Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [619,2,Mod(1,619)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(619, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("619.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 619 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 619.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: | \(4.94273988512\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 619.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.37056 | −0.969134 | −0.484567 | − | 0.874754i | \(-0.661023\pi\) | ||||
−0.484567 | + | 0.874754i | \(0.661023\pi\) | |||||||
\(3\) | −0.725873 | −0.419083 | −0.209542 | − | 0.977800i | \(-0.567197\pi\) | ||||
−0.209542 | + | 0.977800i | \(0.567197\pi\) | |||||||
\(4\) | −0.121559 | −0.0607796 | ||||||||
\(5\) | −0.225133 | −0.100683 | −0.0503414 | − | 0.998732i | \(-0.516031\pi\) | ||||
−0.0503414 | + | 0.998732i | \(0.516031\pi\) | |||||||
\(6\) | 0.994855 | 0.406148 | ||||||||
\(7\) | 2.47282 | 0.934637 | 0.467319 | − | 0.884089i | \(-0.345220\pi\) | ||||
0.467319 | + | 0.884089i | \(0.345220\pi\) | |||||||
\(8\) | 2.90773 | 1.02804 | ||||||||
\(9\) | −2.47311 | −0.824369 | ||||||||
\(10\) | 0.308559 | 0.0975750 | ||||||||
\(11\) | −4.06256 | −1.22491 | −0.612455 | − | 0.790506i | \(-0.709818\pi\) | ||||
−0.612455 | + | 0.790506i | \(0.709818\pi\) | |||||||
\(12\) | 0.0882365 | 0.0254717 | ||||||||
\(13\) | 2.26536 | 0.628298 | 0.314149 | − | 0.949374i | \(-0.398281\pi\) | ||||
0.314149 | + | 0.949374i | \(0.398281\pi\) | |||||||
\(14\) | −3.38915 | −0.905788 | ||||||||
\(15\) | 0.163418 | 0.0421944 | ||||||||
\(16\) | −3.74211 | −0.935526 | ||||||||
\(17\) | 7.19086 | 1.74404 | 0.872019 | − | 0.489471i | \(-0.162810\pi\) | ||||
0.872019 | + | 0.489471i | \(0.162810\pi\) | |||||||
\(18\) | 3.38955 | 0.798924 | ||||||||
\(19\) | −7.47015 | −1.71377 | −0.856885 | − | 0.515507i | \(-0.827603\pi\) | ||||
−0.856885 | + | 0.515507i | \(0.827603\pi\) | |||||||
\(20\) | 0.0273670 | 0.00611945 | ||||||||
\(21\) | −1.79495 | −0.391691 | ||||||||
\(22\) | 5.56800 | 1.18710 | ||||||||
\(23\) | −0.178059 | −0.0371279 | −0.0185639 | − | 0.999828i | \(-0.505909\pi\) | ||||
−0.0185639 | + | 0.999828i | \(0.505909\pi\) | |||||||
\(24\) | −2.11064 | −0.430833 | ||||||||
\(25\) | −4.94931 | −0.989863 | ||||||||
\(26\) | −3.10482 | −0.608905 | ||||||||
\(27\) | 3.97278 | 0.764562 | ||||||||
\(28\) | −0.300594 | −0.0568068 | ||||||||
\(29\) | 10.5609 | 1.96111 | 0.980557 | − | 0.196232i | \(-0.0628707\pi\) | ||||
0.980557 | + | 0.196232i | \(0.0628707\pi\) | |||||||
\(30\) | −0.223975 | −0.0408920 | ||||||||
\(31\) | 1.27650 | 0.229266 | 0.114633 | − | 0.993408i | \(-0.463431\pi\) | ||||
0.114633 | + | 0.993408i | \(0.463431\pi\) | |||||||
\(32\) | −0.686670 | −0.121387 | ||||||||
\(33\) | 2.94891 | 0.513339 | ||||||||
\(34\) | −9.85552 | −1.69021 | ||||||||
\(35\) | −0.556714 | −0.0941018 | ||||||||
\(36\) | 0.300629 | 0.0501048 | ||||||||
\(37\) | 2.08508 | 0.342784 | 0.171392 | − | 0.985203i | \(-0.445173\pi\) | ||||
0.171392 | + | 0.985203i | \(0.445173\pi\) | |||||||
\(38\) | 10.2383 | 1.66087 | ||||||||
\(39\) | −1.64436 | −0.263309 | ||||||||
\(40\) | −0.654627 | −0.103506 | ||||||||
\(41\) | 4.23367 | 0.661188 | 0.330594 | − | 0.943773i | \(-0.392751\pi\) | ||||
0.330594 | + | 0.943773i | \(0.392751\pi\) | |||||||
\(42\) | 2.46009 | 0.379601 | ||||||||
\(43\) | 8.52011 | 1.29930 | 0.649652 | − | 0.760232i | \(-0.274915\pi\) | ||||
0.649652 | + | 0.760232i | \(0.274915\pi\) | |||||||
\(44\) | 0.493842 | 0.0744495 | ||||||||
\(45\) | 0.556779 | 0.0829997 | ||||||||
\(46\) | 0.244041 | 0.0359819 | ||||||||
\(47\) | 9.96677 | 1.45380 | 0.726901 | − | 0.686742i | \(-0.240960\pi\) | ||||
0.726901 | + | 0.686742i | \(0.240960\pi\) | |||||||
\(48\) | 2.71629 | 0.392063 | ||||||||
\(49\) | −0.885174 | −0.126453 | ||||||||
\(50\) | 6.78334 | 0.959310 | ||||||||
\(51\) | −5.21965 | −0.730897 | ||||||||
\(52\) | −0.275375 | −0.0381877 | ||||||||
\(53\) | 0.619984 | 0.0851614 | 0.0425807 | − | 0.999093i | \(-0.486442\pi\) | ||||
0.0425807 | + | 0.999093i | \(0.486442\pi\) | |||||||
\(54\) | −5.44495 | −0.740963 | ||||||||
\(55\) | 0.914619 | 0.123327 | ||||||||
\(56\) | 7.19028 | 0.960842 | ||||||||
\(57\) | 5.42238 | 0.718212 | ||||||||
\(58\) | −14.4744 | −1.90058 | ||||||||
\(59\) | 11.8540 | 1.54326 | 0.771628 | − | 0.636074i | \(-0.219443\pi\) | ||||
0.771628 | + | 0.636074i | \(0.219443\pi\) | |||||||
\(60\) | −0.0198650 | −0.00256456 | ||||||||
\(61\) | 6.30300 | 0.807017 | 0.403508 | − | 0.914976i | \(-0.367791\pi\) | ||||
0.403508 | + | 0.914976i | \(0.367791\pi\) | |||||||
\(62\) | −1.74952 | −0.222190 | ||||||||
\(63\) | −6.11554 | −0.770486 | ||||||||
\(64\) | 8.42533 | 1.05317 | ||||||||
\(65\) | −0.510008 | −0.0632587 | ||||||||
\(66\) | −4.04166 | −0.497494 | ||||||||
\(67\) | 12.5388 | 1.53186 | 0.765928 | − | 0.642927i | \(-0.222280\pi\) | ||||
0.765928 | + | 0.642927i | \(0.222280\pi\) | |||||||
\(68\) | −0.874114 | −0.106002 | ||||||||
\(69\) | 0.129248 | 0.0155597 | ||||||||
\(70\) | 0.763011 | 0.0911972 | ||||||||
\(71\) | −9.50401 | −1.12792 | −0.563959 | − | 0.825803i | \(-0.690723\pi\) | ||||
−0.563959 | + | 0.825803i | \(0.690723\pi\) | |||||||
\(72\) | −7.19113 | −0.847482 | ||||||||
\(73\) | 5.14906 | 0.602652 | 0.301326 | − | 0.953521i | \(-0.402571\pi\) | ||||
0.301326 | + | 0.953521i | \(0.402571\pi\) | |||||||
\(74\) | −2.85773 | −0.332204 | ||||||||
\(75\) | 3.59258 | 0.414835 | ||||||||
\(76\) | 0.908065 | 0.104162 | ||||||||
\(77\) | −10.0460 | −1.14485 | ||||||||
\(78\) | 2.25370 | 0.255182 | ||||||||
\(79\) | −16.3932 | −1.84438 | −0.922190 | − | 0.386737i | \(-0.873602\pi\) | ||||
−0.922190 | + | 0.386737i | \(0.873602\pi\) | |||||||
\(80\) | 0.842473 | 0.0941913 | ||||||||
\(81\) | 4.53559 | 0.503954 | ||||||||
\(82\) | −5.80251 | −0.640780 | ||||||||
\(83\) | 4.79273 | 0.526071 | 0.263035 | − | 0.964786i | \(-0.415276\pi\) | ||||
0.263035 | + | 0.964786i | \(0.415276\pi\) | |||||||
\(84\) | 0.218193 | 0.0238068 | ||||||||
\(85\) | −1.61890 | −0.175595 | ||||||||
\(86\) | −11.6773 | −1.25920 | ||||||||
\(87\) | −7.66589 | −0.821870 | ||||||||
\(88\) | −11.8128 | −1.25925 | ||||||||
\(89\) | −1.64933 | −0.174829 | −0.0874143 | − | 0.996172i | \(-0.527860\pi\) | ||||
−0.0874143 | + | 0.996172i | \(0.527860\pi\) | |||||||
\(90\) | −0.763100 | −0.0804379 | ||||||||
\(91\) | 5.60182 | 0.587231 | ||||||||
\(92\) | 0.0216447 | 0.00225662 | ||||||||
\(93\) | −0.926577 | −0.0960816 | ||||||||
\(94\) | −13.6601 | −1.40893 | ||||||||
\(95\) | 1.68178 | 0.172547 | ||||||||
\(96\) | 0.498435 | 0.0508713 | ||||||||
\(97\) | 3.34400 | 0.339531 | 0.169766 | − | 0.985484i | \(-0.445699\pi\) | ||||
0.169766 | + | 0.985484i | \(0.445699\pi\) | |||||||
\(98\) | 1.21319 | 0.122550 | ||||||||
\(99\) | 10.0472 | 1.00978 | ||||||||
\(100\) | 0.601634 | 0.0601634 | ||||||||
\(101\) | −12.6806 | −1.26176 | −0.630882 | − | 0.775878i | \(-0.717307\pi\) | ||||
−0.630882 | + | 0.775878i | \(0.717307\pi\) | |||||||
\(102\) | 7.15386 | 0.708337 | ||||||||
\(103\) | −4.47808 | −0.441238 | −0.220619 | − | 0.975360i | \(-0.570808\pi\) | ||||
−0.220619 | + | 0.975360i | \(0.570808\pi\) | |||||||
\(104\) | 6.58705 | 0.645914 | ||||||||
\(105\) | 0.404104 | 0.0394365 | ||||||||
