Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2366,2,Mod(1,2366)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2366, 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("2366.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2366 = 2 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2366.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: | \(18.8926051182\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.6052921.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 11x^{4} + 7x^{3} + 33x^{2} - 9x - 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(2.85334\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2366.1 |
$q$-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 | ||||||||
\(3\) | 2.85334 | 1.64738 | 0.823688 | − | 0.567044i | \(-0.191913\pi\) | ||||
0.823688 | + | 0.567044i | \(0.191913\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.532083 | −0.237955 | −0.118977 | − | 0.992897i | \(-0.537962\pi\) | ||||
−0.118977 | + | 0.992897i | \(0.537962\pi\) | |||||||
\(6\) | −2.85334 | −1.16487 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 5.14154 | 1.71385 | ||||||||
\(10\) | 0.532083 | 0.168259 | ||||||||
\(11\) | −2.71490 | −0.818572 | −0.409286 | − | 0.912406i | \(-0.634222\pi\) | ||||
−0.409286 | + | 0.912406i | \(0.634222\pi\) | |||||||
\(12\) | 2.85334 | 0.823688 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −1.51821 | −0.392001 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.94148 | −0.713415 | −0.356707 | − | 0.934216i | \(-0.616101\pi\) | ||||
−0.356707 | + | 0.934216i | \(0.616101\pi\) | |||||||
\(18\) | −5.14154 | −1.21187 | ||||||||
\(19\) | −5.83604 | −1.33888 | −0.669440 | − | 0.742866i | \(-0.733466\pi\) | ||||
−0.669440 | + | 0.742866i | \(0.733466\pi\) | |||||||
\(20\) | −0.532083 | −0.118977 | ||||||||
\(21\) | −2.85334 | −0.622649 | ||||||||
\(22\) | 2.71490 | 0.578818 | ||||||||
\(23\) | −5.52440 | −1.15192 | −0.575959 | − | 0.817479i | \(-0.695371\pi\) | ||||
−0.575959 | + | 0.817479i | \(0.695371\pi\) | |||||||
\(24\) | −2.85334 | −0.582435 | ||||||||
\(25\) | −4.71689 | −0.943378 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 6.11053 | 1.17597 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −8.19741 | −1.52222 | −0.761111 | − | 0.648622i | \(-0.775346\pi\) | ||||
−0.761111 | + | 0.648622i | \(0.775346\pi\) | |||||||
\(30\) | 1.51821 | 0.277186 | ||||||||
\(31\) | −3.42217 | −0.614639 | −0.307320 | − | 0.951606i | \(-0.599432\pi\) | ||||
−0.307320 | + | 0.951606i | \(0.599432\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −7.74652 | −1.34850 | ||||||||
\(34\) | 2.94148 | 0.504460 | ||||||||
\(35\) | 0.532083 | 0.0899384 | ||||||||
\(36\) | 5.14154 | 0.856923 | ||||||||
\(37\) | −6.00763 | −0.987648 | −0.493824 | − | 0.869562i | \(-0.664401\pi\) | ||||
−0.493824 | + | 0.869562i | \(0.664401\pi\) | |||||||
\(38\) | 5.83604 | 0.946731 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.532083 | 0.0841297 | ||||||||
\(41\) | 7.76238 | 1.21228 | 0.606140 | − | 0.795358i | \(-0.292717\pi\) | ||||
0.606140 | + | 0.795358i | \(0.292717\pi\) | |||||||
\(42\) | 2.85334 | 0.440280 | ||||||||
\(43\) | −9.13544 | −1.39314 | −0.696570 | − | 0.717488i | \(-0.745292\pi\) | ||||
−0.696570 | + | 0.717488i | \(0.745292\pi\) | |||||||
\(44\) | −2.71490 | −0.409286 | ||||||||
\(45\) | −2.73572 | −0.407818 | ||||||||
\(46\) | 5.52440 | 0.814529 | ||||||||
\(47\) | 9.98779 | 1.45687 | 0.728435 | − | 0.685115i | \(-0.240248\pi\) | ||||
0.728435 | + | 0.685115i | \(0.240248\pi\) | |||||||
\(48\) | 2.85334 | 0.411844 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 4.71689 | 0.667069 | ||||||||
\(51\) | −8.39305 | −1.17526 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.8839 | 1.76973 | 0.884867 | − | 0.465844i | \(-0.154249\pi\) | ||||
0.884867 | + | 0.465844i | \(0.154249\pi\) | |||||||
\(54\) | −6.11053 | −0.831538 | ||||||||
\(55\) | 1.44455 | 0.194783 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −16.6522 | −2.20564 | ||||||||
\(58\) | 8.19741 | 1.07637 | ||||||||
\(59\) | 1.24624 | 0.162246 | 0.0811232 | − | 0.996704i | \(-0.474149\pi\) | ||||
0.0811232 | + | 0.996704i | \(0.474149\pi\) | |||||||
\(60\) | −1.51821 | −0.196000 | ||||||||
\(61\) | 1.36564 | 0.174852 | 0.0874262 | − | 0.996171i | \(-0.472136\pi\) | ||||
0.0874262 | + | 0.996171i | \(0.472136\pi\) | |||||||
\(62\) | 3.42217 | 0.434616 | ||||||||
\(63\) | −5.14154 | −0.647773 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7.74652 | 0.953530 | ||||||||
\(67\) | 9.49764 | 1.16032 | 0.580161 | − | 0.814502i | \(-0.302990\pi\) | ||||
0.580161 | + | 0.814502i | \(0.302990\pi\) | |||||||
\(68\) | −2.94148 | −0.356707 | ||||||||
\(69\) | −15.7630 | −1.89764 | ||||||||
\(70\) | −0.532083 | −0.0635961 | ||||||||
\(71\) | −1.34074 | −0.159116 | −0.0795580 | − | 0.996830i | \(-0.525351\pi\) | ||||
−0.0795580 | + | 0.996830i | \(0.525351\pi\) | |||||||
\(72\) | −5.14154 | −0.605936 | ||||||||
\(73\) | −11.2652 | −1.31849 | −0.659244 | − | 0.751929i | \(-0.729124\pi\) | ||||
−0.659244 | + | 0.751929i | \(0.729124\pi\) | |||||||
\(74\) | 6.00763 | 0.698372 | ||||||||
\(75\) | −13.4589 | −1.55410 | ||||||||
\(76\) | −5.83604 | −0.669440 | ||||||||
\(77\) | 2.71490 | 0.309391 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.62525 | 0.857907 | 0.428954 | − | 0.903327i | \(-0.358882\pi\) | ||||
0.428954 | + | 0.903327i | \(0.358882\pi\) | |||||||
\(80\) | −0.532083 | −0.0594887 | ||||||||
\(81\) | 2.01079 | 0.223422 | ||||||||
\(82\) | −7.76238 | −0.857211 | ||||||||
\(83\) | 3.49046 | 0.383128 | 0.191564 | − | 0.981480i | \(-0.438644\pi\) | ||||
0.191564 | + | 0.981480i | \(0.438644\pi\) | |||||||
\(84\) | −2.85334 | −0.311325 | ||||||||
\(85\) | 1.56511 | 0.169760 | ||||||||
\(86\) | 9.13544 | 0.985099 | ||||||||
\(87\) | −23.3900 | −2.50767 | ||||||||
\(88\) | 2.71490 | 0.289409 | ||||||||
\(89\) | 14.5067 | 1.53771 | 0.768854 | − | 0.639424i | \(-0.220827\pi\) | ||||
0.768854 | + | 0.639424i | \(0.220827\pi\) | |||||||
\(90\) | 2.73572 | 0.288371 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.52440 | −0.575959 | ||||||||
\(93\) | −9.76460 | −1.01254 | ||||||||
\(94\) | −9.98779 | −1.03016 | ||||||||
\(95\) | 3.10526 | 0.318593 | ||||||||
\(96\) | −2.85334 | −0.291218 | ||||||||
\(97\) | −7.63555 | −0.775273 | −0.387636 | − | 0.921812i | \(-0.626708\pi\) | ||||
−0.387636 | + | 0.921812i | \(0.626708\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −13.9587 | −1.40291 | ||||||||
\(100\) | −4.71689 | −0.471689 | ||||||||
\(101\) | 9.28861 | 0.924252 | 0.462126 | − | 0.886814i | \(-0.347087\pi\) | ||||
0.462126 | + | 0.886814i | \(0.347087\pi\) | |||||||
\(102\) | 8.39305 | 0.831036 | ||||||||
\(103\) | 11.8102 | 1.16369 | 0.581846 | − | 0.813299i | \(-0.302331\pi\) | ||||
0.581846 | + | 0.813299i | \(0.302331\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.51821 | 0.148162 | ||||||||
\(106\) | −12.8839 | −1.25139 | ||||||||
\(107\) | 14.9803 | 1.44820 | 0.724102 | − | 0.689693i | \(-0.242254\pi\) | ||||
0.724102 | + | 0.689693i | \(0.242254\pi\) | |||||||
