418 | + | 0.909631i | \(0.363635\pi\) | |||||||
\(4\) | 4.98889 | 2.49444 | ||||||||
\(5\) | 0.402261 | 0.179897 | 0.0899483 | − | 0.995946i | \(-0.471330\pi\) | ||||
0.0899483 | + | 0.995946i | \(0.471330\pi\) | |||||||
\(6\) | −3.80434 | −1.55312 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −7.90158 | −2.79363 | ||||||||
\(9\) | −0.929138 | −0.309713 | ||||||||
\(10\) | −1.06344 | −0.336289 | ||||||||
\(11\) | −0.489443 | −0.147573 | −0.0737864 | − | 0.997274i | \(-0.523508\pi\) | ||||
−0.0737864 | + | 0.997274i | \(0.523508\pi\) | |||||||
\(12\) | 7.17926 | 2.07247 | ||||||||
\(13\) | −6.45702 | −1.79086 | −0.895428 | − | 0.445206i | \(-0.853130\pi\) | ||||
−0.895428 | + | 0.445206i | \(0.853130\pi\) | |||||||
\(14\) | 2.64365 | 0.706545 | ||||||||
\(15\) | 0.578873 | 0.149464 | ||||||||
\(16\) | 10.9112 | 2.72781 | ||||||||
\(17\) | −1.62326 | −0.393699 | −0.196849 | − | 0.980434i | \(-0.563071\pi\) | ||||
−0.196849 | + | 0.980434i | \(0.563071\pi\) | |||||||
\(18\) | 2.45632 | 0.578959 | ||||||||
\(19\) | −0.818199 | −0.187708 | −0.0938538 | − | 0.995586i | \(-0.529919\pi\) | ||||
−0.0938538 | + | 0.995586i | \(0.529919\pi\) | |||||||
\(20\) | 2.00684 | 0.448742 | ||||||||
\(21\) | −1.43905 | −0.314026 | ||||||||
\(22\) | 1.29392 | 0.275864 | ||||||||
\(23\) | 5.22279 | 1.08903 | 0.544514 | − | 0.838752i | \(-0.316714\pi\) | ||||
0.544514 | + | 0.838752i | \(0.316714\pi\) | |||||||
\(24\) | −11.3708 | −2.32105 | ||||||||
\(25\) | −4.83819 | −0.967637 | ||||||||
\(26\) | 17.0701 | 3.34773 | ||||||||
\(27\) | −5.65422 | −1.08816 | ||||||||
\(28\) | −4.98889 | −0.942812 | ||||||||
\(29\) | −8.57274 | −1.59192 | −0.795959 | − | 0.605351i | \(-0.793033\pi\) | ||||
−0.795959 | + | 0.605351i | \(0.793033\pi\) | |||||||
\(30\) | −1.53034 | −0.279400 | ||||||||
\(31\) | 6.80611 | 1.22241 | 0.611206 | − | 0.791471i | \(-0.290685\pi\) | ||||
0.611206 | + | 0.791471i | \(0.290685\pi\) | |||||||
\(32\) | −13.0423 | −2.30558 | ||||||||
\(33\) | −0.704333 | −0.122609 | ||||||||
\(34\) | 4.29134 | 0.735958 | ||||||||
\(35\) | −0.402261 | −0.0679945 | ||||||||
\(36\) | −4.63537 | −0.772561 | ||||||||
\(37\) | 5.90364 | 0.970552 | 0.485276 | − | 0.874361i | \(-0.338719\pi\) | ||||
0.485276 | + | 0.874361i | \(0.338719\pi\) | |||||||
\(38\) | 2.16303 | 0.350890 | ||||||||
\(39\) | −9.29197 | −1.48791 | ||||||||
\(40\) | −3.17850 | −0.502565 | ||||||||
\(41\) | 5.29790 | 0.827393 | 0.413696 | − | 0.910415i | \(-0.364238\pi\) | ||||
0.413696 | + | 0.910415i | \(0.364238\pi\) | |||||||
\(42\) | 3.80434 | 0.587023 | ||||||||
\(43\) | 6.73364 | 1.02687 | 0.513436 | − | 0.858128i | \(-0.328373\pi\) | ||||
0.513436 | + | 0.858128i | \(0.328373\pi\) | |||||||
\(44\) | −2.44178 | −0.368112 | ||||||||
\(45\) | −0.373756 | −0.0557163 | ||||||||
\(46\) | −13.8072 | −2.03577 | ||||||||
\(47\) | −3.93916 | −0.574586 | −0.287293 | − | 0.957843i | \(-0.592755\pi\) | ||||
−0.287293 | + | 0.957843i | \(0.592755\pi\) | |||||||
\(48\) | 15.7018 | 2.26636 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 12.7905 | 1.80885 | ||||||||
\(51\) | −2.33595 | −0.327099 | ||||||||
\(52\) | −32.2134 | −4.46719 | ||||||||
\(53\) | 12.1186 | 1.66462 | 0.832309 | − | 0.554312i | \(-0.187019\pi\) | ||||
0.832309 | + | 0.554312i | \(0.187019\pi\) | |||||||
\(54\) | 14.9478 | 2.03414 | ||||||||
\(55\) | −0.196884 | −0.0265478 | ||||||||
\(56\) | 7.90158 | 1.05589 | ||||||||
\(57\) | −1.17743 | −0.155954 | ||||||||
\(58\) | 22.6633 | 2.97584 | ||||||||
\(59\) | −12.2165 | −1.59045 | −0.795223 | − | 0.606317i | \(-0.792646\pi\) | ||||
−0.795223 | + | 0.606317i | \(0.792646\pi\) | |||||||
\(60\) | 2.88794 | 0.372831 | ||||||||
\(61\) | −3.99370 | −0.511340 | −0.255670 | − | 0.966764i | \(-0.582296\pi\) | ||||
−0.255670 | + | 0.966764i | \(0.582296\pi\) | |||||||
\(62\) | −17.9930 | −2.28511 | ||||||||
\(63\) | 0.929138 | 0.117060 | ||||||||
\(64\) | 12.6569 | 1.58212 | ||||||||
\(65\) | −2.59741 | −0.322169 | ||||||||
\(66\) | 1.86201 | 0.229198 | ||||||||
\(67\) | −4.87826 | −0.595974 | −0.297987 | − | 0.954570i | \(-0.596315\pi\) | ||||
−0.297987 | + | 0.954570i | \(0.596315\pi\) | |||||||
\(68\) | −8.09827 | −0.982060 | ||||||||
\(69\) | 7.51586 | 0.904803 | ||||||||
\(70\) | 1.06344 | 0.127105 | ||||||||
\(71\) | 16.2985 | 1.93428 | 0.967138 | − | 0.254252i | \(-0.0818292\pi\) | ||||
0.967138 | + | 0.254252i | \(0.0818292\pi\) | |||||||
\(72\) | 7.34166 | 0.865223 | ||||||||
\(73\) | −7.32447 | −0.857265 | −0.428632 | − | 0.903479i | \(-0.641004\pi\) | ||||
−0.428632 | + | 0.903479i | \(0.641004\pi\) | |||||||
\(74\) | −15.6071 | −1.81429 | ||||||||
\(75\) | −6.96239 | −0.803947 | ||||||||
\(76\) | −4.08190 | −0.468226 | ||||||||
\(77\) | 0.489443 | 0.0557773 | ||||||||
\(78\) | 24.5647 | 2.78141 | ||||||||
\(79\) | −7.49834 | −0.843629 | −0.421814 | − | 0.906682i | \(-0.638607\pi\) | ||||
−0.421814 | + | 0.906682i | \(0.638607\pi\) | |||||||
\(80\) | 4.38917 | 0.490724 | ||||||||
\(81\) | −5.34929 | −0.594365 | ||||||||
\(82\) | −14.0058 | −1.54668 | ||||||||
\(83\) | −11.2101 | −1.23047 | −0.615237 | − | 0.788342i | \(-0.710940\pi\) | ||||
−0.615237 | + | 0.788342i | \(0.710940\pi\) | |||||||
\(84\) | −7.17926 | −0.783321 | ||||||||
\(85\) | −0.652975 | −0.0708251 | ||||||||
\(86\) | −17.8014 | −1.91957 | ||||||||
\(87\) | −12.3366 | −1.32262 | ||||||||
\(88\) | 3.86738 | 0.412264 | ||||||||
\(89\) | −5.79688 | −0.614468 | −0.307234 | − | 0.951634i | \(-0.599404\pi\) | ||||
−0.307234 | + | 0.951634i | \(0.599404\pi\) | |||||||
\(90\) | 0.988081 | 0.104153 | ||||||||
\(91\) | 6.45702 | 0.676880 | ||||||||
\(92\) | 26.0559 | 2.71652 | ||||||||
\(93\) | 9.79432 | 1.01562 | ||||||||
\(94\) | 10.4138 | 1.07410 | ||||||||
\(95\) | −0.329130 | −0.0337680 | ||||||||
\(96\) | −18.7686 | −1.91556 | ||||||||
\(97\) | 3.31457 | 0.336544 | 0.168272 | − | 0.985741i | \(-0.446181\pi\) | ||||
0.168272 | + | 0.985741i | \(0.446181\pi\) | |||||||
\(98\) | −2.64365 | −0.267049 | ||||||||
\(99\) | 0.454761 | 0.0457052 | ||||||||
\(100\) | −24.1372 | −2.41372 | ||||||||
\(101\) | 1.85159 | 0.184240 | 0.0921201 | − | 0.995748i | \(-0.470636\pi\) | ||||
0.0921201 | + | 0.995748i | \(0.470636\pi\) | |||||||
\(102\) | 6.17544 | 0.611460 | ||||||||
\(103\) | 6.85532 | 0.675475 | 0.337738 | − | 0.941240i | \(-0.390338\pi\) | ||||
0.337738 | + | 0.941240i | \(0.390338\pi\) | |||||||
\(104\) | 51.0207 | 5.00299 | ||||||||
\(105\) | −0.578873 | −0.0564923 | ||||||||
\(106\) | −32.0374 | −3.11174 | ||||||||
\(107\) | 4.55624 | 0.440468 | 0.220234 | − | 0.975447i | \(-0.429318\pi\) | ||||
0.220234 | + | 0.975447i | \(0.429318\pi\) | |||||||
\(108\) | −28.2083 | −2.71434 | ||||||||
\(109\) | −7.71733 | −0.739186 | −0.369593 | − | 0.929194i | \(-0.620503\pi\) | ||||
−0.369593 | + | 0.929194i | \(0.620503\pi\) | |||||||
\(110\) | 0.520493 | 0.0496270 | ||||||||
\(111\) | 8.49562 | 0.806369 | ||||||||
\(112\) | −10.9112 | −1.03102 | ||||||||
\(113\) | 20.5285 | 1.93116 | 0.965581 | − | 0.260102i | \(-0.0837562\pi\) | ||||
0.965581 | + | 0.260102i | \(0.0837562\pi\) | |||||||
\(114\) | 3.11271 | 0.291532 | ||||||||