\(106\) | −0.849727 | −0.0825328 | ||||||||
\(107\) | 15.0754 | 1.45740 | 0.728699 | − | 0.684834i | \(-0.240125\pi\) | ||||
0.728699 | + | 0.684834i | \(0.240125\pi\) | |||||||
\(108\) | −0.482928 | −0.0464698 | ||||||||
\(109\) | 3.66599 | 0.351138 | 0.175569 | − | 0.984467i | \(-0.443823\pi\) | ||||
0.175569 | + | 0.984467i | \(0.443823\pi\) | |||||||
\(110\) | −1.25354 | −0.119521 | ||||||||
\(111\) | −1.51350 | −0.143655 | ||||||||
\(112\) | −9.25354 | −0.874378 | ||||||||
\(113\) | 6.54316 | 0.615528 | 0.307764 | − | 0.951463i | \(-0.400419\pi\) | ||||
0.307764 | + | 0.951463i | \(0.400419\pi\) | |||||||
\(114\) | −7.43171 | −0.696044 | ||||||||
\(115\) | 0.0400870 | 0.00373814 | ||||||||
\(116\) | −1.28378 | −0.119196 | ||||||||
\(117\) | −5.60248 | −0.517949 | ||||||||
\(118\) | −16.2466 | −1.49562 | ||||||||
\(119\) | 17.7817 | 1.63004 | ||||||||
\(120\) | 0.475176 | 0.0433774 | ||||||||
\(121\) | 5.50443 | 0.500403 | ||||||||
\(122\) | −8.63866 | −0.782107 | ||||||||
\(123\) | −3.07311 | −0.277093 | ||||||||
\(124\) | −0.155170 | −0.0139347 | ||||||||
\(125\) | 2.23992 | 0.200345 | ||||||||
\(126\) | 8.38173 | 0.746704 | ||||||||
\(127\) | −15.0494 | −1.33542 | −0.667711 | − | 0.744420i | \(-0.732726\pi\) | ||||
−0.667711 | + | 0.744420i | \(0.732726\pi\) | |||||||
\(128\) | −10.1741 | −0.899272 | ||||||||
\(129\) | −6.18452 | −0.544516 | ||||||||
\(130\) | 0.698998 | 0.0613062 | ||||||||
\(131\) | 9.57374 | 0.836462 | 0.418231 | − | 0.908341i | \(-0.362650\pi\) | ||||
0.418231 | + | 0.908341i | \(0.362650\pi\) | |||||||
\(132\) | −0.358467 | −0.0312005 | ||||||||
\(133\) | −18.4723 | −1.60175 | ||||||||
\(134\) | −17.1852 | −1.48457 | ||||||||
\(135\) | −0.894406 | −0.0769782 | ||||||||
\(136\) | 20.9091 | 1.79294 | ||||||||
\(137\) | 2.15272 | 0.183919 | 0.0919595 | − | 0.995763i | \(-0.470687\pi\) | ||||
0.0919595 | + | 0.995763i | \(0.470687\pi\) | |||||||
\(138\) | −0.177143 | −0.0150794 | ||||||||
\(139\) | 5.62106 | 0.476772 | 0.238386 | − | 0.971171i | \(-0.423382\pi\) | ||||
0.238386 | + | 0.971171i | \(0.423382\pi\) | |||||||
\(140\) | 0.0676736 | 0.00571947 | ||||||||
\(141\) | −7.23461 | −0.609264 | ||||||||
\(142\) | 13.0258 | 1.09310 | ||||||||
\(143\) | −9.20317 | −0.769608 | ||||||||
\(144\) | 9.25463 | 0.771219 | ||||||||
\(145\) | −2.37762 | −0.197450 | ||||||||
\(146\) | −7.05711 | −0.584050 | ||||||||
\(147\) | 0.642524 | 0.0529945 | ||||||||
\(148\) | −0.253460 | −0.0208343 | ||||||||
\(149\) | 15.1382 | 1.24017 | 0.620086 | − | 0.784534i | \(-0.287098\pi\) | ||||
0.620086 | + | 0.784534i | \(0.287098\pi\) | |||||||
\(150\) | −4.92385 | −0.402031 | ||||||||
\(151\) | −19.7193 | −1.60474 | −0.802369 | − | 0.596828i | \(-0.796427\pi\) | ||||
−0.802369 | + | 0.596828i | \(0.796427\pi\) | |||||||
\(152\) | −21.7212 | −1.76182 | ||||||||
\(153\) | −17.7838 | −1.43773 | ||||||||
\(154\) | 13.7686 | 1.10951 | ||||||||
\(155\) | −0.287383 | −0.0230831 | ||||||||
\(156\) | 0.199888 | 0.0160038 | ||||||||
\(157\) | 15.7111 | 1.25389 | 0.626943 | − | 0.779065i | \(-0.284306\pi\) | ||||
0.626943 | + | 0.779065i | \(0.284306\pi\) | |||||||
\(158\) | 22.4679 | 1.78745 | ||||||||
\(159\) | −0.450030 | −0.0356897 | ||||||||
\(160\) | 0.154592 | 0.0122216 | ||||||||
\(161\) | −0.440308 | −0.0347011 | ||||||||
\(162\) | −6.21630 | −0.488399 | ||||||||
\(163\) | −11.8717 | −0.929864 | −0.464932 | − | 0.885346i | \(-0.653921\pi\) | ||||
−0.464932 | + | 0.885346i | \(0.653921\pi\) | |||||||
\(164\) | −0.514641 | −0.0401867 | ||||||||
\(165\) | −0.663897 | −0.0516843 | ||||||||
\(166\) | −6.56874 | −0.509833 | ||||||||
\(167\) | −5.37936 | −0.416267 | −0.208134 | − | 0.978100i | \(-0.566739\pi\) | ||||
−0.208134 | + | 0.978100i | \(0.566739\pi\) | |||||||
\(168\) | −5.21923 | −0.402673 | ||||||||
\(169\) | −7.86814 | −0.605242 | ||||||||
\(170\) | 2.21881 | 0.170175 | ||||||||
\(171\) | 18.4745 | 1.41278 | ||||||||
\(172\) | −1.03570 | −0.0789711 | ||||||||
\(173\) | −18.6393 | −1.41712 | −0.708560 | − | 0.705651i | \(-0.750655\pi\) | ||||
−0.708560 | + | 0.705651i | \(0.750655\pi\) | |||||||
\(174\) | 10.5066 | 0.796502 | ||||||||
\(175\) | −12.2388 | −0.925163 | ||||||||
\(176\) | 15.2025 | 1.14593 | ||||||||
\(177\) | −8.60448 | −0.646753 | ||||||||
\(178\) | 2.26051 | 0.169432 | ||||||||
\(179\) | −22.6264 | −1.69117 | −0.845587 | − | 0.533837i | \(-0.820750\pi\) | ||||
−0.845587 | + | 0.533837i | \(0.820750\pi\) | |||||||
\(180\) | −0.0676816 | −0.00504469 | ||||||||
\(181\) | 12.1002 | 0.899398 | 0.449699 | − | 0.893180i | \(-0.351531\pi\) | ||||
0.449699 | + | 0.893180i | \(0.351531\pi\) | |||||||
\(182\) | −7.67765 | −0.569105 | ||||||||
\(183\) | −4.57518 | −0.338207 | ||||||||
\(184\) | −0.517747 | −0.0381688 | ||||||||
\(185\) | −0.469420 | −0.0345124 | ||||||||
\(186\) | 1.26993 | 0.0931159 | ||||||||
\(187\) | −29.2133 | −2.13629 | ||||||||
\(188\) | −1.21155 | −0.0883615 | ||||||||
\(189\) | 9.82397 | 0.714588 | ||||||||
\(190\) | −2.30498 | −0.167221 | ||||||||
\(191\) | −0.166765 | −0.0120667 | −0.00603336 | − | 0.999982i | \(-0.501920\pi\) | ||||
−0.00603336 | + | 0.999982i | \(0.501920\pi\) | |||||||
\(192\) | −6.11573 | −0.441364 | ||||||||
\(193\) | −16.5260 | −1.18956 | −0.594782 | − | 0.803887i | \(-0.702762\pi\) | ||||
−0.594782 | + | 0.803887i | \(0.702762\pi\) | |||||||
\(194\) | −4.58316 | −0.329051 | ||||||||
\(195\) | 0.370201 | 0.0265107 | ||||||||
\(196\) | 0.107601 | 0.00768578 | ||||||||
\(197\) | 9.82274 | 0.699841 | 0.349921 | − | 0.936779i | \(-0.386209\pi\) | ||||
0.349921 | + | 0.936779i | \(0.386209\pi\) | |||||||
\(198\) | −13.7703 | −0.978610 | ||||||||
\(199\) | 11.5691 | 0.820113 | 0.410056 | − | 0.912060i | \(-0.365509\pi\) | ||||
0.410056 | + | 0.912060i | \(0.365509\pi\) | |||||||
\(200\) | −14.3913 | −1.01762 | ||||||||
\(201\) | −9.10156 | −0.641975 | ||||||||
\(202\) | 17.3795 | 1.22282 | ||||||||
\(203\) | 26.1152 | 1.83293 | ||||||||
\(204\) | 0.634496 | 0.0444236 | ||||||||
\(205\) | −0.953140 | −0.0665702 | ||||||||
\(206\) | 6.13749 | 0.427619 | ||||||||
\(207\) | 0.440359 | 0.0306071 | ||||||||
\(208\) | −8.47722 | −0.587789 | ||||||||
\(209\) | 30.3480 | 2.09921 | ||||||||
\(210\) | −0.553849 | −0.0382192 | ||||||||
\(211\) | −19.2316 | −1.32396 | −0.661978 | − | 0.749523i | \(-0.730283\pi\) | ||||
−0.661978 | + | 0.749523i | \(0.730283\pi\) | |||||||
\(212\) | −0.0753647 | −0.00517607 | ||||||||
\(213\) | 6.89871 | 0.472692 | ||||||||
\(214\) | −20.6618 | −1.41241 | ||||||||
\(215\) | −1.91816 | −0.130817 | ||||||||
\(216\) | 11.5518 | 0.785999 | ||||||||
\(217\) | 3.15655 | 0.214281 | ||||||||
\(218\) | −5.02447 | −0.340300 | ||||||||
\(219\) | −3.73757 | −0.252561 | ||||||||
\(220\) | −0.111180 | −0.00749577 | ||||||||
\(221\) | 16.2899 | 1.09578 | ||||||||
\(222\) | 2.07435 | 0.139221 | ||||||||
\(223\) | −2.26463 | −0.151651 | −0.0758255 | − | 0.997121i | \(-0.524159\pi\) | ||||
−0.0758255 | + | 0.997121i | \(0.524159\pi\) | |||||||
\(224\) | −1.69801 | −0.113453 | ||||||||
\(225\) | 12.2402 | 0.816013 | ||||||||
\(226\) | −8.96780 | −0.596529 | ||||||||
\(227\) | 12.6616 | 0.840378 | 0.420189 | − | 0.907437i | \(-0.361964\pi\) | ||||
0.420189 | + | 0.907437i | \(0.361964\pi\) | |||||||
\(228\) | −0.659140 | −0.0436526 | ||||||||
