Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0240523407\) |
Analytic rank: | \(0\) |
Dimension: | \(47\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.43 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 3.10004 | 1.78981 | 0.894905 | − | 0.446257i | \(-0.147243\pi\) | ||||
0.894905 | + | 0.446257i | \(0.147243\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.73533 | 0.776062 | 0.388031 | − | 0.921646i | \(-0.373155\pi\) | ||||
0.388031 | + | 0.921646i | \(0.373155\pi\) | |||||||
\(6\) | 3.10004 | 1.26559 | ||||||||
\(7\) | 3.71776 | 1.40518 | 0.702590 | − | 0.711595i | \(-0.252027\pi\) | ||||
0.702590 | + | 0.711595i | \(0.252027\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 6.61026 | 2.20342 | ||||||||
\(10\) | 1.73533 | 0.548759 | ||||||||
\(11\) | 0.351101 | 0.105861 | 0.0529304 | − | 0.998598i | \(-0.483144\pi\) | ||||
0.0529304 | + | 0.998598i | \(0.483144\pi\) | |||||||
\(12\) | 3.10004 | 0.894905 | ||||||||
\(13\) | −3.27955 | −0.909585 | −0.454792 | − | 0.890597i | \(-0.650287\pi\) | ||||
−0.454792 | + | 0.890597i | \(0.650287\pi\) | |||||||
\(14\) | 3.71776 | 0.993612 | ||||||||
\(15\) | 5.37959 | 1.38900 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.752399 | 0.182484 | 0.0912418 | − | 0.995829i | \(-0.470916\pi\) | ||||
0.0912418 | + | 0.995829i | \(0.470916\pi\) | |||||||
\(18\) | 6.61026 | 1.55805 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 1.73533 | 0.388031 | ||||||||
\(21\) | 11.5252 | 2.51500 | ||||||||
\(22\) | 0.351101 | 0.0748550 | ||||||||
\(23\) | −6.92588 | −1.44415 | −0.722073 | − | 0.691817i | \(-0.756810\pi\) | ||||
−0.722073 | + | 0.691817i | \(0.756810\pi\) | |||||||
\(24\) | 3.10004 | 0.632793 | ||||||||
\(25\) | −1.98864 | −0.397727 | ||||||||
\(26\) | −3.27955 | −0.643174 | ||||||||
\(27\) | 11.1919 | 2.15389 | ||||||||
\(28\) | 3.71776 | 0.702590 | ||||||||
\(29\) | 1.99959 | 0.371315 | 0.185657 | − | 0.982615i | \(-0.440559\pi\) | ||||
0.185657 | + | 0.982615i | \(0.440559\pi\) | |||||||
\(30\) | 5.37959 | 0.982174 | ||||||||
\(31\) | −1.76755 | −0.317461 | −0.158730 | − | 0.987322i | \(-0.550740\pi\) | ||||
−0.158730 | + | 0.987322i | \(0.550740\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.08843 | 0.189471 | ||||||||
\(34\) | 0.752399 | 0.129035 | ||||||||
\(35\) | 6.45153 | 1.09051 | ||||||||
\(36\) | 6.61026 | 1.10171 | ||||||||
\(37\) | −9.46076 | −1.55534 | −0.777669 | − | 0.628673i | \(-0.783598\pi\) | ||||
−0.777669 | + | 0.628673i | \(0.783598\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | −10.1668 | −1.62798 | ||||||||
\(40\) | 1.73533 | 0.274379 | ||||||||
\(41\) | 7.34124 | 1.14651 | 0.573255 | − | 0.819377i | \(-0.305681\pi\) | ||||
0.573255 | + | 0.819377i | \(0.305681\pi\) | |||||||
\(42\) | 11.5252 | 1.77838 | ||||||||
\(43\) | 4.84196 | 0.738392 | 0.369196 | − | 0.929352i | \(-0.379633\pi\) | ||||
0.369196 | + | 0.929352i | \(0.379633\pi\) | |||||||
\(44\) | 0.351101 | 0.0529304 | ||||||||
\(45\) | 11.4710 | 1.70999 | ||||||||
\(46\) | −6.92588 | −1.02117 | ||||||||
\(47\) | 9.66475 | 1.40975 | 0.704874 | − | 0.709332i | \(-0.251003\pi\) | ||||
0.704874 | + | 0.709332i | \(0.251003\pi\) | |||||||
\(48\) | 3.10004 | 0.447452 | ||||||||
\(49\) | 6.82172 | 0.974531 | ||||||||
\(50\) | −1.98864 | −0.281236 | ||||||||
\(51\) | 2.33247 | 0.326611 | ||||||||
\(52\) | −3.27955 | −0.454792 | ||||||||
\(53\) | −12.6718 | −1.74060 | −0.870301 | − | 0.492521i | \(-0.836076\pi\) | ||||
−0.870301 | + | 0.492521i | \(0.836076\pi\) | |||||||
\(54\) | 11.1919 | 1.52303 | ||||||||
\(55\) | 0.609275 | 0.0821547 | ||||||||
\(56\) | 3.71776 | 0.496806 | ||||||||
\(57\) | −3.10004 | −0.410610 | ||||||||
\(58\) | 1.99959 | 0.262559 | ||||||||
\(59\) | −2.58178 | −0.336119 | −0.168059 | − | 0.985777i | \(-0.553750\pi\) | ||||
−0.168059 | + | 0.985777i | \(0.553750\pi\) | |||||||
\(60\) | 5.37959 | 0.694502 | ||||||||
\(61\) | −3.16536 | −0.405283 | −0.202642 | − | 0.979253i | \(-0.564953\pi\) | ||||
−0.202642 | + | 0.979253i | \(0.564953\pi\) | |||||||
\(62\) | −1.76755 | −0.224479 | ||||||||
\(63\) | 24.5753 | 3.09620 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.69110 | −0.705895 | ||||||||
\(66\) | 1.08843 | 0.133976 | ||||||||
\(67\) | 14.5796 | 1.78118 | 0.890592 | − | 0.454803i | \(-0.150290\pi\) | ||||
0.890592 | + | 0.454803i | \(0.150290\pi\) | |||||||
\(68\) | 0.752399 | 0.0912418 | ||||||||
\(69\) | −21.4705 | −2.58475 | ||||||||
\(70\) | 6.45153 | 0.771105 | ||||||||
\(71\) | 2.53897 | 0.301321 | 0.150660 | − | 0.988586i | \(-0.451860\pi\) | ||||
0.150660 | + | 0.988586i | \(0.451860\pi\) | |||||||
\(72\) | 6.61026 | 0.779026 | ||||||||
\(73\) | −4.14205 | −0.484791 | −0.242395 | − | 0.970178i | \(-0.577933\pi\) | ||||
−0.242395 | + | 0.970178i | \(0.577933\pi\) | |||||||
\(74\) | −9.46076 | −1.09979 | ||||||||
\(75\) | −6.16485 | −0.711856 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 1.30531 | 0.148754 | ||||||||
\(78\) | −10.1668 | −1.15116 | ||||||||
\(79\) | 2.86347 | 0.322165 | 0.161083 | − | 0.986941i | \(-0.448501\pi\) | ||||
0.161083 | + | 0.986941i | \(0.448501\pi\) | |||||||
\(80\) | 1.73533 | 0.194016 | ||||||||
\(81\) | 14.8647 | 1.65163 | ||||||||
\(82\) | 7.34124 | 0.810704 | ||||||||
\(83\) | 13.5727 | 1.48980 | 0.744899 | − | 0.667177i | \(-0.232498\pi\) | ||||
0.744899 | + | 0.667177i | \(0.232498\pi\) | |||||||
\(84\) | 11.5252 | 1.25750 | ||||||||
\(85\) | 1.30566 | 0.141619 | ||||||||
\(86\) | 4.84196 | 0.522122 | ||||||||
\(87\) | 6.19882 | 0.664583 | ||||||||
\(88\) | 0.351101 | 0.0374275 | ||||||||
\(89\) | 13.1952 | 1.39869 | 0.699345 | − | 0.714784i | \(-0.253475\pi\) | ||||
0.699345 | + | 0.714784i | \(0.253475\pi\) | |||||||
\(90\) | 11.4710 | 1.20915 | ||||||||
\(91\) | −12.1926 | −1.27813 | ||||||||
\(92\) | −6.92588 | −0.722073 | ||||||||
\(93\) | −5.47947 | −0.568194 | ||||||||
\(94\) | 9.66475 | 0.996843 | ||||||||
\(95\) | −1.73533 | −0.178041 | ||||||||
\(96\) | 3.10004 | 0.316397 | ||||||||
\(97\) | 1.69040 | 0.171634 | 0.0858172 | − | 0.996311i | \(-0.472650\pi\) | ||||
0.0858172 | + | 0.996311i | \(0.472650\pi\) | |||||||
\(98\) | 6.82172 | 0.689098 | ||||||||
\(99\) | 2.32087 | 0.233256 | ||||||||
\(100\) | −1.98864 | −0.198864 | ||||||||
\(101\) | 3.23070 | 0.321466 | 0.160733 | − | 0.986998i | \(-0.448614\pi\) | ||||
0.160733 | + | 0.986998i | \(0.448614\pi\) | |||||||
\(102\) | 2.33247 | 0.230949 | ||||||||
\(103\) | −9.39478 | −0.925695 | −0.462848 | − | 0.886438i | \(-0.653172\pi\) | ||||
−0.462848 | + | 0.886438i | \(0.653172\pi\) | |||||||
\(104\) | −3.27955 | −0.321587 | ||||||||
\(105\) | 20.0000 | 1.95180 | ||||||||
\(106\) | −12.6718 | −1.23079 | ||||||||
\(107\) | −11.1153 | −1.07456 | −0.537279 | − | 0.843405i | \(-0.680548\pi\) | ||||
−0.537279 | + | 0.843405i | \(0.680548\pi\) | |||||||
\(108\) | 11.1919 | 1.07694 | ||||||||
\(109\) | −15.2968 | −1.46516 | −0.732582 | − | 0.680678i | \(-0.761685\pi\) | ||||
−0.732582 | + | 0.680678i | \(0.761685\pi\) | |||||||
\(110\) | 0.609275 | 0.0580921 | ||||||||
\(111\) | −29.3287 | −2.78376 | ||||||||
\(112\) | 3.71776 | 0.351295 | ||||||||
