Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4025,2,Mod(1,4025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4025 = 5^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4025.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: | \(32.1397868136\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 3 x^{13} - 18 x^{12} + 58 x^{11} + 111 x^{10} - 414 x^{9} - 244 x^{8} + 1330 x^{7} - 27 x^{6} - 1853 x^{5} + 539 x^{4} + 891 x^{3} - 218 x^{2} - 133 x - 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.42992\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.42992 | −1.71821 | −0.859107 | − | 0.511795i | \(-0.828981\pi\) | ||||
−0.859107 | + | 0.511795i | \(0.828981\pi\) | |||||||
\(3\) | −3.09771 | −1.78847 | −0.894233 | − | 0.447601i | \(-0.852278\pi\) | ||||
−0.894233 | + | 0.447601i | \(0.852278\pi\) | |||||||
\(4\) | 3.90452 | 1.95226 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 7.52721 | 3.07297 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −4.62785 | −1.63619 | ||||||||
\(9\) | 6.59584 | 2.19861 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.16474 | 0.954205 | 0.477102 | − | 0.878848i | \(-0.341687\pi\) | ||||
0.477102 | + | 0.878848i | \(0.341687\pi\) | |||||||
\(12\) | −12.0951 | −3.49156 | ||||||||
\(13\) | 6.21716 | 1.72433 | 0.862164 | − | 0.506629i | \(-0.169108\pi\) | ||||
0.862164 | + | 0.506629i | \(0.169108\pi\) | |||||||
\(14\) | 2.42992 | 0.649424 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.43626 | 0.859065 | ||||||||
\(17\) | 2.97980 | 0.722708 | 0.361354 | − | 0.932429i | \(-0.382315\pi\) | ||||
0.361354 | + | 0.932429i | \(0.382315\pi\) | |||||||
\(18\) | −16.0274 | −3.77769 | ||||||||
\(19\) | −1.94284 | −0.445717 | −0.222859 | − | 0.974851i | \(-0.571539\pi\) | ||||
−0.222859 | + | 0.974851i | \(0.571539\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.09771 | 0.675977 | ||||||||
\(22\) | −7.69007 | −1.63953 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 14.3357 | 2.92627 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −15.1072 | −2.96277 | ||||||||
\(27\) | −11.1389 | −2.14368 | ||||||||
\(28\) | −3.90452 | −0.737886 | ||||||||
\(29\) | 4.69320 | 0.871506 | 0.435753 | − | 0.900066i | \(-0.356482\pi\) | ||||
0.435753 | + | 0.900066i | \(0.356482\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.0190312 | 0.00341810 | 0.00170905 | − | 0.999999i | \(-0.499456\pi\) | ||||
0.00170905 | + | 0.999999i | \(0.499456\pi\) | |||||||
\(32\) | 0.905845 | 0.160132 | ||||||||
\(33\) | −9.80346 | −1.70656 | ||||||||
\(34\) | −7.24069 | −1.24177 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 25.7536 | 4.29227 | ||||||||
\(37\) | −5.79370 | −0.952479 | −0.476239 | − | 0.879316i | \(-0.658000\pi\) | ||||
−0.476239 | + | 0.879316i | \(0.658000\pi\) | |||||||
\(38\) | 4.72094 | 0.765838 | ||||||||
\(39\) | −19.2590 | −3.08390 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.8089 | −1.68806 | −0.844030 | − | 0.536296i | \(-0.819823\pi\) | ||||
−0.844030 | + | 0.536296i | \(0.819823\pi\) | |||||||
\(42\) | −7.52721 | −1.16147 | ||||||||
\(43\) | −1.89992 | −0.289736 | −0.144868 | − | 0.989451i | \(-0.546276\pi\) | ||||
−0.144868 | + | 0.989451i | \(0.546276\pi\) | |||||||
\(44\) | 12.3568 | 1.86286 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.42992 | 0.358273 | ||||||||
\(47\) | 3.77308 | 0.550361 | 0.275180 | − | 0.961393i | \(-0.411262\pi\) | ||||
0.275180 | + | 0.961393i | \(0.411262\pi\) | |||||||
\(48\) | −10.6446 | −1.53641 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.23057 | −1.29254 | ||||||||
\(52\) | 24.2750 | 3.36634 | ||||||||
\(53\) | −10.7735 | −1.47986 | −0.739930 | − | 0.672684i | \(-0.765142\pi\) | ||||
−0.739930 | + | 0.672684i | \(0.765142\pi\) | |||||||
\(54\) | 27.0666 | 3.68330 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.62785 | 0.618422 | ||||||||
\(57\) | 6.01835 | 0.797151 | ||||||||
\(58\) | −11.4041 | −1.49743 | ||||||||
\(59\) | 2.73236 | 0.355724 | 0.177862 | − | 0.984055i | \(-0.443082\pi\) | ||||
0.177862 | + | 0.984055i | \(0.443082\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.62617 | −0.976431 | −0.488215 | − | 0.872723i | \(-0.662352\pi\) | ||||
−0.488215 | + | 0.872723i | \(0.662352\pi\) | |||||||
\(62\) | −0.0462443 | −0.00587303 | ||||||||
\(63\) | −6.59584 | −0.830997 | ||||||||
\(64\) | −9.07366 | −1.13421 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 23.8216 | 2.93224 | ||||||||
\(67\) | −4.77968 | −0.583931 | −0.291966 | − | 0.956429i | \(-0.594309\pi\) | ||||
−0.291966 | + | 0.956429i | \(0.594309\pi\) | |||||||
\(68\) | 11.6347 | 1.41092 | ||||||||
\(69\) | 3.09771 | 0.372921 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.11980 | −0.132896 | −0.0664479 | − | 0.997790i | \(-0.521167\pi\) | ||||
−0.0664479 | + | 0.997790i | \(0.521167\pi\) | |||||||
\(72\) | −30.5245 | −3.59735 | ||||||||
\(73\) | 13.4453 | 1.57366 | 0.786829 | − | 0.617171i | \(-0.211721\pi\) | ||||
0.786829 | + | 0.617171i | \(0.211721\pi\) | |||||||
\(74\) | 14.0783 | 1.63656 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.58585 | −0.870157 | ||||||||
\(77\) | −3.16474 | −0.360655 | ||||||||
\(78\) | 46.7978 | 5.29881 | ||||||||
\(79\) | −14.6291 | −1.64590 | −0.822949 | − | 0.568115i | \(-0.807673\pi\) | ||||
−0.822949 | + | 0.568115i | \(0.807673\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 14.7175 | 1.63528 | ||||||||
\(82\) | 26.2647 | 2.90045 | ||||||||
\(83\) | −2.38154 | −0.261408 | −0.130704 | − | 0.991421i | \(-0.541724\pi\) | ||||
−0.130704 | + | 0.991421i | \(0.541724\pi\) | |||||||
\(84\) | 12.0951 | 1.31968 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.61667 | 0.497828 | ||||||||
\(87\) | −14.5382 | −1.55866 | ||||||||
\(88\) | −14.6459 | −1.56126 | ||||||||
\(89\) | 1.55142 | 0.164450 | 0.0822252 | − | 0.996614i | \(-0.473797\pi\) | ||||
0.0822252 | + | 0.996614i | \(0.473797\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.21716 | −0.651735 | ||||||||
\(92\) | −3.90452 | −0.407075 | ||||||||
\(93\) | −0.0589531 | −0.00611315 | ||||||||
\(94\) | −9.16830 | −0.945638 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.80605 | −0.286391 | ||||||||
\(97\) | −9.22472 | −0.936628 | −0.468314 | − | 0.883562i | \(-0.655138\pi\) | ||||
−0.468314 | + | 0.883562i | \(0.655138\pi\) | |||||||
\(98\) | −2.42992 | −0.245459 | ||||||||
\(99\) | 20.8741 | 2.09793 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.1201 | −1.30550 | −0.652752 | − | 0.757572i | \(-0.726385\pi\) | ||||
−0.652752 | + | 0.757572i | \(0.726385\pi\) | |||||||
\(102\) | 22.4296 | 2.22086 | ||||||||
\(103\) | −20.0577 | −1.97634 | −0.988171 | − | 0.153355i | \(-0.950992\pi\) | ||||
−0.988171 | + | 0.153355i | \(0.950992\pi\) | |||||||
\(104\) | −28.7720 | −2.82133 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 26.1789 | 2.54272 | ||||||||
\(107\) | −0.297274 | −0.0287386 | −0.0143693 | − | 0.999897i | \(-0.504574\pi\) | ||||