\(108\) | 6.11053 | 0.587986 | ||||||||
\(109\) | −12.9227 | −1.23777 | −0.618884 | − | 0.785482i | \(-0.712415\pi\) | ||||
−0.618884 | + | 0.785482i | \(0.712415\pi\) | |||||||
\(110\) | −1.44455 | −0.137732 | ||||||||
\(111\) | −17.1418 | −1.62703 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −13.9606 | −1.31330 | −0.656649 | − | 0.754196i | \(-0.728027\pi\) | ||||
−0.656649 | + | 0.754196i | \(0.728027\pi\) | |||||||
\(114\) | 16.6522 | 1.55962 | ||||||||
\(115\) | 2.93944 | 0.274104 | ||||||||
\(116\) | −8.19741 | −0.761111 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.24624 | −0.114726 | ||||||||
\(119\) | 2.94148 | 0.269645 | ||||||||
\(120\) | 1.51821 | 0.138593 | ||||||||
\(121\) | −3.62934 | −0.329940 | ||||||||
\(122\) | −1.36564 | −0.123639 | ||||||||
\(123\) | 22.1487 | 1.99708 | ||||||||
\(124\) | −3.42217 | −0.307320 | ||||||||
\(125\) | 5.17019 | 0.462436 | ||||||||
\(126\) | 5.14154 | 0.458045 | ||||||||
\(127\) | 5.30082 | 0.470372 | 0.235186 | − | 0.971950i | \(-0.424430\pi\) | ||||
0.235186 | + | 0.971950i | \(0.424430\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −26.0665 | −2.29503 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.7726 | −0.941209 | −0.470605 | − | 0.882344i | \(-0.655964\pi\) | ||||
−0.470605 | + | 0.882344i | \(0.655964\pi\) | |||||||
\(132\) | −7.74652 | −0.674248 | ||||||||
\(133\) | 5.83604 | 0.506049 | ||||||||
\(134\) | −9.49764 | −0.820471 | ||||||||
\(135\) | −3.25131 | −0.279828 | ||||||||
\(136\) | 2.94148 | 0.252230 | ||||||||
\(137\) | −19.5853 | −1.67329 | −0.836644 | − | 0.547748i | \(-0.815485\pi\) | ||||
−0.836644 | + | 0.547748i | \(0.815485\pi\) | |||||||
\(138\) | 15.7630 | 1.34184 | ||||||||
\(139\) | −12.1467 | −1.03027 | −0.515135 | − | 0.857109i | \(-0.672258\pi\) | ||||
−0.515135 | + | 0.857109i | \(0.672258\pi\) | |||||||
\(140\) | 0.532083 | 0.0449692 | ||||||||
\(141\) | 28.4985 | 2.40001 | ||||||||
\(142\) | 1.34074 | 0.112512 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 5.14154 | 0.428461 | ||||||||
\(145\) | 4.36170 | 0.362220 | ||||||||
\(146\) | 11.2652 | 0.932312 | ||||||||
\(147\) | 2.85334 | 0.235339 | ||||||||
\(148\) | −6.00763 | −0.493824 | ||||||||
\(149\) | −7.13948 | −0.584889 | −0.292444 | − | 0.956283i | \(-0.594469\pi\) | ||||
−0.292444 | + | 0.956283i | \(0.594469\pi\) | |||||||
\(150\) | 13.4589 | 1.09891 | ||||||||
\(151\) | 9.61643 | 0.782574 | 0.391287 | − | 0.920269i | \(-0.372030\pi\) | ||||
0.391287 | + | 0.920269i | \(0.372030\pi\) | |||||||
\(152\) | 5.83604 | 0.473365 | ||||||||
\(153\) | −15.1237 | −1.22268 | ||||||||
\(154\) | −2.71490 | −0.218773 | ||||||||
\(155\) | 1.82088 | 0.146256 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.5652 | −1.56147 | −0.780736 | − | 0.624861i | \(-0.785156\pi\) | ||||
−0.780736 | + | 0.624861i | \(0.785156\pi\) | |||||||
\(158\) | −7.62525 | −0.606632 | ||||||||
\(159\) | 36.7620 | 2.91542 | ||||||||
\(160\) | 0.532083 | 0.0420648 | ||||||||
\(161\) | 5.52440 | 0.435384 | ||||||||
\(162\) | −2.01079 | −0.157983 | ||||||||
\(163\) | 12.9875 | 1.01726 | 0.508628 | − | 0.860986i | \(-0.330153\pi\) | ||||
0.508628 | + | 0.860986i | \(0.330153\pi\) | |||||||
\(164\) | 7.76238 | 0.606140 | ||||||||
\(165\) | 4.12179 | 0.320881 | ||||||||
\(166\) | −3.49046 | −0.270912 | ||||||||
\(167\) | −17.7973 | −1.37719 | −0.688597 | − | 0.725144i | \(-0.741773\pi\) | ||||
−0.688597 | + | 0.725144i | \(0.741773\pi\) | |||||||
\(168\) | 2.85334 | 0.220140 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −1.56511 | −0.120039 | ||||||||
\(171\) | −30.0062 | −2.29463 | ||||||||
\(172\) | −9.13544 | −0.696570 | ||||||||
\(173\) | 4.08496 | 0.310574 | 0.155287 | − | 0.987869i | \(-0.450370\pi\) | ||||
0.155287 | + | 0.987869i | \(0.450370\pi\) | |||||||
\(174\) | 23.3900 | 1.77319 | ||||||||
\(175\) | 4.71689 | 0.356563 | ||||||||
\(176\) | −2.71490 | −0.204643 | ||||||||
\(177\) | 3.55594 | 0.267281 | ||||||||
\(178\) | −14.5067 | −1.08732 | ||||||||
\(179\) | 4.10649 | 0.306934 | 0.153467 | − | 0.988154i | \(-0.450956\pi\) | ||||
0.153467 | + | 0.988154i | \(0.450956\pi\) | |||||||
\(180\) | −2.73572 | −0.203909 | ||||||||
\(181\) | 20.3643 | 1.51367 | 0.756834 | − | 0.653607i | \(-0.226745\pi\) | ||||
0.756834 | + | 0.653607i | \(0.226745\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.89664 | 0.288048 | ||||||||
\(184\) | 5.52440 | 0.407264 | ||||||||
\(185\) | 3.19656 | 0.235015 | ||||||||
\(186\) | 9.76460 | 0.715975 | ||||||||
\(187\) | 7.98582 | 0.583981 | ||||||||
\(188\) | 9.98779 | 0.728435 | ||||||||
\(189\) | −6.11053 | −0.444476 | ||||||||
\(190\) | −3.10526 | −0.225279 | ||||||||
\(191\) | 3.10166 | 0.224429 | 0.112214 | − | 0.993684i | \(-0.464206\pi\) | ||||
0.112214 | + | 0.993684i | \(0.464206\pi\) | |||||||
\(192\) | 2.85334 | 0.205922 | ||||||||
\(193\) | 5.26716 | 0.379138 | 0.189569 | − | 0.981867i | \(-0.439291\pi\) | ||||
0.189569 | + | 0.981867i | \(0.439291\pi\) | |||||||
\(194\) | 7.63555 | 0.548201 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 15.0025 | 1.06889 | 0.534443 | − | 0.845204i | \(-0.320521\pi\) | ||||
0.534443 | + | 0.845204i | \(0.320521\pi\) | |||||||
\(198\) | 13.9587 | 0.992005 | ||||||||
\(199\) | 9.16998 | 0.650043 | 0.325021 | − | 0.945707i | \(-0.394628\pi\) | ||||
0.325021 | + | 0.945707i | \(0.394628\pi\) | |||||||
\(200\) | 4.71689 | 0.333534 | ||||||||
\(201\) | 27.1000 | 1.91148 | ||||||||
\(202\) | −9.28861 | −0.653545 | ||||||||
\(203\) | 8.19741 | 0.575345 | ||||||||
\(204\) | −8.39305 | −0.587631 | ||||||||
\(205\) | −4.13023 | −0.288468 | ||||||||
\(206\) | −11.8102 | −0.822854 | ||||||||
\(207\) | −28.4039 | −1.97421 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.8443 | 1.09597 | ||||||||
\(210\) | −1.51821 | −0.104767 | ||||||||
\(211\) | −24.5871 | −1.69264 | −0.846321 | − | 0.532673i | \(-0.821188\pi\) | ||||
−0.846321 | + | 0.532673i | \(0.821188\pi\) | |||||||
\(212\) | 12.8839 | 0.884867 | ||||||||
\(213\) | −3.82557 | −0.262124 | ||||||||
\(214\) | −14.9803 | −1.02404 | ||||||||
\(215\) | 4.86081 | 0.331504 | ||||||||
\(216\) | −6.11053 | −0.415769 | ||||||||
\(217\) | 3.42217 | 0.232312 | ||||||||
\(218\) | 12.9227 | 0.875234 | ||||||||
\(219\) | −32.1433 | −2.17204 | ||||||||
\(220\) | 1.44455 | 0.0973915 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 17.1418 | 1.15048 | ||||||||
\(223\) | −2.77472 | −0.185809 | −0.0929045 | − | 0.995675i | \(-0.529615\pi\) | ||||
−0.0929045 | + | 0.995675i | \(0.529615\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −24.2521 | −1.61680 | ||||||||
\(226\) | 13.9606 | 0.928642 | ||||||||
\(227\) | 19.6685 | 1.30544 | 0.652721 | − | 0.757598i | \(-0.273627\pi\) | ||||
0.652721 | + | 0.757598i | \(0.273627\pi\) | |||||||
\(228\) | −16.6522 | −1.10282 | ||||||||
\(229\) | 24.2762 | 1.60422 | 0.802109 | − | 0.597178i | \(-0.203711\pi\) | ||||
0.802109 | + | 0.597178i | \(0.203711\pi\) | |||||||
\(230\) | −2.93944 | −0.193821 | ||||||||
\(231\) | 7.74652 | 0.509683 | ||||||||
\(232\) | 8.19741 | 0.538186 | ||||||||
\(233\) | 16.5986 | 1.08741 | 0.543706 | − | 0.839276i | \(-0.317021\pi\) | ||||