\(113\) | 4.41686 | 0.415503 | 0.207752 | − | 0.978182i | \(-0.433385\pi\) | ||||
0.207752 | + | 0.978182i | \(0.433385\pi\) | |||||||
\(114\) | −3.10004 | −0.290345 | ||||||||
\(115\) | −12.0187 | −1.12075 | ||||||||
\(116\) | 1.99959 | 0.185657 | ||||||||
\(117\) | −21.6787 | −2.00420 | ||||||||
\(118\) | −2.58178 | −0.237672 | ||||||||
\(119\) | 2.79724 | 0.256422 | ||||||||
\(120\) | 5.37959 | 0.491087 | ||||||||
\(121\) | −10.8767 | −0.988793 | ||||||||
\(122\) | −3.16536 | −0.286578 | ||||||||
\(123\) | 22.7581 | 2.05203 | ||||||||
\(124\) | −1.76755 | −0.158730 | ||||||||
\(125\) | −12.1276 | −1.08472 | ||||||||
\(126\) | 24.5753 | 2.18934 | ||||||||
\(127\) | −1.09609 | −0.0972621 | −0.0486311 | − | 0.998817i | \(-0.515486\pi\) | ||||
−0.0486311 | + | 0.998817i | \(0.515486\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 15.0103 | 1.32158 | ||||||||
\(130\) | −5.69110 | −0.499143 | ||||||||
\(131\) | −3.34665 | −0.292398 | −0.146199 | − | 0.989255i | \(-0.546704\pi\) | ||||
−0.146199 | + | 0.989255i | \(0.546704\pi\) | |||||||
\(132\) | 1.08843 | 0.0947354 | ||||||||
\(133\) | −3.71776 | −0.322370 | ||||||||
\(134\) | 14.5796 | 1.25949 | ||||||||
\(135\) | 19.4217 | 1.67155 | ||||||||
\(136\) | 0.752399 | 0.0645177 | ||||||||
\(137\) | −3.27539 | −0.279835 | −0.139918 | − | 0.990163i | \(-0.544684\pi\) | ||||
−0.139918 | + | 0.990163i | \(0.544684\pi\) | |||||||
\(138\) | −21.4705 | −1.82769 | ||||||||
\(139\) | 11.3529 | 0.962944 | 0.481472 | − | 0.876462i | \(-0.340102\pi\) | ||||
0.481472 | + | 0.876462i | \(0.340102\pi\) | |||||||
\(140\) | 6.45153 | 0.545254 | ||||||||
\(141\) | 29.9611 | 2.52318 | ||||||||
\(142\) | 2.53897 | 0.213066 | ||||||||
\(143\) | −1.15145 | −0.0962895 | ||||||||
\(144\) | 6.61026 | 0.550855 | ||||||||
\(145\) | 3.46995 | 0.288164 | ||||||||
\(146\) | −4.14205 | −0.342799 | ||||||||
\(147\) | 21.1476 | 1.74423 | ||||||||
\(148\) | −9.46076 | −0.777669 | ||||||||
\(149\) | 6.47207 | 0.530212 | 0.265106 | − | 0.964219i | \(-0.414593\pi\) | ||||
0.265106 | + | 0.964219i | \(0.414593\pi\) | |||||||
\(150\) | −6.16485 | −0.503358 | ||||||||
\(151\) | 12.6234 | 1.02728 | 0.513638 | − | 0.858007i | \(-0.328297\pi\) | ||||
0.513638 | + | 0.858007i | \(0.328297\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 4.97355 | 0.402088 | ||||||||
\(154\) | 1.30531 | 0.105185 | ||||||||
\(155\) | −3.06727 | −0.246369 | ||||||||
\(156\) | −10.1668 | −0.813992 | ||||||||
\(157\) | 1.06845 | 0.0852715 | 0.0426358 | − | 0.999091i | \(-0.486425\pi\) | ||||
0.0426358 | + | 0.999091i | \(0.486425\pi\) | |||||||
\(158\) | 2.86347 | 0.227805 | ||||||||
\(159\) | −39.2830 | −3.11535 | ||||||||
\(160\) | 1.73533 | 0.137190 | ||||||||
\(161\) | −25.7487 | −2.02928 | ||||||||
\(162\) | 14.8647 | 1.16788 | ||||||||
\(163\) | −11.4004 | −0.892949 | −0.446475 | − | 0.894796i | \(-0.647321\pi\) | ||||
−0.446475 | + | 0.894796i | \(0.647321\pi\) | |||||||
\(164\) | 7.34124 | 0.573255 | ||||||||
\(165\) | 1.88878 | 0.147041 | ||||||||
\(166\) | 13.5727 | 1.05345 | ||||||||
\(167\) | −4.82792 | −0.373596 | −0.186798 | − | 0.982398i | \(-0.559811\pi\) | ||||
−0.186798 | + | 0.982398i | \(0.559811\pi\) | |||||||
\(168\) | 11.5252 | 0.889189 | ||||||||
\(169\) | −2.24452 | −0.172656 | ||||||||
\(170\) | 1.30566 | 0.100139 | ||||||||
\(171\) | −6.61026 | −0.505499 | ||||||||
\(172\) | 4.84196 | 0.369196 | ||||||||
\(173\) | −17.2487 | −1.31139 | −0.655696 | − | 0.755025i | \(-0.727625\pi\) | ||||
−0.655696 | + | 0.755025i | \(0.727625\pi\) | |||||||
\(174\) | 6.19882 | 0.469931 | ||||||||
\(175\) | −7.39327 | −0.558878 | ||||||||
\(176\) | 0.351101 | 0.0264652 | ||||||||
\(177\) | −8.00362 | −0.601589 | ||||||||
\(178\) | 13.1952 | 0.989023 | ||||||||
\(179\) | 5.93539 | 0.443632 | 0.221816 | − | 0.975089i | \(-0.428802\pi\) | ||||
0.221816 | + | 0.975089i | \(0.428802\pi\) | |||||||
\(180\) | 11.4710 | 0.854995 | ||||||||
\(181\) | 20.9918 | 1.56031 | 0.780156 | − | 0.625585i | \(-0.215140\pi\) | ||||
0.780156 | + | 0.625585i | \(0.215140\pi\) | |||||||
\(182\) | −12.1926 | −0.903775 | ||||||||
\(183\) | −9.81275 | −0.725379 | ||||||||
\(184\) | −6.92588 | −0.510583 | ||||||||
\(185\) | −16.4175 | −1.20704 | ||||||||
\(186\) | −5.47947 | −0.401774 | ||||||||
\(187\) | 0.264168 | 0.0193179 | ||||||||
\(188\) | 9.66475 | 0.704874 | ||||||||
\(189\) | 41.6089 | 3.02660 | ||||||||
\(190\) | −1.73533 | −0.125894 | ||||||||
\(191\) | −24.5408 | −1.77571 | −0.887855 | − | 0.460123i | \(-0.847805\pi\) | ||||
−0.887855 | + | 0.460123i | \(0.847805\pi\) | |||||||
\(192\) | 3.10004 | 0.223726 | ||||||||
\(193\) | −11.0919 | −0.798415 | −0.399208 | − | 0.916860i | \(-0.630715\pi\) | ||||
−0.399208 | + | 0.916860i | \(0.630715\pi\) | |||||||
\(194\) | 1.69040 | 0.121364 | ||||||||
\(195\) | −17.6427 | −1.26342 | ||||||||
\(196\) | 6.82172 | 0.487266 | ||||||||
\(197\) | 8.13853 | 0.579846 | 0.289923 | − | 0.957050i | \(-0.406370\pi\) | ||||
0.289923 | + | 0.957050i | \(0.406370\pi\) | |||||||
\(198\) | 2.32087 | 0.164937 | ||||||||
\(199\) | −21.6215 | −1.53271 | −0.766354 | − | 0.642418i | \(-0.777931\pi\) | ||||
−0.766354 | + | 0.642418i | \(0.777931\pi\) | |||||||
\(200\) | −1.98864 | −0.140618 | ||||||||
\(201\) | 45.1974 | 3.18798 | ||||||||
\(202\) | 3.23070 | 0.227311 | ||||||||
\(203\) | 7.43400 | 0.521764 | ||||||||
\(204\) | 2.33247 | 0.163305 | ||||||||
\(205\) | 12.7395 | 0.889763 | ||||||||
\(206\) | −9.39478 | −0.654565 | ||||||||
\(207\) | −45.7818 | −3.18206 | ||||||||
\(208\) | −3.27955 | −0.227396 | ||||||||
\(209\) | −0.351101 | −0.0242862 | ||||||||
\(210\) | 20.0000 | 1.38013 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | −12.6718 | −0.870301 | ||||||||
\(213\) | 7.87092 | 0.539307 | ||||||||
\(214\) | −11.1153 | −0.759827 | ||||||||
\(215\) | 8.40239 | 0.573038 | ||||||||
\(216\) | 11.1919 | 0.761515 | ||||||||
\(217\) | −6.57131 | −0.446090 | ||||||||
\(218\) | −15.2968 | −1.03603 | ||||||||
\(219\) | −12.8405 | −0.867683 | ||||||||
\(220\) | 0.609275 | 0.0410773 | ||||||||
\(221\) | −2.46753 | −0.165984 | ||||||||
\(222\) | −29.3287 | −1.96842 | ||||||||
\(223\) | −9.23464 | −0.618397 | −0.309199 | − | 0.950997i | \(-0.600061\pi\) | ||||
−0.309199 | + | 0.950997i | \(0.600061\pi\) | |||||||
\(224\) | 3.71776 | 0.248403 | ||||||||
\(225\) | −13.1454 | −0.876359 | ||||||||
\(226\) | 4.41686 | 0.293805 | ||||||||
\(227\) | 4.48137 | 0.297439 | 0.148719 | − | 0.988879i | \(-0.452485\pi\) | ||||
0.148719 | + | 0.988879i | \(0.452485\pi\) | |||||||
\(228\) | −3.10004 | −0.205305 | ||||||||
\(229\) | 0.681758 | 0.0450518 | 0.0225259 | − | 0.999746i | \(-0.492829\pi\) | ||||
0.0225259 | + | 0.999746i | \(0.492829\pi\) | |||||||
\(230\) | −12.0187 | −0.792488 | ||||||||
\(231\) | 4.04651 | 0.266241 | ||||||||
\(232\) | 1.99959 | 0.131280 | ||||||||
\(233\) | −29.9511 | −1.96216 | −0.981080 | − | 0.193603i | \(-0.937983\pi\) | ||||
−0.981080 | + | 0.193603i | \(0.937983\pi\) | |||||||
\(234\) | −21.6787 | −1.41718 | ||||||||
\(235\) | 16.7715 | 1.09405 | ||||||||
\(236\) | −2.58178 | −0.168059 | ||||||||
\(237\) | 8.87686 | 0.576614 | ||||||||
