Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4010,2,Mod(1,4010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4010, 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("4010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4010 = 2 \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4010.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0200112105\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} - 35 x^{18} + 154 x^{17} + 460 x^{16} - 2392 x^{15} - 2591 x^{14} + 19157 x^{13} + 2776 x^{12} - 83577 x^{11} + 34362 x^{10} + 190617 x^{9} - 150697 x^{8} + \cdots + 104 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-0.323343\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4010.1 |
$q$-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 | ||||||||
\(3\) | −0.323343 | −0.186682 | −0.0933412 | − | 0.995634i | \(-0.529755\pi\) | ||||
−0.0933412 | + | 0.995634i | \(0.529755\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0.323343 | 0.132004 | ||||||||
\(7\) | 4.27073 | 1.61418 | 0.807092 | − | 0.590426i | \(-0.201040\pi\) | ||||
0.807092 | + | 0.590426i | \(0.201040\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.89545 | −0.965150 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −6.20730 | −1.87157 | −0.935786 | − | 0.352569i | \(-0.885308\pi\) | ||||
−0.935786 | + | 0.352569i | \(0.885308\pi\) | |||||||
\(12\) | −0.323343 | −0.0933412 | ||||||||
\(13\) | 1.40339 | 0.389232 | 0.194616 | − | 0.980880i | \(-0.437654\pi\) | ||||
0.194616 | + | 0.980880i | \(0.437654\pi\) | |||||||
\(14\) | −4.27073 | −1.14140 | ||||||||
\(15\) | −0.323343 | −0.0834869 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.33608 | 1.05165 | 0.525827 | − | 0.850591i | \(-0.323756\pi\) | ||||
0.525827 | + | 0.850591i | \(0.323756\pi\) | |||||||
\(18\) | 2.89545 | 0.682464 | ||||||||
\(19\) | −2.64762 | −0.607406 | −0.303703 | − | 0.952767i | \(-0.598223\pi\) | ||||
−0.303703 | + | 0.952767i | \(0.598223\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −1.38091 | −0.301340 | ||||||||
\(22\) | 6.20730 | 1.32340 | ||||||||
\(23\) | −4.01015 | −0.836174 | −0.418087 | − | 0.908407i | \(-0.637299\pi\) | ||||
−0.418087 | + | 0.908407i | \(0.637299\pi\) | |||||||
\(24\) | 0.323343 | 0.0660022 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.40339 | −0.275228 | ||||||||
\(27\) | 1.90625 | 0.366859 | ||||||||
\(28\) | 4.27073 | 0.807092 | ||||||||
\(29\) | −5.35613 | −0.994609 | −0.497305 | − | 0.867576i | \(-0.665677\pi\) | ||||
−0.497305 | + | 0.867576i | \(0.665677\pi\) | |||||||
\(30\) | 0.323343 | 0.0590341 | ||||||||
\(31\) | −3.65307 | −0.656111 | −0.328056 | − | 0.944658i | \(-0.606393\pi\) | ||||
−0.328056 | + | 0.944658i | \(0.606393\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.00709 | 0.349389 | ||||||||
\(34\) | −4.33608 | −0.743632 | ||||||||
\(35\) | 4.27073 | 0.721885 | ||||||||
\(36\) | −2.89545 | −0.482575 | ||||||||
\(37\) | 4.46073 | 0.733339 | 0.366669 | − | 0.930351i | \(-0.380498\pi\) | ||||
0.366669 | + | 0.930351i | \(0.380498\pi\) | |||||||
\(38\) | 2.64762 | 0.429501 | ||||||||
\(39\) | −0.453778 | −0.0726627 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −5.68834 | −0.888370 | −0.444185 | − | 0.895935i | \(-0.646507\pi\) | ||||
−0.444185 | + | 0.895935i | \(0.646507\pi\) | |||||||
\(42\) | 1.38091 | 0.213079 | ||||||||
\(43\) | 11.1937 | 1.70702 | 0.853512 | − | 0.521073i | \(-0.174468\pi\) | ||||
0.853512 | + | 0.521073i | \(0.174468\pi\) | |||||||
\(44\) | −6.20730 | −0.935786 | ||||||||
\(45\) | −2.89545 | −0.431628 | ||||||||
\(46\) | 4.01015 | 0.591265 | ||||||||
\(47\) | 11.1258 | 1.62286 | 0.811430 | − | 0.584449i | \(-0.198689\pi\) | ||||
0.811430 | + | 0.584449i | \(0.198689\pi\) | |||||||
\(48\) | −0.323343 | −0.0466706 | ||||||||
\(49\) | 11.2391 | 1.60559 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −1.40204 | −0.196325 | ||||||||
\(52\) | 1.40339 | 0.194616 | ||||||||
\(53\) | 2.41534 | 0.331772 | 0.165886 | − | 0.986145i | \(-0.446952\pi\) | ||||
0.165886 | + | 0.986145i | \(0.446952\pi\) | |||||||
\(54\) | −1.90625 | −0.259408 | ||||||||
\(55\) | −6.20730 | −0.836992 | ||||||||
\(56\) | −4.27073 | −0.570700 | ||||||||
\(57\) | 0.856091 | 0.113392 | ||||||||
\(58\) | 5.35613 | 0.703295 | ||||||||
\(59\) | 2.54166 | 0.330896 | 0.165448 | − | 0.986219i | \(-0.447093\pi\) | ||||
0.165448 | + | 0.986219i | \(0.447093\pi\) | |||||||
\(60\) | −0.323343 | −0.0417434 | ||||||||
\(61\) | 4.37565 | 0.560244 | 0.280122 | − | 0.959964i | \(-0.409625\pi\) | ||||
0.280122 | + | 0.959964i | \(0.409625\pi\) | |||||||
\(62\) | 3.65307 | 0.463941 | ||||||||
\(63\) | −12.3657 | −1.55793 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.40339 | 0.174070 | ||||||||
\(66\) | −2.00709 | −0.247056 | ||||||||
\(67\) | 14.1842 | 1.73287 | 0.866435 | − | 0.499290i | \(-0.166406\pi\) | ||||
0.866435 | + | 0.499290i | \(0.166406\pi\) | |||||||
\(68\) | 4.33608 | 0.525827 | ||||||||
\(69\) | 1.29666 | 0.156099 | ||||||||
\(70\) | −4.27073 | −0.510450 | ||||||||
\(71\) | 12.9847 | 1.54100 | 0.770500 | − | 0.637441i | \(-0.220007\pi\) | ||||
0.770500 | + | 0.637441i | \(0.220007\pi\) | |||||||
\(72\) | 2.89545 | 0.341232 | ||||||||
\(73\) | −10.8750 | −1.27282 | −0.636411 | − | 0.771350i | \(-0.719582\pi\) | ||||
−0.636411 | + | 0.771350i | \(0.719582\pi\) | |||||||
\(74\) | −4.46073 | −0.518549 | ||||||||
\(75\) | −0.323343 | −0.0373365 | ||||||||
\(76\) | −2.64762 | −0.303703 | ||||||||
\(77\) | −26.5097 | −3.02106 | ||||||||
\(78\) | 0.453778 | 0.0513803 | ||||||||
\(79\) | 6.97469 | 0.784714 | 0.392357 | − | 0.919813i | \(-0.371660\pi\) | ||||
0.392357 | + | 0.919813i | \(0.371660\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 8.06997 | 0.896664 | ||||||||
\(82\) | 5.68834 | 0.628172 | ||||||||
\(83\) | 6.32611 | 0.694380 | 0.347190 | − | 0.937795i | \(-0.387136\pi\) | ||||
0.347190 | + | 0.937795i | \(0.387136\pi\) | |||||||
\(84\) | −1.38091 | −0.150670 | ||||||||
\(85\) | 4.33608 | 0.470314 | ||||||||
\(86\) | −11.1937 | −1.20705 | ||||||||
\(87\) | 1.73187 | 0.185676 | ||||||||
\(88\) | 6.20730 | 0.661701 | ||||||||
\(89\) | −0.107411 | −0.0113855 | −0.00569276 | − | 0.999984i | \(-0.501812\pi\) | ||||
−0.00569276 | + | 0.999984i | \(0.501812\pi\) | |||||||
\(90\) | 2.89545 | 0.305207 | ||||||||
\(91\) | 5.99352 | 0.628292 | ||||||||
\(92\) | −4.01015 | −0.418087 | ||||||||
\(93\) | 1.18120 | 0.122484 | ||||||||
\(94\) | −11.1258 | −1.14754 | ||||||||
\(95\) | −2.64762 | −0.271640 | ||||||||
\(96\) | 0.323343 | 0.0330011 | ||||||||
\(97\) | 12.2056 | 1.23929 | 0.619646 | − | 0.784881i | \(-0.287276\pi\) | ||||
0.619646 | + | 0.784881i | \(0.287276\pi\) | |||||||
\(98\) | −11.2391 | −1.13532 | ||||||||
\(99\) | 17.9729 | 1.80635 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 0.337459 | 0.0335785 | 0.0167892 | − | 0.999859i | \(-0.494656\pi\) | ||||
0.0167892 | + | 0.999859i | \(0.494656\pi\) | |||||||
\(102\) | 1.40204 | 0.138823 | ||||||||
\(103\) | −9.67687 | −0.953490 | −0.476745 | − | 0.879042i | \(-0.658183\pi\) | ||||
−0.476745 | + | 0.879042i | \(0.658183\pi\) | |||||||
\(104\) | −1.40339 | −0.137614 | ||||||||
\(105\) | −1.38091 | −0.134763 | ||||||||