−0.0143693 | + | 0.999897i | \(0.504574\pi\) | |||||||
\(108\) | −43.4920 | −4.18502 | ||||||||
\(109\) | 12.0661 | 1.15573 | 0.577863 | − | 0.816134i | \(-0.303887\pi\) | ||||
0.577863 | + | 0.816134i | \(0.303887\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 17.9472 | 1.70348 | ||||||||
\(112\) | −3.43626 | −0.324696 | ||||||||
\(113\) | 18.9079 | 1.77870 | 0.889352 | − | 0.457223i | \(-0.151156\pi\) | ||||
0.889352 | + | 0.457223i | \(0.151156\pi\) | |||||||
\(114\) | −14.6241 | −1.36968 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 18.3247 | 1.70141 | ||||||||
\(117\) | 41.0073 | 3.79113 | ||||||||
\(118\) | −6.63943 | −0.611209 | ||||||||
\(119\) | −2.97980 | −0.273158 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.984428 | −0.0894935 | ||||||||
\(122\) | 18.5310 | 1.67772 | ||||||||
\(123\) | 33.4828 | 3.01904 | ||||||||
\(124\) | 0.0743076 | 0.00667302 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 16.0274 | 1.42783 | ||||||||
\(127\) | −6.89872 | −0.612162 | −0.306081 | − | 0.952005i | \(-0.599018\pi\) | ||||
−0.306081 | + | 0.952005i | \(0.599018\pi\) | |||||||
\(128\) | 20.2366 | 1.78868 | ||||||||
\(129\) | 5.88542 | 0.518183 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.82144 | 0.159140 | 0.0795701 | − | 0.996829i | \(-0.474645\pi\) | ||||
0.0795701 | + | 0.996829i | \(0.474645\pi\) | |||||||
\(132\) | −38.2778 | −3.33166 | ||||||||
\(133\) | 1.94284 | 0.168465 | ||||||||
\(134\) | 11.6143 | 1.00332 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −13.7901 | −1.18249 | ||||||||
\(137\) | 15.1089 | 1.29084 | 0.645418 | − | 0.763829i | \(-0.276683\pi\) | ||||
0.645418 | + | 0.763829i | \(0.276683\pi\) | |||||||
\(138\) | −7.52721 | −0.640758 | ||||||||
\(139\) | −9.71464 | −0.823985 | −0.411993 | − | 0.911187i | \(-0.635167\pi\) | ||||
−0.411993 | + | 0.911187i | \(0.635167\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.6879 | −0.984301 | ||||||||
\(142\) | 2.72103 | 0.228343 | ||||||||
\(143\) | 19.6757 | 1.64536 | ||||||||
\(144\) | 22.6650 | 1.88875 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −32.6711 | −2.70388 | ||||||||
\(147\) | −3.09771 | −0.255495 | ||||||||
\(148\) | −22.6217 | −1.85949 | ||||||||
\(149\) | 17.4977 | 1.43346 | 0.716732 | − | 0.697349i | \(-0.245637\pi\) | ||||
0.716732 | + | 0.697349i | \(0.245637\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.6454 | −1.27321 | −0.636603 | − | 0.771191i | \(-0.719661\pi\) | ||||
−0.636603 | + | 0.771191i | \(0.719661\pi\) | |||||||
\(152\) | 8.99115 | 0.729279 | ||||||||
\(153\) | 19.6543 | 1.58895 | ||||||||
\(154\) | 7.69007 | 0.619684 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −75.1971 | −6.02059 | ||||||||
\(157\) | −2.79894 | −0.223380 | −0.111690 | − | 0.993743i | \(-0.535626\pi\) | ||||
−0.111690 | + | 0.993743i | \(0.535626\pi\) | |||||||
\(158\) | 35.5475 | 2.82801 | ||||||||
\(159\) | 33.3734 | 2.64668 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | −35.7625 | −2.80977 | ||||||||
\(163\) | 12.0150 | 0.941085 | 0.470543 | − | 0.882377i | \(-0.344058\pi\) | ||||
0.470543 | + | 0.882377i | \(0.344058\pi\) | |||||||
\(164\) | −42.2035 | −3.29554 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.78697 | 0.449156 | ||||||||
\(167\) | −15.7187 | −1.21635 | −0.608175 | − | 0.793803i | \(-0.708098\pi\) | ||||
−0.608175 | + | 0.793803i | \(0.708098\pi\) | |||||||
\(168\) | −14.3357 | −1.10603 | ||||||||
\(169\) | 25.6530 | 1.97331 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.8146 | −0.979960 | ||||||||
\(172\) | −7.41830 | −0.565640 | ||||||||
\(173\) | −12.9561 | −0.985037 | −0.492519 | − | 0.870302i | \(-0.663924\pi\) | ||||
−0.492519 | + | 0.870302i | \(0.663924\pi\) | |||||||
\(174\) | 35.3267 | 2.67811 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 10.8749 | 0.819724 | ||||||||
\(177\) | −8.46409 | −0.636200 | ||||||||
\(178\) | −3.76983 | −0.282561 | ||||||||
\(179\) | 10.6322 | 0.794690 | 0.397345 | − | 0.917669i | \(-0.369932\pi\) | ||||
0.397345 | + | 0.917669i | \(0.369932\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.5172 | −1.59936 | −0.799679 | − | 0.600427i | \(-0.794997\pi\) | ||||
−0.799679 | + | 0.600427i | \(0.794997\pi\) | |||||||
\(182\) | 15.1072 | 1.11982 | ||||||||
\(183\) | 23.6237 | 1.74631 | ||||||||
\(184\) | 4.62785 | 0.341169 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.143252 | 0.0105037 | ||||||||
\(187\) | 9.43029 | 0.689611 | ||||||||
\(188\) | 14.7321 | 1.07445 | ||||||||
\(189\) | 11.1389 | 0.810234 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.9054 | −1.44030 | −0.720151 | − | 0.693817i | \(-0.755927\pi\) | ||||
−0.720151 | + | 0.693817i | \(0.755927\pi\) | |||||||
\(192\) | 28.1076 | 2.02849 | ||||||||
\(193\) | 26.1721 | 1.88391 | 0.941955 | − | 0.335740i | \(-0.108986\pi\) | ||||
0.941955 | + | 0.335740i | \(0.108986\pi\) | |||||||
\(194\) | 22.4153 | 1.60933 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.90452 | 0.278895 | ||||||||
\(197\) | −23.2832 | −1.65886 | −0.829428 | − | 0.558613i | \(-0.811334\pi\) | ||||
−0.829428 | + | 0.558613i | \(0.811334\pi\) | |||||||
\(198\) | −50.7224 | −3.60469 | ||||||||
\(199\) | −2.31819 | −0.164332 | −0.0821660 | − | 0.996619i | \(-0.526184\pi\) | ||||
−0.0821660 | + | 0.996619i | \(0.526184\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.8061 | 1.04434 | ||||||||
\(202\) | 31.8809 | 2.24313 | ||||||||
\(203\) | −4.69320 | −0.329398 | ||||||||
\(204\) | −36.0410 | −2.52337 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 48.7386 | 3.39578 | ||||||||
\(207\) | −6.59584 | −0.458442 | ||||||||
\(208\) | 21.3638 | 1.48131 | ||||||||
\(209\) | −6.14857 | −0.425306 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.55629 | 0.589039 | 0.294520 | − | 0.955645i | \(-0.404840\pi\) | ||||
0.294520 | + | 0.955645i | \(0.404840\pi\) | |||||||
\(212\) | −42.0656 | −2.88908 | ||||||||
\(213\) | 3.46882 | 0.237680 | ||||||||
\(214\) | 0.722354 | 0.0493791 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 51.5490 | 3.50746 | ||||||||
\(217\) | −0.0190312 | −0.00129192 | ||||||||
\(218\) | −29.3198 | −1.98579 | ||||||||
\(219\) | −41.6498 | −2.81444 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.5259 | 1.24619 | ||||||||
\(222\) | −43.6104 | −2.92694 | ||||||||
\(223\) | −1.46265 | −0.0979463 | −0.0489732 | − | 0.998800i | \(-0.515595\pi\) | ||||
−0.0489732 | + | 0.998800i | \(0.515595\pi\) | |||||||
\(224\) | −0.905845 | −0.0605243 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −45.9447 | −3.05620 | ||||||||
\(227\) | 11.0295 | 0.732055 | 0.366027 | − | 0.930604i | \(-0.380718\pi\) | ||||
0.366027 | + | 0.930604i | \(0.380718\pi\) | |||||||
\(228\) | 23.4988 | 1.55625 | ||||||||
\(229\) | 18.1813 | 1.20145 | 0.600726 | − | 0.799455i | \(-0.294878\pi\) | ||||
0.600726 | + | 0.799455i | \(0.294878\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.80346 | 0.645020 | ||||||||