\(115\) | 2.10093 | 0.195912 | ||||||||
\(116\) | −42.7684 | −3.97095 | ||||||||
\(117\) | 5.99947 | 0.554651 | ||||||||
\(118\) | 32.2960 | 2.97309 | ||||||||
\(119\) | 1.62326 | 0.148804 | ||||||||
\(120\) | −4.57402 | −0.417549 | ||||||||
\(121\) | −10.7604 | −0.978222 | ||||||||
\(122\) | 10.5579 | 0.955871 | ||||||||
\(123\) | 7.62393 | 0.687427 | ||||||||
\(124\) | 33.9549 | 3.04924 | ||||||||
\(125\) | −3.95752 | −0.353971 | ||||||||
\(126\) | −2.45632 | −0.218826 | ||||||||
\(127\) | −9.34859 | −0.829553 | −0.414777 | − | 0.909923i | \(-0.636140\pi\) | ||||
−0.414777 | + | 0.909923i | \(0.636140\pi\) | |||||||
\(128\) | −7.37582 | −0.651937 | ||||||||
\(129\) | 9.69004 | 0.853161 | ||||||||
\(130\) | 6.86664 | 0.602245 | ||||||||
\(131\) | 7.23135 | 0.631806 | 0.315903 | − | 0.948792i | \(-0.397693\pi\) | ||||
0.315903 | + | 0.948792i | \(0.397693\pi\) | |||||||
\(132\) | −3.51384 | −0.305841 | ||||||||
\(133\) | 0.818199 | 0.0709468 | ||||||||
\(134\) | 12.8964 | 1.11408 | ||||||||
\(135\) | −2.27447 | −0.195756 | ||||||||
\(136\) | 12.8263 | 1.09985 | ||||||||
\(137\) | 9.31540 | 0.795868 | 0.397934 | − | 0.917414i | \(-0.369727\pi\) | ||||
0.397934 | + | 0.917414i | \(0.369727\pi\) | |||||||
\(138\) | −19.8693 | −1.69139 | ||||||||
\(139\) | −11.4421 | −0.970507 | −0.485254 | − | 0.874373i | \(-0.661273\pi\) | ||||
−0.485254 | + | 0.874373i | \(0.661273\pi\) | |||||||
\(140\) | −2.00684 | −0.169609 | ||||||||
\(141\) | −5.66865 | −0.477386 | ||||||||
\(142\) | −43.0875 | −3.61583 | ||||||||
\(143\) | 3.16035 | 0.264282 | ||||||||
\(144\) | −10.1380 | −0.844837 | ||||||||
\(145\) | −3.44848 | −0.286381 | ||||||||
\(146\) | 19.3633 | 1.60252 | ||||||||
\(147\) | 1.43905 | 0.118691 | ||||||||
\(148\) | 29.4526 | 2.42099 | ||||||||
\(149\) | 3.06584 | 0.251163 | 0.125582 | − | 0.992083i | \(-0.459920\pi\) | ||||
0.125582 | + | 0.992083i | \(0.459920\pi\) | |||||||
\(150\) | 18.4061 | 1.50285 | ||||||||
\(151\) | 8.05295 | 0.655340 | 0.327670 | − | 0.944792i | \(-0.393737\pi\) | ||||
0.327670 | + | 0.944792i | \(0.393737\pi\) | |||||||
\(152\) | 6.46506 | 0.524386 | ||||||||
\(153\) | 1.50823 | 0.121933 | ||||||||
\(154\) | −1.29392 | −0.104267 | ||||||||
\(155\) | 2.73783 | 0.219908 | ||||||||
\(156\) | −46.3566 | −3.71150 | ||||||||
\(157\) | 4.35562 | 0.347616 | 0.173808 | − | 0.984780i | \(-0.444393\pi\) | ||||
0.173808 | + | 0.984780i | \(0.444393\pi\) | |||||||
\(158\) | 19.8230 | 1.57703 | ||||||||
\(159\) | 17.4393 | 1.38302 | ||||||||
\(160\) | −5.24643 | −0.414767 | ||||||||
\(161\) | −5.22279 | −0.411614 | ||||||||
\(162\) | 14.1417 | 1.11107 | ||||||||
\(163\) | 13.9624 | 1.09362 | 0.546810 | − | 0.837257i | \(-0.315842\pi\) | ||||
0.546810 | + | 0.837257i | \(0.315842\pi\) | |||||||
\(164\) | 26.4306 | 2.06389 | ||||||||
\(165\) | −0.283326 | −0.0220569 | ||||||||
\(166\) | 29.6357 | 2.30018 | ||||||||
\(167\) | 10.3733 | 0.802711 | 0.401356 | − | 0.915922i | \(-0.368539\pi\) | ||||
0.401356 | + | 0.915922i | \(0.368539\pi\) | |||||||
\(168\) | 11.3708 | 0.877273 | ||||||||
\(169\) | 28.6932 | 2.20717 | ||||||||
\(170\) | 1.72624 | 0.132396 | ||||||||
\(171\) | 0.760220 | 0.0581355 | ||||||||
\(172\) | 33.5934 | 2.56147 | ||||||||
\(173\) | 18.9115 | 1.43782 | 0.718909 | − | 0.695105i | \(-0.244642\pi\) | ||||
0.718909 | + | 0.695105i | \(0.244642\pi\) | |||||||
\(174\) | 32.6136 | 2.47243 | ||||||||
\(175\) | 4.83819 | 0.365732 | ||||||||
\(176\) | −5.34044 | −0.402550 | ||||||||
\(177\) | −17.5801 | −1.32140 | ||||||||
\(178\) | 15.3249 | 1.14865 | ||||||||
\(179\) | −18.2820 | −1.36646 | −0.683230 | − | 0.730204i | \(-0.739425\pi\) | ||||
−0.683230 | + | 0.730204i | \(0.739425\pi\) | |||||||
\(180\) | −1.86463 | −0.138981 | ||||||||
\(181\) | 1.04329 | 0.0775472 | 0.0387736 | − | 0.999248i | \(-0.487655\pi\) | ||||
0.0387736 | + | 0.999248i | \(0.487655\pi\) | |||||||
\(182\) | −17.0701 | −1.26532 | ||||||||
\(183\) | −5.74712 | −0.424840 | ||||||||
\(184\) | −41.2683 | −3.04234 | ||||||||
\(185\) | 2.37480 | 0.174599 | ||||||||
\(186\) | −25.8928 | −1.89855 | ||||||||
\(187\) | 0.794495 | 0.0580992 | ||||||||
\(188\) | −19.6521 | −1.43327 | ||||||||
\(189\) | 5.65422 | 0.411284 | ||||||||
\(190\) | 0.870104 | 0.0631240 | ||||||||
\(191\) | 3.99309 | 0.288929 | 0.144465 | − | 0.989510i | \(-0.453854\pi\) | ||||
0.144465 | + | 0.989510i | \(0.453854\pi\) | |||||||
\(192\) | 18.2140 | 1.31448 | ||||||||
\(193\) | −7.43970 | −0.535522 | −0.267761 | − | 0.963485i | \(-0.586284\pi\) | ||||
−0.267761 | + | 0.963485i | \(0.586284\pi\) | |||||||
\(194\) | −8.76256 | −0.629115 | ||||||||
\(195\) | −3.73780 | −0.267669 | ||||||||
\(196\) | 4.98889 | 0.356349 | ||||||||
\(197\) | 24.0770 | 1.71541 | 0.857706 | − | 0.514140i | \(-0.171889\pi\) | ||||
0.857706 | + | 0.514140i | \(0.171889\pi\) | |||||||
\(198\) | −1.20223 | −0.0854386 | ||||||||
\(199\) | 24.1690 | 1.71330 | 0.856649 | − | 0.515900i | \(-0.172542\pi\) | ||||
0.856649 | + | 0.515900i | \(0.172542\pi\) | |||||||
\(200\) | 38.2293 | 2.70322 | ||||||||
\(201\) | −7.02006 | −0.495157 | ||||||||
\(202\) | −4.89496 | −0.344408 | ||||||||
\(203\) | 8.57274 | 0.601688 | ||||||||
\(204\) | −11.6538 | −0.815930 | ||||||||
\(205\) | 2.13114 | 0.148845 | ||||||||
\(206\) | −18.1231 | −1.26269 | ||||||||
\(207\) | −4.85270 | −0.337286 | ||||||||
\(208\) | −70.4541 | −4.88512 | ||||||||
\(209\) | 0.400462 | 0.0277005 | ||||||||
\(210\) | 1.53034 | 0.105603 | ||||||||
\(211\) | 18.9433 | 1.30411 | 0.652054 | − | 0.758172i | \(-0.273907\pi\) | ||||
0.652054 | + | 0.758172i | \(0.273907\pi\) | |||||||
\(212\) | 60.4584 | 4.15230 | ||||||||
\(213\) | 23.4543 | 1.60706 | ||||||||
\(214\) | −12.0451 | −0.823387 | ||||||||
\(215\) | 2.70868 | 0.184731 | ||||||||
\(216\) | 44.6773 | 3.03990 | ||||||||
\(217\) | −6.80611 | −0.462029 | ||||||||
\(218\) | 20.4019 | 1.38179 | ||||||||
\(219\) | −10.5403 | −0.712246 | ||||||||
\(220\) | −0.982233 | −0.0662221 | ||||||||
\(221\) | 10.4814 | 0.705058 | ||||||||
\(222\) | −22.4595 | −1.50738 | ||||||||
\(223\) | −25.0809 | −1.67954 | −0.839771 | − | 0.542941i | \(-0.817311\pi\) | ||||
−0.839771 | + | 0.542941i | \(0.817311\pi\) | |||||||
\(224\) | 13.0423 | 0.871429 | ||||||||
\(225\) | 4.49534 | 0.299690 | ||||||||
\(226\) | −54.2703 | −3.61001 | ||||||||
\(227\) | −9.90530 | −0.657438 | −0.328719 | − | 0.944428i | \(-0.606617\pi\) | ||||
−0.328719 | + | 0.944428i | \(0.606617\pi\) | |||||||
\(228\) | −5.87406 | −0.389019 | ||||||||
\(229\) | 19.3330 | 1.27756 | 0.638780 | − | 0.769390i | \(-0.279439\pi\) | ||||
0.638780 | + | 0.769390i | \(0.279439\pi\) | |||||||
\(230\) | −5.55412 | −0.366228 | ||||||||
\(231\) | 0.704333 | 0.0463417 | ||||||||
\(232\) | 67.7382 | 4.44723 | ||||||||
\(233\) | 22.8913 | 1.49966 | 0.749829 | − | 0.661631i | \(-0.230136\pi\) | ||||
0.749829 | + | 0.661631i | \(0.230136\pi\) | |||||||
\(234\) | −15.8605 | −1.03683 | ||||||||
\(235\) | −1.58457 | −0.103366 | ||||||||
\(236\) | −60.9465 | −3.96728 | ||||||||
\(237\) | −10.7905 | −0.700917 | ||||||||
\(238\) | −4.29134 | −0.278166 | ||||||||