\(229\) | 27.7524 | 1.83393 | 0.916967 | − | 0.398964i | \(-0.130630\pi\) | ||||
0.916967 | + | 0.398964i | \(0.130630\pi\) | |||||||
\(230\) | −0.0549418 | −0.00362275 | ||||||||
\(231\) | 7.29211 | 0.479786 | ||||||||
\(232\) | 30.7083 | 2.01610 | ||||||||
\(233\) | −10.9164 | −0.715157 | −0.357579 | − | 0.933883i | \(-0.616398\pi\) | ||||
−0.357579 | + | 0.933883i | \(0.616398\pi\) | |||||||
\(234\) | 7.67855 | 0.501962 | ||||||||
\(235\) | −2.24385 | −0.146373 | ||||||||
\(236\) | −1.44096 | −0.0937984 | ||||||||
\(237\) | 11.8994 | 0.772949 | ||||||||
\(238\) | −24.3709 | −1.57973 | ||||||||
\(239\) | 6.41476 | 0.414936 | 0.207468 | − | 0.978242i | \(-0.433478\pi\) | ||||
0.207468 | + | 0.978242i | \(0.433478\pi\) | |||||||
\(240\) | −0.611529 | −0.0394740 | ||||||||
\(241\) | 9.85126 | 0.634576 | 0.317288 | − | 0.948329i | \(-0.397228\pi\) | ||||
0.317288 | + | 0.948329i | \(0.397228\pi\) | |||||||
\(242\) | −7.54417 | −0.484957 | ||||||||
\(243\) | −15.2106 | −0.975761 | ||||||||
\(244\) | −0.766188 | −0.0490501 | ||||||||
\(245\) | 0.199282 | 0.0127317 | ||||||||
\(246\) | 4.21189 | 0.268540 | ||||||||
\(247\) | −16.9226 | −1.07676 | ||||||||
\(248\) | 3.71172 | 0.235694 | ||||||||
\(249\) | −3.47892 | −0.220467 | ||||||||
\(250\) | −3.06995 | −0.194161 | ||||||||
\(251\) | 5.56947 | 0.351542 | 0.175771 | − | 0.984431i | \(-0.443758\pi\) | ||||
0.175771 | + | 0.984431i | \(0.443758\pi\) | |||||||
\(252\) | 0.743400 | 0.0468298 | ||||||||
\(253\) | 0.723376 | 0.0454783 | ||||||||
\(254\) | 20.6262 | 1.29420 | ||||||||
\(255\) | 1.17512 | 0.0735887 | ||||||||
\(256\) | −2.90642 | −0.181651 | ||||||||
\(257\) | 24.0328 | 1.49913 | 0.749564 | − | 0.661932i | \(-0.230263\pi\) | ||||
0.749564 | + | 0.661932i | \(0.230263\pi\) | |||||||
\(258\) | 8.47627 | 0.527709 | ||||||||
\(259\) | 5.15601 | 0.320379 | ||||||||
\(260\) | 0.0619962 | 0.00384484 | ||||||||
\(261\) | −26.1183 | −1.61668 | ||||||||
\(262\) | −13.1214 | −0.810643 | ||||||||
\(263\) | 14.9598 | 0.922463 | 0.461232 | − | 0.887280i | \(-0.347408\pi\) | ||||
0.461232 | + | 0.887280i | \(0.347408\pi\) | |||||||
\(264\) | 8.57462 | 0.527732 | ||||||||
\(265\) | −0.139579 | −0.00857428 | ||||||||
\(266\) | 25.3175 | 1.55231 | ||||||||
\(267\) | 1.19720 | 0.0732677 | ||||||||
\(268\) | −1.52420 | −0.0931055 | ||||||||
\(269\) | 13.4385 | 0.819357 | 0.409679 | − | 0.912230i | \(-0.365641\pi\) | ||||
0.409679 | + | 0.912230i | \(0.365641\pi\) | |||||||
\(270\) | 1.22584 | 0.0746022 | ||||||||
\(271\) | 5.72605 | 0.347833 | 0.173916 | − | 0.984760i | \(-0.444358\pi\) | ||||
0.173916 | + | 0.984760i | \(0.444358\pi\) | |||||||
\(272\) | −26.9089 | −1.63159 | ||||||||
\(273\) | −4.06621 | −0.246098 | ||||||||
\(274\) | −2.95043 | −0.178242 | ||||||||
\(275\) | 20.1069 | 1.21249 | ||||||||
\(276\) | −0.0157113 | −0.000945710 0 | ||||||||
\(277\) | 12.0981 | 0.726905 | 0.363452 | − | 0.931613i | \(-0.381598\pi\) | ||||
0.363452 | + | 0.931613i | \(0.381598\pi\) | |||||||
\(278\) | −7.70401 | −0.462056 | ||||||||
\(279\) | −3.15692 | −0.189000 | ||||||||
\(280\) | −1.61877 | −0.0967402 | ||||||||
\(281\) | −6.21778 | −0.370921 | −0.185461 | − | 0.982652i | \(-0.559378\pi\) | ||||
−0.185461 | + | 0.982652i | \(0.559378\pi\) | |||||||
\(282\) | 9.91549 | 0.590459 | ||||||||
\(283\) | 12.9505 | 0.769826 | 0.384913 | − | 0.922953i | \(-0.374231\pi\) | ||||
0.384913 | + | 0.922953i | \(0.374231\pi\) | |||||||
\(284\) | 1.15530 | 0.0685544 | ||||||||
\(285\) | −1.22076 | −0.0723116 | ||||||||
\(286\) | 12.6135 | 0.745853 | ||||||||
\(287\) | 10.4691 | 0.617971 | ||||||||
\(288\) | 1.69821 | 0.100068 | ||||||||
\(289\) | 34.7084 | 2.04167 | ||||||||
\(290\) | 3.25867 | 0.191356 | ||||||||
\(291\) | −2.42732 | −0.142292 | ||||||||
\(292\) | −0.625915 | −0.0366289 | ||||||||
\(293\) | 14.3490 | 0.838279 | 0.419139 | − | 0.907922i | \(-0.362332\pi\) | ||||
0.419139 | + | 0.907922i | \(0.362332\pi\) | |||||||
\(294\) | −0.880619 | −0.0513588 | ||||||||
\(295\) | −2.66873 | −0.155379 | ||||||||
\(296\) | 6.06283 | 0.352395 | ||||||||
\(297\) | −16.1397 | −0.936520 | ||||||||
\(298\) | −20.7479 | −1.20189 | ||||||||
\(299\) | −0.403368 | −0.0233274 | ||||||||
\(300\) | −0.436710 | −0.0252135 | ||||||||
\(301\) | 21.0687 | 1.21438 | ||||||||
\(302\) | 27.0266 | 1.55521 | ||||||||
\(303\) | 9.20450 | 0.528784 | ||||||||
\(304\) | 27.9541 | 1.60328 | ||||||||
\(305\) | −1.41902 | −0.0812526 | ||||||||
\(306\) | 24.3738 | 1.39335 | ||||||||
\(307\) | −28.7422 | −1.64040 | −0.820202 | − | 0.572075i | \(-0.806139\pi\) | ||||
−0.820202 | + | 0.572075i | \(0.806139\pi\) | |||||||
\(308\) | 1.22118 | 0.0695832 | ||||||||
\(309\) | 3.25052 | 0.184916 | ||||||||
\(310\) | 0.393876 | 0.0223707 | ||||||||
\(311\) | −29.9677 | −1.69931 | −0.849655 | − | 0.527339i | \(-0.823190\pi\) | ||||
−0.849655 | + | 0.527339i | \(0.823190\pi\) | |||||||
\(312\) | −4.78137 | −0.270692 | ||||||||
\(313\) | −13.6402 | −0.770990 | −0.385495 | − | 0.922710i | \(-0.625969\pi\) | ||||
−0.385495 | + | 0.922710i | \(0.625969\pi\) | |||||||
\(314\) | −21.5331 | −1.21518 | ||||||||
\(315\) | 1.37681 | 0.0775746 | ||||||||
\(316\) | 1.99274 | 0.112101 | ||||||||
\(317\) | 12.9433 | 0.726967 | 0.363484 | − | 0.931601i | \(-0.381587\pi\) | ||||
0.363484 | + | 0.931601i | \(0.381587\pi\) | |||||||
\(318\) | 0.616794 | 0.0345881 | ||||||||
\(319\) | −42.9044 | −2.40219 | ||||||||
\(320\) | −1.89682 | −0.106036 | ||||||||
\(321\) | −10.9429 | −0.610771 | ||||||||
\(322\) | 0.603469 | 0.0336300 | ||||||||
\(323\) | −53.7168 | −2.98888 | ||||||||
\(324\) | −0.551342 | −0.0306301 | ||||||||
\(325\) | −11.2120 | −0.621929 | ||||||||
\(326\) | 16.2709 | 0.901163 | ||||||||
\(327\) | −2.66104 | −0.147156 | ||||||||
\(328\) | 12.3104 | 0.679726 | ||||||||
\(329\) | 24.6460 | 1.35878 | ||||||||
\(330\) | 0.909913 | 0.0500891 | ||||||||
\(331\) | 8.48346 | 0.466293 | 0.233147 | − | 0.972442i | \(-0.425098\pi\) | ||||
0.233147 | + | 0.972442i | \(0.425098\pi\) | |||||||
\(332\) | −0.582600 | −0.0319744 | ||||||||
\(333\) | −5.15662 | −0.282581 | ||||||||
\(334\) | 7.37275 | 0.403419 | ||||||||
\(335\) | −2.82290 | −0.154231 | ||||||||
\(336\) | 6.71690 | 0.366437 | ||||||||
\(337\) | −28.4431 | −1.54939 | −0.774697 | − | 0.632332i | \(-0.782098\pi\) | ||||
−0.774697 | + | 0.632332i | \(0.782098\pi\) | |||||||
\(338\) | 10.7838 | 0.586560 | ||||||||
\(339\) | −4.74950 | −0.257958 | ||||||||
\(340\) | 0.196792 | 0.0106726 | ||||||||
\(341\) | −5.18586 | −0.280830 | ||||||||
\(342\) | −25.3204 | −1.36917 | ||||||||
\(343\) | −19.4986 | −1.05283 | ||||||||
\(344\) | 24.7742 | 1.33573 | ||||||||
\(345\) | −0.0290981 | −0.00156659 | ||||||||
\(346\) | 25.5463 | 1.37338 | ||||||||
\(347\) | 6.37057 | 0.341990 | 0.170995 | − | 0.985272i | \(-0.445302\pi\) | ||||
0.170995 | + | 0.985272i | \(0.445302\pi\) | |||||||
\(348\) | 0.931860 | 0.0499529 | ||||||||
\(349\) | −12.7281 | −0.681317 | −0.340659 | − | 0.940187i | \(-0.610650\pi\) | ||||
−0.340659 | + | 0.940187i | \(0.610650\pi\) | |||||||
\(350\) | 16.7740 | 0.896607 | ||||||||
\(351\) | 8.99978 | 0.480373 | ||||||||
\(352\) | 2.78964 | 0.148688 | ||||||||
\(353\) | 1.48049 | 0.0787984 | 0.0393992 | − | 0.999224i | \(-0.487456\pi\) | ||||
0.0393992 | + | 0.999224i | \(0.487456\pi\) | |||||||