\(106\) | −2.41534 | −0.234598 | ||||||||
\(107\) | 13.0574 | 1.26231 | 0.631153 | − | 0.775658i | \(-0.282582\pi\) | ||||
0.631153 | + | 0.775658i | \(0.282582\pi\) | |||||||
\(108\) | 1.90625 | 0.183429 | ||||||||
\(109\) | 4.28493 | 0.410422 | 0.205211 | − | 0.978718i | \(-0.434212\pi\) | ||||
0.205211 | + | 0.978718i | \(0.434212\pi\) | |||||||
\(110\) | 6.20730 | 0.591843 | ||||||||
\(111\) | −1.44235 | −0.136901 | ||||||||
\(112\) | 4.27073 | 0.403546 | ||||||||
\(113\) | 5.51677 | 0.518974 | 0.259487 | − | 0.965747i | \(-0.416447\pi\) | ||||
0.259487 | + | 0.965747i | \(0.416447\pi\) | |||||||
\(114\) | −0.856091 | −0.0801802 | ||||||||
\(115\) | −4.01015 | −0.373949 | ||||||||
\(116\) | −5.35613 | −0.497305 | ||||||||
\(117\) | −4.06346 | −0.375667 | ||||||||
\(118\) | −2.54166 | −0.233979 | ||||||||
\(119\) | 18.5182 | 1.69756 | ||||||||
\(120\) | 0.323343 | 0.0295171 | ||||||||
\(121\) | 27.5306 | 2.50278 | ||||||||
\(122\) | −4.37565 | −0.396152 | ||||||||
\(123\) | 1.83929 | 0.165843 | ||||||||
\(124\) | −3.65307 | −0.328056 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 12.3657 | 1.10162 | ||||||||
\(127\) | −3.91161 | −0.347099 | −0.173550 | − | 0.984825i | \(-0.555524\pi\) | ||||
−0.173550 | + | 0.984825i | \(0.555524\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −3.61941 | −0.318671 | ||||||||
\(130\) | −1.40339 | −0.123086 | ||||||||
\(131\) | −5.58121 | −0.487633 | −0.243816 | − | 0.969821i | \(-0.578399\pi\) | ||||
−0.243816 | + | 0.969821i | \(0.578399\pi\) | |||||||
\(132\) | 2.00709 | 0.174695 | ||||||||
\(133\) | −11.3073 | −0.980465 | ||||||||
\(134\) | −14.1842 | −1.22532 | ||||||||
\(135\) | 1.90625 | 0.164064 | ||||||||
\(136\) | −4.33608 | −0.371816 | ||||||||
\(137\) | −19.2302 | −1.64295 | −0.821473 | − | 0.570247i | \(-0.806847\pi\) | ||||
−0.821473 | + | 0.570247i | \(0.806847\pi\) | |||||||
\(138\) | −1.29666 | −0.110379 | ||||||||
\(139\) | 2.58223 | 0.219022 | 0.109511 | − | 0.993986i | \(-0.465072\pi\) | ||||
0.109511 | + | 0.993986i | \(0.465072\pi\) | |||||||
\(140\) | 4.27073 | 0.360942 | ||||||||
\(141\) | −3.59744 | −0.302959 | ||||||||
\(142\) | −12.9847 | −1.08965 | ||||||||
\(143\) | −8.71129 | −0.728475 | ||||||||
\(144\) | −2.89545 | −0.241287 | ||||||||
\(145\) | −5.35613 | −0.444803 | ||||||||
\(146\) | 10.8750 | 0.900021 | ||||||||
\(147\) | −3.63410 | −0.299735 | ||||||||
\(148\) | 4.46073 | 0.366669 | ||||||||
\(149\) | 4.92135 | 0.403172 | 0.201586 | − | 0.979471i | \(-0.435390\pi\) | ||||
0.201586 | + | 0.979471i | \(0.435390\pi\) | |||||||
\(150\) | 0.323343 | 0.0264009 | ||||||||
\(151\) | −8.56366 | −0.696900 | −0.348450 | − | 0.937327i | \(-0.613292\pi\) | ||||
−0.348450 | + | 0.937327i | \(0.613292\pi\) | |||||||
\(152\) | 2.64762 | 0.214751 | ||||||||
\(153\) | −12.5549 | −1.01500 | ||||||||
\(154\) | 26.5097 | 2.13621 | ||||||||
\(155\) | −3.65307 | −0.293422 | ||||||||
\(156\) | −0.453778 | −0.0363313 | ||||||||
\(157\) | 14.3778 | 1.14747 | 0.573735 | − | 0.819041i | \(-0.305494\pi\) | ||||
0.573735 | + | 0.819041i | \(0.305494\pi\) | |||||||
\(158\) | −6.97469 | −0.554877 | ||||||||
\(159\) | −0.780983 | −0.0619360 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −17.1263 | −1.34974 | ||||||||
\(162\) | −8.06997 | −0.634037 | ||||||||
\(163\) | 5.48063 | 0.429276 | 0.214638 | − | 0.976694i | \(-0.431143\pi\) | ||||
0.214638 | + | 0.976694i | \(0.431143\pi\) | |||||||
\(164\) | −5.68834 | −0.444185 | ||||||||
\(165\) | 2.00709 | 0.156252 | ||||||||
\(166\) | −6.32611 | −0.491001 | ||||||||
\(167\) | 3.20672 | 0.248144 | 0.124072 | − | 0.992273i | \(-0.460405\pi\) | ||||
0.124072 | + | 0.992273i | \(0.460405\pi\) | |||||||
\(168\) | 1.38091 | 0.106540 | ||||||||
\(169\) | −11.0305 | −0.848499 | ||||||||
\(170\) | −4.33608 | −0.332562 | ||||||||
\(171\) | 7.66606 | 0.586238 | ||||||||
\(172\) | 11.1937 | 0.853512 | ||||||||
\(173\) | −14.3715 | −1.09265 | −0.546323 | − | 0.837574i | \(-0.683973\pi\) | ||||
−0.546323 | + | 0.837574i | \(0.683973\pi\) | |||||||
\(174\) | −1.73187 | −0.131293 | ||||||||
\(175\) | 4.27073 | 0.322837 | ||||||||
\(176\) | −6.20730 | −0.467893 | ||||||||
\(177\) | −0.821829 | −0.0617724 | ||||||||
\(178\) | 0.107411 | 0.00805078 | ||||||||
\(179\) | −9.78741 | −0.731546 | −0.365773 | − | 0.930704i | \(-0.619195\pi\) | ||||
−0.365773 | + | 0.930704i | \(0.619195\pi\) | |||||||
\(180\) | −2.89545 | −0.215814 | ||||||||
\(181\) | 10.2982 | 0.765462 | 0.382731 | − | 0.923860i | \(-0.374984\pi\) | ||||
0.382731 | + | 0.923860i | \(0.374984\pi\) | |||||||
\(182\) | −5.99352 | −0.444269 | ||||||||
\(183\) | −1.41484 | −0.104588 | ||||||||
\(184\) | 4.01015 | 0.295632 | ||||||||
\(185\) | 4.46073 | 0.327959 | ||||||||
\(186\) | −1.18120 | −0.0866096 | ||||||||
\(187\) | −26.9154 | −1.96825 | ||||||||
\(188\) | 11.1258 | 0.811430 | ||||||||
\(189\) | 8.14109 | 0.592177 | ||||||||
\(190\) | 2.64762 | 0.192079 | ||||||||
\(191\) | 0.221079 | 0.0159967 | 0.00799835 | − | 0.999968i | \(-0.497454\pi\) | ||||
0.00799835 | + | 0.999968i | \(0.497454\pi\) | |||||||
\(192\) | −0.323343 | −0.0233353 | ||||||||
\(193\) | 20.3644 | 1.46586 | 0.732929 | − | 0.680305i | \(-0.238153\pi\) | ||||
0.732929 | + | 0.680305i | \(0.238153\pi\) | |||||||
\(194\) | −12.2056 | −0.876312 | ||||||||
\(195\) | −0.453778 | −0.0324957 | ||||||||
\(196\) | 11.2391 | 0.802795 | ||||||||
\(197\) | −25.5964 | −1.82367 | −0.911835 | − | 0.410558i | \(-0.865334\pi\) | ||||
−0.911835 | + | 0.410558i | \(0.865334\pi\) | |||||||
\(198\) | −17.9729 | −1.27728 | ||||||||
\(199\) | −11.9209 | −0.845052 | −0.422526 | − | 0.906351i | \(-0.638857\pi\) | ||||
−0.422526 | + | 0.906351i | \(0.638857\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −4.58635 | −0.323496 | ||||||||
\(202\) | −0.337459 | −0.0237436 | ||||||||
\(203\) | −22.8746 | −1.60548 | ||||||||
\(204\) | −1.40204 | −0.0981626 | ||||||||
\(205\) | −5.68834 | −0.397291 | ||||||||
\(206\) | 9.67687 | 0.674219 | ||||||||
\(207\) | 11.6112 | 0.807033 | ||||||||
\(208\) | 1.40339 | 0.0973079 | ||||||||
\(209\) | 16.4346 | 1.13680 | ||||||||
\(210\) | 1.38091 | 0.0952919 | ||||||||
\(211\) | −8.03884 | −0.553417 | −0.276708 | − | 0.960954i | \(-0.589244\pi\) | ||||
−0.276708 | + | 0.960954i | \(0.589244\pi\) | |||||||
\(212\) | 2.41534 | 0.165886 | ||||||||
\(213\) | −4.19851 | −0.287677 | ||||||||
\(214\) | −13.0574 | −0.892585 | ||||||||
\(215\) | 11.1937 | 0.763404 | ||||||||
\(216\) | −1.90625 | −0.129704 | ||||||||
\(217\) | −15.6013 | −1.05908 | ||||||||
\(218\) | −4.28493 | −0.290212 | ||||||||
\(219\) | 3.51636 | 0.237613 | ||||||||
\(220\) | −6.20730 | −0.418496 | ||||||||
\(221\) | 6.08524 | 0.409337 | ||||||||
\(222\) | 1.44235 | 0.0968039 | ||||||||
\(223\) | −5.81581 | −0.389456 | −0.194728 | − | 0.980857i | \(-0.562382\pi\) | ||||
−0.194728 | + | 0.980857i | \(0.562382\pi\) | |||||||
\(224\) | −4.27073 | −0.285350 | ||||||||
\(225\) | −2.89545 | −0.193030 | ||||||||
\(226\) | −5.51677 | −0.366970 | ||||||||
\(227\) | 13.2037 | 0.876358 | 0.438179 | − | 0.898888i | \(-0.355624\pi\) | ||||
0.438179 | + | 0.898888i | \(0.355624\pi\) | |||||||
\(228\) | 0.856091 | 0.0566960 | ||||||||
\(229\) | 25.2511 | 1.66864 | 0.834319 | − | 0.551281i | \(-0.185861\pi\) | ||||
