Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1911,2,Mod(1,1911)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1911, 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("1911.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1911 = 3 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1911.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: | \(15.2594118263\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4x^{9} - 10x^{8} + 52x^{7} + 16x^{6} - 212x^{5} + 64x^{4} + 300x^{3} - 159x^{2} - 80x + 46 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.56844\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1911.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.56844 | −1.10906 | −0.554528 | − | 0.832165i | \(-0.687101\pi\) | ||||
−0.554528 | + | 0.832165i | \(0.687101\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.460010 | 0.230005 | ||||||||
\(5\) | 4.07203 | 1.82107 | 0.910534 | − | 0.413435i | \(-0.135671\pi\) | ||||
0.910534 | + | 0.413435i | \(0.135671\pi\) | |||||||
\(6\) | 1.56844 | 0.640314 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.41539 | 0.853968 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −6.38674 | −2.01967 | ||||||||
\(11\) | −4.60112 | −1.38729 | −0.693645 | − | 0.720317i | \(-0.743996\pi\) | ||||
−0.693645 | + | 0.720317i | \(0.743996\pi\) | |||||||
\(12\) | −0.460010 | −0.132793 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.07203 | −1.05139 | ||||||||
\(16\) | −4.70841 | −1.17710 | ||||||||
\(17\) | 3.53841 | 0.858190 | 0.429095 | − | 0.903259i | \(-0.358833\pi\) | ||||
0.429095 | + | 0.903259i | \(0.358833\pi\) | |||||||
\(18\) | −1.56844 | −0.369685 | ||||||||
\(19\) | 5.76389 | 1.32233 | 0.661164 | − | 0.750242i | \(-0.270063\pi\) | ||||
0.661164 | + | 0.750242i | \(0.270063\pi\) | |||||||
\(20\) | 1.87317 | 0.418854 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 7.21659 | 1.53858 | ||||||||
\(23\) | −4.38609 | −0.914563 | −0.457282 | − | 0.889322i | \(-0.651177\pi\) | ||||
−0.457282 | + | 0.889322i | \(0.651177\pi\) | |||||||
\(24\) | −2.41539 | −0.493038 | ||||||||
\(25\) | 11.5814 | 2.31629 | ||||||||
\(26\) | −1.56844 | −0.307597 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.06860 | 0.755521 | 0.377760 | − | 0.925903i | \(-0.376694\pi\) | ||||
0.377760 | + | 0.925903i | \(0.376694\pi\) | |||||||
\(30\) | 6.38674 | 1.16605 | ||||||||
\(31\) | −3.28375 | −0.589778 | −0.294889 | − | 0.955532i | \(-0.595283\pi\) | ||||
−0.294889 | + | 0.955532i | \(0.595283\pi\) | |||||||
\(32\) | 2.55410 | 0.451505 | ||||||||
\(33\) | 4.60112 | 0.800952 | ||||||||
\(34\) | −5.54979 | −0.951781 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.460010 | 0.0766683 | ||||||||
\(37\) | 8.96014 | 1.47304 | 0.736519 | − | 0.676416i | \(-0.236468\pi\) | ||||
0.736519 | + | 0.676416i | \(0.236468\pi\) | |||||||
\(38\) | −9.04033 | −1.46653 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 9.83552 | 1.55513 | ||||||||
\(41\) | 1.14388 | 0.178644 | 0.0893218 | − | 0.996003i | \(-0.471530\pi\) | ||||
0.0893218 | + | 0.996003i | \(0.471530\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.33023 | −1.11785 | −0.558925 | − | 0.829219i | \(-0.688786\pi\) | ||||
−0.558925 | + | 0.829219i | \(0.688786\pi\) | |||||||
\(44\) | −2.11656 | −0.319083 | ||||||||
\(45\) | 4.07203 | 0.607023 | ||||||||
\(46\) | 6.87933 | 1.01430 | ||||||||
\(47\) | 7.46654 | 1.08911 | 0.544553 | − | 0.838726i | \(-0.316699\pi\) | ||||
0.544553 | + | 0.838726i | \(0.316699\pi\) | |||||||
\(48\) | 4.70841 | 0.679600 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −18.1648 | −2.56889 | ||||||||
\(51\) | −3.53841 | −0.495476 | ||||||||
\(52\) | 0.460010 | 0.0637919 | ||||||||
\(53\) | 4.15199 | 0.570319 | 0.285160 | − | 0.958480i | \(-0.407953\pi\) | ||||
0.285160 | + | 0.958480i | \(0.407953\pi\) | |||||||
\(54\) | 1.56844 | 0.213438 | ||||||||
\(55\) | −18.7359 | −2.52635 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.76389 | −0.763446 | ||||||||
\(58\) | −6.38137 | −0.837915 | ||||||||
\(59\) | 5.96858 | 0.777043 | 0.388522 | − | 0.921440i | \(-0.372986\pi\) | ||||
0.388522 | + | 0.921440i | \(0.372986\pi\) | |||||||
\(60\) | −1.87317 | −0.241826 | ||||||||
\(61\) | −0.567843 | −0.0727049 | −0.0363524 | − | 0.999339i | \(-0.511574\pi\) | ||||
−0.0363524 | + | 0.999339i | \(0.511574\pi\) | |||||||
\(62\) | 5.15036 | 0.654097 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.41087 | 0.676359 | ||||||||
\(65\) | 4.07203 | 0.505073 | ||||||||
\(66\) | −7.21659 | −0.888301 | ||||||||
\(67\) | −9.76134 | −1.19254 | −0.596269 | − | 0.802785i | \(-0.703351\pi\) | ||||
−0.596269 | + | 0.802785i | \(0.703351\pi\) | |||||||
\(68\) | 1.62770 | 0.197388 | ||||||||
\(69\) | 4.38609 | 0.528023 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.7872 | −1.39889 | −0.699444 | − | 0.714688i | \(-0.746569\pi\) | ||||
−0.699444 | + | 0.714688i | \(0.746569\pi\) | |||||||
\(72\) | 2.41539 | 0.284656 | ||||||||
\(73\) | −1.93497 | −0.226471 | −0.113236 | − | 0.993568i | \(-0.536121\pi\) | ||||
−0.113236 | + | 0.993568i | \(0.536121\pi\) | |||||||
\(74\) | −14.0535 | −1.63368 | ||||||||
\(75\) | −11.5814 | −1.33731 | ||||||||
\(76\) | 2.65144 | 0.304142 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.56844 | 0.177591 | ||||||||
\(79\) | 3.44078 | 0.387118 | 0.193559 | − | 0.981089i | \(-0.437997\pi\) | ||||
0.193559 | + | 0.981089i | \(0.437997\pi\) | |||||||
\(80\) | −19.1728 | −2.14358 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.79411 | −0.198126 | ||||||||
\(83\) | 8.69728 | 0.954651 | 0.477325 | − | 0.878727i | \(-0.341606\pi\) | ||||
0.477325 | + | 0.878727i | \(0.341606\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.4085 | 1.56282 | ||||||||
\(86\) | 11.4970 | 1.23976 | ||||||||
\(87\) | −4.06860 | −0.436200 | ||||||||
\(88\) | −11.1135 | −1.18470 | ||||||||
\(89\) | −14.5467 | −1.54194 | −0.770971 | − | 0.636870i | \(-0.780229\pi\) | ||||
−0.770971 | + | 0.636870i | \(0.780229\pi\) | |||||||
\(90\) | −6.38674 | −0.673222 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.01764 | −0.210354 | ||||||||
\(93\) | 3.28375 | 0.340508 | ||||||||
\(94\) | −11.7108 | −1.20788 | ||||||||
\(95\) | 23.4707 | 2.40805 | ||||||||
\(96\) | −2.55410 | −0.260676 | ||||||||
\(97\) | −13.4353 | −1.36415 | −0.682073 | − | 0.731284i | \(-0.738921\pi\) | ||||
−0.682073 | + | 0.731284i | \(0.738921\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.60112 | −0.462430 | ||||||||
\(100\) | 5.32757 | 0.532757 | ||||||||
\(101\) | −0.583693 | −0.0580796 | −0.0290398 | − | 0.999578i | \(-0.509245\pi\) | ||||
−0.0290398 | + | 0.999578i | \(0.509245\pi\) | |||||||
\(102\) | 5.54979 | 0.549511 | ||||||||
\(103\) | −14.0473 | −1.38412 | −0.692060 | − | 0.721840i | \(-0.743297\pi\) | ||||
−0.692060 | + | 0.721840i | \(0.743297\pi\) | |||||||
\(104\) | 2.41539 | 0.236848 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.51215 | −0.632516 | ||||||||
\(107\) | 17.5274 | 1.69444 | 0.847221 | − | 0.531240i | \(-0.178274\pi\) | ||||