\(238\) | 2.79724 | 0.181318 | ||||||||
\(239\) | 13.9618 | 0.903112 | 0.451556 | − | 0.892243i | \(-0.350869\pi\) | ||||
0.451556 | + | 0.892243i | \(0.350869\pi\) | |||||||
\(240\) | 5.37959 | 0.347251 | ||||||||
\(241\) | 12.9567 | 0.834614 | 0.417307 | − | 0.908766i | \(-0.362974\pi\) | ||||
0.417307 | + | 0.908766i | \(0.362974\pi\) | |||||||
\(242\) | −10.8767 | −0.699183 | ||||||||
\(243\) | 12.5054 | 0.802221 | ||||||||
\(244\) | −3.16536 | −0.202642 | ||||||||
\(245\) | 11.8379 | 0.756297 | ||||||||
\(246\) | 22.7581 | 1.45101 | ||||||||
\(247\) | 3.27955 | 0.208673 | ||||||||
\(248\) | −1.76755 | −0.112239 | ||||||||
\(249\) | 42.0759 | 2.66645 | ||||||||
\(250\) | −12.1276 | −0.767015 | ||||||||
\(251\) | −7.56776 | −0.477673 | −0.238836 | − | 0.971060i | \(-0.576766\pi\) | ||||
−0.238836 | + | 0.971060i | \(0.576766\pi\) | |||||||
\(252\) | 24.5753 | 1.54810 | ||||||||
\(253\) | −2.43168 | −0.152879 | ||||||||
\(254\) | −1.09609 | −0.0687747 | ||||||||
\(255\) | 4.04760 | 0.253470 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.6452 | 1.16305 | 0.581527 | − | 0.813527i | \(-0.302455\pi\) | ||||
0.581527 | + | 0.813527i | \(0.302455\pi\) | |||||||
\(258\) | 15.0103 | 0.934498 | ||||||||
\(259\) | −35.1728 | −2.18553 | ||||||||
\(260\) | −5.69110 | −0.352947 | ||||||||
\(261\) | 13.2178 | 0.818162 | ||||||||
\(262\) | −3.34665 | −0.206757 | ||||||||
\(263\) | −19.1324 | −1.17975 | −0.589876 | − | 0.807494i | \(-0.700823\pi\) | ||||
−0.589876 | + | 0.807494i | \(0.700823\pi\) | |||||||
\(264\) | 1.08843 | 0.0669881 | ||||||||
\(265\) | −21.9897 | −1.35082 | ||||||||
\(266\) | −3.71776 | −0.227950 | ||||||||
\(267\) | 40.9057 | 2.50339 | ||||||||
\(268\) | 14.5796 | 0.890592 | ||||||||
\(269\) | −12.4630 | −0.759884 | −0.379942 | − | 0.925010i | \(-0.624056\pi\) | ||||
−0.379942 | + | 0.925010i | \(0.624056\pi\) | |||||||
\(270\) | 19.4217 | 1.18197 | ||||||||
\(271\) | 4.83946 | 0.293976 | 0.146988 | − | 0.989138i | \(-0.453042\pi\) | ||||
0.146988 | + | 0.989138i | \(0.453042\pi\) | |||||||
\(272\) | 0.752399 | 0.0456209 | ||||||||
\(273\) | −37.7975 | −2.28761 | ||||||||
\(274\) | −3.27539 | −0.197873 | ||||||||
\(275\) | −0.698212 | −0.0421037 | ||||||||
\(276\) | −21.4705 | −1.29237 | ||||||||
\(277\) | −10.5967 | −0.636692 | −0.318346 | − | 0.947975i | \(-0.603127\pi\) | ||||
−0.318346 | + | 0.947975i | \(0.603127\pi\) | |||||||
\(278\) | 11.3529 | 0.680904 | ||||||||
\(279\) | −11.6839 | −0.699499 | ||||||||
\(280\) | 6.45153 | 0.385553 | ||||||||
\(281\) | −1.82039 | −0.108595 | −0.0542976 | − | 0.998525i | \(-0.517292\pi\) | ||||
−0.0542976 | + | 0.998525i | \(0.517292\pi\) | |||||||
\(282\) | 29.9611 | 1.78416 | ||||||||
\(283\) | −8.61545 | −0.512135 | −0.256068 | − | 0.966659i | \(-0.582427\pi\) | ||||
−0.256068 | + | 0.966659i | \(0.582427\pi\) | |||||||
\(284\) | 2.53897 | 0.150660 | ||||||||
\(285\) | −5.37959 | −0.318659 | ||||||||
\(286\) | −1.15145 | −0.0680869 | ||||||||
\(287\) | 27.2929 | 1.61105 | ||||||||
\(288\) | 6.61026 | 0.389513 | ||||||||
\(289\) | −16.4339 | −0.966700 | ||||||||
\(290\) | 3.46995 | 0.203762 | ||||||||
\(291\) | 5.24032 | 0.307193 | ||||||||
\(292\) | −4.14205 | −0.242395 | ||||||||
\(293\) | 21.4225 | 1.25152 | 0.625759 | − | 0.780016i | \(-0.284789\pi\) | ||||
0.625759 | + | 0.780016i | \(0.284789\pi\) | |||||||
\(294\) | 21.1476 | 1.23335 | ||||||||
\(295\) | −4.48023 | −0.260849 | ||||||||
\(296\) | −9.46076 | −0.549895 | ||||||||
\(297\) | 3.92950 | 0.228013 | ||||||||
\(298\) | 6.47207 | 0.374917 | ||||||||
\(299\) | 22.7138 | 1.31357 | ||||||||
\(300\) | −6.16485 | −0.355928 | ||||||||
\(301\) | 18.0012 | 1.03757 | ||||||||
\(302\) | 12.6234 | 0.726394 | ||||||||
\(303\) | 10.0153 | 0.575364 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −5.49294 | −0.314525 | ||||||||
\(306\) | 4.97355 | 0.284319 | ||||||||
\(307\) | 31.8435 | 1.81741 | 0.908704 | − | 0.417442i | \(-0.137073\pi\) | ||||
0.908704 | + | 0.417442i | \(0.137073\pi\) | |||||||
\(308\) | 1.30531 | 0.0743768 | ||||||||
\(309\) | −29.1242 | −1.65682 | ||||||||
\(310\) | −3.06727 | −0.174209 | ||||||||
\(311\) | 4.38707 | 0.248768 | 0.124384 | − | 0.992234i | \(-0.460305\pi\) | ||||
0.124384 | + | 0.992234i | \(0.460305\pi\) | |||||||
\(312\) | −10.1668 | −0.575579 | ||||||||
\(313\) | −27.9212 | −1.57820 | −0.789099 | − | 0.614266i | \(-0.789452\pi\) | ||||
−0.789099 | + | 0.614266i | \(0.789452\pi\) | |||||||
\(314\) | 1.06845 | 0.0602961 | ||||||||
\(315\) | 42.6463 | 2.40284 | ||||||||
\(316\) | 2.86347 | 0.161083 | ||||||||
\(317\) | −8.74704 | −0.491283 | −0.245641 | − | 0.969361i | \(-0.578999\pi\) | ||||
−0.245641 | + | 0.969361i | \(0.578999\pi\) | |||||||
\(318\) | −39.2830 | −2.20288 | ||||||||
\(319\) | 0.702059 | 0.0393077 | ||||||||
\(320\) | 1.73533 | 0.0970078 | ||||||||
\(321\) | −34.4579 | −1.92325 | ||||||||
\(322\) | −25.7487 | −1.43492 | ||||||||
\(323\) | −0.752399 | −0.0418646 | ||||||||
\(324\) | 14.8647 | 0.825817 | ||||||||
\(325\) | 6.52184 | 0.361767 | ||||||||
\(326\) | −11.4004 | −0.631411 | ||||||||
\(327\) | −47.4206 | −2.62237 | ||||||||
\(328\) | 7.34124 | 0.405352 | ||||||||
\(329\) | 35.9312 | 1.98095 | ||||||||
\(330\) | 1.88878 | 0.103974 | ||||||||
\(331\) | −3.27865 | −0.180211 | −0.0901055 | − | 0.995932i | \(-0.528720\pi\) | ||||
−0.0901055 | + | 0.995932i | \(0.528720\pi\) | |||||||
\(332\) | 13.5727 | 0.744899 | ||||||||
\(333\) | −62.5380 | −3.42706 | ||||||||
\(334\) | −4.82792 | −0.264172 | ||||||||
\(335\) | 25.3004 | 1.38231 | ||||||||
\(336\) | 11.5252 | 0.628751 | ||||||||
\(337\) | 20.0280 | 1.09099 | 0.545497 | − | 0.838113i | \(-0.316341\pi\) | ||||
0.545497 | + | 0.838113i | \(0.316341\pi\) | |||||||
\(338\) | −2.24452 | −0.122086 | ||||||||
\(339\) | 13.6924 | 0.743671 | ||||||||
\(340\) | 1.30566 | 0.0708093 | ||||||||
\(341\) | −0.620587 | −0.0336067 | ||||||||
\(342\) | −6.61026 | −0.357442 | ||||||||
\(343\) | −0.662803 | −0.0357880 | ||||||||
\(344\) | 4.84196 | 0.261061 | ||||||||
\(345\) | −37.2584 | −2.00592 | ||||||||
\(346\) | −17.2487 | −0.927294 | ||||||||
\(347\) | −5.20405 | −0.279368 | −0.139684 | − | 0.990196i | \(-0.544609\pi\) | ||||
−0.139684 | + | 0.990196i | \(0.544609\pi\) | |||||||
\(348\) | 6.19882 | 0.332292 | ||||||||
\(349\) | −13.4254 | −0.718643 | −0.359321 | − | 0.933214i | \(-0.616992\pi\) | ||||
−0.359321 | + | 0.933214i | \(0.616992\pi\) | |||||||
\(350\) | −7.39327 | −0.395187 | ||||||||
\(351\) | −36.7046 | −1.95915 | ||||||||
\(352\) | 0.351101 | 0.0187137 | ||||||||
\(353\) | 9.77014 | 0.520012 | 0.260006 | − | 0.965607i | \(-0.416275\pi\) | ||||
0.260006 | + | 0.965607i | \(0.416275\pi\) | |||||||
\(354\) | −8.00362 | −0.425387 | ||||||||
\(355\) | 4.40595 | 0.233844 | ||||||||
\(356\) | 13.1952 | 0.699345 | ||||||||
\(357\) | 8.67155 | 0.458947 | ||||||||
\(358\) | 5.93539 | 0.313695 | ||||||||
\(359\) | −27.7370 | −1.46390 | −0.731951 | − | 0.681357i | \(-0.761390\pi\) | ||||
−0.731951 | + | 0.681357i | \(0.761390\pi\) | |||||||
\(360\) | 11.4710 | 0.604573 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 20.9918 | 1.10331 | ||||||||