0.834319 | + | 0.551281i | \(0.185861\pi\) | |||||||
\(230\) | 4.01015 | 0.264422 | ||||||||
\(231\) | 8.57173 | 0.563979 | ||||||||
\(232\) | 5.35613 | 0.351647 | ||||||||
\(233\) | 9.40454 | 0.616112 | 0.308056 | − | 0.951368i | \(-0.400322\pi\) | ||||
0.308056 | + | 0.951368i | \(0.400322\pi\) | |||||||
\(234\) | 4.06346 | 0.265637 | ||||||||
\(235\) | 11.1258 | 0.725765 | ||||||||
\(236\) | 2.54166 | 0.165448 | ||||||||
\(237\) | −2.25522 | −0.146492 | ||||||||
\(238\) | −18.5182 | −1.20036 | ||||||||
\(239\) | −7.68893 | −0.497355 | −0.248678 | − | 0.968586i | \(-0.579996\pi\) | ||||
−0.248678 | + | 0.968586i | \(0.579996\pi\) | |||||||
\(240\) | −0.323343 | −0.0208717 | ||||||||
\(241\) | −22.3622 | −1.44048 | −0.720239 | − | 0.693726i | \(-0.755968\pi\) | ||||
−0.720239 | + | 0.693726i | \(0.755968\pi\) | |||||||
\(242\) | −27.5306 | −1.76973 | ||||||||
\(243\) | −8.32813 | −0.534250 | ||||||||
\(244\) | 4.37565 | 0.280122 | ||||||||
\(245\) | 11.2391 | 0.718041 | ||||||||
\(246\) | −1.83929 | −0.117269 | ||||||||
\(247\) | −3.71566 | −0.236422 | ||||||||
\(248\) | 3.65307 | 0.231970 | ||||||||
\(249\) | −2.04550 | −0.129629 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 16.0991 | 1.01617 | 0.508083 | − | 0.861308i | \(-0.330354\pi\) | ||||
0.508083 | + | 0.861308i | \(0.330354\pi\) | |||||||
\(252\) | −12.3657 | −0.778965 | ||||||||
\(253\) | 24.8922 | 1.56496 | ||||||||
\(254\) | 3.91161 | 0.245436 | ||||||||
\(255\) | −1.40204 | −0.0877993 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 21.0520 | 1.31319 | 0.656593 | − | 0.754245i | \(-0.271997\pi\) | ||||
0.656593 | + | 0.754245i | \(0.271997\pi\) | |||||||
\(258\) | 3.61941 | 0.225335 | ||||||||
\(259\) | 19.0506 | 1.18374 | ||||||||
\(260\) | 1.40339 | 0.0870349 | ||||||||
\(261\) | 15.5084 | 0.959947 | ||||||||
\(262\) | 5.58121 | 0.344808 | ||||||||
\(263\) | 30.9243 | 1.90687 | 0.953437 | − | 0.301594i | \(-0.0975186\pi\) | ||||
0.953437 | + | 0.301594i | \(0.0975186\pi\) | |||||||
\(264\) | −2.00709 | −0.123528 | ||||||||
\(265\) | 2.41534 | 0.148373 | ||||||||
\(266\) | 11.3073 | 0.693294 | ||||||||
\(267\) | 0.0347306 | 0.00212548 | ||||||||
\(268\) | 14.1842 | 0.866435 | ||||||||
\(269\) | −12.5733 | −0.766606 | −0.383303 | − | 0.923623i | \(-0.625214\pi\) | ||||
−0.383303 | + | 0.923623i | \(0.625214\pi\) | |||||||
\(270\) | −1.90625 | −0.116011 | ||||||||
\(271\) | −1.50082 | −0.0911681 | −0.0455841 | − | 0.998961i | \(-0.514515\pi\) | ||||
−0.0455841 | + | 0.998961i | \(0.514515\pi\) | |||||||
\(272\) | 4.33608 | 0.262914 | ||||||||
\(273\) | −1.93796 | −0.117291 | ||||||||
\(274\) | 19.2302 | 1.16174 | ||||||||
\(275\) | −6.20730 | −0.374314 | ||||||||
\(276\) | 1.29666 | 0.0780495 | ||||||||
\(277\) | 11.0854 | 0.666059 | 0.333030 | − | 0.942916i | \(-0.391929\pi\) | ||||
0.333030 | + | 0.942916i | \(0.391929\pi\) | |||||||
\(278\) | −2.58223 | −0.154872 | ||||||||
\(279\) | 10.5773 | 0.633246 | ||||||||
\(280\) | −4.27073 | −0.255225 | ||||||||
\(281\) | −26.8713 | −1.60301 | −0.801503 | − | 0.597990i | \(-0.795966\pi\) | ||||
−0.801503 | + | 0.597990i | \(0.795966\pi\) | |||||||
\(282\) | 3.59744 | 0.214225 | ||||||||
\(283\) | 14.6942 | 0.873479 | 0.436740 | − | 0.899588i | \(-0.356133\pi\) | ||||
0.436740 | + | 0.899588i | \(0.356133\pi\) | |||||||
\(284\) | 12.9847 | 0.770500 | ||||||||
\(285\) | 0.856091 | 0.0507104 | ||||||||
\(286\) | 8.71129 | 0.515110 | ||||||||
\(287\) | −24.2934 | −1.43399 | ||||||||
\(288\) | 2.89545 | 0.170616 | ||||||||
\(289\) | 1.80161 | 0.105977 | ||||||||
\(290\) | 5.35613 | 0.314523 | ||||||||
\(291\) | −3.94660 | −0.231354 | ||||||||
\(292\) | −10.8750 | −0.636411 | ||||||||
\(293\) | 0.346545 | 0.0202454 | 0.0101227 | − | 0.999949i | \(-0.496778\pi\) | ||||
0.0101227 | + | 0.999949i | \(0.496778\pi\) | |||||||
\(294\) | 3.63410 | 0.211945 | ||||||||
\(295\) | 2.54166 | 0.147981 | ||||||||
\(296\) | −4.46073 | −0.259274 | ||||||||
\(297\) | −11.8327 | −0.686602 | ||||||||
\(298\) | −4.92135 | −0.285086 | ||||||||
\(299\) | −5.62783 | −0.325466 | ||||||||
\(300\) | −0.323343 | −0.0186682 | ||||||||
\(301\) | 47.8053 | 2.75545 | ||||||||
\(302\) | 8.56366 | 0.492783 | ||||||||
\(303\) | −0.109115 | −0.00626850 | ||||||||
\(304\) | −2.64762 | −0.151852 | ||||||||
\(305\) | 4.37565 | 0.250549 | ||||||||
\(306\) | 12.5549 | 0.717716 | ||||||||
\(307\) | 17.5826 | 1.00349 | 0.501746 | − | 0.865015i | \(-0.332691\pi\) | ||||
0.501746 | + | 0.865015i | \(0.332691\pi\) | |||||||
\(308\) | −26.5097 | −1.51053 | ||||||||
\(309\) | 3.12895 | 0.178000 | ||||||||
\(310\) | 3.65307 | 0.207481 | ||||||||
\(311\) | −12.9754 | −0.735765 | −0.367883 | − | 0.929872i | \(-0.619917\pi\) | ||||
−0.367883 | + | 0.929872i | \(0.619917\pi\) | |||||||
\(312\) | 0.453778 | 0.0256901 | ||||||||
\(313\) | −4.33743 | −0.245166 | −0.122583 | − | 0.992458i | \(-0.539118\pi\) | ||||
−0.122583 | + | 0.992458i | \(0.539118\pi\) | |||||||
\(314\) | −14.3778 | −0.811384 | ||||||||
\(315\) | −12.3657 | −0.696727 | ||||||||
\(316\) | 6.97469 | 0.392357 | ||||||||
\(317\) | 27.6801 | 1.55467 | 0.777335 | − | 0.629086i | \(-0.216571\pi\) | ||||
0.777335 | + | 0.629086i | \(0.216571\pi\) | |||||||
\(318\) | 0.780983 | 0.0437954 | ||||||||
\(319\) | 33.2471 | 1.86148 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −4.22202 | −0.235650 | ||||||||
\(322\) | 17.1263 | 0.954410 | ||||||||
\(323\) | −11.4803 | −0.638781 | ||||||||
\(324\) | 8.06997 | 0.448332 | ||||||||
\(325\) | 1.40339 | 0.0778463 | ||||||||
\(326\) | −5.48063 | −0.303544 | ||||||||
\(327\) | −1.38550 | −0.0766185 | ||||||||
\(328\) | 5.68834 | 0.314086 | ||||||||
\(329\) | 47.5152 | 2.61960 | ||||||||
\(330\) | −2.00709 | −0.110487 | ||||||||
\(331\) | −1.73730 | −0.0954905 | −0.0477453 | − | 0.998860i | \(-0.515204\pi\) | ||||
−0.0477453 | + | 0.998860i | \(0.515204\pi\) | |||||||
\(332\) | 6.32611 | 0.347190 | ||||||||
\(333\) | −12.9158 | −0.707782 | ||||||||
\(334\) | −3.20672 | −0.175464 | ||||||||
\(335\) | 14.1842 | 0.774963 | ||||||||
\(336\) | −1.38091 | −0.0753349 | ||||||||
\(337\) | −13.3698 | −0.728298 | −0.364149 | − | 0.931341i | \(-0.618640\pi\) | ||||
−0.364149 | + | 0.931341i | \(0.618640\pi\) | |||||||
\(338\) | 11.0305 | 0.599979 | ||||||||
\(339\) | −1.78381 | −0.0968833 | ||||||||
\(340\) | 4.33608 | 0.235157 | ||||||||
\(341\) | 22.6757 | 1.22796 | ||||||||
\(342\) | −7.66606 | −0.414533 | ||||||||
\(343\) | 18.1042 | 0.977533 | ||||||||
\(344\) | −11.1937 | −0.603524 | ||||||||
\(345\) | 1.29666 | 0.0698096 | ||||||||
\(346\) | 14.3715 | 0.772618 | ||||||||
\(347\) | −5.92373 | −0.318002 | −0.159001 | − | 0.987278i | \(-0.550827\pi\) | ||||
−0.159001 | + | 0.987278i | \(0.550827\pi\) | |||||||
\(348\) | 1.73187 | 0.0928380 | ||||||||
\(349\) | −8.56349 | −0.458393 | −0.229197 | − | 0.973380i | \(-0.573610\pi\) | ||||
−0.229197 | + | 0.973380i | \(0.573610\pi\) | |||||||
\(350\) | −4.27073 | −0.228280 | ||||||||
\(351\) | 2.67523 | 0.142793 | ||||||||
\(352\) | 6.20730 | 0.330850 | ||||||||
\(353\) | 13.3185 | 0.708870 | 0.354435 | − | 0.935081i | \(-0.384673\pi\) | ||||
0.354435 | + | 0.935081i | \(0.384673\pi\) | |||||||
\(354\) | 0.821829 | 0.0436797 | ||||||||