\(354\) | 11.7930 | 0.626790 | ||||||||
\(355\) | 2.13967 | 0.113562 | ||||||||
\(356\) | 0.200491 | 0.0106260 | ||||||||
\(357\) | −12.9072 | −0.683124 | ||||||||
\(358\) | 31.0109 | 1.63897 | ||||||||
\(359\) | −27.5753 | −1.45537 | −0.727685 | − | 0.685911i | \(-0.759404\pi\) | ||||
−0.727685 | + | 0.685911i | \(0.759404\pi\) | |||||||
\(360\) | 1.61896 | 0.0853268 | ||||||||
\(361\) | 36.8032 | 1.93701 | ||||||||
\(362\) | −16.5840 | −0.871637 | ||||||||
\(363\) | −3.99552 | −0.209710 | ||||||||
\(364\) | −0.680953 | −0.0356916 | ||||||||
\(365\) | −1.15923 | −0.0606766 | ||||||||
\(366\) | 6.27057 | 0.327768 | ||||||||
\(367\) | 6.08957 | 0.317873 | 0.158936 | − | 0.987289i | \(-0.449193\pi\) | ||||
0.158936 | + | 0.987289i | \(0.449193\pi\) | |||||||
\(368\) | 0.666316 | 0.0347341 | ||||||||
\(369\) | −10.4703 | −0.545063 | ||||||||
\(370\) | 0.643369 | 0.0334472 | ||||||||
\(371\) | 1.53311 | 0.0795950 | ||||||||
\(372\) | 0.112634 | 0.00583980 | ||||||||
\(373\) | 22.4949 | 1.16474 | 0.582371 | − | 0.812923i | \(-0.302125\pi\) | ||||
0.582371 | + | 0.812923i | \(0.302125\pi\) | |||||||
\(374\) | 40.0387 | 2.07035 | ||||||||
\(375\) | −1.62590 | −0.0839611 | ||||||||
\(376\) | 28.9807 | 1.49456 | ||||||||
\(377\) | 23.9243 | 1.23216 | ||||||||
\(378\) | −13.4644 | −0.692532 | ||||||||
\(379\) | −14.1157 | −0.725075 | −0.362538 | − | 0.931969i | \(-0.618090\pi\) | ||||
−0.362538 | + | 0.931969i | \(0.618090\pi\) | |||||||
\(380\) | −0.204436 | −0.0104873 | ||||||||
\(381\) | 10.9240 | 0.559653 | ||||||||
\(382\) | 0.228562 | 0.0116943 | ||||||||
\(383\) | 24.3617 | 1.24482 | 0.622412 | − | 0.782690i | \(-0.286153\pi\) | ||||
0.622412 | + | 0.782690i | \(0.286153\pi\) | |||||||
\(384\) | 7.38511 | 0.376870 | ||||||||
\(385\) | 2.26169 | 0.115266 | ||||||||
\(386\) | 22.6498 | 1.15285 | ||||||||
\(387\) | −21.0711 | −1.07111 | ||||||||
\(388\) | −0.406493 | −0.0206366 | ||||||||
\(389\) | −16.7319 | −0.848341 | −0.424170 | − | 0.905582i | \(-0.639434\pi\) | ||||
−0.424170 | + | 0.905582i | \(0.639434\pi\) | |||||||
\(390\) | −0.507384 | −0.0256924 | ||||||||
\(391\) | −1.28040 | −0.0647525 | ||||||||
\(392\) | −2.57385 | −0.129999 | ||||||||
\(393\) | −6.94932 | −0.350547 | ||||||||
\(394\) | −13.4627 | −0.678240 | ||||||||
\(395\) | 3.69066 | 0.185697 | ||||||||
\(396\) | −1.22132 | −0.0613739 | ||||||||
\(397\) | −21.7689 | −1.09255 | −0.546274 | − | 0.837607i | \(-0.683954\pi\) | ||||
−0.546274 | + | 0.837607i | \(0.683954\pi\) | |||||||
\(398\) | −15.8562 | −0.794799 | ||||||||
\(399\) | 13.4086 | 0.671268 | ||||||||
\(400\) | 18.5209 | 0.926043 | ||||||||
\(401\) | 20.2269 | 1.01008 | 0.505041 | − | 0.863095i | \(-0.331477\pi\) | ||||
0.505041 | + | 0.863095i | \(0.331477\pi\) | |||||||
\(402\) | 12.4743 | 0.622159 | ||||||||
\(403\) | 2.89173 | 0.144047 | ||||||||
\(404\) | 1.54144 | 0.0766895 | ||||||||
\(405\) | −1.02111 | −0.0507395 | ||||||||
\(406\) | −35.7926 | −1.77636 | ||||||||
\(407\) | −8.47075 | −0.419880 | ||||||||
\(408\) | −15.1773 | −0.751390 | ||||||||
\(409\) | 28.5461 | 1.41151 | 0.705757 | − | 0.708454i | \(-0.250607\pi\) | ||||
0.705757 | + | 0.708454i | \(0.250607\pi\) | |||||||
\(410\) | 1.30634 | 0.0645155 | ||||||||
\(411\) | −1.56260 | −0.0770773 | ||||||||
\(412\) | 0.544352 | 0.0268183 | ||||||||
\(413\) | 29.3127 | 1.44238 | ||||||||
\(414\) | −0.603540 | −0.0296624 | ||||||||
\(415\) | −1.07900 | −0.0529662 | ||||||||
\(416\) | −1.55555 | −0.0762673 | ||||||||
\(417\) | −4.08018 | −0.199807 | ||||||||
\(418\) | −41.5938 | −2.03442 | ||||||||
\(419\) | −36.3207 | −1.77438 | −0.887192 | − | 0.461400i | \(-0.847347\pi\) | ||||
−0.887192 | + | 0.461400i | \(0.847347\pi\) | |||||||
\(420\) | −0.0491225 | −0.00239693 | ||||||||
\(421\) | −20.8986 | −1.01853 | −0.509267 | − | 0.860609i | \(-0.670083\pi\) | ||||
−0.509267 | + | 0.860609i | \(0.670083\pi\) | |||||||
\(422\) | 26.3581 | 1.28309 | ||||||||
\(423\) | −24.6489 | −1.19847 | ||||||||
\(424\) | 1.80275 | 0.0875491 | ||||||||
\(425\) | −35.5898 | −1.72636 | ||||||||
\(426\) | −9.45511 | −0.458102 | ||||||||
\(427\) | 15.5862 | 0.754268 | ||||||||
\(428\) | −1.83256 | −0.0885800 | ||||||||
\(429\) | 6.68034 | 0.322530 | ||||||||
\(430\) | 2.62896 | 0.126780 | ||||||||
\(431\) | 5.65795 | 0.272534 | 0.136267 | − | 0.990672i | \(-0.456490\pi\) | ||||
0.136267 | + | 0.990672i | \(0.456490\pi\) | |||||||
\(432\) | −14.8666 | −0.715268 | ||||||||
\(433\) | −0.797593 | −0.0383299 | −0.0191649 | − | 0.999816i | \(-0.506101\pi\) | ||||
−0.0191649 | + | 0.999816i | \(0.506101\pi\) | |||||||
\(434\) | −4.32625 | −0.207667 | ||||||||
\(435\) | 1.72585 | 0.0827481 | ||||||||
\(436\) | −0.445635 | −0.0213420 | ||||||||
\(437\) | 1.33013 | 0.0636286 | ||||||||
\(438\) | 5.12257 | 0.244766 | ||||||||
\(439\) | −18.2826 | −0.872581 | −0.436290 | − | 0.899806i | \(-0.643708\pi\) | ||||
−0.436290 | + | 0.899806i | \(0.643708\pi\) | |||||||
\(440\) | 2.65946 | 0.126785 | ||||||||
\(441\) | 2.18913 | 0.104244 | ||||||||
\(442\) | −22.3263 | −1.06195 | ||||||||
\(443\) | −18.4038 | −0.874391 | −0.437195 | − | 0.899367i | \(-0.644028\pi\) | ||||
−0.437195 | + | 0.899367i | \(0.644028\pi\) | |||||||
\(444\) | 0.183980 | 0.00873130 | ||||||||
\(445\) | 0.371319 | 0.0176022 | ||||||||
\(446\) | 3.10382 | 0.146970 | ||||||||
\(447\) | −10.9884 | −0.519735 | ||||||||
\(448\) | 20.8343 | 0.984329 | ||||||||
\(449\) | 2.95767 | 0.139581 | 0.0697905 | − | 0.997562i | \(-0.477767\pi\) | ||||
0.0697905 | + | 0.997562i | \(0.477767\pi\) | |||||||
\(450\) | −16.7759 | −0.790825 | ||||||||
\(451\) | −17.1996 | −0.809896 | ||||||||
\(452\) | −0.795381 | −0.0374116 | ||||||||
\(453\) | 14.3138 | 0.672519 | ||||||||
\(454\) | −17.3535 | −0.814439 | ||||||||
\(455\) | −1.26116 | −0.0591240 | ||||||||
\(456\) | 15.7668 | 0.738349 | ||||||||
\(457\) | 18.1383 | 0.848472 | 0.424236 | − | 0.905552i | \(-0.360543\pi\) | ||||
0.424236 | + | 0.905552i | \(0.360543\pi\) | |||||||
\(458\) | −38.0365 | −1.77733 | ||||||||
\(459\) | 28.5677 | 1.33343 | ||||||||
\(460\) | −0.00487295 | −0.000227202 0 | ||||||||
\(461\) | −16.5572 | −0.771145 | −0.385573 | − | 0.922677i | \(-0.625996\pi\) | ||||
−0.385573 | + | 0.922677i | \(0.625996\pi\) | |||||||
\(462\) | −9.99429 | −0.464976 | ||||||||
\(463\) | 4.01151 | 0.186430 | 0.0932152 | − | 0.995646i | \(-0.470286\pi\) | ||||
0.0932152 | + | 0.995646i | \(0.470286\pi\) | |||||||
\(464\) | −39.5201 | −1.83467 | ||||||||
\(465\) | 0.208603 | 0.00967376 | ||||||||
\(466\) | 14.9616 | 0.693083 | ||||||||
\(467\) | −4.61263 | −0.213447 | −0.106724 | − | 0.994289i | \(-0.534036\pi\) | ||||
−0.106724 | + | 0.994289i | \(0.534036\pi\) | |||||||
\(468\) | 0.681033 | 0.0314807 | ||||||||
\(469\) | 31.0061 | 1.43173 | ||||||||
\(470\) | 3.07534 | 0.141855 | ||||||||
\(471\) | −11.4043 | −0.525482 | ||||||||
\(472\) | 34.4681 | 1.58652 | ||||||||
\(473\) | −34.6135 | −1.59153 | ||||||||
\(474\) | −16.3089 | −0.749091 | ||||||||
\(475\) | 36.9721 | 1.69640 | ||||||||
\(476\) | −2.16153 | −0.0990733 | ||||||||
\(477\) | −1.53329 | −0.0702044 | ||||||||
\(478\) | −8.79182 | −0.402129 | ||||||||
\(479\) | −37.2886 | −1.70376 | −0.851879 | − | 0.523739i | \(-0.824537\pi\) | ||||
−0.851879 | + | 0.523739i | \(0.824537\pi\) | |||||||