\(363\) | −33.7183 | −1.76975 | ||||||||
\(364\) | −12.1926 | −0.639065 | ||||||||
\(365\) | −7.18782 | −0.376228 | ||||||||
\(366\) | −9.81275 | −0.512921 | ||||||||
\(367\) | 17.4207 | 0.909355 | 0.454677 | − | 0.890656i | \(-0.349755\pi\) | ||||
0.454677 | + | 0.890656i | \(0.349755\pi\) | |||||||
\(368\) | −6.92588 | −0.361036 | ||||||||
\(369\) | 48.5275 | 2.52624 | ||||||||
\(370\) | −16.4175 | −0.853506 | ||||||||
\(371\) | −47.1106 | −2.44586 | ||||||||
\(372\) | −5.47947 | −0.284097 | ||||||||
\(373\) | −14.8013 | −0.766384 | −0.383192 | − | 0.923669i | \(-0.625175\pi\) | ||||
−0.383192 | + | 0.923669i | \(0.625175\pi\) | |||||||
\(374\) | 0.264168 | 0.0136598 | ||||||||
\(375\) | −37.5960 | −1.94145 | ||||||||
\(376\) | 9.66475 | 0.498422 | ||||||||
\(377\) | −6.55777 | −0.337742 | ||||||||
\(378\) | 41.6089 | 2.14013 | ||||||||
\(379\) | −21.6776 | −1.11350 | −0.556752 | − | 0.830679i | \(-0.687953\pi\) | ||||
−0.556752 | + | 0.830679i | \(0.687953\pi\) | |||||||
\(380\) | −1.73533 | −0.0890205 | ||||||||
\(381\) | −3.39792 | −0.174081 | ||||||||
\(382\) | −24.5408 | −1.25562 | ||||||||
\(383\) | −6.00591 | −0.306888 | −0.153444 | − | 0.988157i | \(-0.549036\pi\) | ||||
−0.153444 | + | 0.988157i | \(0.549036\pi\) | |||||||
\(384\) | 3.10004 | 0.158198 | ||||||||
\(385\) | 2.26514 | 0.115442 | ||||||||
\(386\) | −11.0919 | −0.564565 | ||||||||
\(387\) | 32.0066 | 1.62699 | ||||||||
\(388\) | 1.69040 | 0.0858172 | ||||||||
\(389\) | −23.2504 | −1.17884 | −0.589422 | − | 0.807825i | \(-0.700645\pi\) | ||||
−0.589422 | + | 0.807825i | \(0.700645\pi\) | |||||||
\(390\) | −17.6427 | −0.893371 | ||||||||
\(391\) | −5.21102 | −0.263533 | ||||||||
\(392\) | 6.82172 | 0.344549 | ||||||||
\(393\) | −10.3748 | −0.523337 | ||||||||
\(394\) | 8.13853 | 0.410013 | ||||||||
\(395\) | 4.96905 | 0.250020 | ||||||||
\(396\) | 2.32087 | 0.116628 | ||||||||
\(397\) | −39.1450 | −1.96463 | −0.982316 | − | 0.187229i | \(-0.940049\pi\) | ||||
−0.982316 | + | 0.187229i | \(0.940049\pi\) | |||||||
\(398\) | −21.6215 | −1.08379 | ||||||||
\(399\) | −11.5252 | −0.576982 | ||||||||
\(400\) | −1.98864 | −0.0994318 | ||||||||
\(401\) | 19.2227 | 0.959936 | 0.479968 | − | 0.877286i | \(-0.340648\pi\) | ||||
0.479968 | + | 0.877286i | \(0.340648\pi\) | |||||||
\(402\) | 45.1974 | 2.25424 | ||||||||
\(403\) | 5.79677 | 0.288758 | ||||||||
\(404\) | 3.23070 | 0.160733 | ||||||||
\(405\) | 25.7951 | 1.28177 | ||||||||
\(406\) | 7.43400 | 0.368943 | ||||||||
\(407\) | −3.32168 | −0.164650 | ||||||||
\(408\) | 2.33247 | 0.115474 | ||||||||
\(409\) | −0.152173 | −0.00752447 | −0.00376224 | − | 0.999993i | \(-0.501198\pi\) | ||||
−0.00376224 | + | 0.999993i | \(0.501198\pi\) | |||||||
\(410\) | 12.7395 | 0.629157 | ||||||||
\(411\) | −10.1538 | −0.500852 | ||||||||
\(412\) | −9.39478 | −0.462848 | ||||||||
\(413\) | −9.59842 | −0.472308 | ||||||||
\(414\) | −45.7818 | −2.25005 | ||||||||
\(415\) | 23.5531 | 1.15618 | ||||||||
\(416\) | −3.27955 | −0.160793 | ||||||||
\(417\) | 35.1946 | 1.72349 | ||||||||
\(418\) | −0.351101 | −0.0171729 | ||||||||
\(419\) | 27.1022 | 1.32403 | 0.662015 | − | 0.749490i | \(-0.269701\pi\) | ||||
0.662015 | + | 0.749490i | \(0.269701\pi\) | |||||||
\(420\) | 20.0000 | 0.975900 | ||||||||
\(421\) | 9.67776 | 0.471665 | 0.235833 | − | 0.971794i | \(-0.424218\pi\) | ||||
0.235833 | + | 0.971794i | \(0.424218\pi\) | |||||||
\(422\) | −1.00000 | −0.0486792 | ||||||||
\(423\) | 63.8865 | 3.10627 | ||||||||
\(424\) | −12.6718 | −0.615396 | ||||||||
\(425\) | −1.49625 | −0.0725787 | ||||||||
\(426\) | 7.87092 | 0.381348 | ||||||||
\(427\) | −11.7680 | −0.569496 | ||||||||
\(428\) | −11.1153 | −0.537279 | ||||||||
\(429\) | −3.56956 | −0.172340 | ||||||||
\(430\) | 8.40239 | 0.405199 | ||||||||
\(431\) | 28.4143 | 1.36867 | 0.684335 | − | 0.729168i | \(-0.260093\pi\) | ||||
0.684335 | + | 0.729168i | \(0.260093\pi\) | |||||||
\(432\) | 11.1919 | 0.538472 | ||||||||
\(433\) | 6.23986 | 0.299868 | 0.149934 | − | 0.988696i | \(-0.452094\pi\) | ||||
0.149934 | + | 0.988696i | \(0.452094\pi\) | |||||||
\(434\) | −6.57131 | −0.315433 | ||||||||
\(435\) | 10.7570 | 0.515758 | ||||||||
\(436\) | −15.2968 | −0.732582 | ||||||||
\(437\) | 6.92588 | 0.331310 | ||||||||
\(438\) | −12.8405 | −0.613544 | ||||||||
\(439\) | 32.5502 | 1.55353 | 0.776767 | − | 0.629788i | \(-0.216858\pi\) | ||||
0.776767 | + | 0.629788i | \(0.216858\pi\) | |||||||
\(440\) | 0.609275 | 0.0290461 | ||||||||
\(441\) | 45.0933 | 2.14730 | ||||||||
\(442\) | −2.46753 | −0.117369 | ||||||||
\(443\) | 20.3511 | 0.966912 | 0.483456 | − | 0.875369i | \(-0.339381\pi\) | ||||
0.483456 | + | 0.875369i | \(0.339381\pi\) | |||||||
\(444\) | −29.3287 | −1.39188 | ||||||||
\(445\) | 22.8980 | 1.08547 | ||||||||
\(446\) | −9.23464 | −0.437273 | ||||||||
\(447\) | 20.0637 | 0.948979 | ||||||||
\(448\) | 3.71776 | 0.175648 | ||||||||
\(449\) | −16.6193 | −0.784314 | −0.392157 | − | 0.919898i | \(-0.628271\pi\) | ||||
−0.392157 | + | 0.919898i | \(0.628271\pi\) | |||||||
\(450\) | −13.1454 | −0.619680 | ||||||||
\(451\) | 2.57752 | 0.121370 | ||||||||
\(452\) | 4.41686 | 0.207752 | ||||||||
\(453\) | 39.1330 | 1.83863 | ||||||||
\(454\) | 4.48137 | 0.210321 | ||||||||
\(455\) | −21.1581 | −0.991909 | ||||||||
\(456\) | −3.10004 | −0.145173 | ||||||||
\(457\) | −2.63080 | −0.123064 | −0.0615319 | − | 0.998105i | \(-0.519599\pi\) | ||||
−0.0615319 | + | 0.998105i | \(0.519599\pi\) | |||||||
\(458\) | 0.681758 | 0.0318564 | ||||||||
\(459\) | 8.42080 | 0.393049 | ||||||||
\(460\) | −12.0187 | −0.560374 | ||||||||
\(461\) | 21.7075 | 1.01102 | 0.505510 | − | 0.862821i | \(-0.331305\pi\) | ||||
0.505510 | + | 0.862821i | \(0.331305\pi\) | |||||||
\(462\) | 4.04651 | 0.188261 | ||||||||
\(463\) | 37.3602 | 1.73628 | 0.868138 | − | 0.496322i | \(-0.165317\pi\) | ||||
0.868138 | + | 0.496322i | \(0.165317\pi\) | |||||||
\(464\) | 1.99959 | 0.0928287 | ||||||||
\(465\) | −9.50868 | −0.440954 | ||||||||
\(466\) | −29.9511 | −1.38746 | ||||||||
\(467\) | 10.1334 | 0.468919 | 0.234460 | − | 0.972126i | \(-0.424668\pi\) | ||||
0.234460 | + | 0.972126i | \(0.424668\pi\) | |||||||
\(468\) | −21.6787 | −1.00210 | ||||||||
\(469\) | 54.2035 | 2.50288 | ||||||||
\(470\) | 16.7715 | 0.773612 | ||||||||
\(471\) | 3.31224 | 0.152620 | ||||||||
\(472\) | −2.58178 | −0.118836 | ||||||||
\(473\) | 1.70002 | 0.0781668 | ||||||||
\(474\) | 8.87686 | 0.407728 | ||||||||
\(475\) | 1.98864 | 0.0912449 | ||||||||
\(476\) | 2.79724 | 0.128211 | ||||||||
\(477\) | −83.7636 | −3.83527 | ||||||||
\(478\) | 13.9618 | 0.638597 | ||||||||
\(479\) | −42.3174 | −1.93353 | −0.966765 | − | 0.255666i | \(-0.917705\pi\) | ||||
−0.966765 | + | 0.255666i | \(0.917705\pi\) | |||||||
\(480\) | 5.37959 | 0.245544 | ||||||||
\(481\) | 31.0271 | 1.41471 | ||||||||
\(482\) | 12.9567 | 0.590161 | ||||||||
\(483\) | −79.8221 | −3.63203 | ||||||||
\(484\) | −10.8767 | −0.494397 | ||||||||
\(485\) | 2.93340 | 0.133199 | ||||||||
\(486\) | 12.5054 | 0.567256 | ||||||||
\(487\) | 14.7169 | 0.666888 | 0.333444 | − | 0.942770i | \(-0.391789\pi\) | ||||