0.543706 | + | 0.839276i | \(0.317021\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.31433 | −0.346669 | ||||||||
\(236\) | 1.24624 | 0.0811232 | ||||||||
\(237\) | 21.7574 | 1.41330 | ||||||||
\(238\) | −2.94148 | −0.190668 | ||||||||
\(239\) | 3.69206 | 0.238820 | 0.119410 | − | 0.992845i | \(-0.461900\pi\) | ||||
0.119410 | + | 0.992845i | \(0.461900\pi\) | |||||||
\(240\) | −1.51821 | −0.0980002 | ||||||||
\(241\) | −6.84568 | −0.440969 | −0.220485 | − | 0.975390i | \(-0.570764\pi\) | ||||
−0.220485 | + | 0.975390i | \(0.570764\pi\) | |||||||
\(242\) | 3.62934 | 0.233303 | ||||||||
\(243\) | −12.5941 | −0.807913 | ||||||||
\(244\) | 1.36564 | 0.0874262 | ||||||||
\(245\) | −0.532083 | −0.0339935 | ||||||||
\(246\) | −22.1487 | −1.41215 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3.42217 | 0.217308 | ||||||||
\(249\) | 9.95947 | 0.631156 | ||||||||
\(250\) | −5.17019 | −0.326992 | ||||||||
\(251\) | 2.48250 | 0.156694 | 0.0783470 | − | 0.996926i | \(-0.475036\pi\) | ||||
0.0783470 | + | 0.996926i | \(0.475036\pi\) | |||||||
\(252\) | −5.14154 | −0.323886 | ||||||||
\(253\) | 14.9982 | 0.942928 | ||||||||
\(254\) | −5.30082 | −0.332603 | ||||||||
\(255\) | 4.46580 | 0.279659 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −23.6908 | −1.47779 | −0.738895 | − | 0.673820i | \(-0.764652\pi\) | ||||
−0.738895 | + | 0.673820i | \(0.764652\pi\) | |||||||
\(258\) | 26.0665 | 1.62283 | ||||||||
\(259\) | 6.00763 | 0.373296 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −42.1473 | −2.60885 | ||||||||
\(262\) | 10.7726 | 0.665536 | ||||||||
\(263\) | −12.4047 | −0.764908 | −0.382454 | − | 0.923975i | \(-0.624921\pi\) | ||||
−0.382454 | + | 0.923975i | \(0.624921\pi\) | |||||||
\(264\) | 7.74652 | 0.476765 | ||||||||
\(265\) | −6.85528 | −0.421116 | ||||||||
\(266\) | −5.83604 | −0.357831 | ||||||||
\(267\) | 41.3926 | 2.53318 | ||||||||
\(268\) | 9.49764 | 0.580161 | ||||||||
\(269\) | −19.4334 | −1.18487 | −0.592437 | − | 0.805617i | \(-0.701834\pi\) | ||||
−0.592437 | + | 0.805617i | \(0.701834\pi\) | |||||||
\(270\) | 3.25131 | 0.197868 | ||||||||
\(271\) | −27.4623 | −1.66822 | −0.834108 | − | 0.551602i | \(-0.814017\pi\) | ||||
−0.834108 | + | 0.551602i | \(0.814017\pi\) | |||||||
\(272\) | −2.94148 | −0.178354 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 19.5853 | 1.18319 | ||||||||
\(275\) | 12.8059 | 0.772223 | ||||||||
\(276\) | −15.7630 | −0.948821 | ||||||||
\(277\) | −11.6541 | −0.700227 | −0.350114 | − | 0.936707i | \(-0.613857\pi\) | ||||
−0.350114 | + | 0.936707i | \(0.613857\pi\) | |||||||
\(278\) | 12.1467 | 0.728511 | ||||||||
\(279\) | −17.5952 | −1.05340 | ||||||||
\(280\) | −0.532083 | −0.0317980 | ||||||||
\(281\) | −22.4177 | −1.33733 | −0.668663 | − | 0.743566i | \(-0.733133\pi\) | ||||
−0.668663 | + | 0.743566i | \(0.733133\pi\) | |||||||
\(282\) | −28.4985 | −1.69706 | ||||||||
\(283\) | −22.7926 | −1.35488 | −0.677439 | − | 0.735579i | \(-0.736910\pi\) | ||||
−0.677439 | + | 0.735579i | \(0.736910\pi\) | |||||||
\(284\) | −1.34074 | −0.0795580 | ||||||||
\(285\) | 8.86035 | 0.524842 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.76238 | −0.458199 | ||||||||
\(288\) | −5.14154 | −0.302968 | ||||||||
\(289\) | −8.34767 | −0.491040 | ||||||||
\(290\) | −4.36170 | −0.256128 | ||||||||
\(291\) | −21.7868 | −1.27717 | ||||||||
\(292\) | −11.2652 | −0.659244 | ||||||||
\(293\) | −6.47704 | −0.378393 | −0.189196 | − | 0.981939i | \(-0.560588\pi\) | ||||
−0.189196 | + | 0.981939i | \(0.560588\pi\) | |||||||
\(294\) | −2.85334 | −0.166410 | ||||||||
\(295\) | −0.663102 | −0.0386073 | ||||||||
\(296\) | 6.00763 | 0.349186 | ||||||||
\(297\) | −16.5895 | −0.962618 | ||||||||
\(298\) | 7.13948 | 0.413579 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −13.4589 | −0.777048 | ||||||||
\(301\) | 9.13544 | 0.526558 | ||||||||
\(302\) | −9.61643 | −0.553363 | ||||||||
\(303\) | 26.5036 | 1.52259 | ||||||||
\(304\) | −5.83604 | −0.334720 | ||||||||
\(305\) | −0.726635 | −0.0416070 | ||||||||
\(306\) | 15.1237 | 0.864567 | ||||||||
\(307\) | −12.8345 | −0.732505 | −0.366253 | − | 0.930515i | \(-0.619359\pi\) | ||||
−0.366253 | + | 0.930515i | \(0.619359\pi\) | |||||||
\(308\) | 2.71490 | 0.154696 | ||||||||
\(309\) | 33.6984 | 1.91704 | ||||||||
\(310\) | −1.82088 | −0.103419 | ||||||||
\(311\) | −7.16543 | −0.406314 | −0.203157 | − | 0.979146i | \(-0.565120\pi\) | ||||
−0.203157 | + | 0.979146i | \(0.565120\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.0799 | 1.13498 | 0.567491 | − | 0.823380i | \(-0.307914\pi\) | ||||
0.567491 | + | 0.823380i | \(0.307914\pi\) | |||||||
\(314\) | 19.5652 | 1.10413 | ||||||||
\(315\) | 2.73572 | 0.154141 | ||||||||
\(316\) | 7.62525 | 0.428954 | ||||||||
\(317\) | −18.5590 | −1.04238 | −0.521190 | − | 0.853441i | \(-0.674512\pi\) | ||||
−0.521190 | + | 0.853441i | \(0.674512\pi\) | |||||||
\(318\) | −36.7620 | −2.06151 | ||||||||
\(319\) | 22.2551 | 1.24605 | ||||||||
\(320\) | −0.532083 | −0.0297443 | ||||||||
\(321\) | 42.7440 | 2.38574 | ||||||||
\(322\) | −5.52440 | −0.307863 | ||||||||
\(323\) | 17.1666 | 0.955176 | ||||||||
\(324\) | 2.01079 | 0.111711 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −12.9875 | −0.719308 | ||||||||
\(327\) | −36.8728 | −2.03907 | ||||||||
\(328\) | −7.76238 | −0.428606 | ||||||||
\(329\) | −9.98779 | −0.550645 | ||||||||
\(330\) | −4.12179 | −0.226897 | ||||||||
\(331\) | −27.2308 | −1.49674 | −0.748371 | − | 0.663280i | \(-0.769164\pi\) | ||||
−0.748371 | + | 0.663280i | \(0.769164\pi\) | |||||||
\(332\) | 3.49046 | 0.191564 | ||||||||
\(333\) | −30.8884 | −1.69268 | ||||||||
\(334\) | 17.7973 | 0.973823 | ||||||||
\(335\) | −5.05353 | −0.276104 | ||||||||
\(336\) | −2.85334 | −0.155662 | ||||||||
\(337\) | −0.559670 | −0.0304872 | −0.0152436 | − | 0.999884i | \(-0.504852\pi\) | ||||
−0.0152436 | + | 0.999884i | \(0.504852\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −39.8342 | −2.16350 | ||||||||
\(340\) | 1.56511 | 0.0848802 | ||||||||
\(341\) | 9.29083 | 0.503127 | ||||||||
\(342\) | 30.0062 | 1.62255 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 9.13544 | 0.492550 | ||||||||
\(345\) | 8.38722 | 0.451553 | ||||||||
\(346\) | −4.08496 | −0.219609 | ||||||||
\(347\) | −10.2001 | −0.547573 | −0.273786 | − | 0.961791i | \(-0.588276\pi\) | ||||
−0.273786 | + | 0.961791i | \(0.588276\pi\) | |||||||
\(348\) | −23.3900 | −1.25383 | ||||||||
\(349\) | 2.44922 | 0.131104 | 0.0655519 | − | 0.997849i | \(-0.479119\pi\) | ||||
0.0655519 | + | 0.997849i | \(0.479119\pi\) | |||||||
\(350\) | −4.71689 | −0.252128 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.71490 | 0.144704 | ||||||||
\(353\) | −0.674466 | −0.0358982 | −0.0179491 | − | 0.999839i | \(-0.505714\pi\) | ||||
−0.0179491 | + | 0.999839i | \(0.505714\pi\) | |||||||
\(354\) | −3.55594 | −0.188996 | ||||||||
\(355\) | 0.713383 | 0.0378624 | ||||||||
\(356\) | 14.5067 | 0.768854 | ||||||||
\(357\) | 8.39305 | 0.444207 | ||||||||
\(358\) | −4.10649 | −0.217035 | ||||||||