\(480\) | −0.112214 | −0.00512186 | ||||||||
\(481\) | 4.72345 | 0.215371 | ||||||||
\(482\) | −13.5018 | −0.614989 | ||||||||
\(483\) | 0.319607 | 0.0145426 | ||||||||
\(484\) | −0.669114 | −0.0304143 | ||||||||
\(485\) | −0.752845 | −0.0341849 | ||||||||
\(486\) | 20.8471 | 0.945643 | ||||||||
\(487\) | 25.0176 | 1.13366 | 0.566828 | − | 0.823836i | \(-0.308170\pi\) | ||||
0.566828 | + | 0.823836i | \(0.308170\pi\) | |||||||
\(488\) | 18.3274 | 0.829644 | ||||||||
\(489\) | 8.61736 | 0.389690 | ||||||||
\(490\) | −0.273129 | −0.0123387 | ||||||||
\(491\) | −23.7021 | −1.06966 | −0.534830 | − | 0.844960i | \(-0.679624\pi\) | ||||
−0.534830 | + | 0.844960i | \(0.679624\pi\) | |||||||
\(492\) | 0.373564 | 0.0168416 | ||||||||
\(493\) | 75.9421 | 3.42026 | ||||||||
\(494\) | 23.1935 | 1.04352 | ||||||||
\(495\) | −2.26195 | −0.101667 | ||||||||
\(496\) | −4.77680 | −0.214485 | ||||||||
\(497\) | −23.5017 | −1.05419 | ||||||||
\(498\) | 4.76807 | 0.213662 | ||||||||
\(499\) | 27.1748 | 1.21651 | 0.608255 | − | 0.793742i | \(-0.291870\pi\) | ||||
0.608255 | + | 0.793742i | \(0.291870\pi\) | |||||||
\(500\) | −0.272283 | −0.0121769 | ||||||||
\(501\) | 3.90473 | 0.174451 | ||||||||
\(502\) | −7.63331 | −0.340691 | ||||||||
\(503\) | 12.0746 | 0.538381 | 0.269191 | − | 0.963087i | \(-0.413244\pi\) | ||||
0.269191 | + | 0.963087i | \(0.413244\pi\) | |||||||
\(504\) | −17.7823 | −0.792089 | ||||||||
\(505\) | 2.85482 | 0.127038 | ||||||||
\(506\) | −0.991432 | −0.0440745 | ||||||||
\(507\) | 5.71128 | 0.253647 | ||||||||
\(508\) | 1.82940 | 0.0811664 | ||||||||
\(509\) | −43.7176 | −1.93775 | −0.968873 | − | 0.247557i | \(-0.920372\pi\) | ||||
−0.968873 | + | 0.247557i | \(0.920372\pi\) | |||||||
\(510\) | −1.61057 | −0.0713173 | ||||||||
\(511\) | 12.7327 | 0.563261 | ||||||||
\(512\) | 24.3316 | 1.07532 | ||||||||
\(513\) | −29.6773 | −1.31028 | ||||||||
\(514\) | −32.9385 | −1.45286 | ||||||||
\(515\) | 1.00817 | 0.0444251 | ||||||||
\(516\) | 0.751785 | 0.0330955 | ||||||||
\(517\) | −40.4906 | −1.78078 | ||||||||
\(518\) | −7.06663 | −0.310490 | ||||||||
\(519\) | 13.5298 | 0.593891 | ||||||||
\(520\) | −1.48297 | −0.0650323 | ||||||||
\(521\) | −35.3638 | −1.54932 | −0.774659 | − | 0.632379i | \(-0.782078\pi\) | ||||
−0.774659 | + | 0.632379i | \(0.782078\pi\) | |||||||
\(522\) | 35.7968 | 1.56678 | ||||||||
\(523\) | 19.8938 | 0.869897 | 0.434949 | − | 0.900455i | \(-0.356767\pi\) | ||||
0.434949 | + | 0.900455i | \(0.356767\pi\) | |||||||
\(524\) | −1.16378 | −0.0508398 | ||||||||
\(525\) | 8.88378 | 0.387720 | ||||||||
\(526\) | −20.5034 | −0.893990 | ||||||||
\(527\) | 9.17913 | 0.399849 | ||||||||
\(528\) | −11.0351 | −0.480242 | ||||||||
\(529\) | −22.9683 | −0.998622 | ||||||||
\(530\) | 0.191302 | 0.00830962 | ||||||||
\(531\) | −29.3162 | −1.27221 | ||||||||
\(532\) | 2.24548 | 0.0973539 | ||||||||
\(533\) | 9.59079 | 0.415423 | ||||||||
\(534\) | −1.64084 | −0.0710062 | ||||||||
\(535\) | −3.39399 | −0.146735 | ||||||||
\(536\) | 36.4594 | 1.57480 | ||||||||
\(537\) | 16.4239 | 0.708743 | ||||||||
\(538\) | −18.4182 | −0.794067 | ||||||||
\(539\) | 3.59608 | 0.154894 | ||||||||
\(540\) | 0.108723 | 0.00467870 | ||||||||
\(541\) | −15.3119 | −0.658311 | −0.329156 | − | 0.944276i | \(-0.606764\pi\) | ||||
−0.329156 | + | 0.944276i | \(0.606764\pi\) | |||||||
\(542\) | −7.84790 | −0.337096 | ||||||||
\(543\) | −8.78319 | −0.376923 | ||||||||
\(544\) | −4.93774 | −0.211704 | ||||||||
\(545\) | −0.825337 | −0.0353535 | ||||||||
\(546\) | 5.57300 | 0.238502 | ||||||||
\(547\) | 42.3037 | 1.80878 | 0.904388 | − | 0.426711i | \(-0.140328\pi\) | ||||
0.904388 | + | 0.426711i | \(0.140328\pi\) | |||||||
\(548\) | −0.261682 | −0.0111785 | ||||||||
\(549\) | −15.5880 | −0.665280 | ||||||||
\(550\) | −27.5578 | −1.17507 | ||||||||
\(551\) | −78.8917 | −3.36090 | ||||||||
\(552\) | 0.375819 | 0.0159959 | ||||||||
\(553\) | −40.5374 | −1.72383 | ||||||||
\(554\) | −16.5812 | −0.704468 | ||||||||
\(555\) | 0.340739 | 0.0144636 | ||||||||
\(556\) | −0.683291 | −0.0289780 | ||||||||
\(557\) | 7.44351 | 0.315392 | 0.157696 | − | 0.987488i | \(-0.449593\pi\) | ||||
0.157696 | + | 0.987488i | \(0.449593\pi\) | |||||||
\(558\) | 4.32676 | 0.183166 | ||||||||
\(559\) | 19.3011 | 0.816350 | ||||||||
\(560\) | 2.08328 | 0.0880347 | ||||||||
\(561\) | 21.2052 | 0.895283 | ||||||||
\(562\) | 8.52185 | 0.359472 | ||||||||
\(563\) | −30.6551 | −1.29196 | −0.645978 | − | 0.763356i | \(-0.723550\pi\) | ||||
−0.645978 | + | 0.763356i | \(0.723550\pi\) | |||||||
\(564\) | 0.879433 | 0.0370308 | ||||||||
\(565\) | −1.47308 | −0.0619731 | ||||||||
\(566\) | −17.7494 | −0.746064 | ||||||||
\(567\) | 11.2157 | 0.471014 | ||||||||
\(568\) | −27.6351 | −1.15954 | ||||||||
\(569\) | 45.0445 | 1.88836 | 0.944182 | − | 0.329425i | \(-0.106855\pi\) | ||||
0.944182 | + | 0.329425i | \(0.106855\pi\) | |||||||
\(570\) | 1.67313 | 0.0700796 | ||||||||
\(571\) | −20.5533 | −0.860127 | −0.430063 | − | 0.902799i | \(-0.641509\pi\) | ||||
−0.430063 | + | 0.902799i | \(0.641509\pi\) | |||||||
\(572\) | 1.11873 | 0.0467764 | ||||||||
\(573\) | 0.121051 | 0.00505696 | ||||||||
\(574\) | −14.3485 | −0.598897 | ||||||||
\(575\) | 0.881270 | 0.0367515 | ||||||||
\(576\) | −20.8368 | −0.868198 | ||||||||
\(577\) | 2.43980 | 0.101570 | 0.0507851 | − | 0.998710i | \(-0.483828\pi\) | ||||
0.0507851 | + | 0.998710i | \(0.483828\pi\) | |||||||
\(578\) | −47.5700 | −1.97865 | ||||||||
\(579\) | 11.9957 | 0.498526 | ||||||||
\(580\) | 0.289021 | 0.0120009 | ||||||||
\(581\) | 11.8516 | 0.491685 | ||||||||
\(582\) | 3.32679 | 0.137900 | ||||||||
\(583\) | −2.51873 | −0.104315 | ||||||||
\(584\) | 14.9721 | 0.619549 | ||||||||
\(585\) | 1.26131 | 0.0521486 | ||||||||
\(586\) | −19.6662 | −0.812404 | ||||||||
\(587\) | 28.0624 | 1.15826 | 0.579129 | − | 0.815236i | \(-0.303393\pi\) | ||||
0.579129 | + | 0.815236i | \(0.303393\pi\) | |||||||
\(588\) | −0.0781047 | −0.00322098 | ||||||||
\(589\) | −9.53565 | −0.392910 | ||||||||
\(590\) | 3.65765 | 0.150583 | ||||||||
\(591\) | −7.13007 | −0.293292 | ||||||||
\(592\) | −7.80257 | −0.320684 | ||||||||
\(593\) | −20.1600 | −0.827873 | −0.413937 | − | 0.910306i | \(-0.635847\pi\) | ||||
−0.413937 | + | 0.910306i | \(0.635847\pi\) | |||||||
\(594\) | 22.1204 | 0.907613 | ||||||||
\(595\) | −4.00325 | −0.164117 | ||||||||
\(596\) | −1.84019 | −0.0753771 | ||||||||
\(597\) | −8.39771 | −0.343696 | ||||||||
\(598\) | 0.552841 | 0.0226073 | ||||||||
\(599\) | 23.5060 | 0.960427 | 0.480214 | − | 0.877152i | \(-0.340559\pi\) | ||||
0.480214 | + | 0.877152i | \(0.340559\pi\) | |||||||
\(600\) | 10.4462 | 0.426466 | ||||||||
\(601\) | −20.9839 | −0.855952 | −0.427976 | − | 0.903790i | \(-0.640773\pi\) | ||||
−0.427976 | + | 0.903790i | \(0.640773\pi\) | |||||||
\(602\) | −28.8759 | −1.17689 | ||||||||
\(603\) | −31.0097 | −1.26281 | ||||||||
\(604\) | 2.39707 | 0.0975353 | ||||||||
\(605\) | −1.23923 | −0.0503819 | ||||||||
\(606\) | −12.6153 | −0.512463 | ||||||||
\(607\) | 32.2511 | 1.30903 | 0.654516 | − | 0.756048i | \(-0.272872\pi\) | ||||
0.654516 | + | 0.756048i | \(0.272872\pi\) | |||||||
\(608\) | 5.12953 | 0.208030 | ||||||||
\(609\) | −18.9564 | −0.768150 | ||||||||
\(610\) | 1.94485 | 0.0787447 | ||||||||
\(611\) | 22.5783 | 0.913421 | ||||||||