0.333444 | + | 0.942770i | \(0.391789\pi\) | |||||||
\(488\) | −3.16536 | −0.143289 | ||||||||
\(489\) | −35.3418 | −1.59821 | ||||||||
\(490\) | 11.8379 | 0.534783 | ||||||||
\(491\) | −26.8044 | −1.20966 | −0.604832 | − | 0.796353i | \(-0.706760\pi\) | ||||
−0.604832 | + | 0.796353i | \(0.706760\pi\) | |||||||
\(492\) | 22.7581 | 1.02602 | ||||||||
\(493\) | 1.50449 | 0.0677589 | ||||||||
\(494\) | 3.27955 | 0.147554 | ||||||||
\(495\) | 4.02746 | 0.181021 | ||||||||
\(496\) | −1.76755 | −0.0793652 | ||||||||
\(497\) | 9.43929 | 0.423410 | ||||||||
\(498\) | 42.0759 | 1.88547 | ||||||||
\(499\) | −16.4246 | −0.735264 | −0.367632 | − | 0.929971i | \(-0.619831\pi\) | ||||
−0.367632 | + | 0.929971i | \(0.619831\pi\) | |||||||
\(500\) | −12.1276 | −0.542362 | ||||||||
\(501\) | −14.9668 | −0.668665 | ||||||||
\(502\) | −7.56776 | −0.337766 | ||||||||
\(503\) | 27.5604 | 1.22886 | 0.614430 | − | 0.788971i | \(-0.289386\pi\) | ||||
0.614430 | + | 0.788971i | \(0.289386\pi\) | |||||||
\(504\) | 24.5753 | 1.09467 | ||||||||
\(505\) | 5.60632 | 0.249478 | ||||||||
\(506\) | −2.43168 | −0.108101 | ||||||||
\(507\) | −6.95811 | −0.309021 | ||||||||
\(508\) | −1.09609 | −0.0486311 | ||||||||
\(509\) | 3.15059 | 0.139647 | 0.0698237 | − | 0.997559i | \(-0.477756\pi\) | ||||
0.0698237 | + | 0.997559i | \(0.477756\pi\) | |||||||
\(510\) | 4.04760 | 0.179231 | ||||||||
\(511\) | −15.3991 | −0.681218 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −11.1919 | −0.494136 | ||||||||
\(514\) | 18.6452 | 0.822403 | ||||||||
\(515\) | −16.3030 | −0.718397 | ||||||||
\(516\) | 15.0103 | 0.660790 | ||||||||
\(517\) | 3.39330 | 0.149237 | ||||||||
\(518\) | −35.1728 | −1.54540 | ||||||||
\(519\) | −53.4716 | −2.34714 | ||||||||
\(520\) | −5.69110 | −0.249571 | ||||||||
\(521\) | −40.1741 | −1.76006 | −0.880029 | − | 0.474919i | \(-0.842477\pi\) | ||||
−0.880029 | + | 0.474919i | \(0.842477\pi\) | |||||||
\(522\) | 13.2178 | 0.578528 | ||||||||
\(523\) | 16.2791 | 0.711835 | 0.355917 | − | 0.934517i | \(-0.384168\pi\) | ||||
0.355917 | + | 0.934517i | \(0.384168\pi\) | |||||||
\(524\) | −3.34665 | −0.146199 | ||||||||
\(525\) | −22.9194 | −1.00029 | ||||||||
\(526\) | −19.1324 | −0.834210 | ||||||||
\(527\) | −1.32990 | −0.0579314 | ||||||||
\(528\) | 1.08843 | 0.0473677 | ||||||||
\(529\) | 24.9678 | 1.08556 | ||||||||
\(530\) | −21.9897 | −0.955171 | ||||||||
\(531\) | −17.0662 | −0.740610 | ||||||||
\(532\) | −3.71776 | −0.161185 | ||||||||
\(533\) | −24.0760 | −1.04285 | ||||||||
\(534\) | 40.9057 | 1.77016 | ||||||||
\(535\) | −19.2887 | −0.833924 | ||||||||
\(536\) | 14.5796 | 0.629744 | ||||||||
\(537\) | 18.4000 | 0.794017 | ||||||||
\(538\) | −12.4630 | −0.537319 | ||||||||
\(539\) | 2.39511 | 0.103165 | ||||||||
\(540\) | 19.4217 | 0.835776 | ||||||||
\(541\) | −9.18498 | −0.394893 | −0.197447 | − | 0.980314i | \(-0.563265\pi\) | ||||
−0.197447 | + | 0.980314i | \(0.563265\pi\) | |||||||
\(542\) | 4.83946 | 0.207873 | ||||||||
\(543\) | 65.0756 | 2.79266 | ||||||||
\(544\) | 0.752399 | 0.0322588 | ||||||||
\(545\) | −26.5449 | −1.13706 | ||||||||
\(546\) | −37.7975 | −1.61758 | ||||||||
\(547\) | 2.87883 | 0.123090 | 0.0615450 | − | 0.998104i | \(-0.480397\pi\) | ||||
0.0615450 | + | 0.998104i | \(0.480397\pi\) | |||||||
\(548\) | −3.27539 | −0.139918 | ||||||||
\(549\) | −20.9238 | −0.893008 | ||||||||
\(550\) | −0.698212 | −0.0297718 | ||||||||
\(551\) | −1.99959 | −0.0851855 | ||||||||
\(552\) | −21.4705 | −0.913846 | ||||||||
\(553\) | 10.6457 | 0.452700 | ||||||||
\(554\) | −10.5967 | −0.450209 | ||||||||
\(555\) | −50.8950 | −2.16037 | ||||||||
\(556\) | 11.3529 | 0.481472 | ||||||||
\(557\) | 18.1580 | 0.769380 | 0.384690 | − | 0.923046i | \(-0.374308\pi\) | ||||
0.384690 | + | 0.923046i | \(0.374308\pi\) | |||||||
\(558\) | −11.6839 | −0.494621 | ||||||||
\(559\) | −15.8795 | −0.671630 | ||||||||
\(560\) | 6.45153 | 0.272627 | ||||||||
\(561\) | 0.818931 | 0.0345753 | ||||||||
\(562\) | −1.82039 | −0.0767884 | ||||||||
\(563\) | −14.4464 | −0.608843 | −0.304421 | − | 0.952537i | \(-0.598463\pi\) | ||||
−0.304421 | + | 0.952537i | \(0.598463\pi\) | |||||||
\(564\) | 29.9611 | 1.26159 | ||||||||
\(565\) | 7.66470 | 0.322456 | ||||||||
\(566\) | −8.61545 | −0.362134 | ||||||||
\(567\) | 55.2634 | 2.32084 | ||||||||
\(568\) | 2.53897 | 0.106533 | ||||||||
\(569\) | −43.3171 | −1.81595 | −0.907974 | − | 0.419026i | \(-0.862372\pi\) | ||||
−0.907974 | + | 0.419026i | \(0.862372\pi\) | |||||||
\(570\) | −5.37959 | −0.225326 | ||||||||
\(571\) | 25.9611 | 1.08644 | 0.543219 | − | 0.839591i | \(-0.317205\pi\) | ||||
0.543219 | + | 0.839591i | \(0.317205\pi\) | |||||||
\(572\) | −1.15145 | −0.0481447 | ||||||||
\(573\) | −76.0775 | −3.17818 | ||||||||
\(574\) | 27.2929 | 1.13919 | ||||||||
\(575\) | 13.7730 | 0.574376 | ||||||||
\(576\) | 6.61026 | 0.275427 | ||||||||
\(577\) | 21.4138 | 0.891469 | 0.445734 | − | 0.895165i | \(-0.352943\pi\) | ||||
0.445734 | + | 0.895165i | \(0.352943\pi\) | |||||||
\(578\) | −16.4339 | −0.683560 | ||||||||
\(579\) | −34.3855 | −1.42901 | ||||||||
\(580\) | 3.46995 | 0.144082 | ||||||||
\(581\) | 50.4600 | 2.09343 | ||||||||
\(582\) | 5.24032 | 0.217218 | ||||||||
\(583\) | −4.44907 | −0.184262 | ||||||||
\(584\) | −4.14205 | −0.171399 | ||||||||
\(585\) | −37.6196 | −1.55538 | ||||||||
\(586\) | 21.4225 | 0.884957 | ||||||||
\(587\) | 46.6066 | 1.92366 | 0.961831 | − | 0.273644i | \(-0.0882290\pi\) | ||||
0.961831 | + | 0.273644i | \(0.0882290\pi\) | |||||||
\(588\) | 21.1476 | 0.872113 | ||||||||
\(589\) | 1.76755 | 0.0728305 | ||||||||
\(590\) | −4.48023 | −0.184448 | ||||||||
\(591\) | 25.2298 | 1.03781 | ||||||||
\(592\) | −9.46076 | −0.388835 | ||||||||
\(593\) | −8.47897 | −0.348190 | −0.174095 | − | 0.984729i | \(-0.555700\pi\) | ||||
−0.174095 | + | 0.984729i | \(0.555700\pi\) | |||||||
\(594\) | 3.92950 | 0.161229 | ||||||||
\(595\) | 4.85412 | 0.199000 | ||||||||
\(596\) | 6.47207 | 0.265106 | ||||||||
\(597\) | −67.0276 | −2.74326 | ||||||||
\(598\) | 22.7138 | 0.928836 | ||||||||
\(599\) | 44.8446 | 1.83230 | 0.916151 | − | 0.400833i | \(-0.131279\pi\) | ||||
0.916151 | + | 0.400833i | \(0.131279\pi\) | |||||||
\(600\) | −6.16485 | −0.251679 | ||||||||
\(601\) | 42.3239 | 1.72643 | 0.863213 | − | 0.504839i | \(-0.168448\pi\) | ||||
0.863213 | + | 0.504839i | \(0.168448\pi\) | |||||||
\(602\) | 18.0012 | 0.733675 | ||||||||
\(603\) | 96.3750 | 3.92469 | ||||||||
\(604\) | 12.6234 | 0.513638 | ||||||||
\(605\) | −18.8747 | −0.767365 | ||||||||
\(606\) | 10.0153 | 0.406844 | ||||||||
\(607\) | 17.0076 | 0.690317 | 0.345158 | − | 0.938544i | \(-0.387825\pi\) | ||||
0.345158 | + | 0.938544i | \(0.387825\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 23.0457 | 0.933859 | ||||||||
\(610\) | −5.49294 | −0.222403 | ||||||||
\(611\) | −31.6961 | −1.28229 | ||||||||
\(612\) | 4.97355 | 0.201044 | ||||||||
\(613\) | 0.729020 | 0.0294448 | 0.0147224 | − | 0.999892i | \(-0.495314\pi\) | ||||
0.0147224 | + | 0.999892i | \(0.495314\pi\) | |||||||
\(614\) | 31.8435 | 1.28510 | ||||||||
\(615\) | 39.4929 | 1.59251 | ||||||||