\(359\) | 14.9727 | 0.790230 | 0.395115 | − | 0.918632i | \(-0.370705\pi\) | ||||
0.395115 | + | 0.918632i | \(0.370705\pi\) | |||||||
\(360\) | 2.73572 | 0.144185 | ||||||||
\(361\) | 15.0594 | 0.792599 | ||||||||
\(362\) | −20.3643 | −1.07033 | ||||||||
\(363\) | −10.3557 | −0.543534 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.99400 | 0.313740 | ||||||||
\(366\) | −3.89664 | −0.203680 | ||||||||
\(367\) | −26.8987 | −1.40410 | −0.702050 | − | 0.712128i | \(-0.747732\pi\) | ||||
−0.702050 | + | 0.712128i | \(0.747732\pi\) | |||||||
\(368\) | −5.52440 | −0.287979 | ||||||||
\(369\) | 39.9106 | 2.07766 | ||||||||
\(370\) | −3.19656 | −0.166181 | ||||||||
\(371\) | −12.8839 | −0.668896 | ||||||||
\(372\) | −9.76460 | −0.506271 | ||||||||
\(373\) | 26.4013 | 1.36701 | 0.683504 | − | 0.729947i | \(-0.260455\pi\) | ||||
0.683504 | + | 0.729947i | \(0.260455\pi\) | |||||||
\(374\) | −7.98582 | −0.412937 | ||||||||
\(375\) | 14.7523 | 0.761805 | ||||||||
\(376\) | −9.98779 | −0.515081 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 6.11053 | 0.314292 | ||||||||
\(379\) | −1.23207 | −0.0632872 | −0.0316436 | − | 0.999499i | \(-0.510074\pi\) | ||||
−0.0316436 | + | 0.999499i | \(0.510074\pi\) | |||||||
\(380\) | 3.10526 | 0.159296 | ||||||||
\(381\) | 15.1250 | 0.774879 | ||||||||
\(382\) | −3.10166 | −0.158695 | ||||||||
\(383\) | 10.7559 | 0.549602 | 0.274801 | − | 0.961501i | \(-0.411388\pi\) | ||||
0.274801 | + | 0.961501i | \(0.411388\pi\) | |||||||
\(384\) | −2.85334 | −0.145609 | ||||||||
\(385\) | −1.44455 | −0.0736211 | ||||||||
\(386\) | −5.26716 | −0.268091 | ||||||||
\(387\) | −46.9702 | −2.38763 | ||||||||
\(388\) | −7.63555 | −0.387636 | ||||||||
\(389\) | 24.5394 | 1.24420 | 0.622099 | − | 0.782938i | \(-0.286280\pi\) | ||||
0.622099 | + | 0.782938i | \(0.286280\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.2499 | 0.821795 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −30.7380 | −1.55053 | ||||||||
\(394\) | −15.0025 | −0.755817 | ||||||||
\(395\) | −4.05726 | −0.204143 | ||||||||
\(396\) | −13.9587 | −0.701453 | ||||||||
\(397\) | 29.1779 | 1.46440 | 0.732199 | − | 0.681091i | \(-0.238494\pi\) | ||||
0.732199 | + | 0.681091i | \(0.238494\pi\) | |||||||
\(398\) | −9.16998 | −0.459650 | ||||||||
\(399\) | 16.6522 | 0.833653 | ||||||||
\(400\) | −4.71689 | −0.235844 | ||||||||
\(401\) | −11.9570 | −0.597106 | −0.298553 | − | 0.954393i | \(-0.596504\pi\) | ||||
−0.298553 | + | 0.954393i | \(0.596504\pi\) | |||||||
\(402\) | −27.1000 | −1.35162 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 9.28861 | 0.462126 | ||||||||
\(405\) | −1.06991 | −0.0531642 | ||||||||
\(406\) | −8.19741 | −0.406831 | ||||||||
\(407\) | 16.3101 | 0.808461 | ||||||||
\(408\) | 8.39305 | 0.415518 | ||||||||
\(409\) | −32.0698 | −1.58575 | −0.792874 | − | 0.609386i | \(-0.791416\pi\) | ||||
−0.792874 | + | 0.609386i | \(0.791416\pi\) | |||||||
\(410\) | 4.13023 | 0.203977 | ||||||||
\(411\) | −55.8835 | −2.75653 | ||||||||
\(412\) | 11.8102 | 0.581846 | ||||||||
\(413\) | −1.24624 | −0.0613234 | ||||||||
\(414\) | 28.4039 | 1.39598 | ||||||||
\(415\) | −1.85722 | −0.0911671 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −34.6587 | −1.69724 | ||||||||
\(418\) | −15.8443 | −0.774968 | ||||||||
\(419\) | 30.4134 | 1.48579 | 0.742895 | − | 0.669408i | \(-0.233452\pi\) | ||||
0.742895 | + | 0.669408i | \(0.233452\pi\) | |||||||
\(420\) | 1.51821 | 0.0740812 | ||||||||
\(421\) | −31.4025 | −1.53046 | −0.765232 | − | 0.643755i | \(-0.777376\pi\) | ||||
−0.765232 | + | 0.643755i | \(0.777376\pi\) | |||||||
\(422\) | 24.5871 | 1.19688 | ||||||||
\(423\) | 51.3526 | 2.49685 | ||||||||
\(424\) | −12.8839 | −0.625695 | ||||||||
\(425\) | 13.8746 | 0.673019 | ||||||||
\(426\) | 3.82557 | 0.185350 | ||||||||
\(427\) | −1.36564 | −0.0660880 | ||||||||
\(428\) | 14.9803 | 0.724102 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.86081 | −0.234409 | ||||||||
\(431\) | 7.96279 | 0.383554 | 0.191777 | − | 0.981439i | \(-0.438575\pi\) | ||||
0.191777 | + | 0.981439i | \(0.438575\pi\) | |||||||
\(432\) | 6.11053 | 0.293993 | ||||||||
\(433\) | −12.7044 | −0.610533 | −0.305266 | − | 0.952267i | \(-0.598746\pi\) | ||||
−0.305266 | + | 0.952267i | \(0.598746\pi\) | |||||||
\(434\) | −3.42217 | −0.164269 | ||||||||
\(435\) | 12.4454 | 0.596712 | ||||||||
\(436\) | −12.9227 | −0.618884 | ||||||||
\(437\) | 32.2407 | 1.54228 | ||||||||
\(438\) | 32.1433 | 1.53587 | ||||||||
\(439\) | 22.4990 | 1.07382 | 0.536910 | − | 0.843640i | \(-0.319592\pi\) | ||||
0.536910 | + | 0.843640i | \(0.319592\pi\) | |||||||
\(440\) | −1.44455 | −0.0688662 | ||||||||
\(441\) | 5.14154 | 0.244835 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.31651 | 0.442641 | 0.221320 | − | 0.975201i | \(-0.428963\pi\) | ||||
0.221320 | + | 0.975201i | \(0.428963\pi\) | |||||||
\(444\) | −17.1418 | −0.813513 | ||||||||
\(445\) | −7.71877 | −0.365905 | ||||||||
\(446\) | 2.77472 | 0.131387 | ||||||||
\(447\) | −20.3713 | −0.963531 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −6.54442 | −0.308850 | −0.154425 | − | 0.988004i | \(-0.549353\pi\) | ||||
−0.154425 | + | 0.988004i | \(0.549353\pi\) | |||||||
\(450\) | 24.2521 | 1.14325 | ||||||||
\(451\) | −21.0741 | −0.992339 | ||||||||
\(452\) | −13.9606 | −0.656649 | ||||||||
\(453\) | 27.4389 | 1.28919 | ||||||||
\(454\) | −19.6685 | −0.923087 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 16.6522 | 0.779811 | ||||||||
\(457\) | 14.8031 | 0.692459 | 0.346230 | − | 0.938150i | \(-0.387462\pi\) | ||||
0.346230 | + | 0.938150i | \(0.387462\pi\) | |||||||
\(458\) | −24.2762 | −1.13435 | ||||||||
\(459\) | −17.9740 | −0.838956 | ||||||||
\(460\) | 2.93944 | 0.137052 | ||||||||
\(461\) | −1.50317 | −0.0700097 | −0.0350048 | − | 0.999387i | \(-0.511145\pi\) | ||||
−0.0350048 | + | 0.999387i | \(0.511145\pi\) | |||||||
\(462\) | −7.74652 | −0.360401 | ||||||||
\(463\) | −32.7578 | −1.52238 | −0.761192 | − | 0.648526i | \(-0.775386\pi\) | ||||
−0.761192 | + | 0.648526i | \(0.775386\pi\) | |||||||
\(464\) | −8.19741 | −0.380555 | ||||||||
\(465\) | 5.19558 | 0.240939 | ||||||||
\(466\) | −16.5986 | −0.768916 | ||||||||
\(467\) | 16.7557 | 0.775361 | 0.387681 | − | 0.921794i | \(-0.373276\pi\) | ||||
0.387681 | + | 0.921794i | \(0.373276\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.49764 | −0.438560 | ||||||||
\(470\) | 5.31433 | 0.245132 | ||||||||
\(471\) | −55.8261 | −2.57233 | ||||||||
\(472\) | −1.24624 | −0.0573628 | ||||||||
\(473\) | 24.8018 | 1.14039 | ||||||||
\(474\) | −21.7574 | −0.999351 | ||||||||
\(475\) | 27.5280 | 1.26307 | ||||||||
\(476\) | 2.94148 | 0.134823 | ||||||||
\(477\) | 66.2428 | 3.03305 | ||||||||
\(478\) | −3.69206 | −0.168871 | ||||||||
\(479\) | 5.95833 | 0.272243 | 0.136122 | − | 0.990692i | \(-0.456536\pi\) | ||||
0.136122 | + | 0.990692i | \(0.456536\pi\) | |||||||
\(480\) | 1.51821 | 0.0692966 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 6.84568 | 0.311812 | ||||||||
\(483\) | 15.7630 | 0.717241 | ||||||||
\(484\) | −3.62934 | −0.164970 | ||||||||
\(485\) | 4.06275 | 0.184480 | ||||||||