\(232\) | −21.7194 | −1.42595 | ||||||||
\(233\) | 14.6633 | 0.960625 | 0.480312 | − | 0.877097i | \(-0.340523\pi\) | ||||
0.480312 | + | 0.877097i | \(0.340523\pi\) | |||||||
\(234\) | −99.6447 | −6.51398 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 10.6686 | 0.694466 | ||||||||
\(237\) | 45.3167 | 2.94363 | ||||||||
\(238\) | 7.24069 | 0.469344 | ||||||||
\(239\) | 22.9003 | 1.48130 | 0.740648 | − | 0.671893i | \(-0.234519\pi\) | ||||
0.740648 | + | 0.671893i | \(0.234519\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.07771 | 0.262668 | 0.131334 | − | 0.991338i | \(-0.458074\pi\) | ||||
0.131334 | + | 0.991338i | \(0.458074\pi\) | |||||||
\(242\) | 2.39208 | 0.153769 | ||||||||
\(243\) | −12.1741 | −0.780971 | ||||||||
\(244\) | −29.7766 | −1.90625 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −81.3605 | −5.18736 | ||||||||
\(247\) | −12.0789 | −0.768563 | ||||||||
\(248\) | −0.0880733 | −0.00559266 | ||||||||
\(249\) | 7.37734 | 0.467520 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.6618 | 1.30416 | 0.652081 | − | 0.758149i | \(-0.273896\pi\) | ||||
0.652081 | + | 0.758149i | \(0.273896\pi\) | |||||||
\(252\) | −25.7536 | −1.62232 | ||||||||
\(253\) | −3.16474 | −0.198965 | ||||||||
\(254\) | 16.7634 | 1.05183 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −31.0260 | −1.93913 | ||||||||
\(257\) | −19.9061 | −1.24171 | −0.620855 | − | 0.783926i | \(-0.713214\pi\) | ||||
−0.620855 | + | 0.783926i | \(0.713214\pi\) | |||||||
\(258\) | −14.3011 | −0.890349 | ||||||||
\(259\) | 5.79370 | 0.360003 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 30.9556 | 1.91610 | ||||||||
\(262\) | −4.42596 | −0.273437 | ||||||||
\(263\) | −6.87878 | −0.424164 | −0.212082 | − | 0.977252i | \(-0.568024\pi\) | ||||
−0.212082 | + | 0.977252i | \(0.568024\pi\) | |||||||
\(264\) | 45.3689 | 2.79226 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.72094 | −0.289460 | ||||||||
\(267\) | −4.80586 | −0.294114 | ||||||||
\(268\) | −18.6624 | −1.13999 | ||||||||
\(269\) | 19.6883 | 1.20041 | 0.600207 | − | 0.799845i | \(-0.295085\pi\) | ||||
0.600207 | + | 0.799845i | \(0.295085\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.0104 | −1.82300 | −0.911502 | − | 0.411296i | \(-0.865076\pi\) | ||||
−0.911502 | + | 0.411296i | \(0.865076\pi\) | |||||||
\(272\) | 10.2394 | 0.620853 | ||||||||
\(273\) | 19.2590 | 1.16561 | ||||||||
\(274\) | −36.7134 | −2.21793 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 12.0951 | 0.728040 | ||||||||
\(277\) | −23.6208 | −1.41924 | −0.709619 | − | 0.704585i | \(-0.751133\pi\) | ||||
−0.709619 | + | 0.704585i | \(0.751133\pi\) | |||||||
\(278\) | 23.6058 | 1.41578 | ||||||||
\(279\) | 0.125526 | 0.00751507 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.5328 | 0.866957 | 0.433478 | − | 0.901164i | \(-0.357286\pi\) | ||||
0.433478 | + | 0.901164i | \(0.357286\pi\) | |||||||
\(282\) | 28.4008 | 1.69124 | ||||||||
\(283\) | −28.5671 | −1.69814 | −0.849068 | − | 0.528284i | \(-0.822836\pi\) | ||||
−0.849068 | + | 0.528284i | \(0.822836\pi\) | |||||||
\(284\) | −4.37228 | −0.259447 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −47.8104 | −2.82709 | ||||||||
\(287\) | 10.8089 | 0.638027 | ||||||||
\(288\) | 5.97481 | 0.352069 | ||||||||
\(289\) | −8.12078 | −0.477693 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 28.5755 | 1.67513 | ||||||||
\(292\) | 52.4977 | 3.07219 | ||||||||
\(293\) | −23.8859 | −1.39543 | −0.697713 | − | 0.716377i | \(-0.745799\pi\) | ||||
−0.697713 | + | 0.716377i | \(0.745799\pi\) | |||||||
\(294\) | 7.52721 | 0.438996 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 26.8124 | 1.55844 | ||||||||
\(297\) | −35.2516 | −2.04551 | ||||||||
\(298\) | −42.5179 | −2.46300 | ||||||||
\(299\) | −6.21716 | −0.359547 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.89992 | 0.109510 | ||||||||
\(302\) | 38.0172 | 2.18764 | ||||||||
\(303\) | 40.6425 | 2.33485 | ||||||||
\(304\) | −6.67609 | −0.382900 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −47.7584 | −2.73017 | ||||||||
\(307\) | −21.8334 | −1.24610 | −0.623048 | − | 0.782184i | \(-0.714106\pi\) | ||||
−0.623048 | + | 0.782184i | \(0.714106\pi\) | |||||||
\(308\) | −12.3568 | −0.704094 | ||||||||
\(309\) | 62.1330 | 3.53462 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.50116 | 0.141828 | 0.0709139 | − | 0.997482i | \(-0.477408\pi\) | ||||
0.0709139 | + | 0.997482i | \(0.477408\pi\) | |||||||
\(312\) | 89.1276 | 5.04586 | ||||||||
\(313\) | −19.9519 | −1.12775 | −0.563873 | − | 0.825862i | \(-0.690689\pi\) | ||||
−0.563873 | + | 0.825862i | \(0.690689\pi\) | |||||||
\(314\) | 6.80121 | 0.383815 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −57.1195 | −3.21323 | ||||||||
\(317\) | −1.30854 | −0.0734952 | −0.0367476 | − | 0.999325i | \(-0.511700\pi\) | ||||
−0.0367476 | + | 0.999325i | \(0.511700\pi\) | |||||||
\(318\) | −81.0947 | −4.54757 | ||||||||
\(319\) | 14.8528 | 0.831595 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.920871 | 0.0513980 | ||||||||
\(322\) | −2.42992 | −0.135414 | ||||||||
\(323\) | −5.78927 | −0.322124 | ||||||||
\(324\) | 57.4650 | 3.19250 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −29.1955 | −1.61699 | ||||||||
\(327\) | −37.3775 | −2.06698 | ||||||||
\(328\) | 50.0217 | 2.76199 | ||||||||
\(329\) | −3.77308 | −0.208017 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.5899 | −1.24165 | −0.620826 | − | 0.783948i | \(-0.713203\pi\) | ||||
−0.620826 | + | 0.783948i | \(0.713203\pi\) | |||||||
\(332\) | −9.29880 | −0.510338 | ||||||||
\(333\) | −38.2143 | −2.09413 | ||||||||
\(334\) | 38.1952 | 2.08995 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 10.6446 | 0.580708 | ||||||||
\(337\) | 25.4899 | 1.38852 | 0.694261 | − | 0.719724i | \(-0.255731\pi\) | ||||
0.694261 | + | 0.719724i | \(0.255731\pi\) | |||||||
\(338\) | −62.3349 | −3.39057 | ||||||||
\(339\) | −58.5712 | −3.18115 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.0602287 | 0.00326157 | ||||||||
\(342\) | 31.1386 | 1.68378 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 8.79256 | 0.474063 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 31.4824 | 1.69251 | ||||||||
\(347\) | −2.20649 | −0.118451 | −0.0592254 | − | 0.998245i | \(-0.518863\pi\) | ||||
−0.0592254 | + | 0.998245i | \(0.518863\pi\) | |||||||
\(348\) | −56.7648 | −3.04291 | ||||||||
\(349\) | −19.5526 | −1.04663 | −0.523314 | − | 0.852140i | \(-0.675305\pi\) | ||||
−0.523314 | + | 0.852140i | \(0.675305\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −69.2521 | −3.69640 | ||||||||
\(352\) | 2.86676 | 0.152799 | ||||||||
\(353\) | −22.4360 | −1.19415 | −0.597074 | − | 0.802186i | \(-0.703670\pi\) | ||||
−0.597074 | + | 0.802186i | \(0.703670\pi\) | |||||||
\(354\) | 20.5671 | 1.09313 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.05756 | 0.321050 | ||||||||