\(616\) | 1.30531 | 0.0525923 | ||||||||
\(617\) | 17.8269 | 0.717683 | 0.358841 | − | 0.933399i | \(-0.383172\pi\) | ||||
0.358841 | + | 0.933399i | \(0.383172\pi\) | |||||||
\(618\) | −29.1242 | −1.17155 | ||||||||
\(619\) | 30.8609 | 1.24041 | 0.620203 | − | 0.784442i | \(-0.287050\pi\) | ||||
0.620203 | + | 0.784442i | \(0.287050\pi\) | |||||||
\(620\) | −3.06727 | −0.123185 | ||||||||
\(621\) | −77.5140 | −3.11053 | ||||||||
\(622\) | 4.38707 | 0.175905 | ||||||||
\(623\) | 49.0566 | 1.96541 | ||||||||
\(624\) | −10.1668 | −0.406996 | ||||||||
\(625\) | −11.1021 | −0.444086 | ||||||||
\(626\) | −27.9212 | −1.11595 | ||||||||
\(627\) | −1.08843 | −0.0434676 | ||||||||
\(628\) | 1.06845 | 0.0426358 | ||||||||
\(629\) | −7.11826 | −0.283824 | ||||||||
\(630\) | 42.6463 | 1.69907 | ||||||||
\(631\) | −4.70983 | −0.187495 | −0.0937477 | − | 0.995596i | \(-0.529885\pi\) | ||||
−0.0937477 | + | 0.995596i | \(0.529885\pi\) | |||||||
\(632\) | 2.86347 | 0.113903 | ||||||||
\(633\) | −3.10004 | −0.123216 | ||||||||
\(634\) | −8.74704 | −0.347390 | ||||||||
\(635\) | −1.90207 | −0.0754815 | ||||||||
\(636\) | −39.2830 | −1.55767 | ||||||||
\(637\) | −22.3722 | −0.886419 | ||||||||
\(638\) | 0.702059 | 0.0277948 | ||||||||
\(639\) | 16.7833 | 0.663936 | ||||||||
\(640\) | 1.73533 | 0.0685949 | ||||||||
\(641\) | −22.3062 | −0.881042 | −0.440521 | − | 0.897742i | \(-0.645206\pi\) | ||||
−0.440521 | + | 0.897742i | \(0.645206\pi\) | |||||||
\(642\) | −34.4579 | −1.35995 | ||||||||
\(643\) | −6.80290 | −0.268280 | −0.134140 | − | 0.990962i | \(-0.542827\pi\) | ||||
−0.134140 | + | 0.990962i | \(0.542827\pi\) | |||||||
\(644\) | −25.7487 | −1.01464 | ||||||||
\(645\) | 26.0477 | 1.02563 | ||||||||
\(646\) | −0.752399 | −0.0296027 | ||||||||
\(647\) | 38.5285 | 1.51471 | 0.757355 | − | 0.653003i | \(-0.226491\pi\) | ||||
0.757355 | + | 0.653003i | \(0.226491\pi\) | |||||||
\(648\) | 14.8647 | 0.583941 | ||||||||
\(649\) | −0.906464 | −0.0355818 | ||||||||
\(650\) | 6.52184 | 0.255808 | ||||||||
\(651\) | −20.3713 | −0.798416 | ||||||||
\(652\) | −11.4004 | −0.446475 | ||||||||
\(653\) | 12.1794 | 0.476615 | 0.238308 | − | 0.971190i | \(-0.423407\pi\) | ||||
0.238308 | + | 0.971190i | \(0.423407\pi\) | |||||||
\(654\) | −47.4206 | −1.85429 | ||||||||
\(655\) | −5.80754 | −0.226919 | ||||||||
\(656\) | 7.34124 | 0.286627 | ||||||||
\(657\) | −27.3800 | −1.06820 | ||||||||
\(658\) | 35.9312 | 1.40074 | ||||||||
\(659\) | −29.1482 | −1.13545 | −0.567727 | − | 0.823217i | \(-0.692177\pi\) | ||||
−0.567727 | + | 0.823217i | \(0.692177\pi\) | |||||||
\(660\) | 1.88878 | 0.0735206 | ||||||||
\(661\) | 45.7410 | 1.77912 | 0.889560 | − | 0.456818i | \(-0.151011\pi\) | ||||
0.889560 | + | 0.456818i | \(0.151011\pi\) | |||||||
\(662\) | −3.27865 | −0.127428 | ||||||||
\(663\) | −7.64945 | −0.297080 | ||||||||
\(664\) | 13.5727 | 0.526723 | ||||||||
\(665\) | −6.45153 | −0.250180 | ||||||||
\(666\) | −62.5380 | −2.42330 | ||||||||
\(667\) | −13.8489 | −0.536233 | ||||||||
\(668\) | −4.82792 | −0.186798 | ||||||||
\(669\) | −28.6278 | −1.10681 | ||||||||
\(670\) | 25.3004 | 0.977441 | ||||||||
\(671\) | −1.11136 | −0.0429036 | ||||||||
\(672\) | 11.5252 | 0.444594 | ||||||||
\(673\) | 12.8728 | 0.496211 | 0.248105 | − | 0.968733i | \(-0.420192\pi\) | ||||
0.248105 | + | 0.968733i | \(0.420192\pi\) | |||||||
\(674\) | 20.0280 | 0.771449 | ||||||||
\(675\) | −22.2567 | −0.856660 | ||||||||
\(676\) | −2.24452 | −0.0863278 | ||||||||
\(677\) | 1.00243 | 0.0385264 | 0.0192632 | − | 0.999814i | \(-0.493868\pi\) | ||||
0.0192632 | + | 0.999814i | \(0.493868\pi\) | |||||||
\(678\) | 13.6924 | 0.525855 | ||||||||
\(679\) | 6.28451 | 0.241177 | ||||||||
\(680\) | 1.30566 | 0.0500697 | ||||||||
\(681\) | 13.8924 | 0.532359 | ||||||||
\(682\) | −0.620587 | −0.0237635 | ||||||||
\(683\) | −7.55624 | −0.289132 | −0.144566 | − | 0.989495i | \(-0.546179\pi\) | ||||
−0.144566 | + | 0.989495i | \(0.546179\pi\) | |||||||
\(684\) | −6.61026 | −0.252749 | ||||||||
\(685\) | −5.68388 | −0.217170 | ||||||||
\(686\) | −0.662803 | −0.0253060 | ||||||||
\(687\) | 2.11348 | 0.0806342 | ||||||||
\(688\) | 4.84196 | 0.184598 | ||||||||
\(689\) | 41.5578 | 1.58322 | ||||||||
\(690\) | −37.2584 | −1.41840 | ||||||||
\(691\) | 41.3882 | 1.57448 | 0.787240 | − | 0.616646i | \(-0.211509\pi\) | ||||
0.787240 | + | 0.616646i | \(0.211509\pi\) | |||||||
\(692\) | −17.2487 | −0.655696 | ||||||||
\(693\) | 8.62842 | 0.327766 | ||||||||
\(694\) | −5.20405 | −0.197543 | ||||||||
\(695\) | 19.7011 | 0.747304 | ||||||||
\(696\) | 6.19882 | 0.234966 | ||||||||
\(697\) | 5.52354 | 0.209219 | ||||||||
\(698\) | −13.4254 | −0.508157 | ||||||||
\(699\) | −92.8495 | −3.51189 | ||||||||
\(700\) | −7.39327 | −0.279439 | ||||||||
\(701\) | −18.1830 | −0.686764 | −0.343382 | − | 0.939196i | \(-0.611573\pi\) | ||||
−0.343382 | + | 0.939196i | \(0.611573\pi\) | |||||||
\(702\) | −36.7046 | −1.38532 | ||||||||
\(703\) | 9.46076 | 0.356819 | ||||||||
\(704\) | 0.351101 | 0.0132326 | ||||||||
\(705\) | 51.9924 | 1.95815 | ||||||||
\(706\) | 9.77014 | 0.367704 | ||||||||
\(707\) | 12.0109 | 0.451718 | ||||||||
\(708\) | −8.00362 | −0.300794 | ||||||||
\(709\) | −15.6607 | −0.588149 | −0.294074 | − | 0.955783i | \(-0.595011\pi\) | ||||
−0.294074 | + | 0.955783i | \(0.595011\pi\) | |||||||
\(710\) | 4.40595 | 0.165352 | ||||||||
\(711\) | 18.9282 | 0.709865 | ||||||||
\(712\) | 13.1952 | 0.494512 | ||||||||
\(713\) | 12.2418 | 0.458460 | ||||||||
\(714\) | 8.67155 | 0.324525 | ||||||||
\(715\) | −1.99815 | −0.0747266 | ||||||||
\(716\) | 5.93539 | 0.221816 | ||||||||
\(717\) | 43.2821 | 1.61640 | ||||||||
\(718\) | −27.7370 | −1.03514 | ||||||||
\(719\) | −8.86763 | −0.330707 | −0.165353 | − | 0.986234i | \(-0.552876\pi\) | ||||
−0.165353 | + | 0.986234i | \(0.552876\pi\) | |||||||
\(720\) | 11.4710 | 0.427498 | ||||||||
\(721\) | −34.9275 | −1.30077 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 40.1663 | 1.49380 | ||||||||
\(724\) | 20.9918 | 0.780156 | ||||||||
\(725\) | −3.97646 | −0.147682 | ||||||||
\(726\) | −33.7183 | −1.25140 | ||||||||
\(727\) | −41.6682 | −1.54539 | −0.772694 | − | 0.634779i | \(-0.781091\pi\) | ||||
−0.772694 | + | 0.634779i | \(0.781091\pi\) | |||||||
\(728\) | −12.1926 | −0.451887 | ||||||||
\(729\) | −5.82691 | −0.215811 | ||||||||
\(730\) | −7.18782 | −0.266033 | ||||||||
\(731\) | 3.64308 | 0.134744 | ||||||||
\(732\) | −9.81275 | −0.362690 | ||||||||
\(733\) | 24.8732 | 0.918714 | 0.459357 | − | 0.888252i | \(-0.348080\pi\) | ||||
0.459357 | + | 0.888252i | \(0.348080\pi\) | |||||||
\(734\) | 17.4207 | 0.643011 | ||||||||
\(735\) | 36.6980 | 1.35363 | ||||||||
\(736\) | −6.92588 | −0.255291 | ||||||||
\(737\) | 5.11892 | 0.188558 | ||||||||
\(738\) | 48.5275 | 1.78632 | ||||||||
\(739\) | 42.8333 | 1.57565 | 0.787824 | − | 0.615900i | \(-0.211208\pi\) | ||||
0.787824 | + | 0.615900i | \(0.211208\pi\) | |||||||
\(740\) | −16.4175 | −0.603520 | ||||||||
\(741\) | 10.1668 | 0.373485 | ||||||||
\(742\) | −47.1106 | −1.72948 | ||||||||
\(743\) | −20.6014 | −0.755791 | −0.377896 | − | 0.925848i | \(-0.623352\pi\) | ||||