\(612\) | 2.16178 | 0.0873847 | ||||||||
\(613\) | −37.2120 | −1.50298 | −0.751489 | − | 0.659746i | \(-0.770664\pi\) | ||||
−0.751489 | + | 0.659746i | \(0.770664\pi\) | |||||||
\(614\) | 39.3930 | 1.58977 | ||||||||
\(615\) | 0.691859 | 0.0278985 | ||||||||
\(616\) | −29.2110 | −1.17694 | ||||||||
\(617\) | 38.3479 | 1.54383 | 0.771915 | − | 0.635726i | \(-0.219299\pi\) | ||||
0.771915 | + | 0.635726i | \(0.219299\pi\) | |||||||
\(618\) | −4.45504 | −0.179208 | ||||||||
\(619\) | 1.00000 | 0.0401934 | ||||||||
\(620\) | 0.0349340 | 0.00140298 | ||||||||
\(621\) | −0.707390 | −0.0283866 | ||||||||
\(622\) | 41.0726 | 1.64686 | ||||||||
\(623\) | −4.07849 | −0.163401 | ||||||||
\(624\) | 6.15339 | 0.246333 | ||||||||
\(625\) | 24.2423 | 0.969692 | ||||||||
\(626\) | 18.6948 | 0.747193 | ||||||||
\(627\) | −22.0288 | −0.879745 | ||||||||
\(628\) | −1.90983 | −0.0762106 | ||||||||
\(629\) | 14.9935 | 0.597829 | ||||||||
\(630\) | −1.88701 | −0.0751802 | ||||||||
\(631\) | 38.9829 | 1.55188 | 0.775942 | − | 0.630804i | \(-0.217275\pi\) | ||||
0.775942 | + | 0.630804i | \(0.217275\pi\) | |||||||
\(632\) | −47.6670 | −1.89609 | ||||||||
\(633\) | 13.9597 | 0.554848 | ||||||||
\(634\) | −17.7396 | −0.704529 | ||||||||
\(635\) | 3.38813 | 0.134454 | ||||||||
\(636\) | 0.0547052 | 0.00216920 | ||||||||
\(637\) | −2.00524 | −0.0794504 | ||||||||
\(638\) | 58.8032 | 2.32804 | ||||||||
\(639\) | 23.5044 | 0.929822 | ||||||||
\(640\) | 2.29053 | 0.0905412 | ||||||||
\(641\) | −0.319675 | −0.0126264 | −0.00631321 | − | 0.999980i | \(-0.502010\pi\) | ||||
−0.00631321 | + | 0.999980i | \(0.502010\pi\) | |||||||
\(642\) | 14.9979 | 0.591919 | ||||||||
\(643\) | 0.159017 | 0.00627101 | 0.00313550 | − | 0.999995i | \(-0.499002\pi\) | ||||
0.00313550 | + | 0.999995i | \(0.499002\pi\) | |||||||
\(644\) | 0.0535234 | 0.00210912 | ||||||||
\(645\) | 1.39234 | 0.0548234 | ||||||||
\(646\) | 73.6222 | 2.89663 | ||||||||
\(647\) | 24.6688 | 0.969829 | 0.484915 | − | 0.874562i | \(-0.338851\pi\) | ||||
0.484915 | + | 0.874562i | \(0.338851\pi\) | |||||||
\(648\) | 13.1883 | 0.518084 | ||||||||
\(649\) | −48.1575 | −1.89035 | ||||||||
\(650\) | 15.3667 | 0.602732 | ||||||||
\(651\) | −2.29126 | −0.0898014 | ||||||||
\(652\) | 1.44311 | 0.0565167 | ||||||||
\(653\) | −28.3461 | −1.10927 | −0.554635 | − | 0.832094i | \(-0.687142\pi\) | ||||
−0.554635 | + | 0.832094i | \(0.687142\pi\) | |||||||
\(654\) | 3.64713 | 0.142614 | ||||||||
\(655\) | −2.15537 | −0.0842172 | ||||||||
\(656\) | −15.8428 | −0.618559 | ||||||||
\(657\) | −12.7342 | −0.496808 | ||||||||
\(658\) | −33.7789 | −1.31684 | ||||||||
\(659\) | 39.5061 | 1.53894 | 0.769470 | − | 0.638683i | \(-0.220521\pi\) | ||||
0.769470 | + | 0.638683i | \(0.220521\pi\) | |||||||
\(660\) | 0.0807028 | 0.00314135 | ||||||||
\(661\) | −15.7041 | −0.610818 | −0.305409 | − | 0.952221i | \(-0.598793\pi\) | ||||
−0.305409 | + | 0.952221i | \(0.598793\pi\) | |||||||
\(662\) | −11.6271 | −0.451900 | ||||||||
\(663\) | −11.8244 | −0.459221 | ||||||||
\(664\) | 13.9360 | 0.540820 | ||||||||
\(665\) | 4.15874 | 0.161269 | ||||||||
\(666\) | 7.06746 | 0.273859 | ||||||||
\(667\) | −1.88047 | −0.0728120 | ||||||||
\(668\) | 0.653910 | 0.0253006 | ||||||||
\(669\) | 1.64384 | 0.0635544 | ||||||||
\(670\) | 3.86896 | 0.149471 | ||||||||
\(671\) | −25.6064 | −0.988523 | ||||||||
\(672\) | 1.23254 | 0.0475462 | ||||||||
\(673\) | −23.0243 | −0.887522 | −0.443761 | − | 0.896145i | \(-0.646356\pi\) | ||||
−0.443761 | + | 0.896145i | \(0.646356\pi\) | |||||||
\(674\) | 38.9830 | 1.50157 | ||||||||
\(675\) | −19.6626 | −0.756812 | ||||||||
\(676\) | 0.956445 | 0.0367863 | ||||||||
\(677\) | 7.63096 | 0.293282 | 0.146641 | − | 0.989190i | \(-0.453154\pi\) | ||||
0.146641 | + | 0.989190i | \(0.453154\pi\) | |||||||
\(678\) | 6.50949 | 0.249995 | ||||||||
\(679\) | 8.26909 | 0.317339 | ||||||||
\(680\) | −4.70733 | −0.180518 | ||||||||
\(681\) | −9.19070 | −0.352188 | ||||||||
\(682\) | 7.10755 | 0.272162 | ||||||||
\(683\) | 0.644724 | 0.0246697 | 0.0123348 | − | 0.999924i | \(-0.496074\pi\) | ||||
0.0123348 | + | 0.999924i | \(0.496074\pi\) | |||||||
\(684\) | −2.24574 | −0.0858681 | ||||||||
\(685\) | −0.484648 | −0.0185175 | ||||||||
\(686\) | 26.7240 | 1.02033 | ||||||||
\(687\) | −20.1448 | −0.768571 | ||||||||
\(688\) | −31.8831 | −1.21553 | ||||||||
\(689\) | 1.40449 | 0.0535067 | ||||||||
\(690\) | 0.0398808 | 0.00151823 | ||||||||
\(691\) | −29.5024 | −1.12232 | −0.561162 | − | 0.827706i | \(-0.689646\pi\) | ||||
−0.561162 | + | 0.827706i | \(0.689646\pi\) | |||||||
\(692\) | 2.26578 | 0.0861319 | ||||||||
\(693\) | 24.8448 | 0.943776 | ||||||||
\(694\) | −8.73126 | −0.331434 | ||||||||
\(695\) | −1.26549 | −0.0480027 | ||||||||
\(696\) | −22.2903 | −0.844913 | ||||||||
\(697\) | 30.4437 | 1.15314 | ||||||||
\(698\) | 17.4446 | 0.660288 | ||||||||
\(699\) | 7.92393 | 0.299710 | ||||||||
\(700\) | 1.48773 | 0.0562310 | ||||||||
\(701\) | −30.4332 | −1.14944 | −0.574722 | − | 0.818348i | \(-0.694890\pi\) | ||||
−0.574722 | + | 0.818348i | \(0.694890\pi\) | |||||||
\(702\) | −12.3348 | −0.465546 | ||||||||
\(703\) | −15.5758 | −0.587453 | ||||||||
\(704\) | −34.2285 | −1.29003 | ||||||||
\(705\) | 1.62875 | 0.0613424 | ||||||||
\(706\) | −2.02910 | −0.0763662 | ||||||||
\(707\) | −31.3568 | −1.17929 | ||||||||
\(708\) | 1.04595 | 0.0393093 | ||||||||
\(709\) | 10.4754 | 0.393413 | 0.196707 | − | 0.980462i | \(-0.436975\pi\) | ||||
0.196707 | + | 0.980462i | \(0.436975\pi\) | |||||||
\(710\) | −2.93255 | −0.110057 | ||||||||
\(711\) | 40.5422 | 1.52045 | ||||||||
\(712\) | −4.79580 | −0.179730 | ||||||||
\(713\) | −0.227292 | −0.00851217 | ||||||||
\(714\) | 17.6902 | 0.662038 | ||||||||
\(715\) | 2.07194 | 0.0774862 | ||||||||
\(716\) | 2.75044 | 0.102789 | ||||||||
\(717\) | −4.65630 | −0.173893 | ||||||||
\(718\) | 37.7937 | 1.41045 | ||||||||
\(719\) | 0.815327 | 0.0304066 | 0.0152033 | − | 0.999884i | \(-0.495160\pi\) | ||||
0.0152033 | + | 0.999884i | \(0.495160\pi\) | |||||||
\(720\) | −2.08353 | −0.0776484 | ||||||||
\(721\) | −11.0735 | −0.412398 | ||||||||
\(722\) | −50.4410 | −1.87722 | ||||||||
\(723\) | −7.15077 | −0.265940 | ||||||||
\(724\) | −1.47089 | −0.0546650 | ||||||||
\(725\) | −52.2694 | −1.94123 | ||||||||
\(726\) | 5.47611 | 0.203237 | ||||||||
\(727\) | 5.58478 | 0.207128 | 0.103564 | − | 0.994623i | \(-0.466975\pi\) | ||||
0.103564 | + | 0.994623i | \(0.466975\pi\) | |||||||
\(728\) | 16.2886 | 0.603695 | ||||||||
\(729\) | −2.56578 | −0.0950290 | ||||||||
\(730\) | 1.58879 | 0.0588038 | ||||||||
\(731\) | 61.2669 | 2.26604 | ||||||||
\(732\) | 0.556155 | 0.0205561 | ||||||||
\(733\) | 27.7414 | 1.02465 | 0.512327 | − | 0.858791i | \(-0.328784\pi\) | ||||
0.512327 | + | 0.858791i | \(0.328784\pi\) | |||||||
\(734\) | −8.34613 | −0.308061 | ||||||||
\(735\) | −0.144654 | −0.00533563 | ||||||||
\(736\) | 0.122268 | 0.00450685 | ||||||||
\(737\) | −50.9396 | −1.87638 | ||||||||
\(738\) | 14.3502 | 0.528239 | ||||||||
\(739\) | −10.9980 | −0.404569 | −0.202285 | − | 0.979327i | \(-0.564837\pi\) | ||||
−0.202285 | + | 0.979327i | \(0.564837\pi\) | |||||||
\(740\) | 0.0570623 | 0.00209765 | ||||||||
\(741\) | 12.2837 | 0.451251 | ||||||||
\(742\) | −2.10122 | −0.0771382 | ||||||||