\(355\) | 12.9847 | 0.689156 | ||||||||
\(356\) | −0.107411 | −0.00569276 | ||||||||
\(357\) | −5.98774 | −0.316905 | ||||||||
\(358\) | 9.78741 | 0.517281 | ||||||||
\(359\) | 19.2025 | 1.01347 | 0.506734 | − | 0.862102i | \(-0.330853\pi\) | ||||
0.506734 | + | 0.862102i | \(0.330853\pi\) | |||||||
\(360\) | 2.89545 | 0.152604 | ||||||||
\(361\) | −11.9901 | −0.631058 | ||||||||
\(362\) | −10.2982 | −0.541263 | ||||||||
\(363\) | −8.90183 | −0.467225 | ||||||||
\(364\) | 5.99352 | 0.314146 | ||||||||
\(365\) | −10.8750 | −0.569223 | ||||||||
\(366\) | 1.41484 | 0.0739546 | ||||||||
\(367\) | 20.1447 | 1.05154 | 0.525771 | − | 0.850626i | \(-0.323777\pi\) | ||||
0.525771 | + | 0.850626i | \(0.323777\pi\) | |||||||
\(368\) | −4.01015 | −0.209044 | ||||||||
\(369\) | 16.4703 | 0.857410 | ||||||||
\(370\) | −4.46073 | −0.231902 | ||||||||
\(371\) | 10.3153 | 0.535541 | ||||||||
\(372\) | 1.18120 | 0.0612422 | ||||||||
\(373\) | 19.7747 | 1.02390 | 0.511948 | − | 0.859017i | \(-0.328924\pi\) | ||||
0.511948 | + | 0.859017i | \(0.328924\pi\) | |||||||
\(374\) | 26.9154 | 1.39176 | ||||||||
\(375\) | −0.323343 | −0.0166974 | ||||||||
\(376\) | −11.1258 | −0.573768 | ||||||||
\(377\) | −7.51677 | −0.387133 | ||||||||
\(378\) | −8.14109 | −0.418733 | ||||||||
\(379\) | 9.72670 | 0.499627 | 0.249814 | − | 0.968294i | \(-0.419631\pi\) | ||||
0.249814 | + | 0.968294i | \(0.419631\pi\) | |||||||
\(380\) | −2.64762 | −0.135820 | ||||||||
\(381\) | 1.26479 | 0.0647973 | ||||||||
\(382\) | −0.221079 | −0.0113114 | ||||||||
\(383\) | 8.07832 | 0.412783 | 0.206391 | − | 0.978470i | \(-0.433828\pi\) | ||||
0.206391 | + | 0.978470i | \(0.433828\pi\) | |||||||
\(384\) | 0.323343 | 0.0165005 | ||||||||
\(385\) | −26.5097 | −1.35106 | ||||||||
\(386\) | −20.3644 | −1.03652 | ||||||||
\(387\) | −32.4108 | −1.64753 | ||||||||
\(388\) | 12.2056 | 0.619646 | ||||||||
\(389\) | −6.99401 | −0.354610 | −0.177305 | − | 0.984156i | \(-0.556738\pi\) | ||||
−0.177305 | + | 0.984156i | \(0.556738\pi\) | |||||||
\(390\) | 0.453778 | 0.0229780 | ||||||||
\(391\) | −17.3883 | −0.879366 | ||||||||
\(392\) | −11.2391 | −0.567662 | ||||||||
\(393\) | 1.80465 | 0.0910324 | ||||||||
\(394\) | 25.5964 | 1.28953 | ||||||||
\(395\) | 6.97469 | 0.350935 | ||||||||
\(396\) | 17.9729 | 0.903173 | ||||||||
\(397\) | 7.39389 | 0.371089 | 0.185544 | − | 0.982636i | \(-0.440595\pi\) | ||||
0.185544 | + | 0.982636i | \(0.440595\pi\) | |||||||
\(398\) | 11.9209 | 0.597542 | ||||||||
\(399\) | 3.65613 | 0.183036 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −1.00000 | −0.0499376 | ||||||||
\(402\) | 4.58635 | 0.228746 | ||||||||
\(403\) | −5.12671 | −0.255379 | ||||||||
\(404\) | 0.337459 | 0.0167892 | ||||||||
\(405\) | 8.06997 | 0.401000 | ||||||||
\(406\) | 22.8746 | 1.13525 | ||||||||
\(407\) | −27.6891 | −1.37250 | ||||||||
\(408\) | 1.40204 | 0.0694115 | ||||||||
\(409\) | −12.4951 | −0.617841 | −0.308920 | − | 0.951088i | \(-0.599968\pi\) | ||||
−0.308920 | + | 0.951088i | \(0.599968\pi\) | |||||||
\(410\) | 5.68834 | 0.280927 | ||||||||
\(411\) | 6.21795 | 0.306709 | ||||||||
\(412\) | −9.67687 | −0.476745 | ||||||||
\(413\) | 10.8547 | 0.534127 | ||||||||
\(414\) | −11.6112 | −0.570659 | ||||||||
\(415\) | 6.32611 | 0.310536 | ||||||||
\(416\) | −1.40339 | −0.0688071 | ||||||||
\(417\) | −0.834945 | −0.0408874 | ||||||||
\(418\) | −16.4346 | −0.803842 | ||||||||
\(419\) | 12.4835 | 0.609858 | 0.304929 | − | 0.952375i | \(-0.401367\pi\) | ||||
0.304929 | + | 0.952375i | \(0.401367\pi\) | |||||||
\(420\) | −1.38091 | −0.0673816 | ||||||||
\(421\) | 14.8237 | 0.722463 | 0.361232 | − | 0.932476i | \(-0.382356\pi\) | ||||
0.361232 | + | 0.932476i | \(0.382356\pi\) | |||||||
\(422\) | 8.03884 | 0.391325 | ||||||||
\(423\) | −32.2141 | −1.56630 | ||||||||
\(424\) | −2.41534 | −0.117299 | ||||||||
\(425\) | 4.33608 | 0.210331 | ||||||||
\(426\) | 4.19851 | 0.203419 | ||||||||
\(427\) | 18.6872 | 0.904337 | ||||||||
\(428\) | 13.0574 | 0.631153 | ||||||||
\(429\) | 2.81674 | 0.135993 | ||||||||
\(430\) | −11.1937 | −0.539808 | ||||||||
\(431\) | 8.10706 | 0.390503 | 0.195252 | − | 0.980753i | \(-0.437448\pi\) | ||||
0.195252 | + | 0.980753i | \(0.437448\pi\) | |||||||
\(432\) | 1.90625 | 0.0917147 | ||||||||
\(433\) | −7.33157 | −0.352333 | −0.176166 | − | 0.984360i | \(-0.556370\pi\) | ||||
−0.176166 | + | 0.984360i | \(0.556370\pi\) | |||||||
\(434\) | 15.6013 | 0.748886 | ||||||||
\(435\) | 1.73187 | 0.0830368 | ||||||||
\(436\) | 4.28493 | 0.205211 | ||||||||
\(437\) | 10.6174 | 0.507898 | ||||||||
\(438\) | −3.51636 | −0.168018 | ||||||||
\(439\) | 18.4591 | 0.881005 | 0.440502 | − | 0.897751i | \(-0.354800\pi\) | ||||
0.440502 | + | 0.897751i | \(0.354800\pi\) | |||||||
\(440\) | 6.20730 | 0.295921 | ||||||||
\(441\) | −32.5423 | −1.54963 | ||||||||
\(442\) | −6.08524 | −0.289445 | ||||||||
\(443\) | −33.5527 | −1.59414 | −0.797069 | − | 0.603889i | \(-0.793617\pi\) | ||||
−0.797069 | + | 0.603889i | \(0.793617\pi\) | |||||||
\(444\) | −1.44235 | −0.0684507 | ||||||||
\(445\) | −0.107411 | −0.00509176 | ||||||||
\(446\) | 5.81581 | 0.275387 | ||||||||
\(447\) | −1.59128 | −0.0752651 | ||||||||
\(448\) | 4.27073 | 0.201773 | ||||||||
\(449\) | 27.2104 | 1.28414 | 0.642070 | − | 0.766646i | \(-0.278076\pi\) | ||||
0.642070 | + | 0.766646i | \(0.278076\pi\) | |||||||
\(450\) | 2.89545 | 0.136493 | ||||||||
\(451\) | 35.3093 | 1.66265 | ||||||||
\(452\) | 5.51677 | 0.259487 | ||||||||
\(453\) | 2.76900 | 0.130099 | ||||||||
\(454\) | −13.2037 | −0.619679 | ||||||||
\(455\) | 5.99352 | 0.280981 | ||||||||
\(456\) | −0.856091 | −0.0400901 | ||||||||
\(457\) | −40.7803 | −1.90762 | −0.953812 | − | 0.300405i | \(-0.902878\pi\) | ||||
−0.953812 | + | 0.300405i | \(0.902878\pi\) | |||||||
\(458\) | −25.2511 | −1.17991 | ||||||||
\(459\) | 8.26567 | 0.385809 | ||||||||
\(460\) | −4.01015 | −0.186974 | ||||||||
\(461\) | 31.6278 | 1.47305 | 0.736527 | − | 0.676408i | \(-0.236464\pi\) | ||||
0.736527 | + | 0.676408i | \(0.236464\pi\) | |||||||
\(462\) | −8.57173 | −0.398793 | ||||||||
\(463\) | −26.4982 | −1.23148 | −0.615738 | − | 0.787951i | \(-0.711142\pi\) | ||||
−0.615738 | + | 0.787951i | \(0.711142\pi\) | |||||||
\(464\) | −5.35613 | −0.248652 | ||||||||
\(465\) | 1.18120 | 0.0547767 | ||||||||
\(466\) | −9.40454 | −0.435657 | ||||||||
\(467\) | 1.68402 | 0.0779271 | 0.0389635 | − | 0.999241i | \(-0.487594\pi\) | ||||
0.0389635 | + | 0.999241i | \(0.487594\pi\) | |||||||
\(468\) | −4.06346 | −0.187833 | ||||||||
\(469\) | 60.5767 | 2.79717 | ||||||||
\(470\) | −11.1258 | −0.513194 | ||||||||
\(471\) | −4.64895 | −0.214212 | ||||||||
\(472\) | −2.54166 | −0.116989 | ||||||||
\(473\) | −69.4827 | −3.19482 | ||||||||
\(474\) | 2.25522 | 0.103586 | ||||||||
\(475\) | −2.64762 | −0.121481 | ||||||||
\(476\) | 18.5182 | 0.848782 | ||||||||
\(477\) | −6.99349 | −0.320210 | ||||||||
\(478\) | 7.68893 | 0.351683 | ||||||||
\(479\) | 18.4258 | 0.841897 | 0.420948 | − | 0.907085i | \(-0.361697\pi\) | ||||
0.420948 | + | 0.907085i | \(0.361697\pi\) | |||||||
\(480\) | 0.323343 | 0.0147585 | ||||||||
\(481\) | 6.26016 | 0.285439 | ||||||||
\(482\) | 22.3622 | 1.01857 | ||||||||