\(239\) | −0.392340 | −0.0253784 | −0.0126892 | − | 0.999919i | \(-0.504039\pi\) | ||||
−0.0126892 | + | 0.999919i | \(0.504039\pi\) | |||||||
\(240\) | 6.31623 | 0.407711 | ||||||||
\(241\) | −14.5810 | −0.939244 | −0.469622 | − | 0.882868i | \(-0.655610\pi\) | ||||
−0.469622 | + | 0.882868i | \(0.655610\pi\) | |||||||
\(242\) | 28.4469 | 1.82863 | ||||||||
\(243\) | 9.26478 | 0.594336 | ||||||||
\(244\) | −19.9241 | −1.27551 | ||||||||
\(245\) | 0.402261 | 0.0256995 | ||||||||
\(246\) | −20.1550 | −1.28504 | ||||||||
\(247\) | 5.28313 | 0.336158 | ||||||||
\(248\) | −53.7790 | −3.41497 | ||||||||
\(249\) | −16.1319 | −1.02232 | ||||||||
\(250\) | 10.4623 | 0.661694 | ||||||||
\(251\) | −0.400107 | −0.0252545 | −0.0126273 | − | 0.999920i | \(-0.504019\pi\) | ||||
−0.0126273 | + | 0.999920i | \(0.504019\pi\) | |||||||
\(252\) | 4.63537 | 0.292001 | ||||||||
\(253\) | −2.55626 | −0.160711 | ||||||||
\(254\) | 24.7144 | 1.55072 | ||||||||
\(255\) | −0.939663 | −0.0588440 | ||||||||
\(256\) | −5.81478 | −0.363424 | ||||||||
\(257\) | 14.4821 | 0.903370 | 0.451685 | − | 0.892177i | \(-0.350823\pi\) | ||||
0.451685 | + | 0.892177i | \(0.350823\pi\) | |||||||
\(258\) | −25.6171 | −1.59485 | ||||||||
\(259\) | −5.90364 | −0.366834 | ||||||||
\(260\) | −12.9582 | −0.803633 | ||||||||
\(261\) | 7.96526 | 0.493037 | ||||||||
\(262\) | −19.1172 | −1.18106 | ||||||||
\(263\) | −5.62754 | −0.347009 | −0.173505 | − | 0.984833i | \(-0.555509\pi\) | ||||
−0.173505 | + | 0.984833i | \(0.555509\pi\) | |||||||
\(264\) | 5.56534 | 0.342523 | ||||||||
\(265\) | 4.87484 | 0.299459 | ||||||||
\(266\) | −2.16303 | −0.132624 | ||||||||
\(267\) | −8.34200 | −0.510522 | ||||||||
\(268\) | −24.3371 | −1.48663 | ||||||||
\(269\) | −0.321185 | −0.0195830 | −0.00979149 | − | 0.999952i | \(-0.503117\pi\) | ||||
−0.00979149 | + | 0.999952i | \(0.503117\pi\) | |||||||
\(270\) | 6.01291 | 0.365934 | ||||||||
\(271\) | −7.84217 | −0.476378 | −0.238189 | − | 0.971219i | \(-0.576554\pi\) | ||||
−0.238189 | + | 0.971219i | \(0.576554\pi\) | |||||||
\(272\) | −17.7118 | −1.07394 | ||||||||
\(273\) | 9.29197 | 0.562376 | ||||||||
\(274\) | −24.6267 | −1.48775 | ||||||||
\(275\) | 2.36802 | 0.142797 | ||||||||
\(276\) | 37.4958 | 2.25698 | ||||||||
\(277\) | 10.2938 | 0.618493 | 0.309246 | − | 0.950982i | \(-0.399923\pi\) | ||||
0.309246 | + | 0.950982i | \(0.399923\pi\) | |||||||
\(278\) | 30.2489 | 1.81421 | ||||||||
\(279\) | −6.32381 | −0.378597 | ||||||||
\(280\) | 3.17850 | 0.189952 | ||||||||
\(281\) | 27.3135 | 1.62938 | 0.814692 | − | 0.579893i | \(-0.196906\pi\) | ||||
0.814692 | + | 0.579893i | \(0.196906\pi\) | |||||||
\(282\) | 14.9859 | 0.892399 | ||||||||
\(283\) | 28.2761 | 1.68084 | 0.840421 | − | 0.541934i | \(-0.182308\pi\) | ||||
0.840421 | + | 0.541934i | \(0.182308\pi\) | |||||||
\(284\) | 81.3114 | 4.82495 | ||||||||
\(285\) | −0.473634 | −0.0280556 | ||||||||
\(286\) | −8.35486 | −0.494033 | ||||||||
\(287\) | −5.29790 | −0.312725 | ||||||||
\(288\) | 12.1181 | 0.714068 | ||||||||
\(289\) | −14.3650 | −0.845001 | ||||||||
\(290\) | 9.11657 | 0.535344 | ||||||||
\(291\) | 4.76983 | 0.279612 | ||||||||
\(292\) | −36.5410 | −2.13840 | ||||||||
\(293\) | 2.97080 | 0.173556 | 0.0867779 | − | 0.996228i | \(-0.472343\pi\) | ||||
0.0867779 | + | 0.996228i | \(0.472343\pi\) | |||||||
\(294\) | −3.80434 | −0.221874 | ||||||||
\(295\) | −4.91420 | −0.286116 | ||||||||
\(296\) | −46.6480 | −2.71136 | ||||||||
\(297\) | 2.76742 | 0.160582 | ||||||||
\(298\) | −8.10500 | −0.469510 | ||||||||
\(299\) | −33.7237 | −1.95029 | ||||||||
\(300\) | −34.7346 | −2.00540 | ||||||||
\(301\) | −6.73364 | −0.388121 | ||||||||
\(302\) | −21.2892 | −1.22506 | ||||||||
\(303\) | 2.66453 | 0.153073 | ||||||||
\(304\) | −8.92756 | −0.512031 | ||||||||
\(305\) | −1.60651 | −0.0919884 | ||||||||
\(306\) | −3.98724 | −0.227936 | ||||||||
\(307\) | 3.26723 | 0.186470 | 0.0932352 | − | 0.995644i | \(-0.470279\pi\) | ||||
0.0932352 | + | 0.995644i | \(0.470279\pi\) | |||||||
\(308\) | 2.44178 | 0.139133 | ||||||||
\(309\) | 9.86515 | 0.561209 | ||||||||
\(310\) | −7.23787 | −0.411084 | ||||||||
\(311\) | −14.0354 | −0.795873 | −0.397937 | − | 0.917413i | \(-0.630274\pi\) | ||||
−0.397937 | + | 0.917413i | \(0.630274\pi\) | |||||||
\(312\) | 73.4213 | 4.15666 | ||||||||
\(313\) | −10.9185 | −0.617149 | −0.308575 | − | 0.951200i | \(-0.599852\pi\) | ||||
−0.308575 | + | 0.951200i | \(0.599852\pi\) | |||||||
\(314\) | −11.5147 | −0.649814 | ||||||||
\(315\) | 0.373756 | 0.0210588 | ||||||||
\(316\) | −37.4084 | −2.10439 | ||||||||
\(317\) | 23.0589 | 1.29512 | 0.647558 | − | 0.762016i | \(-0.275790\pi\) | ||||
0.647558 | + | 0.762016i | \(0.275790\pi\) | |||||||
\(318\) | −46.1033 | −2.58535 | ||||||||
\(319\) | 4.19587 | 0.234924 | ||||||||
\(320\) | 5.09139 | 0.284618 | ||||||||
\(321\) | 6.55665 | 0.365957 | ||||||||
\(322\) | 13.8072 | 0.769448 | ||||||||
\(323\) | 1.32815 | 0.0739003 | ||||||||
\(324\) | −26.6870 | −1.48261 | ||||||||
\(325\) | 31.2403 | 1.73290 | ||||||||
\(326\) | −36.9117 | −2.04435 | ||||||||
\(327\) | −11.1056 | −0.614142 | ||||||||
\(328\) | −41.8618 | −2.31143 | ||||||||
\(329\) | 3.93916 | 0.217173 | ||||||||
\(330\) | 0.749014 | 0.0412319 | ||||||||
\(331\) | 6.91231 | 0.379935 | 0.189968 | − | 0.981790i | \(-0.439162\pi\) | ||||
0.189968 | + | 0.981790i | \(0.439162\pi\) | |||||||
\(332\) | −55.9262 | −3.06935 | ||||||||
\(333\) | −5.48529 | −0.300592 | ||||||||
\(334\) | −27.4234 | −1.50054 | ||||||||
\(335\) | −1.96233 | −0.107214 | ||||||||
\(336\) | −15.7018 | −0.856604 | ||||||||
\(337\) | 1.49739 | 0.0815678 | 0.0407839 | − | 0.999168i | \(-0.487014\pi\) | ||||
0.0407839 | + | 0.999168i | \(0.487014\pi\) | |||||||
\(338\) | −75.8547 | −4.12595 | ||||||||
\(339\) | 29.5416 | 1.60448 | ||||||||
\(340\) | −3.25762 | −0.176669 | ||||||||
\(341\) | −3.33120 | −0.180395 | ||||||||
\(342\) | −2.00976 | −0.108675 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −53.2064 | −2.86870 | ||||||||
\(345\) | 3.02334 | 0.162771 | ||||||||
\(346\) | −49.9955 | −2.68777 | ||||||||
\(347\) | 25.5669 | 1.37250 | 0.686251 | − | 0.727365i | \(-0.259255\pi\) | ||||
0.686251 | + | 0.727365i | \(0.259255\pi\) | |||||||
\(348\) | −61.5459 | −3.29921 | ||||||||
\(349\) | 11.8755 | 0.635683 | 0.317841 | − | 0.948144i | \(-0.397042\pi\) | ||||
0.317841 | + | 0.948144i | \(0.397042\pi\) | |||||||
\(350\) | −12.7905 | −0.683680 | ||||||||
\(351\) | 36.5094 | 1.94873 | ||||||||
\(352\) | 6.38349 | 0.340241 | ||||||||
\(353\) | 25.7095 | 1.36838 | 0.684190 | − | 0.729304i | \(-0.260156\pi\) | ||||
0.684190 | + | 0.729304i | \(0.260156\pi\) | |||||||
\(354\) | 46.4756 | 2.47015 | ||||||||
\(355\) | 6.55625 | 0.347970 | ||||||||
\(356\) | −28.9200 | −1.53276 | ||||||||
\(357\) | 2.33595 | 0.123632 | ||||||||
\(358\) | 48.3312 | 2.55438 | ||||||||
\(359\) | −18.5032 | −0.976563 | −0.488281 | − | 0.872686i | \(-0.662376\pi\) | ||||
−0.488281 | + | 0.872686i | \(0.662376\pi\) | |||||||
\(360\) | 2.95326 | 0.155651 | ||||||||
\(361\) | −18.3306 | −0.964766 | ||||||||