\(743\) | 27.5706 | 1.01147 | 0.505733 | − | 0.862690i | \(-0.331222\pi\) | ||||
0.505733 | + | 0.862690i | \(0.331222\pi\) | |||||||
\(744\) | −2.69424 | −0.0987755 | ||||||||
\(745\) | −3.40812 | −0.124864 | ||||||||
\(746\) | −30.8307 | −1.12879 | ||||||||
\(747\) | −11.8529 | −0.433677 | ||||||||
\(748\) | 3.55115 | 0.129843 | ||||||||
\(749\) | 37.2788 | 1.36214 | ||||||||
\(750\) | 2.22840 | 0.0813696 | ||||||||
\(751\) | 2.39041 | 0.0872274 | 0.0436137 | − | 0.999048i | \(-0.486113\pi\) | ||||
0.0436137 | + | 0.999048i | \(0.486113\pi\) | |||||||
\(752\) | −37.2967 | −1.36007 | ||||||||
\(753\) | −4.04273 | −0.147325 | ||||||||
\(754\) | −32.7897 | −1.19413 | ||||||||
\(755\) | 4.43948 | 0.161569 | ||||||||
\(756\) | −1.19419 | −0.0434324 | ||||||||
\(757\) | 22.8502 | 0.830505 | 0.415253 | − | 0.909706i | \(-0.363693\pi\) | ||||
0.415253 | + | 0.909706i | \(0.363693\pi\) | |||||||
\(758\) | 19.3465 | 0.702695 | ||||||||
\(759\) | −0.525080 | −0.0190592 | ||||||||
\(760\) | 4.89016 | 0.177385 | ||||||||
\(761\) | 35.2537 | 1.27795 | 0.638974 | − | 0.769229i | \(-0.279359\pi\) | ||||
0.638974 | + | 0.769229i | \(0.279359\pi\) | |||||||
\(762\) | −14.9720 | −0.542379 | ||||||||
\(763\) | 9.06532 | 0.328187 | ||||||||
\(764\) | 0.0202719 | 0.000733410 0 | ||||||||
\(765\) | 4.00372 | 0.144755 | ||||||||
\(766\) | −33.3892 | −1.20640 | ||||||||
\(767\) | 26.8535 | 0.969625 | ||||||||
\(768\) | 2.10970 | 0.0761271 | ||||||||
\(769\) | 14.0283 | 0.505875 | 0.252937 | − | 0.967483i | \(-0.418603\pi\) | ||||
0.252937 | + | 0.967483i | \(0.418603\pi\) | |||||||
\(770\) | −3.09978 | −0.111708 | ||||||||
\(771\) | −17.4448 | −0.628259 | ||||||||
\(772\) | 2.00888 | 0.0723012 | ||||||||
\(773\) | 2.05297 | 0.0738401 | 0.0369200 | − | 0.999318i | \(-0.488245\pi\) | ||||
0.0369200 | + | 0.999318i | \(0.488245\pi\) | |||||||
\(774\) | 28.8793 | 1.03805 | ||||||||
\(775\) | −6.31780 | −0.226942 | ||||||||
\(776\) | 9.72344 | 0.349051 | ||||||||
\(777\) | −3.74261 | −0.134265 | ||||||||
\(778\) | 22.9321 | 0.822156 | ||||||||
\(779\) | −31.6262 | −1.13312 | ||||||||
\(780\) | −0.0450014 | −0.00161131 | ||||||||
\(781\) | 38.6107 | 1.38160 | ||||||||
\(782\) | 1.75486 | 0.0627538 | ||||||||
\(783\) | 41.9563 | 1.49939 | ||||||||
\(784\) | 3.31241 | 0.118300 | ||||||||
\(785\) | −3.53710 | −0.126245 | ||||||||
\(786\) | 9.52448 | 0.339727 | ||||||||
\(787\) | −7.63128 | −0.272026 | −0.136013 | − | 0.990707i | \(-0.543429\pi\) | ||||
−0.136013 | + | 0.990707i | \(0.543429\pi\) | |||||||
\(788\) | −1.19404 | −0.0425361 | ||||||||
\(789\) | −10.8589 | −0.386589 | ||||||||
\(790\) | −5.05828 | −0.179965 | ||||||||
\(791\) | 16.1800 | 0.575296 | ||||||||
\(792\) | 29.2144 | 1.03809 | ||||||||
\(793\) | 14.2786 | 0.507047 | ||||||||
\(794\) | 29.8356 | 1.05882 | ||||||||
\(795\) | 0.101317 | 0.00359333 | ||||||||
\(796\) | −1.40633 | −0.0498461 | ||||||||
\(797\) | 23.8432 | 0.844570 | 0.422285 | − | 0.906463i | \(-0.361228\pi\) | ||||
0.422285 | + | 0.906463i | \(0.361228\pi\) | |||||||
\(798\) | −18.3773 | −0.650548 | ||||||||
\(799\) | 71.6696 | 2.53549 | ||||||||
\(800\) | 3.39854 | 0.120157 | ||||||||
\(801\) | 4.07897 | 0.144123 | ||||||||
\(802\) | −27.7222 | −0.978905 | ||||||||
\(803\) | −20.9184 | −0.738194 | ||||||||
\(804\) | 1.10638 | 0.0390189 | ||||||||
\(805\) | 0.0991279 | 0.00349380 | ||||||||
\(806\) | −3.96330 | −0.139601 | ||||||||
\(807\) | −9.75462 | −0.343379 | ||||||||
\(808\) | −36.8717 | −1.29714 | ||||||||
\(809\) | 19.9428 | 0.701152 | 0.350576 | − | 0.936534i | \(-0.385986\pi\) | ||||
0.350576 | + | 0.936534i | \(0.385986\pi\) | |||||||
\(810\) | 1.39950 | 0.0491733 | ||||||||
\(811\) | −24.3626 | −0.855488 | −0.427744 | − | 0.903900i | \(-0.640692\pi\) | ||||
−0.427744 | + | 0.903900i | \(0.640692\pi\) | |||||||
\(812\) | −3.17455 | −0.111405 | ||||||||
\(813\) | −4.15639 | −0.145771 | ||||||||
\(814\) | 11.6097 | 0.406920 | ||||||||
\(815\) | 2.67272 | 0.0936212 | ||||||||
\(816\) | 19.5325 | 0.683774 | ||||||||
\(817\) | −63.6465 | −2.22671 | ||||||||
\(818\) | −39.1242 | −1.36795 | ||||||||
\(819\) | −13.8539 | −0.484095 | ||||||||
\(820\) | 0.115863 | 0.00404611 | ||||||||
\(821\) | −15.6976 | −0.547850 | −0.273925 | − | 0.961751i | \(-0.588322\pi\) | ||||
−0.273925 | + | 0.961751i | \(0.588322\pi\) | |||||||
\(822\) | 2.14164 | 0.0746982 | ||||||||
\(823\) | −7.38747 | −0.257511 | −0.128755 | − | 0.991676i | \(-0.541098\pi\) | ||||
−0.128755 | + | 0.991676i | \(0.541098\pi\) | |||||||
\(824\) | −13.0210 | −0.453609 | ||||||||
\(825\) | −14.5951 | −0.508135 | ||||||||
\(826\) | −40.1749 | −1.39786 | ||||||||
\(827\) | 11.5262 | 0.400806 | 0.200403 | − | 0.979714i | \(-0.435775\pi\) | ||||
0.200403 | + | 0.979714i | \(0.435775\pi\) | |||||||
\(828\) | −0.0535297 | −0.00186029 | ||||||||
\(829\) | −17.7336 | −0.615914 | −0.307957 | − | 0.951400i | \(-0.599645\pi\) | ||||
−0.307957 | + | 0.951400i | \(0.599645\pi\) | |||||||
\(830\) | 1.47884 | 0.0513314 | ||||||||
\(831\) | −8.78169 | −0.304634 | ||||||||
\(832\) | 19.0864 | 0.661702 | ||||||||
\(833\) | −6.36516 | −0.220540 | ||||||||
\(834\) | 5.59213 | 0.193640 | ||||||||
\(835\) | 1.21107 | 0.0419109 | ||||||||
\(836\) | −3.68907 | −0.127589 | ||||||||
\(837\) | 5.07126 | 0.175288 | ||||||||
\(838\) | 49.7798 | 1.71962 | ||||||||
\(839\) | −28.6447 | −0.988924 | −0.494462 | − | 0.869199i | \(-0.664635\pi\) | ||||
−0.494462 | + | 0.869199i | \(0.664635\pi\) | |||||||
\(840\) | 1.17502 | 0.0405422 | ||||||||
\(841\) | 82.5332 | 2.84597 | ||||||||
\(842\) | 28.6428 | 0.987095 | ||||||||
\(843\) | 4.51332 | 0.155447 | ||||||||
\(844\) | 2.33777 | 0.0804695 | ||||||||
\(845\) | 1.77138 | 0.0609374 | ||||||||
\(846\) | 33.7828 | 1.16148 | ||||||||
\(847\) | 13.6115 | 0.467695 | ||||||||
\(848\) | −2.32005 | −0.0796707 | ||||||||
\(849\) | −9.40041 | −0.322621 | ||||||||
\(850\) | 48.7781 | 1.67307 | ||||||||
\(851\) | −0.371266 | −0.0127269 | ||||||||
\(852\) | −0.838601 | −0.0287300 | ||||||||
\(853\) | 41.6536 | 1.42619 | 0.713097 | − | 0.701066i | \(-0.247292\pi\) | ||||
0.713097 | + | 0.701066i | \(0.247292\pi\) | |||||||
\(854\) | −21.3618 | −0.730987 | ||||||||
\(855\) | −4.15922 | −0.142242 | ||||||||
\(856\) | 43.8353 | 1.49826 | ||||||||
\(857\) | −9.05282 | −0.309238 | −0.154619 | − | 0.987974i | \(-0.549415\pi\) | ||||
−0.154619 | + | 0.987974i | \(0.549415\pi\) | |||||||
\(858\) | −9.15582 | −0.312574 | ||||||||
\(859\) | 9.47579 | 0.323310 | 0.161655 | − | 0.986847i | \(-0.448317\pi\) | ||||
0.161655 | + | 0.986847i | \(0.448317\pi\) | |||||||
\(860\) | 0.233170 | 0.00795103 | ||||||||
\(861\) | −7.59924 | −0.258981 | ||||||||
\(862\) | −7.75457 | −0.264122 | ||||||||
\(863\) | −34.6314 | −1.17887 | −0.589434 | − | 0.807817i | \(-0.700649\pi\) | ||||
−0.589434 | + | 0.807817i | \(0.700649\pi\) | |||||||
\(864\) | −2.72799 | −0.0928081 | ||||||||
\(865\) | 4.19633 | 0.142679 | ||||||||
\(866\) | 1.09315 | 0.0371468 | ||||||||
\(867\) | −25.1939 | −0.855630 | ||||||||
\(868\) | −0.383708 | −0.0130239 | ||||||||
\(869\) | 66.5985 | 2.25920 | ||||||||
\(870\) | −2.36538 | −0.0801940 | ||||||||
\(871\) | 28.4048 | 0.962461 | ||||||||
\(872\) | 10.6597 | 0.360983 | ||||||||
\(873\) | −8.27007 | −0.279899 | ||||||||
\(874\) | −1.82302 | −0.0616647 | ||||||||