0.847221 | + | 0.531240i | \(0.178274\pi\) | |||||||
\(108\) | −0.460010 | −0.0442644 | ||||||||
\(109\) | −4.60883 | −0.441446 | −0.220723 | − | 0.975336i | \(-0.570842\pi\) | ||||
−0.220723 | + | 0.975336i | \(0.570842\pi\) | |||||||
\(110\) | 29.3862 | 2.80186 | ||||||||
\(111\) | −8.96014 | −0.850459 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 21.1046 | 1.98535 | 0.992677 | − | 0.120797i | \(-0.0385451\pi\) | ||||
0.992677 | + | 0.120797i | \(0.0385451\pi\) | |||||||
\(114\) | 9.04033 | 0.846704 | ||||||||
\(115\) | −17.8603 | −1.66548 | ||||||||
\(116\) | 1.87160 | 0.173773 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −9.36138 | −0.861785 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −9.83552 | −0.897856 | ||||||||
\(121\) | 10.1703 | 0.924574 | ||||||||
\(122\) | 0.890629 | 0.0806337 | ||||||||
\(123\) | −1.14388 | −0.103140 | ||||||||
\(124\) | −1.51055 | −0.135652 | ||||||||
\(125\) | 26.7998 | 2.39705 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.9327 | 0.970122 | 0.485061 | − | 0.874480i | \(-0.338797\pi\) | ||||
0.485061 | + | 0.874480i | \(0.338797\pi\) | |||||||
\(128\) | −13.5948 | −1.20162 | ||||||||
\(129\) | 7.33023 | 0.645390 | ||||||||
\(130\) | −6.38674 | −0.560154 | ||||||||
\(131\) | 8.69633 | 0.759801 | 0.379901 | − | 0.925027i | \(-0.375958\pi\) | ||||
0.379901 | + | 0.925027i | \(0.375958\pi\) | |||||||
\(132\) | 2.11656 | 0.184223 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 15.3101 | 1.32259 | ||||||||
\(135\) | −4.07203 | −0.350465 | ||||||||
\(136\) | 8.54662 | 0.732867 | ||||||||
\(137\) | 19.7875 | 1.69056 | 0.845280 | − | 0.534323i | \(-0.179433\pi\) | ||||
0.845280 | + | 0.534323i | \(0.179433\pi\) | |||||||
\(138\) | −6.87933 | −0.585607 | ||||||||
\(139\) | 18.9914 | 1.61083 | 0.805416 | − | 0.592710i | \(-0.201942\pi\) | ||||
0.805416 | + | 0.592710i | \(0.201942\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.46654 | −0.628796 | ||||||||
\(142\) | 18.4876 | 1.55144 | ||||||||
\(143\) | −4.60112 | −0.384765 | ||||||||
\(144\) | −4.70841 | −0.392368 | ||||||||
\(145\) | 16.5675 | 1.37585 | ||||||||
\(146\) | 3.03489 | 0.251169 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.12175 | 0.338806 | ||||||||
\(149\) | −1.17361 | −0.0961458 | −0.0480729 | − | 0.998844i | \(-0.515308\pi\) | ||||
−0.0480729 | + | 0.998844i | \(0.515308\pi\) | |||||||
\(150\) | 18.1648 | 1.48315 | ||||||||
\(151\) | 13.3332 | 1.08504 | 0.542520 | − | 0.840043i | \(-0.317470\pi\) | ||||
0.542520 | + | 0.840043i | \(0.317470\pi\) | |||||||
\(152\) | 13.9220 | 1.12922 | ||||||||
\(153\) | 3.53841 | 0.286063 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −13.3715 | −1.07403 | ||||||||
\(156\) | −0.460010 | −0.0368302 | ||||||||
\(157\) | −15.8299 | −1.26336 | −0.631681 | − | 0.775229i | \(-0.717635\pi\) | ||||
−0.631681 | + | 0.775229i | \(0.717635\pi\) | |||||||
\(158\) | −5.39666 | −0.429335 | ||||||||
\(159\) | −4.15199 | −0.329274 | ||||||||
\(160\) | 10.4004 | 0.822221 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.56844 | −0.123228 | ||||||||
\(163\) | 11.4827 | 0.899394 | 0.449697 | − | 0.893181i | \(-0.351532\pi\) | ||||
0.449697 | + | 0.893181i | \(0.351532\pi\) | |||||||
\(164\) | 0.526195 | 0.0410889 | ||||||||
\(165\) | 18.7359 | 1.45859 | ||||||||
\(166\) | −13.6412 | −1.05876 | ||||||||
\(167\) | 19.8532 | 1.53629 | 0.768144 | − | 0.640278i | \(-0.221181\pi\) | ||||
0.768144 | + | 0.640278i | \(0.221181\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −22.5989 | −1.73326 | ||||||||
\(171\) | 5.76389 | 0.440776 | ||||||||
\(172\) | −3.37197 | −0.257111 | ||||||||
\(173\) | −8.78471 | −0.667889 | −0.333944 | − | 0.942593i | \(-0.608380\pi\) | ||||
−0.333944 | + | 0.942593i | \(0.608380\pi\) | |||||||
\(174\) | 6.38137 | 0.483770 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 21.6640 | 1.63298 | ||||||||
\(177\) | −5.96858 | −0.448626 | ||||||||
\(178\) | 22.8156 | 1.71010 | ||||||||
\(179\) | 18.0234 | 1.34713 | 0.673565 | − | 0.739128i | \(-0.264762\pi\) | ||||
0.673565 | + | 0.739128i | \(0.264762\pi\) | |||||||
\(180\) | 1.87317 | 0.139618 | ||||||||
\(181\) | −3.28601 | −0.244247 | −0.122124 | − | 0.992515i | \(-0.538970\pi\) | ||||
−0.122124 | + | 0.992515i | \(0.538970\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.567843 | 0.0419762 | ||||||||
\(184\) | −10.5941 | −0.781007 | ||||||||
\(185\) | 36.4860 | 2.68250 | ||||||||
\(186\) | −5.15036 | −0.377643 | ||||||||
\(187\) | −16.2806 | −1.19056 | ||||||||
\(188\) | 3.43468 | 0.250500 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −36.8125 | −2.67066 | ||||||||
\(191\) | −3.15363 | −0.228189 | −0.114094 | − | 0.993470i | \(-0.536397\pi\) | ||||
−0.114094 | + | 0.993470i | \(0.536397\pi\) | |||||||
\(192\) | −5.41087 | −0.390496 | ||||||||
\(193\) | −22.5336 | −1.62200 | −0.811001 | − | 0.585045i | \(-0.801077\pi\) | ||||
−0.811001 | + | 0.585045i | \(0.801077\pi\) | |||||||
\(194\) | 21.0724 | 1.51291 | ||||||||
\(195\) | −4.07203 | −0.291604 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.90510 | 0.491968 | 0.245984 | − | 0.969274i | \(-0.420889\pi\) | ||||
0.245984 | + | 0.969274i | \(0.420889\pi\) | |||||||
\(198\) | 7.21659 | 0.512861 | ||||||||
\(199\) | 12.5484 | 0.889532 | 0.444766 | − | 0.895647i | \(-0.353287\pi\) | ||||
0.444766 | + | 0.895647i | \(0.353287\pi\) | |||||||
\(200\) | 27.9736 | 1.97803 | ||||||||
\(201\) | 9.76134 | 0.688512 | ||||||||
\(202\) | 0.915488 | 0.0644135 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.62770 | −0.113962 | ||||||||
\(205\) | 4.65790 | 0.325322 | ||||||||
\(206\) | 22.0324 | 1.53507 | ||||||||
\(207\) | −4.38609 | −0.304854 | ||||||||
\(208\) | −4.70841 | −0.326470 | ||||||||
\(209\) | −26.5204 | −1.83445 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.9769 | 1.16874 | 0.584368 | − | 0.811489i | \(-0.301343\pi\) | ||||
0.584368 | + | 0.811489i | \(0.301343\pi\) | |||||||
\(212\) | 1.90995 | 0.131176 | ||||||||
\(213\) | 11.7872 | 0.807648 | ||||||||
\(214\) | −27.4908 | −1.87923 | ||||||||
\(215\) | −29.8489 | −2.03568 | ||||||||
\(216\) | −2.41539 | −0.164346 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 7.22869 | 0.489589 | ||||||||
\(219\) | 1.93497 | 0.130753 | ||||||||
\(220\) | −8.61870 | −0.581072 | ||||||||
\(221\) | 3.53841 | 0.238019 | ||||||||
\(222\) | 14.0535 | 0.943207 | ||||||||
\(223\) | 6.52248 | 0.436778 | 0.218389 | − | 0.975862i | \(-0.429920\pi\) | ||||
0.218389 | + | 0.975862i | \(0.429920\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.5814 | 0.772096 | ||||||||
\(226\) | −33.1013 | −2.20187 | ||||||||
\(227\) | −10.7148 | −0.711165 | −0.355582 | − | 0.934645i | \(-0.615717\pi\) | ||||
−0.355582 | + | 0.934645i | \(0.615717\pi\) | |||||||
\(228\) | −2.65144 | −0.175596 | ||||||||
\(229\) | 11.5517 | 0.763359 | 0.381680 | − | 0.924295i | \(-0.375346\pi\) | ||||
0.381680 | + | 0.924295i | \(0.375346\pi\) | |||||||
\(230\) | 28.0128 | 1.84711 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.82725 | 0.645190 | ||||||||