\(483\) | 5.53766 | 0.251972 | ||||||||
\(484\) | 27.5306 | 1.25139 | ||||||||
\(485\) | 12.2056 | 0.554228 | ||||||||
\(486\) | 8.32813 | 0.377772 | ||||||||
\(487\) | 1.65439 | 0.0749674 | 0.0374837 | − | 0.999297i | \(-0.488066\pi\) | ||||
0.0374837 | + | 0.999297i | \(0.488066\pi\) | |||||||
\(488\) | −4.37565 | −0.198076 | ||||||||
\(489\) | −1.77212 | −0.0801382 | ||||||||
\(490\) | −11.2391 | −0.507732 | ||||||||
\(491\) | 10.2927 | 0.464503 | 0.232252 | − | 0.972656i | \(-0.425391\pi\) | ||||
0.232252 | + | 0.972656i | \(0.425391\pi\) | |||||||
\(492\) | 1.83929 | 0.0829215 | ||||||||
\(493\) | −23.2246 | −1.04598 | ||||||||
\(494\) | 3.71566 | 0.167175 | ||||||||
\(495\) | 17.9729 | 0.807823 | ||||||||
\(496\) | −3.65307 | −0.164028 | ||||||||
\(497\) | 55.4541 | 2.48746 | ||||||||
\(498\) | 2.04550 | 0.0916612 | ||||||||
\(499\) | −22.2383 | −0.995523 | −0.497762 | − | 0.867314i | \(-0.665845\pi\) | ||||
−0.497762 | + | 0.867314i | \(0.665845\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −1.03687 | −0.0463240 | ||||||||
\(502\) | −16.0991 | −0.718538 | ||||||||
\(503\) | 8.91876 | 0.397668 | 0.198834 | − | 0.980033i | \(-0.436285\pi\) | ||||
0.198834 | + | 0.980033i | \(0.436285\pi\) | |||||||
\(504\) | 12.3657 | 0.550811 | ||||||||
\(505\) | 0.337459 | 0.0150167 | ||||||||
\(506\) | −24.8922 | −1.10659 | ||||||||
\(507\) | 3.56663 | 0.158400 | ||||||||
\(508\) | −3.91161 | −0.173550 | ||||||||
\(509\) | 14.1245 | 0.626058 | 0.313029 | − | 0.949743i | \(-0.398656\pi\) | ||||
0.313029 | + | 0.949743i | \(0.398656\pi\) | |||||||
\(510\) | 1.40204 | 0.0620835 | ||||||||
\(511\) | −46.4442 | −2.05457 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −5.04704 | −0.222832 | ||||||||
\(514\) | −21.0520 | −0.928563 | ||||||||
\(515\) | −9.67687 | −0.426414 | ||||||||
\(516\) | −3.61941 | −0.159336 | ||||||||
\(517\) | −69.0610 | −3.03730 | ||||||||
\(518\) | −19.0506 | −0.837033 | ||||||||
\(519\) | 4.64693 | 0.203978 | ||||||||
\(520\) | −1.40339 | −0.0615429 | ||||||||
\(521\) | −40.2938 | −1.76531 | −0.882653 | − | 0.470026i | \(-0.844245\pi\) | ||||
−0.882653 | + | 0.470026i | \(0.844245\pi\) | |||||||
\(522\) | −15.5084 | −0.678785 | ||||||||
\(523\) | 36.5230 | 1.59704 | 0.798520 | − | 0.601968i | \(-0.205617\pi\) | ||||
0.798520 | + | 0.601968i | \(0.205617\pi\) | |||||||
\(524\) | −5.58121 | −0.243816 | ||||||||
\(525\) | −1.38091 | −0.0602679 | ||||||||
\(526\) | −30.9243 | −1.34836 | ||||||||
\(527\) | −15.8400 | −0.690002 | ||||||||
\(528\) | 2.00709 | 0.0873473 | ||||||||
\(529\) | −6.91868 | −0.300812 | ||||||||
\(530\) | −2.41534 | −0.104916 | ||||||||
\(531\) | −7.35925 | −0.319364 | ||||||||
\(532\) | −11.3073 | −0.490233 | ||||||||
\(533\) | −7.98299 | −0.345782 | ||||||||
\(534\) | −0.0347306 | −0.00150294 | ||||||||
\(535\) | 13.0574 | 0.564520 | ||||||||
\(536\) | −14.1842 | −0.612662 | ||||||||
\(537\) | 3.16469 | 0.136567 | ||||||||
\(538\) | 12.5733 | 0.542072 | ||||||||
\(539\) | −69.7646 | −3.00498 | ||||||||
\(540\) | 1.90625 | 0.0820321 | ||||||||
\(541\) | 4.55782 | 0.195956 | 0.0979780 | − | 0.995189i | \(-0.468763\pi\) | ||||
0.0979780 | + | 0.995189i | \(0.468763\pi\) | |||||||
\(542\) | 1.50082 | 0.0644656 | ||||||||
\(543\) | −3.32987 | −0.142898 | ||||||||
\(544\) | −4.33608 | −0.185908 | ||||||||
\(545\) | 4.28493 | 0.183546 | ||||||||
\(546\) | 1.93796 | 0.0829372 | ||||||||
\(547\) | −30.9905 | −1.32506 | −0.662528 | − | 0.749037i | \(-0.730517\pi\) | ||||
−0.662528 | + | 0.749037i | \(0.730517\pi\) | |||||||
\(548\) | −19.2302 | −0.821473 | ||||||||
\(549\) | −12.6695 | −0.540719 | ||||||||
\(550\) | 6.20730 | 0.264680 | ||||||||
\(551\) | 14.1810 | 0.604132 | ||||||||
\(552\) | −1.29666 | −0.0551893 | ||||||||
\(553\) | 29.7870 | 1.26667 | ||||||||
\(554\) | −11.0854 | −0.470975 | ||||||||
\(555\) | −1.44235 | −0.0612242 | ||||||||
\(556\) | 2.58223 | 0.109511 | ||||||||
\(557\) | −42.7716 | −1.81229 | −0.906145 | − | 0.422968i | \(-0.860988\pi\) | ||||
−0.906145 | + | 0.422968i | \(0.860988\pi\) | |||||||
\(558\) | −10.5773 | −0.447772 | ||||||||
\(559\) | 15.7092 | 0.664428 | ||||||||
\(560\) | 4.27073 | 0.180471 | ||||||||
\(561\) | 8.70290 | 0.367437 | ||||||||
\(562\) | 26.8713 | 1.13350 | ||||||||
\(563\) | −7.66268 | −0.322943 | −0.161472 | − | 0.986877i | \(-0.551624\pi\) | ||||
−0.161472 | + | 0.986877i | \(0.551624\pi\) | |||||||
\(564\) | −3.59744 | −0.151480 | ||||||||
\(565\) | 5.51677 | 0.232092 | ||||||||
\(566\) | −14.6942 | −0.617643 | ||||||||
\(567\) | 34.4647 | 1.44738 | ||||||||
\(568\) | −12.9847 | −0.544825 | ||||||||
\(569\) | −17.2084 | −0.721414 | −0.360707 | − | 0.932679i | \(-0.617465\pi\) | ||||
−0.360707 | + | 0.932679i | \(0.617465\pi\) | |||||||
\(570\) | −0.856091 | −0.0358577 | ||||||||
\(571\) | −14.5373 | −0.608368 | −0.304184 | − | 0.952613i | \(-0.598384\pi\) | ||||
−0.304184 | + | 0.952613i | \(0.598384\pi\) | |||||||
\(572\) | −8.71129 | −0.364238 | ||||||||
\(573\) | −0.0714843 | −0.00298630 | ||||||||
\(574\) | 24.2934 | 1.01399 | ||||||||
\(575\) | −4.01015 | −0.167235 | ||||||||
\(576\) | −2.89545 | −0.120644 | ||||||||
\(577\) | −11.5453 | −0.480635 | −0.240318 | − | 0.970694i | \(-0.577252\pi\) | ||||
−0.240318 | + | 0.970694i | \(0.577252\pi\) | |||||||
\(578\) | −1.80161 | −0.0749369 | ||||||||
\(579\) | −6.58468 | −0.273650 | ||||||||
\(580\) | −5.35613 | −0.222401 | ||||||||
\(581\) | 27.0171 | 1.12086 | ||||||||
\(582\) | 3.94660 | 0.163592 | ||||||||
\(583\) | −14.9927 | −0.620935 | ||||||||
\(584\) | 10.8750 | 0.450011 | ||||||||
\(585\) | −4.06346 | −0.168003 | ||||||||
\(586\) | −0.346545 | −0.0143156 | ||||||||
\(587\) | 22.7503 | 0.939007 | 0.469504 | − | 0.882931i | \(-0.344433\pi\) | ||||
0.469504 | + | 0.882931i | \(0.344433\pi\) | |||||||
\(588\) | −3.63410 | −0.149868 | ||||||||
\(589\) | 9.67196 | 0.398526 | ||||||||
\(590\) | −2.54166 | −0.104639 | ||||||||
\(591\) | 8.27643 | 0.340447 | ||||||||
\(592\) | 4.46073 | 0.183335 | ||||||||
\(593\) | 31.0911 | 1.27676 | 0.638380 | − | 0.769722i | \(-0.279605\pi\) | ||||
0.638380 | + | 0.769722i | \(0.279605\pi\) | |||||||
\(594\) | 11.8327 | 0.485501 | ||||||||
\(595\) | 18.5182 | 0.759173 | ||||||||
\(596\) | 4.92135 | 0.201586 | ||||||||
\(597\) | 3.85455 | 0.157756 | ||||||||
\(598\) | 5.62783 | 0.230139 | ||||||||
\(599\) | −35.5828 | −1.45387 | −0.726936 | − | 0.686705i | \(-0.759056\pi\) | ||||
−0.726936 | + | 0.686705i | \(0.759056\pi\) | |||||||
\(600\) | 0.323343 | 0.0132004 | ||||||||
\(601\) | −20.6968 | −0.844240 | −0.422120 | − | 0.906540i | \(-0.638714\pi\) | ||||
−0.422120 | + | 0.906540i | \(0.638714\pi\) | |||||||
\(602\) | −47.8053 | −1.94840 | ||||||||
\(603\) | −41.0695 | −1.67248 | ||||||||
\(604\) | −8.56366 | −0.348450 | ||||||||
\(605\) | 27.5306 | 1.11928 | ||||||||
\(606\) | 0.109115 | 0.00443250 | ||||||||
\(607\) | 30.3161 | 1.23049 | 0.615247 | − | 0.788334i | \(-0.289056\pi\) | ||||
0.615247 | + | 0.788334i | \(0.289056\pi\) | |||||||
\(608\) | 2.64762 | 0.107375 | ||||||||
\(609\) | 7.39635 | 0.299715 | ||||||||
\(610\) | −4.37565 | −0.177165 | ||||||||
\(611\) | 15.6139 | 0.631669 | ||||||||
\(612\) | −12.5549 | −0.507502 | ||||||||