\(357\) | 9.23057 | 0.488534 | ||||||||
\(358\) | −25.8355 | −1.36545 | ||||||||
\(359\) | −31.0915 | −1.64095 | −0.820474 | − | 0.571684i | \(-0.806290\pi\) | ||||
−0.820474 | + | 0.571684i | \(0.806290\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.2254 | −0.801336 | ||||||||
\(362\) | 52.2851 | 2.74804 | ||||||||
\(363\) | 3.04948 | 0.160056 | ||||||||
\(364\) | −24.2750 | −1.27236 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −57.4037 | −3.00054 | ||||||||
\(367\) | −0.365949 | −0.0191024 | −0.00955119 | − | 0.999954i | \(-0.503040\pi\) | ||||
−0.00955119 | + | 0.999954i | \(0.503040\pi\) | |||||||
\(368\) | −3.43626 | −0.179127 | ||||||||
\(369\) | −71.2935 | −3.71139 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.7735 | 0.559335 | ||||||||
\(372\) | −0.230184 | −0.0119345 | ||||||||
\(373\) | −2.18350 | −0.113058 | −0.0565288 | − | 0.998401i | \(-0.518003\pi\) | ||||
−0.0565288 | + | 0.998401i | \(0.518003\pi\) | |||||||
\(374\) | −22.9149 | −1.18490 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −17.4612 | −0.900495 | ||||||||
\(377\) | 29.1784 | 1.50276 | ||||||||
\(378\) | −27.0666 | −1.39216 | ||||||||
\(379\) | −13.9764 | −0.717918 | −0.358959 | − | 0.933353i | \(-0.616868\pi\) | ||||
−0.358959 | + | 0.933353i | \(0.616868\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 21.3703 | 1.09483 | ||||||||
\(382\) | 48.3685 | 2.47475 | ||||||||
\(383\) | 15.8694 | 0.810889 | 0.405445 | − | 0.914120i | \(-0.367117\pi\) | ||||
0.405445 | + | 0.914120i | \(0.367117\pi\) | |||||||
\(384\) | −62.6872 | −3.19899 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −63.5962 | −3.23696 | ||||||||
\(387\) | −12.5316 | −0.637016 | ||||||||
\(388\) | −36.0181 | −1.82854 | ||||||||
\(389\) | 9.38084 | 0.475627 | 0.237814 | − | 0.971311i | \(-0.423569\pi\) | ||||
0.237814 | + | 0.971311i | \(0.423569\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.97980 | −0.150695 | ||||||||
\(392\) | −4.62785 | −0.233742 | ||||||||
\(393\) | −5.64231 | −0.284617 | ||||||||
\(394\) | 56.5763 | 2.85027 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 81.5034 | 4.09570 | ||||||||
\(397\) | −23.0501 | −1.15685 | −0.578424 | − | 0.815736i | \(-0.696332\pi\) | ||||
−0.578424 | + | 0.815736i | \(0.696332\pi\) | |||||||
\(398\) | 5.63301 | 0.282358 | ||||||||
\(399\) | −6.01835 | −0.301295 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.9886 | 0.748495 | 0.374248 | − | 0.927329i | \(-0.377901\pi\) | ||||
0.374248 | + | 0.927329i | \(0.377901\pi\) | |||||||
\(402\) | −35.9777 | −1.79440 | ||||||||
\(403\) | 0.118320 | 0.00589392 | ||||||||
\(404\) | −51.2279 | −2.54868 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 11.4041 | 0.565977 | ||||||||
\(407\) | −18.3356 | −0.908860 | ||||||||
\(408\) | 42.7177 | 2.11484 | ||||||||
\(409\) | 2.73183 | 0.135080 | 0.0675402 | − | 0.997717i | \(-0.478485\pi\) | ||||
0.0675402 | + | 0.997717i | \(0.478485\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −46.8029 | −2.30862 | ||||||||
\(412\) | −78.3157 | −3.85834 | ||||||||
\(413\) | −2.73236 | −0.134451 | ||||||||
\(414\) | 16.0274 | 0.787702 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.63178 | 0.276121 | ||||||||
\(417\) | 30.0932 | 1.47367 | ||||||||
\(418\) | 14.9406 | 0.730766 | ||||||||
\(419\) | 10.8024 | 0.527734 | 0.263867 | − | 0.964559i | \(-0.415002\pi\) | ||||
0.263867 | + | 0.964559i | \(0.415002\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.8658 | 1.45557 | 0.727786 | − | 0.685805i | \(-0.240550\pi\) | ||||
0.727786 | + | 0.685805i | \(0.240550\pi\) | |||||||
\(422\) | −20.7911 | −1.01210 | ||||||||
\(423\) | 24.8866 | 1.21003 | ||||||||
\(424\) | 49.8583 | 2.42133 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −8.42896 | −0.408384 | ||||||||
\(427\) | 7.62617 | 0.369056 | ||||||||
\(428\) | −1.16072 | −0.0561053 | ||||||||
\(429\) | −60.9496 | −2.94268 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.2852 | −1.31428 | −0.657142 | − | 0.753767i | \(-0.728235\pi\) | ||||
−0.657142 | + | 0.753767i | \(0.728235\pi\) | |||||||
\(432\) | −38.2761 | −1.84156 | ||||||||
\(433\) | −2.14596 | −0.103128 | −0.0515642 | − | 0.998670i | \(-0.516421\pi\) | ||||
−0.0515642 | + | 0.998670i | \(0.516421\pi\) | |||||||
\(434\) | 0.0462443 | 0.00221980 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 47.1125 | 2.25628 | ||||||||
\(437\) | 1.94284 | 0.0929385 | ||||||||
\(438\) | 101.206 | 4.83580 | ||||||||
\(439\) | −17.9322 | −0.855857 | −0.427928 | − | 0.903813i | \(-0.640756\pi\) | ||||
−0.427928 | + | 0.903813i | \(0.640756\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.59584 | 0.314087 | ||||||||
\(442\) | −45.0165 | −2.14122 | ||||||||
\(443\) | 0.703849 | 0.0334409 | 0.0167204 | − | 0.999860i | \(-0.494677\pi\) | ||||
0.0167204 | + | 0.999860i | \(0.494677\pi\) | |||||||
\(444\) | 70.0754 | 3.32563 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.55413 | 0.168293 | ||||||||
\(447\) | −54.2027 | −2.56370 | ||||||||
\(448\) | 9.07366 | 0.428690 | ||||||||
\(449\) | 2.27750 | 0.107482 | 0.0537410 | − | 0.998555i | \(-0.482885\pi\) | ||||
0.0537410 | + | 0.998555i | \(0.482885\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −34.2072 | −1.61075 | ||||||||
\(452\) | 73.8263 | 3.47250 | ||||||||
\(453\) | 48.4651 | 2.27709 | ||||||||
\(454\) | −26.8009 | −1.25783 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −27.8520 | −1.30429 | ||||||||
\(457\) | 17.6083 | 0.823684 | 0.411842 | − | 0.911255i | \(-0.364886\pi\) | ||||
0.411842 | + | 0.911255i | \(0.364886\pi\) | |||||||
\(458\) | −44.1791 | −2.06435 | ||||||||
\(459\) | −33.1916 | −1.54925 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.1980 | 1.35989 | 0.679943 | − | 0.733265i | \(-0.262005\pi\) | ||||
0.679943 | + | 0.733265i | \(0.262005\pi\) | |||||||
\(462\) | −23.8216 | −1.10828 | ||||||||
\(463\) | −9.77411 | −0.454241 | −0.227121 | − | 0.973867i | \(-0.572931\pi\) | ||||
−0.227121 | + | 0.973867i | \(0.572931\pi\) | |||||||
\(464\) | 16.1271 | 0.748680 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −35.6307 | −1.65056 | ||||||||
\(467\) | −14.3400 | −0.663578 | −0.331789 | − | 0.943354i | \(-0.607652\pi\) | ||||
−0.331789 | + | 0.943354i | \(0.607652\pi\) | |||||||
\(468\) | 160.114 | 7.40128 | ||||||||
\(469\) | 4.77968 | 0.220705 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.67032 | 0.399507 | ||||||||
\(472\) | −12.6450 | −0.582032 | ||||||||
\(473\) | −6.01276 | −0.276467 | ||||||||
\(474\) | −110.116 | −5.05780 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −11.6347 | −0.533276 | ||||||||
\(477\) | −71.0605 | −3.25364 | ||||||||
\(478\) | −55.6459 | −2.54519 | ||||||||
\(479\) | 3.59305 | 0.164171 | 0.0820853 | − | 0.996625i | \(-0.473842\pi\) | ||||
0.0820853 | + | 0.996625i | \(0.473842\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −36.0204 | −1.64239 | ||||||||
\(482\) | −9.90851 | −0.451320 | ||||||||