\(233\) | 8.20034 | 0.537222 | 0.268611 | − | 0.963249i | \(-0.413435\pi\) | ||||
0.268611 | + | 0.963249i | \(0.413435\pi\) | |||||||
\(234\) | −1.56844 | −0.102532 | ||||||||
\(235\) | 30.4040 | 1.98334 | ||||||||
\(236\) | 2.74561 | 0.178724 | ||||||||
\(237\) | −3.44078 | −0.223502 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.61709 | 0.169286 | 0.0846429 | − | 0.996411i | \(-0.473025\pi\) | ||||
0.0846429 | + | 0.996411i | \(0.473025\pi\) | |||||||
\(240\) | 19.1728 | 1.23760 | ||||||||
\(241\) | −19.3871 | −1.24883 | −0.624416 | − | 0.781092i | \(-0.714663\pi\) | ||||
−0.624416 | + | 0.781092i | \(0.714663\pi\) | |||||||
\(242\) | −15.9515 | −1.02540 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −0.261213 | −0.0167225 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.79411 | 0.114388 | ||||||||
\(247\) | 5.76389 | 0.366748 | ||||||||
\(248\) | −7.93151 | −0.503651 | ||||||||
\(249\) | −8.69728 | −0.551168 | ||||||||
\(250\) | −42.0339 | −2.65846 | ||||||||
\(251\) | −15.4043 | −0.972311 | −0.486156 | − | 0.873872i | \(-0.661601\pi\) | ||||
−0.486156 | + | 0.873872i | \(0.661601\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.1809 | 1.26876 | ||||||||
\(254\) | −17.1473 | −1.07592 | ||||||||
\(255\) | −14.4085 | −0.902296 | ||||||||
\(256\) | 10.5010 | 0.656310 | ||||||||
\(257\) | −11.7467 | −0.732741 | −0.366371 | − | 0.930469i | \(-0.619400\pi\) | ||||
−0.366371 | + | 0.930469i | \(0.619400\pi\) | |||||||
\(258\) | −11.4970 | −0.715774 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.87317 | 0.116169 | ||||||||
\(261\) | 4.06860 | 0.251840 | ||||||||
\(262\) | −13.6397 | −0.842662 | ||||||||
\(263\) | −16.6278 | −1.02532 | −0.512658 | − | 0.858593i | \(-0.671339\pi\) | ||||
−0.512658 | + | 0.858593i | \(0.671339\pi\) | |||||||
\(264\) | 11.1135 | 0.683987 | ||||||||
\(265\) | 16.9070 | 1.03859 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.5467 | 0.890241 | ||||||||
\(268\) | −4.49031 | −0.274289 | ||||||||
\(269\) | 23.2608 | 1.41823 | 0.709117 | − | 0.705091i | \(-0.249094\pi\) | ||||
0.709117 | + | 0.705091i | \(0.249094\pi\) | |||||||
\(270\) | 6.38674 | 0.388685 | ||||||||
\(271\) | 6.92931 | 0.420926 | 0.210463 | − | 0.977602i | \(-0.432503\pi\) | ||||
0.210463 | + | 0.977602i | \(0.432503\pi\) | |||||||
\(272\) | −16.6603 | −1.01018 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −31.0356 | −1.87493 | ||||||||
\(275\) | −53.2876 | −3.21336 | ||||||||
\(276\) | 2.01764 | 0.121448 | ||||||||
\(277\) | −30.4994 | −1.83253 | −0.916265 | − | 0.400572i | \(-0.868811\pi\) | ||||
−0.916265 | + | 0.400572i | \(0.868811\pi\) | |||||||
\(278\) | −29.7870 | −1.78650 | ||||||||
\(279\) | −3.28375 | −0.196593 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.6855 | 1.05503 | 0.527515 | − | 0.849546i | \(-0.323124\pi\) | ||||
0.527515 | + | 0.849546i | \(0.323124\pi\) | |||||||
\(282\) | 11.7108 | 0.697370 | ||||||||
\(283\) | 1.38350 | 0.0822405 | 0.0411203 | − | 0.999154i | \(-0.486907\pi\) | ||||
0.0411203 | + | 0.999154i | \(0.486907\pi\) | |||||||
\(284\) | −5.42224 | −0.321751 | ||||||||
\(285\) | −23.4707 | −1.39029 | ||||||||
\(286\) | 7.21659 | 0.426726 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.55410 | 0.150502 | ||||||||
\(289\) | −4.47966 | −0.263509 | ||||||||
\(290\) | −25.9851 | −1.52590 | ||||||||
\(291\) | 13.4353 | 0.787590 | ||||||||
\(292\) | −0.890105 | −0.0520895 | ||||||||
\(293\) | 16.2793 | 0.951049 | 0.475524 | − | 0.879702i | \(-0.342258\pi\) | ||||
0.475524 | + | 0.879702i | \(0.342258\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.3043 | 1.41505 | ||||||||
\(296\) | 21.6422 | 1.25793 | ||||||||
\(297\) | 4.60112 | 0.266984 | ||||||||
\(298\) | 1.84074 | 0.106631 | ||||||||
\(299\) | −4.38609 | −0.253654 | ||||||||
\(300\) | −5.32757 | −0.307587 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −20.9123 | −1.20337 | ||||||||
\(303\) | 0.583693 | 0.0335323 | ||||||||
\(304\) | −27.1388 | −1.55651 | ||||||||
\(305\) | −2.31227 | −0.132400 | ||||||||
\(306\) | −5.54979 | −0.317260 | ||||||||
\(307\) | 4.45151 | 0.254061 | 0.127030 | − | 0.991899i | \(-0.459455\pi\) | ||||
0.127030 | + | 0.991899i | \(0.459455\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.0473 | 0.799122 | ||||||||
\(310\) | 20.9724 | 1.19115 | ||||||||
\(311\) | 26.9233 | 1.52668 | 0.763340 | − | 0.645997i | \(-0.223558\pi\) | ||||
0.763340 | + | 0.645997i | \(0.223558\pi\) | |||||||
\(312\) | −2.41539 | −0.136744 | ||||||||
\(313\) | 10.9157 | 0.616991 | 0.308496 | − | 0.951226i | \(-0.400174\pi\) | ||||
0.308496 | + | 0.951226i | \(0.400174\pi\) | |||||||
\(314\) | 24.8282 | 1.40114 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.58279 | 0.0890389 | ||||||||
\(317\) | −21.9087 | −1.23052 | −0.615258 | − | 0.788326i | \(-0.710948\pi\) | ||||
−0.615258 | + | 0.788326i | \(0.710948\pi\) | |||||||
\(318\) | 6.51215 | 0.365183 | ||||||||
\(319\) | −18.7201 | −1.04813 | ||||||||
\(320\) | 22.0332 | 1.23169 | ||||||||
\(321\) | −17.5274 | −0.978287 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.3950 | 1.13481 | ||||||||
\(324\) | 0.460010 | 0.0255561 | ||||||||
\(325\) | 11.5814 | 0.642423 | ||||||||
\(326\) | −18.0099 | −0.997478 | ||||||||
\(327\) | 4.60883 | 0.254869 | ||||||||
\(328\) | 2.76290 | 0.152556 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −29.3862 | −1.61766 | ||||||||
\(331\) | 3.28480 | 0.180549 | 0.0902745 | − | 0.995917i | \(-0.471226\pi\) | ||||
0.0902745 | + | 0.995917i | \(0.471226\pi\) | |||||||
\(332\) | 4.00083 | 0.219574 | ||||||||
\(333\) | 8.96014 | 0.491013 | ||||||||
\(334\) | −31.1386 | −1.70383 | ||||||||
\(335\) | −39.7485 | −2.17169 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.6336 | −1.01504 | −0.507518 | − | 0.861641i | \(-0.669437\pi\) | ||||
−0.507518 | + | 0.861641i | \(0.669437\pi\) | |||||||
\(338\) | −1.56844 | −0.0853120 | ||||||||
\(339\) | −21.1046 | −1.14624 | ||||||||
\(340\) | 6.62805 | 0.359457 | ||||||||
\(341\) | 15.1089 | 0.818193 | ||||||||
\(342\) | −9.04033 | −0.488845 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −17.7053 | −0.954607 | ||||||||
\(345\) | 17.8603 | 0.961566 | ||||||||
\(346\) | 13.7783 | 0.740726 | ||||||||
\(347\) | −9.05462 | −0.486077 | −0.243039 | − | 0.970017i | \(-0.578144\pi\) | ||||
−0.243039 | + | 0.970017i | \(0.578144\pi\) | |||||||
\(348\) | −1.87160 | −0.100328 | ||||||||
\(349\) | −31.4538 | −1.68368 | −0.841840 | − | 0.539727i | \(-0.818528\pi\) | ||||
−0.841840 | + | 0.539727i | \(0.818528\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −11.7517 | −0.626368 | ||||||||
\(353\) | 12.5525 | 0.668104 | 0.334052 | − | 0.942555i | \(-0.391584\pi\) | ||||
0.334052 | + | 0.942555i | \(0.391584\pi\) | |||||||
\(354\) | 9.36138 | 0.497552 | ||||||||
\(355\) | −47.9980 | −2.54747 | ||||||||
\(356\) | −6.69160 | −0.354654 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −28.2686 | −1.49404 | ||||||||
\(359\) | −12.4124 | −0.655099 | −0.327550 | − | 0.944834i | \(-0.606223\pi\) | ||||