\(362\) | −2.75810 | −0.144962 | ||||||||
\(363\) | −15.4848 | −0.812742 | ||||||||
\(364\) | 32.2134 | 1.68844 | ||||||||
\(365\) | −2.94635 | −0.154219 | ||||||||
\(366\) | 15.1934 | 0.794171 | ||||||||
\(367\) | −30.4209 | −1.58796 | −0.793979 | − | 0.607945i | \(-0.791994\pi\) | ||||
−0.793979 | + | 0.607945i | \(0.791994\pi\) | |||||||
\(368\) | 56.9872 | 2.97066 | ||||||||
\(369\) | −4.92248 | −0.256254 | ||||||||
\(370\) | −6.27815 | −0.326385 | ||||||||
\(371\) | −12.1186 | −0.629166 | ||||||||
\(372\) | 48.8628 | 2.53342 | ||||||||
\(373\) | −10.3536 | −0.536090 | −0.268045 | − | 0.963406i | \(-0.586378\pi\) | ||||
−0.268045 | + | 0.963406i | \(0.586378\pi\) | |||||||
\(374\) | −2.10037 | −0.108607 | ||||||||
\(375\) | −5.69506 | −0.294092 | ||||||||
\(376\) | 31.1256 | 1.60518 | ||||||||
\(377\) | 55.3544 | 2.85090 | ||||||||
\(378\) | −14.9478 | −0.768831 | ||||||||
\(379\) | 5.06788 | 0.260320 | 0.130160 | − | 0.991493i | \(-0.458451\pi\) | ||||
0.130160 | + | 0.991493i | \(0.458451\pi\) | |||||||
\(380\) | −1.64199 | −0.0842324 | ||||||||
\(381\) | −13.4531 | −0.689222 | ||||||||
\(382\) | −10.5563 | −0.540108 | ||||||||
\(383\) | −12.9676 | −0.662612 | −0.331306 | − | 0.943523i | \(-0.607489\pi\) | ||||
−0.331306 | + | 0.943523i | \(0.607489\pi\) | |||||||
\(384\) | −10.6142 | −0.541652 | ||||||||
\(385\) | 0.196884 | 0.0100341 | ||||||||
\(386\) | 19.6680 | 1.00107 | ||||||||
\(387\) | −6.25649 | −0.318035 | ||||||||
\(388\) | 16.5360 | 0.839489 | ||||||||
\(389\) | 19.8330 | 1.00557 | 0.502785 | − | 0.864411i | \(-0.332309\pi\) | ||||
0.502785 | + | 0.864411i | \(0.332309\pi\) | |||||||
\(390\) | 9.88144 | 0.500366 | ||||||||
\(391\) | −8.47796 | −0.428749 | ||||||||
\(392\) | −7.90158 | −0.399090 | ||||||||
\(393\) | 10.4063 | 0.524927 | ||||||||
\(394\) | −63.6511 | −3.20670 | ||||||||
\(395\) | −3.01629 | −0.151766 | ||||||||
\(396\) | 2.26875 | 0.114009 | ||||||||
\(397\) | 12.4932 | 0.627014 | 0.313507 | − | 0.949586i | \(-0.398496\pi\) | ||||
0.313507 | + | 0.949586i | \(0.398496\pi\) | |||||||
\(398\) | −63.8945 | −3.20274 | ||||||||
\(399\) | 1.17743 | 0.0589451 | ||||||||
\(400\) | −52.7906 | −2.63953 | ||||||||
\(401\) | 0.490251 | 0.0244820 | 0.0122410 | − | 0.999925i | \(-0.496103\pi\) | ||||
0.0122410 | + | 0.999925i | \(0.496103\pi\) | |||||||
\(402\) | 18.5586 | 0.925618 | ||||||||
\(403\) | −43.9472 | −2.18917 | ||||||||
\(404\) | 9.23738 | 0.459577 | ||||||||
\(405\) | −2.15181 | −0.106924 | ||||||||
\(406\) | −22.6633 | −1.12476 | ||||||||
\(407\) | −2.88950 | −0.143227 | ||||||||
\(408\) | 18.4577 | 0.913793 | ||||||||
\(409\) | 14.2486 | 0.704546 | 0.352273 | − | 0.935897i | \(-0.385409\pi\) | ||||
0.352273 | + | 0.935897i | \(0.385409\pi\) | |||||||
\(410\) | −5.63398 | −0.278243 | ||||||||
\(411\) | 13.4053 | 0.661236 | ||||||||
\(412\) | 34.2005 | 1.68494 | ||||||||
\(413\) | 12.2165 | 0.601132 | ||||||||
\(414\) | 12.8288 | 0.630503 | ||||||||
\(415\) | −4.50941 | −0.221358 | ||||||||
\(416\) | 84.2148 | 4.12897 | ||||||||
\(417\) | −16.4658 | −0.806332 | ||||||||
\(418\) | −1.05868 | −0.0517818 | ||||||||
\(419\) | −25.3305 | −1.23747 | −0.618737 | − | 0.785598i | \(-0.712355\pi\) | ||||
−0.618737 | + | 0.785598i | \(0.712355\pi\) | |||||||
\(420\) | −2.88794 | −0.140917 | ||||||||
\(421\) | −25.2412 | −1.23018 | −0.615091 | − | 0.788456i | \(-0.710881\pi\) | ||||
−0.615091 | + | 0.788456i | \(0.710881\pi\) | |||||||
\(422\) | −50.0794 | −2.43783 | ||||||||
\(423\) | 3.66003 | 0.177957 | ||||||||
\(424\) | −95.7561 | −4.65033 | ||||||||
\(425\) | 7.85364 | 0.380958 | ||||||||
\(426\) | −62.0051 | −3.00416 | ||||||||
\(427\) | 3.99370 | 0.193268 | ||||||||
\(428\) | 22.7306 | 1.09872 | ||||||||
\(429\) | 4.54790 | 0.219574 | ||||||||
\(430\) | −7.16081 | −0.345325 | ||||||||
\(431\) | 40.0857 | 1.93086 | 0.965431 | − | 0.260658i | \(-0.0839397\pi\) | ||||
0.965431 | + | 0.260658i | \(0.0839397\pi\) | |||||||
\(432\) | −61.6946 | −2.96828 | ||||||||
\(433\) | −31.6468 | −1.52085 | −0.760424 | − | 0.649427i | \(-0.775009\pi\) | ||||
−0.760424 | + | 0.649427i | \(0.775009\pi\) | |||||||
\(434\) | 17.9930 | 0.863690 | ||||||||
\(435\) | −4.96253 | −0.237935 | ||||||||
\(436\) | −38.5009 | −1.84386 | ||||||||
\(437\) | −4.27328 | −0.204419 | ||||||||
\(438\) | 27.8648 | 1.33143 | ||||||||
\(439\) | −13.7798 | −0.657673 | −0.328837 | − | 0.944387i | \(-0.606657\pi\) | ||||
−0.328837 | + | 0.944387i | \(0.606657\pi\) | |||||||
\(440\) | 1.55570 | 0.0741649 | ||||||||
\(441\) | −0.929138 | −0.0442447 | ||||||||
\(442\) | −27.7093 | −1.31800 | ||||||||
\(443\) | −13.8783 | −0.659380 | −0.329690 | − | 0.944089i | \(-0.606944\pi\) | ||||
−0.329690 | + | 0.944089i | \(0.606944\pi\) | |||||||
\(444\) | 42.3837 | 2.01144 | ||||||||
\(445\) | −2.33186 | −0.110541 | ||||||||
\(446\) | 66.3051 | 3.13964 | ||||||||
\(447\) | 4.41189 | 0.208675 | ||||||||
\(448\) | −12.6569 | −0.597984 | ||||||||
\(449\) | −3.23136 | −0.152497 | −0.0762486 | − | 0.997089i | \(-0.524294\pi\) | ||||
−0.0762486 | + | 0.997089i | \(0.524294\pi\) | |||||||
\(450\) | −11.8841 | −0.560223 | ||||||||
\(451\) | −2.59302 | −0.122101 | ||||||||
\(452\) | 102.415 | 4.81718 | ||||||||
\(453\) | 11.5886 | 0.544480 | ||||||||
\(454\) | 26.1862 | 1.22898 | ||||||||
\(455\) | 2.59741 | 0.121768 | ||||||||
\(456\) | 9.30354 | 0.435678 | ||||||||
\(457\) | −2.01677 | −0.0943404 | −0.0471702 | − | 0.998887i | \(-0.515020\pi\) | ||||
−0.0471702 | + | 0.998887i | \(0.515020\pi\) | |||||||
\(458\) | −51.1097 | −2.38820 | ||||||||
\(459\) | 9.17828 | 0.428405 | ||||||||
\(460\) | 10.4813 | 0.488693 | ||||||||
\(461\) | −31.7690 | −1.47963 | −0.739814 | − | 0.672811i | \(-0.765087\pi\) | ||||
−0.739814 | + | 0.672811i | \(0.765087\pi\) | |||||||
\(462\) | −1.86201 | −0.0866286 | ||||||||
\(463\) | 10.0070 | 0.465065 | 0.232533 | − | 0.972589i | \(-0.425299\pi\) | ||||
0.232533 | + | 0.972589i | \(0.425299\pi\) | |||||||
\(464\) | −93.5392 | −4.34245 | ||||||||
\(465\) | 3.93987 | 0.182707 | ||||||||
\(466\) | −60.5166 | −2.80338 | ||||||||
\(467\) | 11.1922 | 0.517915 | 0.258957 | − | 0.965889i | \(-0.416621\pi\) | ||||
0.258957 | + | 0.965889i | \(0.416621\pi\) | |||||||
\(468\) | 29.9307 | 1.38355 | ||||||||
\(469\) | 4.87826 | 0.225257 | ||||||||
\(470\) | 4.18906 | 0.193227 | ||||||||
\(471\) | 6.26795 | 0.288812 | ||||||||
\(472\) | 96.5293 | 4.44312 | ||||||||
\(473\) | −3.29574 | −0.151538 | ||||||||
\(474\) | 28.5262 | 1.31025 | ||||||||
\(475\) | 3.95860 | 0.181633 | ||||||||
\(476\) | 8.09827 | 0.371184 | ||||||||
\(477\) | −11.2599 | −0.515553 | ||||||||
\(478\) | 1.03721 | 0.0474409 | ||||||||
\(479\) | 24.3206 | 1.11124 | 0.555619 | − | 0.831437i | \(-0.312481\pi\) | ||||
0.555619 | + | 0.831437i | \(0.312481\pi\) | |||||||
\(480\) | −7.54987 | −0.344603 | ||||||||
\(481\) | −38.1199 | −1.73812 | ||||||||
\(482\) | 38.5470 | 1.75577 | ||||||||
\(483\) | −7.51586 | −0.341983 | ||||||||
\(484\) | −53.6827 | −2.44012 | ||||||||
\(485\) | 1.33332 | 0.0605431 | ||||||||
\(486\) | −24.4928 | −1.11102 | ||||||||