\(613\) | 28.6830 | 1.15850 | 0.579248 | − | 0.815151i | \(-0.303346\pi\) | ||||
0.579248 | + | 0.815151i | \(0.303346\pi\) | |||||||
\(614\) | −17.5826 | −0.709575 | ||||||||
\(615\) | 1.83929 | 0.0741672 | ||||||||
\(616\) | 26.5097 | 1.06811 | ||||||||
\(617\) | −1.00329 | −0.0403910 | −0.0201955 | − | 0.999796i | \(-0.506429\pi\) | ||||
−0.0201955 | + | 0.999796i | \(0.506429\pi\) | |||||||
\(618\) | −3.12895 | −0.125865 | ||||||||
\(619\) | 34.0162 | 1.36723 | 0.683613 | − | 0.729845i | \(-0.260408\pi\) | ||||
0.683613 | + | 0.729845i | \(0.260408\pi\) | |||||||
\(620\) | −3.65307 | −0.146711 | ||||||||
\(621\) | −7.64437 | −0.306758 | ||||||||
\(622\) | 12.9754 | 0.520265 | ||||||||
\(623\) | −0.458722 | −0.0183783 | ||||||||
\(624\) | −0.453778 | −0.0181657 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 4.33743 | 0.173359 | ||||||||
\(627\) | −5.31401 | −0.212221 | ||||||||
\(628\) | 14.3778 | 0.573735 | ||||||||
\(629\) | 19.3421 | 0.771219 | ||||||||
\(630\) | 12.3657 | 0.492660 | ||||||||
\(631\) | −5.20577 | −0.207238 | −0.103619 | − | 0.994617i | \(-0.533042\pi\) | ||||
−0.103619 | + | 0.994617i | \(0.533042\pi\) | |||||||
\(632\) | −6.97469 | −0.277438 | ||||||||
\(633\) | 2.59930 | 0.103313 | ||||||||
\(634\) | −27.6801 | −1.09932 | ||||||||
\(635\) | −3.91161 | −0.155228 | ||||||||
\(636\) | −0.780983 | −0.0309680 | ||||||||
\(637\) | 15.7729 | 0.624946 | ||||||||
\(638\) | −33.2471 | −1.31627 | ||||||||
\(639\) | −37.5965 | −1.48729 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −44.8305 | −1.77070 | −0.885348 | − | 0.464928i | \(-0.846080\pi\) | ||||
−0.885348 | + | 0.464928i | \(0.846080\pi\) | |||||||
\(642\) | 4.22202 | 0.166630 | ||||||||
\(643\) | −29.1809 | −1.15078 | −0.575391 | − | 0.817878i | \(-0.695150\pi\) | ||||
−0.575391 | + | 0.817878i | \(0.695150\pi\) | |||||||
\(644\) | −17.1263 | −0.674870 | ||||||||
\(645\) | −3.61941 | −0.142514 | ||||||||
\(646\) | 11.4803 | 0.451687 | ||||||||
\(647\) | −39.5448 | −1.55467 | −0.777334 | − | 0.629088i | \(-0.783428\pi\) | ||||
−0.777334 | + | 0.629088i | \(0.783428\pi\) | |||||||
\(648\) | −8.06997 | −0.317018 | ||||||||
\(649\) | −15.7769 | −0.619296 | ||||||||
\(650\) | −1.40339 | −0.0550457 | ||||||||
\(651\) | 5.04457 | 0.197712 | ||||||||
\(652\) | 5.48063 | 0.214638 | ||||||||
\(653\) | 27.1640 | 1.06301 | 0.531506 | − | 0.847055i | \(-0.321626\pi\) | ||||
0.531506 | + | 0.847055i | \(0.321626\pi\) | |||||||
\(654\) | 1.38550 | 0.0541774 | ||||||||
\(655\) | −5.58121 | −0.218076 | ||||||||
\(656\) | −5.68834 | −0.222093 | ||||||||
\(657\) | 31.4880 | 1.22846 | ||||||||
\(658\) | −47.5152 | −1.85233 | ||||||||
\(659\) | 12.3231 | 0.480038 | 0.240019 | − | 0.970768i | \(-0.422846\pi\) | ||||
0.240019 | + | 0.970768i | \(0.422846\pi\) | |||||||
\(660\) | 2.00709 | 0.0781258 | ||||||||
\(661\) | −3.78566 | −0.147245 | −0.0736225 | − | 0.997286i | \(-0.523456\pi\) | ||||
−0.0736225 | + | 0.997286i | \(0.523456\pi\) | |||||||
\(662\) | 1.73730 | 0.0675220 | ||||||||
\(663\) | −1.96762 | −0.0764160 | ||||||||
\(664\) | −6.32611 | −0.245501 | ||||||||
\(665\) | −11.3073 | −0.438477 | ||||||||
\(666\) | 12.9158 | 0.500477 | ||||||||
\(667\) | 21.4789 | 0.831667 | ||||||||
\(668\) | 3.20672 | 0.124072 | ||||||||
\(669\) | 1.88050 | 0.0727045 | ||||||||
\(670\) | −14.1842 | −0.547982 | ||||||||
\(671\) | −27.1609 | −1.04854 | ||||||||
\(672\) | 1.38091 | 0.0532698 | ||||||||
\(673\) | 29.6559 | 1.14315 | 0.571575 | − | 0.820549i | \(-0.306332\pi\) | ||||
0.571575 | + | 0.820549i | \(0.306332\pi\) | |||||||
\(674\) | 13.3698 | 0.514984 | ||||||||
\(675\) | 1.90625 | 0.0733717 | ||||||||
\(676\) | −11.0305 | −0.424249 | ||||||||
\(677\) | −40.2461 | −1.54678 | −0.773392 | − | 0.633928i | \(-0.781441\pi\) | ||||
−0.773392 | + | 0.633928i | \(0.781441\pi\) | |||||||
\(678\) | 1.78381 | 0.0685068 | ||||||||
\(679\) | 52.1269 | 2.00045 | ||||||||
\(680\) | −4.33608 | −0.166281 | ||||||||
\(681\) | −4.26932 | −0.163601 | ||||||||
\(682\) | −22.6757 | −0.868299 | ||||||||
\(683\) | 32.1002 | 1.22828 | 0.614141 | − | 0.789197i | \(-0.289503\pi\) | ||||
0.614141 | + | 0.789197i | \(0.289503\pi\) | |||||||
\(684\) | 7.66606 | 0.293119 | ||||||||
\(685\) | −19.2302 | −0.734748 | ||||||||
\(686\) | −18.1042 | −0.691220 | ||||||||
\(687\) | −8.16477 | −0.311505 | ||||||||
\(688\) | 11.1937 | 0.426756 | ||||||||
\(689\) | 3.38967 | 0.129136 | ||||||||
\(690\) | −1.29666 | −0.0493628 | ||||||||
\(691\) | 20.3668 | 0.774791 | 0.387396 | − | 0.921914i | \(-0.373375\pi\) | ||||
0.387396 | + | 0.921914i | \(0.373375\pi\) | |||||||
\(692\) | −14.3715 | −0.546323 | ||||||||
\(693\) | 76.7575 | 2.91578 | ||||||||
\(694\) | 5.92373 | 0.224862 | ||||||||
\(695\) | 2.58223 | 0.0979494 | ||||||||
\(696\) | −1.73187 | −0.0656463 | ||||||||
\(697\) | −24.6651 | −0.934258 | ||||||||
\(698\) | 8.56349 | 0.324133 | ||||||||
\(699\) | −3.04090 | −0.115017 | ||||||||
\(700\) | 4.27073 | 0.161418 | ||||||||
\(701\) | −5.30031 | −0.200190 | −0.100095 | − | 0.994978i | \(-0.531915\pi\) | ||||
−0.100095 | + | 0.994978i | \(0.531915\pi\) | |||||||
\(702\) | −2.67523 | −0.100970 | ||||||||
\(703\) | −11.8103 | −0.445435 | ||||||||
\(704\) | −6.20730 | −0.233946 | ||||||||
\(705\) | −3.59744 | −0.135488 | ||||||||
\(706\) | −13.3185 | −0.501247 | ||||||||
\(707\) | 1.44120 | 0.0542018 | ||||||||
\(708\) | −0.821829 | −0.0308862 | ||||||||
\(709\) | −1.38308 | −0.0519427 | −0.0259713 | − | 0.999663i | \(-0.508268\pi\) | ||||
−0.0259713 | + | 0.999663i | \(0.508268\pi\) | |||||||
\(710\) | −12.9847 | −0.487307 | ||||||||
\(711\) | −20.1949 | −0.757367 | ||||||||
\(712\) | 0.107411 | 0.00402539 | ||||||||
\(713\) | 14.6494 | 0.548624 | ||||||||
\(714\) | 5.98774 | 0.224086 | ||||||||
\(715\) | −8.71129 | −0.325784 | ||||||||
\(716\) | −9.78741 | −0.365773 | ||||||||
\(717\) | 2.48616 | 0.0928474 | ||||||||
\(718\) | −19.2025 | −0.716630 | ||||||||
\(719\) | 30.0613 | 1.12110 | 0.560549 | − | 0.828122i | \(-0.310590\pi\) | ||||
0.560549 | + | 0.828122i | \(0.310590\pi\) | |||||||
\(720\) | −2.89545 | −0.107907 | ||||||||
\(721\) | −41.3273 | −1.53911 | ||||||||
\(722\) | 11.9901 | 0.446225 | ||||||||
\(723\) | 7.23068 | 0.268912 | ||||||||
\(724\) | 10.2982 | 0.382731 | ||||||||
\(725\) | −5.35613 | −0.198922 | ||||||||
\(726\) | 8.90183 | 0.330378 | ||||||||
\(727\) | 31.1256 | 1.15439 | 0.577193 | − | 0.816608i | \(-0.304148\pi\) | ||||
0.577193 | + | 0.816608i | \(0.304148\pi\) | |||||||
\(728\) | −5.99352 | −0.222135 | ||||||||
\(729\) | −21.5171 | −0.796929 | ||||||||
\(730\) | 10.8750 | 0.402502 | ||||||||
\(731\) | 48.5368 | 1.79520 | ||||||||
\(732\) | −1.41484 | −0.0522938 | ||||||||
\(733\) | −36.1823 | −1.33642 | −0.668211 | − | 0.743972i | \(-0.732940\pi\) | ||||
−0.668211 | + | 0.743972i | \(0.732940\pi\) | |||||||
\(734\) | −20.1447 | −0.743553 | ||||||||
\(735\) | −3.63410 | −0.134046 | ||||||||
\(736\) | 4.01015 | 0.147816 | ||||||||
\(737\) | −88.0453 | −3.24319 | ||||||||
\(738\) | −16.4703 | −0.606281 | ||||||||
\(739\) | 22.1965 | 0.816512 | 0.408256 | − | 0.912868i | \(-0.366137\pi\) | ||||
0.408256 | + | 0.912868i | \(0.366137\pi\) | |||||||
\(740\) | 4.46073 | 0.163980 | ||||||||
\(741\) | 1.20143 | 0.0441358 | ||||||||