−0.327550 | + | 0.944834i | \(0.606223\pi\) | |||||||
\(360\) | 9.83552 | 0.518378 | ||||||||
\(361\) | 14.2224 | 0.748549 | ||||||||
\(362\) | 5.15391 | 0.270884 | ||||||||
\(363\) | −10.1703 | −0.533803 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.87926 | −0.412419 | ||||||||
\(366\) | −0.890629 | −0.0465539 | ||||||||
\(367\) | −8.17287 | −0.426621 | −0.213310 | − | 0.976985i | \(-0.568425\pi\) | ||||
−0.213310 | + | 0.976985i | \(0.568425\pi\) | |||||||
\(368\) | 20.6515 | 1.07653 | ||||||||
\(369\) | 1.14388 | 0.0595479 | ||||||||
\(370\) | −57.2261 | −2.97505 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.51055 | 0.0783186 | ||||||||
\(373\) | −17.7190 | −0.917454 | −0.458727 | − | 0.888577i | \(-0.651694\pi\) | ||||
−0.458727 | + | 0.888577i | \(0.651694\pi\) | |||||||
\(374\) | 25.5352 | 1.32040 | ||||||||
\(375\) | −26.7998 | −1.38394 | ||||||||
\(376\) | 18.0346 | 0.930062 | ||||||||
\(377\) | 4.06860 | 0.209544 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.8142 | 0.606855 | 0.303428 | − | 0.952855i | \(-0.401869\pi\) | ||||
0.303428 | + | 0.952855i | \(0.401869\pi\) | |||||||
\(380\) | 10.7968 | 0.553862 | ||||||||
\(381\) | −10.9327 | −0.560100 | ||||||||
\(382\) | 4.94629 | 0.253074 | ||||||||
\(383\) | −20.0568 | −1.02486 | −0.512428 | − | 0.858730i | \(-0.671254\pi\) | ||||
−0.512428 | + | 0.858730i | \(0.671254\pi\) | |||||||
\(384\) | 13.5948 | 0.693758 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 35.3426 | 1.79889 | ||||||||
\(387\) | −7.33023 | −0.372616 | ||||||||
\(388\) | −6.18036 | −0.313760 | ||||||||
\(389\) | −21.6519 | −1.09780 | −0.548898 | − | 0.835889i | \(-0.684952\pi\) | ||||
−0.548898 | + | 0.835889i | \(0.684952\pi\) | |||||||
\(390\) | 6.38674 | 0.323405 | ||||||||
\(391\) | −15.5198 | −0.784869 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.69633 | −0.438672 | ||||||||
\(394\) | −10.8302 | −0.545620 | ||||||||
\(395\) | 14.0109 | 0.704967 | ||||||||
\(396\) | −2.11656 | −0.106361 | ||||||||
\(397\) | 15.2147 | 0.763605 | 0.381802 | − | 0.924244i | \(-0.375303\pi\) | ||||
0.381802 | + | 0.924244i | \(0.375303\pi\) | |||||||
\(398\) | −19.6814 | −0.986541 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −54.5302 | −2.72651 | ||||||||
\(401\) | 35.3974 | 1.76766 | 0.883831 | − | 0.467806i | \(-0.154955\pi\) | ||||
0.883831 | + | 0.467806i | \(0.154955\pi\) | |||||||
\(402\) | −15.3101 | −0.763598 | ||||||||
\(403\) | −3.28375 | −0.163575 | ||||||||
\(404\) | −0.268504 | −0.0133586 | ||||||||
\(405\) | 4.07203 | 0.202341 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −41.2267 | −2.04353 | ||||||||
\(408\) | −8.54662 | −0.423121 | ||||||||
\(409\) | 26.3040 | 1.30065 | 0.650324 | − | 0.759657i | \(-0.274633\pi\) | ||||
0.650324 | + | 0.759657i | \(0.274633\pi\) | |||||||
\(410\) | −7.30565 | −0.360800 | ||||||||
\(411\) | −19.7875 | −0.976046 | ||||||||
\(412\) | −6.46189 | −0.318354 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 6.87933 | 0.338100 | ||||||||
\(415\) | 35.4156 | 1.73848 | ||||||||
\(416\) | 2.55410 | 0.125225 | ||||||||
\(417\) | −18.9914 | −0.930015 | ||||||||
\(418\) | 41.5956 | 2.03451 | ||||||||
\(419\) | 21.1113 | 1.03135 | 0.515676 | − | 0.856783i | \(-0.327541\pi\) | ||||
0.515676 | + | 0.856783i | \(0.327541\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.4626 | 1.58213 | 0.791065 | − | 0.611732i | \(-0.209527\pi\) | ||||
0.791065 | + | 0.611732i | \(0.209527\pi\) | |||||||
\(422\) | −26.6272 | −1.29619 | ||||||||
\(423\) | 7.46654 | 0.363035 | ||||||||
\(424\) | 10.0286 | 0.487034 | ||||||||
\(425\) | 40.9799 | 1.98782 | ||||||||
\(426\) | −18.4876 | −0.895727 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 8.06279 | 0.389730 | ||||||||
\(429\) | 4.60112 | 0.222144 | ||||||||
\(430\) | 46.8163 | 2.25768 | ||||||||
\(431\) | 36.4767 | 1.75702 | 0.878510 | − | 0.477725i | \(-0.158538\pi\) | ||||
0.878510 | + | 0.477725i | \(0.158538\pi\) | |||||||
\(432\) | 4.70841 | 0.226533 | ||||||||
\(433\) | 17.7417 | 0.852611 | 0.426306 | − | 0.904579i | \(-0.359815\pi\) | ||||
0.426306 | + | 0.904579i | \(0.359815\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −16.5675 | −0.794350 | ||||||||
\(436\) | −2.12011 | −0.101535 | ||||||||
\(437\) | −25.2809 | −1.20935 | ||||||||
\(438\) | −3.03489 | −0.145013 | ||||||||
\(439\) | 6.43986 | 0.307358 | 0.153679 | − | 0.988121i | \(-0.450888\pi\) | ||||
0.153679 | + | 0.988121i | \(0.450888\pi\) | |||||||
\(440\) | −45.2544 | −2.15742 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.54979 | −0.263977 | ||||||||
\(443\) | 2.88090 | 0.136875 | 0.0684377 | − | 0.997655i | \(-0.478199\pi\) | ||||
0.0684377 | + | 0.997655i | \(0.478199\pi\) | |||||||
\(444\) | −4.12175 | −0.195610 | ||||||||
\(445\) | −59.2344 | −2.80798 | ||||||||
\(446\) | −10.2301 | −0.484411 | ||||||||
\(447\) | 1.17361 | 0.0555098 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.32686 | 0.204197 | 0.102099 | − | 0.994774i | \(-0.467444\pi\) | ||||
0.102099 | + | 0.994774i | \(0.467444\pi\) | |||||||
\(450\) | −18.1648 | −0.856297 | ||||||||
\(451\) | −5.26312 | −0.247831 | ||||||||
\(452\) | 9.70832 | 0.456641 | ||||||||
\(453\) | −13.3332 | −0.626448 | ||||||||
\(454\) | 16.8055 | 0.788722 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −13.9220 | −0.651958 | ||||||||
\(457\) | −8.66919 | −0.405527 | −0.202764 | − | 0.979228i | \(-0.564992\pi\) | ||||
−0.202764 | + | 0.979228i | \(0.564992\pi\) | |||||||
\(458\) | −18.1182 | −0.846608 | ||||||||
\(459\) | −3.53841 | −0.165159 | ||||||||
\(460\) | −8.21591 | −0.383069 | ||||||||
\(461\) | 9.23553 | 0.430141 | 0.215071 | − | 0.976598i | \(-0.431002\pi\) | ||||
0.215071 | + | 0.976598i | \(0.431002\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.4173 | −0.855925 | −0.427962 | − | 0.903797i | \(-0.640768\pi\) | ||||
−0.427962 | + | 0.903797i | \(0.640768\pi\) | |||||||
\(464\) | −19.1567 | −0.889325 | ||||||||
\(465\) | 13.3715 | 0.620089 | ||||||||
\(466\) | −12.8618 | −0.595809 | ||||||||
\(467\) | −5.58503 | −0.258444 | −0.129222 | − | 0.991616i | \(-0.541248\pi\) | ||||
−0.129222 | + | 0.991616i | \(0.541248\pi\) | |||||||
\(468\) | 0.460010 | 0.0212640 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −47.6869 | −2.19963 | ||||||||
\(471\) | 15.8299 | 0.729402 | ||||||||
\(472\) | 14.4164 | 0.663570 | ||||||||
\(473\) | 33.7273 | 1.55078 | ||||||||
\(474\) | 5.39666 | 0.247877 | ||||||||
\(475\) | 66.7541 | 3.06289 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.15199 | 0.190106 | ||||||||
\(478\) | −4.10476 | −0.187747 | ||||||||
\(479\) | −22.9022 | −1.04643 | −0.523215 | − | 0.852201i | \(-0.675267\pi\) | ||||
−0.523215 | + | 0.852201i | \(0.675267\pi\) | |||||||
\(480\) | −10.4004 | −0.474709 | ||||||||
\(481\) | 8.96014 | 0.408547 | ||||||||
\(482\) | 30.4075 | 1.38503 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.67844 | 0.212656 | ||||||||
\(485\) | −54.7089 | −2.48420 | ||||||||
\(486\) | 1.56844 | 0.0711460 | ||||||||