\(487\) | −20.4072 | −0.924737 | −0.462368 | − | 0.886688i | \(-0.653000\pi\) | ||||
−0.462368 | + | 0.886688i | \(0.653000\pi\) | |||||||
\(488\) | 31.5565 | 1.42850 | ||||||||
\(489\) | 20.0926 | 0.908619 | ||||||||
\(490\) | −1.06344 | −0.0480412 | ||||||||
\(491\) | 15.1666 | 0.684461 | 0.342230 | − | 0.939616i | \(-0.388818\pi\) | ||||
0.342230 | + | 0.939616i | \(0.388818\pi\) | |||||||
\(492\) | 38.0350 | 1.71475 | ||||||||
\(493\) | 13.9158 | 0.626736 | ||||||||
\(494\) | −13.9668 | −0.628394 | ||||||||
\(495\) | 0.182932 | 0.00822220 | ||||||||
\(496\) | 74.2631 | 3.33451 | ||||||||
\(497\) | −16.2985 | −0.731088 | ||||||||
\(498\) | 42.6472 | 1.91107 | ||||||||
\(499\) | −21.4156 | −0.958693 | −0.479346 | − | 0.877626i | \(-0.659126\pi\) | ||||
−0.479346 | + | 0.877626i | \(0.659126\pi\) | |||||||
\(500\) | −19.7436 | −0.882962 | ||||||||
\(501\) | 14.9277 | 0.666921 | ||||||||
\(502\) | 1.05774 | 0.0472093 | ||||||||
\(503\) | 3.32579 | 0.148290 | 0.0741448 | − | 0.997247i | \(-0.476377\pi\) | ||||
0.0741448 | + | 0.997247i | \(0.476377\pi\) | |||||||
\(504\) | −7.34166 | −0.327023 | ||||||||
\(505\) | 0.744823 | 0.0331442 | ||||||||
\(506\) | 6.75786 | 0.300424 | ||||||||
\(507\) | 41.2909 | 1.83379 | ||||||||
\(508\) | −46.6391 | −2.06927 | ||||||||
\(509\) | −23.4678 | −1.04019 | −0.520095 | − | 0.854108i | \(-0.674104\pi\) | ||||
−0.520095 | + | 0.854108i | \(0.674104\pi\) | |||||||
\(510\) | 2.48414 | 0.110000 | ||||||||
\(511\) | 7.32447 | 0.324016 | ||||||||
\(512\) | 30.1239 | 1.33130 | ||||||||
\(513\) | 4.62628 | 0.204255 | ||||||||
\(514\) | −38.2857 | −1.68871 | ||||||||
\(515\) | 2.75763 | 0.121516 | ||||||||
\(516\) | 48.3426 | 2.12816 | ||||||||
\(517\) | 1.92800 | 0.0847933 | ||||||||
\(518\) | 15.6071 | 0.685739 | ||||||||
\(519\) | 27.2146 | 1.19459 | ||||||||
\(520\) | 20.5236 | 0.900021 | ||||||||
\(521\) | 15.7483 | 0.689946 | 0.344973 | − | 0.938613i | \(-0.387888\pi\) | ||||
0.344973 | + | 0.938613i | \(0.387888\pi\) | |||||||
\(522\) | −21.0574 | −0.921656 | ||||||||
\(523\) | 1.01217 | 0.0442593 | 0.0221296 | − | 0.999755i | \(-0.492955\pi\) | ||||
0.0221296 | + | 0.999755i | \(0.492955\pi\) | |||||||
\(524\) | 36.0764 | 1.57600 | ||||||||
\(525\) | 6.96239 | 0.303863 | ||||||||
\(526\) | 14.8773 | 0.648679 | ||||||||
\(527\) | −11.0481 | −0.481262 | ||||||||
\(528\) | −7.68515 | −0.334453 | ||||||||
\(529\) | 4.27758 | 0.185982 | ||||||||
\(530\) | −12.8874 | −0.559792 | ||||||||
\(531\) | 11.3508 | 0.492581 | ||||||||
\(532\) | 4.08190 | 0.176973 | ||||||||
\(533\) | −34.2087 | −1.48174 | ||||||||
\(534\) | 22.0533 | 0.954341 | ||||||||
\(535\) | 1.83280 | 0.0792388 | ||||||||
\(536\) | 38.5460 | 1.66493 | ||||||||
\(537\) | −26.3087 | −1.13530 | ||||||||
\(538\) | 0.849101 | 0.0366073 | ||||||||
\(539\) | −0.489443 | −0.0210818 | ||||||||
\(540\) | −11.3471 | −0.488301 | ||||||||
\(541\) | 37.6945 | 1.62061 | 0.810307 | − | 0.586005i | \(-0.199300\pi\) | ||||
0.810307 | + | 0.586005i | \(0.199300\pi\) | |||||||
\(542\) | 20.7320 | 0.890514 | ||||||||
\(543\) | 1.50135 | 0.0644289 | ||||||||
\(544\) | 21.1711 | 0.907705 | ||||||||
\(545\) | −3.10438 | −0.132977 | ||||||||
\(546\) | −24.5647 | −1.05127 | ||||||||
\(547\) | 10.0185 | 0.428361 | 0.214180 | − | 0.976794i | \(-0.431292\pi\) | ||||
0.214180 | + | 0.976794i | \(0.431292\pi\) | |||||||
\(548\) | 46.4735 | 1.98525 | ||||||||
\(549\) | 3.71069 | 0.158369 | ||||||||
\(550\) | −6.26021 | −0.266936 | ||||||||
\(551\) | 7.01420 | 0.298815 | ||||||||
\(552\) | −59.3871 | −2.52768 | ||||||||
\(553\) | 7.49834 | 0.318862 | ||||||||
\(554\) | −27.2131 | −1.15618 | ||||||||
\(555\) | 3.41746 | 0.145063 | ||||||||
\(556\) | −57.0834 | −2.42088 | ||||||||
\(557\) | 40.4574 | 1.71424 | 0.857119 | − | 0.515119i | \(-0.172252\pi\) | ||||
0.857119 | + | 0.515119i | \(0.172252\pi\) | |||||||
\(558\) | 16.7180 | 0.707727 | ||||||||
\(559\) | −43.4793 | −1.83898 | ||||||||
\(560\) | −4.38917 | −0.185476 | ||||||||
\(561\) | 1.14332 | 0.0482709 | ||||||||
\(562\) | −72.2073 | −3.04588 | ||||||||
\(563\) | 34.6290 | 1.45944 | 0.729719 | − | 0.683747i | \(-0.239651\pi\) | ||||
0.729719 | + | 0.683747i | \(0.239651\pi\) | |||||||
\(564\) | −28.2803 | −1.19081 | ||||||||
\(565\) | 8.25783 | 0.347410 | ||||||||
\(566\) | −74.7523 | −3.14207 | ||||||||
\(567\) | 5.34929 | 0.224649 | ||||||||
\(568\) | −128.784 | −5.40365 | ||||||||
\(569\) | 7.58582 | 0.318014 | 0.159007 | − | 0.987277i | \(-0.449171\pi\) | ||||
0.159007 | + | 0.987277i | \(0.449171\pi\) | |||||||
\(570\) | 1.25212 | 0.0524456 | ||||||||
\(571\) | −23.7976 | −0.995900 | −0.497950 | − | 0.867206i | \(-0.665914\pi\) | ||||
−0.497950 | + | 0.867206i | \(0.665914\pi\) | |||||||
\(572\) | 15.7666 | 0.659236 | ||||||||
\(573\) | 5.74624 | 0.240053 | ||||||||
\(574\) | 14.0058 | 0.584590 | ||||||||
\(575\) | −25.2688 | −1.05378 | ||||||||
\(576\) | −11.7600 | −0.490002 | ||||||||
\(577\) | −3.93178 | −0.163682 | −0.0818411 | − | 0.996645i | \(-0.526080\pi\) | ||||
−0.0818411 | + | 0.996645i | \(0.526080\pi\) | |||||||
\(578\) | 37.9761 | 1.57960 | ||||||||
\(579\) | −10.7061 | −0.444930 | ||||||||
\(580\) | −17.2041 | −0.714361 | ||||||||
\(581\) | 11.2101 | 0.465075 | ||||||||
\(582\) | −12.6098 | −0.522691 | ||||||||
\(583\) | −5.93137 | −0.245652 | ||||||||
\(584\) | 57.8749 | 2.39488 | ||||||||
\(585\) | 2.41335 | 0.0997798 | ||||||||
\(586\) | −7.85375 | −0.324436 | ||||||||
\(587\) | −13.0092 | −0.536949 | −0.268474 | − | 0.963287i | \(-0.586519\pi\) | ||||
−0.268474 | + | 0.963287i | \(0.586519\pi\) | |||||||
\(588\) | 7.17926 | 0.296068 | ||||||||
\(589\) | −5.56875 | −0.229456 | ||||||||
\(590\) | 12.9914 | 0.534849 | ||||||||
\(591\) | 34.6479 | 1.42523 | ||||||||
\(592\) | 64.4160 | 2.64748 | ||||||||
\(593\) | −4.58168 | −0.188147 | −0.0940735 | − | 0.995565i | \(-0.529989\pi\) | ||||
−0.0940735 | + | 0.995565i | \(0.529989\pi\) | |||||||
\(594\) | −7.31610 | −0.300183 | ||||||||
\(595\) | 0.652975 | 0.0267694 | ||||||||
\(596\) | 15.2951 | 0.626512 | ||||||||
\(597\) | 34.7804 | 1.42347 | ||||||||
\(598\) | 89.1537 | 3.64577 | ||||||||
\(599\) | −37.8001 | −1.54447 | −0.772235 | − | 0.635337i | \(-0.780861\pi\) | ||||
−0.772235 | + | 0.635337i | \(0.780861\pi\) | |||||||
\(600\) | 55.0139 | 2.24593 | ||||||||
\(601\) | −1.26908 | −0.0517668 | −0.0258834 | − | 0.999665i | \(-0.508240\pi\) | ||||
−0.0258834 | + | 0.999665i | \(0.508240\pi\) | |||||||
\(602\) | 17.8014 | 0.725531 | ||||||||
\(603\) | 4.53258 | 0.184581 | ||||||||
\(604\) | 40.1753 | 1.63471 | ||||||||
\(605\) | −4.32851 | −0.175979 | ||||||||
\(606\) | −7.04409 | −0.286146 | ||||||||
\(607\) | −39.3144 | −1.59572 | −0.797861 | − | 0.602841i | \(-0.794035\pi\) | ||||
−0.797861 | + | 0.602841i | \(0.794035\pi\) | |||||||
\(608\) | 10.6712 | 0.432776 | ||||||||
\(609\) | 12.3366 | 0.499904 | ||||||||
\(610\) | 4.24705 | 0.171958 | ||||||||
\(611\) | 25.4353 | 1.02900 | ||||||||
\(612\) | 7.52441 | 0.304156 | ||||||||
\(613\) | 14.3223 | 0.578472 | 0.289236 | − | 0.957258i | \(-0.406599\pi\) | ||||
0.289236 | + | 0.957258i | \(0.406599\pi\) | |||||||