\(486\) | 12.5941 | 0.571281 | ||||||||
\(487\) | −16.3486 | −0.740827 | −0.370413 | − | 0.928867i | \(-0.620784\pi\) | ||||
−0.370413 | + | 0.928867i | \(0.620784\pi\) | |||||||
\(488\) | −1.36564 | −0.0618197 | ||||||||
\(489\) | 37.0576 | 1.67580 | ||||||||
\(490\) | 0.532083 | 0.0240371 | ||||||||
\(491\) | −21.9658 | −0.991304 | −0.495652 | − | 0.868521i | \(-0.665071\pi\) | ||||
−0.495652 | + | 0.868521i | \(0.665071\pi\) | |||||||
\(492\) | 22.1487 | 0.998540 | ||||||||
\(493\) | 24.1126 | 1.08597 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.42721 | 0.333828 | ||||||||
\(496\) | −3.42217 | −0.153660 | ||||||||
\(497\) | 1.34074 | 0.0601402 | ||||||||
\(498\) | −9.95947 | −0.446294 | ||||||||
\(499\) | −10.0994 | −0.452112 | −0.226056 | − | 0.974114i | \(-0.572583\pi\) | ||||
−0.226056 | + | 0.974114i | \(0.572583\pi\) | |||||||
\(500\) | 5.17019 | 0.231218 | ||||||||
\(501\) | −50.7816 | −2.26876 | ||||||||
\(502\) | −2.48250 | −0.110799 | ||||||||
\(503\) | 13.4575 | 0.600038 | 0.300019 | − | 0.953933i | \(-0.403007\pi\) | ||||
0.300019 | + | 0.953933i | \(0.403007\pi\) | |||||||
\(504\) | 5.14154 | 0.229022 | ||||||||
\(505\) | −4.94231 | −0.219930 | ||||||||
\(506\) | −14.9982 | −0.666751 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.30082 | 0.235186 | ||||||||
\(509\) | 24.2795 | 1.07617 | 0.538086 | − | 0.842890i | \(-0.319148\pi\) | ||||
0.538086 | + | 0.842890i | \(0.319148\pi\) | |||||||
\(510\) | −4.46580 | −0.197749 | ||||||||
\(511\) | 11.2652 | 0.498342 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −35.6613 | −1.57449 | ||||||||
\(514\) | 23.6908 | 1.04496 | ||||||||
\(515\) | −6.28399 | −0.276906 | ||||||||
\(516\) | −26.0665 | −1.14751 | ||||||||
\(517\) | −27.1158 | −1.19255 | ||||||||
\(518\) | −6.00763 | −0.263960 | ||||||||
\(519\) | 11.6558 | 0.511632 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.6257 | −1.21030 | −0.605151 | − | 0.796110i | \(-0.706887\pi\) | ||||
−0.605151 | + | 0.796110i | \(0.706887\pi\) | |||||||
\(522\) | 42.1473 | 1.84474 | ||||||||
\(523\) | −5.32290 | −0.232754 | −0.116377 | − | 0.993205i | \(-0.537128\pi\) | ||||
−0.116377 | + | 0.993205i | \(0.537128\pi\) | |||||||
\(524\) | −10.7726 | −0.470605 | ||||||||
\(525\) | 13.4589 | 0.587393 | ||||||||
\(526\) | 12.4047 | 0.540872 | ||||||||
\(527\) | 10.0662 | 0.438493 | ||||||||
\(528\) | −7.74652 | −0.337124 | ||||||||
\(529\) | 7.51904 | 0.326915 | ||||||||
\(530\) | 6.85528 | 0.297774 | ||||||||
\(531\) | 6.40758 | 0.278065 | ||||||||
\(532\) | 5.83604 | 0.253024 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −41.3926 | −1.79123 | ||||||||
\(535\) | −7.97078 | −0.344607 | ||||||||
\(536\) | −9.49764 | −0.410235 | ||||||||
\(537\) | 11.7172 | 0.505635 | ||||||||
\(538\) | 19.4334 | 0.837832 | ||||||||
\(539\) | −2.71490 | −0.116939 | ||||||||
\(540\) | −3.25131 | −0.139914 | ||||||||
\(541\) | −27.5719 | −1.18541 | −0.592704 | − | 0.805420i | \(-0.701940\pi\) | ||||
−0.592704 | + | 0.805420i | \(0.701940\pi\) | |||||||
\(542\) | 27.4623 | 1.17961 | ||||||||
\(543\) | 58.1063 | 2.49358 | ||||||||
\(544\) | 2.94148 | 0.126115 | ||||||||
\(545\) | 6.87594 | 0.294533 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.4744 | 1.21748 | 0.608738 | − | 0.793371i | \(-0.291676\pi\) | ||||
0.608738 | + | 0.793371i | \(0.291676\pi\) | |||||||
\(548\) | −19.5853 | −0.836644 | ||||||||
\(549\) | 7.02150 | 0.299670 | ||||||||
\(550\) | −12.8059 | −0.546044 | ||||||||
\(551\) | 47.8404 | 2.03807 | ||||||||
\(552\) | 15.7630 | 0.670918 | ||||||||
\(553\) | −7.62525 | −0.324258 | ||||||||
\(554\) | 11.6541 | 0.495135 | ||||||||
\(555\) | 9.12085 | 0.387159 | ||||||||
\(556\) | −12.1467 | −0.515135 | ||||||||
\(557\) | −2.56189 | −0.108551 | −0.0542753 | − | 0.998526i | \(-0.517285\pi\) | ||||
−0.0542753 | + | 0.998526i | \(0.517285\pi\) | |||||||
\(558\) | 17.5952 | 0.744864 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0.532083 | 0.0224846 | ||||||||
\(561\) | 22.7863 | 0.962037 | ||||||||
\(562\) | 22.4177 | 0.945632 | ||||||||
\(563\) | 23.5957 | 0.994442 | 0.497221 | − | 0.867624i | \(-0.334354\pi\) | ||||
0.497221 | + | 0.867624i | \(0.334354\pi\) | |||||||
\(564\) | 28.4985 | 1.20001 | ||||||||
\(565\) | 7.42817 | 0.312506 | ||||||||
\(566\) | 22.7926 | 0.958044 | ||||||||
\(567\) | −2.01079 | −0.0844454 | ||||||||
\(568\) | 1.34074 | 0.0562560 | ||||||||
\(569\) | 7.62433 | 0.319629 | 0.159814 | − | 0.987147i | \(-0.448910\pi\) | ||||
0.159814 | + | 0.987147i | \(0.448910\pi\) | |||||||
\(570\) | −8.86035 | −0.371119 | ||||||||
\(571\) | 15.4711 | 0.647444 | 0.323722 | − | 0.946152i | \(-0.395066\pi\) | ||||
0.323722 | + | 0.946152i | \(0.395066\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.85010 | 0.369718 | ||||||||
\(574\) | 7.76238 | 0.323995 | ||||||||
\(575\) | 26.0580 | 1.08669 | ||||||||
\(576\) | 5.14154 | 0.214231 | ||||||||
\(577\) | 2.37245 | 0.0987665 | 0.0493832 | − | 0.998780i | \(-0.484274\pi\) | ||||
0.0493832 | + | 0.998780i | \(0.484274\pi\) | |||||||
\(578\) | 8.34767 | 0.347217 | ||||||||
\(579\) | 15.0290 | 0.624583 | ||||||||
\(580\) | 4.36170 | 0.181110 | ||||||||
\(581\) | −3.49046 | −0.144809 | ||||||||
\(582\) | 21.7868 | 0.903092 | ||||||||
\(583\) | −34.9783 | −1.44865 | ||||||||
\(584\) | 11.2652 | 0.466156 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.47704 | 0.267564 | ||||||||
\(587\) | 22.2865 | 0.919864 | 0.459932 | − | 0.887954i | \(-0.347874\pi\) | ||||
0.459932 | + | 0.887954i | \(0.347874\pi\) | |||||||
\(588\) | 2.85334 | 0.117670 | ||||||||
\(589\) | 19.9719 | 0.822928 | ||||||||
\(590\) | 0.663102 | 0.0272995 | ||||||||
\(591\) | 42.8073 | 1.76086 | ||||||||
\(592\) | −6.00763 | −0.246912 | ||||||||
\(593\) | 12.2613 | 0.503513 | 0.251757 | − | 0.967791i | \(-0.418992\pi\) | ||||
0.251757 | + | 0.967791i | \(0.418992\pi\) | |||||||
\(594\) | 16.5895 | 0.680674 | ||||||||
\(595\) | −1.56511 | −0.0641634 | ||||||||
\(596\) | −7.13948 | −0.292444 | ||||||||
\(597\) | 26.1651 | 1.07086 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.5567 | 0.921641 | 0.460820 | − | 0.887493i | \(-0.347555\pi\) | ||||
0.460820 | + | 0.887493i | \(0.347555\pi\) | |||||||
\(600\) | 13.4589 | 0.549456 | ||||||||
\(601\) | −23.8571 | −0.973153 | −0.486576 | − | 0.873638i | \(-0.661754\pi\) | ||||
−0.486576 | + | 0.873638i | \(0.661754\pi\) | |||||||
\(602\) | −9.13544 | −0.372333 | ||||||||
\(603\) | 48.8325 | 1.98861 | ||||||||
\(604\) | 9.61643 | 0.391287 | ||||||||
\(605\) | 1.93111 | 0.0785107 | ||||||||
\(606\) | −26.5036 | −1.07663 | ||||||||
\(607\) | −14.0867 | −0.571760 | −0.285880 | − | 0.958265i | \(-0.592286\pi\) | ||||
−0.285880 | + | 0.958265i | \(0.592286\pi\) | |||||||
\(608\) | 5.83604 | 0.236683 | ||||||||
\(609\) | 23.3900 | 0.947810 | ||||||||
\(610\) | 0.726635 | 0.0294206 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −15.1237 | −0.611341 | ||||||||
\(613\) | 10.2670 | 0.414681 | 0.207341 | − | 0.978269i | \(-0.433519\pi\) | ||||
0.207341 | + | 0.978269i | \(0.433519\pi\) | |||||||
\(614\) | 12.8345 | 0.517959 | ||||||||
\(615\) | −11.7849 | −0.475215 | ||||||||