−0.377896 | + | 0.925848i | \(0.623352\pi\) | |||||||
\(744\) | −5.47947 | −0.200887 | ||||||||
\(745\) | 11.2312 | 0.411478 | ||||||||
\(746\) | −14.8013 | −0.541915 | ||||||||
\(747\) | 89.7190 | 3.28265 | ||||||||
\(748\) | 0.264168 | 0.00965893 | ||||||||
\(749\) | −41.3240 | −1.50995 | ||||||||
\(750\) | −37.5960 | −1.37281 | ||||||||
\(751\) | −17.6587 | −0.644374 | −0.322187 | − | 0.946676i | \(-0.604418\pi\) | ||||
−0.322187 | + | 0.946676i | \(0.604418\pi\) | |||||||
\(752\) | 9.66475 | 0.352437 | ||||||||
\(753\) | −23.4604 | −0.854943 | ||||||||
\(754\) | −6.55777 | −0.238820 | ||||||||
\(755\) | 21.9057 | 0.797231 | ||||||||
\(756\) | 41.6089 | 1.51330 | ||||||||
\(757\) | 32.3760 | 1.17672 | 0.588362 | − | 0.808597i | \(-0.299773\pi\) | ||||
0.588362 | + | 0.808597i | \(0.299773\pi\) | |||||||
\(758\) | −21.6776 | −0.787366 | ||||||||
\(759\) | −7.53831 | −0.273623 | ||||||||
\(760\) | −1.73533 | −0.0629470 | ||||||||
\(761\) | −45.1688 | −1.63737 | −0.818684 | − | 0.574245i | \(-0.805296\pi\) | ||||
−0.818684 | + | 0.574245i | \(0.805296\pi\) | |||||||
\(762\) | −3.39792 | −0.123094 | ||||||||
\(763\) | −56.8697 | −2.05882 | ||||||||
\(764\) | −24.5408 | −0.887855 | ||||||||
\(765\) | 8.63074 | 0.312045 | ||||||||
\(766\) | −6.00591 | −0.217002 | ||||||||
\(767\) | 8.46708 | 0.305729 | ||||||||
\(768\) | 3.10004 | 0.111863 | ||||||||
\(769\) | 12.7741 | 0.460647 | 0.230323 | − | 0.973114i | \(-0.426022\pi\) | ||||
0.230323 | + | 0.973114i | \(0.426022\pi\) | |||||||
\(770\) | 2.26514 | 0.0816299 | ||||||||
\(771\) | 57.8008 | 2.08165 | ||||||||
\(772\) | −11.0919 | −0.399208 | ||||||||
\(773\) | 21.9571 | 0.789742 | 0.394871 | − | 0.918737i | \(-0.370789\pi\) | ||||
0.394871 | + | 0.918737i | \(0.370789\pi\) | |||||||
\(774\) | 32.0066 | 1.15045 | ||||||||
\(775\) | 3.51501 | 0.126263 | ||||||||
\(776\) | 1.69040 | 0.0606819 | ||||||||
\(777\) | −109.037 | −3.91168 | ||||||||
\(778\) | −23.2504 | −0.833569 | ||||||||
\(779\) | −7.34124 | −0.263027 | ||||||||
\(780\) | −17.6427 | −0.631708 | ||||||||
\(781\) | 0.891436 | 0.0318981 | ||||||||
\(782\) | −5.21102 | −0.186346 | ||||||||
\(783\) | 22.3793 | 0.799772 | ||||||||
\(784\) | 6.82172 | 0.243633 | ||||||||
\(785\) | 1.85411 | 0.0661760 | ||||||||
\(786\) | −10.3748 | −0.370055 | ||||||||
\(787\) | −3.37254 | −0.120218 | −0.0601090 | − | 0.998192i | \(-0.519145\pi\) | ||||
−0.0601090 | + | 0.998192i | \(0.519145\pi\) | |||||||
\(788\) | 8.13853 | 0.289923 | ||||||||
\(789\) | −59.3111 | −2.11153 | ||||||||
\(790\) | 4.96905 | 0.176791 | ||||||||
\(791\) | 16.4208 | 0.583857 | ||||||||
\(792\) | 2.32087 | 0.0824684 | ||||||||
\(793\) | 10.3810 | 0.368639 | ||||||||
\(794\) | −39.1450 | −1.38920 | ||||||||
\(795\) | −68.1689 | −2.41770 | ||||||||
\(796\) | −21.6215 | −0.766354 | ||||||||
\(797\) | 30.8540 | 1.09291 | 0.546453 | − | 0.837490i | \(-0.315978\pi\) | ||||
0.546453 | + | 0.837490i | \(0.315978\pi\) | |||||||
\(798\) | −11.5252 | −0.407988 | ||||||||
\(799\) | 7.27175 | 0.257256 | ||||||||
\(800\) | −1.98864 | −0.0703089 | ||||||||
\(801\) | 87.2238 | 3.08190 | ||||||||
\(802\) | 19.2227 | 0.678777 | ||||||||
\(803\) | −1.45428 | −0.0513204 | ||||||||
\(804\) | 45.1974 | 1.59399 | ||||||||
\(805\) | −44.6825 | −1.57485 | ||||||||
\(806\) | 5.79677 | 0.204182 | ||||||||
\(807\) | −38.6359 | −1.36005 | ||||||||
\(808\) | 3.23070 | 0.113656 | ||||||||
\(809\) | −38.9691 | −1.37008 | −0.685040 | − | 0.728506i | \(-0.740215\pi\) | ||||
−0.685040 | + | 0.728506i | \(0.740215\pi\) | |||||||
\(810\) | 25.7951 | 0.906349 | ||||||||
\(811\) | −16.6761 | −0.585577 | −0.292789 | − | 0.956177i | \(-0.594583\pi\) | ||||
−0.292789 | + | 0.956177i | \(0.594583\pi\) | |||||||
\(812\) | 7.43400 | 0.260882 | ||||||||
\(813\) | 15.0025 | 0.526162 | ||||||||
\(814\) | −3.32168 | −0.116425 | ||||||||
\(815\) | −19.7835 | −0.692985 | ||||||||
\(816\) | 2.33247 | 0.0816527 | ||||||||
\(817\) | −4.84196 | −0.169399 | ||||||||
\(818\) | −0.152173 | −0.00532061 | ||||||||
\(819\) | −80.5961 | −2.81626 | ||||||||
\(820\) | 12.7395 | 0.444881 | ||||||||
\(821\) | −7.26920 | −0.253697 | −0.126848 | − | 0.991922i | \(-0.540486\pi\) | ||||
−0.126848 | + | 0.991922i | \(0.540486\pi\) | |||||||
\(822\) | −10.1538 | −0.354156 | ||||||||
\(823\) | 10.8910 | 0.379636 | 0.189818 | − | 0.981819i | \(-0.439210\pi\) | ||||
0.189818 | + | 0.981819i | \(0.439210\pi\) | |||||||
\(824\) | −9.39478 | −0.327283 | ||||||||
\(825\) | −2.16449 | −0.0753577 | ||||||||
\(826\) | −9.59842 | −0.333972 | ||||||||
\(827\) | 49.5583 | 1.72331 | 0.861655 | − | 0.507495i | \(-0.169428\pi\) | ||||
0.861655 | + | 0.507495i | \(0.169428\pi\) | |||||||
\(828\) | −45.7818 | −1.59103 | ||||||||
\(829\) | 15.5170 | 0.538928 | 0.269464 | − | 0.963010i | \(-0.413153\pi\) | ||||
0.269464 | + | 0.963010i | \(0.413153\pi\) | |||||||
\(830\) | 23.5531 | 0.817540 | ||||||||
\(831\) | −32.8501 | −1.13956 | ||||||||
\(832\) | −3.27955 | −0.113698 | ||||||||
\(833\) | 5.13265 | 0.177836 | ||||||||
\(834\) | 35.1946 | 1.21869 | ||||||||
\(835\) | −8.37803 | −0.289934 | ||||||||
\(836\) | −0.351101 | −0.0121431 | ||||||||
\(837\) | −19.7823 | −0.683776 | ||||||||
\(838\) | 27.1022 | 0.936231 | ||||||||
\(839\) | 33.5435 | 1.15805 | 0.579024 | − | 0.815310i | \(-0.303434\pi\) | ||||
0.579024 | + | 0.815310i | \(0.303434\pi\) | |||||||
\(840\) | 20.0000 | 0.690066 | ||||||||
\(841\) | −25.0016 | −0.862125 | ||||||||
\(842\) | 9.67776 | 0.333518 | ||||||||
\(843\) | −5.64328 | −0.194365 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | −3.89498 | −0.133991 | ||||||||
\(846\) | 63.8865 | 2.19646 | ||||||||
\(847\) | −40.4370 | −1.38943 | ||||||||
\(848\) | −12.6718 | −0.435150 | ||||||||
\(849\) | −26.7083 | −0.916625 | ||||||||
\(850\) | −1.49625 | −0.0513209 | ||||||||
\(851\) | 65.5240 | 2.24614 | ||||||||
\(852\) | 7.87092 | 0.269653 | ||||||||
\(853\) | −20.3615 | −0.697164 | −0.348582 | − | 0.937278i | \(-0.613337\pi\) | ||||
−0.348582 | + | 0.937278i | \(0.613337\pi\) | |||||||
\(854\) | −11.7680 | −0.402694 | ||||||||
\(855\) | −11.4710 | −0.392299 | ||||||||
\(856\) | −11.1153 | −0.379913 | ||||||||
\(857\) | −12.7900 | −0.436898 | −0.218449 | − | 0.975848i | \(-0.570100\pi\) | ||||
−0.218449 | + | 0.975848i | \(0.570100\pi\) | |||||||
\(858\) | −3.56956 | −0.121863 | ||||||||
\(859\) | −20.7426 | −0.707729 | −0.353865 | − | 0.935297i | \(-0.615133\pi\) | ||||
−0.353865 | + | 0.935297i | \(0.615133\pi\) | |||||||
\(860\) | 8.40239 | 0.286519 | ||||||||
\(861\) | 84.6093 | 2.88348 | ||||||||
\(862\) | 28.4143 | 0.967796 | ||||||||
\(863\) | 17.8871 | 0.608882 | 0.304441 | − | 0.952531i | \(-0.401530\pi\) | ||||
0.304441 | + | 0.952531i | \(0.401530\pi\) | |||||||
\(864\) | 11.1919 | 0.380758 | ||||||||
\(865\) | −29.9321 | −1.01772 | ||||||||
\(866\) | 6.23986 | 0.212039 | ||||||||
\(867\) | −50.9458 | −1.73021 | ||||||||
\(868\) | −6.57131 | −0.223045 | ||||||||
\(869\) | 1.00537 | 0.0341047 | ||||||||
\(870\) | 10.7570 | 0.364696 | ||||||||
\(871\) | −47.8147 | −1.62014 | ||||||||
\(872\) | −15.2968 | −0.518014 | ||||||||