\(487\) | −10.2038 | −0.462377 | −0.231188 | − | 0.972909i | \(-0.574261\pi\) | ||||
−0.231188 | + | 0.972909i | \(0.574261\pi\) | |||||||
\(488\) | −1.37156 | −0.0620876 | ||||||||
\(489\) | −11.4827 | −0.519265 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.7192 | 0.574010 | 0.287005 | − | 0.957929i | \(-0.407340\pi\) | ||||
0.287005 | + | 0.957929i | \(0.407340\pi\) | |||||||
\(492\) | −0.526195 | −0.0237227 | ||||||||
\(493\) | 14.3964 | 0.648381 | ||||||||
\(494\) | −9.04033 | −0.406743 | ||||||||
\(495\) | −18.7359 | −0.842116 | ||||||||
\(496\) | 15.4612 | 0.694229 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 13.6412 | 0.611276 | ||||||||
\(499\) | 11.2552 | 0.503850 | 0.251925 | − | 0.967747i | \(-0.418936\pi\) | ||||
0.251925 | + | 0.967747i | \(0.418936\pi\) | |||||||
\(500\) | 12.3282 | 0.551333 | ||||||||
\(501\) | −19.8532 | −0.886976 | ||||||||
\(502\) | 24.1608 | 1.07835 | ||||||||
\(503\) | 12.3951 | 0.552670 | 0.276335 | − | 0.961061i | \(-0.410880\pi\) | ||||
0.276335 | + | 0.961061i | \(0.410880\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.37681 | −0.105767 | ||||||||
\(506\) | −31.6526 | −1.40713 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 5.02915 | 0.223133 | ||||||||
\(509\) | 20.8830 | 0.925624 | 0.462812 | − | 0.886456i | \(-0.346840\pi\) | ||||
0.462812 | + | 0.886456i | \(0.346840\pi\) | |||||||
\(510\) | 22.5989 | 1.00070 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 10.7195 | 0.473740 | ||||||||
\(513\) | −5.76389 | −0.254482 | ||||||||
\(514\) | 18.4241 | 0.812651 | ||||||||
\(515\) | −57.2010 | −2.52058 | ||||||||
\(516\) | 3.37197 | 0.148443 | ||||||||
\(517\) | −34.3544 | −1.51091 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.78471 | 0.385606 | ||||||||
\(520\) | 9.83552 | 0.431316 | ||||||||
\(521\) | −37.5800 | −1.64641 | −0.823205 | − | 0.567745i | \(-0.807816\pi\) | ||||
−0.823205 | + | 0.567745i | \(0.807816\pi\) | |||||||
\(522\) | −6.38137 | −0.279305 | ||||||||
\(523\) | −19.9218 | −0.871117 | −0.435559 | − | 0.900160i | \(-0.643449\pi\) | ||||
−0.435559 | + | 0.900160i | \(0.643449\pi\) | |||||||
\(524\) | 4.00039 | 0.174758 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 26.0798 | 1.13713 | ||||||||
\(527\) | −11.6192 | −0.506142 | ||||||||
\(528\) | −21.6640 | −0.942803 | ||||||||
\(529\) | −3.76221 | −0.163574 | ||||||||
\(530\) | −26.5177 | −1.15185 | ||||||||
\(531\) | 5.96858 | 0.259014 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.14388 | 0.0495468 | ||||||||
\(534\) | −22.8156 | −0.987327 | ||||||||
\(535\) | 71.3723 | 3.08569 | ||||||||
\(536\) | −23.5774 | −1.01839 | ||||||||
\(537\) | −18.0234 | −0.777766 | ||||||||
\(538\) | −36.4832 | −1.57290 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.87317 | −0.0806085 | ||||||||
\(541\) | −20.5016 | −0.881431 | −0.440716 | − | 0.897647i | \(-0.645275\pi\) | ||||
−0.440716 | + | 0.897647i | \(0.645275\pi\) | |||||||
\(542\) | −10.8682 | −0.466830 | ||||||||
\(543\) | 3.28601 | 0.141016 | ||||||||
\(544\) | 9.03744 | 0.387477 | ||||||||
\(545\) | −18.7673 | −0.803904 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.4004 | −1.12880 | −0.564399 | − | 0.825502i | \(-0.690892\pi\) | ||||
−0.564399 | + | 0.825502i | \(0.690892\pi\) | |||||||
\(548\) | 9.10244 | 0.388837 | ||||||||
\(549\) | −0.567843 | −0.0242350 | ||||||||
\(550\) | 83.5785 | 3.56380 | ||||||||
\(551\) | 23.4510 | 0.999045 | ||||||||
\(552\) | 10.5941 | 0.450915 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 47.8365 | 2.03238 | ||||||||
\(555\) | −36.4860 | −1.54874 | ||||||||
\(556\) | 8.73624 | 0.370499 | ||||||||
\(557\) | −2.17426 | −0.0921262 | −0.0460631 | − | 0.998939i | \(-0.514668\pi\) | ||||
−0.0460631 | + | 0.998939i | \(0.514668\pi\) | |||||||
\(558\) | 5.15036 | 0.218032 | ||||||||
\(559\) | −7.33023 | −0.310036 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.2806 | 0.687370 | ||||||||
\(562\) | −27.7387 | −1.17009 | ||||||||
\(563\) | −42.5447 | −1.79305 | −0.896523 | − | 0.442997i | \(-0.853915\pi\) | ||||
−0.896523 | + | 0.442997i | \(0.853915\pi\) | |||||||
\(564\) | −3.43468 | −0.144626 | ||||||||
\(565\) | 85.9386 | 3.61546 | ||||||||
\(566\) | −2.16994 | −0.0912093 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −28.4707 | −1.19460 | ||||||||
\(569\) | 26.2861 | 1.10197 | 0.550986 | − | 0.834514i | \(-0.314252\pi\) | ||||
0.550986 | + | 0.834514i | \(0.314252\pi\) | |||||||
\(570\) | 36.8125 | 1.54191 | ||||||||
\(571\) | 10.5325 | 0.440771 | 0.220386 | − | 0.975413i | \(-0.429268\pi\) | ||||
0.220386 | + | 0.975413i | \(0.429268\pi\) | |||||||
\(572\) | −2.11656 | −0.0884978 | ||||||||
\(573\) | 3.15363 | 0.131745 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −50.7972 | −2.11839 | ||||||||
\(576\) | 5.41087 | 0.225453 | ||||||||
\(577\) | −5.44898 | −0.226844 | −0.113422 | − | 0.993547i | \(-0.536181\pi\) | ||||
−0.113422 | + | 0.993547i | \(0.536181\pi\) | |||||||
\(578\) | 7.02609 | 0.292247 | ||||||||
\(579\) | 22.5336 | 0.936463 | ||||||||
\(580\) | 7.62120 | 0.316453 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −21.0724 | −0.873481 | ||||||||
\(583\) | −19.1038 | −0.791198 | ||||||||
\(584\) | −4.67370 | −0.193399 | ||||||||
\(585\) | 4.07203 | 0.168358 | ||||||||
\(586\) | −25.5332 | −1.05477 | ||||||||
\(587\) | 5.10820 | 0.210838 | 0.105419 | − | 0.994428i | \(-0.466382\pi\) | ||||
0.105419 | + | 0.994428i | \(0.466382\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.9271 | −0.779879 | ||||||||
\(590\) | −38.1198 | −1.56937 | ||||||||
\(591\) | −6.90510 | −0.284038 | ||||||||
\(592\) | −42.1880 | −1.73392 | ||||||||
\(593\) | −30.2686 | −1.24298 | −0.621492 | − | 0.783421i | \(-0.713473\pi\) | ||||
−0.621492 | + | 0.783421i | \(0.713473\pi\) | |||||||
\(594\) | −7.21659 | −0.296100 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.539871 | −0.0221140 | ||||||||
\(597\) | −12.5484 | −0.513572 | ||||||||
\(598\) | 6.87933 | 0.281317 | ||||||||
\(599\) | −5.92652 | −0.242151 | −0.121075 | − | 0.992643i | \(-0.538634\pi\) | ||||
−0.121075 | + | 0.992643i | \(0.538634\pi\) | |||||||
\(600\) | −27.9736 | −1.14202 | ||||||||
\(601\) | −37.4912 | −1.52930 | −0.764649 | − | 0.644447i | \(-0.777088\pi\) | ||||
−0.764649 | + | 0.644447i | \(0.777088\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.76134 | −0.397513 | ||||||||
\(604\) | 6.13339 | 0.249564 | ||||||||
\(605\) | 41.4138 | 1.68371 | ||||||||
\(606\) | −0.915488 | −0.0371892 | ||||||||
\(607\) | 18.0265 | 0.731671 | 0.365836 | − | 0.930679i | \(-0.380783\pi\) | ||||
0.365836 | + | 0.930679i | \(0.380783\pi\) | |||||||
\(608\) | 14.7215 | 0.597037 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.62667 | 0.146840 | ||||||||
\(611\) | 7.46654 | 0.302064 | ||||||||
\(612\) | 1.62770 | 0.0657960 | ||||||||
\(613\) | 46.2600 | 1.86842 | 0.934211 | − | 0.356720i | \(-0.116105\pi\) | ||||
0.934211 | + | 0.356720i | \(0.116105\pi\) | |||||||
\(614\) | −6.98193 | −0.281768 | ||||||||