\(483\) | −3.09771 | −0.140951 | ||||||||
\(484\) | −3.84372 | −0.174715 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 29.5822 | 1.34188 | ||||||||
\(487\) | −13.7061 | −0.621081 | −0.310540 | − | 0.950560i | \(-0.600510\pi\) | ||||
−0.310540 | + | 0.950560i | \(0.600510\pi\) | |||||||
\(488\) | 35.2927 | 1.59763 | ||||||||
\(489\) | −37.2190 | −1.68310 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.45921 | −0.336629 | −0.168315 | − | 0.985733i | \(-0.553832\pi\) | ||||
−0.168315 | + | 0.985733i | \(0.553832\pi\) | |||||||
\(492\) | 130.734 | 5.89396 | ||||||||
\(493\) | 13.9848 | 0.629844 | ||||||||
\(494\) | 29.3508 | 1.32056 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.0653960 | 0.00293637 | ||||||||
\(497\) | 1.11980 | 0.0502299 | ||||||||
\(498\) | −17.9264 | −0.803300 | ||||||||
\(499\) | −26.5609 | −1.18903 | −0.594515 | − | 0.804085i | \(-0.702656\pi\) | ||||
−0.594515 | + | 0.804085i | \(0.702656\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 48.6921 | 2.17540 | ||||||||
\(502\) | −50.2066 | −2.24083 | ||||||||
\(503\) | 16.6429 | 0.742072 | 0.371036 | − | 0.928618i | \(-0.379003\pi\) | ||||
0.371036 | + | 0.928618i | \(0.379003\pi\) | |||||||
\(504\) | 30.5245 | 1.35967 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 7.69007 | 0.341865 | ||||||||
\(507\) | −79.4657 | −3.52920 | ||||||||
\(508\) | −26.9362 | −1.19510 | ||||||||
\(509\) | −28.9693 | −1.28404 | −0.642020 | − | 0.766688i | \(-0.721904\pi\) | ||||
−0.642020 | + | 0.766688i | \(0.721904\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.4453 | −0.594787 | ||||||||
\(512\) | 34.9177 | 1.54316 | ||||||||
\(513\) | 21.6410 | 0.955474 | ||||||||
\(514\) | 48.3703 | 2.13352 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 22.9798 | 1.01163 | ||||||||
\(517\) | 11.9408 | 0.525157 | ||||||||
\(518\) | −14.0783 | −0.618563 | ||||||||
\(519\) | 40.1344 | 1.76171 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.7916 | −1.17376 | −0.586881 | − | 0.809673i | \(-0.699644\pi\) | ||||
−0.586881 | + | 0.809673i | \(0.699644\pi\) | |||||||
\(522\) | −75.2197 | −3.29228 | ||||||||
\(523\) | −5.81521 | −0.254281 | −0.127141 | − | 0.991885i | \(-0.540580\pi\) | ||||
−0.127141 | + | 0.991885i | \(0.540580\pi\) | |||||||
\(524\) | 7.11186 | 0.310683 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.7149 | 0.728805 | ||||||||
\(527\) | 0.0567091 | 0.00247029 | ||||||||
\(528\) | −33.6872 | −1.46605 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.0222 | 0.782098 | ||||||||
\(532\) | 7.58585 | 0.328888 | ||||||||
\(533\) | −67.2004 | −2.91077 | ||||||||
\(534\) | 11.6779 | 0.505351 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 22.1196 | 0.955423 | ||||||||
\(537\) | −32.9356 | −1.42128 | ||||||||
\(538\) | −47.8409 | −2.06257 | ||||||||
\(539\) | 3.16474 | 0.136315 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.58459 | −0.197107 | −0.0985535 | − | 0.995132i | \(-0.531422\pi\) | ||||
−0.0985535 | + | 0.995132i | \(0.531422\pi\) | |||||||
\(542\) | 72.9230 | 3.13231 | ||||||||
\(543\) | 66.6540 | 2.86040 | ||||||||
\(544\) | 2.69924 | 0.115729 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −46.7978 | −2.00276 | ||||||||
\(547\) | 18.9427 | 0.809933 | 0.404967 | − | 0.914331i | \(-0.367283\pi\) | ||||
0.404967 | + | 0.914331i | \(0.367283\pi\) | |||||||
\(548\) | 58.9929 | 2.52005 | ||||||||
\(549\) | −50.3009 | −2.14679 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.11813 | −0.388445 | ||||||||
\(552\) | −14.3357 | −0.610170 | ||||||||
\(553\) | 14.6291 | 0.622091 | ||||||||
\(554\) | 57.3968 | 2.43856 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −37.9311 | −1.60864 | ||||||||
\(557\) | 0.0110934 | 0.000470043 0 | 0.000235022 | − | 1.00000i | \(-0.499925\pi\) | ||||
0.000235022 | 1.00000i | \(0.499925\pi\) | ||||||||
\(558\) | −0.305020 | −0.0129125 | ||||||||
\(559\) | −11.8121 | −0.499600 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −29.2124 | −1.23335 | ||||||||
\(562\) | −35.3137 | −1.48962 | ||||||||
\(563\) | 3.35339 | 0.141329 | 0.0706643 | − | 0.997500i | \(-0.477488\pi\) | ||||
0.0706643 | + | 0.997500i | \(0.477488\pi\) | |||||||
\(564\) | −45.6358 | −1.92161 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 69.4158 | 2.91776 | ||||||||
\(567\) | −14.7175 | −0.618079 | ||||||||
\(568\) | 5.18226 | 0.217443 | ||||||||
\(569\) | −17.9798 | −0.753753 | −0.376876 | − | 0.926264i | \(-0.623002\pi\) | ||||
−0.376876 | + | 0.926264i | \(0.623002\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.8932 | 1.46023 | 0.730117 | − | 0.683322i | \(-0.239466\pi\) | ||||
0.730117 | + | 0.683322i | \(0.239466\pi\) | |||||||
\(572\) | 76.8241 | 3.21218 | ||||||||
\(573\) | 61.6612 | 2.57593 | ||||||||
\(574\) | −26.2647 | −1.09627 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −59.8483 | −2.49368 | ||||||||
\(577\) | 3.05779 | 0.127298 | 0.0636488 | − | 0.997972i | \(-0.479726\pi\) | ||||
0.0636488 | + | 0.997972i | \(0.479726\pi\) | |||||||
\(578\) | 19.7329 | 0.820779 | ||||||||
\(579\) | −81.0737 | −3.36931 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.38154 | 0.0988031 | ||||||||
\(582\) | −69.4363 | −2.87823 | ||||||||
\(583\) | −34.0955 | −1.41209 | ||||||||
\(584\) | −62.2230 | −2.57481 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 58.0408 | 2.39764 | ||||||||
\(587\) | 1.13533 | 0.0468600 | 0.0234300 | − | 0.999725i | \(-0.492541\pi\) | ||||
0.0234300 | + | 0.999725i | \(0.492541\pi\) | |||||||
\(588\) | −12.0951 | −0.498794 | ||||||||
\(589\) | −0.0369745 | −0.00152351 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 72.1246 | 2.96681 | ||||||||
\(592\) | −19.9087 | −0.818241 | ||||||||
\(593\) | −33.4469 | −1.37350 | −0.686749 | − | 0.726895i | \(-0.740963\pi\) | ||||
−0.686749 | + | 0.726895i | \(0.740963\pi\) | |||||||
\(594\) | 85.6587 | 3.51462 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 68.3200 | 2.79850 | ||||||||
\(597\) | 7.18108 | 0.293902 | ||||||||
\(598\) | 15.1072 | 0.617780 | ||||||||
\(599\) | 13.7401 | 0.561405 | 0.280702 | − | 0.959795i | \(-0.409433\pi\) | ||||
0.280702 | + | 0.959795i | \(0.409433\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.5817 | 0.757963 | 0.378982 | − | 0.925404i | \(-0.376274\pi\) | ||||
0.378982 | + | 0.925404i | \(0.376274\pi\) | |||||||
\(602\) | −4.61667 | −0.188161 | ||||||||
\(603\) | −31.5260 | −1.28384 | ||||||||
\(604\) | −61.0879 | −2.48563 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −98.7580 | −4.01177 | ||||||||
\(607\) | 19.3287 | 0.784528 | 0.392264 | − | 0.919853i | \(-0.371692\pi\) | ||||
0.392264 | + | 0.919853i | \(0.371692\pi\) | |||||||
\(608\) | −1.75991 | −0.0713738 | ||||||||
\(609\) | 14.5382 | 0.589118 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.4578 | 0.949002 | ||||||||
\(612\) | 76.7406 | 3.10206 | ||||||||
\(613\) | 11.4780 | 0.463591 | 0.231796 | − | 0.972764i | \(-0.425540\pi\) | ||||