\(616\) | −2.71490 | −0.109386 | ||||||||
\(617\) | 8.82812 | 0.355407 | 0.177703 | − | 0.984084i | \(-0.443133\pi\) | ||||
0.177703 | + | 0.984084i | \(0.443133\pi\) | |||||||
\(618\) | −33.6984 | −1.35555 | ||||||||
\(619\) | 16.5151 | 0.663799 | 0.331899 | − | 0.943315i | \(-0.392311\pi\) | ||||
0.331899 | + | 0.943315i | \(0.392311\pi\) | |||||||
\(620\) | 1.82088 | 0.0731282 | ||||||||
\(621\) | −33.7570 | −1.35462 | ||||||||
\(622\) | 7.16543 | 0.287308 | ||||||||
\(623\) | −14.5067 | −0.581199 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.8335 | 0.833339 | ||||||||
\(626\) | −20.0799 | −0.802553 | ||||||||
\(627\) | 45.2090 | 1.80547 | ||||||||
\(628\) | −19.5652 | −0.780736 | ||||||||
\(629\) | 17.6713 | 0.704602 | ||||||||
\(630\) | −2.73572 | −0.108994 | ||||||||
\(631\) | −16.0493 | −0.638913 | −0.319456 | − | 0.947601i | \(-0.603500\pi\) | ||||
−0.319456 | + | 0.947601i | \(0.603500\pi\) | |||||||
\(632\) | −7.62525 | −0.303316 | ||||||||
\(633\) | −70.1552 | −2.78842 | ||||||||
\(634\) | 18.5590 | 0.737074 | ||||||||
\(635\) | −2.82048 | −0.111927 | ||||||||
\(636\) | 36.7620 | 1.45771 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −22.2551 | −0.881089 | ||||||||
\(639\) | −6.89344 | −0.272700 | ||||||||
\(640\) | 0.532083 | 0.0210324 | ||||||||
\(641\) | −15.2785 | −0.603464 | −0.301732 | − | 0.953393i | \(-0.597565\pi\) | ||||
−0.301732 | + | 0.953393i | \(0.597565\pi\) | |||||||
\(642\) | −42.7440 | −1.68697 | ||||||||
\(643\) | 31.7804 | 1.25330 | 0.626649 | − | 0.779302i | \(-0.284426\pi\) | ||||
0.626649 | + | 0.779302i | \(0.284426\pi\) | |||||||
\(644\) | 5.52440 | 0.217692 | ||||||||
\(645\) | 13.8695 | 0.546112 | ||||||||
\(646\) | −17.1666 | −0.675412 | ||||||||
\(647\) | −24.2231 | −0.952309 | −0.476155 | − | 0.879362i | \(-0.657970\pi\) | ||||
−0.476155 | + | 0.879362i | \(0.657970\pi\) | |||||||
\(648\) | −2.01079 | −0.0789914 | ||||||||
\(649\) | −3.38341 | −0.132810 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.76460 | 0.382705 | ||||||||
\(652\) | 12.9875 | 0.508628 | ||||||||
\(653\) | −10.6301 | −0.415989 | −0.207994 | − | 0.978130i | \(-0.566694\pi\) | ||||
−0.207994 | + | 0.978130i | \(0.566694\pi\) | |||||||
\(654\) | 36.8728 | 1.44184 | ||||||||
\(655\) | 5.73193 | 0.223965 | ||||||||
\(656\) | 7.76238 | 0.303070 | ||||||||
\(657\) | −57.9203 | −2.25968 | ||||||||
\(658\) | 9.98779 | 0.389365 | ||||||||
\(659\) | 23.3239 | 0.908571 | 0.454285 | − | 0.890856i | \(-0.349895\pi\) | ||||
0.454285 | + | 0.890856i | \(0.349895\pi\) | |||||||
\(660\) | 4.12179 | 0.160440 | ||||||||
\(661\) | −2.32110 | −0.0902803 | −0.0451401 | − | 0.998981i | \(-0.514373\pi\) | ||||
−0.0451401 | + | 0.998981i | \(0.514373\pi\) | |||||||
\(662\) | 27.2308 | 1.05836 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.49046 | −0.135456 | ||||||||
\(665\) | −3.10526 | −0.120417 | ||||||||
\(666\) | 30.8884 | 1.19690 | ||||||||
\(667\) | 45.2858 | 1.75347 | ||||||||
\(668\) | −17.7973 | −0.688597 | ||||||||
\(669\) | −7.91721 | −0.306097 | ||||||||
\(670\) | 5.05353 | 0.195235 | ||||||||
\(671\) | −3.70758 | −0.143129 | ||||||||
\(672\) | 2.85334 | 0.110070 | ||||||||
\(673\) | −22.1349 | −0.853237 | −0.426619 | − | 0.904432i | \(-0.640295\pi\) | ||||
−0.426619 | + | 0.904432i | \(0.640295\pi\) | |||||||
\(674\) | 0.559670 | 0.0215577 | ||||||||
\(675\) | −28.8227 | −1.10939 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27.8052 | −1.06864 | −0.534320 | − | 0.845282i | \(-0.679432\pi\) | ||||
−0.534320 | + | 0.845282i | \(0.679432\pi\) | |||||||
\(678\) | 39.8342 | 1.52982 | ||||||||
\(679\) | 7.63555 | 0.293026 | ||||||||
\(680\) | −1.56511 | −0.0600194 | ||||||||
\(681\) | 56.1208 | 2.15055 | ||||||||
\(682\) | −9.29083 | −0.355764 | ||||||||
\(683\) | −36.3786 | −1.39199 | −0.695994 | − | 0.718048i | \(-0.745036\pi\) | ||||
−0.695994 | + | 0.718048i | \(0.745036\pi\) | |||||||
\(684\) | −30.0062 | −1.14732 | ||||||||
\(685\) | 10.4210 | 0.398167 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 69.2683 | 2.64275 | ||||||||
\(688\) | −9.13544 | −0.348285 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −8.38722 | −0.319296 | ||||||||
\(691\) | 19.4303 | 0.739163 | 0.369581 | − | 0.929198i | \(-0.379501\pi\) | ||||
0.369581 | + | 0.929198i | \(0.379501\pi\) | |||||||
\(692\) | 4.08496 | 0.155287 | ||||||||
\(693\) | 13.9587 | 0.530249 | ||||||||
\(694\) | 10.2001 | 0.387192 | ||||||||
\(695\) | 6.46306 | 0.245158 | ||||||||
\(696\) | 23.3900 | 0.886595 | ||||||||
\(697\) | −22.8329 | −0.864858 | ||||||||
\(698\) | −2.44922 | −0.0927044 | ||||||||
\(699\) | 47.3615 | 1.79138 | ||||||||
\(700\) | 4.71689 | 0.178282 | ||||||||
\(701\) | −36.0908 | −1.36313 | −0.681566 | − | 0.731757i | \(-0.738701\pi\) | ||||
−0.681566 | + | 0.731757i | \(0.738701\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 35.0608 | 1.32234 | ||||||||
\(704\) | −2.71490 | −0.102322 | ||||||||
\(705\) | −15.1636 | −0.571094 | ||||||||
\(706\) | 0.674466 | 0.0253839 | ||||||||
\(707\) | −9.28861 | −0.349334 | ||||||||
\(708\) | 3.55594 | 0.133640 | ||||||||
\(709\) | 42.3319 | 1.58981 | 0.794905 | − | 0.606734i | \(-0.207521\pi\) | ||||
0.794905 | + | 0.606734i | \(0.207521\pi\) | |||||||
\(710\) | −0.713383 | −0.0267728 | ||||||||
\(711\) | 39.2055 | 1.47032 | ||||||||
\(712\) | −14.5067 | −0.543662 | ||||||||
\(713\) | 18.9054 | 0.708014 | ||||||||
\(714\) | −8.39305 | −0.314102 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.10649 | 0.153467 | ||||||||
\(717\) | 10.5347 | 0.393425 | ||||||||
\(718\) | −14.9727 | −0.558777 | ||||||||
\(719\) | −3.73654 | −0.139350 | −0.0696748 | − | 0.997570i | \(-0.522196\pi\) | ||||
−0.0696748 | + | 0.997570i | \(0.522196\pi\) | |||||||
\(720\) | −2.73572 | −0.101954 | ||||||||
\(721\) | −11.8102 | −0.439834 | ||||||||
\(722\) | −15.0594 | −0.560452 | ||||||||
\(723\) | −19.5330 | −0.726442 | ||||||||
\(724\) | 20.3643 | 0.756834 | ||||||||
\(725\) | 38.6663 | 1.43603 | ||||||||
\(726\) | 10.3557 | 0.384337 | ||||||||
\(727\) | −41.0128 | −1.52108 | −0.760540 | − | 0.649291i | \(-0.775066\pi\) | ||||
−0.760540 | + | 0.649291i | \(0.775066\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −41.9676 | −1.55436 | ||||||||
\(730\) | −5.99400 | −0.221848 | ||||||||
\(731\) | 26.8717 | 0.993887 | ||||||||
\(732\) | 3.89664 | 0.144024 | ||||||||
\(733\) | −6.15408 | −0.227306 | −0.113653 | − | 0.993521i | \(-0.536255\pi\) | ||||
−0.113653 | + | 0.993521i | \(0.536255\pi\) | |||||||
\(734\) | 26.8987 | 0.992849 | ||||||||
\(735\) | −1.51821 | −0.0560001 | ||||||||
\(736\) | 5.52440 | 0.203632 | ||||||||
\(737\) | −25.7851 | −0.949806 | ||||||||
\(738\) | −39.9106 | −1.46913 | ||||||||
\(739\) | 19.5498 | 0.719149 | 0.359575 | − | 0.933116i | \(-0.382922\pi\) | ||||
0.359575 | + | 0.933116i | \(0.382922\pi\) | |||||||
\(740\) | 3.19656 | 0.117508 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.8839 | 0.472981 | ||||||||
\(743\) | −16.6884 | −0.612239 | −0.306119 | − | 0.951993i | \(-0.599031\pi\) | ||||
−0.306119 | + | 0.951993i | \(0.599031\pi\) | |||||||