\(742\) | −10.3153 | −0.378685 | ||||||||
\(743\) | 11.6611 | 0.427804 | 0.213902 | − | 0.976855i | \(-0.431383\pi\) | ||||
0.213902 | + | 0.976855i | \(0.431383\pi\) | |||||||
\(744\) | −1.18120 | −0.0433048 | ||||||||
\(745\) | 4.92135 | 0.180304 | ||||||||
\(746\) | −19.7747 | −0.724004 | ||||||||
\(747\) | −18.3169 | −0.670181 | ||||||||
\(748\) | −26.9154 | −0.984123 | ||||||||
\(749\) | 55.7646 | 2.03759 | ||||||||
\(750\) | 0.323343 | 0.0118068 | ||||||||
\(751\) | −4.32571 | −0.157847 | −0.0789237 | − | 0.996881i | \(-0.525148\pi\) | ||||
−0.0789237 | + | 0.996881i | \(0.525148\pi\) | |||||||
\(752\) | 11.1258 | 0.405715 | ||||||||
\(753\) | −5.20553 | −0.189700 | ||||||||
\(754\) | 7.51677 | 0.273745 | ||||||||
\(755\) | −8.56366 | −0.311663 | ||||||||
\(756\) | 8.14109 | 0.296089 | ||||||||
\(757\) | −39.5617 | −1.43789 | −0.718947 | − | 0.695065i | \(-0.755375\pi\) | ||||
−0.718947 | + | 0.695065i | \(0.755375\pi\) | |||||||
\(758\) | −9.72670 | −0.353290 | ||||||||
\(759\) | −8.04873 | −0.292150 | ||||||||
\(760\) | 2.64762 | 0.0960394 | ||||||||
\(761\) | −44.6905 | −1.62003 | −0.810015 | − | 0.586410i | \(-0.800541\pi\) | ||||
−0.810015 | + | 0.586410i | \(0.800541\pi\) | |||||||
\(762\) | −1.26479 | −0.0458186 | ||||||||
\(763\) | 18.2998 | 0.662496 | ||||||||
\(764\) | 0.221079 | 0.00799835 | ||||||||
\(765\) | −12.5549 | −0.453924 | ||||||||
\(766\) | −8.07832 | −0.291882 | ||||||||
\(767\) | 3.56695 | 0.128795 | ||||||||
\(768\) | −0.323343 | −0.0116676 | ||||||||
\(769\) | 0.326678 | 0.0117803 | 0.00589016 | − | 0.999983i | \(-0.498125\pi\) | ||||
0.00589016 | + | 0.999983i | \(0.498125\pi\) | |||||||
\(770\) | 26.5097 | 0.955343 | ||||||||
\(771\) | −6.80701 | −0.245149 | ||||||||
\(772\) | 20.3644 | 0.732929 | ||||||||
\(773\) | 50.0407 | 1.79984 | 0.899920 | − | 0.436055i | \(-0.143625\pi\) | ||||
0.899920 | + | 0.436055i | \(0.143625\pi\) | |||||||
\(774\) | 32.4108 | 1.16498 | ||||||||
\(775\) | −3.65307 | −0.131222 | ||||||||
\(776\) | −12.2056 | −0.438156 | ||||||||
\(777\) | −6.15987 | −0.220984 | ||||||||
\(778\) | 6.99401 | 0.250747 | ||||||||
\(779\) | 15.0606 | 0.539601 | ||||||||
\(780\) | −0.453778 | −0.0162479 | ||||||||
\(781\) | −80.5999 | −2.88409 | ||||||||
\(782\) | 17.3883 | 0.621806 | ||||||||
\(783\) | −10.2101 | −0.364881 | ||||||||
\(784\) | 11.2391 | 0.401397 | ||||||||
\(785\) | 14.3778 | 0.513164 | ||||||||
\(786\) | −1.80465 | −0.0643696 | ||||||||
\(787\) | −29.7447 | −1.06028 | −0.530141 | − | 0.847909i | \(-0.677861\pi\) | ||||
−0.530141 | + | 0.847909i | \(0.677861\pi\) | |||||||
\(788\) | −25.5964 | −0.911835 | ||||||||
\(789\) | −9.99916 | −0.355979 | ||||||||
\(790\) | −6.97469 | −0.248148 | ||||||||
\(791\) | 23.5606 | 0.837719 | ||||||||
\(792\) | −17.9729 | −0.638640 | ||||||||
\(793\) | 6.14076 | 0.218065 | ||||||||
\(794\) | −7.39389 | −0.262399 | ||||||||
\(795\) | −0.780983 | −0.0276986 | ||||||||
\(796\) | −11.9209 | −0.422526 | ||||||||
\(797\) | −22.0554 | −0.781242 | −0.390621 | − | 0.920552i | \(-0.627740\pi\) | ||||
−0.390621 | + | 0.920552i | \(0.627740\pi\) | |||||||
\(798\) | −3.65613 | −0.129426 | ||||||||
\(799\) | 48.2423 | 1.70669 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 0.311003 | 0.0109887 | ||||||||
\(802\) | 1.00000 | 0.0353112 | ||||||||
\(803\) | 67.5044 | 2.38218 | ||||||||
\(804\) | −4.58635 | −0.161748 | ||||||||
\(805\) | −17.1263 | −0.603622 | ||||||||
\(806\) | 5.12671 | 0.180581 | ||||||||
\(807\) | 4.06548 | 0.143112 | ||||||||
\(808\) | −0.337459 | −0.0118718 | ||||||||
\(809\) | 51.7239 | 1.81852 | 0.909258 | − | 0.416232i | \(-0.136650\pi\) | ||||
0.909258 | + | 0.416232i | \(0.136650\pi\) | |||||||
\(810\) | −8.06997 | −0.283550 | ||||||||
\(811\) | −43.3346 | −1.52168 | −0.760841 | − | 0.648938i | \(-0.775213\pi\) | ||||
−0.760841 | + | 0.648938i | \(0.775213\pi\) | |||||||
\(812\) | −22.8746 | −0.802741 | ||||||||
\(813\) | 0.485279 | 0.0170195 | ||||||||
\(814\) | 27.6891 | 0.970502 | ||||||||
\(815\) | 5.48063 | 0.191978 | ||||||||
\(816\) | −1.40204 | −0.0490813 | ||||||||
\(817\) | −29.6367 | −1.03686 | ||||||||
\(818\) | 12.4951 | 0.436879 | ||||||||
\(819\) | −17.3539 | −0.606395 | ||||||||
\(820\) | −5.68834 | −0.198646 | ||||||||
\(821\) | −14.2942 | −0.498872 | −0.249436 | − | 0.968391i | \(-0.580245\pi\) | ||||
−0.249436 | + | 0.968391i | \(0.580245\pi\) | |||||||
\(822\) | −6.21795 | −0.216876 | ||||||||
\(823\) | −19.2583 | −0.671304 | −0.335652 | − | 0.941986i | \(-0.608957\pi\) | ||||
−0.335652 | + | 0.941986i | \(0.608957\pi\) | |||||||
\(824\) | 9.67687 | 0.337110 | ||||||||
\(825\) | 2.00709 | 0.0698779 | ||||||||
\(826\) | −10.8547 | −0.377685 | ||||||||
\(827\) | 46.3949 | 1.61331 | 0.806655 | − | 0.591023i | \(-0.201276\pi\) | ||||
0.806655 | + | 0.591023i | \(0.201276\pi\) | |||||||
\(828\) | 11.6112 | 0.403517 | ||||||||
\(829\) | 17.4837 | 0.607235 | 0.303618 | − | 0.952794i | \(-0.401805\pi\) | ||||
0.303618 | + | 0.952794i | \(0.401805\pi\) | |||||||
\(830\) | −6.32611 | −0.219582 | ||||||||
\(831\) | −3.58440 | −0.124341 | ||||||||
\(832\) | 1.40339 | 0.0486540 | ||||||||
\(833\) | 48.7338 | 1.68853 | ||||||||
\(834\) | 0.834945 | 0.0289118 | ||||||||
\(835\) | 3.20672 | 0.110973 | ||||||||
\(836\) | 16.4346 | 0.568402 | ||||||||
\(837\) | −6.96369 | −0.240700 | ||||||||
\(838\) | −12.4835 | −0.431235 | ||||||||
\(839\) | 4.25339 | 0.146843 | 0.0734216 | − | 0.997301i | \(-0.476608\pi\) | ||||
0.0734216 | + | 0.997301i | \(0.476608\pi\) | |||||||
\(840\) | 1.38091 | 0.0476460 | ||||||||
\(841\) | −0.311831 | −0.0107528 | ||||||||
\(842\) | −14.8237 | −0.510859 | ||||||||
\(843\) | 8.68865 | 0.299253 | ||||||||
\(844\) | −8.03884 | −0.276708 | ||||||||
\(845\) | −11.0305 | −0.379460 | ||||||||
\(846\) | 32.2141 | 1.10754 | ||||||||
\(847\) | 117.576 | 4.03995 | ||||||||
\(848\) | 2.41534 | 0.0829430 | ||||||||
\(849\) | −4.75127 | −0.163063 | ||||||||
\(850\) | −4.33608 | −0.148726 | ||||||||
\(851\) | −17.8882 | −0.613199 | ||||||||
\(852\) | −4.19851 | −0.143839 | ||||||||
\(853\) | −8.55908 | −0.293057 | −0.146529 | − | 0.989206i | \(-0.546810\pi\) | ||||
−0.146529 | + | 0.989206i | \(0.546810\pi\) | |||||||
\(854\) | −18.6872 | −0.639463 | ||||||||
\(855\) | 7.66606 | 0.262174 | ||||||||
\(856\) | −13.0574 | −0.446293 | ||||||||
\(857\) | −38.3832 | −1.31114 | −0.655572 | − | 0.755133i | \(-0.727572\pi\) | ||||
−0.655572 | + | 0.755133i | \(0.727572\pi\) | |||||||
\(858\) | −2.81674 | −0.0961619 | ||||||||
\(859\) | 7.21381 | 0.246132 | 0.123066 | − | 0.992398i | \(-0.460727\pi\) | ||||
0.123066 | + | 0.992398i | \(0.460727\pi\) | |||||||
\(860\) | 11.1937 | 0.381702 | ||||||||
\(861\) | 7.85510 | 0.267701 | ||||||||
\(862\) | −8.10706 | −0.276128 | ||||||||
\(863\) | 19.9722 | 0.679861 | 0.339931 | − | 0.940451i | \(-0.389596\pi\) | ||||
0.339931 | + | 0.940451i | \(0.389596\pi\) | |||||||
\(864\) | −1.90625 | −0.0648521 | ||||||||
\(865\) | −14.3715 | −0.488646 | ||||||||
\(866\) | 7.33157 | 0.249137 | ||||||||
\(867\) | −0.582537 | −0.0197840 | ||||||||
\(868\) | −15.6013 | −0.529542 | ||||||||
\(869\) | −43.2940 | −1.46865 | ||||||||
\(870\) | −1.73187 | −0.0587159 | ||||||||
\(871\) | 19.9060 | 0.674488 | ||||||||