0.231796 | + | 0.972764i | \(0.425540\pi\) | |||||||
\(614\) | 53.0534 | 2.14106 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 14.6459 | 0.590101 | ||||||||
\(617\) | −0.0442936 | −0.00178319 | −0.000891596 | − | 1.00000i | \(-0.500284\pi\) | ||||
−0.000891596 | 1.00000i | \(0.500284\pi\) | ||||||||
\(618\) | −150.978 | −6.07324 | ||||||||
\(619\) | 44.4063 | 1.78484 | 0.892419 | − | 0.451207i | \(-0.149006\pi\) | ||||
0.892419 | + | 0.451207i | \(0.149006\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.1389 | 0.446988 | ||||||||
\(622\) | −6.07762 | −0.243690 | ||||||||
\(623\) | −1.55142 | −0.0621564 | ||||||||
\(624\) | −66.1789 | −2.64927 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 48.4815 | 1.93771 | ||||||||
\(627\) | 19.0465 | 0.760645 | ||||||||
\(628\) | −10.9285 | −0.436096 | ||||||||
\(629\) | −17.2641 | −0.688364 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.3090 | 1.48525 | 0.742623 | − | 0.669709i | \(-0.233581\pi\) | ||||
0.742623 | + | 0.669709i | \(0.233581\pi\) | |||||||
\(632\) | 67.7011 | 2.69300 | ||||||||
\(633\) | −26.5049 | −1.05348 | ||||||||
\(634\) | 3.17966 | 0.126280 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 130.307 | 5.16701 | ||||||||
\(637\) | 6.21716 | 0.246333 | ||||||||
\(638\) | −36.0911 | −1.42886 | ||||||||
\(639\) | −7.38601 | −0.292186 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.27191 | −0.287223 | −0.143612 | − | 0.989634i | \(-0.545872\pi\) | ||||
−0.143612 | + | 0.989634i | \(0.545872\pi\) | |||||||
\(642\) | −2.23765 | −0.0883128 | ||||||||
\(643\) | 48.9722 | 1.93128 | 0.965638 | − | 0.259889i | \(-0.0836860\pi\) | ||||
0.965638 | + | 0.259889i | \(0.0836860\pi\) | |||||||
\(644\) | 3.90452 | 0.153860 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 14.0675 | 0.553477 | ||||||||
\(647\) | 38.8836 | 1.52867 | 0.764337 | − | 0.644817i | \(-0.223066\pi\) | ||||
0.764337 | + | 0.644817i | \(0.223066\pi\) | |||||||
\(648\) | −68.1105 | −2.67563 | ||||||||
\(649\) | 8.64722 | 0.339433 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.0589531 | 0.00231055 | ||||||||
\(652\) | 46.9127 | 1.83724 | ||||||||
\(653\) | 46.8454 | 1.83320 | 0.916600 | − | 0.399804i | \(-0.130922\pi\) | ||||
0.916600 | + | 0.399804i | \(0.130922\pi\) | |||||||
\(654\) | 90.8243 | 3.55151 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −37.1421 | −1.45015 | ||||||||
\(657\) | 88.6833 | 3.45986 | ||||||||
\(658\) | 9.16830 | 0.357417 | ||||||||
\(659\) | 1.86648 | 0.0727077 | 0.0363538 | − | 0.999339i | \(-0.488426\pi\) | ||||
0.0363538 | + | 0.999339i | \(0.488426\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.20431 | −0.0468421 | −0.0234211 | − | 0.999726i | \(-0.507456\pi\) | ||||
−0.0234211 | + | 0.999726i | \(0.507456\pi\) | |||||||
\(662\) | 54.8917 | 2.13343 | ||||||||
\(663\) | −57.3879 | −2.22876 | ||||||||
\(664\) | 11.0214 | 0.427714 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 92.8578 | 3.59817 | ||||||||
\(667\) | −4.69320 | −0.181722 | ||||||||
\(668\) | −61.3740 | −2.37463 | ||||||||
\(669\) | 4.53087 | 0.175174 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.1348 | −0.931715 | ||||||||
\(672\) | 2.80605 | 0.108246 | ||||||||
\(673\) | −4.62815 | −0.178402 | −0.0892011 | − | 0.996014i | \(-0.528431\pi\) | ||||
−0.0892011 | + | 0.996014i | \(0.528431\pi\) | |||||||
\(674\) | −61.9384 | −2.38578 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 100.163 | 3.85242 | ||||||||
\(677\) | 24.6057 | 0.945672 | 0.472836 | − | 0.881150i | \(-0.343230\pi\) | ||||
0.472836 | + | 0.881150i | \(0.343230\pi\) | |||||||
\(678\) | 142.324 | 5.46590 | ||||||||
\(679\) | 9.22472 | 0.354012 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −34.1663 | −1.30925 | ||||||||
\(682\) | −0.146351 | −0.00560407 | ||||||||
\(683\) | −8.48187 | −0.324550 | −0.162275 | − | 0.986746i | \(-0.551883\pi\) | ||||
−0.162275 | + | 0.986746i | \(0.551883\pi\) | |||||||
\(684\) | −50.0350 | −1.91314 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.42992 | 0.0927749 | ||||||||
\(687\) | −56.3204 | −2.14876 | ||||||||
\(688\) | −6.52863 | −0.248902 | ||||||||
\(689\) | −66.9808 | −2.55177 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.0039 | 0.913150 | 0.456575 | − | 0.889685i | \(-0.349076\pi\) | ||||
0.456575 | + | 0.889685i | \(0.349076\pi\) | |||||||
\(692\) | −50.5876 | −1.92305 | ||||||||
\(693\) | −20.8741 | −0.792941 | ||||||||
\(694\) | 5.36161 | 0.203524 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 67.2806 | 2.55026 | ||||||||
\(697\) | −32.2083 | −1.21997 | ||||||||
\(698\) | 47.5114 | 1.79833 | ||||||||
\(699\) | −45.4227 | −1.71805 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.6324 | 1.53467 | 0.767333 | − | 0.641249i | \(-0.221583\pi\) | ||||
0.767333 | + | 0.641249i | \(0.221583\pi\) | |||||||
\(702\) | 168.277 | 6.35122 | ||||||||
\(703\) | 11.2562 | 0.424536 | ||||||||
\(704\) | −28.7157 | −1.08227 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 54.5177 | 2.05180 | ||||||||
\(707\) | 13.1201 | 0.493434 | ||||||||
\(708\) | −33.0482 | −1.24203 | ||||||||
\(709\) | 40.4391 | 1.51872 | 0.759361 | − | 0.650670i | \(-0.225512\pi\) | ||||
0.759361 | + | 0.650670i | \(0.225512\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −96.4909 | −3.61869 | ||||||||
\(712\) | −7.17974 | −0.269072 | ||||||||
\(713\) | −0.0190312 | −0.000712723 0 | ||||||||
\(714\) | −22.4296 | −0.839406 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 41.5138 | 1.55144 | ||||||||
\(717\) | −70.9386 | −2.64925 | ||||||||
\(718\) | 75.5500 | 2.81950 | ||||||||
\(719\) | 34.7435 | 1.29572 | 0.647858 | − | 0.761761i | \(-0.275665\pi\) | ||||
0.647858 | + | 0.761761i | \(0.275665\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.0577 | 0.746987 | ||||||||
\(722\) | 36.9965 | 1.37687 | ||||||||
\(723\) | −12.6316 | −0.469773 | ||||||||
\(724\) | −84.0143 | −3.12237 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −7.40999 | −0.275011 | ||||||||
\(727\) | −33.7465 | −1.25159 | −0.625794 | − | 0.779988i | \(-0.715225\pi\) | ||||
−0.625794 | + | 0.779988i | \(0.715225\pi\) | |||||||
\(728\) | 28.7720 | 1.06636 | ||||||||
\(729\) | −6.44065 | −0.238543 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.66140 | −0.209394 | ||||||||
\(732\) | 92.2393 | 3.40926 | ||||||||
\(733\) | −25.1115 | −0.927516 | −0.463758 | − | 0.885962i | \(-0.653499\pi\) | ||||
−0.463758 | + | 0.885962i | \(0.653499\pi\) | |||||||
\(734\) | 0.889228 | 0.0328220 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.905845 | −0.0333899 | ||||||||
\(737\) | −15.1264 | −0.557190 | ||||||||
\(738\) | 173.238 | 6.37696 | ||||||||
\(739\) | −27.9564 | −1.02839 | −0.514196 | − | 0.857673i | \(-0.671910\pi\) | ||||
−0.514196 | + | 0.857673i | \(0.671910\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 37.4170 | 1.37455 | ||||||||
\(742\) | −26.1789 | −0.961057 | ||||||||