\(614\) | −8.63741 | −0.348577 | ||||||||
\(615\) | 3.06681 | 0.123666 | ||||||||
\(616\) | −3.86738 | −0.155821 | ||||||||
\(617\) | 11.0111 | 0.443290 | 0.221645 | − | 0.975127i | \(-0.428857\pi\) | ||||
0.221645 | + | 0.975127i | \(0.428857\pi\) | |||||||
\(618\) | −26.0800 | −1.04909 | ||||||||
\(619\) | 30.1483 | 1.21176 | 0.605881 | − | 0.795555i | \(-0.292821\pi\) | ||||
0.605881 | + | 0.795555i | \(0.292821\pi\) | |||||||
\(620\) | 13.6587 | 0.548548 | ||||||||
\(621\) | −29.5308 | −1.18503 | ||||||||
\(622\) | 37.1046 | 1.48776 | ||||||||
\(623\) | 5.79688 | 0.232247 | ||||||||
\(624\) | −101.387 | −4.05873 | ||||||||
\(625\) | 22.5990 | 0.903959 | ||||||||
\(626\) | 28.8647 | 1.15366 | ||||||||
\(627\) | 0.576284 | 0.0230146 | ||||||||
\(628\) | 21.7297 | 0.867110 | ||||||||
\(629\) | −9.58314 | −0.382105 | ||||||||
\(630\) | −0.988081 | −0.0393661 | ||||||||
\(631\) | 21.4260 | 0.852956 | 0.426478 | − | 0.904498i | \(-0.359754\pi\) | ||||
0.426478 | + | 0.904498i | \(0.359754\pi\) | |||||||
\(632\) | 59.2487 | 2.35679 | ||||||||
\(633\) | 27.2603 | 1.08350 | ||||||||
\(634\) | −60.9596 | −2.42102 | ||||||||
\(635\) | −3.76057 | −0.149234 | ||||||||
\(636\) | 87.0026 | 3.44988 | ||||||||
\(637\) | −6.45702 | −0.255837 | ||||||||
\(638\) | −11.0924 | −0.439153 | ||||||||
\(639\) | −15.1436 | −0.599070 | ||||||||
\(640\) | −2.96701 | −0.117281 | ||||||||
\(641\) | 31.9478 | 1.26186 | 0.630931 | − | 0.775839i | \(-0.282673\pi\) | ||||
0.630931 | + | 0.775839i | \(0.282673\pi\) | |||||||
\(642\) | −17.3335 | −0.684099 | ||||||||
\(643\) | 30.7100 | 1.21108 | 0.605542 | − | 0.795813i | \(-0.292956\pi\) | ||||
0.605542 | + | 0.795813i | \(0.292956\pi\) | |||||||
\(644\) | −26.0559 | −1.02675 | ||||||||
\(645\) | 3.89793 | 0.153481 | ||||||||
\(646\) | −3.51117 | −0.138145 | ||||||||
\(647\) | 36.0700 | 1.41806 | 0.709028 | − | 0.705180i | \(-0.249134\pi\) | ||||
0.709028 | + | 0.705180i | \(0.249134\pi\) | |||||||
\(648\) | 42.2678 | 1.66044 | ||||||||
\(649\) | 5.97926 | 0.234707 | ||||||||
\(650\) | −82.5884 | −3.23938 | ||||||||
\(651\) | −9.79432 | −0.383870 | ||||||||
\(652\) | 69.6569 | 2.72798 | ||||||||
\(653\) | −42.4334 | −1.66055 | −0.830273 | − | 0.557356i | \(-0.811816\pi\) | ||||
−0.830273 | + | 0.557356i | \(0.811816\pi\) | |||||||
\(654\) | 29.3594 | 1.14804 | ||||||||
\(655\) | 2.90889 | 0.113660 | ||||||||
\(656\) | 57.8066 | 2.25697 | ||||||||
\(657\) | 6.80545 | 0.265506 | ||||||||
\(658\) | −10.4138 | −0.405971 | ||||||||
\(659\) | 4.39124 | 0.171058 | 0.0855292 | − | 0.996336i | \(-0.472742\pi\) | ||||
0.0855292 | + | 0.996336i | \(0.472742\pi\) | |||||||
\(660\) | −1.41348 | −0.0550197 | ||||||||
\(661\) | 28.0159 | 1.08969 | 0.544847 | − | 0.838536i | \(-0.316588\pi\) | ||||
0.544847 | + | 0.838536i | \(0.316588\pi\) | |||||||
\(662\) | −18.2737 | −0.710229 | ||||||||
\(663\) | 15.0833 | 0.585787 | ||||||||
\(664\) | 88.5779 | 3.43749 | ||||||||
\(665\) | 0.329130 | 0.0127631 | ||||||||
\(666\) | 14.5012 | 0.561910 | ||||||||
\(667\) | −44.7736 | −1.73364 | ||||||||
\(668\) | 51.7513 | 2.00232 | ||||||||
\(669\) | −36.0926 | −1.39542 | ||||||||
\(670\) | 5.18773 | 0.200419 | ||||||||
\(671\) | 1.95469 | 0.0754599 | ||||||||
\(672\) | 18.7686 | 0.724014 | ||||||||
\(673\) | −24.5371 | −0.945834 | −0.472917 | − | 0.881107i | \(-0.656799\pi\) | ||||
−0.472917 | + | 0.881107i | \(0.656799\pi\) | |||||||
\(674\) | −3.95856 | −0.152478 | ||||||||
\(675\) | 27.3562 | 1.05294 | ||||||||
\(676\) | 143.147 | 5.50565 | ||||||||
\(677\) | 11.6750 | 0.448708 | 0.224354 | − | 0.974508i | \(-0.427973\pi\) | ||||
0.224354 | + | 0.974508i | \(0.427973\pi\) | |||||||
\(678\) | −78.0976 | −2.99932 | ||||||||
\(679\) | −3.31457 | −0.127202 | ||||||||
\(680\) | 5.15953 | 0.197859 | ||||||||
\(681\) | −14.2542 | −0.546223 | ||||||||
\(682\) | 8.80654 | 0.337220 | ||||||||
\(683\) | 27.8733 | 1.06654 | 0.533271 | − | 0.845944i | \(-0.320963\pi\) | ||||
0.533271 | + | 0.845944i | \(0.320963\pi\) | |||||||
\(684\) | 3.79265 | 0.145016 | ||||||||
\(685\) | 3.74722 | 0.143174 | ||||||||
\(686\) | 2.64365 | 0.100935 | ||||||||
\(687\) | 27.8211 | 1.06144 | ||||||||
\(688\) | 73.4724 | 2.80111 | ||||||||
\(689\) | −78.2501 | −2.98109 | ||||||||
\(690\) | −7.99265 | −0.304275 | ||||||||
\(691\) | 2.46494 | 0.0937708 | 0.0468854 | − | 0.998900i | \(-0.485070\pi\) | ||||
0.0468854 | + | 0.998900i | \(0.485070\pi\) | |||||||
\(692\) | 94.3476 | 3.58656 | ||||||||
\(693\) | −0.454761 | −0.0172749 | ||||||||
\(694\) | −67.5899 | −2.56568 | ||||||||
\(695\) | −4.60272 | −0.174591 | ||||||||
\(696\) | 97.4786 | 3.69492 | ||||||||
\(697\) | −8.59987 | −0.325743 | ||||||||
\(698\) | −31.3948 | −1.18831 | ||||||||
\(699\) | 32.9417 | 1.24597 | ||||||||
\(700\) | 24.1372 | 0.912300 | ||||||||
\(701\) | −6.53593 | −0.246859 | −0.123429 | − | 0.992353i | \(-0.539389\pi\) | ||||
−0.123429 | + | 0.992353i | \(0.539389\pi\) | |||||||
\(702\) | −96.5182 | −3.64285 | ||||||||
\(703\) | −4.83035 | −0.182180 | ||||||||
\(704\) | −6.19485 | −0.233477 | ||||||||
\(705\) | −2.28028 | −0.0858802 | ||||||||
\(706\) | −67.9670 | −2.55797 | ||||||||
\(707\) | −1.85159 | −0.0696362 | ||||||||
\(708\) | −87.7050 | −3.29616 | ||||||||
\(709\) | −27.7948 | −1.04386 | −0.521928 | − | 0.852989i | \(-0.674787\pi\) | ||||
−0.521928 | + | 0.852989i | \(0.674787\pi\) | |||||||
\(710\) | −17.3324 | −0.650475 | ||||||||
\(711\) | 6.96699 | 0.261283 | ||||||||
\(712\) | 45.8045 | 1.71660 | ||||||||
\(713\) | 35.5469 | 1.33124 | ||||||||
\(714\) | −6.17544 | −0.231110 | ||||||||
\(715\) | 1.27129 | 0.0475434 | ||||||||
\(716\) | −91.2068 | −3.40856 | ||||||||
\(717\) | −0.564597 | −0.0210853 | ||||||||
\(718\) | 48.9161 | 1.82553 | ||||||||
\(719\) | 5.45519 | 0.203444 | 0.101722 | − | 0.994813i | \(-0.467565\pi\) | ||||
0.101722 | + | 0.994813i | \(0.467565\pi\) | |||||||
\(720\) | −4.07814 | −0.151983 | ||||||||
\(721\) | −6.85532 | −0.255306 | ||||||||
\(722\) | 48.4596 | 1.80348 | ||||||||
\(723\) | −20.9827 | −0.780357 | ||||||||
\(724\) | 5.20486 | 0.193437 | ||||||||
\(725\) | 41.4765 | 1.54040 | ||||||||
\(726\) | 40.9364 | 1.51929 | ||||||||
\(727\) | −34.3782 | −1.27502 | −0.637508 | − | 0.770444i | \(-0.720035\pi\) | ||||
−0.637508 | + | 0.770444i | \(0.720035\pi\) | |||||||
\(728\) | −51.0207 | −1.89095 | ||||||||
\(729\) | 29.3803 | 1.08816 | ||||||||
\(730\) | 7.78912 | 0.288288 | ||||||||
\(731\) | −10.9305 | −0.404278 | ||||||||
\(732\) | −28.6718 | −1.05974 | ||||||||
\(733\) | 43.8315 | 1.61895 | 0.809476 | − | 0.587153i | \(-0.199751\pi\) | ||||
0.809476 | + | 0.587153i | \(0.199751\pi\) | |||||||
\(734\) | 80.4222 | 2.96844 | ||||||||
\(735\) | 0.578873 | 0.0213521 | ||||||||
\(736\) | −68.1175 | −2.51084 | ||||||||
\(737\) | 2.38763 | 0.0879496 | ||||||||
\(738\) | 13.0133 | 0.479027 | ||||||||
\(739\) | 26.5622 | 0.977108 | 0.488554 | − | 0.872534i | \(-0.337525\pi\) | ||||
0.488554 | + | 0.872534i | \(0.337525\pi\) | |||||||
\(740\) | 11.8476 | 0.435528 | ||||||||
\(741\) | 7.60268 | 0.279292 | ||||||||
\(742\) | 32.0374 | 1.17613 | ||||||||