\(875\) | 5.53892 | 0.187250 | ||||||||
\(876\) | 0.454335 | 0.0153506 | ||||||||
\(877\) | 15.5441 | 0.524886 | 0.262443 | − | 0.964947i | \(-0.415472\pi\) | ||||
0.262443 | + | 0.964947i | \(0.415472\pi\) | |||||||
\(878\) | 25.0574 | 0.845648 | ||||||||
\(879\) | −10.4156 | −0.351308 | ||||||||
\(880\) | −3.42260 | −0.115376 | ||||||||
\(881\) | 52.4905 | 1.76845 | 0.884224 | − | 0.467063i | \(-0.154688\pi\) | ||||
0.884224 | + | 0.467063i | \(0.154688\pi\) | |||||||
\(882\) | −3.00034 | −0.101027 | ||||||||
\(883\) | −32.8989 | −1.10713 | −0.553567 | − | 0.832804i | \(-0.686734\pi\) | ||||
−0.553567 | + | 0.832804i | \(0.686734\pi\) | |||||||
\(884\) | −1.98018 | −0.0666008 | ||||||||
\(885\) | 1.93716 | 0.0651168 | ||||||||
\(886\) | 25.2236 | 0.847402 | ||||||||
\(887\) | −40.9458 | −1.37483 | −0.687413 | − | 0.726267i | \(-0.741254\pi\) | ||||
−0.687413 | + | 0.726267i | \(0.741254\pi\) | |||||||
\(888\) | −4.40085 | −0.147683 | ||||||||
\(889\) | −37.2145 | −1.24814 | ||||||||
\(890\) | −0.508916 | −0.0170589 | ||||||||
\(891\) | −18.4261 | −0.617298 | ||||||||
\(892\) | 0.275287 | 0.00921729 | ||||||||
\(893\) | −74.4533 | −2.49148 | ||||||||
\(894\) | 15.0603 | 0.503693 | ||||||||
\(895\) | 5.09395 | 0.170272 | ||||||||
\(896\) | −25.1587 | −0.840493 | ||||||||
\(897\) | 0.292794 | 0.00977611 | ||||||||
\(898\) | −4.05367 | −0.135273 | ||||||||
\(899\) | 13.4810 | 0.449617 | ||||||||
\(900\) | −1.48791 | −0.0495969 | ||||||||
\(901\) | 4.45822 | 0.148525 | ||||||||
\(902\) | 23.5731 | 0.784897 | ||||||||
\(903\) | −15.2932 | −0.508925 | ||||||||
\(904\) | 19.0257 | 0.632786 | ||||||||
\(905\) | −2.72415 | −0.0905539 | ||||||||
\(906\) | −19.6179 | −0.651761 | ||||||||
\(907\) | −22.3371 | −0.741692 | −0.370846 | − | 0.928694i | \(-0.620932\pi\) | ||||
−0.370846 | + | 0.928694i | \(0.620932\pi\) | |||||||
\(908\) | −1.53913 | −0.0510778 | ||||||||
\(909\) | 31.3604 | 1.04016 | ||||||||
\(910\) | 1.72849 | 0.0572990 | ||||||||
\(911\) | 15.9284 | 0.527732 | 0.263866 | − | 0.964559i | \(-0.415002\pi\) | ||||
0.263866 | + | 0.964559i | \(0.415002\pi\) | |||||||
\(912\) | −20.2911 | −0.671906 | ||||||||
\(913\) | −19.4708 | −0.644389 | ||||||||
\(914\) | −24.8596 | −0.822283 | ||||||||
\(915\) | 1.03003 | 0.0340516 | ||||||||
\(916\) | −3.37356 | −0.111466 | ||||||||
\(917\) | 23.6741 | 0.781788 | ||||||||
\(918\) | −39.1538 | −1.29227 | ||||||||
\(919\) | −40.6296 | −1.34025 | −0.670124 | − | 0.742249i | \(-0.733759\pi\) | ||||
−0.670124 | + | 0.742249i | \(0.733759\pi\) | |||||||
\(920\) | 0.116562 | 0.00384294 | ||||||||
\(921\) | 20.8632 | 0.687465 | ||||||||
\(922\) | 22.6927 | 0.747343 | ||||||||
\(923\) | −21.5300 | −0.708669 | ||||||||
\(924\) | −0.886423 | −0.0291612 | ||||||||
\(925\) | −10.3197 | −0.339309 | ||||||||
\(926\) | −5.49802 | −0.180676 | ||||||||
\(927\) | 11.0748 | 0.363743 | ||||||||
\(928\) | −7.25187 | −0.238054 | ||||||||
\(929\) | −38.1089 | −1.25031 | −0.625155 | − | 0.780500i | \(-0.714964\pi\) | ||||
−0.625155 | + | 0.780500i | \(0.714964\pi\) | |||||||
\(930\) | −0.285904 | −0.00937516 | ||||||||
\(931\) | 6.61238 | 0.216712 | ||||||||
\(932\) | 1.32699 | 0.0434670 | ||||||||
\(933\) | 21.7527 | 0.712152 | ||||||||
\(934\) | 6.32190 | 0.206859 | ||||||||
\(935\) | 6.57689 | 0.215087 | ||||||||
\(936\) | −16.2905 | −0.532471 | ||||||||
\(937\) | 20.9882 | 0.685653 | 0.342827 | − | 0.939399i | \(-0.388616\pi\) | ||||
0.342827 | + | 0.939399i | \(0.388616\pi\) | |||||||
\(938\) | −42.4958 | −1.38754 | ||||||||
\(939\) | 9.90106 | 0.323109 | ||||||||
\(940\) | 0.272761 | 0.00889648 | ||||||||
\(941\) | 0.271913 | 0.00886412 | 0.00443206 | − | 0.999990i | \(-0.498589\pi\) | ||||
0.00443206 | + | 0.999990i | \(0.498589\pi\) | |||||||
\(942\) | 15.6303 | 0.509263 | ||||||||
\(943\) | −0.753843 | −0.0245485 | ||||||||
\(944\) | −44.3588 | −1.44376 | ||||||||
\(945\) | −2.21170 | −0.0719467 | ||||||||
\(946\) | 47.4399 | 1.54241 | ||||||||
\(947\) | 18.9489 | 0.615756 | 0.307878 | − | 0.951426i | \(-0.400381\pi\) | ||||
0.307878 | + | 0.951426i | \(0.400381\pi\) | |||||||
\(948\) | −1.44648 | −0.0469795 | ||||||||
\(949\) | 11.6645 | 0.378645 | ||||||||
\(950\) | −50.6726 | −1.64404 | ||||||||
\(951\) | −9.39519 | −0.304660 | ||||||||
\(952\) | 51.7043 | 1.67575 | ||||||||
\(953\) | −2.67357 | −0.0866055 | −0.0433027 | − | 0.999062i | \(-0.513788\pi\) | ||||
−0.0433027 | + | 0.999062i | \(0.513788\pi\) | |||||||
\(954\) | 2.10147 | 0.0680375 | ||||||||
\(955\) | 0.0375445 | 0.00121491 | ||||||||
\(956\) | −0.779772 | −0.0252196 | ||||||||
\(957\) | 31.1432 | 1.00672 | ||||||||
\(958\) | 51.1063 | 1.65117 | ||||||||
\(959\) | 5.32327 | 0.171897 | ||||||||
\(960\) | 1.37685 | 0.0444378 | ||||||||
\(961\) | −29.3705 | −0.947437 | ||||||||
\(962\) | −6.47378 | −0.208723 | ||||||||
\(963\) | −37.2832 | −1.20143 | ||||||||
\(964\) | −1.19751 | −0.0385692 | ||||||||
\(965\) | 3.72054 | 0.119769 | ||||||||
\(966\) | −0.438042 | −0.0140938 | ||||||||
\(967\) | 20.1196 | 0.647004 | 0.323502 | − | 0.946227i | \(-0.395140\pi\) | ||||
0.323502 | + | 0.946227i | \(0.395140\pi\) | |||||||
\(968\) | 16.0054 | 0.514433 | ||||||||
\(969\) | 38.9916 | 1.25259 | ||||||||
\(970\) | 1.03182 | 0.0331298 | ||||||||
\(971\) | 15.9577 | 0.512106 | 0.256053 | − | 0.966663i | \(-0.417578\pi\) | ||||
0.256053 | + | 0.966663i | \(0.417578\pi\) | |||||||
\(972\) | 1.84899 | 0.0593063 | ||||||||
\(973\) | 13.8998 | 0.445609 | ||||||||
\(974\) | −34.2882 | −1.09866 | ||||||||
\(975\) | 8.13848 | 0.260640 | ||||||||
\(976\) | −23.5865 | −0.754985 | ||||||||
\(977\) | 42.1759 | 1.34933 | 0.674663 | − | 0.738126i | \(-0.264289\pi\) | ||||
0.674663 | + | 0.738126i | \(0.264289\pi\) | |||||||
\(978\) | −11.8106 | −0.377662 | ||||||||
\(979\) | 6.70051 | 0.214149 | ||||||||
\(980\) | −0.0242246 | −0.000773826 0 | ||||||||
\(981\) | −9.06639 | −0.289467 | ||||||||
\(982\) | 32.4852 | 1.03664 | ||||||||
\(983\) | −31.8772 | −1.01673 | −0.508363 | − | 0.861143i | \(-0.669749\pi\) | ||||
−0.508363 | + | 0.861143i | \(0.669749\pi\) | |||||||
\(984\) | −8.93577 | −0.284862 | ||||||||
\(985\) | −2.21143 | −0.0704619 | ||||||||
\(986\) | −104.083 | −3.31469 | ||||||||
\(987\) | −17.8899 | −0.569441 | ||||||||
\(988\) | 2.05709 | 0.0654449 | ||||||||
\(989\) | −1.51708 | −0.0482404 | ||||||||
\(990\) | 3.10015 | 0.0985291 | ||||||||
\(991\) | 28.4135 | 0.902584 | 0.451292 | − | 0.892376i | \(-0.350963\pi\) | ||||
0.451292 | + | 0.892376i | \(0.350963\pi\) | |||||||
\(992\) | −0.876534 | −0.0278300 | ||||||||
\(993\) | −6.15792 | −0.195416 | ||||||||
\(994\) | 32.2105 | 1.02166 | ||||||||
\(995\) | −2.60459 | −0.0825712 | ||||||||
\(996\) | 0.422894 | 0.0133999 | ||||||||
\(997\) | −38.9058 | −1.23216 | −0.616079 | − | 0.787684i | \(-0.711280\pi\) | ||||
−0.616079 | + | 0.787684i | \(0.711280\pi\) | |||||||
\(998\) | −37.2447 | −1.17896 | ||||||||
\(999\) | 8.28355 | 0.262080 |
(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 | 619.2.a.b.1.8 | ✓ | 30 | |
3.2 | odd | 2 | 5571.2.a.g.1.23 | 30 | |||
4.3 | odd | 2 | 9904.2.a.n.1.18 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
619.2.a.b.1.8 | ✓ | 30 | 1.1 | even | 1 | trivial | |
5571.2.a.g.1.23 | 30 | 3.2 | odd | 2 | |||
9904.2.a.n.1.18 | 30 | 4.3 | odd | 2 |