\(744\) | 9.76460 | 0.357988 | ||||||||
\(745\) | 3.79879 | 0.139177 | ||||||||
\(746\) | −26.4013 | −0.966620 | ||||||||
\(747\) | 17.9463 | 0.656622 | ||||||||
\(748\) | 7.98582 | 0.291991 | ||||||||
\(749\) | −14.9803 | −0.547370 | ||||||||
\(750\) | −14.7523 | −0.538678 | ||||||||
\(751\) | 7.63652 | 0.278661 | 0.139330 | − | 0.990246i | \(-0.455505\pi\) | ||||
0.139330 | + | 0.990246i | \(0.455505\pi\) | |||||||
\(752\) | 9.98779 | 0.364217 | ||||||||
\(753\) | 7.08341 | 0.258134 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.11674 | −0.186217 | ||||||||
\(756\) | −6.11053 | −0.222238 | ||||||||
\(757\) | −8.74215 | −0.317739 | −0.158870 | − | 0.987300i | \(-0.550785\pi\) | ||||
−0.158870 | + | 0.987300i | \(0.550785\pi\) | |||||||
\(758\) | 1.23207 | 0.0447508 | ||||||||
\(759\) | 42.7949 | 1.55336 | ||||||||
\(760\) | −3.10526 | −0.112640 | ||||||||
\(761\) | −1.38527 | −0.0502160 | −0.0251080 | − | 0.999685i | \(-0.507993\pi\) | ||||
−0.0251080 | + | 0.999685i | \(0.507993\pi\) | |||||||
\(762\) | −15.1250 | −0.547922 | ||||||||
\(763\) | 12.9227 | 0.467832 | ||||||||
\(764\) | 3.10166 | 0.112214 | ||||||||
\(765\) | 8.04709 | 0.290943 | ||||||||
\(766\) | −10.7559 | −0.388627 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 2.85334 | 0.102961 | ||||||||
\(769\) | −29.5853 | −1.06687 | −0.533436 | − | 0.845840i | \(-0.679100\pi\) | ||||
−0.533436 | + | 0.845840i | \(0.679100\pi\) | |||||||
\(770\) | 1.44455 | 0.0520580 | ||||||||
\(771\) | −67.5978 | −2.43448 | ||||||||
\(772\) | 5.26716 | 0.189569 | ||||||||
\(773\) | 4.51998 | 0.162572 | 0.0812862 | − | 0.996691i | \(-0.474097\pi\) | ||||
0.0812862 | + | 0.996691i | \(0.474097\pi\) | |||||||
\(774\) | 46.9702 | 1.68831 | ||||||||
\(775\) | 16.1420 | 0.579837 | ||||||||
\(776\) | 7.63555 | 0.274100 | ||||||||
\(777\) | 17.1418 | 0.614958 | ||||||||
\(778\) | −24.5394 | −0.879781 | ||||||||
\(779\) | −45.3016 | −1.62310 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.63996 | 0.130248 | ||||||||
\(782\) | −16.2499 | −0.581097 | ||||||||
\(783\) | −50.0905 | −1.79009 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 10.4103 | 0.371560 | ||||||||
\(786\) | 30.7380 | 1.09639 | ||||||||
\(787\) | −3.37079 | −0.120156 | −0.0600779 | − | 0.998194i | \(-0.519135\pi\) | ||||
−0.0600779 | + | 0.998194i | \(0.519135\pi\) | |||||||
\(788\) | 15.0025 | 0.534443 | ||||||||
\(789\) | −35.3949 | −1.26009 | ||||||||
\(790\) | 4.05726 | 0.144351 | ||||||||
\(791\) | 13.9606 | 0.496380 | ||||||||
\(792\) | 13.9587 | 0.496002 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −29.1779 | −1.03549 | ||||||||
\(795\) | −19.5604 | −0.693737 | ||||||||
\(796\) | 9.16998 | 0.325021 | ||||||||
\(797\) | 12.2603 | 0.434281 | 0.217140 | − | 0.976140i | \(-0.430327\pi\) | ||||
0.217140 | + | 0.976140i | \(0.430327\pi\) | |||||||
\(798\) | −16.6522 | −0.589481 | ||||||||
\(799\) | −29.3789 | −1.03935 | ||||||||
\(800\) | 4.71689 | 0.166767 | ||||||||
\(801\) | 74.5868 | 2.63540 | ||||||||
\(802\) | 11.9570 | 0.422217 | ||||||||
\(803\) | 30.5838 | 1.07928 | ||||||||
\(804\) | 27.1000 | 0.955742 | ||||||||
\(805\) | −2.93944 | −0.103602 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −55.4500 | −1.95193 | ||||||||
\(808\) | −9.28861 | −0.326772 | ||||||||
\(809\) | 23.6424 | 0.831224 | 0.415612 | − | 0.909542i | \(-0.363567\pi\) | ||||
0.415612 | + | 0.909542i | \(0.363567\pi\) | |||||||
\(810\) | 1.06991 | 0.0375928 | ||||||||
\(811\) | −56.5089 | −1.98430 | −0.992148 | − | 0.125071i | \(-0.960084\pi\) | ||||
−0.992148 | + | 0.125071i | \(0.960084\pi\) | |||||||
\(812\) | 8.19741 | 0.287673 | ||||||||
\(813\) | −78.3592 | −2.74818 | ||||||||
\(814\) | −16.3101 | −0.571668 | ||||||||
\(815\) | −6.91040 | −0.242061 | ||||||||
\(816\) | −8.39305 | −0.293815 | ||||||||
\(817\) | 53.3148 | 1.86525 | ||||||||
\(818\) | 32.0698 | 1.12129 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.13023 | −0.144234 | ||||||||
\(821\) | −21.8291 | −0.761840 | −0.380920 | − | 0.924608i | \(-0.624393\pi\) | ||||
−0.380920 | + | 0.924608i | \(0.624393\pi\) | |||||||
\(822\) | 55.8835 | 1.94916 | ||||||||
\(823\) | 41.6120 | 1.45050 | 0.725251 | − | 0.688484i | \(-0.241724\pi\) | ||||
0.725251 | + | 0.688484i | \(0.241724\pi\) | |||||||
\(824\) | −11.8102 | −0.411427 | ||||||||
\(825\) | 36.5395 | 1.27214 | ||||||||
\(826\) | 1.24624 | 0.0433622 | ||||||||
\(827\) | −23.0557 | −0.801726 | −0.400863 | − | 0.916138i | \(-0.631290\pi\) | ||||
−0.400863 | + | 0.916138i | \(0.631290\pi\) | |||||||
\(828\) | −28.4039 | −0.987105 | ||||||||
\(829\) | 30.1019 | 1.04548 | 0.522741 | − | 0.852492i | \(-0.324910\pi\) | ||||
0.522741 | + | 0.852492i | \(0.324910\pi\) | |||||||
\(830\) | 1.85722 | 0.0644649 | ||||||||
\(831\) | −33.2531 | −1.15354 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.94148 | −0.101916 | ||||||||
\(834\) | 34.6587 | 1.20013 | ||||||||
\(835\) | 9.46962 | 0.327710 | ||||||||
\(836\) | 15.8443 | 0.547985 | ||||||||
\(837\) | −20.9113 | −0.722799 | ||||||||
\(838\) | −30.4134 | −1.05061 | ||||||||
\(839\) | −13.0262 | −0.449714 | −0.224857 | − | 0.974392i | \(-0.572192\pi\) | ||||
−0.224857 | + | 0.974392i | \(0.572192\pi\) | |||||||
\(840\) | −1.51821 | −0.0523833 | ||||||||
\(841\) | 38.1976 | 1.31716 | ||||||||
\(842\) | 31.4025 | 1.08220 | ||||||||
\(843\) | −63.9651 | −2.20308 | ||||||||
\(844\) | −24.5871 | −0.846321 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −51.3526 | −1.76554 | ||||||||
\(847\) | 3.62934 | 0.124705 | ||||||||
\(848\) | 12.8839 | 0.442433 | ||||||||
\(849\) | −65.0350 | −2.23199 | ||||||||
\(850\) | −13.8746 | −0.475897 | ||||||||
\(851\) | 33.1886 | 1.13769 | ||||||||
\(852\) | −3.82557 | −0.131062 | ||||||||
\(853\) | −35.1170 | −1.20238 | −0.601191 | − | 0.799105i | \(-0.705307\pi\) | ||||
−0.601191 | + | 0.799105i | \(0.705307\pi\) | |||||||
\(854\) | 1.36564 | 0.0467313 | ||||||||
\(855\) | 15.9658 | 0.546019 | ||||||||
\(856\) | −14.9803 | −0.512018 | ||||||||
\(857\) | −37.6715 | −1.28683 | −0.643416 | − | 0.765516i | \(-0.722484\pi\) | ||||
−0.643416 | + | 0.765516i | \(0.722484\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −42.9068 | −1.46396 | −0.731981 | − | 0.681325i | \(-0.761404\pi\) | ||||
−0.731981 | + | 0.681325i | \(0.761404\pi\) | |||||||
\(860\) | 4.86081 | 0.165752 | ||||||||
\(861\) | −22.1487 | −0.754825 | ||||||||
\(862\) | −7.96279 | −0.271214 | ||||||||
\(863\) | 39.5392 | 1.34593 | 0.672965 | − | 0.739674i | \(-0.265020\pi\) | ||||
0.672965 | + | 0.739674i | \(0.265020\pi\) | |||||||
\(864\) | −6.11053 | −0.207884 | ||||||||
\(865\) | −2.17354 | −0.0739025 | ||||||||
\(866\) | 12.7044 | 0.431712 | ||||||||
\(867\) | −23.8187 | −0.808926 | ||||||||
\(868\) | 3.42217 | 0.116156 | ||||||||
\(869\) | −20.7018 | −0.702259 | ||||||||
\(870\) | −12.4454 | −0.421939 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 12.9227 | 0.437617 | ||||||||
\(873\) | −39.2585 | −1.32870 | ||||||||
\(874\) | −32.2407 | −1.09056 | ||||||||
\(875\) | −5.17019 | −0.174784 | ||||||||
\(876\) | −32.1433 | −1.08602 | ||||||||