\(615\) | −4.65790 | −0.187825 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.10137 | 0.0845981 | 0.0422990 | − | 0.999105i | \(-0.486532\pi\) | ||||
0.0422990 | + | 0.999105i | \(0.486532\pi\) | |||||||
\(618\) | −22.0324 | −0.886271 | ||||||||
\(619\) | 12.5459 | 0.504262 | 0.252131 | − | 0.967693i | \(-0.418869\pi\) | ||||
0.252131 | + | 0.967693i | \(0.418869\pi\) | |||||||
\(620\) | −6.15102 | −0.247031 | ||||||||
\(621\) | 4.38609 | 0.176008 | ||||||||
\(622\) | −42.2276 | −1.69317 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.70841 | 0.188487 | ||||||||
\(625\) | 51.2225 | 2.04890 | ||||||||
\(626\) | −17.1206 | −0.684278 | ||||||||
\(627\) | 26.5204 | 1.05912 | ||||||||
\(628\) | −7.28189 | −0.290579 | ||||||||
\(629\) | 31.7047 | 1.26415 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.262923 | 0.0104668 | 0.00523339 | − | 0.999986i | \(-0.498334\pi\) | ||||
0.00523339 | + | 0.999986i | \(0.498334\pi\) | |||||||
\(632\) | 8.31080 | 0.330586 | ||||||||
\(633\) | −16.9769 | −0.674770 | ||||||||
\(634\) | 34.3625 | 1.36471 | ||||||||
\(635\) | 44.5184 | 1.76666 | ||||||||
\(636\) | −1.90995 | −0.0757346 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 29.3614 | 1.16243 | ||||||||
\(639\) | −11.7872 | −0.466296 | ||||||||
\(640\) | −55.3586 | −2.18824 | ||||||||
\(641\) | 1.34976 | 0.0533123 | 0.0266561 | − | 0.999645i | \(-0.491514\pi\) | ||||
0.0266561 | + | 0.999645i | \(0.491514\pi\) | |||||||
\(642\) | 27.4908 | 1.08497 | ||||||||
\(643\) | −7.89870 | −0.311494 | −0.155747 | − | 0.987797i | \(-0.549778\pi\) | ||||
−0.155747 | + | 0.987797i | \(0.549778\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 29.8489 | 1.17530 | ||||||||
\(646\) | −31.9884 | −1.25857 | ||||||||
\(647\) | −28.1325 | −1.10600 | −0.553001 | − | 0.833181i | \(-0.686517\pi\) | ||||
−0.553001 | + | 0.833181i | \(0.686517\pi\) | |||||||
\(648\) | 2.41539 | 0.0948853 | ||||||||
\(649\) | −27.4622 | −1.07798 | ||||||||
\(650\) | −18.1648 | −0.712482 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.28215 | 0.206865 | ||||||||
\(653\) | −19.2013 | −0.751404 | −0.375702 | − | 0.926741i | \(-0.622598\pi\) | ||||
−0.375702 | + | 0.926741i | \(0.622598\pi\) | |||||||
\(654\) | −7.22869 | −0.282664 | ||||||||
\(655\) | 35.4117 | 1.38365 | ||||||||
\(656\) | −5.38584 | −0.210282 | ||||||||
\(657\) | −1.93497 | −0.0754904 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.9388 | 0.504026 | 0.252013 | − | 0.967724i | \(-0.418907\pi\) | ||||
0.252013 | + | 0.967724i | \(0.418907\pi\) | |||||||
\(660\) | 8.61870 | 0.335482 | ||||||||
\(661\) | 32.2877 | 1.25585 | 0.627924 | − | 0.778275i | \(-0.283905\pi\) | ||||
0.627924 | + | 0.778275i | \(0.283905\pi\) | |||||||
\(662\) | −5.15202 | −0.200239 | ||||||||
\(663\) | −3.53841 | −0.137420 | ||||||||
\(664\) | 21.0073 | 0.815241 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −14.0535 | −0.544561 | ||||||||
\(667\) | −17.8453 | −0.690971 | ||||||||
\(668\) | 9.13266 | 0.353353 | ||||||||
\(669\) | −6.52248 | −0.252174 | ||||||||
\(670\) | 62.3432 | 2.40853 | ||||||||
\(671\) | 2.61271 | 0.100863 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.69092 | 0.103727 | 0.0518637 | − | 0.998654i | \(-0.483484\pi\) | ||||
0.0518637 | + | 0.998654i | \(0.483484\pi\) | |||||||
\(674\) | 29.2257 | 1.12573 | ||||||||
\(675\) | −11.5814 | −0.445770 | ||||||||
\(676\) | 0.460010 | 0.0176927 | ||||||||
\(677\) | −39.4057 | −1.51448 | −0.757242 | − | 0.653134i | \(-0.773454\pi\) | ||||
−0.757242 | + | 0.653134i | \(0.773454\pi\) | |||||||
\(678\) | 33.1013 | 1.27125 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 34.8021 | 1.33460 | ||||||||
\(681\) | 10.7148 | 0.410591 | ||||||||
\(682\) | −23.6974 | −0.907422 | ||||||||
\(683\) | −25.7397 | −0.984902 | −0.492451 | − | 0.870340i | \(-0.663899\pi\) | ||||
−0.492451 | + | 0.870340i | \(0.663899\pi\) | |||||||
\(684\) | 2.65144 | 0.101381 | ||||||||
\(685\) | 80.5753 | 3.07863 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.5517 | −0.440726 | ||||||||
\(688\) | 34.5137 | 1.31582 | ||||||||
\(689\) | 4.15199 | 0.158178 | ||||||||
\(690\) | −28.0128 | −1.06643 | ||||||||
\(691\) | −47.3570 | −1.80155 | −0.900773 | − | 0.434291i | \(-0.856999\pi\) | ||||
−0.900773 | + | 0.434291i | \(0.856999\pi\) | |||||||
\(692\) | −4.04105 | −0.153618 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.2016 | 0.539087 | ||||||||
\(695\) | 77.3337 | 2.93344 | ||||||||
\(696\) | −9.82725 | −0.372501 | ||||||||
\(697\) | 4.04751 | 0.153310 | ||||||||
\(698\) | 49.3334 | 1.86730 | ||||||||
\(699\) | −8.20034 | −0.310165 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.39707 | 0.0905361 | 0.0452680 | − | 0.998975i | \(-0.485586\pi\) | ||||
0.0452680 | + | 0.998975i | \(0.485586\pi\) | |||||||
\(702\) | 1.56844 | 0.0591970 | ||||||||
\(703\) | 51.6453 | 1.94784 | ||||||||
\(704\) | −24.8961 | −0.938306 | ||||||||
\(705\) | −30.4040 | −1.14508 | ||||||||
\(706\) | −19.6879 | −0.740965 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.74561 | −0.103186 | ||||||||
\(709\) | 9.19194 | 0.345211 | 0.172605 | − | 0.984991i | \(-0.444781\pi\) | ||||
0.172605 | + | 0.984991i | \(0.444781\pi\) | |||||||
\(710\) | 75.2821 | 2.82529 | ||||||||
\(711\) | 3.44078 | 0.129039 | ||||||||
\(712\) | −35.1358 | −1.31677 | ||||||||
\(713\) | 14.4028 | 0.539389 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.7359 | −0.700683 | ||||||||
\(716\) | 8.29092 | 0.309846 | ||||||||
\(717\) | −2.61709 | −0.0977372 | ||||||||
\(718\) | 19.4681 | 0.726542 | ||||||||
\(719\) | −30.2655 | −1.12871 | −0.564356 | − | 0.825532i | \(-0.690875\pi\) | ||||
−0.564356 | + | 0.825532i | \(0.690875\pi\) | |||||||
\(720\) | −19.1728 | −0.714528 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −22.3070 | −0.830182 | ||||||||
\(723\) | 19.3871 | 0.721014 | ||||||||
\(724\) | −1.51160 | −0.0561780 | ||||||||
\(725\) | 47.1203 | 1.75000 | ||||||||
\(726\) | 15.9515 | 0.592017 | ||||||||
\(727\) | −1.08475 | −0.0402311 | −0.0201156 | − | 0.999798i | \(-0.506403\pi\) | ||||
−0.0201156 | + | 0.999798i | \(0.506403\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 12.3582 | 0.457396 | ||||||||
\(731\) | −25.9373 | −0.959327 | ||||||||
\(732\) | 0.261213 | 0.00965472 | ||||||||
\(733\) | −1.00679 | −0.0371865 | −0.0185933 | − | 0.999827i | \(-0.505919\pi\) | ||||
−0.0185933 | + | 0.999827i | \(0.505919\pi\) | |||||||
\(734\) | 12.8187 | 0.473146 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11.2025 | −0.412930 | ||||||||
\(737\) | 44.9131 | 1.65440 | ||||||||
\(738\) | −1.79411 | −0.0660419 | ||||||||
\(739\) | −13.9633 | −0.513649 | −0.256825 | − | 0.966458i | \(-0.582676\pi\) | ||||
−0.256825 | + | 0.966458i | \(0.582676\pi\) | |||||||
\(740\) | 16.7839 | 0.616989 | ||||||||
\(741\) | −5.76389 | −0.211742 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.134889 | 0.00494861 | 0.00247431 | − | 0.999997i | \(-0.499212\pi\) | ||||
0.00247431 | + | 0.999997i | \(0.499212\pi\) | |||||||
\(744\) | 7.93151 | 0.290783 | ||||||||