\(872\) | −4.28493 | −0.145106 | ||||||||
\(873\) | −35.3407 | −1.19610 | ||||||||
\(874\) | −10.6174 | −0.359138 | ||||||||
\(875\) | 4.27073 | 0.144377 | ||||||||
\(876\) | 3.51636 | 0.118807 | ||||||||
\(877\) | 46.7667 | 1.57920 | 0.789599 | − | 0.613623i | \(-0.210289\pi\) | ||||
0.789599 | + | 0.613623i | \(0.210289\pi\) | |||||||
\(878\) | −18.4591 | −0.622965 | ||||||||
\(879\) | −0.112053 | −0.00377945 | ||||||||
\(880\) | −6.20730 | −0.209248 | ||||||||
\(881\) | 0.182159 | 0.00613710 | 0.00306855 | − | 0.999995i | \(-0.499023\pi\) | ||||
0.00306855 | + | 0.999995i | \(0.499023\pi\) | |||||||
\(882\) | 32.5423 | 1.09576 | ||||||||
\(883\) | 42.2776 | 1.42276 | 0.711378 | − | 0.702810i | \(-0.248072\pi\) | ||||
0.711378 | + | 0.702810i | \(0.248072\pi\) | |||||||
\(884\) | 6.08524 | 0.204669 | ||||||||
\(885\) | −0.821829 | −0.0276255 | ||||||||
\(886\) | 33.5527 | 1.12723 | ||||||||
\(887\) | 44.0745 | 1.47988 | 0.739939 | − | 0.672674i | \(-0.234854\pi\) | ||||
0.739939 | + | 0.672674i | \(0.234854\pi\) | |||||||
\(888\) | 1.44235 | 0.0484020 | ||||||||
\(889\) | −16.7054 | −0.560282 | ||||||||
\(890\) | 0.107411 | 0.00360042 | ||||||||
\(891\) | −50.0928 | −1.67817 | ||||||||
\(892\) | −5.81581 | −0.194728 | ||||||||
\(893\) | −29.4568 | −0.985736 | ||||||||
\(894\) | 1.59128 | 0.0532205 | ||||||||
\(895\) | −9.78741 | −0.327157 | ||||||||
\(896\) | −4.27073 | −0.142675 | ||||||||
\(897\) | 1.81972 | 0.0607587 | ||||||||
\(898\) | −27.2104 | −0.908024 | ||||||||
\(899\) | 19.5664 | 0.652574 | ||||||||
\(900\) | −2.89545 | −0.0965150 | ||||||||
\(901\) | 10.4731 | 0.348910 | ||||||||
\(902\) | −35.3093 | −1.17567 | ||||||||
\(903\) | −15.4575 | −0.514394 | ||||||||
\(904\) | −5.51677 | −0.183485 | ||||||||
\(905\) | 10.2982 | 0.342325 | ||||||||
\(906\) | −2.76900 | −0.0919939 | ||||||||
\(907\) | 38.8630 | 1.29042 | 0.645212 | − | 0.764004i | \(-0.276769\pi\) | ||||
0.645212 | + | 0.764004i | \(0.276769\pi\) | |||||||
\(908\) | 13.2037 | 0.438179 | ||||||||
\(909\) | −0.977096 | −0.0324082 | ||||||||
\(910\) | −5.99352 | −0.198683 | ||||||||
\(911\) | 3.50179 | 0.116019 | 0.0580097 | − | 0.998316i | \(-0.481525\pi\) | ||||
0.0580097 | + | 0.998316i | \(0.481525\pi\) | |||||||
\(912\) | 0.856091 | 0.0283480 | ||||||||
\(913\) | −39.2681 | −1.29958 | ||||||||
\(914\) | 40.7803 | 1.34889 | ||||||||
\(915\) | −1.41484 | −0.0467730 | ||||||||
\(916\) | 25.2511 | 0.834319 | ||||||||
\(917\) | −23.8358 | −0.787129 | ||||||||
\(918\) | −8.26567 | −0.272808 | ||||||||
\(919\) | −38.0048 | −1.25366 | −0.626831 | − | 0.779155i | \(-0.715648\pi\) | ||||
−0.626831 | + | 0.779155i | \(0.715648\pi\) | |||||||
\(920\) | 4.01015 | 0.132211 | ||||||||
\(921\) | −5.68521 | −0.187334 | ||||||||
\(922\) | −31.6278 | −1.04161 | ||||||||
\(923\) | 18.2226 | 0.599806 | ||||||||
\(924\) | 8.57173 | 0.281989 | ||||||||
\(925\) | 4.46073 | 0.146668 | ||||||||
\(926\) | 26.4982 | 0.870784 | ||||||||
\(927\) | 28.0189 | 0.920261 | ||||||||
\(928\) | 5.35613 | 0.175824 | ||||||||
\(929\) | −50.3771 | −1.65282 | −0.826409 | − | 0.563070i | \(-0.809620\pi\) | ||||
−0.826409 | + | 0.563070i | \(0.809620\pi\) | |||||||
\(930\) | −1.18120 | −0.0387330 | ||||||||
\(931\) | −29.7570 | −0.975245 | ||||||||
\(932\) | 9.40454 | 0.308056 | ||||||||
\(933\) | 4.19549 | 0.137354 | ||||||||
\(934\) | −1.68402 | −0.0551028 | ||||||||
\(935\) | −26.9154 | −0.880227 | ||||||||
\(936\) | 4.06346 | 0.132818 | ||||||||
\(937\) | 1.47657 | 0.0482376 | 0.0241188 | − | 0.999709i | \(-0.492322\pi\) | ||||
0.0241188 | + | 0.999709i | \(0.492322\pi\) | |||||||
\(938\) | −60.5767 | −1.97790 | ||||||||
\(939\) | 1.40248 | 0.0457682 | ||||||||
\(940\) | 11.1258 | 0.362883 | ||||||||
\(941\) | −29.4025 | −0.958494 | −0.479247 | − | 0.877680i | \(-0.659090\pi\) | ||||
−0.479247 | + | 0.877680i | \(0.659090\pi\) | |||||||
\(942\) | 4.64895 | 0.151471 | ||||||||
\(943\) | 22.8111 | 0.742832 | ||||||||
\(944\) | 2.54166 | 0.0827240 | ||||||||
\(945\) | 8.14109 | 0.264830 | ||||||||
\(946\) | 69.4827 | 2.25908 | ||||||||
\(947\) | −30.9155 | −1.00462 | −0.502309 | − | 0.864688i | \(-0.667516\pi\) | ||||
−0.502309 | + | 0.864688i | \(0.667516\pi\) | |||||||
\(948\) | −2.25522 | −0.0732461 | ||||||||
\(949\) | −15.2619 | −0.495423 | ||||||||
\(950\) | 2.64762 | 0.0859002 | ||||||||
\(951\) | −8.95018 | −0.290230 | ||||||||
\(952\) | −18.5182 | −0.600179 | ||||||||
\(953\) | 0.417113 | 0.0135116 | 0.00675581 | − | 0.999977i | \(-0.497850\pi\) | ||||
0.00675581 | + | 0.999977i | \(0.497850\pi\) | |||||||
\(954\) | 6.99349 | 0.226423 | ||||||||
\(955\) | 0.221079 | 0.00715394 | ||||||||
\(956\) | −7.68893 | −0.248678 | ||||||||
\(957\) | −10.7502 | −0.347506 | ||||||||
\(958\) | −18.4258 | −0.595311 | ||||||||
\(959\) | −82.1270 | −2.65202 | ||||||||
\(960\) | −0.323343 | −0.0104359 | ||||||||
\(961\) | −17.6550 | −0.569518 | ||||||||
\(962\) | −6.26016 | −0.201836 | ||||||||
\(963\) | −37.8070 | −1.21831 | ||||||||
\(964\) | −22.3622 | −0.720239 | ||||||||
\(965\) | 20.3644 | 0.655552 | ||||||||
\(966\) | −5.53766 | −0.178171 | ||||||||
\(967\) | 12.8291 | 0.412555 | 0.206277 | − | 0.978494i | \(-0.433865\pi\) | ||||
0.206277 | + | 0.978494i | \(0.433865\pi\) | |||||||
\(968\) | −27.5306 | −0.884867 | ||||||||
\(969\) | 3.71208 | 0.119249 | ||||||||
\(970\) | −12.2056 | −0.391899 | ||||||||
\(971\) | 15.7514 | 0.505487 | 0.252743 | − | 0.967533i | \(-0.418667\pi\) | ||||
0.252743 | + | 0.967533i | \(0.418667\pi\) | |||||||
\(972\) | −8.32813 | −0.267125 | ||||||||
\(973\) | 11.0280 | 0.353541 | ||||||||
\(974\) | −1.65439 | −0.0530100 | ||||||||
\(975\) | −0.453778 | −0.0145325 | ||||||||
\(976\) | 4.37565 | 0.140061 | ||||||||
\(977\) | −14.7346 | −0.471403 | −0.235702 | − | 0.971825i | \(-0.575739\pi\) | ||||
−0.235702 | + | 0.971825i | \(0.575739\pi\) | |||||||
\(978\) | 1.77212 | 0.0566663 | ||||||||
\(979\) | 0.666731 | 0.0213088 | ||||||||
\(980\) | 11.2391 | 0.359021 | ||||||||
\(981\) | −12.4068 | −0.396118 | ||||||||
\(982\) | −10.2927 | −0.328454 | ||||||||
\(983\) | 6.04795 | 0.192900 | 0.0964498 | − | 0.995338i | \(-0.469251\pi\) | ||||
0.0964498 | + | 0.995338i | \(0.469251\pi\) | |||||||
\(984\) | −1.83929 | −0.0586343 | ||||||||
\(985\) | −25.5964 | −0.815570 | ||||||||
\(986\) | 23.2246 | 0.739623 | ||||||||
\(987\) | −15.3637 | −0.489032 | ||||||||
\(988\) | −3.71566 | −0.118211 | ||||||||
\(989\) | −44.8885 | −1.42737 | ||||||||
\(990\) | −17.9729 | −0.571217 | ||||||||
\(991\) | −31.7203 | −1.00763 | −0.503814 | − | 0.863812i | \(-0.668070\pi\) | ||||
−0.503814 | + | 0.863812i | \(0.668070\pi\) | |||||||
\(992\) | 3.65307 | 0.115985 | ||||||||
\(993\) | 0.561744 | 0.0178264 | ||||||||
\(994\) | −55.4541 | −1.75890 | ||||||||
\(995\) | −11.9209 | −0.377919 | ||||||||
\(996\) | −2.04550 | −0.0648143 | ||||||||
\(997\) | −24.3015 | −0.769635 | −0.384817 | − | 0.922993i | \(-0.625736\pi\) | ||||
−0.384817 | + | 0.922993i | \(0.625736\pi\) | |||||||
\(998\) | 22.2383 | 0.703941 | ||||||||
\(999\) | 8.50328 | 0.269032 |
(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 | 4010.2.a.m.1.8 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4010.2.a.m.1.8 | ✓ | 20 | 1.1 | even | 1 | trivial |