\(873\) | 11.1740 | 0.378182 | ||||||||
\(874\) | 6.92588 | 0.234271 | ||||||||
\(875\) | −45.0874 | −1.52423 | ||||||||
\(876\) | −12.8405 | −0.433841 | ||||||||
\(877\) | 46.9121 | 1.58411 | 0.792054 | − | 0.610451i | \(-0.209012\pi\) | ||||
0.792054 | + | 0.610451i | \(0.209012\pi\) | |||||||
\(878\) | 32.5502 | 1.09851 | ||||||||
\(879\) | 66.4108 | 2.23998 | ||||||||
\(880\) | 0.609275 | 0.0205387 | ||||||||
\(881\) | −22.2504 | −0.749636 | −0.374818 | − | 0.927098i | \(-0.622295\pi\) | ||||
−0.374818 | + | 0.927098i | \(0.622295\pi\) | |||||||
\(882\) | 45.0933 | 1.51837 | ||||||||
\(883\) | −3.22230 | −0.108439 | −0.0542196 | − | 0.998529i | \(-0.517267\pi\) | ||||
−0.0542196 | + | 0.998529i | \(0.517267\pi\) | |||||||
\(884\) | −2.46753 | −0.0829921 | ||||||||
\(885\) | −13.8889 | −0.466870 | ||||||||
\(886\) | 20.3511 | 0.683710 | ||||||||
\(887\) | −57.0542 | −1.91569 | −0.957846 | − | 0.287281i | \(-0.907249\pi\) | ||||
−0.957846 | + | 0.287281i | \(0.907249\pi\) | |||||||
\(888\) | −29.3287 | −0.984208 | ||||||||
\(889\) | −4.07499 | −0.136671 | ||||||||
\(890\) | 22.8980 | 0.767544 | ||||||||
\(891\) | 5.21901 | 0.174843 | ||||||||
\(892\) | −9.23464 | −0.309199 | ||||||||
\(893\) | −9.66475 | −0.323419 | ||||||||
\(894\) | 20.0637 | 0.671030 | ||||||||
\(895\) | 10.2999 | 0.344286 | ||||||||
\(896\) | 3.71776 | 0.124202 | ||||||||
\(897\) | 70.4137 | 2.35105 | ||||||||
\(898\) | −16.6193 | −0.554594 | ||||||||
\(899\) | −3.53437 | −0.117878 | ||||||||
\(900\) | −13.1454 | −0.438180 | ||||||||
\(901\) | −9.53423 | −0.317631 | ||||||||
\(902\) | 2.57752 | 0.0858219 | ||||||||
\(903\) | 55.8045 | 1.85706 | ||||||||
\(904\) | 4.41686 | 0.146903 | ||||||||
\(905\) | 36.4277 | 1.21090 | ||||||||
\(906\) | 39.1330 | 1.30011 | ||||||||
\(907\) | −30.3769 | −1.00865 | −0.504324 | − | 0.863515i | \(-0.668258\pi\) | ||||
−0.504324 | + | 0.863515i | \(0.668258\pi\) | |||||||
\(908\) | 4.48137 | 0.148719 | ||||||||
\(909\) | 21.3557 | 0.708325 | ||||||||
\(910\) | −21.1581 | −0.701386 | ||||||||
\(911\) | −21.2285 | −0.703331 | −0.351665 | − | 0.936126i | \(-0.614385\pi\) | ||||
−0.351665 | + | 0.936126i | \(0.614385\pi\) | |||||||
\(912\) | −3.10004 | −0.102653 | ||||||||
\(913\) | 4.76539 | 0.157711 | ||||||||
\(914\) | −2.63080 | −0.0870192 | ||||||||
\(915\) | −17.0283 | −0.562940 | ||||||||
\(916\) | 0.681758 | 0.0225259 | ||||||||
\(917\) | −12.4420 | −0.410872 | ||||||||
\(918\) | 8.42080 | 0.277928 | ||||||||
\(919\) | −48.6280 | −1.60409 | −0.802044 | − | 0.597265i | \(-0.796254\pi\) | ||||
−0.802044 | + | 0.597265i | \(0.796254\pi\) | |||||||
\(920\) | −12.0187 | −0.396244 | ||||||||
\(921\) | 98.7163 | 3.25281 | ||||||||
\(922\) | 21.7075 | 0.714899 | ||||||||
\(923\) | −8.32670 | −0.274077 | ||||||||
\(924\) | 4.04651 | 0.133120 | ||||||||
\(925\) | 18.8140 | 0.618600 | ||||||||
\(926\) | 37.3602 | 1.22773 | ||||||||
\(927\) | −62.1019 | −2.03969 | ||||||||
\(928\) | 1.99959 | 0.0656398 | ||||||||
\(929\) | −8.09057 | −0.265443 | −0.132721 | − | 0.991153i | \(-0.542372\pi\) | ||||
−0.132721 | + | 0.991153i | \(0.542372\pi\) | |||||||
\(930\) | −9.50868 | −0.311802 | ||||||||
\(931\) | −6.82172 | −0.223573 | ||||||||
\(932\) | −29.9511 | −0.981080 | ||||||||
\(933\) | 13.6001 | 0.445247 | ||||||||
\(934\) | 10.1334 | 0.331576 | ||||||||
\(935\) | 0.458418 | 0.0149919 | ||||||||
\(936\) | −21.6787 | −0.708590 | ||||||||
\(937\) | −9.57968 | −0.312955 | −0.156477 | − | 0.987682i | \(-0.550014\pi\) | ||||
−0.156477 | + | 0.987682i | \(0.550014\pi\) | |||||||
\(938\) | 54.2035 | 1.76981 | ||||||||
\(939\) | −86.5567 | −2.82467 | ||||||||
\(940\) | 16.7715 | 0.547027 | ||||||||
\(941\) | 46.1734 | 1.50521 | 0.752604 | − | 0.658473i | \(-0.228797\pi\) | ||||
0.752604 | + | 0.658473i | \(0.228797\pi\) | |||||||
\(942\) | 3.31224 | 0.107918 | ||||||||
\(943\) | −50.8445 | −1.65573 | ||||||||
\(944\) | −2.58178 | −0.0840297 | ||||||||
\(945\) | 72.2051 | 2.34883 | ||||||||
\(946\) | 1.70002 | 0.0552723 | ||||||||
\(947\) | −47.1625 | −1.53258 | −0.766288 | − | 0.642498i | \(-0.777898\pi\) | ||||
−0.766288 | + | 0.642498i | \(0.777898\pi\) | |||||||
\(948\) | 8.87686 | 0.288307 | ||||||||
\(949\) | 13.5841 | 0.440958 | ||||||||
\(950\) | 1.98864 | 0.0645199 | ||||||||
\(951\) | −27.1162 | −0.879303 | ||||||||
\(952\) | 2.79724 | 0.0906590 | ||||||||
\(953\) | 12.9228 | 0.418610 | 0.209305 | − | 0.977850i | \(-0.432880\pi\) | ||||
0.209305 | + | 0.977850i | \(0.432880\pi\) | |||||||
\(954\) | −83.7636 | −2.71195 | ||||||||
\(955\) | −42.5864 | −1.37806 | ||||||||
\(956\) | 13.9618 | 0.451556 | ||||||||
\(957\) | 2.17641 | 0.0703534 | ||||||||
\(958\) | −42.3174 | −1.36721 | ||||||||
\(959\) | −12.1771 | −0.393219 | ||||||||
\(960\) | 5.37959 | 0.173625 | ||||||||
\(961\) | −27.8758 | −0.899219 | ||||||||
\(962\) | 31.0271 | 1.00035 | ||||||||
\(963\) | −73.4750 | −2.36770 | ||||||||
\(964\) | 12.9567 | 0.417307 | ||||||||
\(965\) | −19.2482 | −0.619620 | ||||||||
\(966\) | −79.8221 | −2.56824 | ||||||||
\(967\) | −32.3219 | −1.03940 | −0.519701 | − | 0.854348i | \(-0.673957\pi\) | ||||
−0.519701 | + | 0.854348i | \(0.673957\pi\) | |||||||
\(968\) | −10.8767 | −0.349591 | ||||||||
\(969\) | −2.33247 | −0.0749297 | ||||||||
\(970\) | 2.93340 | 0.0941859 | ||||||||
\(971\) | −25.3033 | −0.812021 | −0.406011 | − | 0.913868i | \(-0.633080\pi\) | ||||
−0.406011 | + | 0.913868i | \(0.633080\pi\) | |||||||
\(972\) | 12.5054 | 0.401111 | ||||||||
\(973\) | 42.2075 | 1.35311 | ||||||||
\(974\) | 14.7169 | 0.471561 | ||||||||
\(975\) | 20.2180 | 0.647493 | ||||||||
\(976\) | −3.16536 | −0.101321 | ||||||||
\(977\) | −25.6983 | −0.822162 | −0.411081 | − | 0.911599i | \(-0.634849\pi\) | ||||
−0.411081 | + | 0.911599i | \(0.634849\pi\) | |||||||
\(978\) | −35.3418 | −1.13010 | ||||||||
\(979\) | 4.63285 | 0.148067 | ||||||||
\(980\) | 11.8379 | 0.378149 | ||||||||
\(981\) | −101.116 | −3.22837 | ||||||||
\(982\) | −26.8044 | −0.855362 | ||||||||
\(983\) | 17.5857 | 0.560898 | 0.280449 | − | 0.959869i | \(-0.409517\pi\) | ||||
0.280449 | + | 0.959869i | \(0.409517\pi\) | |||||||
\(984\) | 22.7581 | 0.725503 | ||||||||
\(985\) | 14.1230 | 0.449997 | ||||||||
\(986\) | 1.50449 | 0.0479128 | ||||||||
\(987\) | 111.388 | 3.54553 | ||||||||
\(988\) | 3.27955 | 0.104337 | ||||||||
\(989\) | −33.5348 | −1.06634 | ||||||||
\(990\) | 4.02746 | 0.128001 | ||||||||
\(991\) | 30.2210 | 0.960001 | 0.480001 | − | 0.877268i | \(-0.340636\pi\) | ||||
0.480001 | + | 0.877268i | \(0.340636\pi\) | |||||||
\(992\) | −1.76755 | −0.0561197 | ||||||||
\(993\) | −10.1640 | −0.322543 | ||||||||
\(994\) | 9.43929 | 0.299396 | ||||||||
\(995\) | −37.5204 | −1.18948 | ||||||||
\(996\) | 42.0759 | 1.33323 | ||||||||
\(997\) | −11.0113 | −0.348732 | −0.174366 | − | 0.984681i | \(-0.555788\pi\) | ||||
−0.174366 | + | 0.984681i | \(0.555788\pi\) | |||||||
\(998\) | −16.4246 | −0.519910 | ||||||||
\(999\) | −105.884 | −3.35003 |
(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 | 8018.2.a.j.1.43 | ✓ | 47 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.j.1.43 | ✓ | 47 | 1.1 | even | 1 | trivial |