\(745\) | −4.77897 | −0.175088 | ||||||||
\(746\) | 27.7912 | 1.01751 | ||||||||
\(747\) | 8.69728 | 0.318217 | ||||||||
\(748\) | −7.48925 | −0.273834 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 42.0339 | 1.53486 | ||||||||
\(751\) | −13.3462 | −0.487010 | −0.243505 | − | 0.969900i | \(-0.578297\pi\) | ||||
−0.243505 | + | 0.969900i | \(0.578297\pi\) | |||||||
\(752\) | −35.1555 | −1.28199 | ||||||||
\(753\) | 15.4043 | 0.561364 | ||||||||
\(754\) | −6.38137 | −0.232396 | ||||||||
\(755\) | 54.2931 | 1.97593 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −43.6217 | −1.58546 | −0.792729 | − | 0.609574i | \(-0.791341\pi\) | ||||
−0.792729 | + | 0.609574i | \(0.791341\pi\) | |||||||
\(758\) | −18.5299 | −0.673036 | ||||||||
\(759\) | −20.1809 | −0.732521 | ||||||||
\(760\) | 56.6909 | 2.05639 | ||||||||
\(761\) | 2.96599 | 0.107517 | 0.0537585 | − | 0.998554i | \(-0.482880\pi\) | ||||
0.0537585 | + | 0.998554i | \(0.482880\pi\) | |||||||
\(762\) | 17.1473 | 0.621182 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1.45070 | −0.0524846 | ||||||||
\(765\) | 14.4085 | 0.520941 | ||||||||
\(766\) | 31.4580 | 1.13662 | ||||||||
\(767\) | 5.96858 | 0.215513 | ||||||||
\(768\) | −10.5010 | −0.378921 | ||||||||
\(769\) | −28.6571 | −1.03340 | −0.516700 | − | 0.856166i | \(-0.672840\pi\) | ||||
−0.516700 | + | 0.856166i | \(0.672840\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.7467 | 0.423048 | ||||||||
\(772\) | −10.3657 | −0.373068 | ||||||||
\(773\) | 44.6810 | 1.60707 | 0.803533 | − | 0.595261i | \(-0.202951\pi\) | ||||
0.803533 | + | 0.595261i | \(0.202951\pi\) | |||||||
\(774\) | 11.4970 | 0.413252 | ||||||||
\(775\) | −38.0305 | −1.36610 | ||||||||
\(776\) | −32.4514 | −1.16494 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 33.9598 | 1.21752 | ||||||||
\(779\) | 6.59318 | 0.236225 | ||||||||
\(780\) | −1.87317 | −0.0670704 | ||||||||
\(781\) | 54.2345 | 1.94066 | ||||||||
\(782\) | 24.3419 | 0.870464 | ||||||||
\(783\) | −4.06860 | −0.145400 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −64.4597 | −2.30067 | ||||||||
\(786\) | 13.6397 | 0.486511 | ||||||||
\(787\) | −46.4162 | −1.65456 | −0.827280 | − | 0.561790i | \(-0.810113\pi\) | ||||
−0.827280 | + | 0.561790i | \(0.810113\pi\) | |||||||
\(788\) | 3.17641 | 0.113155 | ||||||||
\(789\) | 16.6278 | 0.591967 | ||||||||
\(790\) | −21.9754 | −0.781848 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −11.1135 | −0.394900 | ||||||||
\(793\) | −0.567843 | −0.0201647 | ||||||||
\(794\) | −23.8634 | −0.846880 | ||||||||
\(795\) | −16.9070 | −0.599630 | ||||||||
\(796\) | 5.77238 | 0.204597 | ||||||||
\(797\) | −3.09573 | −0.109656 | −0.0548282 | − | 0.998496i | \(-0.517461\pi\) | ||||
−0.0548282 | + | 0.998496i | \(0.517461\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.4197 | 0.934661 | ||||||||
\(800\) | 29.5801 | 1.04581 | ||||||||
\(801\) | −14.5467 | −0.513981 | ||||||||
\(802\) | −55.5188 | −1.96044 | ||||||||
\(803\) | 8.90304 | 0.314181 | ||||||||
\(804\) | 4.49031 | 0.158361 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.15036 | 0.181414 | ||||||||
\(807\) | −23.2608 | −0.818818 | ||||||||
\(808\) | −1.40984 | −0.0495981 | ||||||||
\(809\) | 28.8937 | 1.01585 | 0.507924 | − | 0.861402i | \(-0.330413\pi\) | ||||
0.507924 | + | 0.861402i | \(0.330413\pi\) | |||||||
\(810\) | −6.38674 | −0.224407 | ||||||||
\(811\) | 1.22047 | 0.0428564 | 0.0214282 | − | 0.999770i | \(-0.493179\pi\) | ||||
0.0214282 | + | 0.999770i | \(0.493179\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.92931 | −0.243022 | ||||||||
\(814\) | 64.6617 | 2.26639 | ||||||||
\(815\) | 46.7579 | 1.63786 | ||||||||
\(816\) | 16.6603 | 0.583227 | ||||||||
\(817\) | −42.2506 | −1.47816 | ||||||||
\(818\) | −41.2563 | −1.44249 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.14268 | 0.0748257 | ||||||||
\(821\) | −26.4548 | −0.923279 | −0.461639 | − | 0.887068i | \(-0.652739\pi\) | ||||
−0.461639 | + | 0.887068i | \(0.652739\pi\) | |||||||
\(822\) | 31.0356 | 1.08249 | ||||||||
\(823\) | −35.7622 | −1.24659 | −0.623296 | − | 0.781986i | \(-0.714207\pi\) | ||||
−0.623296 | + | 0.781986i | \(0.714207\pi\) | |||||||
\(824\) | −33.9296 | −1.18199 | ||||||||
\(825\) | 53.2876 | 1.85524 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.9518 | −0.624245 | −0.312122 | − | 0.950042i | \(-0.601040\pi\) | ||||
−0.312122 | + | 0.950042i | \(0.601040\pi\) | |||||||
\(828\) | −2.01764 | −0.0701180 | ||||||||
\(829\) | −25.4594 | −0.884240 | −0.442120 | − | 0.896956i | \(-0.645773\pi\) | ||||
−0.442120 | + | 0.896956i | \(0.645773\pi\) | |||||||
\(830\) | −55.5473 | −1.92808 | ||||||||
\(831\) | 30.4994 | 1.05801 | ||||||||
\(832\) | 5.41087 | 0.187588 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 29.7870 | 1.03144 | ||||||||
\(835\) | 80.8429 | 2.79768 | ||||||||
\(836\) | −12.1996 | −0.421933 | ||||||||
\(837\) | 3.28375 | 0.113503 | ||||||||
\(838\) | −33.1118 | −1.14383 | ||||||||
\(839\) | −20.0448 | −0.692022 | −0.346011 | − | 0.938230i | \(-0.612464\pi\) | ||||
−0.346011 | + | 0.938230i | \(0.612464\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.4465 | −0.429188 | ||||||||
\(842\) | −50.9157 | −1.75467 | ||||||||
\(843\) | −17.6855 | −0.609122 | ||||||||
\(844\) | 7.80952 | 0.268815 | ||||||||
\(845\) | 4.07203 | 0.140082 | ||||||||
\(846\) | −11.7108 | −0.402627 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −19.5493 | −0.671324 | ||||||||
\(849\) | −1.38350 | −0.0474816 | ||||||||
\(850\) | −64.2745 | −2.20460 | ||||||||
\(851\) | −39.3000 | −1.34719 | ||||||||
\(852\) | 5.42224 | 0.185763 | ||||||||
\(853\) | −7.78420 | −0.266526 | −0.133263 | − | 0.991081i | \(-0.542545\pi\) | ||||
−0.133263 | + | 0.991081i | \(0.542545\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 23.4707 | 0.802682 | ||||||||
\(856\) | 42.3355 | 1.44700 | ||||||||
\(857\) | 12.4762 | 0.426179 | 0.213090 | − | 0.977033i | \(-0.431647\pi\) | ||||
0.213090 | + | 0.977033i | \(0.431647\pi\) | |||||||
\(858\) | −7.21659 | −0.246370 | ||||||||
\(859\) | 6.48868 | 0.221391 | 0.110696 | − | 0.993854i | \(-0.464692\pi\) | ||||
0.110696 | + | 0.993854i | \(0.464692\pi\) | |||||||
\(860\) | −13.7308 | −0.468216 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −57.2115 | −1.94863 | ||||||||
\(863\) | 30.7541 | 1.04688 | 0.523441 | − | 0.852062i | \(-0.324648\pi\) | ||||
0.523441 | + | 0.852062i | \(0.324648\pi\) | |||||||
\(864\) | −2.55410 | −0.0868921 | ||||||||
\(865\) | −35.7716 | −1.21627 | ||||||||
\(866\) | −27.8268 | −0.945593 | ||||||||
\(867\) | 4.47966 | 0.152137 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.8314 | −0.537044 | ||||||||
\(870\) | 25.9851 | 0.880978 | ||||||||
\(871\) | −9.76134 | −0.330750 | ||||||||
\(872\) | −11.1321 | −0.376981 | ||||||||
\(873\) | −13.4353 | −0.454715 | ||||||||
\(874\) | 39.6517 | 1.34124 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.890105 | 0.0300739 | ||||||||
\(877\) | −27.8274 | −0.939666 | −0.469833 | − | 0.882755i | \(-0.655686\pi\) | ||||