\(743\) | 28.1244 | 1.03178 | 0.515892 | − | 0.856654i | \(-0.327461\pi\) | ||||
0.515892 | + | 0.856654i | \(0.327461\pi\) | |||||||
\(744\) | −77.3906 | −2.83728 | ||||||||
\(745\) | 1.23327 | 0.0451834 | ||||||||
\(746\) | 27.3713 | 1.00214 | ||||||||
\(747\) | 10.4158 | 0.381093 | ||||||||
\(748\) | 3.96365 | 0.144925 | ||||||||
\(749\) | −4.55624 | −0.166481 | ||||||||
\(750\) | 15.0558 | 0.549759 | ||||||||
\(751\) | 33.1393 | 1.20927 | 0.604636 | − | 0.796502i | \(-0.293319\pi\) | ||||
0.604636 | + | 0.796502i | \(0.293319\pi\) | |||||||
\(752\) | −42.9812 | −1.56736 | ||||||||
\(753\) | −0.575773 | −0.0209823 | ||||||||
\(754\) | −146.338 | −5.32930 | ||||||||
\(755\) | 3.23939 | 0.117893 | ||||||||
\(756\) | 28.2083 | 1.02593 | ||||||||
\(757\) | −13.4566 | −0.489090 | −0.244545 | − | 0.969638i | \(-0.578639\pi\) | ||||
−0.244545 | + | 0.969638i | \(0.578639\pi\) | |||||||
\(758\) | −13.3977 | −0.486627 | ||||||||
\(759\) | −3.67859 | −0.133524 | ||||||||
\(760\) | 2.60064 | 0.0943353 | ||||||||
\(761\) | −4.34193 | −0.157395 | −0.0786975 | − | 0.996899i | \(-0.525076\pi\) | ||||
−0.0786975 | + | 0.996899i | \(0.525076\pi\) | |||||||
\(762\) | 35.5652 | 1.28839 | ||||||||
\(763\) | 7.71733 | 0.279386 | ||||||||
\(764\) | 19.9211 | 0.720719 | ||||||||
\(765\) | 0.606704 | 0.0219354 | ||||||||
\(766\) | 34.2817 | 1.23865 | ||||||||
\(767\) | 78.8819 | 2.84826 | ||||||||
\(768\) | −8.36775 | −0.301945 | ||||||||
\(769\) | 3.25027 | 0.117208 | 0.0586039 | − | 0.998281i | \(-0.481335\pi\) | ||||
0.0586039 | + | 0.998281i | \(0.481335\pi\) | |||||||
\(770\) | −0.520493 | −0.0187573 | ||||||||
\(771\) | 20.8405 | 0.750552 | ||||||||
\(772\) | −37.1159 | −1.33583 | ||||||||
\(773\) | −15.5861 | −0.560591 | −0.280296 | − | 0.959914i | \(-0.590433\pi\) | ||||
−0.280296 | + | 0.959914i | \(0.590433\pi\) | |||||||
\(774\) | 16.5400 | 0.594517 | ||||||||
\(775\) | −32.9292 | −1.18285 | ||||||||
\(776\) | −26.1903 | −0.940178 | ||||||||
\(777\) | −8.49562 | −0.304779 | ||||||||
\(778\) | −52.4314 | −1.87976 | ||||||||
\(779\) | −4.33473 | −0.155308 | ||||||||
\(780\) | −18.6475 | −0.667687 | ||||||||
\(781\) | −7.97719 | −0.285446 | ||||||||
\(782\) | 22.4128 | 0.801479 | ||||||||
\(783\) | 48.4722 | 1.73225 | ||||||||
\(784\) | 10.9112 | 0.389687 | ||||||||
\(785\) | 1.75210 | 0.0625350 | ||||||||
\(786\) | −27.5105 | −0.981268 | ||||||||
\(787\) | −16.2109 | −0.577857 | −0.288929 | − | 0.957351i | \(-0.593299\pi\) | ||||
−0.288929 | + | 0.957351i | \(0.593299\pi\) | |||||||
\(788\) | 120.117 | 4.27900 | ||||||||
\(789\) | −8.09831 | −0.288307 | ||||||||
\(790\) | 7.97402 | 0.283703 | ||||||||
\(791\) | −20.5285 | −0.729911 | ||||||||
\(792\) | −3.59333 | −0.127683 | ||||||||
\(793\) | 25.7874 | 0.915737 | ||||||||
\(794\) | −33.0276 | −1.17210 | ||||||||
\(795\) | 7.01514 | 0.248801 | ||||||||
\(796\) | 120.577 | 4.27373 | ||||||||
\(797\) | 2.19319 | 0.0776868 | 0.0388434 | − | 0.999245i | \(-0.487633\pi\) | ||||
0.0388434 | + | 0.999245i | \(0.487633\pi\) | |||||||
\(798\) | −3.11271 | −0.110189 | ||||||||
\(799\) | 6.39429 | 0.226214 | ||||||||
\(800\) | 63.1013 | 2.23097 | ||||||||
\(801\) | 5.38611 | 0.190309 | ||||||||
\(802\) | −1.29605 | −0.0457652 | ||||||||
\(803\) | 3.58491 | 0.126509 | ||||||||
\(804\) | −35.0223 | −1.23514 | ||||||||
\(805\) | −2.10093 | −0.0740479 | ||||||||
\(806\) | 116.181 | 4.09230 | ||||||||
\(807\) | −0.462201 | −0.0162702 | ||||||||
\(808\) | −14.6305 | −0.514699 | ||||||||
\(809\) | −47.9315 | −1.68518 | −0.842592 | − | 0.538553i | \(-0.818971\pi\) | ||||
−0.842592 | + | 0.538553i | \(0.818971\pi\) | |||||||
\(810\) | 5.68864 | 0.199878 | ||||||||
\(811\) | 42.4308 | 1.48995 | 0.744974 | − | 0.667094i | \(-0.232462\pi\) | ||||
0.744974 | + | 0.667094i | \(0.232462\pi\) | |||||||
\(812\) | 42.7684 | 1.50088 | ||||||||
\(813\) | −11.2853 | −0.395792 | ||||||||
\(814\) | 7.63882 | 0.267740 | ||||||||
\(815\) | 5.61654 | 0.196739 | ||||||||
\(816\) | −25.4881 | −0.892263 | ||||||||
\(817\) | −5.50946 | −0.192752 | ||||||||
\(818\) | −37.6682 | −1.31704 | ||||||||
\(819\) | −5.99947 | −0.209638 | ||||||||
\(820\) | 10.6320 | 0.371286 | ||||||||
\(821\) | −43.2450 | −1.50926 | −0.754631 | − | 0.656150i | \(-0.772184\pi\) | ||||
−0.754631 | + | 0.656150i | \(0.772184\pi\) | |||||||
\(822\) | −35.4390 | −1.23608 | ||||||||
\(823\) | 13.5021 | 0.470652 | 0.235326 | − | 0.971916i | \(-0.424384\pi\) | ||||
0.235326 | + | 0.971916i | \(0.424384\pi\) | |||||||
\(824\) | −54.1679 | −1.88703 | ||||||||
\(825\) | 3.40769 | 0.118641 | ||||||||
\(826\) | −32.2960 | −1.12372 | ||||||||
\(827\) | 46.3065 | 1.61024 | 0.805118 | − | 0.593115i | \(-0.202102\pi\) | ||||
0.805118 | + | 0.593115i | \(0.202102\pi\) | |||||||
\(828\) | −24.2096 | −0.841341 | ||||||||
\(829\) | −10.9243 | −0.379417 | −0.189708 | − | 0.981840i | \(-0.560754\pi\) | ||||
−0.189708 | + | 0.981840i | \(0.560754\pi\) | |||||||
\(830\) | 11.9213 | 0.413794 | ||||||||
\(831\) | 14.8132 | 0.513866 | ||||||||
\(832\) | −81.7261 | −2.83334 | ||||||||
\(833\) | −1.62326 | −0.0562427 | ||||||||
\(834\) | 43.5297 | 1.50731 | ||||||||
\(835\) | 4.17278 | 0.144405 | ||||||||
\(836\) | 1.99786 | 0.0690975 | ||||||||
\(837\) | −38.4832 | −1.33018 | ||||||||
\(838\) | 66.9649 | 2.31326 | ||||||||
\(839\) | −1.40430 | −0.0484819 | −0.0242409 | − | 0.999706i | \(-0.507717\pi\) | ||||
−0.0242409 | + | 0.999706i | \(0.507717\pi\) | |||||||
\(840\) | 4.57402 | 0.157819 | ||||||||
\(841\) | 44.4918 | 1.53420 | ||||||||
\(842\) | 66.7289 | 2.29963 | ||||||||
\(843\) | 39.3054 | 1.35375 | ||||||||
\(844\) | 94.5059 | 3.25303 | ||||||||
\(845\) | 11.5421 | 0.397062 | ||||||||
\(846\) | −9.67583 | −0.332662 | ||||||||
\(847\) | 10.7604 | 0.369733 | ||||||||
\(848\) | 132.229 | 4.54076 | ||||||||
\(849\) | 40.6908 | 1.39650 | ||||||||
\(850\) | −20.7623 | −0.712140 | ||||||||
\(851\) | 30.8335 | 1.05696 | ||||||||
\(852\) | 117.011 | 4.00873 | ||||||||
\(853\) | −3.73677 | −0.127944 | −0.0639722 | − | 0.997952i | \(-0.520377\pi\) | ||||
−0.0639722 | + | 0.997952i | \(0.520377\pi\) | |||||||
\(854\) | −10.5579 | −0.361285 | ||||||||
\(855\) | 0.305807 | 0.0104584 | ||||||||
\(856\) | −36.0015 | −1.23051 | ||||||||
\(857\) | −14.6273 | −0.499658 | −0.249829 | − | 0.968290i | \(-0.580374\pi\) | ||||
−0.249829 | + | 0.968290i | \(0.580374\pi\) | |||||||
\(858\) | −12.0230 | −0.410460 | ||||||||
\(859\) | 1.00000 | 0.0341196 | ||||||||
\(860\) | 13.5133 | 0.460800 | ||||||||
\(861\) | −7.62393 | −0.259823 | ||||||||
\(862\) | −105.973 | −3.60944 | ||||||||
\(863\) | −46.1094 | −1.56958 | −0.784792 | − | 0.619760i | \(-0.787230\pi\) | ||||
−0.784792 | + | 0.619760i | \(0.787230\pi\) | |||||||
\(864\) | 73.7443 | 2.50883 | ||||||||
\(865\) | 7.60737 | 0.258658 | ||||||||
\(866\) | 83.6631 | 2.84299 | ||||||||
\(867\) | −20.6720 | −0.702057 | ||||||||
\(868\) | −33.9549 | −1.15250 | ||||||||
\(869\) | 3.67001 | 0.124497 | ||||||||
\(870\) | 13.1192 | 0.444782 | ||||||||
\(871\) | 31.4990 | 1.06730 | ||||||||
\(872\) | 60.9791 | 2.06501 | ||||||||
\(873\) | −3.07969 | −0.104232 | ||||||||