\(743\) | −25.4587 | −0.933989 | −0.466995 | − | 0.884260i | \(-0.654663\pi\) | ||||
−0.466995 | + | 0.884260i | \(0.654663\pi\) | |||||||
\(744\) | 0.272826 | 0.0100023 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.30575 | 0.194257 | ||||||||
\(747\) | −15.7083 | −0.574736 | ||||||||
\(748\) | 36.8208 | 1.34630 | ||||||||
\(749\) | 0.297274 | 0.0108622 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.2105 | 0.591528 | 0.295764 | − | 0.955261i | \(-0.404426\pi\) | ||||
0.295764 | + | 0.955261i | \(0.404426\pi\) | |||||||
\(752\) | 12.9653 | 0.472796 | ||||||||
\(753\) | −64.0044 | −2.33245 | ||||||||
\(754\) | −70.9012 | −2.58207 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 43.4920 | 1.58179 | ||||||||
\(757\) | −9.54004 | −0.346739 | −0.173369 | − | 0.984857i | \(-0.555465\pi\) | ||||
−0.173369 | + | 0.984857i | \(0.555465\pi\) | |||||||
\(758\) | 33.9615 | 1.23354 | ||||||||
\(759\) | 9.80346 | 0.355843 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −41.8640 | −1.51757 | −0.758784 | − | 0.651342i | \(-0.774206\pi\) | ||||
−0.758784 | + | 0.651342i | \(0.774206\pi\) | |||||||
\(762\) | −51.9281 | −1.88116 | ||||||||
\(763\) | −12.0661 | −0.436824 | ||||||||
\(764\) | −77.7210 | −2.81185 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −38.5614 | −1.39328 | ||||||||
\(767\) | 16.9875 | 0.613384 | ||||||||
\(768\) | 96.1098 | 3.46806 | ||||||||
\(769\) | −4.24418 | −0.153049 | −0.0765244 | − | 0.997068i | \(-0.524382\pi\) | ||||
−0.0765244 | + | 0.997068i | \(0.524382\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 61.6635 | 2.22076 | ||||||||
\(772\) | 102.190 | 3.67789 | ||||||||
\(773\) | −36.4215 | −1.30999 | −0.654994 | − | 0.755634i | \(-0.727329\pi\) | ||||
−0.654994 | + | 0.755634i | \(0.727329\pi\) | |||||||
\(774\) | 30.4508 | 1.09453 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 42.6906 | 1.53250 | ||||||||
\(777\) | −17.9472 | −0.643854 | ||||||||
\(778\) | −22.7947 | −0.817230 | ||||||||
\(779\) | 20.9999 | 0.752398 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.54387 | −0.126810 | ||||||||
\(782\) | 7.24069 | 0.258926 | ||||||||
\(783\) | −52.2770 | −1.86823 | ||||||||
\(784\) | 3.43626 | 0.122724 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 13.7104 | 0.489033 | ||||||||
\(787\) | 42.4245 | 1.51227 | 0.756135 | − | 0.654415i | \(-0.227085\pi\) | ||||
0.756135 | + | 0.654415i | \(0.227085\pi\) | |||||||
\(788\) | −90.9097 | −3.23852 | ||||||||
\(789\) | 21.3085 | 0.758603 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.9079 | −0.672287 | ||||||||
\(792\) | −96.6021 | −3.43261 | ||||||||
\(793\) | −47.4131 | −1.68369 | ||||||||
\(794\) | 56.0098 | 1.98772 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.05142 | −0.320819 | ||||||||
\(797\) | 49.6964 | 1.76034 | 0.880169 | − | 0.474660i | \(-0.157429\pi\) | ||||
0.880169 | + | 0.474660i | \(0.157429\pi\) | |||||||
\(798\) | 14.6241 | 0.517689 | ||||||||
\(799\) | 11.2430 | 0.397750 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.2329 | 0.361562 | ||||||||
\(802\) | −36.4212 | −1.28608 | ||||||||
\(803\) | 42.5510 | 1.50159 | ||||||||
\(804\) | 57.8108 | 2.03883 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.287508 | −0.0101270 | ||||||||
\(807\) | −60.9886 | −2.14690 | ||||||||
\(808\) | 60.7180 | 2.13605 | ||||||||
\(809\) | 44.5145 | 1.56505 | 0.782524 | − | 0.622621i | \(-0.213932\pi\) | ||||
0.782524 | + | 0.622621i | \(0.213932\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30.3020 | −1.06405 | −0.532023 | − | 0.846730i | \(-0.678568\pi\) | ||||
−0.532023 | + | 0.846730i | \(0.678568\pi\) | |||||||
\(812\) | −18.3247 | −0.643072 | ||||||||
\(813\) | 92.9637 | 3.26038 | ||||||||
\(814\) | 44.5540 | 1.56162 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −31.7187 | −1.11038 | ||||||||
\(817\) | 3.69124 | 0.129140 | ||||||||
\(818\) | −6.63814 | −0.232097 | ||||||||
\(819\) | −41.0073 | −1.43291 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.318150 | −0.0111035 | −0.00555176 | − | 0.999985i | \(-0.501767\pi\) | ||||
−0.00555176 | + | 0.999985i | \(0.501767\pi\) | |||||||
\(822\) | 113.727 | 3.96670 | ||||||||
\(823\) | 12.0689 | 0.420695 | 0.210348 | − | 0.977627i | \(-0.432540\pi\) | ||||
0.210348 | + | 0.977627i | \(0.432540\pi\) | |||||||
\(824\) | 92.8239 | 3.23367 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.63943 | 0.231015 | ||||||||
\(827\) | −14.4275 | −0.501692 | −0.250846 | − | 0.968027i | \(-0.580709\pi\) | ||||
−0.250846 | + | 0.968027i | \(0.580709\pi\) | |||||||
\(828\) | −25.7536 | −0.894999 | ||||||||
\(829\) | 29.7311 | 1.03260 | 0.516301 | − | 0.856407i | \(-0.327308\pi\) | ||||
0.516301 | + | 0.856407i | \(0.327308\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 73.1706 | 2.53826 | ||||||||
\(832\) | −56.4123 | −1.95575 | ||||||||
\(833\) | 2.97980 | 0.103244 | ||||||||
\(834\) | −73.1241 | −2.53208 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −24.0072 | −0.830308 | ||||||||
\(837\) | −0.211986 | −0.00732730 | ||||||||
\(838\) | −26.2491 | −0.906760 | ||||||||
\(839\) | −31.1191 | −1.07435 | −0.537176 | − | 0.843470i | \(-0.680509\pi\) | ||||
−0.537176 | + | 0.843470i | \(0.680509\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.97385 | −0.240478 | ||||||||
\(842\) | −72.5717 | −2.50098 | ||||||||
\(843\) | −45.0186 | −1.55052 | ||||||||
\(844\) | 33.4082 | 1.14996 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −60.4726 | −2.07909 | ||||||||
\(847\) | 0.984428 | 0.0338253 | ||||||||
\(848\) | −37.0207 | −1.27130 | ||||||||
\(849\) | 88.4926 | 3.03706 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.79370 | 0.198606 | ||||||||
\(852\) | 13.5441 | 0.464013 | ||||||||
\(853\) | −28.9135 | −0.989980 | −0.494990 | − | 0.868899i | \(-0.664828\pi\) | ||||
−0.494990 | + | 0.868899i | \(0.664828\pi\) | |||||||
\(854\) | −18.5310 | −0.634118 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.37574 | 0.0470218 | ||||||||
\(857\) | −5.51431 | −0.188365 | −0.0941827 | − | 0.995555i | \(-0.530024\pi\) | ||||
−0.0941827 | + | 0.995555i | \(0.530024\pi\) | |||||||
\(858\) | 148.103 | 5.05615 | ||||||||
\(859\) | −25.5513 | −0.871798 | −0.435899 | − | 0.899995i | \(-0.643570\pi\) | ||||
−0.435899 | + | 0.899995i | \(0.643570\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −33.4828 | −1.14109 | ||||||||
\(862\) | 66.3010 | 2.25822 | ||||||||
\(863\) | −35.9398 | −1.22341 | −0.611703 | − | 0.791087i | \(-0.709515\pi\) | ||||
−0.611703 | + | 0.791087i | \(0.709515\pi\) | |||||||
\(864\) | −10.0901 | −0.343272 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 5.21452 | 0.177197 | ||||||||
\(867\) | 25.1559 | 0.854338 | ||||||||
\(868\) | −0.0743076 | −0.00252217 | ||||||||
\(869\) | −46.2972 | −1.57052 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29.7160 | −1.00689 | ||||||||
\(872\) | −55.8402 | −1.89099 | ||||||||
\(873\) | −60.8447 | −2.05928 | ||||||||