−0.469833 | + | 0.882755i | \(0.655686\pi\) | |||||||
\(878\) | −10.1005 | −0.340877 | ||||||||
\(879\) | −16.2793 | −0.549088 | ||||||||
\(880\) | 88.2163 | 2.97377 | ||||||||
\(881\) | −9.94004 | −0.334889 | −0.167444 | − | 0.985882i | \(-0.553551\pi\) | ||||
−0.167444 | + | 0.985882i | \(0.553551\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.9098 | −0.535409 | −0.267704 | − | 0.963501i | \(-0.586265\pi\) | ||||
−0.267704 | + | 0.963501i | \(0.586265\pi\) | |||||||
\(884\) | 1.62770 | 0.0547455 | ||||||||
\(885\) | −24.3043 | −0.816979 | ||||||||
\(886\) | −4.51852 | −0.151803 | ||||||||
\(887\) | −24.1568 | −0.811106 | −0.405553 | − | 0.914072i | \(-0.632921\pi\) | ||||
−0.405553 | + | 0.914072i | \(0.632921\pi\) | |||||||
\(888\) | −21.6422 | −0.726265 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 92.9057 | 3.11421 | ||||||||
\(891\) | −4.60112 | −0.154143 | ||||||||
\(892\) | 3.00040 | 0.100461 | ||||||||
\(893\) | 43.0363 | 1.44015 | ||||||||
\(894\) | −1.84074 | −0.0615635 | ||||||||
\(895\) | 73.3917 | 2.45321 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.38609 | 0.146447 | ||||||||
\(898\) | −6.78643 | −0.226466 | ||||||||
\(899\) | −13.3603 | −0.445590 | ||||||||
\(900\) | 5.32757 | 0.177586 | ||||||||
\(901\) | 14.6914 | 0.489442 | ||||||||
\(902\) | 8.25490 | 0.274858 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 50.9758 | 1.69543 | ||||||||
\(905\) | −13.3807 | −0.444791 | ||||||||
\(906\) | 20.9123 | 0.694765 | ||||||||
\(907\) | −40.0985 | −1.33145 | −0.665725 | − | 0.746197i | \(-0.731878\pi\) | ||||
−0.665725 | + | 0.746197i | \(0.731878\pi\) | |||||||
\(908\) | −4.92890 | −0.163571 | ||||||||
\(909\) | −0.583693 | −0.0193599 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.5863 | 0.913974 | 0.456987 | − | 0.889473i | \(-0.348929\pi\) | ||||
0.456987 | + | 0.889473i | \(0.348929\pi\) | |||||||
\(912\) | 27.1388 | 0.898654 | ||||||||
\(913\) | −40.0173 | −1.32438 | ||||||||
\(914\) | 13.5971 | 0.449753 | ||||||||
\(915\) | 2.31227 | 0.0764414 | ||||||||
\(916\) | 5.31390 | 0.175576 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5.54979 | 0.183170 | ||||||||
\(919\) | −2.47113 | −0.0815149 | −0.0407575 | − | 0.999169i | \(-0.512977\pi\) | ||||
−0.0407575 | + | 0.999169i | \(0.512977\pi\) | |||||||
\(920\) | −43.1395 | −1.42227 | ||||||||
\(921\) | −4.45151 | −0.146682 | ||||||||
\(922\) | −14.4854 | −0.477051 | ||||||||
\(923\) | −11.7872 | −0.387982 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 103.771 | 3.41198 | ||||||||
\(926\) | 28.8865 | 0.949268 | ||||||||
\(927\) | −14.0473 | −0.461374 | ||||||||
\(928\) | 10.3916 | 0.341121 | ||||||||
\(929\) | −52.6033 | −1.72586 | −0.862928 | − | 0.505326i | \(-0.831372\pi\) | ||||
−0.862928 | + | 0.505326i | \(0.831372\pi\) | |||||||
\(930\) | −20.9724 | −0.687713 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 3.77223 | 0.123564 | ||||||||
\(933\) | −26.9233 | −0.881429 | ||||||||
\(934\) | 8.75980 | 0.286629 | ||||||||
\(935\) | −66.2953 | −2.16809 | ||||||||
\(936\) | 2.41539 | 0.0789493 | ||||||||
\(937\) | −15.0724 | −0.492393 | −0.246196 | − | 0.969220i | \(-0.579181\pi\) | ||||
−0.246196 | + | 0.969220i | \(0.579181\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.9157 | −0.356220 | ||||||||
\(940\) | 13.9861 | 0.456177 | ||||||||
\(941\) | −10.4483 | −0.340606 | −0.170303 | − | 0.985392i | \(-0.554475\pi\) | ||||
−0.170303 | + | 0.985392i | \(0.554475\pi\) | |||||||
\(942\) | −24.8282 | −0.808948 | ||||||||
\(943\) | −5.01715 | −0.163381 | ||||||||
\(944\) | −28.1025 | −0.914660 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −52.8992 | −1.71990 | ||||||||
\(947\) | 45.1536 | 1.46729 | 0.733647 | − | 0.679531i | \(-0.237817\pi\) | ||||
0.733647 | + | 0.679531i | \(0.237817\pi\) | |||||||
\(948\) | −1.58279 | −0.0514066 | ||||||||
\(949\) | −1.93497 | −0.0628118 | ||||||||
\(950\) | −104.700 | −3.39692 | ||||||||
\(951\) | 21.9087 | 0.710439 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −43.1993 | −1.39936 | −0.699681 | − | 0.714455i | \(-0.746675\pi\) | ||||
−0.699681 | + | 0.714455i | \(0.746675\pi\) | |||||||
\(954\) | −6.51215 | −0.210839 | ||||||||
\(955\) | −12.8417 | −0.415548 | ||||||||
\(956\) | 1.20389 | 0.0389365 | ||||||||
\(957\) | 18.7201 | 0.605136 | ||||||||
\(958\) | 35.9208 | 1.16055 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −22.0332 | −0.711119 | ||||||||
\(961\) | −20.2170 | −0.652162 | ||||||||
\(962\) | −14.0535 | −0.453102 | ||||||||
\(963\) | 17.5274 | 0.564814 | ||||||||
\(964\) | −8.91825 | −0.287237 | ||||||||
\(965\) | −91.7574 | −2.95377 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.4260 | 0.689014 | 0.344507 | − | 0.938784i | \(-0.388046\pi\) | ||||
0.344507 | + | 0.938784i | \(0.388046\pi\) | |||||||
\(968\) | 24.5652 | 0.789556 | ||||||||
\(969\) | −20.3950 | −0.655182 | ||||||||
\(970\) | 85.8077 | 2.75512 | ||||||||
\(971\) | 18.1710 | 0.583134 | 0.291567 | − | 0.956550i | \(-0.405823\pi\) | ||||
0.291567 | + | 0.956550i | \(0.405823\pi\) | |||||||
\(972\) | −0.460010 | −0.0147548 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 16.0040 | 0.512802 | ||||||||
\(975\) | −11.5814 | −0.370903 | ||||||||
\(976\) | 2.67364 | 0.0855811 | ||||||||
\(977\) | −21.7732 | −0.696586 | −0.348293 | − | 0.937386i | \(-0.613239\pi\) | ||||
−0.348293 | + | 0.937386i | \(0.613239\pi\) | |||||||
\(978\) | 18.0099 | 0.575894 | ||||||||
\(979\) | 66.9309 | 2.13912 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.60883 | −0.147149 | ||||||||
\(982\) | −19.9493 | −0.636609 | ||||||||
\(983\) | −22.5164 | −0.718163 | −0.359082 | − | 0.933306i | \(-0.616910\pi\) | ||||
−0.359082 | + | 0.933306i | \(0.616910\pi\) | |||||||
\(984\) | −2.76290 | −0.0880782 | ||||||||
\(985\) | 28.1178 | 0.895907 | ||||||||
\(986\) | −22.5799 | −0.719090 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.65144 | 0.0843537 | ||||||||
\(989\) | 32.1510 | 1.02234 | ||||||||
\(990\) | 29.3862 | 0.933954 | ||||||||
\(991\) | −4.75019 | −0.150895 | −0.0754474 | − | 0.997150i | \(-0.524038\pi\) | ||||
−0.0754474 | + | 0.997150i | \(0.524038\pi\) | |||||||
\(992\) | −8.38700 | −0.266288 | ||||||||
\(993\) | −3.28480 | −0.104240 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 51.0974 | 1.61990 | ||||||||
\(996\) | −4.00083 | −0.126771 | ||||||||
\(997\) | 19.0546 | 0.603465 | 0.301733 | − | 0.953393i | \(-0.402435\pi\) | ||||
0.301733 | + | 0.953393i | \(0.402435\pi\) | |||||||
\(998\) | −17.6531 | −0.558798 | ||||||||
\(999\) | −8.96014 | −0.283486 |
(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 | 1911.2.a.x.1.3 | ✓ | 10 | |
3.2 | odd | 2 | 5733.2.a.bw.1.8 | 10 | |||
7.6 | odd | 2 | 1911.2.a.y.1.3 | yes | 10 | ||
21.20 | even | 2 | 5733.2.a.bx.1.8 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1911.2.a.x.1.3 | ✓ | 10 | 1.1 | even | 1 | trivial | |
1911.2.a.y.1.3 | yes | 10 | 7.6 | odd | 2 | ||
5733.2.a.bw.1.8 | 10 | 3.2 | odd | 2 | |||
5733.2.a.bx.1.8 | 10 | 21.20 | even | 2 |