\(877\) | −20.1984 | −0.682051 | −0.341026 | − | 0.940054i | \(-0.610774\pi\) | ||||
−0.341026 | + | 0.940054i | \(0.610774\pi\) | |||||||
\(878\) | −22.4990 | −0.759305 | ||||||||
\(879\) | −18.4812 | −0.623355 | ||||||||
\(880\) | 1.44455 | 0.0486958 | ||||||||
\(881\) | 17.7169 | 0.596899 | 0.298449 | − | 0.954425i | \(-0.403531\pi\) | ||||
0.298449 | + | 0.954425i | \(0.403531\pi\) | |||||||
\(882\) | −5.14154 | −0.173125 | ||||||||
\(883\) | 31.8330 | 1.07127 | 0.535633 | − | 0.844451i | \(-0.320073\pi\) | ||||
0.535633 | + | 0.844451i | \(0.320073\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.89206 | −0.0636007 | ||||||||
\(886\) | −9.31651 | −0.312994 | ||||||||
\(887\) | −30.0786 | −1.00994 | −0.504970 | − | 0.863137i | \(-0.668496\pi\) | ||||
−0.504970 | + | 0.863137i | \(0.668496\pi\) | |||||||
\(888\) | 17.1418 | 0.575241 | ||||||||
\(889\) | −5.30082 | −0.177784 | ||||||||
\(890\) | 7.71877 | 0.258734 | ||||||||
\(891\) | −5.45910 | −0.182887 | ||||||||
\(892\) | −2.77472 | −0.0929045 | ||||||||
\(893\) | −58.2892 | −1.95057 | ||||||||
\(894\) | 20.3713 | 0.681319 | ||||||||
\(895\) | −2.18499 | −0.0730363 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.54442 | 0.218390 | ||||||||
\(899\) | 28.0529 | 0.935617 | ||||||||
\(900\) | −24.2521 | −0.808402 | ||||||||
\(901\) | −37.8976 | −1.26255 | ||||||||
\(902\) | 21.0741 | 0.701689 | ||||||||
\(903\) | 26.0665 | 0.867438 | ||||||||
\(904\) | 13.9606 | 0.464321 | ||||||||
\(905\) | −10.8355 | −0.360185 | ||||||||
\(906\) | −27.4389 | −0.911597 | ||||||||
\(907\) | −47.4949 | −1.57704 | −0.788521 | − | 0.615008i | \(-0.789153\pi\) | ||||
−0.788521 | + | 0.615008i | \(0.789153\pi\) | |||||||
\(908\) | 19.6685 | 0.652721 | ||||||||
\(909\) | 47.7578 | 1.58402 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.6543 | 1.41320 | 0.706600 | − | 0.707613i | \(-0.250228\pi\) | ||||
0.706600 | + | 0.707613i | \(0.250228\pi\) | |||||||
\(912\) | −16.6522 | −0.551409 | ||||||||
\(913\) | −9.47625 | −0.313618 | ||||||||
\(914\) | −14.8031 | −0.489642 | ||||||||
\(915\) | −2.07333 | −0.0685423 | ||||||||
\(916\) | 24.2762 | 0.802109 | ||||||||
\(917\) | 10.7726 | 0.355744 | ||||||||
\(918\) | 17.9740 | 0.593231 | ||||||||
\(919\) | 0.153611 | 0.00506716 | 0.00253358 | − | 0.999997i | \(-0.499194\pi\) | ||||
0.00253358 | + | 0.999997i | \(0.499194\pi\) | |||||||
\(920\) | −2.93944 | −0.0969105 | ||||||||
\(921\) | −36.6212 | −1.20671 | ||||||||
\(922\) | 1.50317 | 0.0495043 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 7.74652 | 0.254842 | ||||||||
\(925\) | 28.3373 | 0.931725 | ||||||||
\(926\) | 32.7578 | 1.07649 | ||||||||
\(927\) | 60.7225 | 1.99439 | ||||||||
\(928\) | 8.19741 | 0.269093 | ||||||||
\(929\) | −54.1539 | −1.77673 | −0.888366 | − | 0.459136i | \(-0.848159\pi\) | ||||
−0.888366 | + | 0.459136i | \(0.848159\pi\) | |||||||
\(930\) | −5.19558 | −0.170370 | ||||||||
\(931\) | −5.83604 | −0.191269 | ||||||||
\(932\) | 16.5986 | 0.543706 | ||||||||
\(933\) | −20.4454 | −0.669352 | ||||||||
\(934\) | −16.7557 | −0.548263 | ||||||||
\(935\) | −4.24912 | −0.138961 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.1549 | 1.50781 | 0.753907 | − | 0.656981i | \(-0.228167\pi\) | ||||
0.753907 | + | 0.656981i | \(0.228167\pi\) | |||||||
\(938\) | 9.49764 | 0.310109 | ||||||||
\(939\) | 57.2947 | 1.86974 | ||||||||
\(940\) | −5.31433 | −0.173334 | ||||||||
\(941\) | 10.2273 | 0.333402 | 0.166701 | − | 0.986008i | \(-0.446689\pi\) | ||||
0.166701 | + | 0.986008i | \(0.446689\pi\) | |||||||
\(942\) | 55.8261 | 1.81891 | ||||||||
\(943\) | −42.8825 | −1.39645 | ||||||||
\(944\) | 1.24624 | 0.0405616 | ||||||||
\(945\) | 3.25131 | 0.105765 | ||||||||
\(946\) | −24.8018 | −0.806375 | ||||||||
\(947\) | −8.29170 | −0.269444 | −0.134722 | − | 0.990883i | \(-0.543014\pi\) | ||||
−0.134722 | + | 0.990883i | \(0.543014\pi\) | |||||||
\(948\) | 21.7574 | 0.706648 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −27.5280 | −0.893125 | ||||||||
\(951\) | −52.9552 | −1.71719 | ||||||||
\(952\) | −2.94148 | −0.0953340 | ||||||||
\(953\) | 52.5932 | 1.70366 | 0.851830 | − | 0.523818i | \(-0.175493\pi\) | ||||
0.851830 | + | 0.523818i | \(0.175493\pi\) | |||||||
\(954\) | −66.2428 | −2.14469 | ||||||||
\(955\) | −1.65034 | −0.0534038 | ||||||||
\(956\) | 3.69206 | 0.119410 | ||||||||
\(957\) | 63.5014 | 2.05271 | ||||||||
\(958\) | −5.95833 | −0.192505 | ||||||||
\(959\) | 19.5853 | 0.632443 | ||||||||
\(960\) | −1.51821 | −0.0490001 | ||||||||
\(961\) | −19.2888 | −0.622219 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 77.0220 | 2.48200 | ||||||||
\(964\) | −6.84568 | −0.220485 | ||||||||
\(965\) | −2.80256 | −0.0902177 | ||||||||
\(966\) | −15.7630 | −0.507166 | ||||||||
\(967\) | 44.2570 | 1.42321 | 0.711605 | − | 0.702580i | \(-0.247969\pi\) | ||||
0.711605 | + | 0.702580i | \(0.247969\pi\) | |||||||
\(968\) | 3.62934 | 0.116651 | ||||||||
\(969\) | 48.9822 | 1.57353 | ||||||||
\(970\) | −4.06275 | −0.130447 | ||||||||
\(971\) | −27.7388 | −0.890182 | −0.445091 | − | 0.895485i | \(-0.646829\pi\) | ||||
−0.445091 | + | 0.895485i | \(0.646829\pi\) | |||||||
\(972\) | −12.5941 | −0.403956 | ||||||||
\(973\) | 12.1467 | 0.389406 | ||||||||
\(974\) | 16.3486 | 0.523844 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.36564 | 0.0437131 | ||||||||
\(977\) | 10.4341 | 0.333817 | 0.166908 | − | 0.985972i | \(-0.446622\pi\) | ||||
0.166908 | + | 0.985972i | \(0.446622\pi\) | |||||||
\(978\) | −37.0576 | −1.18497 | ||||||||
\(979\) | −39.3842 | −1.25873 | ||||||||
\(980\) | −0.532083 | −0.0169968 | ||||||||
\(981\) | −66.4424 | −2.12134 | ||||||||
\(982\) | 21.9658 | 0.700958 | ||||||||
\(983\) | 26.7410 | 0.852906 | 0.426453 | − | 0.904510i | \(-0.359763\pi\) | ||||
0.426453 | + | 0.904510i | \(0.359763\pi\) | |||||||
\(984\) | −22.1487 | −0.706074 | ||||||||
\(985\) | −7.98259 | −0.254347 | ||||||||
\(986\) | −24.1126 | −0.767900 | ||||||||
\(987\) | −28.4985 | −0.907119 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 50.4678 | 1.60478 | ||||||||
\(990\) | −7.42721 | −0.236052 | ||||||||
\(991\) | 7.10312 | 0.225638 | 0.112819 | − | 0.993616i | \(-0.464012\pi\) | ||||
0.112819 | + | 0.993616i | \(0.464012\pi\) | |||||||
\(992\) | 3.42217 | 0.108654 | ||||||||
\(993\) | −77.6988 | −2.46570 | ||||||||
\(994\) | −1.34074 | −0.0425256 | ||||||||
\(995\) | −4.87919 | −0.154681 | ||||||||
\(996\) | 9.95947 | 0.315578 | ||||||||
\(997\) | −13.6792 | −0.433223 | −0.216612 | − | 0.976258i | \(-0.569501\pi\) | ||||
−0.216612 | + | 0.976258i | \(0.569501\pi\) | |||||||
\(998\) | 10.0994 | 0.319691 | ||||||||
\(999\) | −36.7098 | −1.16145 |
(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 | 2366.2.a.be.1.6 | ✓ | 6 | |
13.5 | odd | 4 | 2366.2.d.q.337.12 | 12 | |||
13.8 | odd | 4 | 2366.2.d.q.337.6 | 12 | |||
13.12 | even | 2 | 2366.2.a.bg.1.6 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2366.2.a.be.1.6 | ✓ | 6 | 1.1 | even | 1 | trivial | |
2366.2.a.bg.1.6 | yes | 6 | 13.12 | even | 2 | ||
2366.2.d.q.337.6 | 12 | 13.8 | odd | 4 | |||
2366.2.d.q.337.12 | 12 | 13.5 | odd | 4 |