\(874\) | −4.72094 | −0.159688 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −162.623 | −5.49452 | ||||||||
\(877\) | −18.3007 | −0.617971 | −0.308986 | − | 0.951067i | \(-0.599990\pi\) | ||||
−0.308986 | + | 0.951067i | \(0.599990\pi\) | |||||||
\(878\) | 43.5738 | 1.47055 | ||||||||
\(879\) | 73.9916 | 2.49567 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.8245 | 1.00481 | 0.502407 | − | 0.864631i | \(-0.332448\pi\) | ||||
0.502407 | + | 0.864631i | \(0.332448\pi\) | |||||||
\(882\) | −16.0274 | −0.539670 | ||||||||
\(883\) | 14.2733 | 0.480336 | 0.240168 | − | 0.970731i | \(-0.422797\pi\) | ||||
0.240168 | + | 0.970731i | \(0.422797\pi\) | |||||||
\(884\) | 72.3348 | 2.43288 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.71030 | −0.0574586 | ||||||||
\(887\) | 45.0595 | 1.51295 | 0.756475 | − | 0.654023i | \(-0.226920\pi\) | ||||
0.756475 | + | 0.654023i | \(0.226920\pi\) | |||||||
\(888\) | −83.0571 | −2.78721 | ||||||||
\(889\) | 6.89872 | 0.231376 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 46.5772 | 1.56039 | ||||||||
\(892\) | −5.71095 | −0.191217 | ||||||||
\(893\) | −7.33048 | −0.245305 | ||||||||
\(894\) | 131.708 | 4.40499 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −20.2366 | −0.676057 | ||||||||
\(897\) | 19.2590 | 0.643038 | ||||||||
\(898\) | −5.53415 | −0.184677 | ||||||||
\(899\) | 0.0893171 | 0.00297889 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32.1030 | −1.06951 | ||||||||
\(902\) | 83.1209 | 2.76762 | ||||||||
\(903\) | −5.88542 | −0.195855 | ||||||||
\(904\) | −87.5028 | −2.91030 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −117.766 | −3.91252 | ||||||||
\(907\) | 4.89799 | 0.162635 | 0.0813175 | − | 0.996688i | \(-0.474087\pi\) | ||||
0.0813175 | + | 0.996688i | \(0.474087\pi\) | |||||||
\(908\) | 43.0650 | 1.42916 | ||||||||
\(909\) | −86.5383 | −2.87030 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.6033 | −1.27899 | −0.639493 | − | 0.768797i | \(-0.720855\pi\) | ||||
−0.639493 | + | 0.768797i | \(0.720855\pi\) | |||||||
\(912\) | 20.6806 | 0.684804 | ||||||||
\(913\) | −7.53696 | −0.249437 | ||||||||
\(914\) | −42.7869 | −1.41527 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 70.9892 | 2.34555 | ||||||||
\(917\) | −1.82144 | −0.0601493 | ||||||||
\(918\) | 80.6531 | 2.66195 | ||||||||
\(919\) | 18.2605 | 0.602358 | 0.301179 | − | 0.953568i | \(-0.402620\pi\) | ||||
0.301179 | + | 0.953568i | \(0.402620\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 67.6335 | 2.22860 | ||||||||
\(922\) | −70.9488 | −2.33657 | ||||||||
\(923\) | −6.96197 | −0.229156 | ||||||||
\(924\) | 38.2778 | 1.25925 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 23.7503 | 0.780484 | ||||||||
\(927\) | −132.297 | −4.34521 | ||||||||
\(928\) | 4.25131 | 0.139556 | ||||||||
\(929\) | −36.0755 | −1.18360 | −0.591799 | − | 0.806086i | \(-0.701582\pi\) | ||||
−0.591799 | + | 0.806086i | \(0.701582\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.94284 | −0.0636739 | ||||||||
\(932\) | 57.2532 | 1.87539 | ||||||||
\(933\) | −7.74788 | −0.253654 | ||||||||
\(934\) | 34.8452 | 1.14017 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −189.776 | −6.20301 | ||||||||
\(937\) | −48.0248 | −1.56890 | −0.784451 | − | 0.620190i | \(-0.787055\pi\) | ||||
−0.784451 | + | 0.620190i | \(0.787055\pi\) | |||||||
\(938\) | −11.6143 | −0.379219 | ||||||||
\(939\) | 61.8052 | 2.01694 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.23415 | −0.203227 | −0.101614 | − | 0.994824i | \(-0.532401\pi\) | ||||
−0.101614 | + | 0.994824i | \(0.532401\pi\) | |||||||
\(942\) | −21.0682 | −0.686440 | ||||||||
\(943\) | 10.8089 | 0.351985 | ||||||||
\(944\) | 9.38912 | 0.305590 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14.6106 | 0.475030 | ||||||||
\(947\) | 21.9266 | 0.712519 | 0.356260 | − | 0.934387i | \(-0.384052\pi\) | ||||
0.356260 | + | 0.934387i | \(0.384052\pi\) | |||||||
\(948\) | 176.940 | 5.74674 | ||||||||
\(949\) | 83.5918 | 2.71350 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.05350 | 0.131444 | ||||||||
\(952\) | 13.7901 | 0.446939 | ||||||||
\(953\) | 46.6376 | 1.51074 | 0.755371 | − | 0.655298i | \(-0.227457\pi\) | ||||
0.755371 | + | 0.655298i | \(0.227457\pi\) | |||||||
\(954\) | 172.672 | 5.59045 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 89.4147 | 2.89188 | ||||||||
\(957\) | −46.0096 | −1.48728 | ||||||||
\(958\) | −8.73083 | −0.282080 | ||||||||
\(959\) | −15.1089 | −0.487890 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9996 | −0.999988 | ||||||||
\(962\) | 87.5267 | 2.82197 | ||||||||
\(963\) | −1.96077 | −0.0631850 | ||||||||
\(964\) | 15.9215 | 0.512797 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 7.52721 | 0.242184 | ||||||||
\(967\) | −38.2271 | −1.22930 | −0.614650 | − | 0.788800i | \(-0.710703\pi\) | ||||
−0.614650 | + | 0.788800i | \(0.710703\pi\) | |||||||
\(968\) | 4.55578 | 0.146428 | ||||||||
\(969\) | 17.9335 | 0.576107 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.22879 | 0.103617 | 0.0518084 | − | 0.998657i | \(-0.483501\pi\) | ||||
0.0518084 | + | 0.998657i | \(0.483501\pi\) | |||||||
\(972\) | −47.5342 | −1.52466 | ||||||||
\(973\) | 9.71464 | 0.311437 | ||||||||
\(974\) | 33.3047 | 1.06715 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −26.2055 | −0.838818 | ||||||||
\(977\) | −49.3683 | −1.57943 | −0.789716 | − | 0.613472i | \(-0.789772\pi\) | ||||
−0.789716 | + | 0.613472i | \(0.789772\pi\) | |||||||
\(978\) | 90.4392 | 2.89193 | ||||||||
\(979\) | 4.90984 | 0.156919 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 79.5863 | 2.54099 | ||||||||
\(982\) | 18.1253 | 0.578402 | ||||||||
\(983\) | 24.6436 | 0.786010 | 0.393005 | − | 0.919536i | \(-0.371435\pi\) | ||||
0.393005 | + | 0.919536i | \(0.371435\pi\) | |||||||
\(984\) | −154.953 | −4.93972 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −33.9820 | −1.08221 | ||||||||
\(987\) | 11.6879 | 0.372031 | ||||||||
\(988\) | −47.1624 | −1.50044 | ||||||||
\(989\) | 1.89992 | 0.0604141 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.7831 | 0.914324 | 0.457162 | − | 0.889384i | \(-0.348866\pi\) | ||||
0.457162 | + | 0.889384i | \(0.348866\pi\) | |||||||
\(992\) | 0.0172393 | 0.000547348 0 | ||||||||
\(993\) | 69.9770 | 2.22065 | ||||||||
\(994\) | −2.72103 | −0.0863057 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 28.8050 | 0.912722 | ||||||||
\(997\) | −17.1504 | −0.543159 | −0.271579 | − | 0.962416i | \(-0.587546\pi\) | ||||
−0.271579 | + | 0.962416i | \(0.587546\pi\) | |||||||
\(998\) | 64.5410 | 2.04301 | ||||||||
\(999\) | 64.5353 | 2.04181 |
(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 | 4025.2.a.z.1.2 | ✓ | 14 | |
5.4 | even | 2 | 4025.2.a.bc.1.13 | yes | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4025.2.a.z.1.2 | ✓ | 14 | 1.1 | even | 1 | trivial | |
4025.2.a.bc.1.13 | yes | 14 | 5.4 | even | 2 |