\(874\) | 11.2971 | 0.382129 | ||||||||
\(875\) | 3.95752 | 0.133789 | ||||||||
\(876\) | −52.5843 | −1.77666 | ||||||||
\(877\) | 57.9445 | 1.95665 | 0.978324 | − | 0.207080i | \(-0.0663962\pi\) | ||||
0.978324 | + | 0.207080i | \(0.0663962\pi\) | |||||||
\(878\) | 36.4289 | 1.22942 | ||||||||
\(879\) | 4.27512 | 0.144196 | ||||||||
\(880\) | −2.14825 | −0.0724175 | ||||||||
\(881\) | −36.0607 | −1.21492 | −0.607459 | − | 0.794351i | \(-0.707811\pi\) | ||||
−0.607459 | + | 0.794351i | \(0.707811\pi\) | |||||||
\(882\) | 2.45632 | 0.0827085 | ||||||||
\(883\) | 5.91195 | 0.198953 | 0.0994765 | − | 0.995040i | \(-0.468283\pi\) | ||||
0.0994765 | + | 0.995040i | \(0.468283\pi\) | |||||||
\(884\) | 52.2907 | 1.75873 | ||||||||
\(885\) | −7.07178 | −0.237715 | ||||||||
\(886\) | 36.6895 | 1.23261 | ||||||||
\(887\) | −49.8167 | −1.67268 | −0.836340 | − | 0.548211i | \(-0.815309\pi\) | ||||
−0.836340 | + | 0.548211i | \(0.815309\pi\) | |||||||
\(888\) | −67.1288 | −2.25270 | ||||||||
\(889\) | 9.34859 | 0.313542 | ||||||||
\(890\) | 6.16463 | 0.206639 | ||||||||
\(891\) | 2.61817 | 0.0877121 | ||||||||
\(892\) | −125.126 | −4.18952 | ||||||||
\(893\) | 3.22302 | 0.107854 | ||||||||
\(894\) | −11.6635 | −0.390086 | ||||||||
\(895\) | −7.35413 | −0.245821 | ||||||||
\(896\) | 7.37582 | 0.246409 | ||||||||
\(897\) | −48.5301 | −1.62037 | ||||||||
\(898\) | 8.54258 | 0.285070 | ||||||||
\(899\) | −58.3470 | −1.94598 | ||||||||
\(900\) | 22.4268 | 0.747559 | ||||||||
\(901\) | −19.6717 | −0.655358 | ||||||||
\(902\) | 6.85504 | 0.228248 | ||||||||
\(903\) | −9.69004 | −0.322464 | ||||||||
\(904\) | −162.208 | −5.39495 | ||||||||
\(905\) | 0.419675 | 0.0139505 | ||||||||
\(906\) | −30.6362 | −1.01782 | ||||||||
\(907\) | −22.3211 | −0.741160 | −0.370580 | − | 0.928801i | \(-0.620841\pi\) | ||||
−0.370580 | + | 0.928801i | \(0.620841\pi\) | |||||||
\(908\) | −49.4165 | −1.63994 | ||||||||
\(909\) | −1.72038 | −0.0570615 | ||||||||
\(910\) | −6.86664 | −0.227627 | ||||||||
\(911\) | −0.338172 | −0.0112041 | −0.00560207 | − | 0.999984i | \(-0.501783\pi\) | ||||
−0.00560207 | + | 0.999984i | \(0.501783\pi\) | |||||||
\(912\) | −12.8472 | −0.425413 | ||||||||
\(913\) | 5.48673 | 0.181584 | ||||||||
\(914\) | 5.33163 | 0.176355 | ||||||||
\(915\) | −2.31184 | −0.0764272 | ||||||||
\(916\) | 96.4501 | 3.18680 | ||||||||
\(917\) | −7.23135 | −0.238800 | ||||||||
\(918\) | −24.2642 | −0.800837 | ||||||||
\(919\) | 1.00120 | 0.0330266 | 0.0165133 | − | 0.999864i | \(-0.494743\pi\) | ||||
0.0165133 | + | 0.999864i | \(0.494743\pi\) | |||||||
\(920\) | −16.6006 | −0.547307 | ||||||||
\(921\) | 4.70170 | 0.154926 | ||||||||
\(922\) | 83.9861 | 2.76593 | ||||||||
\(923\) | −105.240 | −3.46401 | ||||||||
\(924\) | 3.51384 | 0.115597 | ||||||||
\(925\) | −28.5629 | −0.939142 | ||||||||
\(926\) | −26.4550 | −0.869366 | ||||||||
\(927\) | −6.36954 | −0.209203 | ||||||||
\(928\) | 111.809 | 3.67030 | ||||||||
\(929\) | 4.63616 | 0.152107 | 0.0760537 | − | 0.997104i | \(-0.475768\pi\) | ||||
0.0760537 | + | 0.997104i | \(0.475768\pi\) | |||||||
\(930\) | −10.4157 | −0.341543 | ||||||||
\(931\) | −0.818199 | −0.0268154 | ||||||||
\(932\) | 114.202 | 3.74082 | ||||||||
\(933\) | −20.1976 | −0.661239 | ||||||||
\(934\) | −29.5884 | −0.968160 | ||||||||
\(935\) | 0.319594 | 0.0104519 | ||||||||
\(936\) | −47.4053 | −1.54949 | ||||||||
\(937\) | 42.1780 | 1.37789 | 0.688947 | − | 0.724812i | \(-0.258073\pi\) | ||||
0.688947 | + | 0.724812i | \(0.258073\pi\) | |||||||
\(938\) | −12.8964 | −0.421083 | ||||||||
\(939\) | −15.7122 | −0.512749 | ||||||||
\(940\) | −7.90526 | −0.257841 | ||||||||
\(941\) | 16.7642 | 0.546498 | 0.273249 | − | 0.961943i | \(-0.411902\pi\) | ||||
0.273249 | + | 0.961943i | \(0.411902\pi\) | |||||||
\(942\) | −16.5703 | −0.539889 | ||||||||
\(943\) | 27.6698 | 0.901054 | ||||||||
\(944\) | −133.297 | −4.33844 | ||||||||
\(945\) | 2.27447 | 0.0739886 | ||||||||
\(946\) | 8.71278 | 0.283277 | ||||||||
\(947\) | 61.2497 | 1.99035 | 0.995174 | − | 0.0981282i | \(-0.0312855\pi\) | ||||
0.995174 | + | 0.0981282i | \(0.0312855\pi\) | |||||||
\(948\) | −53.8325 | −1.74840 | ||||||||
\(949\) | 47.2943 | 1.53524 | ||||||||
\(950\) | −10.4652 | −0.339534 | ||||||||
\(951\) | 33.1829 | 1.07603 | ||||||||
\(952\) | −12.8263 | −0.415704 | ||||||||
\(953\) | −49.1554 | −1.59230 | −0.796150 | − | 0.605099i | \(-0.793134\pi\) | ||||
−0.796150 | + | 0.605099i | \(0.793134\pi\) | |||||||
\(954\) | 29.7671 | 0.963746 | ||||||||
\(955\) | 1.60626 | 0.0519774 | ||||||||
\(956\) | −1.95734 | −0.0633050 | ||||||||
\(957\) | 6.03806 | 0.195183 | ||||||||
\(958\) | −64.2952 | −2.07728 | ||||||||
\(959\) | −9.31540 | −0.300810 | ||||||||
\(960\) | 7.32676 | 0.236470 | ||||||||
\(961\) | 15.3231 | 0.494293 | ||||||||
\(962\) | 100.776 | 3.24914 | ||||||||
\(963\) | −4.23338 | −0.136419 | ||||||||
\(964\) | −72.7429 | −2.34289 | ||||||||
\(965\) | −2.99270 | −0.0963385 | ||||||||
\(966\) | 19.8693 | 0.639284 | ||||||||
\(967\) | 37.7498 | 1.21395 | 0.606976 | − | 0.794720i | \(-0.292383\pi\) | ||||
0.606976 | + | 0.794720i | \(0.292383\pi\) | |||||||
\(968\) | 85.0245 | 2.73279 | ||||||||
\(969\) | 1.91127 | 0.0613990 | ||||||||
\(970\) | −3.52484 | −0.113176 | ||||||||
\(971\) | 27.0786 | 0.868994 | 0.434497 | − | 0.900673i | \(-0.356926\pi\) | ||||
0.434497 | + | 0.900673i | \(0.356926\pi\) | |||||||
\(972\) | 46.2210 | 1.48254 | ||||||||
\(973\) | 11.4421 | 0.366817 | ||||||||
\(974\) | 53.9494 | 1.72865 | ||||||||
\(975\) | 44.9563 | 1.43975 | ||||||||
\(976\) | −43.5762 | −1.39484 | ||||||||
\(977\) | 0.683774 | 0.0218759 | 0.0109379 | − | 0.999940i | \(-0.496518\pi\) | ||||
0.0109379 | + | 0.999940i | \(0.496518\pi\) | |||||||
\(978\) | −53.1178 | −1.69852 | ||||||||
\(979\) | 2.83725 | 0.0906788 | ||||||||
\(980\) | 2.00684 | 0.0641060 | ||||||||
\(981\) | 7.17046 | 0.228935 | ||||||||
\(982\) | −40.0953 | −1.27949 | ||||||||
\(983\) | 11.2418 | 0.358557 | 0.179279 | − | 0.983798i | \(-0.442624\pi\) | ||||
0.179279 | + | 0.983798i | \(0.442624\pi\) | |||||||
\(984\) | −60.2411 | −1.92042 | ||||||||
\(985\) | 9.68523 | 0.308597 | ||||||||
\(986\) | −36.7885 | −1.17158 | ||||||||
\(987\) | 5.66865 | 0.180435 | ||||||||
\(988\) | 26.3570 | 0.838526 | ||||||||
\(989\) | 35.1684 | 1.11829 | ||||||||
\(990\) | −0.483610 | −0.0153701 | ||||||||
\(991\) | 4.41767 | 0.140332 | 0.0701660 | − | 0.997535i | \(-0.477647\pi\) | ||||
0.0701660 | + | 0.997535i | \(0.477647\pi\) | |||||||
\(992\) | −88.7676 | −2.81837 | ||||||||
\(993\) | 9.94716 | 0.315664 | ||||||||
\(994\) | 43.0875 | 1.36665 | ||||||||
\(995\) | 9.72226 | 0.308217 | ||||||||
\(996\) | −80.4805 | −2.55012 | ||||||||
\(997\) | −43.2265 | −1.36900 | −0.684498 | − | 0.729014i | \(-0.739979\pi\) | ||||
−0.684498 | + | 0.729014i | \(0.739979\pi\) | |||||||
\(998\) | 56.6153 | 1.79213 | ||||||||
\(999\) | −33.3805 | −1.05611 |
(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 | 6013.2.a.f.1.3 | ✓ | 110 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6013.2.a.f.1.3 | ✓ | 110 | 1.1 | even | 1 | trivial |